Answer: [tex]\frac{3}{4}[/tex]c
Step-by-step explanation:
If one pound of chicken costs c dollars, and we are writing an expression for 3/4 a pound of chicken, our expression will be the price (c) multiplied by how much chicken there is (3/4):
3/4c
- In mathematics, an expression is a combination of numbers, variables (represented by letters), symbols, and operators, arranged in a way that represents some meaningful mathematical relationship or calculation.
- Expressions can be simple, like 3x or 4 + 5, or complex, like (3x + 4y) / (2x - 5y). Expressions are not equations or inequalities, as they do not contain an equal sign, but they can be used to build equations or inequalities.
Solving the Question:The price of 1 pound of chicken is c dollars. To find the price of 3/4 pound of chicken, we can multiply the price of 1 pound by 3/4:
[tex]\begin{aligned}\sf Price\: of\: \dfrac{3}{4}\: pound\: of\: chicken& =\sf \dfrac{3}{4} \times c \\&=\boxed{\bold{\:\dfrac{3}{4}c\:}}\end{aligned}[/tex]
Therefore, the expression for the price of 3/4 pound of chicken is 3/4c.
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https://brainly.com/question/13667588Prahar wants to bake homemade apple pies for the school bake sale. The recipe for the filling of a homemade apple pie that serves 8 consists of the following:
three fourths cup sugar
three fifths teaspoon cinnamon
one eighth teaspoon ground nutmeg
one fourth teaspoon salt
Prahar would like to serve 22 people. Choose one of the ingredients from the recipe and determine the amount he would need for a serving of this size. Set up the proportion and show all necessary work using fractions or decimals.
Prahar would need approximately [tex]2.0625[/tex] cups of sugar to make apple pies that serve [tex]22[/tex] people. We can round this up to [tex]2 1/8[/tex] cups of sugar for practical purposes.
What is the use of proportion?To determine the amount of one of the ingredients needed to make an apple pie that serves [tex]22[/tex] people, we can set up a proportion comparing the number of servings:
Number of servings of the original recipe: [tex]8[/tex]
Number of servings needed: [tex]22[/tex]
Let's choose sugar as the ingredient to calculate:
Original amount of sugar for 8 servings: [tex]3/4[/tex] cup
Unknown amount of sugar for [tex]22[/tex] servings: x
We can set up the proportion as follows:
[tex]8/22 = 3/4x[/tex]
To solve for x, we can cross-multiply:
[tex]8x = 22 \times 3/4[/tex]
[tex]8x = 16.5[/tex]
[tex]x = 16.5/8[/tex]
[tex]x = 2.0625[/tex]
Therefore, Prahar would need approximately [tex]2.0625[/tex] cups of sugar to make apple pies that serve [tex]22[/tex] people. We can round this up to [tex]2 1/8[/tex] cups of sugar for practical purposes.
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A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 25 oz of beans. When she plants 32 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
The linear relationship between the number of bean stalks, n, and the yield, y, is y = -0.5n + 40. This equation can be used to predict the yield of beans for any number of bean stalks planted by the farmer.
To find the linear relationship between the number of bean stalks, n, and the yield, y, we can use the two data points provided by the farmer. We know that when 30 stalks are planted, each plant yields 25 oz of beans, and when 32 stalks are planted, each plant yields 24 oz of beans.
First, we need to find the slope, m, of the line. We can use the formula:
m = (y2 - y1) / (x2 - x1)
where x1 = 30, y1 = 25, x2 = 32, and y2 = 24.
m = (24 - 25) / (32 - 30) = -0.5
Next, we need to find the y-intercept, b, of the line. We can use the point-slope form of the equation:
y - y1 = m(x - x1)
where x1 = 30 and y1 = 25.
y - 25 = -0.5(x - 30)
y - 25 = -0.5x + 15
y = -0.5x + 40
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Your company must charge $100 for a software upgrade to make a profit on its development. You must find out if your customers are willing to pay this much. A random sample of 50 customers finds that 17 would pay $100 for the upgrade. If the upgrade is to be profitable, you will need to sell it to more than 20% of your customers. Do the sample data provide good evidence that more than 20% are willing to buy at the 5% level of significance?
a) State the appropriate null and alternative hypotheses. Explain how you decided the alternative.
b) Give the z statistic and its p-value for this test.
c) Should you proceed with plans to develop and market the upgrade? Explain in context of this hypothesis test.
d) Give the 90% confidence interval for the proportion of all customers willing to pay $100.00 for the upgrade. Explain how this supports your hypothesis test conclusion.
e) You company’s overseas division also took a random sample of 50 customers and found that 38 would pay the $100.00 upgrade. Explain why or why not these two populations are different.
a. Hypotheses are: [tex]\rm H_{0}:p=0.20,H_{a}:p > 0.20[/tex]
b. Z-statistics will be 2.47 and p-value = 0.0068
c. you should proceed with plans to develop and market the upgrade.
d. Confidence interval for population proportion will be (0.23, 0.45)
e. The populations are different because they are frοm different regiοns sο prefrences οf peοple may different.
What is Probability?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
a. Hypotheses are:
[tex]\rm H_{0}:p=0.20,H_{a}:p > 0.20[/tex]
b) Here we have following information:
[tex]\rm n=50, \hat{p}=\frac{17}{50}=0.34[/tex]
Standard deviation of the proportion is:
[tex]\rm \sigma=\sqrt{\frac{p\left ( 1-p \right )}{n}}=\sqrt{\frac{0.20\left ( 1-0.20 \right )}{50}}=0.0566[/tex]
Test statistics will be:
[tex]$ \rm z=\frac{\hat{p}-p}{\sigma}=\frac{0.34-0.20}{0.0566}=2.47[/tex]
Alternative hypothesis shows that the test is right tailed so p-value of the test is
[tex]\rm p-value = P(z > 2.47) = 1 - P(z \leq 2.47)=1-0.9932=0.0068[/tex]
c. Since p-value of the test is less than 0.05 so we reject the null hypothesis at 0.05 level of significance. So based on this sample, you should proceed with plans to develop and market the upgrade.
d. For 90% confidence interval [tex]\alpha[/tex] = 0.10 so critical value of z will be[tex]\rm z_{c}=z_{\alpha/2}=1.645[/tex]
Confidence interval for population proportion will be
[tex]\rm \hat{p}\pm z_{c}\sqrt{\frac{\hat{p}\left ( 1-\hat{p} \right )}{n}}=0.34\pm 1.645\sqrt{\frac{0.34\left (1-0.34 \right )}{50}}=0.34\pm 0.11 =(0.23, 0.45)[/tex]
e. The populations are different because they are frοm different regiοns sο prefrences οf peοple may different.
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In a school computer lab, students must use a six-digit passcode to log on to the computers.
The digits 0-9 can be used in the passcodes.
a. How many different passcodes are possible if the digits can be repeated?
b. How many different passcodes are possible if the digits cannot be repeated?
a. the total number of different passcodes possible if the digits can be repeated is 10⁶
b. the total number of different passcodes possible is 151,200.
What is probability?The possibility or chance of an event occurring is measured by probability. It is stated as a number between 0 and 1, where 0 denotes an impossibility (i.e., an event that won't happen) and 1 denotes a certainty (i.e., an event that will happen) (i.e., an event that will always occur).
a. Since there are 10 digits (0-9) that can be used for each digit in the passcode, there are 10 options for each of the six digits.
Therefore, the total number of different passcodes possible if the digits can be repeated is 10⁶, which is equal to 1,000,000.
b. If the digits cannot be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and so on.
Therefore, the total number of different passcodes possible is 10x9x8x7x6x5, which is equal to 151,200.
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Find the distance between the point (2,1) and the line 3x- 4y+15=0
Answer:
Step-by-step explanation:
3
x
−
4
y
+
15
=
0
.
y
=
3
4
x
−
1
2
Correct answers 5.4
Distance from point (2,3) to the line 3x+4y+9=0
=>r=
3
2
+4
2
∣3(2)+4(3)+9∣
=>r=
9+16
∣16+12+9∣
=>r=
5
27
=>r=5.4
Emery bought 3 cans of beans that had a total weight of 2.4 pounds. If each can of beans weighed the same amount, which model correctly illustrates the relationship? Check all that apply.
The equation will be y = 2.4x. Thus, 2nd option is correct.
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
We can use a proportion to model the relationship between the number of cans and the total weight. Since we have three cans, we can represent the weight of each can as x, and the total weight as 2.4 pounds:
3x = 2.4
Solving for x, we get:
x = 0.8
Therefore, each can weighs 0.8 pounds.
Hence the equation will be y = 2.4x. Thus, 2nd option is correct.
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Emery bought 3 cans of beans that had a total weight of 2.4 pounds. If each can of beans weighed the same amount, which model correctly illustrates the relationship? Check all that apply.
y = 0.8x
y = 2.4x
y = 3x
y = x/2.4
CRA CDs Inc. wants the mean lengths of the “cuts” on a CD to be 148 seconds (2 minutes and 28 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows a normal distribution with a standard deviation of eight seconds. Suppose that we select a sample of 26 cuts from various CDs sold by CRA CDs Inc. Use Appendix B.1 for the z values. a. What can we say about the shape of the distribution of the sample mean? Shape of the distribution is (Click to select) b. What is the standard error of the mean? (Round the final answer to 2 decimal places.) Standard error of the mean seconds. c. What percentage of the sample means will be greater than 152 seconds? (Round the z values to 2 decimal places and the final answers to 2 decimal places.) Percentage % d. What percentage of the sample means will be greater than 144 seconds? (Round the z values to 2 decimal places and the final answers to 2 decimal places.) Percentage % e. What percentage of the sample means will be greater than 144 but less than 152 seconds? (Round the z values to 2 decimal places and the final answers to 2 decimal places.) Percentage %
a. The shape of the distribution of the sample mean will be approximately normal, according to the Central Limit Theorem.
b. The standard error of the mean is given by:
SE = σ / sqrt(n)
where σ is the population standard deviation (8 seconds), and n is the sample size (26). Substituting the given values, we get:
SE = 8 / sqrt(26) ≈ 1.57 seconds
Rounded to 2 decimal places, the standard error of the mean is 1.57 seconds.
c. To find the percentage of sample means that will be greater than 152 seconds, we need to calculate the z-score corresponding to a sample mean of 152 seconds:
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean (152 seconds), μ is the population mean (148 seconds), σ is the population standard deviation (8 seconds), and n is the sample size (26).
Substituting the given values, we get:
z = (152 - 148) / (8 / sqrt(26)) ≈ 1.98
Using Appendix B.1, we find that the area to the right of a z-score of 1.98 is 0.0242, or 2.42%. Therefore, approximately 2.42% of the sample means will be greater than 152 seconds.
d. To find the percentage of sample means that will be greater than 144 seconds, we need to calculate the z-score corresponding to a sample mean of 144 seconds:
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean (144 seconds), μ is the population mean (148 seconds), σ is the population standard deviation (8 seconds), and n is the sample size (26).
Substituting the given values, we get:
z = (144 - 148) / (8 / sqrt(26)) ≈ -1.98
Using Appendix B.1, we find that the area to the right of a z-score of -1.98 is also 0.0242, or 2.42%. Therefore, approximately 2.42% of the sample means will be less than 144 seconds.
e. To find the percentage of sample means that will be greater than 144 but less than 152 seconds, we need to find the area between the z-scores corresponding to sample means of 144 and 152 seconds.
The z-score corresponding to a sample mean of 144 seconds is:
z1 = (144 - 148) / (8 / sqrt(26)) ≈ -1.98
The z-score corresponding to a sample mean of 152 seconds is:
z2 = (152 - 148) / (8 / sqrt(26)) ≈ 1.98
Using Appendix B.1, we find that the area to the right of a z-score of -1.98 is 0.0242, and the area to the right of a z-score of 1.98 is 0.0242. Therefore, the area between these two z-scores is:
0.5 - 0.0242 - 0.0242 = 0.4516
Multiplying by 100, we get that approximately 45.16% of the sample means will be greater than 144 but less than 152 seconds.
An element with a mass of 540 grams decays by 12.8% per minute. To the nearest tenth of a minute, how long will it be until there are 110 grams of the element remaining?
Therefore, to the nearest tenth of a minute, it will be about 9.4 minutes until there are 110 grams of the element remaining.
What is initial amount?"Initial amount" usually refers to the starting quantity or value of something, such as money, an investment, or a substance. It is the amount or quantity that exists at the beginning of a particular time period or situation. For example, if you invest $1,000 in a savings account, the initial amount is $1,000. Similarly, if you are given 10 liters of water, the initial amount of water is 10 liters.
We can use the exponential decay formula to solve this problem:
[tex]N(t) = N₀ * e^{(-kt)}[/tex]
where N(t) is the amount of the element remaining at time t, N₀ is the initial amount of the element, k is the decay constant (which is equal to ln (1 - 0.128) = -0.142), and e is the base of the natural logarithm.
We can plug in the given values and solve for the time t when the remaining amount N(t) is equal to 110 grams:
[tex]110 = 540 * e^{(-0.142t)}[/tex]
Dividing both sides by 540, we get:
[tex]0.2037 = e^{(-0.142t)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.2037) = -0.142t[/tex]
Solving for t, we get:
t = ln (0.2037) / (-0.142) ≈ 9.4 minutes
Therefore, to the nearest tenth of a minute, it will be about 9.4 minutes until there are 110 grams of the element remaining.
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The _______________ is a collection of people and companies where shares in the various companies are bought, sold, and traded.
A. Life Insurance Company
B. Savings Institution
C. Stock Market
D. Bonds
Answer:
C) Stock Market.
Brainly wants me to put at least 20 characters and since I only provided the answer choice and was too lazy to do an explanation I am putting this here.
Answer:
C) Stock Market.
Step-by-step explanation:
The term stock market refers to several exchanges in which shares of publicly held companies are bought and sold.
34kg of apples cost $374. how many kilograms of apples can you get with $220
Answer:
20 kilograms.
Step-by-step explanation:
First, we need to find the cost per kilogram.
We can do this by dividing 374 by 34.
That gives us 11. So, our cost per kilogram is $11.
Next, to find how many kilograms we can get with $220 dollars, we need to divide 220 by 11.
That leaves us with a final answer of 20 kilograms.
teri's car holds 17.4 gallons og gas. if she can drive 478.5 miles ona full tank of gas, how many miles can she per gallons
Teri can drive approximately 27.47 miles per gallon of gas.
To find how many miles per gallon Teri can drive, we need to divide the total distance she can travel on a full tank of gas by the amount of gas she needs to fill the tank. This gives us the average number of miles she can travel on one gallon of gas.
Teri's car can hold 17.4 gallons of gas.
Teri can drive 478.5 miles on a full tank of gas.
Mathematically, we can represent this as:
Miles per gallon = Total distance traveled ÷ Amount of gas used
Plugging in the values we have:
Miles per gallon = [tex]\frac{478.4 miles}{17.4 gallons}[/tex]
Performing the division:
Miles per gallon = 27.47126437
Rounding to two decimal places, we get:
Miles per gallon ≈ 27.47
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PLEASE HELP!!!!! MIDDLE SCHOOL MATH!!!!!!!!!!!!
Use the figure shown. Match each angle to the correct angle measure. Some angle measures may be used more than once or not at all.
PLEASE LOOK AT THE PICTURE BELOW!!!!! SHOW WORK!!!!!!!!
The values of all angles [tex] \angle \: GAL, \angle \: LAO, \angle CAO, \: angle \: KAC[/tex] are 71°, 90°, 90°, 90° respectively.
Given angle GAK is 19°.
It is clear that angle KAL is equal to 90°.
So,
[tex] \angle KAL = {90}^{o} [/tex]
Now,
[tex] \angle \: KAL = \angle KAG+ \angle \: GAL[/tex]
So,
[tex] \angle \: GAL = {90}^{o} - {19}^{o} \\ = {71}^{o} [/tex]
Now,
[tex] \angle \: KAO = 180°[/tex]
Now
[tex] \angle \: KAL + \angle \: LAO = {180}^{o} \\ \angle \: LAO = {180}^{o} - {90}^{o} \\ \angle \: LAO = {90}^{o} [/tex]
Again,
[tex] \angle \: CAO = {180}^{o} - \angle \: LAO \\ \angle \: CAO = {180}^{o} - {90}^{o} = {90}^{o} [/tex]
Similarly,
[tex] \angle \: KAC = \angle \: KAO - \angle \: CAO \\ \angle \: KAC = {180}^{o} - {90}^{o} \\ = {90}^{o} [/tex]
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example of improper sampling in day to day life?
Answer: Sampling is very often used in our daily life. For example, while purchasing fruits from a shop, we usually examine a few to assess the quality. A doctor examines a few drops of blood as a sample and draws a conclusion about the blood constitution of the whole body.
Mario Brothers, a game manufacturer, has a new idea for an adventure game. It can either market the game as a traditional board game or as a PC game, but not both. Consider the following cash flows of the two mutually exclusive projects. Assume the discount rate for both projects is 9 percent.
Year Board Game PC
0 −$ 1,550 −$ 3,400
1 760 2,100
2 1,300 1,640
3 280 1,150
a. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b. What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
c. What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
d. What is the incremental IRR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Please note this is for a Finance class for MBA program.
HELP PLSSSSSSSSSSSSSSSSSS NEED THIS ASAP
Answer:
Step-by-step explanation:
First you have to find out how many red were in the original 27 marbles.
If there were 7 Black and 4 Yellow - this is 11 so 27 - 11 = 16 RED.
Removing 3 Black - changes the the can to 24 marbles.
4 Black - 4 Yellow and 16 Red.
So probability the random pick is red after the removal of 3 Black is
16 out of 24. [tex]\frac{16}{24}[/tex]
This reduces to 2/3.
Choice (K)
Answer:
Step-by-step explanation:
There are 27 marbles which include 7 black marbles
4 yellow marbles
Therefore, the number of red marbles=27-(7+4) marbles
=16 red marbles
When 3 black marbles are removed from the can, the total number of marbles become 24, which includes the 4 black marbles,4 yellow marbles and 16 red marbles.
So, the probability of the picking of a random red marble from the can after removing the black marbles = 16÷24
This when reduced gives the result 2÷3.
Hence, the answer is option K which means the probability that it was red is 2/3.
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Burt ran the length of the trail in his town’s park. There are 9 parts to the trail, and each part is the same length. Burt ran a total of 1.8 kilometers.
There are 9 parts to the trail, and each part is the same length. and hence each part of the trail is 0.2 kilometers long.
What is perimeter of rectangle?The following equation may be used to determine a rectangle's perimeter:
Perimeter is equal to 2 x (length + breadth).
where "length" denotes the rectangle's length and "width" denotes the rectangle's width. In order to account for both sides of the rectangle, we add the length and breadth together and multiply the result by 2, which is the distance around the outside of the rectangle.
The distance ran by Brurt is:
1.8 km ÷ 9 = 0.2 km
Hence, each part of the trail is 0.2 kilometers long.
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The following inequalities represent a system.
y ≥ 5x + 2
y > −3x − 2
Which of the following graphs represents the system?
See the image linked below.
To graph system of inequalities y ≥ 5x + 2 and y > -3x - 2, draw lines for y = 5x + 2 and y = -3x - 2, then shade areas above each line. The intersection of shaded areas shows solutions to the system of inequalities.
Explanation:In order to graph the system of inequalities y ≥ 5x + 2 and y > -3x - 2 you would start by graphing each inequality as if it was an equality. For the first inequality, you would graph the line y = 5x + 2 and shade the area above the line because it's y 'greater than or equal to'. For the second inequality, you draw the line y = -3x - 2 and also shade the area above because it's y 'greater than'. The intersection of the shaded areas represents the solution to the system of inequalities. Therefore, the graph would have two shaded lines, with the common shaded area above both lines representing the solutions to the system of inequalities.
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What is 4 and 5/6 - 1 and 1/3 =
Answer:
Step-by-step explanation:
3
. Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52,
7.52, 7.70, 7.62, and 7.55.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE.
By iterating through different alpha values, you can identify the optimal alpha for this data set that results in the smallest MSE.
How to solvea. To construct a time series plot, you would typically use software like Excel or programming languages like Python or R.
However, I can describe the general trend based on the given data points.
Week 1: 7.35
Week 2: 7.40
Week 3: 7.55
Week 4: 7.56
Week 5: 7.60
Week 6: 7.52
Week 7: 7.52
Week 8: 7.70
Week 9: 7.62
Week 10: 7.55
Based on the data, there seems to be a slight overall upward trend in the Commodity Futures Index over the ten weeks, but there are also small fluctuations up and down throughout the period.
b. To find the best exponential smoothing coefficient (alpha) using the trial and error method, you would typically use software or programming languages to calculate the Mean Squared Error (MSE) for each alpha value.
Choose an initial value for alpha (e.g., 0.1).
Apply the exponential smoothing formula to the data series: St = α * Xt + (1 - α) * St-1, where St is the smoothed value at time t, α is the smoothing coefficient, Xt is the observed value at time t, and St-1 is the smoothed value at time t-1.
Calculate the forecast errors (Et) as the difference between the observed value and the smoothed value for each time period: Et = Xt - St-1.
Compute the Mean Squared Error (MSE) by taking the average of the squared forecast errors.
Repeat steps 2-4 with different values of alpha (e.g., 0.2, 0.3, 0.4, etc.) until you find the alpha value that minimizes the MSE.
By iterating through different alpha values, you can identify the optimal alpha for this data set that results in the smallest MSE.
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Question 7 of 10
In the triangle below, b=_ If necessary, round your
answer to two decimal places.
A
33.7°
C
Answer here
8
26.4
24
SUBMIT
the length of the missing side is approximately 4.73 units. Rounded to two decimal places, the answer is 4.73.
How to solve the problem?To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.
Let's label the missing side as b, and use sin(A) = opposite/hypotenuse to find the length of the side opposite angle A:
sin(A) = opposite/hypotenuse
sin(33.7°) = b/8
b = 8 × sin(33.7°)
b ≈ 4.726
Therefore, the length of the missing side is approximately 4.73 units. Rounded to two decimal places, the answer is 4.73.
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2. Using the link on the activity page, cut out each net. Fold and tape each net into a
solid. Your solids do not need to be perfect. (9 points: 3 points for
three-dimensional
each solid)
To fold and tape a net into a solid shape, cut out the net, fold it along the lines, tape the edges together, and flatten the edges
Instructions for Folding and Taping a Net into a Solid ShapeThe net cannot be fold and tape as it is given as a picture, however the general steps to fold and tape a net into a solid shape:
Choose a netCut out the net: Cut out the net along the lines so that you have a flat, two-dimensional shape.Fold along the lines: Fold the net along the lines indicated on the paper. Tape the edges: Use small pieces of clear tape to connect the edges of the net together, forming a solid shape.Flatten the edges: After taping, you may notice that some edges of the solid shape are not lying flat.When the above stapes are followed, some of the nets that can be gotten from the given shape are triangular pyramids and triangles
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PLEASE HELPPPP GIVNG BRAINLIESt
MNOP is a trapezium. If MN//OP and A is the midpoint of NO prove : Area of triangle MAP = 1/2area of trapezium MNOP
To prove: Area of triangle MAP = 1/2 area of trapezium MNOP
Given: MN//OP and A is the midpoint of NO
Proof:
Let h be the height of trapezium MNOP.
The area of trapezium MNOP is given by:
Area of trapezium MNOP = (1/2) × (MN + OP) × h
Since MN//OP, we have MN = OP.
Therefore, Area of trapezium MNOP = (1/2) × 2MN × h = MN × h
Now, consider triangle MAP.
The base of triangle MAP is MA, which is half of NO.
Therefore, the base of triangle MAP is (1/2) × NO.
The height of triangle MAP is h, which is the same as the height of trapezium MNOP.
Therefore, the area of triangle MAP is given by:
Area of triangle MAP = (1/2) × (base) × (height) = (1/2) × (1/2NO) × h
Substituting NO = 2OA, we get:
Area of triangle MAP = (1/2) × (1/2 × 2OA) × h = (1/2) × OA × h
Since A is the midpoint of NO, we have OA = 1/2NO.
Therefore, Area of triangle MAP = (1/2) × (1/2NO) × h = (1/2) × (base of trapezium MNOP) × h
Hence, Area of triangle MAP = 1/2 Area of trapezium MNOP.
Therefore, the given statement is proved.
Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.
To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:
Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.
Proof:
Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:
css
Copy code
M _______N
|\ |
| \ |
| \ |
| \|
O--------P
A
We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.
Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.
Since MNOP is a trapezium, the area of trapezium is given by:
Area of trapezium MNOP = (1/2)(MN+OP) × height
Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.
Therefore, the area of trapezium MNOP can be written as:
Area of trapezium MNOP = (1/2)(MN+OP) × height
= (1/2)(MA+AP+OP) × height
= (1/2)(MA+MP) × height (Since AP = NO/2 = height)
So, we have proved that:
Area of trapezium MNOP = (1/2)(MA+MP) × height
Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,
Area of triangle MAP = (1/2) × Area of triangle MAP
Substituting the above in the expression for the area of trapezium, we get:
Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP
= (3/2) × Area of triangle MAP
Therefore, we have:
Area of triangle MAP = (1/2) × Area of trapezium MNOP
Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.
Step-by-step explanation:
A group of people were asked if they had run a red light in the last year. 348 responded "yes", and 400 responded "no".
The probability of people who run red lights is
=0.465
Probability is the measure of the likelihood or chance that an event will occur.
Probability = Possible outcome of an event ÷ Total outcome
Total number of people asked if they had run a red light = number of people that responded 'yes' + number of people that responded 'no'
Total outcome = 348+400
Total outcome = 748
Possible outcome = number of people that responded yes = 394
The probability that if a person is chosen at random, they have run a red light in the last year will be
[tex]=\frac{348}{748}\\\\=0.465[/tex]
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Assume the random variable x is normally distributed with mean u=89 and standard deviation o=4. Find the indicated probability. P(x<87)
The random variable x is normally distributed with mean u=89 and standard deviation o=4. The indicated probability, P(x<87)= 0.3085.
Describe Standard Deviation?In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a commonly used measure of the spread of a distribution and is calculated as the square root of the variance.
A higher standard deviation indicates that the data points are more spread out from the mean, while a lower standard deviation indicates that the data points are more tightly clustered around the mean.
Standard deviation is an important concept in statistics and is used in many statistical analyses, such as hypothesis testing and confidence interval estimation. It is also used in finance and economics to measure the risk associated with investments and to assess the variability of economic data.
To solve this problem, we need to standardize the value using z-score formula.
z = (x - mu) / sigma
Here, x = 87, mu = 89, and sigma = 4.
z = (87 - 89) / 4 = -0.5
We can look up the corresponding area under the standard normal distribution curve using a table or calculator. The area to the left of z = -0.5 is 0.3085.
Therefore, P(x < 87) = P(z < -0.5) = 0.3085.
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Solve for ∠A
. Round your answer to the nearest tenth.
∠A
= degrees
(60 points)
Answer:
∠A = 48.2
Step-by-step explanation:
Cos^-1(6/9
Use the Cosine with the negative one because you are finding an angle. Then, because Cosine is adjacent/hypotenuse, 6 would be your adjacent side length to theta and 9 would be the hypotenuse as it is across from the right angle.
5.2, 5.2, 4.7, 5.4, 3.9, 3.5, 4.1, 4.2, 5.4, 4.7, 4.8, 4.2, 4.6, 5.1, 3.8, 3.9, 4.6, 5.1, 3.6, 4.6, 4.3, 3.4, 4.9, 4.2, 4.0
A manufacturer of pencils randomly selects 25 pencils and measures their length (in inches). Their data is shown. Create a frequency distribution with 6 classes and a class width of 0.4 inches. What is the shape of the frequency histogram?
The histogram is bimodal.
The histogram is roughly symmetrical.
The histogram is skewed right.
The histogram is uniform.
The histogram is skewed left.
Answer:
A) The histogram is bimodal.
Answer:
To create a frequency distribution, we first need to determine the range of the data. The smallest measurement is 3.4 inches and the largest is 5.4 inches, so the range is 5.4 - 3.4 = 2 inches. To create 6 classes with a width of 0.4 inches, we divide the range by 0.4 and round up to the nearest integer:
Number of classes = (range / class width) rounded up = 2 / 0.4 = 5
So we will use 5 classes with a width of 0.4 inches each. The classes and their corresponding frequency counts are:
Class 1: 3.4 - 3.8 | Frequency: 3
Class 2: 3.9 - 4.3 | Frequency: 8
Class 3: 4.4 - 4.8 | Frequency: 6
Class 4: 4.9 - 5.3 | Frequency: 7
Class 5: 5.4 - 5.8 | Frequency: 1
To create a histogram, we can plot the frequency counts on the y-axis and the class intervals on the x-axis. The shape of the histogram can give us information about the distribution of the data. In this case, the histogram is bimodal, meaning there are two peaks in the data. This suggests that the data may be composed of two separate subpopulations.
y varies directly as the square root of z. If y = 36, then z = 36.
Equation: [tex]y=k\sqrt{z}[/tex].
Value of the constant of proportionality (k): 6.
Step-by-step explanation:1. Write the equation using variables.So if y varies directly as the square root of z, there's a constant coefficient (k) multiplying the square root of z. Why? Because taking the square root of z will reduce it's value, then a number (k) must be multiplying it to make it match the value of y.
So:
[tex]y=k\sqrt{z}[/tex]
2. Substitute the equation with the given values.[tex]y = 36;\\ \\z = 36;\\ \\(36)=k\sqrt{(36)}\\ \\[/tex]
3. Divide both sides of the equation by [tex]\sqrt{36}[/tex] to calculate the value of k.[tex]\frac{36}{\sqrt{(36)}} =\frac{k\sqrt{(36)}\\ \\}{\sqrt{(36)}} \\ \\\frac{36}{6} =k\\ \\k=6[/tex]
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[tex]\blue{\huge {\mathrm{SOLVING \; EQUATIONS}}}[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
y varies directly as the square root of z. If y = 36, then z = 36.[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
[tex]\qquad\qquad\begin{aligned}\bold{y = k\sqrt{z}}\\\\\bold{\:k = 6\:\:\:}\end{aligned}[/tex]
*Please read and understand my solution. Don't just rely on my direct answer*
[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}} [/tex]
From the given information, we are given that:
[tex]\sf \red{y} = \red{36}[/tex][tex]\sf \blue{z} = \blue{36}[/tex]Since y varies directly as the square root of z, we can write this as an equation:
[tex]\sf \red{y} = k\sqrt{\blue{z}}[/tex]where:
k is the constant of proportionality.Substitute the given values into the equation and solve for k:
[tex]\qquad\qquad\begin{aligned}\sf \red{y} &=\sf k\sqrt{\blue{z}}\\\sf \red{36} &=\sf k\sqrt{\blue{36}}\\\sf \dfrac{\red{36}}{\sqrt{\blue{36}}} &=\sf \dfrac{k \cancel{\sqrt{\blue{36}}}}{ \cancel{\sqrt{\blue{36}}}}\\\sf \dfrac{\red{36}}{\blue{6}}&=\sf k\\\sf 6& =\sf k\\\sf \bold{\:k}& = \bold{6}\:\end{aligned}[/tex]
[tex]{===========================================}[/tex]
Bear in Mind!Equations are mathematical statements that show that two quantities are equal. They typically contain an equal sign (=) and one or more variables. Equations are used to express relationships between quantities and to solve problems in various fields of science, engineering, and mathematics.
Example equations include:
[tex]\sf -4t^2 - 16t = -8[/tex][tex]\sf -2x + 5 = 13[/tex][tex]\sf -\dfrac{y}{7} = 3[/tex]To solve an equation, we want to determine the value of the variable(s) that make the equation true.
There are different techniques to solve equations, but some common steps include:
1. Simplify both sides of the equation by combining like terms and using the order of operations if necessary.
2. Isolate the variable on one side of the equation by undoing any operations that were performed on it.
For example, if the variable is multiplied by a number, divide both sides of the equation by that number. If the variable is added to a number, subtract that number from both sides of the equation.3. Check the solution by plugging it back into the original equation to see if it makes the equation true.
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[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]
translate the triangle 3 to the right and 2 down
According to the assumption the translated triangle would have vertices at (4,0), (6,2), and (5,-1).
Given,
To translate a triangle 3 units to the right and 2 units down, we would take each point of the original triangle and add 3 to the x-coordinate and subtract 2 from the y-coordinate.
For example, if the original triangle has vertices at (1,2), (3,4), and (2,1), the translated triangle would have vertices at:
(1+3, 2-2) = (4,0)
(3+3, 4-2) = (6,2)
(2+3, 1-2) = (5,-1)
So, the translated triangle would have vertices at (4,0), (6,2), and (5,-1).
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Which equation of a circle has the center, C, and radius, r, as shown in the graph?
The equation of a circle given by the graph is (x-3)²+(y+2)²=29,
hence option b is correct.
A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. A circle with an (h, k) center and a radius of r has the equation:
(x-h)² + (y-k)²= r²
This is the equation's standard form. Hence, we can quickly determine the equation of a circle if we know its radius and center coordinates.
We know that the equation of the circle is -
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center of the circle and r is the radius,
given that,
center of the circle is = (3,-2)
and the radius is=√29
Hence the equation of a circle is
[tex](x-3)^2+(y+2)^2=(\sqrt29)^2\\\\(x-3)^2+(y+2)^2=29[/tex]
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A scientist was in a submarine, 52.3 feet below sea level, studying ocean life. Over the next ten minutes, she went down 21.5 feet. How many feet was she now below sea level?
After descending [tex]21.5[/tex] feet, the scientist's new position in the submarine would be [tex]30.8[/tex] feet below sea level.
What is the sea level?The scientist was initially in a submarine, located 52.3 feet below sea level. This means that her position was [tex]52.3[/tex]feet lower than the surface of the sea.
Over the next ten minutes, the scientist descended further into the ocean by [tex]21.5[/tex] feet. This means that she traveled down an additional [tex]21.5[/tex]feet from her initial position.
To calculate her new position below sea level, we can subtract the distance she traveled downward (21.5 feet) from her initial position (52.3 feet below sea level).
[tex]52.3 feet - 21.5 feet = 30.8 feet[/tex]
Therefore, after descending 21.5 feet, the scientist's new position in the submarine would be 30.8 feet below sea level.
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