The width of the interval will be reduced to 1.5 if the sample size is increased by a factor of 25.
To find how much the sample size n must be increased if the width of the confidence interval is to be halved, use the following formula:
W = (zα/2 x σ/√n)W/2 = (zα/2 x σ/√n')
Where W is the initial width of the confidence interval,
zα/2 is the critical value of the standard normal distribution that corresponds to the level of significance α and the appropriate two-tailed area,
σ is the population standard deviation,
n is the initial sample size, and
n' is the new sample size needed to halve the width of the interval.
Rearranging the second equation to solve for n', we get:
n' = n(4)
So the sample size needs to be increased by a factor of 4, or 300% if the width of the confidence interval is to be halved.
If the sample size is increased by a factor of 25, the effect it will have on the width of the interval can be found using the following formula:
W' = (zα/2*σ/√25n) = (zα/2*σ/5√n)
The width of the interval will be divided by 5, or reduced to one-fifth of its initial value.
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1. Two congruent solids 1 and 2 have the property that 1 ∩ 2 is a right
triangular prism with height√3 and a base that is an equilateral triangle of
side length 2. If the volume of 1 ∪ 2 is 25 units
3
, find the volume of 1.
The volume of solid 1 is 14 cubic units calculated through the formula of volume.
What is volume?Volume is the maximum quantity of space that an object can contain. Volume, which is essentially a measurement of an object's size, is the quantity of space a thing occupies. A three-dimensional object's volume, which is calculated in cubic units, is the quantity of space it takes up. For instance, glass has a cylindrical form and can hold a certain volume of water.
Let V1 and V2 be the volumes of the congruent solids 1 and 2, respectively. The volume of their union is given
V1 U V2 = V1+V2-V1∩V2
We know that V1 ∩ V2 is a right triangular prism with height √3 and a base that is an equilateral triangle of side length 2. So, the volume can be calculated with the following formula:
V1 ∩ V2 = (1/2) * base * height * heightbase
where base is the area of the equilateral triangle, which is √3, height is √3, and height base is 2. Plugging in these values, we get:
V1 ∩ V2 = (1/2) * √3 * √3 * 2 = 3
Now we can use the given information to find the volume of 1:
25 = V1 + V2 - V1 ∩ V2
25 = V1 + V2 - 3
We also know that V1 = V2, since the solids are congruent.
Substituting the following value with the above equation, we get:
25 = 2V1 - 3
28 = 2V1
V1 = 14
Therefore, the volume of solid 1 is 14 cubic units.
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4) Tom has ran 10 miles of a 75 mile running challenge. If he runs 4 miles each day until he finishes the challenge, write an equation that can be used to find the number of days, d, it will take Tom to finish running the challenge miles.
Step-by-step explanation:
Let's use d to represent the number of days it will take Tom to finish the challenge miles.
Since Tom is currently 10 miles into the challenge and plans to run 4 miles each day until he finishes, the total number of miles he will run is 75 - 10 = 65 miles.
If he runs 4 miles each day, we can use the equation:
total distance = distance per day * number of days
to find the number of days it will take Tom to run 65 miles. Plugging in the known values, we get:
65 = 4d
Simplifying this equation, we can solve for d:
d = 65/4
So, it will take Tom d = 16.25 days to finish the running challenge if he runs 4 miles each day. However, since he cannot run a fraction of a day, we can round up the answer to the nearest whole number of days. Therefore, it will take Tom 17 days to finish the challenge.
The equation that can be used to find the number of days, d, it will take Tom to finish running the challenge miles is:
d = ceil(65/4)
where ceil is the ceiling function, which rounds up the result to the nearest whole number.
Answer:
16 days + 1 mile
Step-by-step explanation:
On April 15 Mary purchased a washer and dryer from her local
Appliance store tax free sale day the cost of the washer and dryer was 1,1234. 46 Mary decided to pay using three month no interest credit plan Mary make down payment of 100$ before leaving the store Mary decides she needs a rack for the dryer that cost 50. 00$ what is the total amount Mary still owe
The total amount Mary still owes is $1,184.46.
The total cost of the washer and dryer is $1,234.46, and Mary made a down payment of $100. This means she still owes:
$1,234.46 - $100 = $1,134.46
In addition, Mary decides to purchase a rack for the dryer for $50.00. Therefore, the total amount Mary still owes is:
$1,134.46 + $50.00 = $1,184.46
Mary purchased a washer and dryer for $1,234.46 on a tax-free sale day using a three-month no-interest credit plan. She made a down payment of $100 and later decided to buy a rack for the dryer for $50.00. So Mary still owes $1,184.46.
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Which statement describes the graph of this polynomial function?
f (x) = x Superscript 5 Baseline minus 6 x Superscript 4 Baseline + 9 x cubed
Answer:
The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.
A mythical king promised to give his favorite jester one gold coin on January 1 and every day thereafter four times the number of coins given on the previous day. The function represents the number of new coins, C , the jester receives on the n th day after January 1 .
The most reasonable domain of the function C = 4ⁿ is all positive integers, which is answer choice (c) i.e. all whole numbers .
What is function?A function is a mathematical object that takes one or more inputs, performs a specified operation on them, and produces an output.
The inputs to a function are called the domain, and the outputs are called the range.
An equation, a graph, or a table can all be used to depict a function.
The function that represents the number of new coins the jester receives on the n-th day after January 1 is given by C = 4ⁿ.
Since n represents the number of days after January 1, it is most reasonable to assume that n is a positive integer, because it doesn't make sense to talk about a negative or fractional number of days in this context.
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The complete question is given below.
Consider the expression 2(3n + 6z)
Enter an expression that shows the sum of exactly two terms that is equivalent to 2(3n+6z)
Answer:
6n+12z
Step-by-step explanation:
then we got this bc we do like terms so 6n from 2 x3n then 12z bc 2x6
Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers
The given series diverges to negative infinity as the terms cancel out, leaving only two terms at the beginning and end of the series.
To determine the convergence of the given series, we can use the telescoping series method.
Let's write out a few terms of the series to see if we can spot a pattern:
n=1: 1/2 - 3/4 = -1/4
n=2: 2/3 - 4/5 = -2/15
n=3: 3/4 - 5/6 = -1/8
n=4: 4/5 - 6/7 = -2/35
...
We can see that the terms of the series cancel out, leaving only two terms at the beginning and end of the series. Therefore, we can write the series as:
∑ (n/n+1 - n+2/n+3) = 1/2 - (n+2)/(n+3)
As n approaches infinity, the second term approaches 1, so the series diverges to negative infinity.
Therefore, the given series diverges.
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_____The given question is incomplete, the complete question is given below:
Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers
(∑ ∞ to n = 1) = (n/n+1 - n+2/n+3)
please help me
ill give brainlyist
The constant of proportionality is calculated as:
Option D: 8.5
How to find the constant of proportionality?The constant of proportionality is defined as the constant value of the ratio between two proportional quantities.
Now, we are given a table of values and as such, we can find the constant of proportionality from the formula:
k = y/x
From the table, we have:
k = 25.50/3
k = 8.5
k = 42.5/5
k = 8.5
k = 59.50/7
k = 8.5
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suppose that the value of a stock varies each day from $8.82 to $16.17 with a uniform distribution. find the third quartile, i.e., 75% of all days the stock is below what value?
The third quartile is $10.6575, which means that 75% of all days the stock is below this value.
The range of the stock price is from $8.82 to $16.17, and the distribution is uniform, which means that the probability of the stock price being any value between the minimum and maximum is the same.
To find the third quartile, we need to find the value x such that 75% of the observations are less than or equal to x, and 25% of the observations are greater than or equal to x.
Since the distribution is uniform, we can find x by finding the value that separates the bottom 25% of the distribution from the top 75% of the distribution.
The bottom 25% of the distribution spans from $8.82 to some value x. Since the distribution is uniform, we can find x by setting the probability of the stock price being less than or equal to x to 0.25, which gives:
(x - 8.82) / (16.17 - 8.82) = 0.25
Solving for x, we get:
x - 8.82 = 0.25 * (16.17 - 8.82)
x - 8.82 = 1.8375
x = 10.6575
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you're playing a game in which the probability of winning each round is .20. if you play five times, what is the probability of winning exactly 2 of the 5 times?
the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%
define probabilityProbability refers to the measure of the likelihood or chance of a particular event occurring. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.
The formula for the binomial distribution can be used to resolve this issue:
P(X=k) = (n choose k) × pᵇ×(1-p)ⁿ⁻ˣ
where:
The number of trials, n, is five in this instance.
bis the number of successes we want (in this case, b = 2)
p is the probability of success on each trial (in this case, p = 0.20)
So, plugging in the values:
P(X=2) = (5 choose 2) ×0.20² × (1-0.20)⁵⁻²
= 10 × 0.04×0.512
= 0.2048
Therefore, the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%.
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Since the beginning of school, Steven has been saving money to buy a new phone. His bank balance is represented by the graph below.
a. According to the graph, about how much money had Steven saved after 2 weeks of school?
b. About how much money did Steven probably have after 4 weeks of school? How can you tell?
c. If he keeps saving at the same rate, how much will he have saved by Week 7? Explain how you know.
a. According to the graph, Steven had saved about $100 after 2 weeks of school.
b. According to the graph, Steven probably had about $200 after 4 weeks of school because the graph shows that he saves an average of $50 per week, so after 4 weeks, he would have saved $50 x 4 = $200.
c. If Steven keeps saving at the same rate, he will have saved $350 by Week 7. This is because he saves $50 per week, so after 7 weeks, he will have saved $50 x 7 = $350.
a spinner with the letters a, b, c, and d is spun. what is the theoretical probability of landing on the letter c?
The probability of the spinner landing on the letter C is 1/4
To understand the probability of the spinner landing on the letter C, we need to start by looking at the total number of possible outcomes. In this case, there are four possible outcomes, corresponding to the four letters A, B, C, and D.
Since each of the four quadrants on the spinner is equal in size, each of the four letters has an equal chance of being landed on. Therefore, the probability of the spinner landing on the letter C is the number of ways that the spinner can land on C, divided by the total number of possible outcomes.
Since there is only one way for the spinner to land on C, and there are four possible outcomes in total, the probability of the spinner landing on the letter C is 1/4
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The given question is incomplete, the complete question is:
A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner landing on the letter C
analysis of a pert problem shows the estimated time for the critical path to be 108 days with a variance of 64. there is a .90 probability that the project will be completed before approximately day: group of answer choices 108. 98. 115. 118. 109.
There is a .90 probability that the project will be completed before approximately day 118.
The given information can be solved by using the formula of z-score as follows:
Z = (X - μ)/σ
Where: Z = z-score
X = the time for project completion
μ = the mean time for the critical path
σ = standard deviation for the critical path
σ² = variance of the critical pathσ = √64
σ = 8
Given that the mean time for the critical path is μ = 108 days and σ = 8 days,
Therefore, the z-score of the completion of the project before 108 days is given by:
Z = (X - μ)/σ0.90
= P(Z < z)
= P(Z < (X - 108)/8)P(Z < (X - 108)/8)
= 0.90
Using a z-table or calculator, we find the z-value to be 1.28.
Then,1.28 = (X - 108)/8
Multiplying both sides by 8, we get:10.24 = X - 108
Adding 108 to both sides, we get: X = 118.24
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If YZ is the requested side and XZ is the given side, which ratio amongst sin 35,3° or cos 35,5° will be used to calculate YZ
The answer of the given question based on the trigonometry is , to calculate YZ, we should use the cosine function with the angle 35.5°.
What is Sine function?The sine function is a mathematical function that relates the ratios of the lengths of two sides of a right triangle with the measure of one of its non-right angles. Specifically, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse.
To use trigonometry to calculate YZ, we need to find a trigonometric ratio that involves the given side XZ and the angle opposite the requested side, which is angle YXZ. We don't have the measure of this angle, but we know that it is supplementary to the given angle 35.5°, so it must measure:
180° - 35.5° = 144.5°
We can use this angle and the given side XZ to find the length of YZ using the sine or cosine function.
In this case, the length of the opposite side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 144.5°. So we can write:
sin(144.5°) = YZ / XZ
Solving for YZ, we get:
YZ = XZ * sin(144.5°)
On the other hand, the cosine function , this case, the length of the adjacent side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 35.5°. So we can write:
cos(35.5°) = YZ / XZ
Solving for YZ, we get:
YZ = XZ * cos(35.5°)
Therefore, to calculate YZ, we should use the cosine function with the angle 35.5°.
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Cydni is working with some algebra tiles at her desk. She makes groups that look like this:
A:
x + 1 + 1 + 1 + x + 1 + 1 + 1 + x + 1 + 1 + 1
B:
3x + 9
C:
3(x + 9)
D:
3(x + 3)
E:
x + 2x + 3(x + 2)
F:
x3 + 13
(Please answer quickly!!)
Answer:
B. 3x+9
hope this helped
3.1.1) Determine the Accumulated amount for the investment at CAPITEC.
3.1.2) Determine the Accumulated amount for the investment at FNB.
3.1.3) Use the information you worked out to help Lebo decide which bank will give her the better investment. Explain your answer.
1. The accumulated amount for the investment at CAPITEC is R36,750.
2. The accumulated amount for the investment at FNB is R33,480.
3. Lebo will earn more interest if she invests her money at Capitec than at FNB.
What is the Accumulated amount for the investment at CAPITEC?The accumulated amount for the investment at Capitec with a principal amount of R30,000 invested at a simple interest rate of 7.5% for 3 years can be calculated as follows:
[tex]= Principal + (Principal * Rate * Time)\\= R30,000 + (R30,000 * 0.075 * 3)\\= R30,000 + R6,750\\= R36,750[/tex]
What is the Accumulated amount for the investment at FNB?The accumulated amount for the investment at FNB with a principal amount of R30,000 invested at a compound interest rate of 3.5% per annum for 3 years can be calculated using the compound interest formula:
[tex]= Principal * (1 + Rate)^Time\\= R30,000 * (1 + 0.035)^3\\= R30,000 * 1.116\\= R33,480[/tex]
Now, based on the calculations, the investment at Capitec will yield R36,750 after 3 years while the investment at FNB will yield R33,480 after 3 years. Therefore, Lebo will earn more interest if she invests her money at Capitec than at FNB.
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At 4 p.m. Jack, who is 6 feet tall, casts a shadow 4 feet long. At the same time, a nearby tree casts a shadow 12 feet long.
What is the height (x) of the tree?
Therefore [tex]x/6=12/4[/tex].[tex]5x=16ft[/tex]The height of the tree will be 16ft.the correct answer is (c).
What is trigonometry?The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant areas of mathematics in history: trigonometry. Hipparchus, a Greek scholar, introduced this idea. In this article, we will study the fundamentals of trigonometry, including its formulas, tables, ratios, functions, and many solved examples. What are similar triangles If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be similar. To put it another way, similar triangles have the same shape but may differ in height. In addition, if the matching sides of the triangles are equal in length, the triangles are congruent. In the given figures, these are two similar triangles as the form the same angle with the ground The height of the tree will be 16ft using the property of similar triangles.
by the question.
Let's first find the ratio of Jack's height to his shadow length:
Jack's height / Jack's shadow length = 6 / 4
Simplifying this ratio, we get:
[tex]Jack's height / 4 = 3 / 2[/tex]
Multiplying both sides by 4, we get:
[tex]Jack's height = 6[/tex]
Now, let's find the ratio of the tree's height to its shadow length:
Tree's height / Tree's shadow length = x / 12
Since the two triangles are similar, we know that these ratios are equal. So, we can write:
Jack's height / Jack's shadow length = Tree's height / Tree's shadow length
Substituting the known values, we get:
[tex]6/4=x/12[/tex]
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Help help help help help help help help
Answer:
(5^3)^(-2)
Step-by-step explanation:
5^2 × 5^-8 = 5^-6
(5^3)^(-2) = 5^-6
A sphere has radius 2. 7cm. What is its surface area to the nearest sqaure cenitmeter
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2.7 \end{cases}\implies SA=4\pi (2.7)^2\implies SA\approx 91.61~cm^2[/tex]
ten identical protein samples were analyzed by the bradford method for protein analysis. the following values for protein concentration were obtained. observation number protein concentration (mg/ml) 1 1.02 2 0.98 3 0.99 4 1.01 5 1.03 6 0.97 7 1.00 8 0.98 9 1.03 10 1.01 calculate sample mean
The sample mean protein concentration obtained using the Bradford method for protein analysis is 1.00 mg/ml.
We must add together all the protein concentrations and divide the total by the number of observations in order to determine the sample mean for the protein concentrations acquired using the Bradford technique for protein analysis.
We have ten identical protein samples in this instance, and the measured protein concentrations are as follows:
Protein concentration (mg/ml) observations: 1: 1.02, 2: 0.98, 3: 0.99, 5: 1.01, 6: 0.97, 8: 1.00, 9: 1.03, and 10: 1.01.
We add up the protein concentrations and divide the total by the number of observations to determine the sample mean:
[tex](1.02 + 0.98 + 0.99 + 1.01 + 1.03 + 0.97 + 1.00 + 0.98 + 1.03 + 1.01) / 10[/tex] is the sample mean.
= 1.00 mg/ml
As a result, the Bradford method for protein analysis yielded a sample mean protein content of 1.00 mg/ml.
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which statistical method could a scientist use to estimate the strength of evidence that a particular node in a phylogeny exists?
A scientist can use bootstrap analysis to estimate the strength of evidence that a particular node in a phylogeny exists.
Bootstrap analysis is a statistical method used to determine the reliability and robustness of phylogenetic trees' topologies. In bootstrap analysis, a series of random resampling with replacement is used to assess how well the observed data fit the phylogenetic hypothesis.
Bootstrap values range from 0 to 100 and reflect the proportion of times that a particular node or branch occurs in the bootstrap replicate trees. Bootstrap values greater than 70% are usually considered strong evidence that a particular node or branch exists in the phylogenetic tree.
Bootstrap analysis is an important tool for understanding the reliability of phylogenetic trees and the evolutionary relationships among organisms.
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when we make inferences about one population proportion, what assumptions do we need to make? mark all that apply.
The data should come from a binomial distribution. There should be no non-response or other forms of bias. The sample size should not be more than 10% of the population size, and the sample should be independent of one another.
When making inferences about one population proportion, the following assumptions need to be made:
Option 1: The sample is a simple random sample from the population.
Option 2: The sample size should be large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
Option 3: The data comes from a binomial distribution.
Option 4: There is no non-response or other forms of bias.
Option 5: The sample size is no more than 10% of the population size.
Option 6: The sample is independent of one another.In order to make inferences about one population proportion, the assumptions mentioned above need to be made. It is vital to make sure that the sample is a simple random sample from the population, and that the sample size is large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
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the temperature at 12 noon was 10 degree Celsius above zero .if it decreases at the rate of 2 degree Celsius per hour until midnight ,at what time would the temperature be 8 degree Celsius below zero? what would be the temperature at midnight?
Answer:
The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.
a small cube with side length 6y is placed inside a larger cube with side length . what is the difference in the volume of the cubes?
The difference in the volume of a small cube with a side length 6y is placed inside a larger cube with a side length is 5616y³
To find: the difference in the volume of the cubes.
Let the length of the larger cube be x.
So, the volume of the smaller cube is (6y)³ and the volume of the larger cube is x³.
As the smaller cube is placed inside the larger cube, it means that its side length is equal to the side length of the smaller cube plus twice the side length of the smaller cube.
So, x = 6y + 2(6y) = 18y.
The volume of the smaller cube = (6y)³ = 216y³
The volume of the larger cube = x³ = (18y)³ = 5832y³.
So, the difference in volume
= Volume of the larger cube - Volume of the smaller cube
= 5832y³ - 216y³
= 5616y³.
Therefore, the difference in the volume of the cubes is 5616y³.
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if one flag pole is y feet tall and casts a shadow x feet long, then how tall is another nearby flag pole that casts a shadow p feet long at the same time of day?
If one flag pole is y feet tall and casts a shadow x feet long, and another nearby flag pole casts a shadow p feet long at the same time of day, we can use similar triangles to determine the shadow of the second flag pole.
In this scenario, the two flag poles and the ground form two similar right triangles. The height of the first flag pole (y) corresponds to one leg of the first triangle, and the length of its shadow (x) corresponds to the other leg.
Similarly, the height of the second flag pole (h) corresponds to one leg of the second triangle, and the length of its shadow (p) corresponds to the other leg.
Therefore, the height of the second flag pole is equal to the product of the height of the first flag pole and the length of the shadow of the second flag pole, divided by the length of the shadow of the first flag pole.
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a population has a mean µ=77 and a standard deviation δ=9. find the mean and standard deviation of a sampling distribution of sample means with sample size n = 81.
µx = ___
Mean = 77
Standard Deviation = 1
Let's dive deeper into the details below.
The population has a mean µ=77 and a standard deviation δ=9.
To find the mean and standard deviation of a sampling distribution of sample means with a sample size n = 81.
μx = 77 (the mean of the population)
σx = δ/√nσx = 9/√81σx = 1
The mean of the sampling distribution is 77, and the standard deviation is 1.
Therefore, the value of μx is 77.
The formula to find the standard deviation of the sampling distribution is given by;
σx = δ/√nσx = 9/√81σx = 1
The value of the standard deviation of the sampling distribution is 1.
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WILL MARK BRAINLIEST is this a right triangle (explain your presses)
Answer:yes it is a triangle
Step-by-step explanation:
let's assume this triangle's sides are a,b and c.
we know this equation: [tex]a+b > c > |a-b|\\c+b > a > |c-b|\\a+c > b > |a-c|\\a=6\\b=7\\c=9\\13 > 9 > 1--- > which is true\\16 > 6 > 2----- > which is true as well\\15 > 7 > 3------ > it is true,too\\all of this equations are true so, this is a triangle[/tex]
What is the area of this parallelogram?
O A = 20 ft²
O A=213ft²
O A = 33 ft²
O A=41 ft²
5 ft
4 ft
81 ft
The area of the given parallelogram is A- 33(1/2) ft² using the base and height of the parallelogram. the correct answer is (c).
What is a parallelogram?A quadrilateral with two sets of analogous edges is appertained to as a parallelogram. In a parallelogram, the opposing edges are of equal length, and the opposing angles are of equal size. also, the internal angles that are supplementary to the transversal on the same side. 360 ° is the sum of all internal angles. A parallelepiped is a three- dimensional shape with parallelogram- shaped sides. The base( one of the analogous lines) and height( the distance from top to bottom) of the parallelogram determine its area. A parallelogram's border is determined by the lengths of its four edges. The characteristics of a parallelogram are participated by the shapes of a square and cell. What's area? The size of a section on a face is determined by its area. face area refers to the area of an open face or the border of a three- dimensional object, whereas the area of an area area plane region or area area plane area refers to the area of a shape or planar lamella.
The area of a parallelogram is given by
[tex]base*height.base=8(1/3)ft[/tex]
height=4ft
[tex]Area=b*h =(25/3)*4 =100/3 = 33[/tex]
[tex][base]\frac{1}{3}[(hieght)] ft^{2}[/tex]
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Find g(x) and f(x) from h(x)
H(x) = (sinx)^3
The functions g(x) and f(x) that correspond to h(x) = [tex]\rm (sin\ x)^{3}[/tex] are g(x) = cos x and f(x) = [tex]\rm (sin\ x)^{1/3[/tex].
What are trigonometric functions?Trigonometric functions are mathematical functions that are related to the angles of a right triangle to the lengths of its sides. They are widely used in mathematics, physics, engineering, and other fields to describe and analyze periodic phenomena and wave motion.
To find g(x) and f(x) from h(x) = [tex]\rm (sin\ x)^{3}[/tex], we need to use inverse operations to isolate sin x.
First, we can take the cube root of both sides of the equation to undo the cube power:
[tex]\rm h(x)^{1/3}[/tex] = (sin x)
Now we can substitute this expression for sin x in the standard functions g(x) and f(x):
g(x) = cos x
f(x) = [tex]\rm h(x)^{1/3}[/tex] = [tex]\rm (sin\ x)^{3}[/tex]
Therefore, the functions g(x) and f(x) that correspond to h(x) = [tex]\rm (sin\ x)^{3}[/tex] are g(x) = cos x and f(x) = [tex]\rm (sin\ x)^{3}[/tex].
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Thank you for the help!
Using the volume formula it is obtained that the least number of bags Martin should buy is Option C: 13.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
First, we need to convert the height of the cylinder from inches to feet -
6 inches = 6/12 feet = 0.5 feet
The volume of the cylinder can be calculated as -
V = πr²h
where r is the radius and h is the height.
Substituting the given values, we get -
V = 3.14 x 2² x 0.5
V = 6.28 cubic feet
Since each bag contains 0.5 cubic feet of sand, we can find the number of bags needed by dividing the total volume by the volume of each bag -
n = V / 0.5
n = 6.28 / 0.5
n = 12.56
Since we can't buy a fractional number of bags, we must round up to the nearest whole number.
Therefore, Martin needs to buy at least 13 bags of sand.
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