The value of m∠N is 21° ,the value of m∠M is 55° and the value m∠O is 106°.
To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:
m∠M + m∠N + m∠O = 180
Substituting the given angle measures, we get:
(4x-13) + (2x-13) + (5x+19) = 180
Simplifying the equation, we get:
11x - 7 = 180
11x = 187
x = 17
Now that we know the value of x, we can find the measure of each angle. Substituting x = 17, we get:
m∠M = (4x-13) = (417-13) = 59 degrees
m∠N = (2x-13) = (217-13) = 21 degrees
m∠O = (5x+19) = (5*17+19) = 106 degrees
Therefore, the measure of ∠MNO is:
m∠N = 21 degrees
Note: The question also asks for the measure of ∠P, but there is no information given about ∠P in the problem.
In AMNO, m angle M = (4x - 13) deg m angle N = (2x - 13) deg and m angle O = (5x + 19) deg Find m/N.
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What the heck is 5u(2) it’s supposed to be multiplication
Answer:
10u
Step-by-step explanation:
2. (a) Arnold walked a distance of 50km due north. He continued to move 25km due east.
Sketch a diagram to illustrate the Arnold's movement from the starting point.
Find correct to the nearest whole number the distance between where he started the
journey and where he ended the journey
The bearing of his starting point from his end point.
Answer:
Step-by-step explanation:
The sketch is a right-angled triangle.
We can use Pythagoras' theorem.
[tex]z^{2} =x^{2} +y^{2}[/tex]
z=√(50^2+25^2)
z= 25√5
z=25*2.23
z=55.75
z≈56km
the distance between where he started the
journey=56km
tan(90-Θ)=25/50
cotΘ=1/2
tanΘ=2
Θ=[tex]tan^{-1} (2)[/tex]
bearing of his starting point from his end point[tex]tan^{-1} (2)[/tex]
In a lab group, there are 3 students taller than 62 inches and 2 students shorter than
62 inches.
The teacher selects 2 students at random.
What is the probability that both students are shorter than 62 inches?
Hence, there is a 1/10 or 0.1 chance that both of the chosen kids will be under 62 inches tall.
what is probability ?In the field of mathematics known as probability, random chance and their results are examined. It entails putting a number between zero and 1, where 1 indicates that now the event is guaranteed to happen and 0 that it is impossible, to reflect the possibility of an event occurring. From straightforward games of chance to intricate real-world systems like share prices and weather patterns, probability theory offers a framework for the analysis and modelling of a wide range of phenomena. It has uses in physics, economics, computer science, statistics, and other disciplines.
given
Let A represent the scenario in which the first student chosen is under 62 inches, and B represent the scenario in which the second student chosen is under 62 inches as well.
Since there are two shorter kids out of a total of five students, the likelihood of choosing one on the first try is 2/5.
Given that the first student was shorter, the likelihood of choosing another shorter student on the second try is 1/4 because there would only be 1 shorter student left out of the other 4 students.
Thus, the likelihood of picking two consecutive students who are shorter
The formula for P(A and B) is P(A) P(B|A) = (2/5) (1/4) = 1/10.
Hence, there is a 1/10 or 0.1 chance that both of the chosen kids will be under 62 inches tall.
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For what to go through a phase change, it’s temperature must be greater than or equal to 212°F or less than or equal to 32°F. If a glass of water is currently at 75°F, what temperature changes will produce a phase change?
Heating the water to a temperature of 212°F or higher, which will cause it to boil and transform from a liquid to a gas (water vapor).
Cooling the water down to a temperature of 32°F or lower, which will cause it to freeze and transform from a liquid to a solid (ice).
What is the temperature range for a stage change in water?The temperature range for a stage change in water is either more noteworthy than or equivalent to 212°F or not exactly or equivalent to 32°F, which compares to the bubbling and edges of freezing over of water, separately.
The water is still in its liquid state at 75°F, but it will change phases if it reaches 212°F or is cooled to 32°F or lower.
Therefore, the temperature changes that will produce a phase change in a glass of water at 75°F are:
Heating the water to a temperature of 212°F or higher, which will cause it to boil and transform from a liquid to a gas (water vapor).
Cooling the water down to a temperature of 32°F or lower, which will cause it to freeze and transform from a liquid to a solid (ice).
It is important to note that the temperature of the water will not change during the phase change until the entire change is complete. To put it another way, when water is boiling, it will remain at 212°F until all of the liquid has evaporated, and when it is frozen, it will remain at 32°F until all of the liquid has frozen solid.
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Write the fifteenth term of the binomial expansion of (v−w^2)^22
Answer:
Step-by-step explanation:
[tex]T_{r+1}=nc_{r}x^{n-r}a^r\\x=v\\a=-w^2\\n=22\\r+1=15\\r=15-1=14\\22c_{14}=22c_{22-14}=22c_{8}\\ T_{15}=22c_{8}v^{22-14}(-w^2})^{14}\\T_{15}=22c_{8}v^8w^{28}[/tex]
On 36 acres of land , there are a total of 2808 trees. If the trees are sread out evenly , how many trees are on each acre of land ?
There are approximately 78 trees on each acre of land when the trees are spread out evenly.
To find the number of trees on each acre of land mathematically, we can use the formula for average or mean.
The average number of trees per acre can be found by dividing the total number of trees by the total number of acres. In this case, we have 2808 trees and 36 acres:
Average number of trees per acre = Total number of trees / Total number of acres
Average number of trees per acre = 2808 / 36
Average number of trees per acre = 78
Therefore, there are approximately 78 trees on each acre of land when the trees are spread out evenly.
This means that if the land is divided into 36 equal sections, each section will have approximately 78 trees.
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Which data set is represented by the modified box plot?
Box and whisker plot on a number line from 90 to 160 in increments of 5. The whisker ranges from 100 to 126. The box ranges from 109 to 124 with the vertical bar inside the box at 117. One dot mark above one hundred and fifty-one.
Responses
116, 118, 114, 117, 151, 126, 122, 114, 124
116, 118, 104, 117, 151, 136, 142, 104, 124
106, 108, 104, 107, 151, 126, 132, 104, 124
100, 104, 114, 116, 117, 118, 122, 126, 151
Answer:
The data set represented by the modified box plot is:
116, 118, 114, 117, 151, 126, 122, 114, 124
Step-by-step explanation:
Find the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%. P = [?]% Round to the nearest tenth of a percent. Enter
the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55% is 0.29 = 29%
A binomial experiment is an experiment that has the following four properties:
The experiment consists of n repeated trials
Each trial has only two possible outcomes
The probability of success, denoted p, is the same for each trial
Each trial is independent
the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%
We know that the binomial distribution
[tex]^nc_rp^rq^{n-r[/tex]
Where n is the number of trails
p is the probability of success in each trial
q =1-p which is the probability of failure
Here r=4
n=7
p= 55 % =0.55
then by the formula
[tex]p(4)=^7c_4(o.55)^4(0.45)^3\\\\p(4)=35*0.091*0.091\\p(4)=0.29[/tex]
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Select the correct answer.
Mary owns a wholesale flower company that has grown steadily over the past three years. Writing employee paychecks by hand every two weeks
has become a challenge, and Mary's accountant has advised her to switch to direct deposit. Which functionality of her accounting software will she
need to use to do that?
O A. data mining
OB.
OC.
O D.
electronic funds transfer
customizable reports
general ledger entries
Answer:
electronic funds transfer
10 times as many as 6 hundreds equals what
Answer: 6000
Step-by-step explanation:
10 times 600
10 x 600
6000
Gildong decided to save 20,000 won a week. He saved for 15 weeks and then for 15 weeks he spent 20,000 won a week on eating Maratang. Write an absolute-value function to represent the amount of money Gildong had in savings.
Answer:
Step-by-step explanation:
Let's start by defining a coordinate system where the horizontal axis represents the number of weeks that Gildong has been saving (and spending), and the vertical axis represents the amount of money he has in savings.
During the first 15 weeks, Gildong saved 20,000 won per week, so his savings increased linearly from week 0 to week 15. We can represent this with the equation:
y = 20,000x
where x is the number of weeks since the beginning (x = 0 corresponds to the start of the saving period) and y is the amount of money Gildong has saved after x weeks.
During the next 15 weeks, Gildong spent 20,000 won per week on eating Maratang, so his savings decreased linearly from week 15 to week 30. We can represent this with the equation:
y = -20,000(x - 15) + 20,000(15)
where x is the number of weeks since the beginning (x = 15 corresponds to the start of the spending period) and y is the amount of money Gildong has saved after x weeks.
To represent the total amount of money Gildong had in savings at any given time, we can combine the two equations above using an absolute value:
y = |20,000x| - 20,000(x - 15)
where x is the number of weeks since the beginning, and y is the amount of money Gildong has in savings after x weeks.
This function represents the absolute value of the difference between the amount of money Gildong has saved and the amount of money he has spent on Maratang, taking into account the fact that his savings increased linearly during the first 15 weeks and decreased linearly during the next 15 weeks.
The sum of 1/2 and 2/3 is ______1. a. equal to b. less than c. greater than
Answer:
c. greater than
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{6}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{7}{6}[/tex] ≈ 1.167
1.167 > 1
So, the answer is c. greater than
I need help with this please
Answer: 384 cm cubed
Step-by-step explanation: The first thing you will do is 48 square centimeters times 8 cm. Since 48 is squared you have that 2 right above it. Your 8 technically has a 1 above it. So add the 2 and the 1, and you will get cubed. (AKA 3)
Solve for b.
8b−1=24b+4
ANSWER: -7
i just took the test
Answer:
[tex]b = - 0.3125[/tex]
Step-by-step explanation:
[tex]8b - 1 = 24b + 4[/tex]
Collect like-terms (also, when moving a term to the other side, its sign changes to the opposite of the previous one):
[tex]8b - 24b = 4 + 1[/tex]
[tex] - 16b = 5[/tex]
Divide both sides of the equation by (-16) to make b the subject:
[tex]b = - 0.3125[/tex]
- A circle is divided into 5 equal parts.
What is the measure of the angle that
turns through 2 parts?
The measure of the angle in the given circle which pass through 2 parts out of 5 is 144°.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The radius of a circle is the separation between any point on the circle and its center.
The radius must typically be a positive integer. A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.
In common usage, the word "circular" can be used to describe both the figure's edge and its entirety, including its interior.
So, we know that:
The angle of the center of the circle is 360°.
We also know that in the given situation, the circle is divided into 5 parts.
Then,
= 360/5
= 72
Now,
The measure of 2 parts:
72 + 72 = 144
Therefore, the measure of the angle in the given circle which pass through 2 parts out of 5 is 144°.
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Eric had a box of 24 candy bars that he planned to sell for 63 cents each. Unfortunately, his sister ate 7 of his candy bars before he started selling them. In order to bring in the same amount of money as he would have if his sister had not eaten any of the candy bars, what price (in cents) should he charge for each of the remaining candy bars?
The price (in cents) should he charge for each of the remaining candy bars 49
First, we would want to calculate how much the box would sell for before the sister ate some.
We would get 24*63(in cents) and we can further get 1512 cents before the sister ate the candy bars.
The sister ate 7 candy bars leaving us with 31 candy bars. To deduct the price for each candy bar, it would be a situation like the following:
$6 for 3 boxes of 500 cookies (i know that's cheap)
6/3...
$2 per box.
Using our situation we get 1512 cents for 31 candy bars.
1512÷31
=48.77
That does seem unrealistic, so we round to the nearest whole number and we get...
49 cents
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Create a rational inequality for which −1 < ≤ 2 is the solution.
Thus, the rational inequality formed for the given solution is found as:
x - 3 ≤ 0
Explain about the rational inequality:A rational inequality is a specific type of statistical inequality statement that typically has a ratio of two polynomials (commonly known as a "rational expression") on the left side and a zero on the right.
A rational expression seems to be a ratio of two polynomials, and a rational inequality is just an inequality that contains a rational expression. To put it another way, a rational expression has the form R(x) / Q(x), when R(x) and Q(x) represent polynomials and Q(x) is not zero. A rational expression appears on the left side of a rational inequality's general form, and a zero appears on the right.Given expression is:
−1 + x ≤ 2
Subtract both side by 2
−1 + x - 2 ≤ 2 - 2
x - 3 ≤ 0
Thus, the rational inequality formed for the given solution is found as:
x - 3 ≤ 0
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Correct question:
Create a rational inequality for which −1 + x ≤ 2 is the solution.
[tex]A= \left[\begin{array}{ccc}2&-1&3\\1&-3&-1\end{array}\right] B= \left[\begin{array}{ccc}-2&1&3\\-1&-2&-2\end{array}\right] find 3A-2B[/tex]
According the given question 3A - 2B matrix is equal to:
[tex]\left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]
What are Matrix ?A matrix is a rectangular array οf numerical values, symbοls, οr verbal expressiοns that are οrganised in rοws and cοlumns. In many disciplines, such as cοmputer science, engineering, physics, and mathematics, it is used tο represent data.
Calculating 3A and 2B first, then deducting 2B frοm 3A, is required tο find 3A - 2B.
Calculating 3A:
[tex]3A = 3 * \left[\begin{array}{ccc}2 & -1 & 3\1 & 1 & -3 & -1\end{array}\right]= \left[\begin{array}{ccc}6 & -3 & 9\3 & 3 & -9 & -3\end{array}\right][/tex]
Calculating 2B:
[tex]2B = 2 * \left[\begin{array}{ccc}-2 & 1 & 3 & -1 & -2 & -2 \end{array}\right]= \left[\begin{array}{ccc}-4 & 2 & 6 & -2 & -4 & -4\end{array}\right][/tex]
Nοw, we can find 3A - 2B by subtracting 2B frοm 3A:
[tex]3A - 2B = \left[\begin{array}{ccc}6 & -3 & 9 &3& -9 & -3\end{array}\right] - \left[\begin{array}{ccc}-4 & 2 & 6 &-2 & -4 & -4\end{array}\right]= \left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]
Therefore, 3A - 2B is equal to:
[tex]\left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]
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The volume of a rectangular prism is 6,142.5 cm3. If the height is 16.25 cm and the length is 28 cm, what is the value of the width?
13.125 cm
13.25 cm
13.5 cm
13.75 cm
Answer:
A. 13.125cm
Step-by-step explanation:
To solve for the width of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
volume = length x width x height
We are given that the volume is 6,142.5 cm^3, the height is 16.25 cm, and the length is 28 cm. Let's substitute these values into the formula and solve for the width:
6,142.5 cm^3 = 28 cm x width x 16.25 cm
Dividing both sides by (28 cm x 16.25 cm), we get:
width = 6,142.5 cm^3 / (28 cm x 16.25 cm)
= 13.125 cm
Therefore, the width of the rectangular prism is 13.125 cm. So, the correct answer is A) 13.125 cm.
Bob runs an auto repair shop. Over 6 months, he finds that out of 700 cars that are brought in, 144 require more than one day to repair. Based on this information, what is the probability that the next car brought to his shop can be fixed in a day? Responses 20.6% 20.6% 55.6% 55.6% 79.4% 79.4% 82.9%
The answer to the given question about probability of Bob's shop is option 7) 79.4%.
Out of 700 cars, 144 require more than one day to repair. So the number of cars that can be fixed in one day is
700 - 144 = 556.
The probability that the next car brought to the shop can be fixed in a day is the ratio of the number of cars that can be fixed in a day to the total number of cars:
probability = 556/700
= 0.794 or 79.4%
Therefore, the correct answer is option 7) 79.4%.
Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to quantify the likelihood of an event occurring, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability theory is widely used in various fields, such as statistics, physics, economics, and finance, to make predictions and decisions based on uncertain or incomplete information. It provides a powerful tool for analyzing and understanding uncertainty, risk, and randomness in real-world situations, and it has numerous practical applications in diverse areas of research and industry
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Determine if (0,3)
is a solution to y>2
. If so, graph the inequality.
An image of a coordinate plane shows a dashed line with a positive slope. The line crosses the y-axis at (0, 2) and passes through the point (negative 2, negative 2). The area above and to the left of the line is shaded.
An image of a coordinate plane shows a dashed vertical line. The line crosses the x-axis at (2, 0) and passes through the points (2, negative 2) and (2, 2). The area to the right of the line is shaded.
is not a solution.
An image of a coordinate plane shows a dashed horizontal line. The line crosses the y-axis at (0, 2) and passes through the points (2, 2) and (negative 2, 2). The area above the line is shaded.
Answer:
To determine if (0,3) is a solution to y>2, we need to check if y is greater than 2 when x=0 and y=3. Since 3 is greater than 2, the point (0,3) satisfies the inequality y>2.
To graph the inequality y>2, we need to shade the region above the horizontal line y=2. The line y=2 is a solid line since it includes the points where y=2, but the region above the line is shaded with a dashed line since it does not include the points where y=2.
Here is a description of the graph:
Draw a horizontal line passing through the point (0,2).
Shade the region above the line with a dashed line.
The graph visually represents all the points that satisfy the inequality y>2. Since the point (0,3) is above the line, it is part of the shaded region and satisfies the inequality.
In 2002 you could buy a Broadway show ticket for $40. Use the CPI chart below to find the cost of Broadway show in 2014 based on inflation
The cost of a Broadway show ticket in 2014, based on inflation, would be approximately $52.59.
What is inflation?Inflatiοn, in general, is the prοcess thrοugh which mοney lοses value οver time. As a result, 100 dοllars suddenly have less purchasing pοwer than they had previοusly. This indicates that the awards will increase tο maintain a steady purchasing pοwer.
Tο find the cοst οf a Brοadway shοw ticket in 2014, we need tο adjust the price frοm 2002 using the Cοnsumer Price Index (CPI) fοr each year. The CPI measures the changes in the cοst οf gοοds and services οver time due tο inflatiοn.
Here is the CPI data for the relevant years:
2002 CPI: 179.9
2014 CPI: 236.7
To adjust the 2002 price of $40 to its equivalent in 2014 dollars, we can use the following formula:
Adjusted Price in 2014 Dollars = Price in 2002 Dollars x (CPI in 2014 / CPI in 2002)
Plugging in the numbers, we get:
Adjusted Price in 2014 Dollars = $40 x (236.7 / 179.9) = $52.59
Therefore, the cost of a Broadway show ticket in 2014, based on inflation, would be approximately $52.59.
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Complete question:
In 2002 you could buy a Broadway show ticket for $40. Use the CPI chart below to find the cost of Broadway show in 2014 based on inflation.
4(3x=2)-9 in written form
he expression 4(3x=2)-9 can be written as 12x - 9. I
(5, 5, 6, 9, 9, 11, 13}
This set has two_____
-medians
-means
-modes
Answer:
modes
Step-by-step explanation:
The only one of the three (median, mode, mean) that there can be more than one for a set is the mode, and in fact it has two modes: 5 and 9.
Answer: modes
The center of the circle is shown.
9
What is the exact area of the circle?
324n
18n
9r
81n
Answer:
The area is (9^2)π = 81π.
Handy Dandy Grocery is having a sale this week. If you buy a 5−pound bag of apples for the regular price, you can get another bag for $1.49. If you buy a 5−pound bag of oranges for the regular price, you can get another bag for $2.49.
Handy Dandy Grocery
Regular price
5−pound bag of apples 2.89
5−pound bag of oranges 3.89
Part 1 out of 2
Enter an addition equation to find the discount for apples. Use a for apples.
An equation is
Enter an addition equation to find the discount for oranges. Use r for oranges.
An equation is
the equation to find the discount for oranges is: [tex]r = 3.89 + 2.49[/tex] [tex]r= 6.38[/tex]
What is the equation?
The discount for apples is $ [tex]2.89[/tex] + $ [tex]1.49[/tex], since you can get another bag for $1.49 when you buy a 5-pound bag of apples at the regular price.
So the equation to find the discount for apples is:
[tex]a = 2.89 + 1.49[/tex]
[tex]a = 4.38[/tex]
Similarly, the discount for oranges is $ [tex]3.89[/tex] + $ [tex]2.49[/tex], since you can get another bag for $2.49 when you buy a 5-pound bag of oranges at the regular price.
Therefore, the equation to find the discount for oranges is: [tex]r = 3.89 + 2.49[/tex]
[tex]r = 6.38[/tex]
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pls help i have no idea what it could be someone needss to help meeeeee.
Answer:
Step-by-step explanation:
Calculate the area of the shapes below
the area of the shape shown in the diagram is 91 m².
What is area?Area is the space bounded by a plane shape.
To calculate the area of the shape, we use the formula below
Note: Area of the shape = Area of the rectangle+ Area of the triangle
Formula:
A = LW+Lh/2.......................... EquationWhere:
A = Area of the shapeL = Length of the rectangle = Base of the triangleh = Height of the triangleW = Width of the rectangleFrom the question,
Given:
L = 13 mW = 9-4 = 5 mh = 4 mSubstitute these values into equation 1
A = (13×5)+(13×4/2)A = 65+26A = 91 m²Hence, the area is 91 m².
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What is the probability of getting a even number from the bag
Answer: The actual answer is 7/12, but the closest match is (A) 1/2.
A rectangle has side lengths (4x-5) and (3x+6). Write a linear expression in simplest form to represent the perimeter. Find perimeter if the value of x=12
Answer:
P = 14x + 2
if x=12, P = 170
Step-by-step explanation:
The perimeter is the distance around the outside of the shape.
The rectangle has four sides. Two long sides and two short sides.
We add up all four sides.
P = 4x-5+3x+6+4x-5+3x+6
combine like terms.
P = 14x + 2 this is the equation in simplest form.
If x = 12, we can calculate the perimeter.
P = 14(12) + 2
P = 168 + 2
P = 170
The perimeter would be 170.