Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3

Answers

Answer 1

Okay, here are the steps to solve this:

1) cos a = -5/9. This means cos a is negative, so the angle a lies in the 2nd or 3rd quadrant. Since the question specifies that a is in quadrant 3, we can take a as lying in the 3rd quadrant.

2) In the 3rd quadrant, cos a is negative and sin a is positive.

3) We know: cos a = adj/hyp. Here, adj = -5 and hyp = 9. So in a right-angled triangle with hypotenuse 9, the adjacent side is 5.

4) Use the Pythagorean theorem: a^2 + b^2 = c^2. Here, 5^2 + b^2 = 9^2.

So b^2 = 64 and b = 8.

5) Now sin a = opp/adj = b/hyp = 8/9.

6) Therefore, the exact value of sin a is 8/9.

Does this make sense? Let me know if you have any other questions!


Related Questions

morbidity surveys of the general population: group of answer choices include the health and nutrition examination survey. all of these are correct. collect data on the health status of a population group. typically use a scientifically designed representative sample.

Answers

In morbidity surveys of the general population, they collect data on the health status of a population group which includes the health and nutrition examination survey, that are typically uses a scientifically designed representative sample. So the answer is all of these are correct or option B.

What are Morbidity Surveys?

Morbidity surveys are research investigations designed to determine the frequency and incidence of diseases, illnesses, and injuries in a certain community. They are intended to collect data on people's health status within a certain community or population, as well as to determine the distribution and drivers of health issues in that group.

Morbidity surveys often employ structured questionnaires and physical examinations to gather data on the occurrence of certain health disorders, as well as risk factors and other variables that may be related to the development of these illnesses.

Morbidity survey data may be used to design public health policies and programs, distribute resources, and track changes in health status over time.

The answer is (b) All of these are correct.

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Final answer:

Health surveys provide a structured way to collect and interpret data about the health status of a population, helping researchers and policy makers understand health trends and conditions. One such survey is the Health and Nutrition Examination Survey.

Explanation:

Surveys, such as the Health and Nutrition Examination Survey, provide an important method for collecting data on the health status of a population group. In public health and epidemiology, these surveys typically use a scientifically designed representative sample to provide accurate data. To conduct this survey, researchers ask the same questions to all respondents, interpret the answers, and tabulate the results. A simple example could be comparing the eating habits of students eating off campus versus those in dining facilities. With the data gathered, we can identify health trends, understand the distribution of certain health conditions, and then make informed policy or healthcare decisions based on these insights.

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The market price of a dress was 80 000 at the botique

Answers

The dress was sold at a profit of 20%.

Profit percent is the percentage of profit earned on a product or investment, calculated as the profit divided by the cost price multiplied by 100%.

The profit or loss percent can be calculated using the following formula:

Profit/Loss percent = (Profit or Loss / Cost Price) x 100%

Here, the Cost Price (CP) of the dress is Rs. 2500, and the Selling Price (SP) is Rs. 3000.

Profit = SP - CP = Rs. 3000 - Rs. 2500 = Rs. 500

Therefore, the profit percent is

Profit percent = (Profit / CP) x 100%

Substitute the values in the equation

= (500 / 2500) x 100%

= 20%

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I have solved the question in general, as the given question is incomplete.

The complete question is:

A dress was bought for Rs. 2500 and sold for Rs. 3000. Find the profit or loss percent

Juliet conducted a survey to find the favorite type of book of the students at her school. She asked 20 students from her class what their favorite type of book is. Juliet concludes that short stories is the favorite type of book of the students in her school because 80% of the students in her class like short stories.

Use at least two sentences to explain why Juliet's sample may not be valid. Make sure to use facts to support your answer

Answers

Answer: See Bellow

Step-by-step explanation:

Juliet's sample may not be valid for several reasons. Firstly, her sample size of 20 students may not represent the entire student population at her school. If her class is not a random sample of the whole student population, her results may not generalize to the entire school. Additionally, the model may suffer from selection bias if she only surveyed students she knew liked short stories or if she conducted the survey in a way that only sure students responded. Therefore, it is essential to have a large and representative sample to ensure the validity of the conclusions drawn from the survey results.

Help please? I just need an answer. A clear explanation earns brainliest. this is a repost since i posted the wrong photo last time.

Answers

Answer: x^2+2x-7/x-1

hat kind of cups for measuring are sometimes made from glass or something transparent so the markings on the side with different measurements are visible? a tare measuring cups b maillard measuring cups c standard measuring cups d graduated measuring cups

Answers

The graduated measuring cups are made from something glass or something transparent to markings on the side with different measurements are visible. Option (d) is the correct answer.

The kind of cups for measuring that are sometimes made from glass or something transparent so the markings on the side with different measurements are visible are called graduated measuring cups. These cups are designed to make measuring precise amounts of liquid or dry ingredients easy, and the transparent material allows you to see the measurement markings clearly. Graduated measuring cups are commonly used in baking and cooking, as well as in scientific research and other applications where accurate measurements are essential.

Therefore, Graduated measuring cups is the answer.

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There are only Ured counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3
7
The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6
13
Find the number of red counters and the number of green counters that were in the bag originally

Answers

Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

since we are comparing the start and end weights of the ferrets, this would be [ select ] data. b. what parameter are we trying to estimate?

Answers

This data would be considered "paired" data.

The population of ferrets from which our sample was drawn, represented as μd, where μd = μend - μstart, and μ represents the population mean.

What type of data would comparing ?

       We are dealing with "paired" data since we are comparing the weights of the same ferrets at two different points in time.

how is this parameter represented symbolically?

      The parameter we are trying to estimate is the mean difference in weight between the start and end of the study for the population of ferrets from which our sample was drawn.

This mean difference in weight can be represented as μd, where μd = μend - μstart, and μ represents the population mean. To estimate this parameter, we would need to calculate the difference in weight for each ferret and then take the average of these differences. This estimate would then provide us with an understanding of how much, on average, the ferrets in the population have gained or lost weight over the course of the study.  

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A traffic expert wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. She assumes that each car is 20 feet long, travels at speed N, and follows the car in front of it at a safe distance for that speed. She finds that the number
of cars that can pass a given spot per minute is modeled by the function

N = 81s/20+20(s/24)^2

Answers

Answer: The given function is:

N = 81s / (20 + 20(s/24)^2)

where:

N = number of cars that can pass a given spot per minute

s = speed of the cars in miles per hour (mph)

To find the maximum number of cars that can safely travel on the road at a given speed, we need to find the value of s that maximizes the function N.

Taking the derivative of N with respect to s:

dN/ds = (81 / (20 + 20(s/24)^2)) * (20/24 - (2s/24^2) * (s/24))

Setting dN/ds to zero to find the critical point:

0 = (81 / (20 + 20(s/24)^2)) * (20/24 - (2s/24^2) * (s/24))

Simplifying and solving for s:

20/24 = (2s/24^2) * (s/24)

20 * 24 = 2s * s

s^2 = (20 * 24) / 2

s^2 = 240

s = sqrt(240)

s ≈ 15.4919 mph

Therefore, the maximum number of cars that can safely travel on the road at a speed of 15.4919 mph is:

N = 81s / (20 + 20(s/24)^2) = 81(15.4919) / (20 + 20((15.4919)/24)^2) ≈ 180.19 cars per minute.

Step-by-step explanation:

A recipe calls for 3 teaspoons of orange juice. A can of orange juice is 11 FL oz. How many teaspoons of juice are in the can?

Answers

So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.

what is unitary method ?

A mathematical method called the unitary method is used to address proportionality-related issues. It is a technique that entails determining the value of a single unit prior to applying that value to determine the value of any quantity of units. Problems involving ratios et proportions are frequently solved using the unitary technique. The unitary approach can be used to determine the price of any quantity of apples, for instance, if 5 vegetables cost $2. We can build up a proportion to determine how much 10 apples would cost: 5 apples x $2 Equals 10 apples x. where 10 apples cost x dollars.

given

We can start by applying the conversion rule that states that 6 teaspoons (tsp) of liquid equal 1 fluid ounce (FL oz). The following is how we can convert 11 FL oz to teaspoons:

6 teaspoons per FL oz times 11 FL oz equals 66 teaspoons.

Thus, an 11 FL oz can of orange juice has 66 teaspoons of orange juice.

We can also figure out how many cans of orange juice are required for the recipe as it calls for 3 tablespoons of orange juice.

[tex]0.5 FL oz = 3 tsp * 6 tsp/FL oz[/tex]

So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.

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according to the centers for disease control and prevention, 60% of all american adults ages 18 to 24 currently drink alcohol. is the proportion of california college students who currently drink alcohol different from the proportion nationwide? a survey of 450 california college students indicates that 66% curre quizlert

Answers


the proportion of California college students who currently drink alcohol different from the proportion nationwide p0 = 0.60 (nationwide proportion from CDC)

Information provided; we can determine if the proportion of California college students who currently drink alcohol is different from the proportion nationwide by conducting a hypothesis test. Here are the steps:
The null hypothesis (H0) and alternative hypothesis (H1):
H0: The proportion of California college students who drink alcohol is the same as the nationwide proportion.

(p = 0.60).
H1: The proportion of California college students who drink alcohol is different from the nationwide proportion.

(p ≠ 0.60).
The sample proportion (p-hat), sample size (n), and the population proportion (p0):
p-hat = 0.66 (66% of the 450 California college students surveyed)
n = 450 (sample size)
p0 = 0.60 (nationwide proportion from CDC)
The test statistic (z) using the following formula:
[tex]z = (p-hat - p0) / \sqrt((p0 \times (1 - p0)) / n)[/tex]
A standard normal distribution table or calculator to find the p-value associated with the test statistic.
Compare the p-value to a predetermined significance level (α), usually set at 0.05.
- If the p-value is less than α, reject the null hypothesis (H0), suggesting that the proportion of California college students who drink alcohol is different from the nationwide proportion.
- If the p-value is greater than α, fail to reject the null hypothesis (H0), indicating that there is not enough evidence to suggest a difference between the two proportions.
Determine if the proportion of California college students who drink alcohol is significantly different from the nationwide proportion.

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Instructions: Write the equation of the line in Slope-Intercept Form given the information below.
Thanks​

Answers

Answer:

y=4x+5

Step-by-step explanation:

y=mx+b

m=4

b=5

a line segment is plotted in the coordinate plane. It has endpoints of (-3, -3) and (5, -3). The line segment is one side of a square. What is the area of the square?

Answers

The Area of square is 64 square unit.

We have the coordinates (-3, -3) and (5, -3).

Using distance formula

d = √ (5 + 3)² + (-3 + 3)²

d= √8² + 0

d= 8 units

So, the Area of square

= d x d

= 8 x 8

= 64 square unit

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what is the general formula for the bayesian credible interval? what distribution is the critical value taken from?

Answers

Answer:  p(θ|x) dθ = 1 − α.

Step-by-step explanation: the critical value is computed based on the given significance level α and the type of probability distribution of the idealized model

Can someone help me asap? It’s due tomorrow. I will give brainliest if it’s correct

Answers

The sampling method used by the principal in this scenario is stratified sampling.

What is the sampling?

Stratified sampling involves dividing the population into distinct subgroups, or strata, based on certain characteristics (in this case, grade level), and then randomly sampling from each stratum to ensure that each subgroup is represented in the sample.

By organizing the school's population by grade level and sampling from each grade level (freshman, sophomore, junior, and senior), the principal is using stratified sampling to gather data on preferred elective courses.

Therefore, This method helps ensure that the sample is representative of the entire population and can provide more accurate results compared to other sampling methods, such as convenience sampling, systematic sampling, or volunteer sampling, which may introduce biases or limitations in the sample.

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See text below



3. A principal wants to know what electives should be added to the school schedule. He organizes the school's population by grade level and then randomly samples fifty students in the freshman, sophomore, junior, and senior classes about their preferred elective course. What sampling method did the principal use?

convenience sampling

stratified sampling

systematic sampling

volunteer sampling

bianca runs a fruit store.she startied thursday with 14 pear brainlys in stock.duriiiing th eday,she sold 11 pears and goat a shipment contained 4 times as many pears as she started the day with

Answers

Answer: Bianca runs a fruit store. She started Thursday with 14 pears in stock. During the day, she sold 11 pears and got a shipment containing 4 times as many pears as she started the day with. This means that Bianca received a shipment of 14 * 4 = 56 pears. By the end of the day, Bianca had 14 - 11 + 56 = 59 pears in stock

please help, due today

The table represents a linear relationship.



x −1 0 1
y −3 1 5



Which equation represents the table?


A. y equals one fourth times x minus 2
B. y equals negative one fourth times x plus 1
C. y = −4x − 2
D. y = 4x + 1

Answers

The equation that represents the linear relationship in the table is D. y = 4x + 1.

Which equation represents the table of values?

To find the equation that represents the linear relationship in the table, we need to determine the slope and y-intercept of the line that passes through the given points.

We can use the formula for the slope of a line, which is:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Using the first two points from the table, we get:

m = (1 - (-3))/(0 - (-1)) = 4/1 = 4

So, the slope of the line is 4.

To find the y-intercept, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

Using the point (0, 1) and the slope m = 4, we get:

y - 1 = 4(x - 0)

y = 4x + 1

So, the equation is D. y = 4x + 1.

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7(x + 2) = 7x + 14 how many solutions are there

Answers

When we simplify the left-hand side of the equation 7(x + 2), we get:

7(x + 2) = 7x + 14

Expanding the brackets, we get:

7x + 14 = 7x + 14

Notice that the simplified left-hand side and the right-hand side are exactly the same. This means that the equation is an identity and it is true for all values of x.

So, there are infinitely many solutions to the equation 7(x + 2) = 7x + 14.
Answer: infinitely many solutions.

Explanation:

Let's solve the equation:

7(x + 2) = 7x + 14

Distribute the 7 on the left side:

7x + 14 = 7x + 14

Now, subtract 7x from both sides:

14 = 14

Since this equation is true for any value of x, there are infinitely many solutions.

a work system has five continuous stations that have process times of 5, 8, 4, 7, and 8 min/unit respectively. what is the process time of the system?

Answers

The process time of the system is 32 min/unit.

a local politician is concerned that a program for the homeless in the city is discriminating against blacks and other minorities. the following data were taken from a random sample of black and white homeless people. race black white received services yes 6 7 13 no 4 9 13 10 16 26 a. is there a statistically significant relationship between race and whether the person received services from the program? b. compute column and row percentages for the table to determine the pattern of the relationship. which group was more likely to receive services in the sample? interpret both the column and row percentages that you have obtained.

Answers

(a) There is no statistically significant relationship between race and receiving services from the program.

(b) Black homeless people were more likely to receive services (60%) than white homeless people (43.75%).

How to find the relationship between race and receiving services?

a. To test whether there is a statistically significant relationship between race and whether the person received services from the program, we can use a chi-squared test of independence.

The null hypothesis is that there is no relationship between race and receiving services, and the alternative hypothesis is that there is a relationship.

Using a chi-squared calculator, we obtain a chi-squared statistic of 0.267 and a p-value of 0.605. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is no statistically significant relationship between race and receiving services from the program.

How to find more likely to receive services?

b. To compute column and row percentages, we can first calculate the total number of black and white homeless people who received services and who did not receive services:

Black homeless people who received services: 6/10 = 60%Black homeless people who did not receive services: 4/10 = 40%White homeless people who received services: 7/16 = 43.75%White homeless people who did not receive services: 9/16 = 56.25%

We can also calculate the percentage of all homeless people who received services or did not receive services, by adding up the numbers in each column:

Percentage of homeless people who received services: 13/26 = 50%Percentage of homeless people who did not receive services: 13/26 = 50%

In the sample, black homeless people were more likely to receive services (60%) than white homeless people (43.75%).

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Consider the two triangles shown below. Two triangles. The first triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. The second triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. Two triangles. The first triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. The second triangle has a side length of five units, a one hundred seventeen degree angle, a side of seven units. Note: The triangles are not drawn to scale. Are the two triangles congruent

Answers

In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.

Congruent?

Congruent is a mathematical term used to describe two figures or shapes that have the same size and shape. In other words, two figures are congruent if they have exactly the same dimensions and the same angles. When two figures are congruent, they can be superimposed on each other without any overlap or gap between them. Congruent figures are often denoted by the symbol ≅. For example, if two triangles have the same size and shape, we can write them as ∆ABC ≅ ∆DEF, which means that triangle ABC is congruent to triangle DEF. Congruent figures play an important role in geometry and other branches of mathematics.

Yes, the two triangles are congruent.

In Euclidean geometry, if two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles are congruent. This is known as the angle-side-angle (ASA) congruence criterion.

In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.

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in the anova test, degrees of freedom within (dfw) are equal to ______ and degrees of freedom between (dfb) are equal to (k - 1).

Answers

In the ANOVA test, degrees of freedom within (dfw) is equal to the total number of observations minus the total number of groups if we have N total observations and k groups, then dfw = N - k.

The ANOVA (Analysis of Variance) test is a statistical method used to compare the means of three or more groups.

Degrees of freedom within (dfw) are determined by the total number of observations minus the total number of groups, and degrees of freedom between (dfb) is simply the number of groups minus one.

On the other hand, degrees of freedom between (dfb) is equal to the number of groups minus 1, which is simply k - 1.

So, the final answer is:

dfw = N - k

dfb = k - 1

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the pairs of figures that have the same volume. 3-D shape of a cone is represented. The cone has a radius of 4 units and a height of 12 units. 3-D shape of a rectangular prism is represented. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units. 3-D shape of a rectangular prism is represented. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units. 3-D shape of a cylinder is represented. The cylinder has a radius of 3 units and a height of 8 units. 3-D shape of a cone is represented. The cone has a radius of 8 units and a height of 9 units. 3-D shape of a rectangular prism is represented. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units. arrowBoth 3-D shape of a cylinder is represented. The cylinder has a radius of 4 units and a height of 12 units. arrowBoth 3-D shape of a cone is represented. The cone has a radius of 6 units and a height of 6 units. arrowBoth Reset Next © 2023 Edmentum. All rights reserved.

Answers

The pair of figures having same volume are:

a. The cylinder has a radius of 3 units and a height of 8 units ; The cone has a radius of 6 units and a height of 6 units.

b. The cone has a radius of 8 units and a height of 9 units ; The cylinder has a radius of 4 units and a height of 12 units.

c. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units ; The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

What is volume of a figure?

Volume is a unit of measurement for three-dimensional space. It is usually stated quantitatively in terms of a number of imperial or US-standard units as well as SI-derived units.

i. The cone has a radius of 4 units and a height of 12 units.

⇒ Volume = π[tex]r^{2} \frac{h}{3}[/tex]

⇒ Volume = π[tex]4^{2} \frac{12}{3}[/tex]

⇒ Volume = 64 π

⇒ Volume = 201 cubic units

ii. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 18 * 6 * 6

⇒ Volume = 648 cubic units

iii. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 16 * 6 * 6

Volume = 576 cubic units

iv. The cylinder has a radius of 3 units and a height of 8 units.

⇒ Volume = π[tex]r^{2}[/tex]h

⇒ Volume = π[tex]3^{2}[/tex] * 8

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

v. The cone has a radius of 8 units and a height of 9 units.

⇒ Volume = π[tex]r^{2} \frac{h}{3}[/tex]

⇒ Volume = π[tex]8^{2} \frac{9}{3}[/tex]

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

vi. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

⇒ Volume = length * width * height

⇒ Volume = 8 * 8 * 9

⇒ Volume = 576 cubic units

vii. The cylinder has a radius of 4 units and a height of 12 units.

⇒ Volume = π[tex]r^{2}[/tex]h

⇒ Volume = π[tex]4^{2}[/tex] * 12

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

viii. The cone has a radius of 6 units and a height of 6 units.

⇒ Volume = π[tex]r^{2} \frac{h}{3}[/tex]

⇒ Volume = π[tex]6^{2} \frac{6}{3}[/tex]

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

Hence, three pairs have the same volume.

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The missing figures have been attached below.

A rectangle with dimensions 6 cm and w cm is partitioned into two smaller rectangles.

Explain why each of these expressions represents the area, in cm2, of the shaded region.

Answers

The  Area of shaded region is  6 (w- 4).

We have,

length= w unit

shorter length = 4 unit

width = 6 unit

So, Area of larger rectangle

= l w

= 6 x  w

and, Area of smaller rectangle

= l w

=  6 x 4

= 24 cm²

So, the Area of shaded region

= 6w - 24

= 6 (w- 4)

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A rectangular prism is shown in the image.

A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.

What is the volume of the prism?

Answers

Therefore, the volume of the rectangular prism is 87.5 cubic yards.

What is prism?

A prism is a transparent object, usually made of glass or plastic, that refracts or bends light as it passes through it. It has at least two flat surfaces, called faces, that are usually parallel and rectangular in shape, and two non-parallel faces, called bases, which are usually triangular in shape. When light enters a prism, it is refracted, or bent, as it passes through the prism and is separated into its component colors, creating a rainbow effect. Prisms are often used in optics and science experiments to study the properties of light, such as its wavelength and polarization. They are also commonly used in optical instruments such as binoculars, telescopes, and cameras to help focus and direct light.

The volume V of a rectangular prism is given by the formula:

V = length x width x height

In this case, the length is 5 yards, the width is also 5 yards, and the height is 3- and one-half yard.

To calculate the volume, we can plug this value into the formula:

V = 5 yards x 5 yards x 3.5 yards

Simplifying this expression, we get:

V = 87.5 cubic yards

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Answer:

The volume of a rectangular prism is the product of its length, width, and height. In this case, the length is 5 yards, the width is 5 yards, and the height is 3.5 yards. Therefore, the volume of the prism is 5 * 5 * 3.5 = 87.5 cubic yards.

Here is the calculation:

Volume = length * width * height

= 5 yards * 5 yards * 3.5 yards

= 87.5 cubic yards

Step-by-step explanation:

Find if the table is linear or quadratic or neither

Answers

For table 14, the table is neither.

Option C is correct.

For table 15, the table is neither.

Option C is correct.

How do we calculate?

Table 14:

The difference between 22 and 48 is -26

The difference between 39 and 22 is 17

The difference between 40 and 39 is 1

The difference between 42 and 40 is 2

The difference between 42 and 42 is 0

Because  the differences are not constant, the table is neither linear nor quadratic.

For table 15, we check if the difference in y-values is constant:

The difference between 4 and 1 is 3

The difference between 1 and 1 is 0

The difference between 0 and 1 is -1

The difference between 1 and 4 is 3

The difference between 4 and 9 is 5

The difference between 9 and 16 is 7

Because  the differences between y-values are not constant, the table is neither linear nor quadratic.

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Find the base area (B), lateral area (L) and surface area (S) of the solid. Round to the
nearest tenth, if necessary.
10.4 cm
B = 96
L =
12 cm
S=
12 cm
12 cm
8 cm
cm²
cm²
cm²

Answers

The base, lateral area and surface area is B = 96 cm², L = 499.2 cm²,S = 691.2 cm²

What is Lateral Area ?

The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.

To find the lateral area (L) of this solid, we need to calculate the area of the four rectangles that make up the sides of the solid. Since each rectangle has a height of 10.4 cm and a width of 12 cm, the area of one rectangle is:

A = 10.4 cm * 12 cm = 124.8 cm²

Since there are four rectangles, the total lateral area is:

L = 4 * A = 4 * 124.8 cm² = 499.2 cm²

To find the surface area (S) of the solid, we need to add the lateral area to the area of the two circular bases. The base area is given as 96 cm², so the area of both bases is:

A = 2 * 96 cm² = 192 cm²

Therefore, the total surface area is:

S = L + A = 499.2 cm² + 192 cm² = 691.2 cm²

Rounding to the nearest tenth, we have:

B = 96 cm²

L = 499.2 cm²

S = 691.2 cm²

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Two bank accounts open with deposits of $1,810 and annual interest rates of 2.5%. Bank A uses simple interest and Bank B uses interest compounded monthly How much more in interest does the account at Bank B earn in 5 years?​

Answers

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank A} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1810)(0.025)(5) \implies I = 226.25 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank B} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]A = 1810\left(1+\frac{0.025}{12}\right)^{12\cdot 5} \implies A \approx 2050.73~\hfill \underset{ interest }{\stackrel{2050.73~~ - ~~1810 }{\approx 240.73}} \\\\[-0.35em] ~\dotfill\\\\ 240.73~~ - ~~226.25 ~~ \approx ~~ \text{\LARGE 14.48}[/tex]

You solved this problem in another question: A video rental store keeps a list of their top 15 movie rentals each week. This week the is includes 5 action,

4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to

show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie? EXPLAIN how the probability would

change if two more comedy movies were added to the list in place of the 2 mystery movies.

Answers

The probability of the store manager selecting 2 comedies and 1 action movie out of the list of 15 movies is 0.066

The probability of the store manager selecting 2 comedies and 1 action movie out of the new list of 15 movies is 0.165

Using this formula, we can find the total number of ways in which the manager can select any 3 movies from the list of 15, which is:

¹⁵C₃ = 455

Next, we need to determine the number of ways in which the manager can select 2 comedies and 1 action movie out of the list of 15 movies. To do this, we first need to determine the total number of comedies and action movies in the list, which is 4 and 5, respectively.

⁴C₂ x ⁵C₁ = 30

Therefore, the probability of the store manager selecting 2 comedies and 1 action movie out of the list of 15 movies is:

30/455 = 0.066

Now, if two more comedy movies were added to the list in place of the 2 mystery movies, the total number of comedies in the list would increase from 4 to 6, while the total number of action movies would remain the same at 5.

Using the same formula as before, the new total number of ways in which the manager can select any 3 movies from the list of 15 movies would still be 455.

The number of ways in which the manager can select 2 comedies and 1 action movie from the new list of movies can be found using the same product rule of probability as before. We can select 2 comedies from 6 in 6C2 ways, and 1 action movie from 5 in 5C1 ways. The new total number of ways in which 2 comedies and 1 action movie can be selected is:

⁶C₂ x ⁵C₁ = 75

Therefore, the probability of the store manager selecting 2 comedies and 1 action movie out of the new list of 15 movies is:

75/455 = 0.165

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The lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes. Write an expression that shows how many sweatshirts were not adult sizes.

Answers

The expression for the number of sweatshirts that were not adult sizes would be: s - 19.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions, without an equals sign. It can be a single term, or a combination of terms separated by operators, such as addition, subtraction, multiplication, division, and exponentiation

Given : total number of team booster sweatshirts = s

            No. of team booster sweatshirts of adult size = 19

So,

No. of team booster sweatshirts that were not adult sizes :

= total number of team booster sweatshirts -   No. of team booster sweatshirts of adult size

= s - 19.

Hence, s - 19 expression shows how many sweatshirts were not adult sizes.

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for a certain type of hay fever, medicine h has a 30% probability of working. in which distributions does the variable x have a binomial distribution? select each correct answer.

Answers

The distribution in which variable x has binomial distribution are as follow,

Option A) When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

Option D) When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution .

Because there are two independent trials two patients.

With a constant probability of success 30%.

And the outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

This variable X does not follow a binomial distribution.

Because the probability of success is not constant it's the complement of 30%, which is 70%.

Also, the outcome of one trial affects the outcome of the other trials.

As there are only six patients .

Number of patients for whom medicine does not work depends on number of patients for whom it worked.

When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution.

Because there are six independent trials six patients with a constant probability of success (30%) .

The outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with two patients, X is the number of doses each patient needs to take.

This variable X does not follow a binomial distribution.

Because it's not a count of successes out of a fixed number of independent trials.

But rather a continuous variable that can take any non-negative value.

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The above question is incomplete, the complete question is:

For a certain type of hay fever, Medicine H has a 30% probability of working.

In which distributions does the variable X have a binomial distribution?

Select EACH correct answer.

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.

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