what is the name of the property given below? if a • b = 0, then a = 0, b = 0, or both a = 0 and b = 0.

Answers

Answer 1

if a • b = 0, then a = 0, b = 0, or both a = 0 and b = 0 it is called the Zero Product Property.

The property given is known as the Zero Product Property. It states that if the product of two numbers, a • b, equals zero, then either a is zero, b is zero, or both a and b are zero. In other words, if the product of any two numbers is zero, at least one of the numbers must be zero.

This property is a fundamental concept in algebra and plays a crucial role in solving equations and understanding the behavior of real numbers. It stems from the fact that zero is the additive identity, meaning that any number added to zero remains unchanged. When two non-zero numbers are multiplied together, their product will not be zero. Therefore, if the product is zero, it implies that one or both of the numbers must be zero.

The Zero Product Property is widely used in various algebraic manipulations, such as factoring, solving equations, and determining the roots of polynomials. It provides a key principle for identifying critical values and potential solutions in mathematical expressions and equations.

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Related Questions

Timothy wanted to get some exercise. He walked 12 blocks in 10 minutes. What was his average speed of his walk?

Answers

Average speed: distance/time
12 blocks/10 minutes = 1.2 blocks per minute

Answer: 1.2 blocks

Step-by-step explanation:

Timothy walks 12 blocks in 10 minutes so it can be written as

12 blocks = 10 minutes

divide both sides by 10

1.2 blocks per minute

Can someone please help me on this and show work if you can? Thanks!

Answers

Answer:

area = 18.81 m²

Step-by-step explanation:

solving for the 7 sided polygon first:

divide into 7 equal isosceles triangles, each having sides of 10 m and a peak angle of 360°/7 = 51.43°. Drop a line from the peak & perpendicular to the base makes a right triangle with a 25.71° peak angle and a 10 m hypotenuse.

sin 25.71° = x/10, x = 4.34, the base of the full triangle will be 2 x 4.34 = 8.68 m

cos 25.71° = x/10, x = 9.01, the rise of the triangle is 9.01 m

The area of each triangle will be 1/2(8.68)(9.01) = 39.10 m²

39.10 x 7 triangles = 273.72 m²

area of 7 sided polygon = 273.72 m²

Next solve for the inner circle:

The rise of the triangle (9.01) is the radius of the inner circle.

area of inner circle = πr² = 3.14(9.01²) = 254.91 m²

273.72 - 254.91 = 18.81 m²

I Need Answers Quick

Answers

Answer:

42.78cm2

Step-by-step explanation:

Area =100°/360 * 22/7 * 7^2

=42.78cm2

The measure of ∠CBD is 45% of the measure of ∠ABC. Find the value of x.

Answers

Answer:

x = 49.5°

Step-by-step explanation:

∠ABC = 90°

∠CBD = 45%∠ABC

∠CBD = 0.45(90)

∠CBD = 40.5°

x = ∠ABC - ∠CBD

x = 90 - 40.5

x = 49.5°

find the slope of the points 2,8 and 12,55

Answers

Answer:

m = 4.7

Step-by-step explanation:

If you plug in these values in the slope formula, this is what happens:)

Answer:

47/10x

**Do not leave your answer as a decimal, slope is usually in fraction form**

Step-by-step explanation:

Slope Formula: [tex]\frac{\text{rise}}{\text{run}} / \frac{y_2 - y_1}{x_2 - x_1}[/tex] In this formula, subtract the 1st coordinate from the second. So, the 2nd y coordinate goes first, place a "minus" sign, and then the 2nd y-coordinate. This is the same for the x coordinates.

Finding the Answer: To find the answer, we just plug the numbers correctly into the equation, just as I explained above. We would do 55-8 first, which is 47, and then 12-2 which is 10.

Combined, the answer is 47/10x. You always place an x after the slope, which can be used to plug in other numbers. The answer cannot be simplified anymore, so this is simplfied.  

The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph.
Initially, as xxx increases, yyy

.
Afterward, the slope of the graph of the function is equal to
for all xxx between x=3x=3x, equals, 3 and x=5x=5x, equals, 5.
The slope of the graph is equal to
for xxx between x=5x=5x, equals, 5 and x=9x=9x, equals, 9.
The greatest value of yyy is y=\:y=y, equals
, and it occurs when x=\:x=x, equals
.

Answers

answer in the picture

Answer:

The illustration below shows the graph of yyy as a function of xxx.

Complete the following sentences based on the graph.

Initially, as xxx increases, yyy

Step-by-step explanation:

[48 (72-12) -225] ÷ 9

someone pls help​

Answers

Answer:

295

Step-by-step explanation:

Answer:

295!

Step-by-step explanation:

72 - 12 = 60

48 x 60 = 2880

2880 - 225 = 2655

2655 / 9 = 295

Have you ever heard of PEMDAS? It is the order in which to solve equations like this one. Here's what it stands for:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

I hope this is helpful for future math equations similar to this one.

A vending machine dispenses coffee into a twenty-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.03 ounce. You can allow the cup to overfill 4% of the time. What amount should you set as the mean amount of coffee to be dispensed? Click to view page 1 of the table. Click to view page 2 of the table. 19.9 ounces

Answers

The mean amount of coffee to be dispensed should be set at μ + 0.0525 ounce, where μ represents the original mean amount of coffee. This ensures that the cup overfills only 4% of the time.

To determine the mean amount of coffee to be dispensed, we need to find the value that corresponds to the 96th percentile of the normal distribution. This value represents the amount of coffee that should not be exceeded 96% of the time.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to the 96th percentile is approximately 1.75.

Since the standard deviation is given as 0.03 ounce, we can set up the equation:

1.75 = (x - μ) / 0.03

Solving for x, the mean amount of coffee to be dispensed, we get:

x - μ = 1.75 * 0.03

x - μ = 0.0525

x = μ + 0.0525

Therefore, the mean amount of coffee to be dispensed should be set at μ + 0.0525 ounce to ensure that the cup overfills only 4% of the time.

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3. Savannah estimates that her dog weights 30
pounds. When she takes her dog to the vet for
his check-up, the dog is placed on the scale and
actually weights 32.5 pounds. What was
Savannah's percent of error of her estimate?
Round to the nearest percent.

Answers

Answer:

8%

Step-by-step explanation:

Which equation best represents the graph?

Answers

It’s the last choice
Slope is decreasing so negative slope is 1/2
Y intercept is 3

13. Which graph best represents -5y = -6x + 15?
А
Help ASAP !!!

Answers

The answer is C i think bc the y-int is -3

An online store sold a gift basket at five different prices and recorded the number of gift baskets that were sold at each price. The results are shown in the scatterplot.

Answers

Complete question :

An online store sold a gift basket at five different prices and recorded the number of gift baskets that were sold at each price. The results are shown in the scatterplot.

Which statement is correct based on the scatterplot?

There is no relationship between price and gift baskets sold because the points do not form a straight line.

There is no relationship between price and gift baskets sold because there are multiple prices at which 80 gift baskets were sold.

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold increases.

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Answer:

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Step-by-step explanation:

From the scatterplot provided, it could be observed thatbthere is a linear trend in the plot created. This shows that there is a relationship between the price of gifts and the number if gift basket sold.

Furthermore, the slope of the linear trend line that could be drawn from the plotted data is negative, A negative slope Indicates a negative relationship, that is an increase in x leads to corresponding decrease in y. He ce, as price increases the number sold decreases

Answer:

d and/ or the other dude

Step-by-step explanation:

The temperature at sunrise is 40°F. Each​ hour, the temperature rises 4°F. Write an equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours. What is the graph of the​ equation?
Write an equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours.

Answers

Answer:

y = 4x + 40

Step-by-step explanation:

At sunrise, 0 hours have passed, meaning x = 0.

When x = 0, the temperature is 40, meaning that 40 is the y-intercept.

And every x hours the temperature rises by 4 degrees F

Find the distance between the set of points (-4,5) and (4,0)

Answers

Answer:

√89

Step-by-step explanation:

√(4+4)2+(0-5)2

√(8)2+(-5)2

√64+25

√89

WILL MARK BRANLIEST
What is true about the decimal form of an irrational number ?
A) The decimal both repeats and terminates
B) The decimal does not repeat or terminate
C) The decimal repeats
D) The decimal terminates

Answers

Therefore, the decimal representations of irrational numbers satisfy conditions 1 and 2; that is, irrational numbers are decimals that do not terminate and do not repeat. Knowing these properties, it is now possible for us to construct irrational numbers in decimal form at will.

for spanish people

Por lo tanto, las representaciones decimales de números irracionales cumplen las condiciones 1 y 2; es decir, los números irracionales son decimales que no terminan y no se repiten. Conociendo estas propiedades, ahora es posible para nosotros construir números irracionales en forma decimal a voluntad.

STRESSING OUT ABOUT THIS ONE

Answers

I had this one before. I'm pretty sure it is 1.61

Answer:

1.61

Step-by-step explanation:

It just makes since.

Daniel is baking cookies but does not have all of the he needs. The ratio of flour:sugar in his recipe is 3:2cups. If he only has 1.5cups of sugar, how much flour should he use to keep the ratio the same?

Answers

Answer:

Step-by-step explanation:

3:2 = 2.5:1.5

half of 2 is 1 so if you had 1.5 it would only be half. For a better explanation, 1 minute is 60 seconds half of a minute is 30 seconds. if you have 45 seconds it would be 3/4 of a second. this is hard for me to explain so if you need more examples just tell me in the comments.

i hope this helps

have a nice day/night

mark brainliest please:)

You are interested in estimating the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 3 years of the actual mean with a confidence level of 98%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 22 years.

Answers

71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

We need to find out the sample size of citizens that should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

The formula for the Margin of error is

E: E = Zc/2 * (σ/√n)

Where E is the margin of error Zc/2 is the Z-value for the level of confidence cσ is the population standard deviation is the sample size.

So the formula for the sample size n is: n = (Zc/2 / E)² * σ²

We have Zc/2 = Z0.02/2 = Z0.01 = 2.33 (using z-table) σ = 22 years

E = 3 years

n = (2.33 / 3)² * 22²

n ≈ 70.36 ≈ 71 (rounded up)

Therefore, 71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

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A cruise ship heads due west from a port 3 miles directly south of San Francisco. If the ship is travelling at a constant rate of 17 mph, how fast is the distance between the ship and San Francisco changing 1 hour after leaving port? Round your answer to the nearest tenth.

Answers

If the ship is travelling at a constant rate of 17 mph, the distance between the ship and San Francisco is changing at a rate of approximately 1 mile per hour. So, the rate of change is 1mph.

What is the concept of related rates?

The concept of related rates is a fundamental topic in calculus that deals with how the rates of change of different variables are related to each other. It involves analyzing how the rates of change of two or more related quantities are connected through their derivatives.

To solve this problem, we can use the concept of related rates. Let's assume that the cruise ship starts at point A, the port 3 miles directly south of San Francisco, and moves towards the west.

Let's denote the position of the cruise ship at a given time as point B. We are interested in finding the rate at which the distance between point B and San Francisco (let's call it point C) is changing.

We can create a right triangle with points A, B, and C, where the distance between A and C is the constant 3 miles. Let's call the distance between B and C as "x" (in miles).

We are given that the ship is traveling at a constant rate of 17 mph, which means its speed is 17 miles per hour.

To find how fast the distance between the ship and San Francisco is changing, we need to find dx/dt (the rate at which "x" is changing) when 1 hour has passed.

Using the Pythagorean theorem, we have:

[tex]x^2 + 3^2 = (distance\ traveled \ by\ the\ ship)^2[/tex]

Taking the derivative of both sides with respect to time (t):

2x(dx/dt) = 2(distance traveled by the ship)(speed of the ship)

Plugging in the given values:

2x(dx/dt) = 2(17 mph)

Simplifying:

x(dx/dt) = 17 mph

Now, we need to find x when 1 hour has passed. The ship is traveling at a constant speed of 17 mph for 1 hour, so the distance it travels is 17 miles.

Plugging in x = 17 and solving for dx/dt:

17(dx/dt) = 17 mph

dx/dt = 1 mph

Therefore, 1 hour after leaving port, the distance between the ship and San Francisco is changing at a rate of approximately 1 mile per hour.

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I suckkk at math.. Help?

Answers

Answer:

B. x=6

Step-by-step explanation:

substitute -7 into 2y to get -14. your new equation should be 4x-14=10. add 14 to both sides to get 4x=24, divide both sides by 4 to get x=6.

Answer:

B. 6

Step-by-step explanation:

y = -7

4x + 2(-7) = 10

4x + (-14) = 10

4x = 10 - (-14)

4x = 24

x = 6

The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.



2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27


What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.

Answers

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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A new car is valued at $28,000. It increases 9% per year. What is the total value of the car two year after purchase?​

Answers

Answer:

$33,040

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

$30520

Step-by-step explanation:

Can someone help me with this problem

Answers

Answer:

51 degrees

Step-by-step explanation:

As we already know that this triangle is a right triangle.

To find x, you need to subtract both angles.

90 - 39

= 51

In a diving meet, you score 8.4 and 7.88.

What is your total score?

Answers

Answer: 16.28?

Step-by-step explanation:

Is the equation cosine theta - sine theta =1 an identity? Explain

Answers

Answer: No, because an identity is an equation that is always true and cos(theta) - sin(theta) does not always equal 1.

Hope this helped! :)

Janice wants to go to the Sadie Hawkins dance. The probability of a random boy saying yes is 45%. How many does she need to be willing to ask to have a 99.7% chance of going?

Answers

Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.

To determine how many boys Janice needs to be willing to ask in order to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance, we can use the concept of probability and the binomial distribution.

The probability of a random boy saying yes is 45%, which means the probability of a boy saying no is 55%. Let's assume Janice asks "n" boys.

The probability of at least one boy saying yes can be calculated using the complement rule. The complement of the event "at least one boy saying yes" is the event "all boys saying no."

The probability of all "n" boys saying no is (0.55)^n, as the probability of each boy saying no is 55%.

To find the number of boys Janice needs to ask to have a 99.7% chance of going, we want the complement probability (all boys saying no) to be 0.003. Therefore:

(0.55)^n ≤ 0.003

Taking the logarithm of both sides:

n * log(0.55) ≤ log(0.003)

Solving for "n":

n ≥ log(0.003) / log(0.55)

Using a calculator:

n ≥ 15.154

Since Janice can't ask a fraction of a boy, we need to round up the value of "n" to the nearest whole number.

Therefore, Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.

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The U.S. Energy Information Agency reported that the mean monthly household electric bill in the United States in a recent year was $110.14. Assume the amounts are normally distributed with standard deviation $20.00. a. Find the 7th percentile of the bill amounts. b. Find the 62nd percentile of the bill amounts c. Find the median of the bill amounts.

Answers

a) The 7th percentile of the bill amounts is given as follows: $80.64.

b) The 62nd percentile of the bill amounts is given as follows: $116.24.

c) The median of the bill amounts is given as follows: $110.14.

How to obtain probabilities using the normal distribution?

We first must use the z-score formula, as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 110.14, \sigma = 20[/tex]

The median is the same as the mean, hence it is given as follows:

$110.14.

The 7th percentile is X when Z = -1.475, hence:

-1.475 = (X - 110.14)/20

X - 110.14 = -1.475 x 20

X = $80.64.

The 62nd percentile is X when Z = 0.305, hence:

0.305 = (X - 110.14)/20

X - 110.14 = 0.305 x 20

X = $116.24.

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HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP

Answers

Answer:

i think the answer would be A

what is the degree form for 3π/4 radians? enter your answer in the box.

Answers

The degree form for 3π/4 radians is 135°.The degree form for 3π/4 radians is 135°. To convert radians to degrees, we multiply the radian measure by the conversion factor of 180°/π.

In this case, we have (3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°. Therefore, 3π/4 radians is equivalent to 135° in the degree form.

To convert an angle from radians to degrees, we use the conversion factor of 180°/π. This conversion factor represents the relationship between a full circle (360°) and 2π radians.

In this case, we want to convert the angle 3π/4 radians to degrees. We multiply the radian measure (3π/4) by the conversion factor (180°/π):

(3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°

By canceling out the common factor of π and simplifying the expression, we find that 3π/4 radians is equal to 135°.

Therefore, the degree form of the angle 3π/4 radians is 135°.

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Solve 3(2x - 7)<4x - 8

Answers

Simplify to 6x - 21 < 4x - 8. Add 21 to both sides and subtract 4x from both sides. You will get 2x < 13. Divide both sides by two and you get x < 6.5

Answer:

x < 6.5

Step-by-step explanation:

3(2x - 7) < 4x - 8

6x - 21 < 4x - 8

6x - 4x < -8 + 21

2x < 13

x < 6.5

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Let B be the event that exactly one head falls.a. 2/4 b.3/4 c.0 d. 1/42. A rat is placed in a box with three push buttons (one red, one white, and one blue). If it pushes two buttons at random, determine the following. What is the probability that he will press the red key once?a. 1/3 b.1/9 c. 4/9 d. 5/9 what is the main idea of the reading about louis pasteur? a. louis pasteur wanted to test ideas in a laboratory. b. louis pasteur designed and conducted an experiment to test the theory of spontaneous generation. c. louis pasteur was the inventor of pasteurization. d. louis pasteur was a scientist. Suppose we are testing the null hypothesis H0: = 16 against the alternative Ha: > 16 from a normal population with known standard deviation =4. A sample of size 324 is taken. We use the usual z statistic as our test statistic. Using the sample, a z value of 2.34 is calculated. (Remember z has a standard normal distribution.)a) What is the p value for this test?b) Would the null value have been rejected if this was a 2% level test? For each of the following studies, identify the appropriate test or confidence interval to be run.Note: the number in the answer refers to the number of populations in the study (1 population or 2 populations).Group of answer choicesA study was run to estimate the average hours of work a week of Bay Area community college students. A random sample of 100 Bay Area community college students averaged 18 hours of work per week with a standard deviation of 12 hours. Find the 95% confidence interval.[ Choose ] 2 - mean - interval (t-dist) 1 - mean - test (z-dist) mean difference - interval (t-dist) 2 - proportion - test 1 - mean - interval (z-dist) 1 - proportion - interval 2 - proportion - interval 1 - mean - test (t-dist) 2 - mean - test (t-dist) mean difference - test (t-dist) 1 - mean - interval (t-dist) 1 - proportion - testA study was run to determine if more than 30% of Cal State East Bay students work full-time. A random sample of 100 Cal State East Bay students had 36 work full-time. Can we conclude at the 5% significance level that more than 30% of Cal State East Bay students work full-time?[ Choose ] 2 - mean - interval (t-dist) 1 - mean - test (z-dist) mean difference - interval (t-dist) 2 - proportion - test 1 - mean - interval (z-dist) 1 - proportion - interval 2 - proportion - interval 1 - mean - test (t-dist) 2 - mean - test (t-dist) mean difference - test (t-dist) 1 - mean - interval (t-dist) 1 - proportion - testA study was run to determine if the average hours of work a week of Bay Area community college students is higher than 15 hours. It is known that the standard deviation in hours of work is 12 hours. A random sample of 100 Bay Area community college students averaged 18 hours of work per week. Can we conclude at the 5% significance level that Bay Area community college students average more than 15 hours of work per week?[ Choose ] 2 - mean - interval (t-dist) 1 - mean - test (z-dist) mean difference - interval (t-dist) 2 - proportion - test 1 - mean - interval (z-dist) 1 - proportion - interval 2 - proportion - interval 1 - mean - test (t-dist) 2 - mean - test (t-dist) mean difference - test (t-dist) 1 - mean - interval (t-dist) 1 - proportion - testA study was run to determine if Peralta students average less hours of sleep a night than Cal State East Bay students. A random sample of 100 Peralta students averaged 6.8 hours of sleep a night with a standard deviation of 1.5 hours. A random sample of 100 Cal State East Bay students averaged 7.1 hours of sleep a night with a standard deviation of 1.3 hours. Can we conclude at the 5% significance level that Peralta students average less sleep a night than Cal State East Bay students?[ Choose ] 2 - mean - interval (t-dist) 1 - mean - test (z-dist) mean difference - interval (t-dist) 2 - proportion - test 1 - mean - interval (z-dist) 1 - proportion - interval 2 - proportion - interval 1 - mean - test (t-dist) 2 - mean - test (t-dist) mean difference - test (t-dist) 1 - mean - interval (t-dist) 1 - proportion - testA study was run to estimate the proportion of Peralta students who intend to transfer to a four-year institution. A random sample of 100 Peralta students had 38 intend to transfer. Find the 95% confidence interval.