Select all the rectangles that have an area of 15/24 square inches.

The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.857 or 85.7%.

The random variable X represents the outcome of the first test, where it takes on a value of 1 if the student passes and 0 if the student fails.

Similarly, the random variable Y represents the outcome of the second test, taking on a value of 1 if the student passes and 0 if the student fails. Given that the joint probability of passing both tests is 0.6, we can interpret this as the probability of X=1 and Y=1.

The marginal probability of failing the first test is 0.3, which can be represented as P(X=0). To find the conditional probability of passing the second test, given that the student passed the first test, we use the formula \(P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1).\)

Since we know that \(P(X=1 and Y=1) = 0.6, and P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7\), we can substitute these values into the formula:
\(P(Y=1 | X=1) = 0.6 / 0.7\)

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The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.8571 or 85.71%.

The conditional probability of passing the second test, given that the student passed the first test, can be calculated using the formula for conditional probability:

P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1)

We are given that the joint probability of passing both tests is 0.6, which means P(X=1 and Y=1) = 0.6.

To find P(X=1), we need to use the marginal probability of failing the first test, which is given as 0.3. Since the marginal probability of passing the first test is the complement of failing the first test (i.e., 1 - 0.3 = 0.7), we can say P(X=1) = 0.7.

Now we can substitute these values into the conditional probability formula:

P(Y=1 | X=1) = 0.6 / 0.7

Simplifying this expression, we have:

P(Y=1 | X=1) = 0.8571

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Answer:

\(\boxed{\tt v < 6.8}\)

Step-by-step explanation:

\(\tt 0.5v+0.06 < 3.46\)

Multiply both sides by 100:-

\(\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100\)

\(\tt 50v+6 < 346\)

Subtract 6 from both sides:-

\(\tt 50v < 340\)

Divide both sides by 50:-

\(\tt \cfrac{50v}{50} < \cfrac{340}{50}\)

\(\tt v < \cfrac{34}{5}\)

Or

\(\tt v < 6.8\)

Therefore, your answer is v < 6.8!!! :)

______________________

Hope this helps!

Have a great day!

Answer:

$6

Step-by-step explanation:

A=P(1+i.n)

A=200(1+0.01.x 3)

A=206

Thus 206 - 200 = $6

You will earn $6 in interest.

The interest you will earn per year is:

= Interest rate x Amount deposited

= 200 x 1%

= $2

Because it is simple interest, you will earn the same amount of interest every year. In 3 years you will have:

= Interest per year x number of years

= 2 x 3

= $6

You will therefore earn $6 in interest.

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Answer:

x=3y-29/y-8

Step-by-step explanation:

3(y-10)+1=x(y-8)

xy-8x=3y-29

x(y-8)=3y-29

/y-8        /y-8

x=3y-29/y-8

The correct conclusion is that we do not have enough evidence to suggest that the average test score obtained by early finishers is significantly different from the overall average.

The significance level (alpha) is a probability value used to specify the threshold at which the null hypothesis can be denied. It is often referred to as the alpha level, alpha value, or significance level. The significance level specifies how strong the evidence must be for the null hypothesis to be denied. The significance level, alpha, is typically set at 0.05 (5%) or 0.01 (1%) in many scientific investigations, including hypothesis testing.

Any p value less than the α significance level is considered statistically significant and the null hypothesis is denied. Therefore, we need to look at the p-value to decide whether the mean test score of the first finishers is significantly different from the overall means. The null and alternative hypotheses for the given question can be stated as follows:

Null hypothesis: H0: The mean test score obtained by early finishers is not significantly different from the overall mean. Alternative hypothesis:

Ha: The average test score obtained by the first finishers is significantly different from the overall average.

The test that is reinforced in this situation is a one-sample t-test, which compares the mean of the first-finishers tests with the population means. If the p-value is found to be less than the 0.05 significance level, we will deny the null hypothesis and conclude that there is sufficient evidence to believe that the average score of the early finishers test is significantly different from the overall mean.

In this case, the p-value is greater than the alpha level of 0.05, so we cannot deny the null hypothesis. Thus, we can infer that the average test score obtained by early finishers is not significantly different from the overall average. Therefore, the correct conclusion is that we do not have enough evidence to suggest that the average test score obtained by early finishers is significantly different from the overall average.

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Answer:

Step-by-step explanation:

unit price=44.28/9

=$4.92

Both f(t) and g(t) are of exponential order.

To show that a function f(t) is of exponential order, we need to find positive constants M and k such that:

|f(t)| <= M * e^(k*t) for all t >= t0, where t0 is some arbitrary constant.

Let's start by considering f(t) = t³ * sin(t). We can use the fact that |sin(t)| <= 1 to obtain an upper bound for f(t):

|f(t)| = |t³ * sin(t)| <= t³ for all t

Now we need to find k such that t³ <= M * e^(k*t) for all t >= t0. Taking logarithms of both sides yields:

ln(t³) <= ln(M * e^(kt)) = ln(M) + kt

Simplifying the left-hand side:

3 ln(t) <= ln(M) + k*t

Now we can choose M = 1 and k = 1 to obtain:

3 ln(t) <= ln(1) + t

3 ln(t) <= t

This inequality holds for all t >= 1, so we have shown that f(t) is of exponential order with M = 1 and k = 1.

Next, consider g(t) = t² * e^t. We can once again obtain an upper bound using the fact that e^t >= 1:

|g(t)| = |t² * e^t| <= t² * e^t for all t

To find M and k such that t² * e^t <= M * e^(k*t) for all t >= t0, we can again take logarithms of both sides:

ln(t² * e^t) <= ln(M * e^(kt)) = ln(M) + kt

Simplifying the left-hand side:

2 ln(t) + t <= ln(M) + k*t

Now we can choose M = 1 and k = 2 to obtain:

2 ln(t) + t <= ln(1) + 2t

2 ln(t) + t <= 2t

This inequality holds for all t >= 1, so we have shown that g(t) is of exponential order with M = 1 and k = 2.

Therefore, both f(t) and g(t) are of exponential order.

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Answer:75 children

Step-by-step explanation: Let the number of children will be x, so the number of adults will be 215-x

Making equation: 3x+5(215-x)=925

3x+1075-5x=925

-2x=925-1075

-2x=-150

x=75

Answer:

Step-by-step explanation:

10.6_

Answer:

96/9  or  10   6/9  or  10     2/3

Step-by-step explanation:

Lets make common denominators first LCM(9,1)=9

8/1 x 9/9 = 72/9

24/9 + 72/9 = 96/9

Answer: 96/9  or  10   6/9  or  10     2/3

Hope this helps :D

This is because the amount Rachel owes her parents increases by $75 every week, which is represented by the linear term 75x. The starting amount she owes her parents is $800, which is represented by the constant term 800. Therefore, the linear model for this situation is f(x) = 800x + 75.

Since Rachel is paying back $75 every week, the relationship between the amount owed and the number of weeks is linear. We can represent this linear model relationship as a function f(x), where x is the number of weeks.

Now, let's look at the given options and identify the correct linear model:

a. f(x) = 800x + 75
b. f(x) = 800x - 75
c. f(x) = 75x + 800
d. f(x) = 75 - 800
e. f(x) = -75 + 800
f. f(x) = -75 - 800

Since Rachel initially owes $800 and is paying back $75 every week, the correct model should have a starting value of 800 and a decrease of 75 for each week. The model that represents this is:

f(x) = -75x + 800

Comparing this to the given options, we can see that the correct answer is:
c. f(x) = 75x + 800

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Step 1: Problem

Compound interest

Step 2: Concept

Step 3: Method

A = ?

r = 3% = 3/100 = 0.03

t = 4 years

P = $ 1,000

Answer:

esa esdjsjaoqsknwkww0w

Step-by-step explanation:

-f+2+4f=3f

3f+2=8-3f

3f+3f=8-2

f=6/6

f=1

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Thus, a sample size of 802 residers of Indian River County would be needed to estimate the proportion of residers without health insurance with a periphery of error of no further than0.024, with 98 confidence.

To determine the sample size needed to limit the periphery of error to within0.024 of the population proportion for a 98-confidence interval, we can use the formula

n = (Z^2 * p * q) / E^2

where:

Plugging in these values, we get:

\(n = (2.33^2 * 0.27 * 0.73) / 0.024^2\)

\(n \approx 801.83\)

Since we need a whole number for the sample size, we round up to the nearest integer:

\(n = 802\)

thus, a sample size of 802 residers of Indian River County would be needed to estimate the proportion of residers without health insurance with a periphery of error of no further than0.024, with 98 confidence..

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Answer:

16.49 seconds to nearest hundredth.

Step-by-step explanation:

y=-16X^2+258x+97

When the rocket hits the ground y = 0, so we have

-16X^2+258x+97 = 0

Using the quadratic formula:

x =  [-258 +/- √(258^2 - 4*-16*97)]/ (2*-16)

  =   [-258 +/- √(72772)]/ (2*-16)

  =   [-258 +/- 269.763]/ (2*-16)

  =   8.0625 +/- -8.430

  = -0.3675, 16.4925.

We take the positive value

so the answer is 16.49 seconds.

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Note that graph for the above equation y-5 = -(3/4) (x+3) is attached accordingly.

y-5 = -(3/4) (x+3)

Lets solve for x. First, flip the equation:

-3/4x + -9/4x  = y-5

Next Add 9/4 to both sides:


-3/4x + -9/4x  + 9/4  = y-5 + 9/4

⇒-3/4 x = y + -11/4; divide both sides by -3/4

(-3/4 x)/-3/4 = (y + -11/4) /-3/4

Thus, x = (-4y + 11)/3

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Answer:

1/24

Step-by-step explanation:

1/4*1/6=1/24

Answer:

the answer is C

Step-by-step explanation:

The room that would stop Barry from hosting the event is the semicircular room.

Would the first rectangular room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a rectangle = length x width

25 x 30 = 750 feet²

Number of people per square foot - 750 / 150 = 1 person for every 5 feet

Would the trapezoidal room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a trapezoid = 1/2 x (sum of parallel sides) x height

1/2 x (24 + 36) x 28 = 840 feet²

Number of people per square foot = 840 / 150 = 1 person for every 5.6 feet

Would the square room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a square = length x width

28 x 28 = 784 feet²

Number of people per square foot - 784 / 150 = 1 person for every 5.2 feet

Would the semi circular room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a semicircle = 1/2πr²

Where:

r = 3.14

r = radius = diameter / 2 = 28 / 2 = 14 feet

1/2 x 3.14 x 14² = 307.72 feet²

Number of people per square foot - 307.72/ 150 = 1 person for every 2.05 feet

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Answer:

The semicircle

Step-by-step explanation:

ewomazinoade's answer is correct, not sure why at time of writing the rating is so low for their answer (3.7).

See pic!

The area of ΔAFD is 42 squared unit.

The area of a triangle is the amount of space that the triangle would occupy on a 2 dimensional plane.

Area of a triangle = 1/2 x base x height

To solve the given problem, let the height be resented by x and the base be represented by y. So that applying the trigonometric function to determine the values, we have;

i. Sin θ = opposite/ hypotenuse

Sin 30 = x/ 14

x = 14 x Sin 30

     = 7

The height is 7 units.

ii. Cos θ = adjacent/ hypotenuse

   Cos 30 = y/ 14

  y = 14 x Cos 30

       = 12

The base is 12 units.

Therefore, the area of triangle AFD can be determined by;

Area of ΔAFD = 1/2 x 12 x 7

                       = 42

The area of ΔAFD is 42 squared unit.

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Let's factor out the number 18:

18 = 2 * 3 * 3

this is the factor decomposition of 18 with all positive factors.

Therefore all possible positive factors for 18 are:

1 x 18

2 x 9

3 x 6

Answer:

108.90

Step-by-step explanation:

You start with finding  

10

%

of  

90

.

$

90

⋅

.1

=

$

9

You add the money and the interest to get  

$

99

for the first year. However, the next year is different. It's compound interest, so you have to multiply  

10

%

by  

$

99

.

$

99

⋅

.1

=

$

9.90

$

99

+

$ 9.90

= $  108.90   The total would then be  $

108.90  i think lol

Answer:

I think its $172800  bc I = PRT so I multiplied 36x 800 x 6 which is 172800

If my answer is wrong pls let me know and that I am very very very sorry :(

Step-by-step explanation:

Answer: **Incomplete question**

Step-by-step explanation: Your question is incomplete, and missing very important details. However I would attempt to use assumed values in place of the omitted ones so that after explaining, it would be pretty much easy to figure out the solution.

If Rahul was given a total of 32 questions and he has worked out for example 25% of them on Monday and then 50% of them on Tuesday, to find the number  of problems left, we would need to find the number of questions represented by the percentage indicated.

If he has worked out 25% of them on Monday, then that means he had done the following

Percentage done = 25% (or 25/100 which equals 0.25)

Number of problems solved = 32 * 25%

Number of problems solved = 32 * 0.25

Number of problems solved = 8

Further he solved 50% of them on Tuesday

Percentage done = 50% (or 50/100 which equals 0.50)

Number of problems solved = 32 * 50%

Number of problems solved = 32 * 0.5

Number of problems solved = 16

This means he has now solved a total of

8 + 16 = 24

If therefore he has solved 24 problems, then the number of problems left is derived simply as

Unsolved problems = 32 - 24

Unsolved problems = 8

Please remember that the use of 25% and 50% are simply assumptions in order to make explaining the solution easier. Please insert the correct values  of the percentage as appropriate.

The correct answer is c. Both a. and b. are reasons why we can't infer cause and effect from a correlation.

Correlational data can only show us that there is a relationship between two variables, but it cannot tell us which variable is causing the other. This is because there are other factors that could be influencing the relationship between the two variables, and we cannot be sure which one is the cause and which one is the effect.

For example, let's say that there is a positive correlation between ice cream sales and crime rates. We cannot conclude that ice cream sales are causing crime or that crime is causing people to buy more ice cream. It is possible that some other factors, such as the weather, are influencing both ice cream sales and crime rates, and that the relationship between the two variables is just a coincidence.

Therefore, to establish a cause-and-effect relationship between two variables, we need to conduct an experiment where we can manipulate one variable and observe the effect on the other variable while controlling for other factors that could influence the relationship.

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Answer:  5/log (8) - 8/3

Step-by-step explanation:

Answer:

A:2^5=3x + 8 /x=8/The next part is B.x3=64 /x=4

Step-by-step explanation:

I just did it hope this helps