Keith has $500 in a savings account at the beginning of Summer. He wants to have at least $300 in the account by the end of the summer. He withdraws $25 each week for food, clothes and movie tickets how many weeks can Keith withdraw money from his account?

Answer:

17.25 ; 1:01:13 ; 4 hours 47 minutes, 38 seconds

Step-by-step explanation:

From the picture attached :

The shortest distance cycled :

17.25 < 25.80 < 27.42

Hence, shortest distance cycled is : 17.25

Shortest cycling time :

1:01:13 < 1:50:05 < 1:56:20

Hence, shortest distance cycled is : 1:01:13

Total cycling time:

1:01:13 + 1:50:05 + 1:56:20

1 + 1 + 1 = 3 hrs

01 + 50 + 56 = 107 = 107/60 = 1 hr 47 minutes

13 + 05 + 20 = 38 seconds

Total cycling time :

(3 + 1 hr 47 minutes + 38 seconds) = 4 hours 47 minutes, 38 seconds

There is not enough information provided to determine if there is sufficient evidence at the 0.02 level to refute the publisher's claim. The null hypothesis is that proportion of readers owning a Rolls Royce is equal to 0.78 and alternative hypothesis is that proportion of readers owning a Rolls Royce is not equal to 0.78.

To determine if there is sufficient evidence at the 0.02 level to refute the newsletter publisher's claim that 78% of their readers own a Rolls Royce, we need to conduct a hypothesis test. Here are the null and alternative hypotheses for this scenario:

Null Hypothesis (H0): The proportion of readers who own a Rolls Royce is equal to 0.78 (P = 0.78)

Alternative Hypothesis (H1): The proportion of readers who own a Rolls Royce is not equal to 0.78 (P ≠ 0.78)

To test these hypotheses, follow these steps:

1. Collect a random sample of readers and record the number of Rolls Royce owners in the sample.

2. Calculate the sample proportion (p-hat) of Rolls Royce owners.

3. Calculate the test statistic using the formula: z = (p-hat - P) / sqrt(P * (1-P) / n), where P is the claimed proportion (0.78) and n is the sample size.

4. Determine the critical value for a two-tailed test at the 0.02 significance level (α = 0.02), which is approximately ±2.576 (from a z-table or calculator).

5. Compare the test statistic (z) to the critical value. If the test statistic is greater than or equal to the critical value or less than or equal to the negative critical value, reject the null hypothesis in favor of the alternative hypothesis. If not, fail to reject the null hypothesis.

Based on the results, you can determine if there is sufficient evidence to refute the publisher's claim at the 0.02 significance level. However, just based on the given information, there is not enough information to determine if there is sufficient evidence at the 0.02 level to refute the publisher's claim. We need the sample size.

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Answer:

Step-by-step explanation:

Given is 30 x 60 x 90 right triangle

The side ratios of this triangle is

Find the value of x and y using this ratio

Let's find

And

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

Step-by-step explanation:

This question deals with Slope of a line.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet

Thus, slope =  6/4 = 3/2 ≈ 1.5

For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet

Thus, slope=   10/6 = 5/3 ≈ 1.66

Thus,

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

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The derivative of the function f(x, y) at P0(-7, 0) in the direction of vector A = 9i + j is -7.

To find the derivative of the function f(x, y) = xy - 3y^2 at the point P0(-7, 0) in the direction of vector A = 9i + j, we can use the gradient operator. The gradient of f(x, y) is a vector that points in the direction of the maximum rate of increase of the function at each point.

The gradient of f(x, y) is given by:

∇f = (∂f/∂x) i + (∂f/∂y) j

Let's calculate the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = y

∂f/∂y = x - 6y

Now, evaluate these partial derivatives at the point P0(-7, 0):

∂f/∂x(P0) = 0

∂f/∂y(P0) = -7 - 6(0) = -7

The gradient ∇f at P0 is therefore:

∇f(P0) = (∂f/∂x(P0)) i + (∂f/∂y(P0)) j

= 0i - 7j

= -7j

To find the derivative of f(x, y) at P0 in the direction of vector A, we need to take the dot product of the normalized A with ∇f(P0), and multiply it by the magnitude of A.

First, normalize vector A:

|A| = √(9^2 + 1^2) = √(81 + 1) = √82

A_normalized = A / |A| = (9i + j) / √82

Now, calculate the dot product:

Daf = A_normalized · ∇f(P0)

= (9i + j) · (-7j)

= -7(0) + 1(-7)

= -7

Therefore, the derivative of the function f(x, y) at P0(-7, 0) in the direction of vector A = 9i + j is -7.

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Answer:

-8.66666667 feet because:

Step-by-step explanation:

-2 1/3 x 3 = 7

-2 1/3 ÷ 2 = 1.66666666667

7 + 1.6666666667 = 8.66666667

The 500,00th number in the sequence = 98828

A sequence is a numbered collection of objects where repeats are permitted and order is important. It has members, just like a set. The length of something like the sequence is defined as the number of items.

here n^th iteration n+3 element are listed and n element are skipped.

now before nth iteration total skipped natural number : 1+2+3+.........n-1

                                                                                           = n(n-1)/2

now after completion of nth iteration total listed natural number = 4+5+6+.....n+3

= ((n+3)(n+4)/2)-6

to find 50000th number total listed element must be greater than or equal to 50000.

((n+3)(n+4)/2)-6 ≥ 50000

(n+3)(n+4) ≥ 100012

n = 313

total skipped before 313th iteration

=( 313 * 312)/2

=  48828

total listed before 313th is 48828.

listed after 312th iteration

= ((315)(316))/2)-6

= 49764

total number remaining for 50000

= 50000 - 49764

= 236

total number passed.

skipped+ listed

= 48828 + 49764

= 98592

50000th element = 98592 + 236

                              = 98828

The 500,00th number in the sequence = 98828

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Answer:

2426.55 or 2456.549148

Step-by-step explanation:

Heres the function 3100(1-0.04)^6 Feel free to check! Hope this helps! ;-)

Answer:

Step-by-step explanation:

so coz there was already 11 inches but after 20min the tank is 56inch so wht u do is this

45+11t if im right

The surface area of the triangular prism is 2160 square centimeters.

To calculate the surface area of a triangular prism, you need to find the area of each face and add them up.

In this case, the triangular prism has two identical triangular faces and three rectangular faces.

The area of one triangular face is:

0.5 x base x height = 0.5 x 30 cm x 24 cm = 360 cm²

Since there are two triangular faces, the total area of the triangular faces is:

2 x 360 cm² = 720 cm²

The area of each rectangular face can be calculated as:

length x height

Two of the rectangular faces have a length of 30 cm (the same as the base of the triangular face) and a height of 24 cm.

The area of each of these faces is:

30 cm x 24 cm = 720 cm²

The third rectangular face has a length of 30 cm (the same as the base of the triangular face) and a height of the height of the prism, which is also 24 cm.

The area of this face is:

30 cm x 24 cm = 720 cm²

Therefore, the total surface area of the triangular prism is:

720 cm² + 720 cm² + 720 cm² = 2160 cm²

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Answer:

The number of cups of strawberries to be used is 11 2/5 cups

Step-by-step explanation:

Here, we want to know how many cups of strawberries to be used given that the recipe was tripled.

From the question, we are told that the recipe required 3 4/5 cups of strawberries.

Now, by tripling the recipe, it means we will be tripling the individual cups too.

So the number of cups of strawberries to be used will be ;

3 4/5 * 3

3 4/5 as improper fraction is 19/5

so we have 19/5 * 3 = 57/5 = 11 2/5

Answer:

122fee/meter

Step-by-step explanation:

Given the expression for the initial fee plus a constant fee per meter expressed as;

F = 110 + 0.12d

Is d = 100m

Substiutte into the expression and get F

F = 110 + 0.12(100)

F = 110 + 12

F = 122

Hence the required increase in price is 122fee/meter

Answer:

110

Step-by-step explanation:

Answer:

$3,272

Step-by-step explanation:

Continuous Compounding Formula

\(\large \text{$ \sf A=Pe^{rt} $}\)

where:

Given:

Substitute the given values into the formula and solve for A:

\(\sf \implies A=2600e^{(0.023 \times 10)}\)

\(\sf \implies A=2600e^{0.23}\)

\(\implies \sf A=3272.360026...\)

Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.

To ensure internal validity, it is important to have a random and representative sample that accurately reflects the population of interest.

The types of questions you are asking indicate that you are concerned about the threat to internal validity known as selection bias.

Selection bias refers to the systematic differences between the characteristics of the selected participants and the characteristics of the population from which they are drawn. It occurs when the process of selecting participants introduces a non-random element that may impact the results of the study.

In this case, you are specifically interested in how participants were selected and whether certain subgroups, such as those living on or off-campus, sorority or fraternity members, non-traditional age students, and men and women, were included in the survey. These questions suggest that you are concerned about whether the selection process introduced any biases that could affect the internal validity of the survey results.

For example, if participants were only selected from a specific residence hall or from Greek organizations, it could introduce bias because those groups may have different drinking behaviors compared to the broader student population. Similarly, if non-traditional age students or men and women were underrepresented or overrepresented in the sample, it could affect the generalizability of the findings.

To ensure internal validity, it is important to have a random and representative sample that accurately reflects the population of interest. This helps minimize the potential for selection bias and increases the generalizability of the survey results to the larger college campus population.

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Answer:

59 ° F

Step-by-step explanation:

F = 9/5 C + 32

 = 9/5 (15) + 32 = 59 °  F

Answer: 18(6 x 22) = (18 x 6) x 22

Step-by-step explanation: The associative property of multiplication states that when multiplying three or more numbers, the way they are grouped does not affect the product. In other words, (a x b) x c = a x (b x c) for any numbers a, b, and c.

To show the associative property of multiplication, we need to find an equation that has three factors and two different ways of grouping them with parentheses. The equation 18(6 x 22) = (18 x 6) x 22 satisfies this condition. It shows that we can multiply 18 by 6 and then by 22, or we can multiply 6 by 22 and then by 18 and get the same result: 2376.

The other equations do not show the associative property of multiplication because:

Hope this helps, and have a great day! =)

Answer:

i need help

Step-by-step explanation:

Answer:

\(\text{(C) }300\pi\:\mathrm{cm^3}\)

Step-by-step explanation:

The volume of a cylinder with radius \(r\) and height \(h\) is given by \(V=r^2\pi \cdot h\).

What we're given:

Substituting given values, we get:

\(V=5^2\pi \cdot 12 =\boxed{300\pi\:\mathrm{cm^3}}\)

Answer:

c

Step-by-step explanation:

The formula for the volume of a cylinder is \(V=\pi r^2h\)

We know r is 5, and h is 12.

Then we can just plug the values into the formula.

\(V=\pi (5)^2(12)\\ V=\pi (25)(12)\\\V=\pi (300)\)

So the answer is c, 300pi

Answer:

Step-by-step explanation:

Both angles are equal so,

1+16x =17x-3

16x-17x= -3-1

-x = -4

x = 4

The pair of equivalent radical expression is option D. √180 and 3√20.

Radicals are defined as the nth root of a number using the symbol  \(\sqrt[n]{x}\).

This is the opposite form of the exponential functions.

\(\sqrt[n]{x}\) can be written in the exponential form as \(x^{1/n\).

A.√45 can be written as the square root of (15 × 3).

√45 = √(15 × 3) ≠ 3√15

B. √75 cannot be written as 3√5, since, if we have to take 3 outside, inside he root there must be 3² = 9. But 75 is not a multiple of 9.

C. √54 = √(9 × 6) = 3√6 ≠ 9√6

D. √180 = √(9 × 20) = √9 × √20 = 3√20

Hence the correct option is D.

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The clear question is given below.

Which of the following is a pair of equivalent radical expressions?

A. √45 and 3√15

B. √ 75 and 3√5

C. √54 and 9√6

D. √180 and 3√20

Answer:

The number 56 divided by 12 is equal to 4 with a remainder of 8 (56 ÷ 12 = 4 R. 8).

Step-by-step explanation: SOOOOO bestie.. you divide 56 by 12 which is 4 so each child gets 4 apples and there are 8 left so im guessing just put {4 r8 } !!! <3

Answer:

4 apples, if they only receive whole apples, or 4 2/3 apples if they can be in fractions

Step-by-step explanation:

56 divided by 12 is 4 2/3. If you are splitting the amount of apples evenly, each child would receive 4 2/3 apples. If you are only giving the children whole apples, they will each receive 4 apples with 8 apples left over.

Step-by-step explanation:

the first one is acute equilateral

the second one is obtuse scalene

the third one is right scalene

the fourth one is obtuse isosceles

Answer:

the answer is c

Step-by-step explanation:

45% of 1500=675

38% of 1500=570

675+570=1245

1500-1245=255

Answer:

\(1290 = \frac{h}{10} + \frac{h}{5} \\ 12900 = h + 2h \\ 3h = 12900 \\ h = 4300\)