The finishing times for a local 5k road race follows a normallt distribution with a mean of 25 minutes and a standard deviation of 3 minutes. What percent of finishers do you expect to be above 31 minutes?

The entrance fee is $\boxed{5.50\$$}.

Given that P = 0.80n + 5.50 represents the total price (in dollars) as a function of n, the number of balls used and ppp models the same function. We need to determine the entrance fee .Given equation, $$P = 0.80n + 5.50$$ .Now, let us substitute the given values to get the entrance fee.$$P = 0.80n + 5.50$$ $$P = 0.80(0) + 5.50$$ $$P = 5.50$$

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. The notation f: XY denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the input x.

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The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is

As a parallel line part of the qualities include that the slopes of the lines  are equal  

The equation of line is y = 3x + 2

The slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Line has slope, m = 3, a new parallel line of slope 3 passing through point  (-1, 3)

(y - y₁) = m  (x - x₁)

y - 3 = 3 (x - -1)

y = 3x + 1 + 3

y = 3x +  4

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Answer:

x = 6

My Step-by-step explanation:

You can solve this problem through simple inspection. Because 18 – 6 = 12,

x= 6.

Answer: I don’t think this has a solution but

Step-by-step explanation:

Answer:

The three paths intersect in pairs at the points A, B, and C. Measure and record the angle formed at each intersection

Step-by-step explanation:

By using a seasonal sales forecast, Gabi can better plan her inventory and staffing levels throughout the year, which can help her optimize her business operations and maximize profits.

To create this forecast, she will need to estimate the expected sales for each month based on historical data and market trends.

Here's an example of how Gabi could create a seasonal sales forecast:

Start with historical sales data: Gabi can use the previous owner's sales records to get an idea of how much revenue the store generated in each month. She should look for patterns or trends in the data that can help her predict future sales.

Identify seasonal trends: Based on the information she has been given, Gabi knows that 60 percent of sales occur during the Christmas holiday season. She should also consider other seasonal factors that could affect sales, such as the weather, local events, and school holidays.

Determine the baseline sales: Gabi can calculate the baseline sales by dividing the non-holiday sales (40 percent) by the number of non-holiday months (eight). This will give her an estimate of the average monthly sales during the non-holiday period.

Adjust for seasonal factors: Gabi should adjust her baseline sales estimate based on the seasonal trends she identified. For example, she might increase sales projections for November and December to reflect the holiday season, and adjust sales projections for other months based on other seasonal factors.

Review and adjust: Gabi should regularly review her sales forecast and adjust it as needed based on actual sales performance and any changes in market conditions.

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Based on the given information that P(A|B) = 0.4 and P(A) = 0.4, we can conclude that Event A is dependent on Event B. This corresponds to answer option (B) among the choices.

The conditional probability P(A|B) represents the probability of Event A occurring given that Event B has already occurred. In this case, P(A|B) = 0.4, indicating that Event A is influenced by the occurrence of Event B.

If Event A were independent of Event B, the conditional probability P(A|B) would be equal to the marginal probability P(A). However, since P(A|B) ≠ P(A), we can conclude that Event A is dependent on Event B.

Therefore, answer option (B) is the correct conclusion: Event A is dependent on Event B.

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To find the height above the pool deck where the two divers pass each other, we need to set the functions u(t) = –16t² + 4t + 33 and v(t) = 2t equal to each other and solve for t.

Setting u(t) = v(t), we have:

–16t² + 4t + 33 = 2t

Combining like terms:

–16t² + 2t + 33 = 0

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = -16, b = 2, and c = 33. Plugging these values into the quadratic formula:

t = (-2 ± √(2² - 4(-16)(33))) / (2(-16))

Simplifying further:

t = (-2 ± √(4 + 2112)) / (-32)

t = (-2 ± √2116) / (-32)

t = (-2 ± 46) / (-32)

We have two possible values for t:

t₁ = (46 - 2) / (-32) = 44 / (-32) = -11/8

t₂ = (-46 - 2) / (-32) = -48 / (-32) = 3/2

Since time cannot be negative, we discard t₁ = -11/8. Therefore, the two divers pass each other at t = 3/2 seconds.

To find the height above the pool deck at t = 3/2 seconds, we substitute this value into either of the functions. Let's use u(t):

u(3/2) = -16(3/2)² + 4(3/2) + 33

u(3/2) = -16(9/4) + 6/2 + 33

u(3/2) = -36/2 + 6/2 + 33

u(3/2) = (-36 + 6 + 66)/2

u(3/2) = 36/2

u(3/2) = 18

Therefore, the two divers pass each other at a height of 18 feet above the pool deck.

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Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  \(x = 12.7\)

Population standard deviation of  \(\sigma = 6.37\)

Sample size of .n = 50

The margin of error is:

\(M = z \frac{\sigma }{\sqrt{n} }\)

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  \(\frac{1+\alpha }{2}\) , in which  \(\alpha\) is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

Answer:

=

−

2

Step-by-step explanation: Distribute −

3

(

4

+

3

)

=

5

(

2

+

7

)

−

1

2

−

9

=

5

(

2

+

7

)

Answer:

6.4 x 10¹¹

Step-by-step explanation:

(8 x 10⁵)(8 x 10⁵) = 6.4 x 10¹¹

Answer:

D. 23​

Step-by-step explanation:

To find f(-2) for the function f(x) = 3x^2 - 2x + 7, we need to substitute x = -2 into the function and calculate the value.

Let's substitute x = -2 into the function:

f(-2) = 3(-2)^2 - 2(-2) + 7

Now, let's simplify the expression:

f(-2) = 3(4) + 4 + 7

= 12 + 4 + 7

= 16 + 7

= 23

Therefore, f(-2) = 23.

Answer:

$1278.23

Step-by-step explanation:

The area of the triangle is 4.5 square unit.

We have, y= 4x/ (1 + x³)

Now, differentiating the above equation wrt to x we get

y' = 4(1 + x³)- 4x . 3x² / (1+ x³)²

y'= -8x³ + 4/ (1+x³)²

When x = 1 then y' = -4/4 = -1

so, y -2 = -1 (x-1)

y= -x+ 3

Here the x intercept is (3, 0) and y intercept is (0, 3).

so, Area of Triangle is

= 1/2 x 3 x 3

= 9/2

= 4.5 square unit

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Answer:

6 packages

Step-by-step explanation:

30/5 is 6

Answer:

the answer is 6

Step-by-step explanation:

30 divided by 5

The number of equilibrium points for the given nonlinear system is 3.

To find the equilibrium points, we need to set both equations to zero and solve for x and y:

1. x′ = y² − xy = 0
2. y′ = x³y² − x = 0

First, let's look at equation 2. We can factor x out:

x(y²x² - 1) = 0

There are two possibilities:

a. x = 0: Substitute x = 0 in equation 1:

y² - 0 = y² = 0 => y = 0

So, we have one equilibrium point (0, 0).

b. y²x² - 1 = 0: Replacing this in equation 1:

y² - (y²x² - 1)y = 0

Factor out y:

y(y²(1 - x²) - 1) = 0

There are two more possibilities:

i. y = 0: We already considered this case (0, 0).

ii. y²(1 - x²) - 1 = 0: This equation gives us two equilibrium points: (-1, 1) and (1, 1).

Thus, the system has a total of 3 equilibrium points: (0, 0), (-1, 1), and (1, 1).

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Answer: 2/3

Step-by-step explanation:

You can do cross multiplication 12 x 2 = 24 and 3 x 8 = 24

Answer:

The answer is A.

Step-by-step explanation:

The answer is A because if you divide the price by how many are sold it comes out to 14.75.

Answer: A

Step-by-step explanation:

1 book cost $14.75

2 books cost $29.50

3 books cost $44.25

4 books cost $59.00

5 books cost $73.75

6 books cost $88.50

7 books cost $103.25

Answer:

C. 12

Step-by-step explanation:

16 divided by 4 is 4 which means 1/4 of 16 equals 4. If you want 3/4 of 16, you multiply 4 by 3 which is 12.

Here the diameter = dm

Formula of circumference for circle: 2πr  or  πd

                                        where "d" is diameter and "r" is radius

For this question:

circumference:

Thus,  the average cost per unit for an output of q units is given by the equation c/q = 12000/q + 7, where the fixed cost is $12,000 and the variable cost is given by the function cv = 7q.

The given equation for the total cost of producing q units of a product is c = 5000 + 6q.

To find the average cost per unit for an output of q units, we need to divide the total cost by the number of units produced.

Thus, the average cost per unit can be written as c/q.

Substituting the given equation for c in terms of q, we get

c/q = (5000 + 6q)/q.

Simplifying this expression, we get c/q = 5000/q + 6.

Now, we are given that the fixed cost is $12,000 and the variable cost is given by the function cv = 7q.

The total cost equation c can be written as the sum of the fixed cost and the variable cost, i.e., c = 12000 + cv. Substituting the given equation for cv, we get c = 12000 + 7q.

Substituting this equation for c in terms of q in the expression we derived earlier for c/q, we get c/q = (12000 + 7q)/q. Simplifying this expression, we get c/q = 12000/q + 7.

Therefore, the average cost per unit for an output of q units is given by the equation c/q = 12000/q + 7, where the fixed cost is $12,000 and the variable cost is given by the function cv = 7q.

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Answer:

3,000 feet

A calculator will help you get the answer that you need.

The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:

n = 9604.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The margin of error is modeled as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

We have no estimate of the proportion, hence it is used as follows:

\(\pi = 0.5\)

The margin of error is of M = 0.01, hence the sample size is obtained as follows:

\(0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.01\sqrt{n} = 1.96 \times 0.5\)

\(\sqrt{n} = 98\)

n = 98²

n = 9604.

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Answer:

43%

Step-by-step explanation:

There are 39 girls. 21 of them like biology. 11 out of 34 who like chemistry are girls.

No. of girls who prefer biology = 21

There are (100-39) boys. 16 of them like physics. (34-11) of them like chemistry.

No. of boys who prefer biology = 100-39-16-34+11

                                                    = 22

Percentage of students who prefer biology = \(\frac{21+22}{100}\) × 100%

                                                                        = \(\frac{43}{100}\) × 100%

                                                                        = 43%

The term you are looking for is the "z-value." The z-value for a point is the number of standard errors a point is away from the mean.

The z-value for a point is the number of standard errors a point is away from the mean. This is a long answer but it accurately explains the concept.

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The rate of change of the circle diameter with respect to the radius is a constant value of 2.

The diameter of a circle is twice the radius, so we can write:

Diameter = 2 * Radius

To find the rate of change of the diameter with respect to the radius, we can take the derivative of both sides of this equation with respect to the radius:

diameter/d(radius) = d(2 * radius)/d(radius)

The derivative of 2*radius with respect to radius is simply 2, so we can simplify the equation:

diameter/d(radius) = 2

Therefore, the rate of change of the circle diameter with respect to the radius is a constant value of 2. This means that if we increase the radius by a small amount, the diameter will increase by twice that amount. Conversely, if we decrease the radius by a small amount, the diameter will decrease by twice that amount.

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Your answer should be:She can make 92 key chains with the yarns she has.

Step-by-step explanation

1. Let's add and see the total of yarns she has!

36 + 216 + 24 = 276

2. Let's divide the total we got in 1 by the yard she needs to make one key chain!

276 ÷ 3 = 92

3. Your answer should be 92.