Kaitlin is riding her bike. The number of revolutions (turns) her wheels make varies directly with the distance she travels. See the graph below.



How far does Kaitlin travel per revolution?

What is the slope of the graph?

Answer:

95.73%

Step-by-step explanation:

Given data:

mean μ= 95

standard deviation, σ = 11

to calculate, the probability that a randomly selected firm will earn less than 114 million dollars;

Use normal distribution formula

[tex]P(X<114)=P(Z<\frac{X-\mu}{\sigma} )[/tex]

Substitute the required values in the above equation;

[tex]P(X<114)=P(Z<\frac{114-95}{11} )\\P(X<114)=P(Z<1.7272)\\P(X<114)=0.9573[/tex]

Therefore, the probability that a randomly selected firm will earn less than 114 million dollars = 95.73%

Answer:

f(n+1=-2f(n)

f(x)=-2f(n)

f(4)

f(4)=-2f(4)

Answer:

f(4) = - 1280

Step-by-step explanation:

Using the recursive rule and f(1) = 60 , then

f(2) = - 2f(1) = - 2 × 160 = - 320

f(3) = - 2f(2) = - 2 × - 320 = 640

f(4) = - 2f(3) = - 2 × 640 = - 1280

Answer:

Note: See the attached photo for the graph showing Weight Not Over (lbs.) vs Price($). The attached excel file also shows the same graph with the data used to draw it in the excel.

Step-by-step explanation:

In the attached graph, Weight Not Over (lbs.) is on the horizontal axis while Price ($) is on the vertical axis.

From the attached, it can be observed that the graph shows an upward trend. That implies that there is a positive relation between Weight Not Over (lbs.) and Price. That is, as Weight Not Over (lbs.) rises, the Price also rises.

Answer:

80 telephones should be sampled

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

89% confidence level

So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].

How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?

n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.09\sqrt{n} = 1.6*0.5[/tex]

[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]

[tex]n = 79.01[/tex]

Rounding up(as 79 gives a margin of error slightly above the desired value).

80 telephones should be sampled

Answer:

f(3) = g(3)

Step-by-step explanation:

on the graph the only point, where both lines cross (both functions create the same functional value) is at x=3.

since both lines have the same y-value there, we express this in math by the "=" sign. and both functions have the same input value (x=3) there.

Answer:

E. by the SAS similarity theorem.

Step-by-step explanation:

Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)

DC/BC = 240/150 = 1.6

EC/AC = 320/200 = 1.6

This implies that the ratio of two corresponding sides of both triangles are the same.

Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.

Answer:

y = 5x + 1

Step-by-step explanation:

Given the coordinate points (0,1) and (5,0)

First, get the slope

Slope m =(0-1)/5-0

m = -1/5

Since the required line is perpendicular, then the required slope is;

M = -1/(-1/5)

M = 5

Since 1the y intecept id (0,1) i.e. 1

Required equation is y = mx+b

y = 5x + 1

This gives the required equation

Note that the coordinate (0,1) was used instead os (0,0)

Answer:

The equation of the tangent line is [tex]y = -\frac{5}{18}\cdot x +\frac{14}{9}[/tex].

Step-by-step explanation:

Firstly, we obtain the equation for the slope of the tangent line by implicit differentiation:

[tex]2\cdot x + 6\cdot y + 6\cdot x \cdot y' + 24\cdot y \cdot y' = 0[/tex]

[tex]2\cdot (x + 3\cdot y) + 6\cdot (x + 4\cdot y) \cdot y' = 0[/tex]

[tex]6\cdot (x + 4\cdot y) \cdot y' = -2\cdot (x+3\cdot y)[/tex]

[tex]y' = -\frac{1}{3}\cdot \left(\frac{x + 3\cdot y}{x + 4\cdot y} \right)[/tex] (1)

If we know that [tex](x,y) = (2, 1)[/tex], then the slope of the tangent line is:

[tex]y' = -\frac{1}{3}\cdot \left(\frac{2+3\cdot 1}{2 + 4\cdot 1} \right)[/tex]

[tex]y' =-\frac{5}{18}[/tex]

By definition of tangent line, we determine the intercept of the line ([tex]b[/tex]):

[tex]y = m\cdot x + b[/tex]

[tex]b = y - m\cdot x[/tex] (2)

If we know that [tex](x,y) = (2,1)[/tex] and [tex]m = -\frac{5}{18}[/tex], then the intercept of the tangent line is:

[tex]b = 1 - \left(-\frac{5}{18} \right)\cdot (2)[/tex]

[tex]b = \frac{14}{9}[/tex]

The equation of the tangent line is [tex]y = -\frac{5}{18}\cdot x +\frac{14}{9}[/tex].

Answer:

17 miles

By adding the miles they have traveled, you get you total distance.

Answer:

The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Step-by-step explanation:

Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:

7000 x 0.11 + 1000 x 0.05 = X

770 + 50 = X

820 = X

8000 = 100

820 = X

820 x 100/8000 = X

82,000 / 8,000 = X

10.25 = X

Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Answer:

2sin.2(x) sd s

Step-by-step explanation:

Answer:

6m + 8 is the answer.

Step-by-step explanation:

( m x 6 ) + 8

= 6m + 8

Answer:

the answer is d

Step-by-step explanation:

because when we put-1 from x the equation hasn't any value

Hey there!

We are given two functions - one is Exponential while the another one is Linear.

[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]

1. Operation of Function

[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]

2. Substitution

[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]

3. Evaluate/Simplify

[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]

4. Final Answer

Answer:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]

[tex]P(x < 70) = 0.225[/tex]

Step-by-step explanation:

Given

[tex]Lower = 30[/tex]

[tex]Width = 10[/tex]

Solving (a): The relative frequency table

First, we construct the frequency table using the given parameters.

[tex]\begin{array}{cc}{Class} & {Frequency} &{30-39} & {1} & {40-49} & {1} & {50 - 59} & {2} & {60 - 69} & {5} & {70 - 79} & {13} & {80 - 89} & {10} & {90 - 99} & {8} & {Total} & {40}\ \end{array}[/tex]

The relative frequency (RF) is calculated as:

[tex]RF = \frac{Frequency}{Total}[/tex]

Using the above formula to calculate the relative frequency, the relative frequency table is:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]

Solving (b): [tex]P(x < 70)[/tex]

To do this, we add up the relative frequencies of classes less than 70.

i.e.

[tex]P(x < 70) = [30 - 39] + [40 - 49] + [50 - 59] + [60 - 69][/tex]

So, we have:

[tex]P(x < 70) = 0.025 + 0.025 + 0.050 + 0.125[/tex]

[tex]P(x < 70) = 0.225[/tex]

Answer:

The mean of the sampling distribution is always equal to the mean of the population.

The mean of the sampling distribution of the sample mean is 45.

Given that,

Based on the above information, the calculation is as follows:

= mean of the random variable X

= 45

As the sampling distribution mean should always be equivalent to the population mean.

Therefore we can conclude that the mean of the sampling distribution of the sample mean is 45.

Learn more: brainly.com/question/521501

Answer:

The rotation rule states that rotation 90° counterclockwise means (x, y) = (-y, x)

The new points would be equal to:

Try graphing it to see if the new points make sense(because I'm not too sure :\)

Answer:

Volume = 63 feet

Step-by-step explanation:

To find the volume of a cube or a rectangular prism, the formula is

(L x W x H)/3. In other words, it is the length of the prism, times the width of the prism, times the height of the prism, whole divided by three, since it has a "triangular shape."

Let's substitute in values for these letters, L, W, and H. You said the length was 7, the width was 6, and the height was 4.5. Therefore, it will result in

(7 x 6 x 4.5)/3. That results in 189/3, which is 63.

Hope this helped!!!

Answer:

The equation is [tex]A(d) = 80 - 4d[/tex]

Step-by-step explanation:

Linear function:

A linear function for the amount of money in an account after t days is given by:

[tex]A(d) = A(0) - md[/tex]

In which A(0) is the initial value and m is the daily cost.

Your EZ Pass account begins with $80. It costs you $4/day.

This means that [tex]A(0) = 80, m = 4[/tex]

So

[tex]A(d) = A(0) - md[/tex]

[tex]A(d) = 80 - 4d[/tex]

Answer:

[tex]\mu =2.16[/tex] --- Mean

[tex]\sigma^2 = 1.4944[/tex] -- Variance

[tex]\sigma = 1.222[/tex] --- Standard deviation

Step-by-step explanation:

Given

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.12} & {0.2} & {0.2} & {0.36} & {0.12} \ \end{array}[/tex]

Solving (a): The population mean

This is calculated as:

[tex]\mu = \sum x * P(x)[/tex]

So, we have:

[tex]\mu =0*0.12 + 1 * 0.2 + 2 * 0.2 + 3 * 0.36 + 4 * 0.12[/tex]

[tex]\mu =2.16[/tex]

Solving (b): The population variance

First, calculate:

[tex]E(x^2)[/tex] using:

[tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2*0.12 + 1^2 * 0.2 + 2^2 * 0.2 + 3^2 * 0.36 + 4^2 * 0.12[/tex]

[tex]E(x^2) =6.160[/tex]

So, the population variance is:

[tex]\sigma^2 = E(x^2) - \mu^2[/tex]

[tex]\sigma^2 = 6.16 - 2.160^2[/tex]

[tex]\sigma^2 = 6.160 - 4.6656[/tex]

[tex]\sigma^2 = 1.4944[/tex]

Solving (c): The population standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\sigma^2}[/tex]

[tex]\sigma = \sqrt{1.4944}[/tex]

[tex]\sigma = 1.222[/tex]

divide .2÷20 =10 10 students are Studing word problems

Answer:

19219.48

Step-by-step explanation:

16540x0.162+16540

The original price would be 100%

It was marked down 16.2%

100 % - 16.2% = 83.8%

The price you paid was 83.8% of the original price.

To find the original price divide the amount you paid by the percentage of the original price:

16,540 / 0.838 = 19.737.47

Original price: $19,737.47

Answer:

When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.

Step-by-step explanation:

Exponential model:

The variable keeps growing consistently, at a fixed rate.

Logistic model:

The variable starts growing, but as it approaches a limit, for example, the carry capacity of an environment, the growth rate starts to decrease, until the variable stabilizes at a fixed value.

Growth of smartphones shipped from manufacturers to stores around the world.

When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.

Answer:

[tex] L + C \ge 12 [/tex]

Step-by-step explanation:

L = hours landscaping

C = hours clearing tables

The sum of the hours must be no less than 12, so it must be 12 or more.

[tex] L + C \ge 12 [/tex]

Answer:

You can go ahead with option D

Step-by-step explanation:

The probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"

For given question,

a bag contains 12 red, 3 white and 1 blue balls.

Total balls = 12 + 3 + 1

Total = 16

Two balls are drawn from a bag.

The number of possible ways of drawing 2 balls from the bag are:

Using combination formula,

[tex]^{16}C_2\\\\=\frac{16!}{2!(16-2)!}\\\\ =\frac{16!}{2!\times 12!}\\\\ =120[/tex]

So, n(S) = 120

Two balls are drawn with replacement from a bag.

We need to find the probability that both are red.

Let event A: both the balls are red

[tex]\Rightarrow n(A)=^{12}C_2[/tex]

Using combination formula,

[tex]^{12}C_2\\\\=\frac{12!}{2!\times (12-2)!}\\\\= \frac{12!}{2!\times 10!}\\\\ =66[/tex]

Using probability formula,

[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\\Rightarrow P(A)=\frac{66}{120}\\\\\Rightarrow P(A)=\frac{11}{20}[/tex]

Therefore, the probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

Answer:

D. None of the above

Step-by-step explanation:

Both triangles have the same shape but different size. Their area cannot be the same. Also, the ratio of their corresponding side lengths are the same.

Thus:

8/4 = 10/5 = 6/3 = 2

This implies that both triangles are similar.

Therefore, both triangles cannot have the same area, they are not of the same size and cannot be congruent to each other.

Answer:

[tex]z = 1.6[/tex]

Step-by-step explanation:

Given

[tex]Pr = 0.05[/tex]

Required

The z value to the right

The z value to the right is represented as:

[tex]P(Z > z)[/tex]

So, the probability is represented as:

[tex]P(Z > z) = 0.05[/tex]

From z table, the z value that satisfies the above probability is:

[tex]z = 1.645[/tex]

[tex]z = 1.6[/tex] --- approximated

Answer:

-7

Step-by-step explanation:

If it is 7 below (a key word, which you can connect to 'negative'), then you just write it as -7.