The annual rainfall in Frostbite Falls is normally distributed with mean
32 inches and standard deviation 5 inches.
What is the probability that, in a given year, the rainfall is over 40
inches?

Step-by-step explanation:

This is a geometric series, where the first term is -5 and the common ratio is -⅔.

aₙ = -5 (-⅔)ⁿ⁻¹

The answer to number 2 is- no it's not a right triangle

the answer to number 3 is- yes it is a right triangle

The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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Answer:

A = 60 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 14*5

A = 60 cm^2

\( area \: of \: parallelogram \: = \: base \times height\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: a \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: 14cm \times 5cm\)

\(a \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 70 {cm}^{2} \)

Answer: Chuck can paint 65 posts per hour.

Step-by-step explanation:

The data we have here is:

Diana can paint 150 fence posts in a time T

Chuck can pint 130 fence posts in a time T.

In one hour, Diana can paint 10 more fence posts than Chuck.

If D is the hourly rate of Daian, and C is the hourly rate for Chuck, we have:

D = 150/T

C = 130/T

D = C + 10

we can replace the last equation in the first one and geT:

C + 10 =150/T

C = 130/T

Now we can replace the bottom equation in the above one:

130/T + 10 = 150/T

10 = 150/T - 130/T =  20/T

T*10 = 20

T = 20/10 = 2

So T is 2 hours, then whe have:

D = 150post/2hours = 75 posts per hour.

C = 130 posts/2hours = 65 posts per hour.

Answer:

This means that the fraction 3/4 is 3 out of 4 equal parts. So, count 3 parts from 0 and you will get 3/4. That's it! You've shown the fractions 1/4 and 3/4 on a number line!

Step-by-step explanation:

It is.

Answer:

This means that the fraction 3/4 is 3 out of 4 equal parts. So, count 3 parts from 0 and you will get 3/4. That's it! You've shown the fractions 1/4 and 3/4 on a number line!

Step-by-step explanation:

The math is just correct

Answer:

225 calories

Step-by-step explanation:

1 recipe makes

12 standard sized pancakes

2 pancakes are 1/6 of the recipe

1/6 of the recipe has 150 calories

6 × 150 calories = 900 calories

The full recipe of 12 pancakes has 900 calories

1/2 recipe was made

1/2 recipe has 1/2 × 900 calories = 450 calories

1/2 recipe made 8 pancakes

4 pancakes are half of the half recipe or 1/4 recipe

1/4 × 900 calories = 225 calories

The number of cookbooks = 3.

The number of travel books = 5

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Cookbook.

Number = x

Cost = $1

Travel book.

Number = y

Cost = $8

Now,

We can make an equation.

Total cost = $43

So,

x + y = 8

x = 8 - y _____(1)

x + 8y = 43 _____(2)

Substituting (1) in (2).

8 - y + 8y = 43

8 + 7y = 43

7y = 43 - 8

7y = 35

y = 5

And,

x = 8 - y

x = 8 - 5

x = 3

Thus,

The number of cookbooks = 3.

The number of travel books = 5

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9514 1404 393

Answer:

  2.244

Step-by-step explanation:

Your answer looks like it may have a transcription error.

The period is reasonably computed as the difference of the x-values of the given points:

  period = 4.114 -1.870 = 2.244 . . . seconds

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer: 6

Step-by-step explanation:

1 + 1 + 4

2 + 4

6

The x-intercept of CD is -7, and the point (-7, 0) lies on CD.

How to find the x-intercept of a line that is perpendicular to another line and passes through a given point?

To find the x-intercept of a line that is perpendicular to another line and passes through a given point, we first need to determine the equation of the perpendicular line using the point-slope form of a line. This involves using the given point and the slope of the original line. The slope of the perpendicular line is the negative reciprocal of the slope of the original line. Once we have the equation of the perpendicular line, we can find the x-intercept by setting y = 0 and solving for x.

Calculation of the intercept and the point passing lies on CD -

To find the x-intercept of CD, we need to first determine the equation of CD. Since CD is perpendicular to AB and passes through point C, we can use the point-slope form of the equation of a line:

\(y - y_1 = m(x - x_1)\)

where \((x_1, y_1) = (5, 12)\) is the given point on CD, and m is the slope of AB. To find the slope of AB, we use the slope formula:

\(m = (y_2 - y_1)/(x_2 - x_1)\)

where \((x_1, y_1) = (-10, -3)\) and \((x_2, y_2) = (7, 14)\) are the given points on AB:

\(m = (14 - (-3))/(7 - (-10)) = 17/17 = 1\)

Substituting the values of \((x_1, y_1)\), m, and simplifying the equation, we get:

\(y - 12 = 1(x - 5)\)

\(y = x - 5 + 12\)

\(y = x + 7\)

To find the x-intercept, we set \(y=0\) and solve for x:

\(0 = x + 7\)

\(x = -7\)

Therefore, the x-intercept of CD is -7, and the point (-7, 0) lies on CD.

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Answer:

Thus, the x-intercept of CD is 17 and The point lies on CD is (2, 19).

Step-by-step explanation:

Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.

Answer:

P(Red) = 1/3

Step-by-step explanation:

Total number of marbles = 15

5 red

6 green

4 blue

Answer:

M=$75

Step-by-step explanation:

I used M for money that Heather earned.

$20+M=$95

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.

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The ordered pair which is a solution to every linear equation of the form given is; (0, 0).

It follows from the task content that the ordered pair which satisfies the equation of the form y =Mx be determined.

On this note, since the product of any real number, slope in this scenario and 0 is; 0.

Ultimately, it follows that the required ordered pair is; (0, 0) for any real number value of the slope, m.

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Answer:

200 Square yards = $700

Price per carpet = $3.5

Step-by-step explanation:

Find price per carpet first

Let x = price of 1 square yard of carpet

66x = $231.00

x = $3.5

200x = $700

Answer:

13f=29

Step-by-step explanation:

I hope this helps you out!

Answer:

The critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998.

The test statistic (t=1.729) is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.

Step-by-step explanation:

We have a matched-pair t-test for the difference.

We have the null and alternative hypothesis written as:

\(H_0: \mu_d=0\\\\H_a: \mu_d>0\)

We have n=8 pairs of data. We calculate the difference as:

\(d_1=U_1-A_1=36.4-28.5=7.9\)

Then, with this procedure we get the sample for d:

\(d=[7.9,\, 35,\, 5.5,\, 4.2,\, 6.7,\, -3.7,\, -0.9,\, 3.3]\)

The sample mean and standard deviation are:

\(M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(7.9+35+5.5+. . .+3.3)\\\\\\M=\dfrac{58}{8}\\\\\\M=7.25\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((7.9-7.25)^2+(35-7.25)^2+(5.5-7.25)^2+. . . +(3.3-7.25)^2)}\\\\\\s=\sqrt{\dfrac{985.08}{7}}\\\\\\s=\sqrt{140.73}=11.86\\\\\\\)

Now, we can perform the one-tailed hypothesis test.

The significance level is 0.01.

The sample has a size n=8.

The sample mean is M=7.25.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.86.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{11.86}{\sqrt{8}}=4.1931\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.25-0}{4.1931}=\dfrac{7.25}{4.1931}=1.729\)

The degrees of freedom for this sample size are:

\(df=n-1=8-1=7\)

This test is a right-tailed test, with 7 degrees of freedom and t=1.729, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t>1.729)=0.0637\)

As the P-value (0.0637) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.

If we use the critical value approach, the critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998. The test statistic is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.

1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Answer:

37.5

Step-by-step explanation:

If 50 apples cost 25 then all you need to do is 25 x 1.5 = 37.5

And we know this is correct because 25 divided by 2 is 12.5.

so 12.5 is how much for 25 apples and if you multiply 25 times 3 it is equal to 75 so you need to mutliply 12.5 times 3.

12.5 x 3 = 37.5

Answer:

227826

i used a calculator

18 x 12,657= 227,826

Please comment if you have further questions to this problem.

Answer:

1. (0,5), (0,9), (10,4), (10,0), (5,0)

2. \(Q_{max}=912\)

\(Q_{min}=300\)

Step-by-step explanation:

1.

In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.

The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.

0+y=5

y=5

(0,5)

The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:

0+2y=18

\(y=\frac{18}{2}\)

y=9

(0,9)

The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:

10+2y=18

2y=18-10

2y=8

\(y=\frac{8}{2}\)

y=4, so the oint is

(10,4)

The next point is the intercept between the lines x=10 and y=0, so the point is:

(10,0)

The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:

x+0=5

x=5

so the point is:

(5,0).

2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.

(0,5)

Q=60(0)+78(5)

Q=390

(0,9)

Q=60(0)+78(9)

Q=702

(10,4)

Q=60(10)+78(4)

Q=912

(10,0)

Q=60(10)+78(0)

Q=600

(5,0)

Q=60(5)+78(0)

Q=300

So now we compare the answers and pick the minimum and maximum results.

We get that:

\(Q_{max}=912\)

when x=10 and y=4

and

\(Q_{min}=300\)

When x=5 and y=0

The feasible region is the possible set of a constraint

(a) The coordinates of the vertices at the feasible region

The constraints are given as:

\(\mathbf{x \ge 0}\)

\(\mathbf{y \ge 0}\)

\(\mathbf{x \le 0}\)

\(\mathbf{x + y\ge 5}\)

\(\mathbf{x + 2y\ge 18}\)

See attachment for the graph of the constraints

From the graph, the vertices are:

\(\mathbf{(x,y) \to (0,5), (0,9), (5,0)}\)

(b) The minimum and the maximum values of objective function Q

The objective function is:

\(\mathbf{Q=60x +78y}\)

Substitute \(\mathbf{(x,y) \to (0,5), (0,9), (5,0)}\) in Q

\(\mathbf{Q=60(0) +78(5) = 390}\)

\(\mathbf{Q=60(0) +78(9) = 702}\)

\(\mathbf{Q=60(5) +78(0) = 300}\)

Hence, the maximum and the minimum values are 702 and 300, respectively.

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30

you can easily find out the answer by multiplying 2/3 by 10 on both the numerator and denominator to get 20/30 which is the amount of people that like the chip flavor. the other 10 is the people that don't like it.sorry if I gave you a stroke but 20 people like the chip and 10 people don't so theres 30 people in total

Answer: The length is 8 yards

Step-by-step explanation: First, take the volume of the prism (115 cubic yards), divide it by the width (2 1/2), the divide that by the height (5 3/4) getting you the length: 8 yards

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

3n

Step-by-step explanation:

3 x n

simplifies to be

3n

hope this helps

Answer:

a) x=0, x=1

b)x=0, x=4/3

Step-by-step explanation:

I didnt use the graph, just used algebra. For part a, you can find the answers using the graph by looking at the value of x when y = whatever value they give.

A)

3x²-3x+2=2

3x²-3x+0

x(3x-3)=0

For the product of two things to equal zero, one of them has to be zero. For example, if ab=0, then either a or b (or both) are zero.

Therefore..

x=0

or 3x-3=0, ∴x=1

b)

3x²-3x-1 = x-1

3x²-4x=0

x(3x-4)=0

∴x=0, x=4/3

Answer:

I checked it over twice the first guy is correct make him brainliest

Step-by-step explanation: