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What is the equation of the trend line in the scatter plot ?

Answer: 40 degrees

Step-by-step explanation: Complementary angles always have a sum of 90 degrees. In order to find the other complementary angle take 90 and subtract 50 in order to get your missing value (value of the other angle).

Answer: 6120

Step-by-step explanation:

The equation for the interior angles of a polygon is (n-2)180. So using the equation, (36-2)180=(34)180=6120.

Answer:

The null hypothesis is [tex]H_0: p_1 - p_2 = 0[/tex]

The alternate hypothesis is [tex]H_a: p_1 - p_2 \neq 0[/tex]

The pvalue of the test is 0.03 < 0.05, which means that we have enough evidence to accept the alternative hypothesis that he proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

Step-by-step explanation:

Before testing the null hypothesis, we need to understand the Central Limit Theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Out of 500 randomly selected people who rode a jet ski, 85% wore life vests.

This means that [tex]p_1 = 0.85, s_1 = \sqrt{\frac{0.85*0.15}{500}} = 0.016[/tex]

Out of 250 randomly selected boaters, 90.4% wore life vests.

This means that [tex]p_2 = 0.904, s_2 = \sqrt{\frac{{0.904*0.096}{250}} = 0.019[/tex]

Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

At the null hypothesis, we test that the proportions are the same, that is, the subtraction between them is zero. So

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternate hypothesis, we test that the proportions are different, that is, the subtraction between them is different of zero. So

[tex]H_a: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples, we have that:

[tex]X = p_1 - p_2 = 0.85 - 0.904 = -0.054[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.016^2 + 0.019^2} = 0.0248[/tex]

Test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.054 - 0}{0.0248}[/tex]

[tex]z = -2.17[/tex]

Pvalue of the test and decision:

The pvalue of the test is the probability that the difference differs from 0 by at least 0.054, which is P(|Z| > 2.17), which is 2 multiplied by the pvalue of z = -2.17

Looking at the z-table, z = -2.17 has a pvalue of 0.015

2*0.015 = 0.03

The pvalue of the test is 0.03 < 0.05, which means that we have enough evidence to accept the alternative hypothesis that he proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

Answer:

A

Step-by-step explanation:

Because it's reflected across the x-axis, the x coordinate doesn't change. On the other hand, the y coordinate becomes its opposite. So we get:

(4, 2) -> (4, -2)

Answer:

Eighteen point zero one

Step-by-step explanation:

Eighteen point zero one

Answer:

−60x + 135

Step-by-step explanation:

Answer:

150 - (0.4×150+15)

= 150-75

= 75

Answer:

1/6

Step-by-step explanation:

Given the following data;

A single fair die = 6

To find an outcome of A5;

Since the die was tossed just once, the outcome would be a fraction of the total number of outcomes.

P(A5) = number of times tossed/total number of outcomes

P(A5) = 1/6

Answer:

2 1/5

Step-by-step explanation:

4 3/5 - 2 2/5

I like to make them vertical

4 3/5

- 2 2/5

-----------------

2 1/5

Answer:

y = (3/2)x - 4

Step-by-step explanation:

Use (y2-y1)/(x2-x1) to find slope, and then y-intercept is -4.

Answer:

jnnm mnn m

Step-by-step explanation:

Answer:

Agree

Step-by-step explanation:

Answer:

243 ft^3

Step-by-step explanation:

The volume of a triangular prism is the triangular base times the height.

To get the area of the triangle, multiply the base time height and divide by 2.

9*6/2=27

Now multiply by the height

27*9=243

Answer: 243 ft^3

Answer:

243ft^3

Step-by-step explanation:

Answer:

119 hotdogs

Step-by-step explanation:

Let 7x = no. of hotdogs

then 3x = no. of hamburgers

3x = 51

x = 17

7(17) = 119 hotdogs

Answer:

3rd Option, 33° = ∠PCB

Step-by-step explanation:

First find the measure of ∠CPB;

∠CPB = 180 - 105

∠CPB = 75

Now we can find the measure of ∠PCB;

180 - (Angle 1 + Angle 2)

180 - (75 + 72)

33 = ∠PCB

Hope this helps!

Answer:

H0: mu = 120 , Ha: : mu not equal to 120

The p-value  is greater than or equal to 0.10

z= -1.636

Since the calculated value of  z does not fall in the critical region H0 is not rejected.

Step-by-step explanation:

State the null and alternate hypothesis

H0: mu = 120

average braking distance for a small car traveling at 65 miles per hour equals 120 feet.

against the claim

Ha: : mu not equal to 120

average braking distance for a small car traveling at 65 miles per hour  does not equal 120 feet.

The p-value equals 0.101764 which is greater than 0.01 and thus supports H0.

The p-value  is greater than or equal to 0.10

The test statistic z is applied

Here

Sample Mean  x~ = 114

Population mean μ =120

Sample size n= 36

Population SD =σ= 22

Z= u- μ/σ√n

Z= 114- 120/ 22/ √36

z= -1.636

This is a two tailed test and the critical region for two tailed test at alpha = 0.01 is z ∝/2= ± 2.58

Since the calculated value of  z does not fall in the critical region H0 is not rejected.

Answer:

$1,545

Step-by-step explanation:

3% of 1500 is 45

1500 + 45 = 1545

Answer:

1.8 in.

Step-by-step explanation:

Hi there!

1) Determine the radius of the base

[tex]V=\frac{1}{3} \pi r^2h[/tex] where r is the radius of the base and h is the height of the cone

Plug in the known values (h=4.2, V=3.6)

[tex]3.6=\frac{1}{3} \pi r^2(4.2)[/tex]

Isolate r; divide both sides by 4.2

[tex]\frac{3.6}{4.2} =\frac{1}{3} \pi r^2\\\frac{6}{7} =\frac{1}{3} \pi r^2[/tex]

Multiply both sides by 3

[tex]\frac{6}{7}*3 =\pi r^2\\\frac{18}{7}=\pi r^2[/tex]

Divide both sides by π

[tex]\frac{18}{7\pi }=r^2[/tex]

Take the square root of both sides

[tex]\sqrt{\frac{18}{7\pi }} =r[/tex]

2) Determine the diameter

Now that we have the radius, to find the diameter, multiply r by 2:

[tex]d=\sqrt{\frac{18}{7\pi }}*2\\d=1.8[/tex]

Therefore, the diameter is 1.8 in. when rounded to the nearest tenth.

I hope this helps!

Answer:

1.8 in

Step-by-step explanation:

we know the equation for the volume of a cone is pi*r^2 h/3=3.6

pi r^2 *4.2=10.8

solve for r

r is about 0.9 so diameter is 1.8 in

Answer:

f(3) = -41

Step-by-step explanation:

f(x) = x³-9x²+5x-2

now,

f(3) = 3³-9×(3)²+5×3-2

= 27-9×9+5×3-2

= 27-81+15-2

= -41

Step-by-step explanation:

The graph of a quadratic equation in two variables (y = ax^2 + bx + c ) is called a parabola. The following graphs are two typical parabolas their x-intercepts are marked by red dots, their y-intercepts are marked by a pink dot, and the vertex of each parabola is marked by a green dot: (Given in attachment for diagram)

We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape). In order to graph a parabola we need to find its intercepts, vertex, and which way it opens.

Given y = ax^2 + bx + c , we have to go through the following steps to find the points and shape of any parabola:

Label a, b, and c.

Decide the direction of the paraola:

If a > 0 (positive) then the parabola opens upward.

If a < 0 (negative) then the parabola opens downward.

Find the x-intercepts:

Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0. We can find these points by plugging 0 in for y and solving the resulting quadratic equation (0 = ax^2 + bx + c). If the equation factors we can find the points easily, but we may have to use the quadratic formula in some cases. If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them.

Find the y-intercept:

The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. Notice that if we plug in 0 for x we get: y = a(0)2 + b(0) + c or y = c. So the y-intercept of any parabola is always at (0,c).

Find the vertex (h,k):

To find the x-coordinate for the vertex we use the following formula:

To find the y-coordinate for the vertex we plug in h in the original equation:

k = a(h)2 + b(h) + c

Plot the points and graph the parabola  

-Please Mark As Brainliest

Answer:

The answer is 4

Step-by-step explanation:

MRK ME BRAINLIEST PLZZZZZZZ

Answer:

4

:P

Step-by-step explanation:

Answer:

0.66

Step-by-step explanation:

Answer:

i think 0.6

Step-by-step explanation:

i thank hope it helps

Answer:

Let's cut the figure into:

Parallelogram, square, and rectangle.

Let's find the area of the parallelogram first:

10 x 3.5 = 35

Let's find the area of the square:

4 x 4 = 16

When given one length of a square you already know are sides and lengths are equal so therefore 1 given length of a square is all the lengths.

Let's find the area of a rectangle:

6 x 12.5 = 75

Now let's add all the areas up:

35 + 16 + 75 = 126 square inches is your answer.

Answer:

The volume of the sculpture is 111.439  

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

So you train of though might lead you to soemthing like this: it must be 90 degrees, since that looks like a 90 degree triangle, and there are 180 degrees in a line. So 90 degrees and 90 degrees make up the 180.

That is exactly what I though.

But, its a bit different from that. We do not know for sure that its a 90 degree traingle. Depending on the angle of the traingle, the outcome of the mystery number is different.

So, to find the angle of the trainge, lets take our 155 degree line.

Now, this is just a simple line. We know the line is 180, and that the other number must add onto 155 to make 180:

180-155=missing angle

=

25. So we know that the smallest angle of the traingle is 25.

We also know that a traingle has a total of 180 degrees.

We can add the 60 degrees and our new 25 degrees, subtract if from 180, and we will get our last angle of the traingle we need to solve:

60+25

=

85

Now subtract it from 180:

180-85

=

95

So that last angle of the traingle is 95.

Now, we need to solve the missing angle of the line that will give us the answer.

Again, we know the line has to be 180, so lets subtract 95 from that:

180-95

=

85

So we know that the missing angle answer is 85!

I hope this isnt too confusing and helps! :)

Answer:

2b + 10

Step-by-step explanation:

Answer:

Y = 10.1 + 1.50x

Step-by-step explanation:

From the data contained in the computer output for linear regression

The coefficient of intercept = 10.1

coefficient of fertilizer = 1.50

Sample of an Equation of least squares regression line

y = a + bx

where : a = intercept , b = slope

hence the required equation will be

Y = 10.1 + 1.50x

y = yield , x = fertilizer

Answer:

C. [tex] y + 9 = 2.5(x + 3) [/tex]

Step-by-step explanation:

Point-slope equation takes the form of [tex] y - b = m(x - a) [/tex].

Where,

a and b area coordinates of a point the line passes through. In this case, a = -3, and b = -9

m = slope, in this case, slope will be the same as the slope value of the line it is parallel too = 2.5.

Substitute a = -3, b = -9 and m = 2.5 into [tex] y - b = m(x - a) [/tex].

Thus:

[tex] y - (-9) = 2.5(x - (-3) [/tex]

[tex] y + 9 = 2.5(x + 3) [/tex]