M(2,4) is the midpoint of RS. The coordinates of S are (3,1) what are the coordinates of R

The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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Answer:

the first equation

Step-by-step explanation:

The 6 is the same amount no matter the weight of the dog.  .5x represents 50 for each pound.

If a dog weight 20 pounds, it would cost 6 + .5(20)  

If a dog weight 30 points it would cost 6 + .5(30) and so on.

Answer:

150 Miles.

Step-by-step explanation:

Answer:

√61

Step-by-step explanation:

→ Find the distance between y coordinates

2 --4 = 6

→ Find distance between x coordinates

2--3 = 5

→ Find distance

√6² + 5² = √36 + 25 = √61

Answer:

the residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 5 to 8. If there were 6776 no votes, what was the total number of votes?

-------

5 to 8 is the same as 5x to 8x where 8x is the number of no votes.

----

If 8x = 6776, then x = 847

Step-by-step explanation:

HOPE THIS HELPED ✨

The image of the point after the dilation is (-2, -1)

Dilation is the process of altering the side length of a shape or a function

From the question, the given parameters are:

Point =  (-8, -4)

The scale factor of dilation is given as

Scale factor = 1/4

Mathematically, this transformation can be represented as

(x, y) = k(x, y)

Where k = 1/4 i.e. the scale factor

So, we have

(x, y) = (kx, ky)

This gives

(x, y) = (1/4x, 1/4y)

When represented as an equation, we have

Image = 1/4 * Point

Substitute the equation Point =  (-8, -4) in the equation Image = 1/4 * Point

So, we have the following equation

Image = 1/4 * (-8, -4)

Evaluate the product

Image = (-2, -1)

Hence, the image is (-2, -1)

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The composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

To find the composite function k(t(x)), we substitute the expression for t(x) into the function k(t) as follows:

k(t(x)) = 4.5 + 3 - 7t(x)^2 + 3t(x) - 4

k(t(x)) = 4.5 + 3 - 7(ln x)^2 + 3(ln x) - 4

Simplifying this expression, we obtain:

k(t(x)) = -2.5 - 7(ln x)^2 + 3(ln x)

To find the derivative of the composite function, we use the chain rule as follows:

k'(t(x)) = k'(t) * t'(x)

where k'(t) is the derivative of the function k(t) with respect to t, and t'(x) is the derivative of the function t(x) with respect to x.

The derivative of k(t) with respect to t is:

k'(t) = -14t + 3

The derivative of t(x) with respect to x is:

t'(x) = 1/x

Substituting these expressions into the chain rule, we obtain:

k'(t(x)) = (-14t(x) + 3) * (1/x)

k'(t(x)) = (-14ln x + 3/x)

Therefore, the composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

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Answer:

When you solve for y, you get y = 20.

Step-by-step explanation:

You isolate the variable by dividing each side of the equation by the number with the variable, therefore getting 20.

\(\longrightarrow{\green{d.\:y\:=\:20}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

➝\(\:56 = 2.8y\)

➝\(\:y = \frac{56}{2.8} \)

➝\(\:y = 20\)

Therefore, the value of \(y\) is 20.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

➝\(\:56 = 2.8y\)

➝\(\:56 = 2.8 \times 20\)

➝\(\:56 = 56\)

➝\(\:L.H.S.=R. H. S\)

Hence verified.

\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)

Step-by-step explanation:

3y + 10.5 = 6.5 + 2.5y

3y - 2.5y = 6.5 - 10.5

0.5y = - 4

y = 4 ÷ 0.5

y = 2

The number of miles in 4 weeks is 20 mules

From the question, we have the following parameters that can be used in our computation:

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Answer:

9

Step-by-step explanation:

1.08 divided by 0.12 equals 9

Answer:

slope -4

Step-by-step explanation:

m=y2-y1/x2-x1

m=-1-11/3-0

m=-12/3

m=-4

The first-order partial derivative is ∂y/∂z = \(-2x + z^-^1^/^2\).

The second-order partial derivative is ∂²y/∂z∂x = -2

The first-order partial derivatives of the given function y = 6x² - 2zx + 3x¹² + z¹/2 - x - 9 are:

∂y/∂x = 12x - 2z + 36x¹¹ - 1,

∂y/∂z =\(-2x + z^-^1^/^2\).

The second-order partial derivatives of the function are:

∂²y/∂x² = 12 + 396x¹⁰,

∂²y/∂z² = \(z^-^3^/^2\)

∂²y/∂x∂z = -2,

∂²y/∂z∂x = -2.

In the first paragraph, I have provided the first-order partial derivatives of the given function with respect to x (∂y/∂x) and z (∂y/∂z). These derivatives represent the rates of change of the function with respect to each variable, while keeping the other variables constant.

In the second paragraph, I have provided the second-order partial derivatives. These represent the rates of change of the first-order partial derivatives with respect to each variable. ∂²y/∂x² measures the curvature of the function with respect to x, while ∂²y/∂z² measures the curvature with respect to z. ∂²y/∂x∂z and ∂²y/∂z∂x represent the cross-partial derivatives, indicating how the function changes simultaneously with respect to both x and z. These partial derivatives provide additional information about the behavior of the function in multiple dimensions and can be used to analyze critical points, extrema, and curvature.

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Answer:

\( \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C\)

Step-by-step explanation:

we would like to integrate the following integration:

\( \displaystyle \int \frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x) - \cos( \alpha ) } dx\)

notice that you can simplify the integrand

recall that,

\( \displaystyle \cos(2 \theta) = 2 \cos(\theta) ^{2} - 1\)

thus substitute:

\(\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - \{2\cos ^{2} (\alpha ) - 1 \} }{ \cos(x) - \cos( \alpha ) } dx\)

remove parentheses:

\(\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - 2\cos ^{2} (\alpha ) + 1}{ \cos(x) - \cos( \alpha ) } dx\)

\(\displaystyle \int \frac{ 2\cos^{2} (x) - 2\cos ^{2} (\alpha ) }{ \cos(x) - \cos( \alpha ) } dx\)

factor out 2:

\(\displaystyle \int \frac{ 2(\cos^{2} (x) - \cos ^{2} (\alpha )) }{ \cos(x) - \cos( \alpha ) } dx\)

we can use algebraic identity i.e

a²-b²=(a+b)(a-b) to factor the denominator

\(\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cos(x) - \cos( \alpha ) ) }{ \cos(x) - \cos( \alpha ) } dx\)

reduce fraction:

\(\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cancel{\cos(x) - \cos( \alpha ) ) }}{ \cancel{\cos(x) - \cos( \alpha ) }} dx\)

\( \displaystyle \int 2( \cos(x) + \cos( \alpha ) )dx\)

distribute:

\( \displaystyle \int 2 \cos(x) + 2\cos( \alpha ) dx\)

use sum integration formula:

\( \rm \displaystyle \int 2 \cos(x) dx+ \int2\cos( \alpha ) dx\)

recall integration rules:

\( \displaystyle 2 \sin(x) + 2x \cos( \alpha ) \)

and we of course have to add constant of integration

\( \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C\)

Answer:

-14x+6

Step-by-step explanation:

that's the expression simplified.

The cost of the jalapeno poppers was $9.24 if each friend paid $9.73.

The cost of the jalapeno poppers can be determined by using multiplication followed by subtraction.

First, we determine the total amount paid by the three friends;

If each friend paid $9.73, then;

Total amount = 9.73 × 3

Total amount = $29.19

Now to find the cost of jalapeno poppers, we subtract the cost of nachos from the total amount paid by the three friends;

cost of jalapeno poppers = total amount - cost of nachos

cost of jalapeno poppers = 29.19 - 19.95

cost of jalapeno poppers = $9.24

Therefore, the cost of jalapeno poppers is calculated to be $9.24.

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Answer:

K^1= (-8,10)

L^1 = (-4,10)

m^1 =(-5,10)

Step-by-step explanation:

all you have to do is move the points 90 degrees counterclockwise, which then you would get the points above.

Answer:

10.5 : 12  : 13.5

Step-by-step explanation:

7:8:9

We need to get 8 to 12

12/8 = 3/2

We need to multiply each number by 3/2

7 * 3/2:8* 3/2  :9*3/2

21/2  : 12  : 27/2

10.5 : 12  : 13.5

Answer:

x = \(\frac{29}{7}\)

Step-by-step explanation:

Given f(x) = 7x + 2 and f(x) = 31 then equate the right sides

7x + 2 = 31 ( subtract 2 from both sides )

7x = 29 ( divide both sides by 7 )

x = \(\frac{29}{7}\)

Answer:

combination

Step-by-step explanation:

permutation is when there is a specific order, whereas combination is when they are not in any specific pattern (in this case, 5/13 students, not in any particular order. just 5.

I don't want to explain circular permutation right now (it's difficult to explain), but it's not it from my knowledge

The number of ways selecting 5 out of the 13 students will ride in a car instead of a van is 1287.

The way of selecting 5 out of the 13 students will ride in a car instead of a van is evaluated by the combinations.

We consider the group of 5 students can be selected to ride in a car instead of a van.

Thus, for selecting a random group of the data from the universal data, we have to apply combinations to evaluate it.

Therefore, the ways can be formulated as:

\(^{13}C_5=\dfrac{13!}{5! \times 6!}\\=1287\;\rm{ways}\)

Thus, the number of ways selecting 5 out of the 13 students will ride in a car instead of a van is 1287.

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Answer:

Step-by-step explanation:

If a person's monthly bill from the number of  kilowatt-hours (kWh), x is modeled by the equation b = 0.15(x - 200) +20, to know the bill for a person who uses 600 kWh in a month, we will substitute x = 600 into the modeled equation as shown;

\(b(x) = 0.15(x - 200) +20\\\\b(600) = 0.15(600 - 200) +20\\\\b(600 )= 0.15(400) +20\\\\b(600 )= 15/100*(400) +20\\\\b(600 )= (15*4)+20\\\\b(600 )= 60+20\\\\b(600 )= 80\)

Hence the bill for a person who uses 600 kWh in a month is $80

Answer:

pie * r^2 bro where r= 10mi

Answer:

I think OA because you would need to know how much yarn for each cap and how many caps she will make

Answer:

75 miles- 3 gallons

Step-by-step explanation:

What is the gallons for 50 miles? It doesn't say...

Answer: The ratio would be 73.6

Answer:

your answer is in this attachment

Step-by-step explanation:

hope it's helpful to you

have a great day ahead