Benecio skis 748 yd in 3 min. At this rate, how many miles does Benecio ski in an
hour in miles?

Answers

Answer 1

Answer:

8.5 miles an hour.

Step-by-step explanation:

There are many ways to do this, but I am going to do it the way I think is the most simple.

First, divide 748 yards by 3 minutes to get the amount of yards per minute. 748 / 3 = 249.33333

Second, divide the previously gotten number (249.33333, [3's go on forever]) by the amount of yards in a mile (which is 1760 yards per mile). This turns into 249.33333 / 1760 = 0.1416666 (6's go on forever). This is miles per minute so you must make it per hour.

You then multiply that infinite number by the amount of minutes in an hour (60 minutes per hour). 0.14166666 * 60 = 8.5 miles per hour.


Related Questions

los tornillos vienen en bolsa de 100. cada 10 bolsas se empaqueta una caja. las cajas se embalan de a 10 en cajones y los cajones se guardan de a 10 en un contenedor para ser transportados. ¿ cuantos tornillos lleva un contenedor?

Answers

Answer:

lleva 10 000 tornillos un contenedor

Step-by-step explanation:

Determine which data are qualitative and which data are quantitative. Explain your reasoning
a. The yearly salaries of the employees at a school district. (9)
b. The employee numbers of the employees at an accounting firm.
c. The area codes of a sample of 350 residents of nursing homes. (2)
d. The ages of a sample of 350 residents of nursing home. (eta)
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (20)
f. The IQ index of the students in a statistics class.
What are the levels of measurement of data in question 4? Justify
a. Yearly salaries: (20)
b. Employee numbers: (ca)
c. Area codes: (eca)
d. The ages:
e. Survey answers: (ca)
f. IQ index: (en)

Answers

Answer:

1. A. Quantitative data

B. Quantitative data

C. Qualitative data

D. Quantitative data

E. Qualitative data

F. Quantitative data

2.a. Yearly salaries: interval or ratio data

b. Employee numbers: interval or ratio data

c. Area codes : nominal data

d. The ages: interval or ratio data

e. Survey answers: ordinal data

f. IQ index: interval or ratio data

Explanation:

Qualitative data is data in the form of a quality such as a characteristic. It is usually a noun, such as whether a person is fair or dark in complexion. Quantitative data is data in form of quantity such as the amount in dollars of one's salary.

There are four levels of data measurement. They are: nominal data, ordinal data, interval data, and ratio data. Nominal and ordinal data are qualitative data while interval and ratio data are quantitative data.

Find the following list of data calculate a demean be the maid and see mode or mothers for the following numbers listed in the picture above above

Answers

Answer:

Mean = 4.8875

Median = 4.6

Mode = 4.5 and 7.7

Step-by-step explanation:

Mean is the sum of total of data divided by the sample size

Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5

Sum total = 39.1

Sample size = 8

Mean = 39.1/8

Mean = 4.8875

To get the median we need to first rearrange

1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7

Median = 4.5 + 4.7/2

Median = 4.6

Hence the median is 4.6

Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7

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What is the slope of the line?
Pro

Answers

Answer:

1/2

Step-by-step explanation:

choose 2 points, I chose (-3,2) (1,4)

[tex]m = \frac{4 - 2}{1 - ( - 3)} = \frac{2}{4} = \frac{1}{2} [/tex]


4(x+9)=2x-6
Solve for x

Answers

Answer:

-21

Step-by-step explanation:

4(x+9) = 4x+36

4x+36 = 2x-6

    -36        -36

minus 36 from both sides

4x = 2x-42

2x = -42

-42/2 = -21

x = -21

Hi there!

We are given the equation below:

[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]

1. Expand 4 in the expression.

When expand in the expression, it is like multiply everything in the expression. So when we expand 4 in x+9, it becomes 4(x)+9(4).

[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]

Cancel the brackets.

[tex] \large{4x + 36 = 2x - 6}[/tex]

2. Isolate x-term and solve for the variable.

Think it easy. If you want to isolate x-term then what should you do? Well simply swap sides, and change the operator/sign.

[tex] \large{4x - 2x = - 6 - 36}[/tex]

Finally, combine like terms.

[tex] \large{2x = - 42}[/tex]

Then divide both sides by 2 so we can finally leave only x-term.

[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]

3. Check the solution if it is right or wrong.

This step is optional but if you are not confident on your answer, this step is recommended.

To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,

[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]

Since both sides are equal when substitute in x = -21.

4. Answer

Hence, the answer for this equation is x = -21.

I hope this helps and let me know if you have any doubts!

Consider the following conditional statement. Determine the contrapositive
of the statement and then determine if the contrapositive is true or false.
If two angles are not complements, then their measures do not add up to 180°.

The contrapositive of the statement is true.
The contrapositve of the statement is false.

Answers

Answer:

The contrapositive of the statement is true.

Step-by-step explanation:

For a general statement:

p ⇒ q

The contrapositive statement is:

¬q ⇒ ¬p

where:

¬q is the negation of the proposition q.

Here we have the statement:

If two angles are not complements, then their measures do not add up to 180°

So we have:

p = two angles are not complements

q = their measures do not add up to 180°

Then the negations are:

¬p = two angles are complements

¬q = their measures do add up to 180°

The contrapositive statement is:

"if for two angles their measures do add up to 180°, then the two angles are complements"

This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.

Then: The contrapositive of the statement is true.

Suppose you have a regular hexagon with all side lengths equal to1. Prove that if you pick seven points from the interior of the hexagon, there is a pair of two points that are distance at most 1 apart.

Answers

Answer:

Proved

Step-by-step explanation:

Given

[tex]n = 6[/tex] --- sides of hexagon

[tex]l = 1[/tex] --- side length

Required

Prove that for 7 points picked from the interior, 2 points are at most 1 unit apart

1. Draw a hexagon  (see attachment)

2. Divide the hexagon into 6 triangles

3. Select 7 points on the hexagon

You will notice that at least 2 points will be in one of the triangle.

The maximum distance between these two points is 1 unit. This is because

1. The triangle is equilateral (all sides equal)

2. The length of each is 1 unit (in other words, the distance between points, cannot exceed the side length)

No step by steps or links please

Answers

Answer:

Six at top, ten at second, twenty-seven at third, and four at bottom.

In communicating with an orbiting satellite, suppose that a 30-bit message is sent to thesatellite. Transmission of messages can sometimes be distorted. If the probability of eachbit being received incorrectly is 0.001, where each bit is received independently of the others,what is the probability that at least one bit is received incorrectly?

Answers

Answer:

0.0296 = 2.96% probability that at least one bit is received incorrectly.

Step-by-step explanation:

For each bit, there are only two possible outcomes. Either it is received correctly, or it its not. Each bit is received independently of the others, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability of each bit being received incorrectly is 0.001

This means that [tex]p = 0.001[/tex]

30-bit message

This means that [tex]n = 30[/tex]

What is the probability that at least one bit is received incorrectly?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.001)^{0}.(0.999)^{30} = 0.9704[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9704 = 0.0296[/tex]

0.0296 = 2.96% probability that at least one bit is received incorrectly.

Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)

[1 0 0 1]
[0 0 1 0]
[0 0 0 0]

(x1, x2, x3, x4) = _________

Answers

Answer:

[tex]x_1 = -t[/tex]

[tex]x_2 = s[/tex]

[tex]x_3 = 0[/tex]

[tex]x_4 = t[/tex]

Step-by-step explanation:

Given

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]

Required

Determine x1 to x4

First, we write the augmented matrix

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right] = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]

Taking the position of each column, we have:

[tex]x_1 + 0 + 0 +x_4 = 0[/tex]

[tex]0 + 0 + x_3 +0 = 0[/tex]

[tex]0 + 0 + 0 + 0 = 0[/tex]

There is no explicit equation for [tex]x_2[/tex]

So: [tex]x_2 = s[/tex] ----- arbitrary variable

[tex]x_1 + 0 + 0 +x_4 = 0[/tex] implies that:

[tex]x_1 + x_4 = 0[/tex]

[tex]0 + 0 + x_3 +0 = 0[/tex] implies that

[tex]x_3 = 0[/tex]

[tex]0 + 0 + 0 + 0 = 0[/tex] implies that

[tex]0 = 0[/tex]

So, we have:

[tex]x_1 + x_4 = 0[/tex]

[tex]x_3 = 0[/tex]

[tex]x_1 + x_4 = 0[/tex] becomes

[tex]x_1 = -x_4[/tex]

Let

[tex]x_4 = t[/tex]

So:

[tex]x_1 = -x_4[/tex]

[tex]x_1 = -t[/tex]

Where t , s are real numbers

The ratio of girls to boys in a particular classroom is 4: 3. What fraction of the total number of students are boys?

The ratio of boys to the total number of students in a particular classroom is

Answers

Answer:

3 : 7

Step-by-step explanation:

The ratio of girls to boys = 4 : 3

Since there are only two possible genders :

Then the total fraction of student is the sum of the ratio = (4 + 3)

Since,

Boys = 3

The ratio of boys to the total number of student in the class will be :

Boys : Total

3 : 7

Natural logs can be written as _______.

Answers

Answer:

Step-by-step explanation:

The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

Answer:

Ln x as opposed to log x

Step-by-step explanation:

Ahmed packs 8 text books each of mass x grams. And two dictionaries each mass y grams into a box of mass 250 grams. What is total mass of the box now?​

Answers

Answer:

8x + 2y + 250 grams

Step-by-step explanation:

The box contains

8 text   books each with a mass of x grams = 8x

2 dictionaries each with a mass of  y grams = 2y

1 box                                                                 = 250 grams

Total                                                                 = 8x + 2y + 250

Consider the following system of equations:

y = −2x + 3
y = x − 5

Which description best describes the solution to the system of equations?

Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.
Line y = −2x + 3 intersects line y = x − 5.
Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.
Line y = −2x + 3 intersects the origin.

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

"Line y = −2x + 3 intersects line y = x − 5."  

»»————- ★ ————-««  

Here’s why:  

When the system of equations are graphed, they would intersect at a point. This means that there is a solution to the system. The solution is [tex](\frac{8}{3} ,-\frac{7}{3} )[/tex].While the statement that the lines intersect the x-axis is true, the question asks the statement that describes the solution. The solution is the point of intersection between the two lines.

⸻⸻⸻⸻

See the Graph Attached

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

George would like to build a garden this year, George measure out his proposed garden and would like to know how many square feet of space he will have to use . Calculate the area of the garden from the picture below

Answers

Answer:

The area is 105.5ft^2

Step-by-step explanation:

Required

The area of the composite figure

The figure can be divided to 2 shapes

(1) Rectangle: Length = 6ft and Width = 8ft

(2) Trapezoid: Height = 5ft (i.e. 8 - 3), Parallel sides = 9ft and 14ft (i.e. 20 - 6)

The area of the rectangle is:

[tex]Area = 6 * 8 = 48[/tex]

The area of the trapezoid is:

[tex]Area = \frac{1}{2}(9 + 14) * 5[/tex]

[tex]Area = \frac{1}{2}(23) * 5[/tex]

[tex]Area = 11.5 * 5[/tex]

[tex]Area = 57.5[/tex]

So, the area of the garden is:

[tex]Total = 48 + 57.5[/tex]

[tex]Total = 105.5[/tex]

In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.​

Answers

Answer:

Correct answers= 18

Incorrect answers=30-18= 12 answers

Step-by-step explanation:

total questions=30

correct answers= x

incorrect answers= 30-x

given: 5 marks for each correct answer

therefore, marks for correct answers = 5*x = 5x

Given: 1 mark deducted for every incorrect answer

therefore, marks deducted = 1(30-x) = 30-x

Total marks scored= 78

★  The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78

5x- (30-x) =78

5x-30+x=78

5x+x=78+30

6x= 108

x=108/6 = 18

Correct answers= 18

Incorrect answers=30-18= 12 answers

90 dollars ratio in 1:2:3

Answers

Answer:

3:6:9

Step-by-step explanation:

1/1+2+3 × 90 = 15

2/1+2+3 × 90 = 30

3/1+2+3 × 90 = 45

Find the measure of the are or central angle indicated. Assume that lines which appear to be
diameters are actual diameters.
2) m SPU

Answers

Answer:

120°

Step-by-step explanation:

m L SPU = 180° - 60° = 120°

16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)

Answers

2: it is, because last digit is even
3: it is, because the sum of the digit, 2+4+7+2=15, is divisible by 3
4. it is, because the last 2 digits, 20, is divisible by 4
5. it is, because last digit is 0
6. it is, because it is divisible by 2 and 3
8. it is, because the last 3 digits, 720, is divisible by 8
9. It is not, because the sum of the digits, which is 15, is not divisible by 9
10. It is, because the last digit is 0
11. It is not, because the difference of alternating digits, which is 2+0+2-4-7-0, is not divisible by 11

Rico can walk 3 miles in the same amount of time that Donna can walk 2 miles. Rico walks at a rate 2 miles per hour faster than Donna. At that rate, what is the number of miles that Rico walks in 2 hours and 10 minutes?

Answers

Answer:

[tex]13[/tex]

Step-by-step explanation:

Donna's Rate is [tex]R[/tex]

Rico's Rate is [tex]R+2[/tex]

[tex]\frac{R}{R+2}=\frac{2}{3}[/tex]

Cross-Multiply

[tex]2(R+2)=32[/tex]

[tex]2R+4=3R[/tex]

[tex]4=R[/tex]

Donna's Rate is [tex]R=4[/tex]

Rico's Rate is [tex]R+2=6[/tex]

[tex]\frac{6(130)}{60} = \frac{130}{10}=13[/tex]

Help!!
f is a quadratic function where f(2) = 0, f(-2) = 0, and f(0) = -0.12. Find an algebraic equation for
f(u).

Answers

Answer:

bad gvkvkgcnhvvjzadhljang

v

gjddkfzutwdjtabkf

f(u) = k(u - 2)(u + 2)
f(0) = k x -2 x 2 = -0.12
so k = -0.12 / -4 = 0.03

f(u) = 0.03(u - 2)(u + 2)

14x^4y^6/7x^8y^2 assume the denominator does not equal zero

Answers

Answer:

(y/x)⁴

Step-by-step explanation:

14x^4y^6/7x^8y^2

= 2x^(-4)/2y^(-4)

= (y/x)

Answer:

2y^4/x^2

Step-by-step explanation:

4x^4y^6 ÷ 7x^8y^2

you will find the GCF of the equation which is: 7x^4y^2 . Then, you will divide both of the equation by the GCF and it will become

14x^4y^6 ÷ 7x^4y^2 = 2y^4

7x^8y^2 ÷ 7x^4y^2 = x^2

then you'll get the answer 2y^4/x^2

what is the average rate of change from 0 to 2 of the function represented by the graph? Enter your answer, as a simplified fraction, in the box​

Answers

Answer:

=>The graph of an exponential relation is also non-linear.

=>The graph of an exponential relation becomes nearly parallel to x-axis on one and then curves upward and becomes nearly parallel to the y-axis on the other sid.

The average rate of change from 0 to 2 of the function represented by the graph is  [tex]\frac{3}{2}[/tex].

What is average rate of change?

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

According to the question

[tex]x_{1} =0[/tex], [tex]x_{2} =2[/tex]

f(0) = 1, f(2) = 4

The average rate of change = [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]

= [tex]\frac{f(2)-f(0) }{2-0 }[/tex]

= [tex]\frac{4-1}{2}[/tex]

= [tex]\frac{3}{2}[/tex]

Hence, the average rate of change from 0 to 2 of the function represented by the graph is  [tex]\frac{3}{2}[/tex].

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how would I classify a triangle which has a angle of 49 and 82, acute, right, or obtuse?

Answers

9514 1404 393

Answer:

  acute

Step-by-step explanation:

The third angle is ...

  180° -49° -82° = 49°

So, the triangle has two angles the same, 49°. When two angle are the same, the triangle is an isosceles triangle.

The largest angle, 82°, is less than 90°, so is an acute angle. The classification acute, right, or obtuse is based on the measure of the largest angle.

The triangle is an acute isosceles triangle.

sammy is on level 40 , which is five times as much as rocky.what islevel rocky on​

Answers

Answer:

8

Step-by-step explanation:

40÷5=8

Hope this helps! :)

Rocky is on level 8 because 40 divided by 5 is 8

Suppose an test consisted of 10 multiple choice problems, each with five possible responses (A-E), only 1 of which is correct. If a student randomly guesses the answers to each question then what is the probability that a student guesses the correct answer to exactly 7 questions?

Answers

Answer:

Step-by-step explanation:

[tex]10C_{7}\times (0.2)^{7} \times (0.8)^{3}\\[/tex]

The probability that a student guesses the correct answer to exactly 7 questions is 0.004.

What is binomial probability?

The probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes is called binomial probability.

Binomial probability formula

[tex]P_{x} =nC_{x} P^{x} q^{n-x}[/tex]

where,

P is binomial probability

x is number of times for a specific outcome within n trials

[tex]nC_{x}[/tex] number of combinations

p is probability of success on a single trial

q is probability of failure on a single trial

n is number of trials

According to the given question.

A test consisted of 10 multiple choices.

⇒ Number of trials,  n = 10

The student have to give exactly 7 correct answers.

⇒ x = 7

The probability of being correct in one trial, p = [tex]\frac{1}{5}[/tex]    

(only one option is correct among fives)

So, the probability of being incorrect/wrong in one trial, q = [tex]1-\frac{1}{5} =\frac{4}{5}[/tex]

Therefore, the probability that a student guesses the correct answer to exactly 7 questions is given by

[tex]P_{x} = 10C_{7} (\frac{1}{5}) ^{7} (\frac{4}{5} )^{3}[/tex]

⇒ [tex]P_{x} = \frac{10!}{7!3!} (0.2)^{7}( 0.8)^{3}[/tex]

⇒[tex]P_{x} = 120(0.0000128)(0.512)[/tex]

⇒ [tex]P_{x} =0.004[/tex]

Hence, the probability that a student guesses the correct answer to exactly 7 questions is 0.004.

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the radius of a circle in cm ,with area 77 over 2 cm square is​

Answers

Answer:

7/√2 cm

Step-by-step explanation:

Area of circle = 77 cm^2

=> π(r)^2 = 77

=> (22/7) x (r)^2 = 77

=> (r)^2 = (77 x 7) / 22

=> (r)^2 = 49/2

=> (r) = 7/√2 cm

The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is modeled by , where t is measured in years since 1990. Discuss the meaning of . Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020

Answers

The question is incomplete. The complete question is :

The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?

Solution :

According to the question,

The rate of change of population is given as :

[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]  in 1990.

Now integrating,

[tex]$\int_0^{20}\frac{dP(t)}{dt}dt=\int_0^{20}200e^{0.02t} \ dt$[/tex]

                    [tex]$=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$[/tex]

                   [tex]$=10,000[e^{0.4}-1]$[/tex]

                    [tex]$=10,000[0.49]$[/tex]

                    =4900

[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]

[tex]$\int1.dP(t)=200e^{0.02t}dt$[/tex]

[tex]$P=\frac{200}{0.02}e^{0.02t}$[/tex]

[tex]$P=10,000e^{0.02t}$[/tex]

[tex]$P=P_0e^{kt}$[/tex]

This is initial population.

k is change in population.

So in 1995,

[tex]$P=P_0e^{kt}$[/tex]

   [tex]$=10,000e^{0.02(5)}$[/tex]

   [tex]$=11051$[/tex]

In 2000,

[tex]$P=10,000e^{0.02(10)}$[/tex]

   [tex]=12,214[/tex]

Therefore, the change in the population between 1995 and 2000 = 1,163.

Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?


need help with this, i’ll mark you brainliest!!

Answers

Answer:

Equation: [tex](x-2)^2=16(y-2)[/tex]

Vertex: [tex](2,2)[/tex]

Directrix: [tex]y=-2[/tex]

Focus: [tex](2,6)[/tex]

Step-by-step explanation:

Standard Form of Vertical Parabola:

Equation -> [tex](x-h)^2=4p(y-k)[/tex] where [tex]p\neq 0[/tex]Vertex -> [tex](h,k)[/tex]Directrix -> [tex]y=k-p[/tex]Focus -> [tex](h,k+p)[/tex]

We know that our vertex is [tex](h,k)[/tex] -> [tex](2,2)[/tex], therefore, we can determine the value of [tex]p[/tex] by selecting a point from the parabola as [tex](x,y)[/tex]:

[tex](x-h)^2=4p(y-k)[/tex]

[tex](x-2)^2=4p(y-2)[/tex]

[tex](6-2)^2=4p(3-2)[/tex]

[tex](4)^2=4p(1)[/tex]

[tex]16=4p[/tex]

[tex]4=p[/tex]

Therefore:

Directrix -> [tex]y=k-p[/tex] -> [tex]y=2-4[/tex] -> [tex]y=-2[/tex]Focus -> [tex](h,k+p)[/tex] -> [tex](2,2+4)[/tex] -> [tex](2,6)[/tex]

Conclusion:

Equation -> [tex](x-2)^2=16(y-2)[/tex]Vertex -> [tex](2,2)[/tex]Directrix -> [tex]y=-2[/tex]Focus -> [tex](2,6)[/tex]

Review the graph for a visual

Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 67.5 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quadruple (4x) the sample size. What is the standard error for the new sample size

Answers

Answer:

The standard error for the new sample size will be of 33.75.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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.

Standard error as 67.5 for samples of a particular size.

We have that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], that is, the standard error is inversely proportional to the square root of the sample size, so if you quadruple (4x) the sample size, the standard error will be divided by half. So

67.5/2 = 33.75

The standard error for the new sample size will be of 33.75.

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