The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.

32 36 29 31 30 35 34 26 30

The 35th percentile of this data set is:________

a. 31
b. 32
c. 31.5
d. 30

Answer:

Step-by-step explanation:

f(x) = (x+1)³ + 4

To find f-¹(x) equate f(x) to y

That's

y = (x+1)³ + 4

Next interchange the terms x becomes y and y becomes x

That's

x = ( y+1)³ + 4

Make y the subject

(y+1)³ = x - 4

Find the cube root of both sides

That's

[tex]y + 1 = \sqrt[3]{x - 4} [/tex]

Send 1 to the right side of the equation

That's

[tex]y = \sqrt[3]{x - 4} - 1[/tex]

So we have the final answer as

[tex]f ^{ - 1} (x) = \sqrt[3]{x - 4} - 1[/tex]

Hope this helps you

Answer:

option 1

Step-by-step explanation:

f(x)=(x+1)³+4

to find the inverse interchange the variable and solve for y

inverse f(x)=(y+1)³+4

x=(y+1)³+4

x-4=(y+1)³

y+1=∛x-4

y=∛x-4 -1

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = probability of obtaining head.

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.5

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.5

(a) The significance level of the test which is represented by [tex]\alpha[/tex] is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

            P(Type I error) = [tex]\alpha[/tex]

         P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]

[tex]\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}[/tex]  = [tex]\alpha[/tex]

[tex](1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})[/tex] = [tex]\alpha[/tex]

[tex]\alpha[/tex] = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - [tex]\beta[/tex]).

So, here, X ~ Binom(n = 10, p = 0.1)

[tex]1-\beta[/tex] = P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true)

[tex]1-\beta[/tex] = [tex]\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}[/tex]  

[tex]1-\beta[/tex] = [tex](1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})[/tex]

[tex]1-\beta[/tex] = 0.3487

Hence, the power of the test is 0.3487.

Answer:

≈ 3.6

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)

d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]

   = [tex]\sqrt{(-2)^2+3^2}[/tex]

   = [tex]\sqrt{4+9}[/tex]

    = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )

Answer:

3.6

Step-by-step explanation:

Look above bru

                                                0        0

                                                      ,    

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

Answer:

the real answer is: 4493.75472

BUT for ESTIMATION STRATEGY it is: 4500

Step-by-step explanation:

The area of the entire shape is 33,562 square units

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.

Area of Square:-

= 100  x  100   =  10,000

Area of each circle

= π r² = 3.1416  x  50  x  50  =  7854

Area of each 3/4 circle  

= 7854  x  ( 3/4 ) =   5890.5

Area of all four 3/4 circles

= 5890.5  x  4=23562

The TOTAL area will be the sum of all the areas

A  = 23562  +  10,000 = 33,562 square units

Therefore the area of the entire shape is 33,562 square units

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The area of the entire shape is 33,562 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Here, we have,

The figure is made up of a square and four 3/4 circles.

So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.

Area of Square:-

= 100  x  100   =  10,000

Area of each circle

= π r² = 3.1416  x  50  x  50  =  7854

Area of each 3/4 circle  

= 7854  x  ( 3/4 ) =   5890.5

Area of all four 3/4 circles

= 5890.5  x  4=23562

The TOTAL area will be the sum of all the areas

A  = 23562  +  10,000 = 33,562 square units

Therefore the area of the entire shape is 33,562 square units

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Answer: Option "a" is the only expression that represents a function.

Step-by-step explanation:

A function f(x) = y is a "operator" that takes an input element, x, and assigns it to only one output element, y.

So, if we have that for a given value of x.

f(x) = y and f(x) = h

where y and h are different values, then this is not a function, because is assigning the input value x to two different output values.

Let's see the different options:

a) {(1, 2), (4, −2), (8, 3), (9, −3)}

This points are of the form (x, y)

We can see that each value of x is assigned to only one value of y, so this can represent a function.

b)  y^2 = 16 − x^2

Ok, suppose that x = 0, then:

y^2 = 16 - 0 = 16

then we have that y*y = 16.

So y can take two different values:

y = 4 ---> 4*4 = 16

y = -4 ---> -4*-4 = 16.

So this is not a function.

c) 2x^2 + y^2 = 5

First, we want to isolate y in one side:

y^2 = 5 - 2*x^2

Here we have a similar case to the option b, and we can use a similar argument to prove that this is not a function, so we can discard this.

d) x = 7.

Ok, this is not a relation between two variables, so this is not a function, as if x is the input value, we have only one value of x that solves the equation.

The fraction that each person gets is 1/2.

It should be noted that 2 1/2 cases of soda to split between 5 families.

In their case, the fraction that each person will get will be:

= Total / Number of people

= 2 1/2 ÷ 5

= 2.5/5

= 0.5 or 1/2.

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2 1/2 cases of soda to split between 5 families. What fraction will each person get?

Answer:

  C.  -1

  D.  1

Step-by-step explanation:

A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.

The appropriate choices are ...

  C.  -1

  D.  1

Answer:

c=-1

d=1

Step-by-step explanation:

Answer:

Its commutative property..

Step-by-step explanation:

Commutative property says A×B=B×A

Explanation is attached below.

Answer:x = 8, y = 5

Step-by-step explanation:The sum of two numbers is 13. Two times the first number minus three times the second numberis 1. If you let x stand for the first number and y for the second number, the two numbers are: A. x = 8, y = 5

Answer: 60°

Step-by-step explanation:

apply concept: the interior angle sum of triangle is 180°

x+x+x=180

     3x=180

       x=60

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

this is also an equilateral triangle which if you know it, you will know that each angles are all 60°

Answer: x=60°

Step-by-step explanation:

We know that the sum of the angles in a triangle is 180°. Since all of the angles are x°, we know that they are equal in degrees. Since there are 3x, we can use that to solve for x.

3x=180                              [divide both sides by 3]

x=60°

Answer:

23% increase

Step-by-step explanation:

13 - 10 = 3

3/13 = 0.2307 = 23%

Hope that helped!!! k

Answer:

-11.2 pounds

Step-by-step explanation:

It is given that,

Shawna finds a study of American men that has an equation to predict weight (in pounds) from  height (in inches):

y = -210 + 5.6x

Height of Shawna's dad is 72 inches

Weight is 182 pounds

We need to find the residual of weight and height for Shawna's dad.

Predicted weight of 72 inches men,

y' = -210 + 5.6(72)

y' = 193.2 pounds

So, residual is :

Y = 182 - 193.2

Y = -11.2 pounds

So, the residual of weight and height for Shawna's dad is -11.2 pounds.

Answer:

-11.2 pounds

Step-by-step explanation:

Got it right on the test.

Answer:

We have to remember

slope = m

if the slope of line is parellel so it will be the same with other slope

m1= m2

2/3= 2/3

so the answer is 2/3

hope it helps ^°^

Answer:

2/3

Step-by-step explanation:

Parallel lines have the same slopes. Therefore,

[tex]m_{k} =m_{p}[/tex]

The slope of line k ([tex]m_{k}[/tex]) will be equal to the slope of the line parallel to k ([tex]m_{p}[/tex]).

We know that the slope of line k is 2/3.

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

Therefore, the slope of the line parallel to line k is also 2/3.

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

The slope of a line parallel to line k is 2/3.

Answer:

Here's what I get  

Step-by-step explanation:

h = 0.5d + 4

A function rule tells you how to convert an input value (x) into an output value (y).

Your function rule is

ƒ(x) = 0.5x + 4

An easy way to represent your function is to make a graph.

The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.  

Here's a typical table.

[tex]\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}[/tex]

The graph is like the one below.

Answer:

P value = 0.1575

Step-by-step explanation:

Data provided in the question

t = 1.021

n = 33

[tex]\mu[/tex] = 98.6° F

Based on the above information, the P-value could be determined by using the excel spreadsheet i.e. shown in the attachment

So, the P value is 0.1575

The 1.021 denotes the test statistic

32 denotes degrees of freedom

And,

1 denotes one tailed alternative hypothesis.

Answer:

75°

Step-by-step explanation:

Let's find the size of x°

BCFE has four sides so the sum of its angles sizes is 360°.

● CBE + 110 + 110 + CFE = 360

CFE is equal to 65° since they have the same vertex

● CBE + 220 + 65 = 360

● CBE + 285 = 360

● CBE = 360-285

● CBE = 75

CBE and x° have the same size since they share the same vertex.so:

● x° = 75°

Answer:

75°

Step-by-step explanation:

CBE = x (vertically opposite angles are equal)

CFR = 65° (vertically opposite angles are equal)

C+F+E+B= 360 (angles in a quadrilateral sum up to 360°)

110+65+110+x=360

x= 75°

Answer:

B

Step-by-step explanation:

x can not be greater than (1,325-270)/26 because $270 is fixed for the rental

Answer:

3 only

Step-by-step explanation:

Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.

Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.

Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.

Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.

Therefore, the true statement is III only.

More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.

Data given in the table shows the data of elections between two candidates among the different cities.

Statistics is the study of mathematics that deals with relations between comprehensive data.

I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.

II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false

III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.

IV. Overall, more residents support candidate A than candidate B. it is also false.

Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.

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Answer:

f(2) = 2

Step-by-step explanation:

f(x)=x^2-2x+2

Let x=2

f(2)=2^2-2*2+2

    = 4 -4 +2

    = 2

Answer:

Step-by-step explanation:

[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]

Answer:

7

Step-by-step explanation:

because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7

Answer:

1 square foot is the answer

Answer:

1 ft^2

Step-by-step explanation:

We know 12 inches = 1 ft

12 inches by 12 inches

1 ft by 1 ft

The area is 1 * 1 = 1 ft^2

==================================================

Explanation:

Dividing the side lengths, the scale factor is 6/3 = 2. This means the larger figure has a side length twice as long compared to its smaller counterpart.

How can we use this to figure out how the areas are connected? By simply squaring the scale factor to get 2^2 = 2*2 = 4, then we divide the larger area over 4 to get 24/4 = 6.

The longer side is 2 times longer

The larger area is 4 times larger

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

Let's say we had a 3 by 3 square. It's area would be 9.

Also, let's say we had a 6 by 6 square. It's area is 36.

Notice the ratio of areas is 36/9 = 4, so the larger square is 4 times larger than the smaller. This 4 matches with what we got earlier.

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

Another example:

square A is 7 by 7 with area 49

square B is 21 by 21 with area 441

ratio of areas is 441/49 = 9, which is exactly equal to 3^2, and the 3 comes from the ratio of the sides 21/7 = 3.

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

So in short, you find the linear scale factor by dividing the sides. Then you square the result to get the area scale factor, which you use to find the smaller area.

linear scale factor = (new side)/(old side)

area scale factor = (linear scale factor)^2

smaller area = (larger area)/(area scale factor)

Answer:

{x | x < 0} and {x I x > 0} has no solution

Step-by-step explanation:

x cannot be less than zero AND more than zero at the same time, so the first inequality has no solution.

{x | x < 0} and {x I x > 0}

Answer:

A

Step-by-step explanation:

Choice A has the two options:

[tex]x<0 \text{ and } x>0[/tex]

In other words, x must be a number such that it is negative (left option) and positive (right option) at the same time.

There can't be such number (and 0 is not included in the answer choices since it is not less/more than or equal to). Thus, Choice A has no solution.

The keyword here is and. If instead of and it was or, then the choice does indeed have a solution.

Answer:

Step-by-step explanation:

5x - 15 = 5(-4x - 3)

Multiply the terms in the bracket

5x - 15 = - 20x - 15

Group like terms

Send the constants to the right side of the line and those with variables to the left side

That's

5x + 20x = - 15 + 15

Simplify

25x = 0

Divide both sides by 25

We have the final answer as

Hope this helps you

Answer:

x=0

Step-by-step explanation:

5x - 15 = 5(-4x - 3)

To find the solution to this equation, we have to get x by itself on one side of the equation.

First, distribute the 5 on the right side. Multiply each term by 5.

5x - 15= (5*-4x) + (5*-3)

5x-15 = -20x + (5*-3)

5x-15= -20x -15

Next, add 20x to both sides of the equation.

(5x+20x) -15 = (-20x+20x) -15

(5+20x) -15 = -15

25x -15=-15

Next, add 15 to both sides of the equation.

25x -15 +15 = -15+15

25x= -15+15

25x=0

Finally, divide both sides of the equation by 25.

25x/25=0/25

x= 0/25

x= 0

The solution to this equation is x=0

Aswer:I am sure of the answer it is 6 and 42

Step-by-step explanation:

Step-by-step explanation:

check the tile whose side length is divisible by both 150 and180 in such a way that you don't get decimal points

150÷4=37.5 so that is impossible

150÷8=18.75 so that is also impossible

150÷6=25 180÷6=30

so the six sided tile is applicable

The correct answer is A. y = 2x +1

Explanation:

An equation is a statement that shows equality. In this context, the equation should lead to two equal numbers even if the values of y and x change. In this context, the correct equation is y= 2X + 1 because this is the only one, in which, the value of Y is always equivalent to 2x + 1. To prove this, let's replace y and x for the values of the table.

First  column

5 = 2 · 2 + 1

5 = 4 + 1

5 = 5

Second Column

9 = 2 · 4 + 1

9 = 8 + 1

9 = 9

Third column

13 = 6 · 2 + 1

13 = 12 + 1

13 =  13

Fourth column

17 = 8 · 2 + 1

17 = 16 + 1

17 = 17

Answer:

[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]

Step-by-step explanation:

Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).

Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0

To find b we use the equation of the focus which is:

[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]

Substituting the values of a, b, h and k:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]