Yesterday, Jack drove 31 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon.?

Mean for start of school year is 6.5; Mean for end of school year is 7.2.

Median for start of school year is 6.5; Median for end of school year is 7.

To find the means, list out each data value given for each dot plot and calculated the mean.

Mean for start of school year:

We have, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9

Mean = ( 4 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 9)/14

= 91/14

Mean ≈ 6.5

Mean for end of school year:

We have, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9

Mean = ( 5 + 5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9 + 9 + 9)/14

= 101/14

Mean ≈ 7.2

Median represents the middle data value in a data set, therefore:

Median for start of school year = ( 6 + 7)/2 = 6.5

Median for end of school year = ( 7 + 7)/2 = 7

Learn more about mean and median on:

https://brainly.com/question/16800683

#SPJ1

Step-by-step explanation:

how do we find the difference between 2 numbers ? by subtracting one from the other.

p - 6 = -14

p = -8

The composite function in the form f(g(x)) is f(g(x)) = 3(1 + 4x), with the inner function g(x) = 1 + 4x and the outer function f(u) = 3u.

Given the function y = 3(1 + 4x), we need to write it in the form f(g(x)) by identifying the inner function g(x) and the outer function f(u).

First, let's identify g(x), which is the inner function. In this case, g(x) = 1 + 4x.

Next, let's identify the outer function f(u). Since y = 3(1 + 4x), we can rewrite this expression as y = 3u, where u = 1 + 4x. So, f(u) = 3u.

Now, we can write the composite function in the form f(g(x)): f(g(x)) = f(1 + 4x) = 3(1 + 4x).

So, the composite function in the form f(g(x)) is f(g(x)) = 3(1 + 4x), with the inner function g(x) = 1 + 4x and the outer function f(u) = 3u.

To learn more about composite function here:

brainly.com/question/5614233#

#SPJ11

Prime numbers are numbers with no factors other than 1 and themselves.

Use the prime factorization method to find the prime number. Factors should be 1 and the number itself.

What is a prime number?

Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.

A number is prime if it only has the factors 1 and itself. Therefore, we may quickly discover a prime number by prime factorising the provided number.

For example take - 11

The prime factorisation of 11 is 1 × 11 since 11 has only two factors 1 and itself, hence it is a prime number.

Some prime numbers in between 1 to 50 are -

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Therefore, a prime number has a factor which is 1 and the number itself.

To learn more about prime number from the given link

https://brainly.com/question/881160

#SPJ4

Answer: 84 m

Step-by-step explanation:

To find area, you multiply the width by the length ( A = L x W). Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:

5628 / 67 = 84

This tells us that the length of the pool is 87 meters. To check this answer, multiply 67 and 84. If it's equivalent to 5628, the given area, then 84 is indeed the length of the pool.

67 x 84 = 5628.

Thus, the length of the pool is 84 m.

Given that z₁= −7i and z₂ = 4+3i, the difference z₁ −  z₂ in rectangular form is; -4 - 10i

Addition of complex numbers is basically the same thing as adding two-dimensional vectors that are located on the x-y Cartesian plane.

Now, it is pertinent to note that when doing vector addition, we denote the x-component with i^ and y-component with j^.

We should also not that when adding complex numbers, the x-component is the real part and y-component is the imaginary part.

Geometrically, we can say that the addition of complex numbers can be equated to the addition of vectors in x-y plane.

Thus by the the parallelogram law of vector addition, we will be able to find the resultant vector.

In rectangular coordinates,

z₁ = -7i

z₂ = 4 + 3i

Then, z₁ - z₂ = -7i - (4 + 3i)

= -7i - 4 - 3i

= -4 - 10i

Read more about Vector in Rectangular form at; https://brainly.com/question/2840850

#SPJ1

Answer:

I got 9

Step-by-step explanation:

Of the four variables, employee number, pay rate, hire date, and sex, the "Sex" variable is the best fit to use as a dummy variable.

The variable "Sex" is the best fit to use as a dummy variable. A dummy variable is used to represent a categorical variable with a numerical value, such as 0 or 1. In this case, "Sex" is a categorical variable with two categories (male and female) and can be transformed into a dummy variable with values 0 or 1 to represent the categories. The other variables, Employee Number, Pay Rate, and Hire Date, are not categorical variables and would not be appropriate to use as dummy variables.

Read more about variables:

brainly.com/question/15158734

#SPJ4

Step-by-step explanation:

This is an algebraic expression, not an equation

For ð inputs, there can be an infinite number of subsets of those features. This is because a subset is a collection of some or all of the features within the inputs. Therefore, the number of possible subsets is determined by the number of possible ways in which we can choose from the available features.

For instance, if we have three features within an input, we can create subsets of one, two, or all three features. This gives us a total of seven possible subsets. However, this is not the only way in which we can create subsets. We can also create subsets that contain no features or any combination of features, which increases the number of possible subsets even further.

Therefore, the total number of possible subsets for ð inputs is limitless. It is important to note that not all subsets will be relevant or useful, but the more subsets we have, the more options we have for creating effective models or making informed decisions based on the inputs and features.

learn more about subsets here: brainly.com/question/20161144

#SPJ11

For ð inputs, there can be an infinite number of subsets of those features. This is because a subset is a collection of some or all of the features within the inputs. Therefore, the number of possible subsets is determined by the number of possible ways in which we can choose from the available features.

For instance, if we have three features within an input, we can create subsets of one, two, or all three features. This gives us a total of seven possible subsets. However, this is not the only way in which we can create subsets. We can also create subsets that contain no features or any combination of features, which increases the number of possible subsets even further.

Therefore, the total number of possible subsets for ð inputs is limitless. It is important to note that not all subsets will be relevant or useful, but the more subsets we have, the more options we have for creating effective models or making informed decisions based on the inputs and features.

learn more about subsets here: brainly.com/question/20161144

#SPJ11

Answer:

??

Step-by-step explanation:

7x+2-3x-7 I believe this is impossible because ther will be no equal sign so please enter it again or?

By splitting the range into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of f(x) from x=-2 to x=4 is calculated.

Area = (55 - (-2)^2) + (55 - (1)^2) + (55 - (4)^2) = 55 + 9 + 1 = 65

By splitting the interval into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of

f(x)=55x2 from x=2 to x=4

is calculated. We begin by calculating the area of the rectangle whose right endpoint is at

x = -2. F(-2)

provides the height of this rectangle, which is equal to

55 - (-2)2 = 55 + 4 = 59.

The rectangle's width is

(4 - (-2))/3 = 6/3 = 2.

The area of this rectangle is therefore 59 x 2 = 118. The area of the rectangle with x = 1 as its right terminus can also be determined in a similar manner. This rectangle has a height of f(1), which equals

55 - (1)2 = 55 - 1 = 54.

The rectangle's width is

(4 - (-2))/3 = 6/3 = 2

The area of this rectangle is therefore 54 x 2 = 108. f(4), which equals 55 - (4)2 = 55 - 16 = 39, gives the area of the rectangle with x = 4 as the right endpoint. The rectangle's width is

(4 - (-2))/3 = 6/3 = 2.

The area of this rectangle is therefore 39 x 2 = 78. The sum of the areas of the three rectangles, which equals 118 + 108 + 78 = 304, represents the total area under the graph.

Learn more about area here

https://brainly.com/question/13194650

#SPJ4

The required value of y that satisfies the equation 9y = 27 is y = 3 as per the equation's simplification rule.

The equation is given as follows:

9y = 27

To find the value of y in the equation 9y = 27, we can follow these steps:

Start with the equation 9y = 27.

Divide both sides of the equation by 9 to isolate the variable y.

This step cancels out the 9 on the left side:

(9y)/9 = 27/9

Simplify the above equation, we have:

y = 3

Therefore, the value of y that satisfies the equation 9y = 27 is y = 3.

Learn more about the solution to the equation here:

brainly.com/question/15272274

#SPJ6

Answer: The choice with the two equivalent expressions is B.

Step-by-step explanation:

Here's how I got my answer:

Do each equation carefully and be sure to pay attention to the order of the multiplication, subtraction, addition, parentheses and division signs. Since B. is just the Associative Property (it means that it has been grouped in a different way) then it is the same as the first equation.

Answer:

18

Step-by-step explanation:

2x9=18

If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.

Let the equation be AB + BC = AC

substitute the values in the above equation, we get

AB + x + 3 = 34

simplifying the value of x,

Subtract A B from both sides AB + x + 3 - AB = 34 - A B

x + 3 = 34 - AB

Subtract 3 from both sides,

x + 3 - 3 = 34 - AB - 3

x = -AB + 31

Plug in this value of x into the line segments to find BC and AC.

Where, BC = x + 3

substitute the value of x in the above equation, we get

BC = [-AB + 31 ] + 3

BC = -AB + 34

Then, AB + BC = AC

x = -AB + 31

AB = 31/x

Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,

BC = x + 3, and AC = 34, then AB = 31/x.

To learn more about Congruent angles, refer to:

https://brainly.com/question/28262429

#SPJ1

Answer:

$200

Step-by-step explanation:

Since $80 is 40% of the original price, we can think of it this way:

80 ÷ 4 = 20 (The 4 represents the 40%)

20 · 6 = 120 (The 6 represents the remaining 60%)

80 + 120 = 200

Therefore, the original cost of the jacket was $200

If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

Learn more about null hypothesis at : https://brainly.com/question/28920252

#SPJ4

Answer:

6n^2-8n+2

Step-by-step explanation:

(4n^2-5n+6)+(2n^2-3n-4)

4n^2+2n^2-5n-3n+6-4

6n^2-8n+2

Answer:

6n^2-8n+2

Step-by-step explanation:

cuz I’m smart

When comparing two sample means, we can safely reject the null hypothesis if the calculated test statistic exceeds the critical value corresponding to the chosen significance level.

In hypothesis testing, when comparing two sample means, we typically perform a t-test or z-test depending on the characteristics of the data and assumptions. The null hypothesis assumes that there is no significant difference between the means of the two samples.

To determine whether we can reject the null hypothesis and conclude that there is a significant difference, we calculate a test statistic. The specific test statistic (t or z) depends on factors such as sample size and whether population parameters are known.

Next, we compare the calculated test statistic to the critical value. The critical value is determined based on the chosen significance level (commonly denoted as α). If the calculated test statistic exceeds the critical value, we reject the null hypothesis, indicating that there is evidence to support a significant difference between the two sample means.

The significance level determines the threshold for rejecting the null hypothesis and is typically set at 0.05 (5%) or lower, depending on the desired level of confidence.

To know more about null hypothesis, refer here:
https://brainly.com/question/30535681
#SPJ11

The volume of a cylinder is given below:

Here, r=7 feet and h=4 feet. So, the volume of the cylinder is:

Thus, the volume of the cylinder is 616 square feet.

The line y = - (1 / 3) · x + 4 is a equation perpendicular to line y = 3 · x + 7.

Algebraically speaking, lines are described by the following equation:

y = m · x + b

Where:

And two lines are perpendicular to each other if the product of their slopes is equal to:

m · m' = - 1

Where:

Now we proceed to determine the equation of the perpendicular line. First, write the slope of the original line:

m = 3

Second, calculate the slope of the perpendicular line:

m' = - 1 / 3

Third, find the y-intercept:

b = y - m' · x

b = 0 - (- 1 / 3) · 12

b = 4

Fourth, write the resulting equation of the line:

y = - (1 / 3) · x + 4

To learn more on equations of perpendicular lines: https://brainly.com/question/29206001

#SPJ1

Answer:

p = £7.00

Step-by-step explanation:

Represent the original price by p.  Then 0.80p = £5.60, or p = £7.00.

If a price is discounted by 20%, the discounted price is (1 - 0.20), or 0.80, times the original price.

Answer:

C = 4s + 6a

C = 4(3) + 6(2)

C = 12 + 12

C = 24

Answer:

d = 1.405

Step-by-step explanation:

LIKE IT PLS

Answer:

No

Step-by-step explanation:

If you use the Pythagorean theorem:

sqrt (7^2+18^2)= sqrt 373 and 27^2 does not equal to 373

Answer:

No

Step-by-step explanation:

A right triangle is exactly 90 degrees and 27, 18, and 17 equal less than 90 so it does not equal a right triangle.

Answer:

y int= 12.50

slope= 2.00

equation= y=2x+12.5

Step-by-step explanation:

the y intercept in this case is the cost when you've watched 0 movies- its the initial price you pay, or the y value when the x value is equal to 0

the slope is the cost of each movie, or the increment by which the y values goes up when the x value goes up by 1 in this case. (for example the slope would be 5 if the movie price were 5 for each one movie)

y=mx+b is the equation for a linear equation, where m is the slope and b is the y intercept.