Question 19 Here are the fuel efficiencies (in mpg) of 8 new cars. 44, 19, 51, 12, 34, 21, 15, 24 What is the percentage of these cars with a fuel efficiency less than 24 mpg?

m = 15/8 and yes it dep

Here, we want to find the slope from the given table

Mathematically, that could be calculated using the formula;

Now, we want to find out if it differs if we use any other random two points

Let us select the 1st and the 3rd point

Mathematically, the slope here would be;

From these, we can see that the value of the slope obtained depends on the two points that are selected

Answer: $24.85

Step-by-step explanation:

10.95+14.20= 25.15

25.15+24.85= 50

Answer:

24.35

Step-by-step explanation:

Add 10.95 to 14.20:

10.95+14.20=25.15

Then subtract the answer 25.15 from 50

50-25.15=24.35

Answer:

(3, 0)

Step-by-step explanation:

I assume this means a clockwise rotation.

let's think this through logically :

the last option (0, 3) cannot be right, because that is F before the rotation. to go back to the original position requires a full rotation of 360° (remember, a circle has 360°, and that means to travel one complete time around the circle).

(0, -3) cannot be right, because this is just mirrored down, and would represent a turn of 180° (a half-circle).

for the other options imagine you use a math compass, put the pin on the origin, and the writing arm on F. and the you draw a circle through F.

(3, 0) is the result of the clockwise (right) turn of 90°, (-3, 0) would be the result of a counterclockwise (left) turn of 90°.

so, if my assumption above is incorrect, please pick (-3, 0) for the counterclockwise solution.

The final expression that represent the total owed is 3c  + 25

He owed 3 months cable at a price of c dollars for each month, plus a one-time equipment fee of $25,

Therefore, the situation can be expressed as follows:

For a single month he pays c dollars

Hence, 3 month will be 3 × c.

Recall he also needs to pay a one time fees of 25 dollar.

Therefore, the final expression that represent the total owed is as follows:

total owed  =  3c  + 25

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To determine the missing number:

collect like terms

Therefore the missing number = -1

Answer:

the answer is -5.0

Step-by-step explanation:

Tom subtracted -1.1 from -3.9 instead of adding them together

Answer:

It is a function because circles are functions

Step-by-step explanation:

the formula for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h,k) = center

r=radius

radius is 4 because diameter is 8

Center is (2,1)

plug it into the equation:

[tex](x-2)^2+(y-1)^2=16[/tex]

After solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.

So, the total value of money by 35 bills is $0, and $20 is $520.

Therefore, after solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.

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Answer:

[tex]x=-7i, 7i, 5/8, -5/8[/tex]

Step-by-step explanation:

[tex](64x^2-25)(x^2+49)=0 \\ \\ (8x-5)(8x+5)(x+7i)(x-7i)=0 \\ \\ x=-7i, 7i, 5/8, -5/8[/tex]

Answer: $108

Step-by-step explation:

Answer:

33

Step-by-step explanation:

The quotient of 581 and 14 has a value of 40.07

The quotient expression is given as

581/14

Next, we express 581 as the sum of a multiple of 14 and another number

Say 581 = 280 + 280 + 1

So, we have the following equation

581/14 = (280 + 280 + 1)/14

Expand the bracket

So, we have the following equation

581/14 = 280/14 + 280/14 + 1/14

Evaluate the quotients

581/14 = 20 + 20 + 0.07

Evaluate the sum

581/14 = 40.07

Hence, the value of the quotient expression is 40.07

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The two approximations of the region's area between the graph of the function and the x-axis over the given interval are 14.31 < AREA < 17.01

We have :
f(x) = 9 -x [ 2, 4 ], 6 rectangles.

Here, a = 2 and b = 4 , n = 6

The width of the rectangles will be

x' = [tex]\frac{b-a}{n}[/tex]

x' = [tex]\frac{4-2}{6} = \frac{2}{6} = \frac{1}{3} = 0.33[/tex]

Now, The given function is f(x) = 9 -x

[tex]f(x_{i}) = x_{i} - 9[/tex]

For [tex]x_{0} = 0[/tex], [tex]f(x_{0} ) = 9[/tex]

For  [tex]x_{1} = 0.3[/tex], [tex]f(x_{1} ) = 9 -0.3 = 8.7[/tex]

For [tex]x_{2} = 0.6[/tex], [tex]f(x_{2} ) = 9 -0.6 = 8.4[/tex]

For [tex]x_{3} = 0.9[/tex], [tex]f(x_{3} ) = 9 -0.9 = 8.1[/tex]

For [tex]x_{4} = 1.2[/tex], [tex]f(x_{4} ) = 9 -1.2 = 7.8[/tex]

For [tex]x_{5} = 1.5[/tex], [tex]f(x_{3} ) = 9 -1.5 = 7.5[/tex]

For [tex]x_{6} = 2.1[/tex], [tex]f(x_{3} ) = 9 -2.1 = 7.2[/tex]

Now, The area by using an approximation using 6 approximating rectangles and right endpoints is given by.

A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6})x'\\[/tex]

A = (8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3

A = 47.7*0.3 = 14.31

The area by using an approximation using 6 approximating rectangles and left endpoints is given by:

A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{0} + f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6} } )x'\\[/tex]

A = (9+8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3

A = 17.01

Thus  14.31 < AREA < 17.01

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Answer:

10 cups

Step-by-step explanation:

6 divided by 4 is 1.5 and if you take 15 divided by 1.5 it'd be 10

Answer:

10 cups of sugar

Step-by-step explanation:

you can easily make it into a ratio.... ( the amountof sugar needed to make 15 batches of cookies is x)

x/15 = 4/6

when you multiply you get 6x = 4 × 15

6x = 60, then you divide by 6

giving you x=10

The  volume of the cube is  2744 cm³.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square all angles are 90° and all sides present the same value.

A square is a 2D figure, when the square is associated a 3D figure, the figure is called a cube. The cube presents 6 faces with length (l) , height (h) and width (w) equal. Thus, the cube presents congruent edges.

The volume is given from the formula V=a³, where a is a congruent edge.

The question gives:

Therefore,

V=a³

V=14³

V=14*14*14

V=2744 cm³

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Answer: Around 141 guests can be invited

Explanation: 423 divided by 3/4 is 141, and 141 x 3/4 is 423

Answer:

v=20m/s ,u= 0m/s( from rest) a=1.25m/s Distance s=?

V²= UT +2as

make s subject

2as=v²-u²

S= v²-u²/2a

S =20²-0²/2*1.25

S=400/2.5

S= 160m

Answer:

21 Degrees.

Step-by-step explanation:

It was 22 degrees by noon, by then the temperature had already risen by
eight degrees, but since we are going back in time, we would subtract the eight degrees.

22 - 8 = 14.

Now we are at 9 A.M, it is 14 degrees. But, the temperature had doubled from 5-9 A.M, so we would divide our fourteen by two in order to half it.

14 ÷ 2 = 7.

Now we are at 5 A.M.

From midnight to 5 A.M the temperature dropped fourteen degrees so we would add that fourteen back into the equation.

7 + 14 = 21.

Hope this helped!!

Answer:

Answer bellow with explanations

Step-by-step explanation:

if Miriam buys 0.5 pounds of strawberries and 3 pounds of apples she will in total would have bought 3.5 pounds of fruit.

if you are looking for the price she had to pay for the fruits above the equation to solve that is as following.

0.5 x 3$ = 1.5$

3.0 x 3.25 = 9.75$

total for the fruits needed above would be 1.5$ + 9.75$ = 11.25$

if you are looking for the amount of pounds converted into the amount of fruit

0.5/3$ = 0.16(6) pounds of strawberries

3/3.25$= 0.92307692307 pounds of apples

total of pounds of fruit that have been purchased is equal to 0.16(6) + 0.92307692307 = 1.08974358973 pounds

If Miriam buys x pounds of strawberries and y pounds of apples

it can be shown in an equation using 2 unknown values

X(strawberries)

Y(apples)

x/3$ + y/3.25$

to calculate the amount of pounds that have been purchased

14/4 = ?

There are 4x5 = 20 squares

Then 14/4 = 3 + 2/4

also 14/4 = 70/20 = 7/2

Take 14 squares, from figure

Now graph portion shade

Simplify the integrand.

[tex]\displaystyle \frac{x^3-x^2-1}{x^2-x-1} = x + \frac{x-1}{x^2-x-1}[/tex]

Expand into partial fractions, recalling that [tex]\phi[/tex] and [tex]-\frac1\phi[/tex] are roots to the quadratic in the denominator.

[tex]\dfrac{x-1}{(x - \phi) \left(x + \frac1\phi\right)} = \dfrac1{1+\phi^2} \left(\dfrac1{x-\phi} + \dfrac{\phi^2}{x + \dfrac1\phi}\right)[/tex]

Then the integral is

[tex]\displaystyle I = \int_0^1 \frac{x^3-x^2-1}{x^2-x-1} \, dx \\\\ ~~~~ = \int_0^1 x \, dx + \frac1{1+\phi^2} \int_0^1 \left(\frac1{x-\phi} + \frac{\phi^2}{x+\frac1\phi}\right) \, dx \\\\ ~~~~ = \frac12 + \frac{1}{1+\phi^2} \left(\ln|1-\phi| + \phi^2 \ln\left|1 + \frac1\phi\right| - \ln|-\phi| - \phi^2 \ln\left|\frac1\phi\right|\right)[/tex]

and this reduces significantly, when we recall that [tex]\phi = 1 + \frac1\phi[/tex], to

[tex]\displaystyle I = \boxed{\frac12 + \frac{2\phi}{1 + \phi^2} \ln(\phi)}[/tex]

The domain and range are the set of all real numbers, so:

Domain: x ∈ R

Range: x ∈ R

Thus, the correct option is  the second one

For any function y = f(x), we define the domain as the set of the possible values of x (the ones on the horizontal axis) and the range is the set of the possible values of y (vertical axis).

In this case, we have a linear equation (you can see that the lines extend to the bottom left and the top right)

So both domain and range are the sets of all real numbers.

Thus, the correct option is  the second one.

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The value of a, b, c and d are 25, 3, 14 and 7 such that the sum of all rows, columns and diagonals are 48.

Given to us a magic square in which the sum of all rows, columns and diagonals are same. Then, we have to complete the missing numbers i.e., a, b, c and d respectively.

Let's proceed to solve this magic square accordingly.

First let's calculate that what will be the sum of all rows, columns and diagonals.

From the figure of magic square one diagonal is completely filled from that we can easily calculate the sum of the diagonals.

Sum = 5+16+27 = 48

Then, we can find the value of a, b, c and d easily.

5+a+18 = 48

23+a = 48

a = 48-23

a = 25

Therefore, the value of a is 25.

29+16+b = 48

45+b = 48

b = 48-45

b = 3

Therefore, the value of b is 3.

Now, 5+29+c = 48

34+b = 48

c = 48-34

c = 14

Therefore, the value of c is 14.

Then, we have

c+d+27 = 48

14+d+27 = 48

41+d = 48

d = 48-41

d = 7

Therefore, the value of d is 7.

Hence, we have completed the magic square in which the sum of all rows, columns and diagonals are 48.

Therefore, the value of a, b, c and d are 25, 3, 14 and 7 respectively.

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Check the picture below.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ S(-6,-5)\qquad R(-11,10)\qquad \qquad \stackrel{\textit{ratio from S to R}}{2:3} \\\\\\ \cfrac{S\underline{T}}{\underline{T} R} = \cfrac{2}{3}\implies \cfrac{S}{R} = \cfrac{2}{3}\implies 3S=2R\implies 3(-6,-5)=2(-11,10)[/tex]

[tex](\stackrel{x}{-18}~~,~~ \stackrel{y}{-15})=(\stackrel{x}{-22}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-18 -22}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-15 +20}}{2+3} \right)} \\\\\\ T=\left( \cfrac{ -40 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} T=(-8~~,~~1) \end{array}}[/tex]

Graph (D) shows a complex number with an imaginary component, i.

So, we are aware that a complex number is shown as:

Where x stands for a number's real value and y for a number's imaginary value.

As a result, the number I is written as:

This indicates that the symbol for the number I is a point (0,1).

Therefore, graph (D) shows a complex number with an imaginary component, i.

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The complete question is given below:

Which graph depicts a complex number with i as the imaginary part?

Answer:

225

Step-by-step explanation:

if it is 1/3 off, then it means it's at 2/3 the price. now, you have to divide 450/2 to get the answer. 2/3 divided by 2=1/3

450/2=225, and thats how much money you will save

Applying the Chain Rule, the derivatives are given as follows:

The function Z is defined as follows:

z = x^7y^7.

The variables x and y are functions of variables s and t, as follows:

Hence the derivative of z as a function of s is given as follows:

∂z/∂s = (dz/dx)(dx/ds) + (dz/dy)(dy/ds).

Hence, applying the derivative rules for the exponents, and for the exponents, we have that:

[tex]\frac{\partial z}{\partial s} = 7x^6y^7\cos{(t)} + 7y^6x^7\sin{(t)} = 7x^6y^6(y\cos{t} + x\sin{t})[/tex]

Replacing the values of x and y, we have that:

[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex]

We follow the same logic as above, only that now the inside derivatives, that is, the derivatives of x and y, are as function of t and not of s, hence:

∂z/∂t = (dz/dx)(dx/dt) + (dz/dy)(dy/dt).

Then:

[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7sx^6y^6(-y\sin{t} + x\cos{t})[/tex]

Then, replacing x and y as functions of s and t, we have that:

[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]

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Answer:

Step-by-step explanation:

it should be 180

9 1/4 to 9

20 stays the same

Answer:

ab^4/b-a^2

Step-by-step explanation:

...........

Answer:

Step-by-step explanation: