A family is planning a three-week vacation for which they will drive across the country. They have a van that gets 12 miles per gallon, and they have a sedan that gets 36 miles per gallon. How much more will they pay for gasoline if they take the van? (Assume that the family will drive 2500 miles and that gas costs $2.50 a gallon. Round your answers to the nearest cent.)

Answer: compare the relative strength of coefficients.

Step-by-step explanation: The Coefficient of determination usually denoted as R^2 is obtained by taking the squared value of the correlation Coefficient (R). It's value ranges from 0 to 1 and the value obtained gives the proportion of variation in the dependent variable which could be attributed to it's correlation or relationship to th independent variable. With a R^2 value close to 1, this means a large portion of Variation in a variable A could be explained due to changes in variable B while a low value signifies a low variance between the variables. Hence, the Coefficient of determination is used in comparing the relative strength of the Coefficients in other to establish whether a weak or strong relationship exist.

Answer:

21

Step-by-step explanation:

8x+y, when x=2 and y=5,

then 8*2+5. Because the 2 is right next to the 8, it isn't '82', but '8*2'

According to  PEMDAS, multiplication is done first, so

8*2= 16,

16+5, which is 16+5= 21

Answer:

width are 33 dimensions

Answer:

reciprocal of 5 is 1 /5.......

Answer:

4.35

Step-by-step explanation:

The fraction is 23/5.

To find the fraction of given problem.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

Let the two fractions be a/b  and  c/d then:

a/b−c/d=ad−bc/bd

It must have like denominators to subtract fractions.

For = 9 1/10 - 4 3/4= 9 1/10 - 19/4

Taking LCM of 10 and 4 is 20.

=9 1/10 - 19/4

=[tex]\frac{91*2-19*2.5}{20} \\\\\frac{182-47.5}{20} \\\\\frac{92}{20}[/tex]

After cancel out numerator and denominators

=23/5

So, the fraction is 23/5.

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Answer:

Step-by-step explanation:

Lets illustrate one method by an example:

Find the square root of  12:

The 2 perfect squares around 12 are 3^2 and 4^2 so the square root of 12 is going to be between 3 and 4.

We might predict it to be 3.5

If we square 3.5 we get 12.25 so we are pretty close.

It is less than 3.5 so we might try 3.4 .

Working 3.4^2 out we get  11.56  so we know the square root is between 3.4 and 3.5  Since 12.25 is closer to 12 than 11.56, the square root is closer to 3.5 than 3.4 so we might try 3.46.

This is called the method of trial and improvement and requires you to do long multiplications.

Answer:

38°

Step-by-step explanation:

<ABD and <DBC are two interior angles that make up <ABC.

Based on the Angle Addition Theorem, the following equation can be used to find m<DBC:

[tex] (3x + 5) + (6x - 16) = 70 [/tex]

Find x

[tex] 3x + 5 + 6x - 16 = 70 [/tex]

[tex] 9x - 11 = 70 [/tex]

[tex] 9x = 70 + 11 [/tex]

[tex] 9x = 81 [/tex]

[tex]x = \frac{81}{9} [/tex]

[tex] x = 9 [/tex]

We are given that, m<DBC = (6x - 16)°

Plug in the value of x to find the measure

m<DBC = 6(9) - 16 = 54 - 16 = 38°

Answer:

AC = 22

Step-by-step explanation:

Given that B is the midpoint of AC , then AB = BC , that is

2x + 1 = 5x - 14 ( subtract 2x from both sides )

1 = 3x - 14 ( add 14 to both sides )

15 = 3x ( divide both sides by 3 )

5 = x

Thus

AC = AB + BC = 2x + 1 + 5x - 14 = 7x - 13 = 7(5) - 13 = 35 - 13 = 22

Answer:

Random sample

Step-by-step explanation:

In statistics, a sample randomly taken from an investigated population, usually known as a random sample. To avoid having bais from our response and for it to have the best chance of it being indicative of the entire population, our sample must be random. This random sample chosen must contain subjects related to the data in the population we what to obtain a result from.

Answer:

1/4

Step-by-step explanation:

-1/2(-5/6 +1/3)

PEMDAS

parentheses first

(-5/6 +1/3)

Get a common denominator

-5/6 + 1/3 *2/2

-5/6 + 2/6 = -3/6 = -1/2

Substitute this back in

-1/2 ( -1/2)

Multiply

1/4

Answer: 7%

Step-by-step explanation:

Given: Initial jobs = 428.5 thousand

Average rate of declining of jobs  from 2010 to 2020 =  3 thousand jobs per year

From 2010 to 2020 , there are 10 years.

Total jobs declines till 2020 = 10 x (3 thousand)

= 30 thousand  (Change in jobs)

Now, utilities percent change for 2010 to 2020​ : [tex]\dfrac{change \ in \ job\ numbers}{Initial\ jobs}\times 100[/tex]

[tex]=\dfrac{30}{428.5}\times100\\\\\approx7.00\%[/tex]

Utilities percent change for 2010 to 2020 = 7 %

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation: Let the unknown no be x

1.

[tex]\frac{1}{3}\times x +27\\\\\frac{1}{3} x +27[/tex]

2.

[tex]x^2 \times 4\\\\= 4x^2[/tex]

3. The sum of the product and of 5 and a cubed number and 9

Answer:

C

Step-by-step explanation:

So we have the rational expression:

[tex]\frac{x^2-11x+30}{x^2-x-30}[/tex]

We can factor the numerator and the denominator:

Numerator:

[tex]x^2-11x+30[/tex]

Factor:

[tex](x-5)(x-6)[/tex]

Denominator:

[tex]x^2-x-30[/tex]

Factor:

[tex](x-6)(x+5)[/tex]

Substitute:

[tex]\frac{x^2-11x+30}{x^2-x-30}\\=\frac{(x-6)(x-5)}{(x-6)(x+5)}[/tex]

We can cancel out the (x-6). Thus:

[tex]=\frac{x-5}{x+5}[/tex]

Our answer is C.

Answer:

The additive inverse of −5 is +5, so 18 − (−5) = 23. The additive inverse of −5 is −5, so 18 − (−5) = 23. The additive inverse of −5 is −5, so 18 − (−5) = 13.

Answer:

-33-4x=-1(4x-7)

-33-4x=-4x+7.

-33-7=-4x+4x.

=-40.

Answer:

It is irrational because there isn’t any repeating parts.

Answer:

140

Step-by-step explanation:

A=1 B=2 C=3 D=4

4 x 5= 20

20 x 12=240

240 - 100=140

Answer: 140

Answer:

140

Step-by-step explanation:

Answer:

6x−7

Step-by-step explanation:

2x−7+4x

=2x+−7+4x

Combine Like Terms:

=2x+−7+4x

=(2x+4x)+(−7)

=6x+−7

Answer:6x-7

The like terms in the expression are 2x and 4x, so therefore you add them together and you get 6x.

Answer:

A. 19.1

the total measure of a triangle is 180°

118.6+42.3+x=180

160.9+x=180

x=180-160.9

x=19.1°

Answer:

2x^3+x^2-7x+3

Step-by-step explanation:

To do this you have to multiply the first term in the first parenthesis so you would multiply 2x by x^2 x and -3 so you get 2x^3+2x^2-6x  for the first part and then you would multiply -1 by the terms again so you would get -x^2-x+3 so you would get 2x^3+2x^2-6x-x^2-x+3 then you would add add teh like terms together so you get 2x^3+x^2-7x+3 as the final answer

Answer:

1291962 golf balls

Step-by-step explanation:

golf ball: 4/3П(0.8)^3=2.14 in^3

storage unit: 120(240)(96)=2764800 in^3

2764800/2.14=1291962 golf balls

Number of golf balls that will fit inside of a storage will be 1291962 golf balls

diameter of golf ball = 1.6 in³

radius will be = 0.8 in³  

it is known that 1 ft = 12 in

What is volume ?

Volume is a three dimensional space occupy by the body of particular shape  such as here :

volume (V) of sphere golf ball with radius r : [tex]\frac{4}{3}\pi r^{3}[/tex]

[tex]\begin{aligned}V&= \frac{4}{3}\pi r^{3} \\&=\frac{4}{3}\pi (.8)^{3}\\&\approx 2.14 \text{\:in}^{3}\end{aligned}[/tex]

Volume of rectangle ([tex]V_{1}[/tex]) with length (l= 10x12 in.), breadth (b =20x12 in.) and height (h = 8x12 in.) : lbh

[tex]\begin{aligned}V_{1}&=lbh\\&=120\cdot240\cdot96\\&=2764800 \text{\:in}^3\end{aligned}[/tex]

therefore, number of golf balls will fit inside of a rectangular storage

will be : [tex]\frac{V_{1}}{V}[/tex]

[tex]\begin{aligned}\text{no. of golf ball}&= \frac{V_{1}}{V}\\&=\frac{2764800 \text{\:in}^3}{2.14}\\&\approx 1291962\end{aligned}[/tex]

number of golf balls will be 1291962.

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Answer:

y = 34

Step-by-step explanation:

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

Remember to follow PEMDAS. First, multiply -6 with 4:

-6 * 4 = -24

-24 + y = 10

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. Add 24 to both sides:

-24 (+24) + y = 10 (+24)

y = 10 + 24

y = 34

y = 34 is your answer.

~

Answer:

Step-by-step explanation:

[tex]4\left(-6\right)+y=10\\\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\-4\times\:6+y=10\\\\\mathrm{Multiply\:the\:numbers:}\:4\times\:6=24\\-24+y=10\\\\\mathrm{Add\:}24\mathrm{\:to\:both\:sides}\\-24+y+24=10+24\\\\Simplify \\y=34[/tex]

Answer: C. The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread fo home games is higher than that of away games.

Step-by-step explanation: In Hypothesis Testing using p-value, after stating the null an alternative hypothesis, you have to compare p-value with level of significance, also known as α. If p-value is less than α, reject null hypothesis and accept alternative. If p-value is bigger, we would fail to reject null hypothesis and not accept the alternative.

In the above testing, P-value is 0.4351. Level of significance is, generally, 0.05. Comparing them, p-value is bigger than α. What it means is there is not enough evidence to support null hypothesis and, consequently, we can't conclude the difference in mean point spread of home games is higher than of the away games.

Answer: The 1st option is correct! :D

Hopefully this will help others as well!

Step-by-step explanation:

Answer:

So the breadth of the rectangle is y= 3.39 inches

And the length is = x= 4y= 4* 3.39= 13.56 inches

Step-by-step explanation:

Let the length of the rectangle be given by x and the breadth be defined by y.

Then according to the area of rectangle

Area= Length * breadth

But length is 4 times its width so x= 4y  

Therefore putting the values

Area= Length * breadth

46= x*y

46= 4y*y

46/4= y²

or

y ²= 11.5

Now taking the square root of both sides we get

y= √11.5=3.39116 inches

So the breadth of the rectangle is y= 3.39 inches

And the length is = x= 4y= 4* 3.39= 13.56 inches

Answer:

Step-by-step explanation:

volume=1/3×area of base×height=1/3×6×6×√7=12√7 cubic units

Answer:

Step-by-step explanation:

Hope this helped