You are running a fuel economy study. One of the cars you find is blue. It can travel 45 1/2 miles on 1 1/4 of gasoline. Another car is red. It can travel 23 3/5 miles on 4/5 of gasoline. What is the unit rate for miles per gallon for each​ car? Which car could travel the greater distance on 1 gallon of​ gasoline?

Answer:

y = -2/7(x) + 3

Step-by-step explanation:

The equation of a line can be stated as y = mx + b, where m is the slope and b is the y-intercept (the value of the function when x = 0).  To find the equation of the line, we'll start by finding the slope.

The slope can be expressed as [tex]\frac{y_{2} - y_{1}}{x_{2}-{x_1}}[/tex]

Substituting in our coordinates, we have:

[tex]m = \frac{1 - 5}{7 - (-7)} = \frac{-4}{7 + 7} = \frac{-4}{14}[/tex], which can be simplified to [tex]-\frac{2}{7}[/tex]

Plugging that back into our equation, we have y = [tex]-\frac{2}{7}[/tex]x + b

Now, to find b, we substitute in one of our sets of coordinates.  Let's use (-7, 5)

x = -7 and y = 5, which gives us:

[tex]5 = -\frac{2}{7} (-7) + b[/tex]

[tex]-\frac{2}{7} (-7) = 2[/tex], which gives us:

5 = 2 + b

Subtracting 2 from both sides, we get:

3 = b

Plugging that back into our equation, we have [tex]y = -\frac{2}{7} x + 3[/tex]

Answer:

3

Step-by-step explanation:

The slope is 3. It's the correct answer.

Answer:

8/10

Step-by-step explanation:

Answer:

-8b - 32

Step-by-step explanation:

8(-b-4)

Distribute

8 *(-b) + 8 * (-4)

-8b - 32

Answer:

-8b-32

Step-by-step explanation:

8(-b-4) next it would be -8b-32

Answer:

0

Step-by-step explanation:

Because it is a line parallel to x-axis.

Answer:

The answer is A

Step-by-step explanation:

When you reflect something over the x-axis all of the negative y coordinates become positive.

Answer:

21 pounds

tell me if it helped :P

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Using the mean concept, it is found that we will need 15 more points to bring up his average up to 90%.

The mean of a data-set is the sum of all observations divided by the number of observations.

In this problem:

Hence, the mean is:

[tex]M = \frac{0.84(5) + n}{5 + n} = \frac{4.2 + n}{5 + n}[/tex]

We want the mean to be of 0.9, thus:

[tex]M = 0.9[/tex]

[tex]\frac{4.2 + n}{5 + n} = 0.9[/tex]

[tex]4.2 + n = 0.9n + 4.5[/tex]

[tex]0.1n = 0.3[/tex]

[tex]n = \frac{0.3}{0.1}[/tex]

[tex]n = 3[/tex]

3 more testes are need, each worth 5 points, hence, 15 more points are needed to bring up his average up to 90%.

A similar problem is given at https://brainly.com/question/25323941

Step-by-step explanation:

this is a kind of trick question, actually.

with whatever we draw, we produce X values as power of 3.

to be precise, we can have only

3⁰ = 1

3¹ = 3

3² = 9

3⁴ = 81

due to the possible combinations of drawn numbers (e.g. 3 cannot be created by a multiplication of 0s, 1s and 2s).

so, mostly, these results cannot be exact factors of 1024.

1024 cannot be divided by 3, nor by 9 nor by 81.

but 1024 is a multiple of 1 (as is every number).

so, we are looking at the probability to get 0 as multiplication result of the numbers on the 2 drawn balls.

the only possibilities are

1 and 0

2 and 0

out of in total 6 (2×3) different outcomes

1 and 0

1 and 1

1 and 2

2 and 0

2 and 1

2 and 2

the probability of this "0" event is again

number of desired outcomes / number of possible outcomes = 2/6 = 1/3

Answer:

1 minute every mile

Step-by-step explanation:

just divide

Using the information given, it is found that:

a) 0.39

b) z = 1.96

c) s = 0.0218

d) M = 0.0428

e)

f) The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more  safety regulations is (0.3472, 0.4328).

Item a:

The point estimate is the sample proportion, hence:

[tex]\pi = \frac{195}{500} = 0.39[/tex]

Item b:

95% confidence level, hence [tex]\alpha = 0.95[/tex], the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].

Item c:

The standard error is:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, [tex]\pi = 0.39, n = 500[/tex], hence:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]s = \sqrt{\frac{0.39(0.61)}{500}}[/tex]

[tex]s = 0.0218[/tex]

Item d:

The margin of error is:

[tex]M = zs[/tex]

In this problem, [tex]z = 1.96, s = 0.0218[/tex], hence:

[tex]M = zs = 1.96(0.0218) = 0.0428[/tex]

Item e:

The lower bound is:

[tex]\pi - M = 0.39 - 0.0428 = 0.3472[/tex]

The upper bound is:

[tex]\pi + M = 0.39 + 0.0428 = 0.4328[/tex]

The lower bound is 0.3472.

The upper bound is 0.4328.

Item f:

The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more  safety regulations is (0.3472, 0.4328).

A similar problem is given at https://brainly.com/question/15136737

Answer:

the answer will be choice D

as we can see that the triangle have angles measuring 30 60 and 90 so we will use the 30-60-90 rule

you can look up the explantion about the rule online

Answer:

inding the Greatest Common Factor (GCF): To find the GCF of two expressions:

Factor each coefficient into primes. Write all variables with exponents in expanded form.

List all factors—matching common factors in a column. ...

Bring down the common factors that all expressions share.

Multiply the factors

Answer:

Step-by-step explanation:

2x = 2*x

4y = 2 *2 *y

6z = 2* 3 * z

GCF = 2

GCF is the greatest common factor. Here 2 is common factor

2x - 4y + 6z = 2*(x - 2y + 3z)

Step-by-step explanation:

e^4x = 5

x = 1/4 × ln(5)

x ÷ 1/4 = ln(5)

x.4 = ln(5)

4x = ln(5)

ln(5) = 4x

Option → D

Step-by-step explanation:

82÷100= 0.82

0.82×164= 134.48 /134

Answer:

Step-by-step explanation:

The slope is most easily found using two grid intersections. We know that the line crosses the grid intersection (0, -1) at the y-axis. (That is the y-intercept.) And it crosses another one at (1, 1), just above the x-axis in the first quadrant.

The slope of the line between these points can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-1))/(1 -0) = 2/1 = 2

The slope can also be found by counting the grid squares of "rise" (2) for each grid square of "run" (1) between those two points or any other convenient points on the line.

  m = rise/run = 2/1 = 2

The slope of the line is 2.

__

The y-intercept is the point where the line crosses the y-axis. That point is on an unmarked grid line between y = 0 and y = -2. That is, it is halfway between the values 0 and -2, so is y = -1.

The y-intercept is (0, -1).

Answer:

Graph A

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  ( 0 ,  2 )

Focus:  

( 0 ,  41 /20 )

Axis of Symmetry:  x = 0

Directrix:  y = 39 /20

x                   y

− 2                22

− 1                 7

0                  2

1                    7

2                  22

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{8}\div 1\frac{1}{3}\implies \cfrac{5}{8}\div \cfrac{4}{3}\implies \cfrac{5}{8}\cdot \cfrac{3}{4}\implies \cfrac{15}{32}[/tex]

Answer: approximate width= 5.2 yd

Step-by-step explanation:

Answer:

-x² + 4x - 8

Step-by-step explanation:

Given: 2x² - x + 6 is subtracted from x² + 3x - 2

Rewriting: (x² + 3x - 2) - (2x² - x + 6)

Distrubte negative: x² + 3x - 2 - 2x² + x - 6

Combine like terms:  -x² + 4x - 8

Answer: -x² + 4x - 8

Hope this helps, have a nice day :D

Answer:

9 players rushed 20 or more yards this season

Step-by-step explanation:

Answer:

all of the expressions are equivalent

Step-by-step explanation:

if you simplify each expression, you get the same answer for all of them

9514 1404 393

Answer:

  d(32) = 28.80

  the price Marcus pays on an item with an original price of 32

Step-by-step explanation:

  d(32) = 32 -0.1(32)

  d(32) = 28.8

The problem statement tells you d(32) is the price Marcus pays when the original price is 32.