A man takes a 375-mile trip to Miami. His large car gets 18 miles per gallon, and his small car gets 32 miles
per gallon. How many gallons of gas will he save if he takes the smaller car?

Answer:

x = 10.75

Step-by-step explanation:

4(x+9)=8x-7

Step 1: Distribute the 4 to the x and 9

4 * x = 4x

4 * 9 = 36

We now have 4x + 36 = 8x - 7

Step 2: add 7 to both sides

36 + 7 = 43

-7 + 7 cancels out

We now have 4x + 43 = 8x

Step 3 subtract 4x from both sides

4x - 4x cancels out

8x - 4x = 4x

We now have 4x = 43

step 4 divide both sides by 4

4x / 4 ( the 4s cancel out and we're left with x )

43/4 = 10.75

We're left with x = 10.75

Answer:

answer :

12 = x / 5

12 × 5 = x

60 = x

or

x = 60

9514 1404 393

Answer:

  B.  -∞

Step-by-step explanation:

There is a vertical asymptote at x=2. Left of that line, the denominator is negative. As x approaches 2 from the left, the function approaches negative infinity.

Answer:

He had to arrive at 5:00pm

If he traveled at 15km per hour, he would arrive one hour too early

If he traveled at 10km per hour, he would arrive one hour too late.

At what time did he leave, what distance did he travel, and at what speed did he travel

:

Let d = distance traveled

:

Write an time equation; time = dist/speed

Travel time at 10 km/hr - travel time at 15 km/h = 2 hrs

d%2F10 - d%2F15 = 2

Multiply by 30

3d - 2d = 30(2)

d = 60 km is the distance

:

Find the travel time at 15 km/hr

60%2F15 = 4 hrs

:

let s = speed required to get there on time

:

required travel time - 15km/hr travel time = 1

60%2Fs - 4 = 1 hr

60 - 4s = 1s

60 = 1s + 4s

60 = 5s

s = 12 km/hr to arrive on time

:

Required travel time: 60%2F12 = 5 hrs

He would have to leave at noon

;

Summarize, depart at noon, travel for 5 hrs at 12 km/hr, a dist of 60 km

Step-by-step explanation:

Answer:

a). 106

b). See Explanation

Step-by-step explanation:

According to the Question,

Given, The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 4247 employees at the company and wants to conduct a systematic sample of size 40.

a). Thus, the Required Value of K is 4247/40 = 106.175 ≈ 106

b). The individuals who will be administered the survey. Randomly select a number from 1 to k. Suppose that we randomly select 19. Starting with the first individual selected, the individuals in the survey will be

Answer:

h=A-πr²÷2πr

Step-by-step explanation:

M making h subject

A=2πrh+πr²

A-πr²=2πrh

A-πr²÷2πr=h

h=A-πr²÷2πr

Answer:

3/10

Step-by-step explanation:

If we have two points on a line, we can find the slope using the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -1 - -4)/( 5 - -5)

   = ( -1 +4)/ ( 5 + 5)

  = 3/10

Answer: [tex]6x^3 +30x^2 +4x+20[/tex]

Step-by-step explanation:

[tex](6x^2 +4)(x+5)\\\\ =6x^3 +30x^2 +4x+20[/tex]

Answer:

C

Step-by-step explanation:

C is the only answer that doesnt share x-values

Answer:  [tex]\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]

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

Work Shown:

x^2+y^2 = r^2

(8)^2+(-7)^2 = r^2

113 = r^2

r = sqrt(113)

The distance from (0,0) to (8,-7) is exactly sqrt(113) units.

This is the exact length of the hypotenuse of the right triangle.

Next, we do the following steps:

[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\theta) = \frac{x}{r}\\\\\cos(\theta) = \frac{8}{\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113}*\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113*113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113^2}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]

Side note: cosine is positive in quadrant Q4.

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

Explanation:

It appears that -20 is the mean. It's not entirely clear however. If that assumption is correct, then the distance from -30 to -20 is 10 units. So the left endpoint is 1 standard deviation below the mean (because the standard deviation is 10 units).

Recall that through the empirical rule, roughly 68% of the distribution is within 1 standard deviation of the mean. This cuts in half to 34%. So the area from x = -30 to x = -20 is roughly 0.34

We'll use this value later so let A = 0.34

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

The area under the curve from x = -20 to x = -10 is also 0.34

The area under the curve from x = -20 to x = 0 is 0.95/2 = 0.475

For the second part there, I'm using the idea that 95% of the normal distribution (roughly) is within 2 standard deviations of the mean.

So the area from x = -20 to x = -5 is somewhere between 0.34 and 0.475

Let B = 0.34 and C = 0.475

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

The full shaded blue area is somewhere between A+B = 0.34+0.34 = 0.68 and A+C = 0.34+0.475 = 0.815

Based on that alone, the answer is between B and C.

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

Unfortunately, we can't nail down an actual value unless we use a Z table or a calculator.

When I use a calculator, I'm getting 0.7745 (approximate) which rounds to 0.775 and converts to 77.5%

As for how to get this without a table or calculator, I'm not entirely sure what your teacher wanted you to do.

Answer:

D. -4

Step-by-step explanation:

the only graph I see is a red line in a coordinate grid.

this red line represents the function y = -4, for x in the interval [-1,4].

so, [-1,4] is the domain of the function, and [-4] is the range of the function.

when the question asks about what values are graphed below, and it mentions "range", I assume it means functional values (results of the function).

the only function I can see is the mentioned constant function y=-4, so that -4 is the only functional value (the only value in the range of the function) in this graphic.

Answer:

The awnser should be 3.

Step-by-step explanation:

if f(x) means the same thing as x + 1. Than that means f = 1. So if re write the question. 1 plus 2 equals 3.

Answer:

a

Step-by-step explanation:

Answer:

HOPE IT HELPS

Answer:

The answer is "9 and 7".

Step-by-step explanation:

Given:

[tex]A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right][/tex]

Using formula:

[tex]|A-\lambda \cdot I|= 0\\\\[/tex]

[tex]\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\[/tex]

[tex]\to \lambda=7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda=9\\\\[/tex]

Answer:

y=3/4x−12.

Step-by-step explanation:

Slope of the perpendicular line is negative inverse: m=34.

The equation of the perpendicular line is y=3x4+a.

To find a, we use the fact that the line should pass through the given point: −12=(34)⋅(0)+a.

a=−12.

Therefore, the equation of the line is y=3x4−12.

If this helps you, please give bainliest!

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]3v + 8 \geq 22[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Breaking down the phrase...}}\\\\\text{Three times a number, v, added to eight is greater than or equal to twenty-two. }\\------------------\\\rightarrow \text{"Three times a number, v..."} - 3v \text{ This expresses the product of '3' and 'v'.}\\\\\rightarrow \text{"added to eight..."} - + 8 \text{ The product gets added to eight.}\\\\--------------\\\text{The First Part Is:}}\\\\3v + 8\\---------------\\\rightarrow \text{is greater than or equal to twenty-two. } - \geq 22[/tex]

[tex]\text{The value of '3v + 8' is greater than or equal to 22.}\\---------------\\\text{\underline{Putting it together, we would have:}}\\\\\boxed{3v + 8 \geq 22}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

They need to survey 4145 residents.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

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

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?

This is n for which [tex]M = 0.02[/tex]. As we have no estimate for the proportion, we use [tex]\pi = 0.5[/tex]. So

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

[tex]0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.02})^2[/tex]

[tex]n = 4144.1[/tex]

Rounding up:

They need to survey 4145 residents.

Answer:

JK ≈ 12.3

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{FI}{JM}[/tex] = [tex]\frac{FG}{JK}[/tex] , substitute values

[tex]\frac{59}{26}[/tex] = [tex]\frac{28}{JK}[/tex] ( cross- multiply )

59 JK = 728 ( divide both sides by 59 )

JK ≈ 12.3 ( to the nearest tenth )

The values of A, B, C and D are (d) A = 1, B = 0, C = 3 and D = -3

From the question, we have:

x^3 + 8x - 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D

Collect like terms

x^3 + 8x - 3 = Ax^3 + Bx^2 + 5Ax  + Cx + 5B + D

By comparing the coefficients, we have:

Ax^3 = x^3

Bx^2 = 0

5Ax + Cx = 8x

5B + D = -3

Remove the x factors

A = 1

B = 0

5A + C = 8

5B + D = -3

Substitute A = 1 in 5A + C = 8

5(1) + C = 8

Solve for C

C = 3

Substitute B = 0 in 5B + D = -3

5(0) + D = -3

Solve for B

D = -3

Hence, the values of A, B, C and D are (d) A = 1, B = 0, C = 3 and D = -3

Read more about partial fractions at:https://brainly.com/question/18958301

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Answer:

A) The probability that Kevin will win the spring break cruise is 0.42%.

B) Kevin's expected earnings are $ 8.4.

C) Kevin effectively contributed with $ 50.

Step-by-step explanation:

Since the college student senate is sponsoring a spring break Caribbean cruise raffle, and the proceeds are to be donated to the Samaritan Center for the Homeless, ya local travel agency donated the cruise, valued at $ 2000, and the students sold 2357 raffle tickets at $ 5 per ticket, to determine A) if Kevin bought ten tickets, what is the probability that Kevin will win the spring break cruise to the Caribbean; B) Kevin's expected earnings and C) how much did Kevin effectively contribute to the Samaritan Center for the Homeless; the following calculation must be performed:

A) 10/2357 = 0.0042 x 100 = 0.42

Therefore, the probability that Kevin will win the spring break cruise is 0.42%.

B) 2000 x 0.0042 = 8.4

Therefore, Kevin's expected earnings are $ 8.4.

C) 5 x 10 = 50

Kevin effectively contributed with $ 50.

Answer:

1 × 32,  2 × 16,  4 × 8,  8 × 4,  16 × 2,  32 × 1

Step-by-step explanation:

There are 6 different ways for Evan to create a array of 32 miniature cars.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

An array would constitute the shape of a parallelogram, in which you are essentially solving for s₁ and s₂.

Since there are 32 miniature cars in all, in which both sides, when multiplied, must result in said number:

32 x 1 = 32

2 x 16 = 32

4 x 8 = 32

8 x 4 = 32

16 x 2 = 32

1 x 32 = 32

Hence, There are 6 different ways for Evan to create a array of 32 miniature cars.

Learn more about multiplications;

https://brainly.com/question/14059007

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Step-by-step explanation:

Kindly find 4 attached files

The proportionality is determined by the lines that only passes through the origin

And all the lines drawn are passing through the origin

So by either one of the 2 ways

By using rule of direct variation y=kx that has no y intercept

Or by finding the equation of straight line and find the slope with neglecting the y intercept since it's 0

Answer:

8,000 cm cubed

Step-by-step explanation:

Volume of a cube = length x width x height

All sides on a cube are the same length

If one is 20 cm, all are.

20x20x20=8,000.

Answer:

Step-by-step explanation:

-1<x<3.   I hope it helpful!

Step-by-step explanation:

answer in the photo above look

Answer:

117 units higher

Step-by-step explanation:

|-172 + 55| = 172 - 55 = 117

117 units higher

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

30 more then 172

Step-by-step explanation: