can you please explain this?​

Given:

Blue car travels [tex]44\dfrac{1}{2}[/tex] miles on [tex]1\dfrac{1}{4}[/tex] gallons of gasoline.

Red car travels [tex]20\dfrac{4}{5}[/tex] miles on [tex]\dfrac{4}{5}[/tex] gallons of gasoline.

To find:

The unit rate for miles per gallon for each car and find which car could travel the greatest distance on one gallon of gasoline.

Solution:

We know that,

[tex]\text{Unit rate}=\dfrac{\text{Total distance covered by the car}}{\text{Number of gallons of gasoline}}[/tex]

Using this formula, the unit rate of blue car is

[tex]\text{Unit rate of blue car}=\dfrac{44\dfrac{1}{2}}{1\dfrac{1}{4}}[/tex]

[tex]\text{Unit rate of blue car}=\dfrac{\dfrac{88+1}{2}}{\dfrac{4+1}{4}}[/tex]

[tex]\text{Unit rate of blue car}=\dfrac{89}{2}\times \dfrac{4}{5}[/tex]

[tex]\text{Unit rate of blue car}=\dfrac{178}{5}[/tex]

[tex]\text{Unit rate of blue car}=35.6[/tex]

Unit rate of red car is

[tex]\text{Unit rate of red car}=\dfrac{20\dfrac{4}{5}}{\dfrac{4}{5}}[/tex]

[tex]\text{Unit rate of red car}=\dfrac{\dfrac{100+4}{5}}{\dfrac{4}{5}}[/tex]

[tex]\text{Unit rate of red car}=\dfrac{104}{5}\times \dfrac{5}{4}[/tex]

[tex]\text{Unit rate of red car}=26[/tex]

Therefore, the unit rate of blue car is 35.6 miles per gallon of gasoline and  unit rate of red car is 26 miles per gallon of gasoline.

Since, unit rate of blue car is greater than the red car, therefore blue car travel the greatest distance on one gallon of gasoline.

Step - 1: Calculate 20% of 840.

[tex]840 \times \frac {20}{100} = 168[/tex]

Step - 2: Subtract from 840.

[tex]840-168=672 [/tex]

Answer:

pipe will empty the tank in 10.5 hours, working alone.

Step-by-step explanation:

Let x be the rate of work of the slower pipe (measured in the tank volume per hour).

Then the rate of work of the faster pipe is 2.5x of the tank volume per hour.

The combined rate of the two pipes is then  x + 2.5x = 3.5x.

We are given

7.5*3.5*x = 1;  hence   x = 1%2F%287.5%2A3.5%29.

Then  2.5x = 2.5%2F%287.5%2A3.5%29 = 1%2F%283%2A3.5%29 = 1%2F10.5.

It means that the faster pipe will empty the tank in 10.5 hours, working alone.

The faster pipe will empty the tank in 10.5 hours, working alone.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Let x be the rate of work of the slower pipe (measured in the tank volume per hour).

Then the rate of work of the faster pipe is 2.5x of the tank volume per hour.

The combined rate of the two pipes is then  x + 2.5x = 3.5x.

We are given

7.5×3.5×x = 1

7.5×3.5 x=1

Divide both sides by 7.5×3.5

x=1/ 7.5×3.5

2.5x=2.5/ 7.5×3.5

x=1/10.5

It means that the faster pipe will empty the tank in 10.5 hours, working alone.

Hence, the faster pipe will empty the tank in 10.5 hours, working alone.

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Answer:

The answer is below

Step-by-step explanation:

How much sleep do high school students get on a typical school night? An interested student designed a survey to find out. To make data collection easier, the student surveyed the first 100

students to arrive at school on a particular morning. These students reported an average of 7.2 hours of sleep on the previous night.

(a) What type of sample did the student obtain?

(b) Explain why this sampling method is biased. Is 7.2 hours probably higher or lower than the true average amount of sleep last night for all students at the school? Why?

Solution:

a) A voluntary response sample is a sample made up of volunteers. It samples more people who have strong opinions and sample people who have less opinion on the survey. It is biased.

Convenience sample is a type of sampling where the group of people are conveniently selected from a population. It is biased.

Since the first 30 students to arrive at school on a particular morning was used, this is convenience sampling since only the first 30 was conveniently selected.

b) This sampling method is biased because the first 30 students are those who would have woken up earlier while those who woke up late would not be sampled.

This means that the 7.2 hours is lower than the true average amount of sleep last night for all students at the school

Answer:

x = 3

Step-by-step explanation:

6x - 7 = 11

First, add 7 to 11 which gets you 6x = 18

Then, divide 18 by 6 to solve for x which gets you 3

This means that x = 3

(hope this helps)

Answer:

Step-by-step explanation:

6x-7+11

(add 7 to both sides, canceling out the negative 7 on the left, and resulting in a sum of 18 on the right)

6x=18

(divide both sides by 6, which should isolate x because the sixes will cancel each other out, and give you a quotient of 3 on the right side)

x=3

Answer:

d) m=1/2

Step-by-step explanation:

have you ever heard of the equation y=mx + b

the m is your slope

in your equation above the number with x is 1/2, so that is ur slope..

Hope this helps!! Pls mark me brainliest!!

Answer:

The answer is B.

Step-by-step explanation:

Let us first set up an equation.

(3x - 7) + (2x + 3) = 90

5x - 4 = 90

5x = 94

x = 18.8

Hope this helps!

Please mark as brainliest.

Answer:

D  m<A = 49.4 deg

Step-by-step explanation:

Since the lines are perpendicular, the sum of the measures of angles A and B is 90 deg.

m<A + m<B = 90

3x - 7 + 2x + 3 = 90

5x - 4 = 90

5x = 94

x = 18.8

m<A = 3x - 7 = 3(18.8) - 7 = 56.4 - 7 = 49.4

Answer: D  m<A = 49.4 deg

Answer:

x=10

y=25

Step-by-step explanation:

3x-10+5x+30+6x+20=180

14x+40=180

14x=180-40

14x=140

x=10

9x-10=4y-20

9(10)-10=4y-20

90-10=4y-20

80=4y-20

80+20=4y

100=4y

25=y

Answer:

30

Step-by-step explanation:

Answer:

-9x²

Step-by-Step explanation:

-(3x)²

In PEMDAS, we solve the exponent first then multiply.

-(3x)²

-(9x²)

-9x²

Answer:

[tex]3(-2m + 3)[/tex]

Step-by-step explanation:

Given

[tex]-6m + 9[/tex]

Required

Factorize

Expression: [tex]-6m + 9[/tex]

Start by expressing the expression as a sum of products.

[tex]-6m = 3 * -2m[/tex] and

[tex]9 = 3 * 3[/tex]

So;

[tex]3 * -2m + 3 * 3[/tex]

Notice that constant 3 is common in both terms.

This can then be factorizes as:

[tex]3(-2m + 3)[/tex]

Hence:

[tex]-6m + 9 = 3(-2m + 3)[/tex]

Answer:

3(-2m+3)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Hoped I helped! Im Eve btw. Have a great day and consider marking this brainiest if you do thank you in advanced!

Answer:

Step-by-step explanation:

For a quadratic equation to have 2 equal root, the discriminant value must be equal to zero.

Discriminant D = b² - 4ac = 0

Given the equation

x^2 − 2(2k + 1)x + (k + 2) = 0

From the equation, a  = 1, b = -2(2k+1), c = k+2

a = 1, b = -4k - 2, c = k+2

Substitute into the discriminant formula;

Recall that: b² - 4ac = 0

(-4k - 2)²-4(1)(k+2) = 0

16k²+16k + 4 - 4k - 8  =0

16k²+12k - 4 = 0

16k²+16k - 4k - 4 = 0

16k(k+1)-4(k+1) = 0

16k - 4 = 0 and k+1 = 0

16k = 4 and k = -1

k = 4/16 and k = -1

k = 1/4 and -1

Hence the required value of k is 1/4 and  -1

Answer:

Jack eat 3/8 pounds of the blueberries.

Step-by-step explanation:

Jane had 3/4 of a pound of blueberries.

Jack eat 1/2 of the blueberries.

How many pounds of blueberries did Jack eat?

= 1/2 of 3/4 pounds of blueberries

= 1/2 × 3/4

= (1*3) / (2*4)

= 3/8 pounds

Jack eat 3/8 pounds of the blueberries.

Answer:

She could plant 9 plants.

Step-by-step explanation:

1 1/2 hours = 90 minutes, so 12 plants per 90 minutes. Which would mean 6 plants per 45 minutes. So in between 45 and 90 minutes (1 hour), and in between 6 and 12 plants (9).

Sorry if you didn't understand, I'm bad at explaining.

Answer:

25%

Step-by-step explanation:

100-80=20

80÷20=4

100÷4=25

25%

Answer:B

Step-by-step explanation:

Answer:

[tex]5 {g}^{2} - 11 {g}^{} + 8[/tex]

Step-by-step explanation:

[tex]this \: is \: your \: answer \: ie \: option \: b \\ hope \: it \: helps \\ need \: thanks \: and \: brainliest...[/tex]

Answer:

3y = 11x-16

Step-by-step explanation:

The general equation of a line that passes through two points can be written as;

y = mx + b

where m is slope and b is the y-intercept

Mathematically in this case;

m = (9-(-2)/(5-2) = 11/3

To write the equation, we use the one-point form

y-y1 = m(x-x1)

(x1,y1) = (2,-2)

y + 2 = 11/3(x-2)

y = 11x/3-22/3+ 2

y = 11x/3 -16/3

so;

3y = 11x - 16

Answer:

well for me I think

Step-by-step explanation:

4/3×120

480/3

160

Answer:

You would need 35.75 or 35 3/4 yards of material

Step-by-step explanation:

You must take 9 3/4 and divide it by three so we can figure out exactly how much material is needed for just one curtain. We figure the number 3.25 or 3 1 /4. There are 11 windows total windows, and 3 1/4 per window; therefore, you must multiply the two to get your final answer which would of course be 35 and 3/4 yards of material.

I hope this helped!

Have a great day/night and good luck with your school endeavors! you're doing great!!

Answer:

[tex]18 + 24 = 6 * 7[/tex]

Step-by-step explanation:

Given

[tex]18 + 24[/tex]

Required

Write as a product

Start by expanding the expression with a common factor

[tex]6 * 3 + 6 * 4[/tex]

Factorize:

[tex]6 ( 3 + 4)[/tex]

Express 3 + 4 as 7

[tex]6 (7)[/tex]

Convert () to multiplication

[tex]6 * 7[/tex]

Hence:

[tex]18 + 24 = 6 * 7[/tex]

Area -78 cm²

perimeter-58

green=53/78

blue=23/78

Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest

The bird is made of 79 squares each square is 1u^2(u=unit, either cm or inch)

the area of the bird is 79u^2

the perimeter is 64u^2 you count all edges

51/79 squares are green, 51u^2

26/79 squares are blue, 26u^2

Answer:

−8+32

Step-by-step explanation:

...................

Answer:

x=-2

Step-by-step explanation:

same on both sides

Answer:

Step-by-step explanation:

let the number be x

20-x/2=10

40-x=20

40-20=x

x=20

Answer:

Price at store B = $66.94

Step-by-step explanation:

Given:

Price of headphones at Store A = $89.25

Find:

Price at store B

Computation:

Price at store B = 3/4[Price of headphones at Store A]

Price at store B = 3/4[89.25

Price at store B = $66.94