what is the unit rate for 4 gallons

Speed is the rate at which a body changes its position. The speed by which Marina runs is 4 miles/ hr.

Speed is the rate at which a body changes its position. It is given by the formula,

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given to us

Marina can bicycle 19. 5 miles at the same time it takes her to run 6 miles.

Marina bikes 9 miles per hour faster than she runs.

Let the speed of the Marina running be s, and the time is taken to run 6 miles be t.

Time is taken by Marina to cover a distance of 6 miles by running,

[tex]\rm t = \dfrac{6\ miles}{s}[/tex]

Since the speed of Marina's bicycle is 9 miles per hour faster than she runs. Time is taken by Marina to cover a distance of 19. 5 miles by bicycle,

[tex]\rm t = \dfrac{19.5\ miles}{s+9}[/tex]

We know that Marina can bicycle 19. 5 miles at the same time it takes her to run 6 miles. therefore,

[tex]\rm t = \dfrac{6\ miles}{s}= \dfrac{19.5\ miles}{s+9}[/tex]

[tex]\dfrac{6}{s}= \dfrac{19.5}{s+9}[/tex]

Solving the given equation we will get,

[tex]\rm s = 4\ miles/hr[/tex]

Hence, the speed by which Marina runs is 4 miles/ hr.

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Answer:

GCF = 7

Step-by-step explanation:

7 * 2 = 14

7 * 7 = 49

4*7 = 28

[RevyBreeze]

Answer:

- B

x = 9

y = 3

Answer:

it is 800.00

Step-by-step explanation:

i did this a while ago

Answer:

A. [tex]5x^4 - 37x^3 - 6x^2 + 41x - 6[/tex]

step-by-step-explanation:

Answer:

[tex]5x^4- 37x^3-6x^2+ 41x-6[/tex]

Step-by-step explanation:

simplify the following expression:  

[tex](5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2-3x + 2) - (-4x^3 + 5x - 1)(2x -7)[/tex]

Expand [tex](-4x^3 + 5x - 1)(2x -7)[/tex]

[tex]\implies -8x^4 +28x^3+10x^2-35x-2x+7\\\\\implies -8x^4 +28x^3+10x^2-37x+7\\[/tex]

Therefore:

[tex](5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2- 3x + 2)-(-8x^4 +28x^3+10x^2-37x+7)[/tex]

Group and combine like terms:

[tex]5x^4 -8x^4- 9x^3 +4x^2+ 7x - 3x- 1 + 2-(-8x^4 +28x^3+10x^2-37x+7)\\\\\implies -3x^4- 9x^3 +4x^2+ 4x +1-(-8x^4 +28x^3+10x^2-37x+7)[/tex]

Apply the distributive rule:  [tex]-(-a+b)=a-b[/tex]

[tex]\implies -3x^4- 9x^3 +4x^2+ 4x +1+8x^4-28x^3-10x^2+37x-7[/tex]

Group and combine like terms:

[tex]\implies -3x^4+8x^4- 9x^3 -28x^3+4x^2-10x^2+ 4x+37x +1-7\\\\\implies 5x^4- 37x^3-6x^2+ 41x-6[/tex]

Answer:

if it took her 14 hours to make a 30-inch scarf, we can assume it will take her to double that time to make a 60-inch scarf. 28 hours is double of 14, if she only knits one hour every day it will take her 4 weeks, 28 days is equal to exactly 4 weeks 28/7=4 weeks

Answer:

4 weeks

Step-by-step explanation:

14 hours for a 30-inch

multiply them both by 2

28 hours for 60-inch

28 divided by 7 = 4

Have a blessed and great day<3

Answer:

4 Cases

Step-by-step explanation:

If they bought 3 cases they would only have 864

Answer:

4 cases

Step-by-step explanation:

Find out how many pencils per case:

1 case = 24 boxes

1 box = 12 pencils

1 case = 24•12 = 288 pencils

Divide the amount of needed pencils (900) by how many per case there are (288) to find how many cases you need:

900÷288=3.125 (or 3 1/8)

Since you can't get a part of a case (for the 1/8 of a case you need), you will need to round up to 4 cases.

Value of [tex]x[/tex]is [tex] - 12[/tex].

Final Answer is [tex]480[/tex]

Step-by-step explanation:

Assume that:

First number = x

Second number = 20 - x

Putting the given conditions,

[tex]2x^{2} + 3(20 - x)^{2} [/tex]

Putting the formula (a-b)²=(a²+2ab+b²) in (20-x)²,

[tex]2 {x}^{2} + 3(20^{2} - 2 \times 20 \times x + {x}^{2})[/tex]

[tex] = > 2 {x}^{2} + 3(400 - 40x + x^{2})[/tex]

Opening the brackets,

[tex]2 {x}^{2} + 3 \times 400 - 3 \times 40x + 3 \times {x}^{2} [/tex]

[tex] = > 2 {x}^{2} - 1200 - 120x + 3{x}^{2}[/tex]

[tex] = > (2x^{2} + 3 {x}^{2}) - 120x + 1200[/tex]

[tex] = > 5 {x}^{2} - 120x + 1200[/tex]

[tex]As \: x= - \frac{b}{2a}[/tex]

[tex] = > - \frac{120}{2 \times 5}[/tex]

[tex] = > - \frac{120}{10} [/tex]

[tex] = > - 12[/tex]

Now substituting the value of x in 5x²-120x+1200,

[tex] = > (5 \times {12}^{2} )-(120 \times 12)+1200[/tex]

[tex] = > (5 \times 144)-(1440)+1200[/tex]

[tex] = > 720 - 1440 + 1200[/tex]

[tex] = > 720 - (1440 - 1200)[/tex]

[tex] = > 720 - 240[/tex]

[tex] = > 480[/tex]

Step-by-step explanation:

the ratio of 1/18 simply means that 1 inch in the drawing represents 18 inches in reality.

so, the real flag is therefore

2×18 = 36 inches long and 1×18 = 18 inches wide (or high).

the area of the actual flag is therefore

36 × 18 = 648 in²

Answer:

side = 20 cm

Step-by-step explanation:

Since the triangle is equilateral then the 3 sides are congruent.

Equate the 2 given sides and solve for x

5(x - 3) = 2x + 6

5x - 15 = 2x + 6 ( subtract 2x from both sides )

3x - 15 = 6 ( add 15 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

then length of side is

2x + 6 = 2(7) + 6 = 14 + 6 = 20 cm

Answer:

20 cm

Step-by-step explanation:

Properties of an Equilateral Triangle

Given information

Find value of x

As side lengths are equal, equate the expressions and solve for x.

   2x + 6 = 5(x - 3)

⇒ 2x + 6 = 5x - 15

⇒ 2x + 6 + 15 = 5x - 15 + 15

⇒ 2x + 21 = 5x

⇒ 2x + 21 - 2x = 5x - 2x

⇒ 21 = 3x

⇒ 21 ÷ 3 = 3x ÷ 3

⇒ 7 = x

⇒ x = 7

Side lengths

Substitute x = 7 into one of the given expressions.

⇒ length of one side:  2(7) + 6 = 20 cm

Answer:

1.) Option C

2.) Option B

3.) Option D

4.) Option A

Step-by-step explanation:

[tex] \frac{3x {}^{2} }{y {}^{ - 3} } \\ [/tex]

Here, we know that

[tex]a {}^{ - 1} = \frac{1}{a} \\ [/tex]

So,

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

Thus, Option C is correct

[tex]( {4}^{0} )( {4}^{2} ) \\ [/tex]

We know that,

n⁰ = 1

where, n = any real number

So,

[tex]( {4}^{0} )(4 {}^{2} ) = 1 \times 16 = 16 \\ [/tex]

Thus, The answer is 16

[tex]( \frac{5}{3} ) {}^{ - 3} \\ [/tex]

We know that

[tex]a {}^{ - 1} = \frac{1}{a} \\ [/tex]

So,

[tex]( { \frac{5}{3} )}^{ - 3} = ( { \frac{3}{5} )}^{3} = \frac{27}{125} \\ [/tex]

Thus, Option D is correct

[tex] \frac{a {}^{2} {b}^{5}c {}^{0} }{ab {}^{7} } \\ [/tex]

[tex] \frac{a {}^{2} {b}^{5} c {}^{0} }{ab {}^{7} } = \frac{a}{ {b}^{2} } \\ [/tex]

Thus, Option A is correct

-TheUnknownScientist 72

Answer:

  (b)  56.5 ft

Step-by-step explanation:

The circumference of a circle of diameter d is given by ...

  C = πd

For the given diameter, the circumference of the frame is ...

  C = (3.14)(18 ft) ≈ 56.52 ft

The length of the outside edge of the frame is about 56.5 feet.

Answer:

yes cost is proportional and ratios of cost are equal

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Answer:

b and c are correct

Step-by-step explanation:

Hope this helps! :)

Answer:

B

Step-by-step explanation:

Because max has 40/100 of a dollar which could = 4 or 40% so he has 4.

Max=4

Ben has 2/10 of a dollar which could be 2 or 20% so ben has 2

Ben=2

Alex has 3/10 of a dollar which could be 3 or 30% so Alex has 3.

Alex=3

4+2+3=9/10

Hope it helps,have a great day:)

Answer:

C. 2.4 degrees Fahrenheit

Step-by-step explanation:

1.1 per hour for 7 hours

1.1 x 7 = 7.7

5.2 - 7.7= -2.5

-2.5 + 4.9 = 2.4

Answer:

tomato B weighs more than tomato A

Step-by-step explanation:

Tomato A: 6oz = 169.8g

Tomato B: 6.10oz = 173g

Answer:

-123

Step-by-step explanation:

13(-x+4)-6 when .x is 13

we just replace x with 13

13(-13+4)-6

13(-9)-6

applying bodmas we multiply 13 by negative 9 before the subtraction aspect

13*-9=-117

-117-6=-123

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Since the value under the square root is the same, you only subtract the coefficients, and you do not show the one in your final answer.

Answer:

Check the attachment.

Hope it helps ⚜

Arithmetic sequence is done by adding or subtracting the difference. The 12th term of the arithmetic sequence will be 58.

The arithmetic sequence is the series of numbers where every two consecutive terms have the same difference between them.

We know that the nth term of an arithmetic sequence is given as,

[tex]a_n = a_1 + (n-1)d[/tex]

Also, we are given two functions adding the two functions we get,

[tex]f(x) + g(x)\\\\ = 25 + 3(n-1)[/tex]

comparing the sum we get with the arithmetic sequence formula for nth term, we will understand that,

[tex]a_1 + d(n-1)\\25+3(n-1)[/tex]

therefore,

a₁ = 25

and d = 3

that means the first term of the sequence is 25 while the difference between the two terms is 3.

Now, substituting the values in the formula we will get that the 12th terms of the sequence can be written as,

[tex]a_n = a_1 + (n-1)d\\\\a_{12} = 25 + (12-1)3\\\\a_{12} = 25 + 33\\\\a_{12} = 58[/tex]

Hence, the 12th term of the arithmetic sequence will be 58.

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Answer:

.071 times 101

Step-by-step explanation: The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Answer:

(8, 9) and (12, 3)

Step-by-step explanation:

The ends of the line would be (8, 9) and (12, 3)

Because the scale factor is negative, the guide lines go through the centre of enlargement rather than from it.

Answer:

40

Step-by-step explanation:

140/100 = 56/x

=> x = (100x56)/140 = 40

Answer:

40

Step-by-step explanation:

140%  x __ = 56

140/100 x __ = 56

x = 56 x 140/100

x = 40

Answer:

95

Step-by-step explanation:

the interior angles of a square add upto 360

and from the arrows we know that the parallel sides are equal

so there will be two angles which are 85

so:

360-85-85 = 190

190/2 = 95

Answer:

Time goes down to 16.47 min

Step-by-step explanation:

Formula

Time to melt = k / Temperature      (I doubt it is this simple)

Givens

Temp = 70

Time = 20

k  =

Solution

20 = k / 70             Multiply both sides by 70

20*70 = k

k = 1400

Problem

What happens when Temp = 85?

Time = k / Temp

Time = 1400 / 85

Time = 16.47 Min

Answer:

Step-by-step explanation:

F because im guessing and im taking a tes

Answer:

x>-10/7 or ≈ -1.4285714285714285714285714285714

Step-by-step explanation:

transfer the -7 coefficient over to the right

Hey there!

-7x > 10

DIVIDE -7 to BOTH SIDES

-7x/-7 > 10/-7
CANCEL out; -7/-7 because it give you 1

KEEP: 10/-7 because it give you the x value

NEW EQUATION: x = 10/-7

SIMPLIFY IT!

x = - 10/7 OR x = -1 3/7

⇡ EITHER OF THOSE SHOULD WORK BECAUSE THEY ARE EQUIVALENT TO EACH OTHER! ⇡

It is an OPEN circle shaded to the left starting between -1 & -2. (Little over -1)

Therefore, your answer is:

x = - 10/7 OR x = -1 3/7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

-1/2 or the decimal form -0.5

Prediction for some count is usually expressible as expectation of some random variable. The reasonable prediction for the number of times a white or red marble will be drawn is 54

A  random variable is usually taking some numerical information of each elementary event of the sample space . (map from sample space to real numbers). Its expected value is the best prediction value in most of the cases.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

For the given case, as the ball being drawn is being replaced too, so we can take all 180 experiments to be independent from each other.

If we call

Success = Event of drawing white or  red marble

Failure = Event of drawing any other marble instead of white or red

Then, each marble drawing event is having two outcomes: success or failure. This makes each drawing a Bernoulli  experiment.

Modelling this situation with binomial distribution would be good.

Let X = number of successes in those 180 experiments.

Thus, we get

[tex]X \sim B(n = 180, p= 0.3)[/tex]

The expectation of random variable X is the best prediction of count of times we will get in those 180 trials.

The expectation of a  random variable is: [tex]E(X) = np[/tex]

Thus, we get:

[tex]E(X) = 180 \times 0.3 = 54[/tex]

Thus, the reasonable prediction for the number of times a white or red marble will be drawn is 54

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