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On average, Leah's car gets 31.4 miles on every gallon of gasoline. If she fills up her tank for $2.18 per gallon, how much will it cost her to drive
358 miles?

The pool is full for 4 hrs.

Add the rates of filling of the 2 filling pipes and

subtract the rate of draining of the emptying pipe;

1st pipe's rate: ( 1 pool filled ) / ( 3 h);

2nd pipe's rate: ( 1 pool filled ) / ( 6 h );

3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 h);

Let t = the time in hrs to fill the pool with all 3 pipes open

1/3+16-1/4 = 1/t;

Multiply both sides by 24t;

t = 4 hrs

volume is a measure of occupied three-dimensional space. it's miles frequently quantified numerically using SI derived units (consisting of the cubic meter and liter) or by way of diverse imperial devices (inclusive of the gallon, quart, cubic inch).

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The principal amount is calculated as $720.

Simple interest is a simple and quick method to calculate the interest on a loan.

The formula for calculating the simple interest is;

SI = PRT/100

Where,

SI = simple interest

P = principal amount

R = rate of interest (%)

T = time period in years

For the given values in the question

Substitute the given values in the question;

39.60 = (P×11×0.5)/100

P = 39.60×100/(11×0.5)

P = 720

Therefore, the value of the principal amount is estimated as $720.

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The number of answers that each school got correct in the final round is 18.

School A point = 128

School B point = 56

Let x = the number of correct answers given by School A in the final round.

Therefore, the equation for A will be:

128 + 9x - 4x = 128 + 5x

The equation for B will be:

= 56 + 9x.

We will equate the equations.

128 + 5x = 56 + 9x

9x - 5x = 128 - 56

4x = 72

x = 72/4

x = 18

School A and B gave 18 correct answers

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Answer:

B.

4*2=8

5*3=15

Answer:

A is 3\5; B is 8\3; C is 3\8; D is 5\3

Step-by-step explanation:

divide or multiply
i don't know  if these are right bc I didn't do them in a long time.

Answer:

Step-by-step explanation:

0.82, 45/50 ,80%

14. The numbers ordered from lowest to highest are

0.82 = 0.82

45/50 = 0.9

80% = 4/5 = 0.8

Solution:

B. [tex](-6-\sqrt{29},-6+\sqrt{29})[/tex]

Hope this helps! If so, lmk! Thanks and good luck!

Answer: (-6-[tex]\sqrt{29}[/tex], -6+[tex]\sqrt{29}[/tex]) ==> D

Step-by-step explanation:

x^2 + 12x +7 < 0

x^2+12x+36-29<0

(x+6)^2-29<0

(x+6)^2<29

x+6<[tex]\sqrt{29}[/tex]

x<-6+[tex]\sqrt{29}[/tex]

x+6>-[tex]\sqrt{29}[/tex]

x>-6-[tex]\sqrt{29}[/tex]

(-6-[tex]\sqrt{29}[/tex], -6+[tex]\sqrt{29}[/tex]) ==> D

-6-[tex]\sqrt{29}[/tex] and -6+[tex]\sqrt{29}[/tex] aren't included in the solution since if these values are plugged in to x^2 + 12x +7, the expression will equal 0. That's not supposed to happen. The expression is supposed to be LESS than 0.

If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and  then she has to run 176 miles in total to achieve her 26 miles goal.

Given,

Total distance for the marathon = 26 miles

Distance she add each day =2

She starts with 6 miles

Then,

Equation of nth term in the arithmetic sequence

[tex]t_{n}=a+(n-1)d[/tex]

Substitute the values and find the value of n

26=6+(n-1)2

26=6+2n-2

26=4+2n

2n=22

n=11

To find the total distance she run to achieve her 26 miles goal, we have to apply the sum of n terms of arithmetic sequence,

[tex]S=\frac{n}{2}[2a+(n-1)d]\\ S=\frac{11}{2}[2(6)+(11-1)2]\\ S=\frac{11}{2}[12+20]\\ S=\frac{11}{2}[32]\\ S=176[/tex]

If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and  then she has to run 176 miles in total to achieve her 26 miles goal.

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Answer:

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

In order to find the distance you run each month you need to divide the total distance by the number of months:

Based on the ratio, 5¹/₂ : 1¹/₂, the unit rate can be found to be so the statement is TRUE.

To find the unit rate of a ratio, you should divide the first number in the ratio by the second number in the ratio.

When given the ratio, 5¹/₂ : 1¹/₂, therefore, the unit rate is:

= 5¹/₂ ÷ 1¹/₂

= 11/2 ÷ 3/2

= 11/2 x 2/3

= 22 / 6

= 3.6667

= 3²/₃

In conclusion, the unit rate of 5¹/₂ : 1¹/₂ is 3²/₃.

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the height of pyramid vabcdef gh is 45.2º.

A polygon is a closed polygonal chain made up of a limited number of straight line segments that are joined to form a planar figure in geometry (or polygonal circuit). A polygon can be defined as the region that is circumscribed by a bounding circuit, the bounded plane, or both.

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In reality, the lateral face VAB is an isosceles triangle with a 14-length base and 25-length legs. This triangle's altitude must cut over angle V and the base, forming a right triangle with a hypotenuse that is 25 inches long and a short leg that is 7 inches long. We can calculate the altitude, which is also the slant height of the pyramid, using the Pythagorean theorem.

s.h. = alt. = √(252 - 72) = 24

Now, by adding the pyramid's height and half of its base, we may utilize this slant height as the hypotenuse of another right triangle.

We look at a regular octagon to identify half the base. You'll see that four of the sides are horizontal or vertical, while the other four are at an angle of 45 degrees to the first four. So, in this example, 14 + 28/2 = 14 + 142, the distance between parallel sides of a regular octagon would be equal to s + 2s/2.

hence, the base's half would equal 7 + 72.

The height of the pyramid and the dihedral angle with the base are both provided by this right triangle.

h = √(242 - (7 + 7√2)2) = 17.0"

θ = cos-1((7 + 7√2)/24) = 45.2º

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Answer: If we are looking at percentages you want to find what 262.50 is 5% of what number using the percentage rates equation, the original price would be, $525.00! Hope this helps!

The Probability that Outcome B is drawing a green marble on the second draw without replacing the first marble is

P(B|A) = 3/7.

The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

Probability is another word for possibility. It is a field of mathematics that examines the occurrence of a random event. The value is given as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.

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Answer:

Step-by-step explanation:

Using a proportional relationship, the costs are given as follows:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

A proportional relationship may also involve multiple variables, as is the case in this problem, in which the cost is a function of the number of bags of popcorn p and the number of drinks d.

The constants are the prices of each product, hence the function for the total cost of p bags of popcorn and d drinks is given by:

C(p,d) = 3.35p + 4d.

Hence, for 3 bags and 8 drinks, the cost is:

C(3,8) = 3.35(3) + 4(8) = $42.05.

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Answer:

0.32×0.5=0.16

Answer:

ANSWERS

1st Question: 8/15

2nd Question: 3

3rd Question: -2 1/7

4th Question: -10

Used a Calculator :3 hope it helps

Answer:

75% of 48 = 36 oranges used on M. 36/12=3, 3 is 1/12 of 36, so he sold 33 more oranges on M then on T when he only sold 3.

The equation of the line is y+x+1=0.

It is required to find the equation of the line.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The given line is

y=-x-5.

Slope of line

y+x-5=0

We have to find the  equation of the line.

According to given question we have

Slope =-1

Thus the slope of the required line is

-1

The point (5, -6)

The equation of the line is

  y+6=-1​(x−5)

=>y+6=-x+5

=>y+x+1=0

Therefore, the equation of the line is y+x+1=0.

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The edge length and area of the face of the cube are 5. 82 meters and 203 square meters respectively

The formuka for the volume of a cube is expressed as;

Volume = a^3

Where 'a' is the length of it's edge

From the information given, we have that the volume of the cube has a value of 197 cubic meters.

Now, substitute the value of the volume

We have;

197 = a^3

Take the cube root of both sides

a = 5. 82 meters

The formula for area of the face of a cube is given as;

Area = 6a ^2

Area = 6(5.82)^2

Area = 6(33. 85)

Area = 203 square meters

Thus, the edge length and area of the face of the cube are 5. 82 meters and 203 square meters respectively

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Answer:

0.5

Step-by-step explanation:

7 1/2 • 2 = 15

7 times 2 is equal to 14

1/2 times 2 is equal to 1

14 plus 1 is equal to 15

Answer:

bsosbsodndodnelsnsodnendk

Answer:

38.4895cm²

Step-by-step explanation:

The area=3.142×(3.5cm)²=38.4895cm²

Answer:

The Area of circle is 34.49cm

Step-by-step explanation:

⟼ Area of a circle = [tex] \sf \pi {r}^{2} [/tex]

where,

⟼ Area = (3.142)(3.5)(3.5)

⟼ Area = (3.142)(12.25)

⟼ Area = 38.4895cm

Answer:

x-

[tex]x = - {y}^{2} + 8k[/tex]

Answer:  490*x + 700*y ≤ 4000

Answer:

its b

Step-by-step explanation:

Step-by-step explanation:

5.6 × 10⁶

hope it's helpful

Using the decay formula, the particular antibiotic with half-life of 16 hours, will decrease to 30-milligrams in the blood after 27.79 hours.

We can use the decay formula to solve the problem:

A(t) = A(0) . (0.5)^(t/T)

Where:

A(t) is the remaining quantity at time t

A(o) is the initial quantity

t  is the time interval

T is the half-life rate

In the given problem:

A(0) = 100 milligram

T = 16 hours

A(t) = 30 milligram

We need to find t such that the remaining quantity of this antibiotic is 30 mg.

Substitute the given parameters into the formula:

A(t) = A(0) . (0.5)^(t/T)

30 = 100 . (0.5) ^(t/16)

Taking the logarithm:

log (30) = log [100 . (0.5) ^(t/16)]

Use the logarithm property, log(A.B) = log A + log B

log (30) = log (100) + log [(0.5) ^(t/16)]

Use the logarithm property, log(Aⁿ) = n.log A

log (30) = log (100) + (t/16) . log (0.5)

log (30) = 2 + (t/16) . log (0.5)

(t/16) . log (0.5)  = log (30) - 2

t/16 = 1.737

t = 1.737 . (16) = 27.79 hours

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Answer:

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

Since all numbers are positive, their sum or product can be a positive number but never negative or zero.

The order of the steps for copying the angle from the paper using a compass and a straight edge are;

5. Label the original angle as ‹A. On a separate piece of paper, draw a horizontal ray directed to the right, using the straight edge. Label the left endpoint D

4. Draw an arc centered at the vertex A that passes through both sides of ‹A using the compass. Label the points of intersection B and C.

1. Using the same compass setting, draw an arc centered at point D that intersects the ray and looks like the arc through B and C. Label the intersection of the arc and the ray as E.

3. Adjust the compass to the length BC. Draw an arc with radius BC centered at point E that intersects the arc through E. Label the point of intersection F.

2. Draw [tex] \overrightarrow{DF} [/tex]. You now have [tex] \angle A \cong \angle D [/tex]

The steps for copying an angle includes;

The order of the steps based on the appearance of the step in the question are therefore;

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Answer:

The answer is C.

(0,4) and (3,0)

Step-by-step explanation:

To find the x, substitute 0 to the y.

* 4x + 3(0) = 12

> 4x = 12

> x = 3 (3,0)

To the y, substitute 0 to the x.

* 4(0) + 3y = 12

> 3y = 12

> y = 4 (0,4)

I hope you get this right!

Answer:

(0,4) and (3,0)

Step-by-step explanation:

Hope this helps :D

Answer:

Grace's work was done correctly.

Step-by-step explanation:

She expanded the equation and grouped the like terms, then added them together to get the answer.

[tex]6-3x-2\left(6x-8\right)\\=6-3x-12x+16\\3x - 12x = -15x\\= -15x + 6 + 16\\6 + 16 = 22\\= -15x + 22[/tex]

Hope this helps!

160 boxes needed to pack these items

Therefore contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.

Given no of groceries bags = 640

number of cases of bottled water = 320

number of small toys = 800

We have to find out how many boxes are needed and the contents of each box.

(i) How many boxes are needed:

To do this we need to find the greatest common factor of these three items

as

640 - 2⁷ * 5

320 - 2⁶ * 5

800 - 2³ * 5²

GCF = 2⁵ * 5 = 160

Therefore 160 boxes needed to pack these items

(ii) Contents of each box:

No of bags of groceries in each box = 640 / 160 = 4

No of cases of bottled water = 320 / 160 = 2

No of toys in each box = 800 / 160 = 5

Therefore, contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.

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