4. A swimming pool has a length that is 13 feet more than its width. If the area of
the pool is 608 feet squared, find the length of the pool.

Given:

The given expression is [tex]\left(\frac{3}{10}\right)^{3}[/tex]

We need to determine the value of the given expression.

Value of the expression:

Let us determine the value of the expression.

The value of the expression can be determined by simplifying the given expression.

Applying the exponent rule, [tex]\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}[/tex], we get;

[tex]\left(\frac{3}{10}\right)^{3}=\frac{3^{3}}{10^{3}}[/tex]

Since, the value of 3³ is 27 and the value of 10³ is 1000, substituting these values, we get;

[tex]\frac{27}{1000}[/tex]

Hence, the value of the expression is [tex]\frac{27}{1000}[/tex]

Thus, Option b is the correct answer.

Answer:

[tex]\frac{27}{1000}[/tex]

Step-by-step explanation:

I got it right on edg. 2020.

Step-by-step explanation:

As we have to use the number 0-6 once to make 2 equivalent ratios.

so lets solve the problem.

Determining first equivalent ratio

as

and

so

Therefore, first equivalent ratio

[tex]\:\frac{5}{32}=\frac{10}{64}[/tex]

Determining second equivalent ratio

[tex]\frac{13}{65}=\frac{4}{20}[/tex]

as

[tex]\frac{13}{65}=\frac{1}{5}[/tex]

and

[tex]\frac{4}{20}=\frac{1}{5}[/tex]

Therefore, second equivalent ratio

[tex]\frac{13}{65}=\frac{4}{20}[/tex]

Both can be simplified to 1:2.

To create two equivalent ratios using the numbers 0-6 once, we first need to understand that a ratio compares two quantities and equivalent ratios can be simplified or expanded from one another by the same factor. Here, we select the numbers carefully to form such ratios.

Let's use the numbers 2, 3, 4, and 6. The ratio of 2:4 is equivalent to 3:6 because when both sides of the first ratio are multiplied by 2, the result is the second ratio. Therefore, the ratios 2:4 and 3:6 are equivalent because they express the same relationship between numbers, as both can be simplified to the ratio of 1:2.

Answer:

4/10 or 40%

Step-by-step explanation:

4 black marbles out of 10 which equals to 4/10

Answer:

4/10 or 2/5

Step-by-step explanation:

Answer:

22,000

Step-by-step explanation:

When you are rounding, anything from 1-4 you round down, and any number 5-9 you round up. So, in this case the middle would be 500, but since the number is 119, it is 22,000.

Answer: 22000

Step-by-step explanation:

22,119 to the nearest thousandth

Thousand has 3 zeros at the back

Looking at the last 3 figures

It is not up to 500,so it is rounded up as 0

Therefore, nearest thousandth is

=22000

Answer:

6.75 round to 7

Step-by-step explanation:

Answer:

7 hours

Step-by-step explanation:

6.75 is closer to 7, because it is 0.25 from 7 and 0.75 from 6. Since 0.75>0.25, 6.75 rounds up to 7 hours a day. Hope this helps!

Answer:

Trends:

In the graph or a table you easily can see trends in the data, for example, parts where if x increases also does y, or things like that.

Of course you, with some mathematical knowledge, also can notice those things when you have the equation, so this is a thing that the 3 have in common.

Range:

You usually can see the whole range (all the possible y values) of your equation by looking at the graph or the data set. And obviously, if you have the equation you can easily find the range of it.

Step-by-step explanation:

9z=-25+22

9z=-3

z= -3/9

z=-1/3

Answer:

The author helps persuade readers that math is fun by showing the number devil doing math in clever ways. The author also shows how Robert becomes less afraid of math. Readers can relate to this message and might be convinced to like math more themselves.

Step-by-step explanation:

sample response

Author helps persuade readers that math is fun by showing the number devil doing math in clever ways.

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes.

The author helps persuade readers that math is fun by showing the number devil doing math in clever ways.

The author also shows how Robert becomes less afraid of math.

Readers can relate to this message and might be convinced to like math more themselves.

Hence,  author helps persuade readers that math is fun by showing the number devil doing math in clever ways.

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Answer:i think its 1,3,4

Step-by-step explanation:

Answer:

Rachel has to drive for 5.789 seconds

Step-by-step explanation:

The equation that represents Rachel's remaining distance is:

[tex]D=-38t+220[/tex]

When Rachel completely escaped from the explosion, she has no distance to cover.

Hence D=0.

[tex] - 38t + 220 = 0[/tex]

[tex] - 38t = - 220[/tex]

Divide both sides by -38 to get:

[tex]t = \frac{ - 220}{ - 38} [/tex]

[tex]t = 5.789[/tex]

Rachel will cover 220m in approximately 6 seconds.

The total distance she has to drive is 220m

Rachel has to drive for approximately 6 seconds to reach her destination before the building explodes.

The given equation represents the relationship between Rachel's remaining distance (D) in meters and the time elapsed (t) in seconds.

The equation is:

D = -38t + 220

To find how long the distance Rachel has to drive, we need to find the value of D when she reaches her destination, which means D = 0 (since the distance remaining will be zero when she reaches the destination).

0 = -38t + 220

Now, solve for t:

38t = 220

t = 220 / 38

t ≈ 5.79 seconds

So, Rachel has to drive for approximately 6 seconds to reach her destination before the building explodes.

The total distance she has to drive is 220m.

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Answer:

[tex]\frac{3x^2}{x^2-6x-7}[/tex]

Step-by-step explanation:

The first step is to find the multiplied out numerator and denominator, and then to simplify if possible. For the numerator, 3x*x=3x^2. For the denominator, (x+1)(x-7)=x^2-6x-7. This gives a final fraction of [tex]\frac{3x^2}{x^2-6x-7}[/tex]. Hope this helps!

Answer:

C

Step-by-step explanation:

Cia collected the most money

Jen collected the least money.

Step-by-step explanation:

Let Jen collected money = x

Mark collected money = 23x

while Cia collected money = 212 (23x)

So, we can observe that Cia and Mark collected more money than Jen as Jen money is multiplied by 23 to make Mark's money and Mark's money is multiplied by 212 to get Cia's Money.

So, Cia collected the most money

Jen collected the least money.

Answer:

cai has the most

jen has the least money

Step-by-step explanation:

Answer:

B. x

Step-by-step explanation:

-3x+8y=-6

3x-2y=-12

if we add these

-3x+3x+8y-2y=-6-12

6y=-12      so x will be eliminated

Final answer:

When solving a system by elimination, the variable eliminated is the one with coefficients that add up to zero when equations are combined.

Explanation:

When solving the following system by elimination, which variable would be eliminated after adding the 2 equations together?

When adding the two equations together in a system, the variable that will be eliminated will be the one that has coefficients with additive inverse values. For example, if one equation has x and the other has -x, adding them would result in the elimination of the x variable.

After adding the two equations together, look for a pair of variables that will cancel each other out, resulting in the elimination of one variable.

5.702 cm

hoping this helps

Answer:

30% decrease

Step-by-step explanation:

Answer: 30%

Step-by-step explanation:

Exact value =125m

Another value =87.5m

To know the decrease

=125-87.5

=37.5

To get the percentage

37.5×100/125

=30%

Answer:

60

Step-by-step explanation:

2 times 150

Answer:

y=1/3x+5/3

Step-by-step explanation:

Slope intercept form: y=mx+b

Equation given info: y=1/3x+b

Point given: (-2,1)

New equation to solve for b: 1=1/3(-2)+b

1=1/3(-2)+b

1=-2/3+b

5/3=b

Final equation: y=1/3x+5/3

Answer: You need to wait at least 6.4 hours to eat the ribs.

t ≥ 6.4 hours.

Step-by-step explanation:

The initial temperature is 40°F, and it increases by 25% each hour.

This means that during hour 0 the temperature is 40° F

after the first hour, at h = 1h we have an increase of 25%, this means that the new temperature is:

T = 40° F + 0.25*40° F = 1.25*40° F

after another hour we have another increase of 25%, the temperature now is:

T = (1.25*40° F) + 0.25*(1.25*40° F) = (40° F)*(1.25)^2

Now, we can model the temperature at the hour h as:

T(h) = (40°f)*1.25^h

now we want to find the number of hours needed to get the temperature equal to 165°F. which is the minimum temperature that the ribs need to reach in order to be safe to eaten.

So we have:

(40°f)*1.25^h = 165° F

1.25^h = 165/40 = 4.125

h = ln(4.125)/ln(1.25)  = 6.4 hours.

then the inequality is:

t ≥ 6.4 hours.

Answer:

40 × 1.25 ^ t greater or equal to ( >) 165

Mark lives 5,000 feet away from school and walks at a steady rate of 250 feet per minute, so it takes him 20 minutes to walk to school.

Step-by-Step Explanation

Mark lives 5,000 feet from school and walks at a steady rate of 250 feet per minute. To calculate the time it takes for Mark to walk to school, we divide the total distance by his speed:

Time = Distance \/ Speed

Time = 5,000 feet \/ 250 feet per minute

Time = 20 minutes

Thus, Mark takes 20 minutes to walk to school from his home.

Answer:

1,1,2,3,5,8,13

Step-by-step explanation:

To find the length and width, we use the provided information and the formulas for area and length. After determining the width is 7 feet, we find the length is 42 feet. Using these dimensions, the rectangle's perimeter is 98 feet.

Given the length of the rectangle is six times its width, we can denote this as L = 6W. The area of a rectangle is given by the formula Area = Length x Width or A = LW. Substituting L = 6W into our area formula gives A = 6W^2. We're given that the area is 294 square feet, so we set our formula equal to this: 6W^2 = 294. Solving this gives W = 7 ft.

Now, we substitute W = 7 ft back into our length formula, L = 6W, giving L = 42 ft. The perimeter of a rectangle is given by the formula Perimeter = 2(Length + Width) or P = 2(L + W), therefore P = 2(42 ft + 7 ft) = 98 ft.

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Answer:

choice A.  line BC = line EF

Step-by-step explanation:

we need the sides  BC = EF

This is the side between the congruent angles.

For the congruence of the triangles, AB ≅ DE, BC ≅ EF, or CA ≅ FD should be congruent. Then the correct option is A.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are congruent, then the ratio of the corresponding sides will be one.

If any two sides and one angle of the triangles are congruent, then the triangles are congruent.

Or if any two angles and one side of the triangles are congruent, then the triangles are congruent.

In the figure, the two angle of the triangle are congruent.

For SAS postulate, then the sides will be

AB ≅ DE

BC ≅ EF

CA ≅ FD

Then the correct option is A.

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Answer:

Volume of wood chips in the pickup truck is  [tex]70[/tex] cubic units.

Step-by-step explanation:

Given that,

The pickup truck rectangular bed with an area of [tex]35[/tex] square feet.

Height of wood chips is [tex]2[/tex] feet.

From the question,

The shape formed by combination of rectangular bed and wood chips is a cuboid shape.

So, Volume of cuboid is [tex]= l\times b\times h[/tex] cubic unit.

Then, Volume of wood chips [tex]=Area\times height[/tex]

                                                 [tex]= 35 \times 2=70[/tex] cubic units.

Therefore, Volume of wood chips in the pickup truck is  [tex]70[/tex] cubic units.

The volume of wood chips in Ernesto's pickup truck is calculated by multiplying the bed's area of 35 square feet by the height of 2 feet, resulting in a total volume of 70 cubic feet.

To determine the volume of wood chips that Ernesto's pickup truck can carry, we start with the given area of the rectangular bed, which is 35 square feet. Knowing the bed area and that Ernesto fills the bed to a height of 2 feet, we can calculate the volume by multiplying the area by the height.

Here is a step-by-step explanation:

Identify the area of the truck's bed: 35 square feet.

Identify the height to which the wood chips are filled: 2 feet.

Calculate the volume by multiplying the area by the height: Volume = area * height = 35 ft² * 2 ft.

Therefore, the volume of wood chips that the truck can carry is 70 cubic feet.

Answer:

Option(B):  [tex]\(\dfrac{15}{108}\)[/tex]   is Correct Choice.

Explanation:

To find the probability that the next movie shown at Cinemania theater is an action movie, we can use the formula:

[tex]\[ \text{Probability} = \frac{\text{Number of action movies}}{\text{Total number of movies}} \][/tex]

Given that there were 15 action movies out of 108 total movies shown last year:

[tex]\[ \text{Probability} = \frac{15}{108} \][/tex]

So, the reasonable estimate of the probability that the next movie is an action movie is:

[tex]\[ \frac{15}{108} \][/tex]

Thus, the correct choice is:

(Choice B)  [tex]\(\dfrac{15}{108}\)[/tex]

Question:

The Cinemania theater showed 108 different movies last year. Of those, 15 movies were action movies.

Based on this data, what is a reasonable estimate of the probability that the next movie is an action movie?

Choose 1 answer:

(A) [tex]$\frac{108}{93}$[/tex]

(B) [tex]$\frac{15}{108}$[/tex]

(C) [tex]$\frac{15}{93}$[/tex]

(D)[tex]$\frac{93}{108}$[/tex]

Fractions

The values are  [tex]\frac{1}{4} , \frac{1}{8} , \frac{1}{81}[/tex]

Step-by-step explanation:

As we know the fractions whose numerators are 1 can be represented in exponents and vice versa provided that the power of the exponent is (-1) ,

like 1/a = a^(-1)  

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

so accordingly

a)

   4^(-1) or [tex]4^{-1}[/tex] can be represented exponentially as ¼ .

⇒   [tex]\frac{1}{4}[/tex]

Part b)

2^(-3)  or [tex]2^{-3}[/tex]

We can simplify the exponent so that the power should be equal to -1.

And, so [tex]2^{3}[/tex] = 8

So we can write the above the expression as 8^(-1)  or [tex]8^{-1}[/tex]

So the fraction corresponding to it is [tex]\frac{1}{8}[/tex].

⇒ [tex]\frac{1}{8}[/tex]

Part c)

3^(-4) now we  can simplify the exponent so that the power of the exponent is -1.

And thus , (3 ^4)^(-1) = 81^(-1)  = [tex]\frac{1}{81}[/tex]

So the fraction obtained is [tex]\frac{1}{81}[/tex].

⇒ [tex]\frac{1}{81}[/tex]

The values are  [tex]\frac{1}{4} , \frac{1}{8} , \frac{1}{81}[/tex]

Given:

[tex]$\frac{80}{4 x}>4[/tex]

To find:

The solution set for the inequality.

Solution:

If the greater number of the set satisfies the inequality, then that set is the solution set.

Option A: {2, 4, 6, 8}

Greater number = 8. Thus substitute x = 8 in given expression.

[tex]$\frac{80}{4 \times 8}>4[/tex]

[tex]$2.5>4[/tex]

This is not true because 2.5 < 4.

It is not solution set.

Option B: {3, 6, 9, 12}

Greater number = 12. Thus substitute x = 12 in given expression.

[tex]$\frac{80}{4 \times 12}>4[/tex]

[tex]$1.67>4[/tex]

This is not true because 1.67 < 4.

It is not solution set.

Option C: {1, 2, 3, 4}

Greater number = 4. Thus substitute x = 4 in given expression.

[tex]$\frac{80}{4 \times 4}>4[/tex]

[tex]$5>4[/tex]

This is true because 5 is greater than 4.

It is the solution set.

Option D: {3, 4, 5, 6}

Greater number = 6. Thus substitute x = 6 in given expression.

[tex]$\frac{80}{4 \times 6}>4[/tex]

[tex]$3.33>4[/tex]

This is not true because 3.33 < 4.

It is not solution set.

Hence {1, 2, 3, 4} is the solution set for the expression.

Answer:

Step-by-step explanation:

3rd choice is correct

Answer:920 × 0.74

= 680.8

Answer:

68.08

Step-by-step explanation: