Reese is installing an in-ground rectangular pool in her backyard. Her pool will be 30 feet long, 14 feet wide, and have an average depth of 8 feet. She is installing two pipes to bring water to fill the pool; these pipes will also be used to drain the pool at the end of each season. One pipe can fill and drain the pool at a rate that is 1 more than 2 times faster than the other pipe. If both pipes are open and working properly, it will take 3.5 hours to fill the pool.
Use this information and what you know about solving rational equations to answer the questions below.
1. When Reese opens the pipes to fill the pool, she finds that only the slower pipe is working. Write a rational equation that you can use to find out how long it will take to fill the pool under these circumstances. Explain how you came up with your equation.
2. Solve the equation that you wrote in question 1. You can round your final answer(s) to the nearest hundredth. Show all your work.
3. Interpret your answer(s) to question 2 in context of the problem. What do the number(s)

The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.

We know that,

Sum of all angles of triangle = 180°.

Therefore, m∠3 + 42° + 25° = 180°.

m∠3 = 180° - 67°

m∠3 = 113°

Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.

We know that,

Vertical or opposite angles have equal measures.

So, 42° and m∠2 are vertical or opposite angles.

Therefore, the value of m∠2 = 42°.

Similarly, for m∠3, We know that,

Sum of all angles of triangle = 180°.

∴ ∠1 + ∠2 + 50° = 180°.

=> ∠1 + 42° + 50° = 180°

=> m∠1 = 88°.

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Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86

Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

well, as I said a while back, Heron's Area formula works for any triangle, so long we have all sides, and in this case we do, since it's not a right-triangle SOH CAH TOA won't work, so let's plug the values in Heron's

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a = 12\\ b = 8\\ c = 6\\ s=\frac{12+8+6}{2}\\ \qquad 13 \end{cases} \\\\\\ A=\sqrt{13(13-12)(13-8)(13-6)} \implies A=\sqrt{13(1)(5)(7)} \\\\\\ A=\sqrt{455}\implies {\Large \begin{array}{llll} A\approx 21.33 \end{array}}~cm^2[/tex]

The new height of painting by Jacob will be 2.5 inches.

The ratio and proportion will be used to relate the original and reduced dimensions of painting. The original width and height = 42.88/33.5. Let us assume the new height be x. So, new width and height = 3.2/x. Equating these two fractions -

42.88/33.5 = 3.2/x

Rewriting the equation according to x

x = (3.2 × 33.5) ÷ 42.88

Performing multiplication in numerator

x = 107.2 ÷ 42.88

Performing division on Right Hand Side of the equation

x = 2.5

Thus, the new height will be 2.5 inches.

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Answer:

A

288 nickels

Step-by-step explanation:

There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.

435 - 147 = 288

So, there were 288 nickels in the jar at the start.

Answer:

-160 I think so

Step-by-step explanation:

(2)4-168

8-168

-160

The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.

The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.

Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.

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The library is 5 kilometres far from the community pool.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.

The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle

So, using Pythagoras theorem, we get

[tex]13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km[/tex]

So, the library is 5 kilometres far from the community pool.

Therefore, the distance between the library and the community pool is 5 kilometres.

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The slope of the line represented by the equation  2x - 5y = 9 is 2/5  .

In the question ,

it is given that ,

the equation of the line is  2x - 5y = 9  .

we know that the equation of the line is represented as y = mx + c ,

where slope of the equation is  "m" .

So , rewriting  2x - 5y = 9 in the form of y = mx + c ,

w get ,

2x - 5y = 9

5y = 2x - 9

dividing both sides of the equation 5y = 2x - 9 by 5 ,we get

y = 2/5x - 9/5

y = (2/5)x - 9/5

the slope is = 2/5 .

Therefore , The slope of the line represented by the equation  2x - 5y = 9 is 2/5  .

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The Average speed is 17.4 mph.

The average speed is calculated by dividing the total distance travelled by the total amount of motion time.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Average speed = Distance travelled/ Time taken

Given:

Distance = 5 4/5 = 29/5 miles

Time= 1/3 hours

So, Average speed = Distance travelled/ Time taken

Average speed= 29/5 x 3/1

                         = 87/5

                         = 17.4 mph

Hence, the Average speed is 17.4 mph.

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Answer:

Erin would need $10 more dollars in order to buy all three books.

Step-by-step explanation:

Step one: find the cost of all books

12 +16 +11 = 39

Step two: subtract

39 -29 = 10

Step two: Get your Answer!

Erin would need $10 more dollars in order to buy all three books.

Answer:

a). 18x+30 - 18x+4=17

18x-18x 30+4 =17

34=17

[tex](a) \: { \pink{ \boxed{ \blue{ \sf{x = \frac{13}{30}}}}}}[/tex]

[tex](b) \: { \pink{ \boxed{ \blue{ \sf{x = -2}}}}}[/tex]

Step-by-step explanation:

[tex](a){ \red{ \sf{6x(3x + 5) - 2x(9x - 2) = 17}}}[/tex]

[tex]{ \red{ \sf{ { \cancel{18x}^{2} + 30x \: { \cancel { - 18x}^{2} + 4 = 17}}}}} [/tex]

[tex]{ \red{ \sf{30x + 4 = 17}}}[/tex]

[tex]{ \red{ \sf{30x = 17 - 4}}}[/tex]

[tex]{ \red{ \sf{30x = 13}}}[/tex]

Divide both the sides by 30 then,

[tex]{ \red{ \sf{ \cancel {\frac{30}{30}}}}}{ \red{ \sf{x} = \frac{13}{30}}} [/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{13}{30}}}}}} [/tex]

[tex](b) { \red{ \sf{2x(3x - 1) - 3x(2x + 11) - 70 = 0}}}[/tex]

[tex]{ \red{ \sf{ { \cancel{6x}^{2} - 2x}}}} \: \: { \red{ \sf{ \cancel { - 6x}^{2} - 33x - 70 = 0}}} [/tex]

[tex]{ \red{ \sf{ - 2x - 33x - 70 = 0}}}[/tex]

[tex]{ \red{ \sf{ - 35x - 70 = 0}}}[/tex]

[tex]{ \red{ \sf{ - 35x = 70}}}[/tex]

Divide both the sides by -35 then,

[tex]{ \red{ \sf{ \cancel {\frac{ - 35}{ - 35}}}x}}= { \red{ \sf{ { - \frac{ \cancel{70} ^{2} } { \cancel{35_{1} }}}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]

Answer:

box a - 252 inches squared (6 x 7 x 6)

box b - 216 inches squared (3 x 8 x 9)

Step-by-step explanation:

The value of the variables in the figure is x = 60 degrees and y = 10 degrees.

From the figure:

x + 120 = 180 (since consecutive interior angles equal to 180)

x = 180 - 120

x = 60 degrees.

3y + 40 + 3x - 70 = 180(since supplementary angles = 180)

3y + 3x - 30 = 180

3(y + x) = 180 + 30

y + x = 210/3

y + x = 70

substitute x value

y + 60 = 70

y = 70 - 60

y = 10 degrees.

Therefore the value of the variables in the figure is x = 60 degrees and y = 10 degrees.

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Answer:

November 2nd

Step-by-step explanation:

Halloween = Oct. 31

3 days before Halloween (Oct. 31) is Oct. 28

7 days after that it is Nov. 4

2 days before is November 2nd

The values of the statements are x³, b ÷ 3, 3a, y-3, z+3.

What is an Expression?

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

Hence the answer is, the statements are:

A variable cubed : x³

Quotient of some number and three:   b ÷ 3

Product of an unknown value and three : 3a

Three less than a variable : y-3

Three more than some number : z+3

Hence the answer is, the values of the statements are x³, b ÷ 3, 3a, y-3, z+3.

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Answer: x=7°

Combine like terms and divide.

8x+5°+3x+8°=90°

(8x+3x)+(5°+8°)=90°

11x+13°=90°

-13°       -13°

11x=77°

[tex]\frac{11x}{11} =\frac{77}{11}[/tex]

x=7°

Answer:

  11

Step-by-step explanation:

You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.

The ratio of interest is ...

  2B/A = 2(2115000)/(3.7×10⁵)

A calculator provides an easy answer to the value of this expression. (See attached.)

City C is about 11 times the population of City A.

__

Additional comment

If you want to work this out "by hand", you will need to find the quotient of ...

  4230000/370000 = 423/37 = 11 17/37 ≈ 11

because 17/37 < 1/2.

The given sequence is geometric sequence not arithmetic.

An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.

Difference between arithmetic and geometric sequence:

An arithmetic sequence has a constant difference between each consecutive pair of terms

while

A geometric sequence has a constant ratio between each pair of consecutive terms.

Here, we have a sequence 5,10,20.

So a₁ = 5, a₂ = 10, a₃ = 20

Difference = a₃- a₂ = 20 - 0 = 10

                    a₂ - a₁ = 10 - 5 = 5

Since the difference is not constant, therefore the given sequence is not arithmetic.

Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.

Therefore, the sequence is geometric sequence.

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The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.

p = 0.69

1 - p = 0.31

n = 209

μp = p = 0.69

σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199

= 1 - p(p < 0.72)

= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)

= 1 - p(z < 0.94)

= 1 - 0.8264

= 0.1736

Hence, the probability is 0.1736.

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Answer: 9.

Step-by-step explanation:

These are all multiples of 9, meaning that they can all be divided by 9 into a whole number.

90/9 =10

81/9 =9

72/9 =8

63/9 =7

Answer:

9:N

Step-by-step explanation:

90-9=81

81-9=72

72-9=63

The same number (9) is used to fing the sum of the next number in the sequence therefore that is your nth term

Answer:

D

Step-by-step explanation:

-4x + 9 ≥ -3  Subtract 9 from both sides

-4x ≥ -12  Divide both sides by -4.  When you divide both sides by a negative number, you must flip the inequality sign.

x ≤ 3

D: 5 is not a solution.

Answer:

D) 5

Step-by-step explanation:

To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?

How do you isolate a variable?

Here's an example.

x+3=18

What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.

x + 3 - 3= 18 - 3

Combine like terms.

x = 21

That's how you solve for an equation.

Next, an example with division.

3x = 21

How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.

[tex]\frac{3x}{3} =\frac{21} {3}[/tex]

Simplify:

3x/3 means 3 times x divided by 3. 3/3 = 1

1x = 21/3

21/3 = 7

x = 7

Now lets get to the problem.

[tex]-4x + 9 \geq -3[/tex]

The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.

[tex]-4x + 9 -9\geq -3 - 9[/tex]

Simplify.

[tex]-4x \geq -12[/tex][tex]-4x \geq -12[/tex]

Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:

A [tex]\geq , \leq , > , or < B[/tex]

If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!

When you multiply/divide by a negative number or both sides in an equality:

[tex]\leq[/tex] [tex]\geq[/tex]

[tex]\geq[/tex] [tex]\leq[/tex]

> <

< >

So, we currently have:

[tex]-4x \geq -12[/tex]

Divide by -4 on both sides.

[tex]\frac{-4x}{-4} \geq \frac{-12}{-4}[/tex]

Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).

[tex]x \geq 3[/tex]

Flip the sign (This is a crucial step!)

[tex]x \leq 3[/tex]

Now, [tex]x \leq 3[/tex] means any number equal to or lower than 3 satisfies the conditions of the inequality.

Is -3 lower than or equal to 3?

Yes; Lower

Is -1 lower than or equal to 3?

Yes;

Is 3 lower than or equal to 3?

Yes; Equal

Is 5 lower than or equal to 3?

No; Greater

D, 5 is your answer as it does not satisfy the inequality.

The size that is the better one is 30.6-ounce package costs 7.98.

The 11.5-ounce package costs 3.19. The price per package will be:

= 3.19 / 11.5

= 0.27

A 30.6-ounce package costs 7.98. The cost per package will be:

= 7.98 / 30.6

= 0.26

In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.

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Answer:

X=14

Side GF: 41 ft

Side FE: 58 ft

Side DE: 98 ft

Side DG: 28 ft

Step-by-step explanation:

(13+2x)+(4x+2)+(7x)+(X+14)

6x+15+8x+14

14x+29=225

     -29.  -29

     14x=196

      /14.  /14

        X=14

Fill in 14 for x for each side

13+2(14)

13+28

Side GF: 41 ft

4(14)+2

56+2

Side FE: 58 ft

7(14)

Side DE:98 ft

14+14

Side DG: 28 ft

Hopes this helps please mark brainliest

The Confidence interval is (0.85,1.05) which contain the sample proportion for 95%of samples size.

Confidence interval is an interval with a confidence level. Confidence interval is always constructed on basis of sample , p = sample statistic - margin of error to sample statistic + margin of error

Confidence interval for a proportion are calculated using the following formula:

p= ( p' - Z√p'(1-q')/n , p'+ Z √p'(1-p')/n ) ---(1)

where, p' ---> sample proportion for sucess

1-p' -----> sample proportion for failure

Z --> Z-value (statistic value)

n---> sample size

we have given that,

sample size ( n)=850 , sample proportion (p') = 0.95 and population proportion= 0.75

a) mean of sample of proportion is same as poplution proportion i.e 0.75 ..

1 -p' = q' = 0.05

Using the formula for margin of error ,

M .E = Z √ p'q'/n ---(2)

as the Z-value for given proportion is 13.46

putting all values in equation( 2) we get,

M.E = 13.45 √0.95×0.05/850 = 0.1005

Now, we shall calculate the confidence interval for given data

confidence interval (p)

= ( 0.95 - 0.100 , 0.95 + 0.100)

p= ( 0.85 , 1.05)

Hence,confidence interval(CI) is (0.85, 1.05).

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Complete Question:

75% of all credit card users carry a balance from month to month. a. If you randomly select 850 credit card users and will compute the sample proportion that carry a balance from month to month, what is the mean of the sample proportion? b. If you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?

The elevation of the hole after placing the bush in the hole is 17/8 feet

Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes

After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole

This involves subtraction and multiplication of fractions

Since the rate of digging = 3/4 feet every 10 minutes

Thus, after digging for 40 minutes, the depth will be:

3/4 × 4 = 3 feet

If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:

3 feet - 7/8 feet = 17/8 feet

Therefore,  after placing the bush in the hole, the elevation of the hole is 17/8 feet

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the slope of the given point is m=9

Answer: Use your brain aka 12 and 7

Step-by-step explanation:isn't this urgent?

Answer:

10 - x

Step-by-step explanation:

Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:

10 - 3 - x + 3

7 - x + 3

10 - x