A rectangular swimming is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a consistent 2 feet wide and has as area of 196 square feet. What are the dimensions of the pool? If the depth of the pool is 6 feet, how much water can the pool hold if the height of water is 1 foot below the top of the pool?

Convert cubic feet to gallons

The probability that all three girls are together is 0.03

Here we will use the string method

Consider 3 girls as a single element, and consider the other 3 boys as 3 separate elements

So total we have 4 element

So the arrangement of  4 elements is given by  4!

Arrangement of girls inside a single element given by 3!

So the way of getting all girls together is given by 4! × 3! = 24 × 6 =144

Total way of arranging 7 people given by 7! = 5040

Probability = Required cases / Total cases

= 144 / 5040

= 0.03

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Answer:

2/3

Step-by-step explanation:

the slope is rise over run so y/x

Answer: 5 hours.

Step-by-step explanation: First you need to subtract the $12 fee from the total to find out how many hours he paid for. 57-12=45. So if he paid $45 at $9 per hour, 45 divided by 9 equals 5.

The average age of all the animals at the animal rescue center is 5.4 months .

In the question ,

it is given that ,

at an animal rescue center .

percent of dogs that are present in the animal rescue = 80%

percent of cats that are present in the animal rescue = 20%

let suppose that there are total of 100 animals in the animal rescue .

So , the number of dogs = 80

and the number of cats = 20

also given that ,

the average age of dogs = 6 months

the average age of cats = 3 months .

So , the average age of all the animals can be calculated by

Average age = (80×6 + 20×3)/100

= (480 + 60)/100

= 540/100

= 5.4 months

Therefore , The average age of all the animals at the animal rescue center is 5.4 months .

At an animal rescue 80% of the animals are dogs and 20% of the animals are cats. If the average age of the dogs is six months and the average age of the cat is three months what is the average age of all the animals ?

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The volume of the rectangular prism is 12 cubic inches

It is given that Each cube represent 1 unit

The base length of the rectangular prism = 4 inches

The base width of the rectangular prism = 3 inches

The height of the rectangular prism = 1 inches

The volume of the rectangular prism = The base length of the rectangular prism × The base width of the rectangular prism × The height of the rectangular prism

Substitute the values in the equation

The volume of the rectangular prism  = 4 × 3 × 1

= 12 cubic inches

Hence, the volume of the rectangular prism is 12  cubic inches

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The expression when the brackets are removed is 15x - 4

From the question, we have the following expression that can be used in our computation:

6 + 5(3x - 2)

The above expression has brackets

So, we start by expanding the brackets

Solving further, we have

6 + 5(3x - 2) = 6 + 15x - 10

Collect the like terms

This gives

6 + 5(3x - 2) = 15x - 10 + 6

Evaluate the like terms

So, we have

6 + 5(3x - 2) = 15x - 4

Hence, the expression is 15x - 4

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Answer:

The answer is false.

Step-by-step explanation:

If you do not already know this, a negative and a negative equals a positive. Therefore, instead of –8 • –4 = –32, the correct answer would be –8 • –4 = 32.

Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)

Answer: is false.

hope this helps

have a good day

Step-by-step explanation:

Answer:

[tex] \sf \: 2x + 2[/tex]

Step-by-step explanation:

Given expression,

→ (3x + 4) - (x + 2)

Let's simplify the expression,

→ (3x + 4) - (x + 2)

→ 3x + 4 - x - 2

→ (3x - x) + (4 - 2)

→ (2x) + (2)

→ 2x + 2

Hence, the answer is 2x + 2.

The function that includes all the ordered pairs in the given table is y = -x - 4

First choose two points

First point = (0, -4)

Second point = (2, -6)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (-6 - (-4) / (2 - 0)

= -6 + 4 / 2

= -2 / 2

= -1

Here at X = 0, the value of Y = -4

Therefore the y intercept of the line = -4

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Substitute the values in the slope intercept form

y = -1x - 4

y = -x - 4

Hence, The function that includes all the ordered pairs in the given table is y = -x - 4

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From the given data

a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks

b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km

In the graph,

The x axis represents the Time since start in minutes and the y axis represents the distance from the start in kilometers.

In x axis each block represents 5 minutes

The maximum value of time taken in table = 35 minutes

Then the number of squares wide does the grid need to be so that the data fits on the graph = 35 / 5

= 7 blocks

Part b

If the grid is 20 squares tall

The maximum value of distance = 1.8 km

Then the value of A will be

1.8 / 20 = 0.09 km

Hence, from the given data

a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks

b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km

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25 is 2.87 percent of 872.

First, let us understand the percentage:

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.

We need to find 25 is what percent of 872.

Let 25 be x percent of 872.

So,

872 * x % = 25

872 * x / 100 = 25

872x = 25 * 100

x = 25 * 100 / 872

x = 2.87 %

So, 2.87 % of 872 is 25.

Thus, 25 is 2.87 percent of 872.

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The value of y in the  expression is y= - (x + 4) or,  y= (x -4)

Algebraic expression in mathematics is a phrase that include coefficients, unknown variables  operations, and constants

To solve for y in the equation 10x+5y=5x+20 we apply algebraic rule;

Step 1: Collect the like terms by moving the unknown 'ý' to the left side of the equation

5y =5x -10x+20

Step 2: Evaluate the the expression 5y =5x -10x+20

5y = -5x + 20

Step 3: Divide both sides by 5

[tex]\frac{5y }{5}[/tex] = [tex]\frac{-5x +20}{5}[/tex]  

y = -5x/5  + 20/5

y = - (x + 4) or,  y= (x -4)

Therefore, the value of y in the expression is y= - (x + 4) or,  y= (x -4)

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Answer:

The angle is approximately 111.199 degrees.

Step-by-step explanation:

Cosine is adjacent over hypotenuse.

The hypotenuse is the longest side of the triangle.  

In this cos the hypoteneuse is a. However, we can only use cos on right triangles and on the angles that are not 90 degrees. In this case, p would be the 90 degree angle if we could use cosine.

In this case, you need the law of cosines, not cosine. The law of cosine says [tex]c=\sqrt{a^2+b^2-2 a b cosp}[/tex] where c is the side opposite to the angle, a and b are the sides adjacent to the angle, and p is the angle. The law of cosine works for all the triangles.

Plugging in the numbers:

[tex]5.3=\sqrt{3.6^2+2.8^2-2*3.6*2.8* cosp}\\5.3^2=20.8-20.16* cosp}\\7.29=-20.16*cosp\\cos^{-1}\frac{7.29}{ -20.16}=p\\p=111.198929[/tex]

The value of x is -8.

1).

N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1).

slope between NO = y2 - y1 / x2 - x1

= 3 - (-8) / 5 - (-6)

= 3+8 / 5+6

= 11/11

= 1

slope between PQ = 1-9 / x-0

= -8/x.

Given lines are parallel so there slopes are equal

1 = -8/x

x = -8.

Therefore the value of x is -8.

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For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by        ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.

As given in the question,

Confidence interval for population mean is given by:

[tex]\bar{x}[/tex] ± z × ( σ / √n)

Where,

σ = population standard deviation.

n= sample size

[tex]\bar{x}[/tex] = Sample mean

Given values from the random sample size are :

σ = 0.01 inches

n= 10

[tex]\bar{x}[/tex] = 1.5045

Critical value confidence interval (using x-value table)

z  for 99% = 2.576 and Significance level = 0.01

z for 95% = 1.960 and Significance level = 0.05

99% two-sided confidence interval on the mean hole diameter is equal to :

[tex]\bar{x}[/tex] ± z × ( σ / √n)

= 1.5045 ± 2.576 × ( 0.01 / √10)

= 1.5045 ± 0.00815 (approximately)

= 1.5045 - 0.00815 , 1.5045 + 0.00815

= ( 1.49635 , 1.51265 )

95% two-sided confidence interval on the mean hole diameter is equal to :

[tex]\bar{x}[/tex] ± z × ( σ / √n)

= 1.5045 ± 1.960 × ( 0.01 / √10)

= 1.5045 ± 0.00620 (approximately)

= 1.5045 - 0.00620 , 1.5045 + 0.00620

= ( 1.4983 , 1.5107 )

Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and  ( 1.49635 , 1.51265 ) respectively.

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The student that correctly used partial quotients to show 552 divided by 23 was Gavin.

The purpose of partial quotients is to facilitate division as by using partial quotients students can easily divide big numbers by using easy multiples first and then adding the multiplers to find the final divisiors. The recommended numbers to use are 5 or 10.

Based on the information provided, it can be conclude Gavin was better at applying this method because he used only easy multiples (10, 2) to make the number easier to divide, while Brianna completed the process only through to steps, which is not recommended when applying this method.

In conclusion, Gavin was the one who correctly used the method and calculated the result.

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Answer: 7(x^3-5)

Step-by-step explanation:

the common number between 7 and 35 is seven( 7*1=7, 7*5=35)

so with the 7 outside the parenthesis we end up having inside the parenthesis x^3 and 5 because x=1 and 7*1=7 and the 5 because 7*5=35 so if we distribute the seven we would get the original answer

Answer:

[tex]7(x^3-5)[/tex]

Step-by-step explanation:

Given expression:

[tex]7x^3-35[/tex]

To factor the given expression, begin by rewriting 35 as 7 · 5:

[tex]\implies 7x^3-7 \cdot 5[/tex]

Now factor out the common term 7:

[tex]\implies 7(x^3-5)[/tex]

The equation of the line is y = (-3/5)x - 3

The equation of the line given

y = (5/3)x + 1

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Comparing the given equation

slope of the line m = 5/3

The slope of the perpendicular line = -1/m

= -1 ÷ 5/3

= -3/5

The line is passing through the point (-10, 3)

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values in the equation

y - 3 = (-3/5)(x - (-10))

y - 3 = (-3/5)x - 6

y = (-3/5)x - 6 + 3

y = (-3/5)x - 3

Hence, the equation of the line is y = (-3/5)x - 3

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The commonly used technique in problem solving is means-end analysis

One typical heuristic is to define subproblems or subgoals. Means-ends analysis, which entails determining how to close the gap between a goal and the actual situation, is another frequently employed heuristic. You can divide a problem into smaller problems and deal with each one separately by using means-ends analysis.

Heuristic problem-solving entails what?

A problem-solving heuristic is a non-formal, speculative process that, in certain circumstances, produces a solution but not in others. The strategy can be either more or less successful than employing an algorithm because the results of applying a heuristic are unpredictable.

So,therefore the means-end analysis is commonly used technique in problem solving

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The money that the group will be able to donate with the savings from all 20 youth is $1400.

Let the daily pay plan for each youth = y.

Daily pay plan for 20 youths = 20y

Weekly pay plan = 7 × 20y = 140y

Assuming each youth saves $10 daily

Daily savings for 20 youth:

= 20 × $10

= $200

Weekly savings for 20 youth:

= 7 × $200

= $1400

If they used the early pay plan 140y to go swimming, they saved $1400 which they donated to the church.

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The probability of Johnny winning is  [tex]20 *(\frac{2^3}{3^6} )[/tex].

Given data;

Johnny throws six equal dice with six sides and the numbers 1 through 6 on them. He needs a 5 or 6 on precisely 3 of the dice to take home the prize. What are Johnny's odds of winning?

The probability of 5 or 6 = 2/6

                                 = 1/3

The probability of not 5 or 6 = 4/6

                                = 2/3

The total probability of getting in exactly 3 chances;

⇒ ⁶C₃ * (1/3)³ * (2/3)³

⇒ [tex]20 *(\frac{2^3}{3^6} )[/tex]

Hence, the chances for Johnny to win are  [tex]20 *(\frac{2^3}{3^6} )[/tex].

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Answer:9072

Step-by-step explanation:

453.6 x 20 = 9072

The amount of money spend on music from the fractional value is $1.30;

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

spends 3/4 of her money on game apps

spends $0.98 on music apps.

So, we can assume the total amount to be K;

So, The fraction of money spend on music is K/4;

According to the question, we have:

[tex]\frac{1}{4} \times k[/tex] = $0.98;

⇒K = $3.92;

So, The total amount with Kim is $1.30;

Hence,

The amount of money spend on music is $1.30;

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The linear function rule of the equation is y =  x + 18

From the question, the points on the line are given as

(2, 20) and (9, 27).

So, we have the following ordered pairs

(x, y) = (2, 20) and (9, 27).

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2, 20) and (9, 27).

Substitute the known values in the above equation

So, we have the following equation

Slope = (27 - 20)/(9 - 2)

Evaluate the above quotient

Slope = 1

The equation is then calculated as

y = Slope(x - X) + Y

Substitute the known values in the above equation

So, we have the following equation

y = 1 * (x - 2) + 20

So, we have

y =  x + 18

Hence, the equation of the line is y =  x + 18

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Answer:A. 20% B.45%

A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45

Step-by-step explanation:

hope i helped!

Irrational Number

Step-by-step explanation:

Alternatively, 3 is a prime number or rational number, but √3 is not rational number.

Here, the given number √3 is equal to

1.73205080756 which gives the result of non

terminating and non recurring decimal and keep on extending , and cannot be expressed as fraction ..,

Therefore √3 is Irrational Number.

Answer:

(3x+10)(x+1)

Step-by-step explanation:

This is the answer for 3x^2+13x+10.

I think you made an error while typing.

Hope this helps!

An equation of the line that passes through the point (-3, -1) and is perpendicular to the line x - 2y = 6 is y = -2x - 7.

Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would rewrite the given equation representing a line in standard form:

x - 2y = 6

2y = x - 6

y = x/2 - 6

Therefore, slope (m) = 1/2

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

At point (-3, -1), an equation of this line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - (-1) = -2(x - (-3))

y + 1 = -2(x + 3)

y + 1 = -2x - 6

y = -2x - 6 - 1

y = -2x - 7

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The equivalent expressions are (6^(-4) )^(-4), (6^(-2) )^(-8) and (6^8 )^2

Using exponent property, we have

[tex](a^{m})^{n} = a^{m*n}[/tex]

The given expressions is 6^16

From the question, we have

(6^0 )^16=6^(0×16)

⇒6^0 ≠ 6^16

(6^8 )^8=6^(8×8)

⇒6^64 ≠ 6^16

(6^(-4) )^(-4)=6^(-4x-4)

⇒6^16

(6^(-2) )^(-8)=6^(-2×-8)

⇒6^16

(6^(-1) )^16=6^(-1×16)

⇒6^(-16)≠6^16

(6^8 )^2=6^(8×2)

⇒6^16

Multiplication:

In mathematics, multiplying the numbers is used to find the product of two or more numbers. We frequently perform one of the basic mathematical operations. The simplest basic application is to use multiplication tables. Mathematicians multiply two integers to express the repetitive addition of one number to another. It is possible to contain natural numbers, fractions, integers, whole numbers, and other forms of numbers. M would either be added to itself 'n' times or subtracted from itself when M is multiplied by n.

Complete question:

Which expressions are equivalent to 6^16?

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