The cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit. For how many hours is the cost of renting a pool the same for both plans?

Using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units  

Given,

The points =  O(-12,0) and P(-8,3)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance [tex]=\sqrt{(-8--12)^{2}+(3-0)^{2} }[/tex]

[tex]=\sqrt{4^{2}+3^{2} } \\=\sqrt{16+9} \\=\sqrt{25}[/tex]

= 5 units

Hence, using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units  

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Answer:

im guessing c?

Step-by-step explanation:

The probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132

In this question,

We have been given a standard deck of 52 cards.

Three cards are selected from a standard deck of 52 cards.

Sample space n(S) = 52

We need to find the probability that all three cards are diamonds if neither the first nor the second card is replaced.

We know that, in a standard deck of 52 cards, there are 13 diamond cards.

The probability that the first card is diamond,

P1 = 13/52

The card is not replaced, so the total number of cards in a standard deck = 51

And the number of diamonds = 12

Now the probability that second card would be diamond,

P2 = 12/51

Similarly the probability that the third card is diamond,

P3 = 11/50

So, the probability that all three cards are diamonds if neither the first nor the second card is replaced:

⇒ P = P1 × P2 × P3

⇒ P = 13/52 × 12/51 × 11/50

⇒ P = 0.25 × 0.24 × 0.22

⇒ P = 0.0132

Therefore, the probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132

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The boxes will be 1.2 times taller than old boxes.

We are given that increase in amount of juice is achieved by keeping the base same but increasing the height only. So, we are aware that length and width are part of base but height is not. Now, there will 20% increase in volume, so finding the increase in height when volume of boxes is increased.

V₁ = V₂

L₁×B₁×H₁ = L₂×B₂×H₂

We know,  L₁B₁ = L₂B₂

So, relating the height of boxes -

H₂ = H₁ (1 + 20%)

H₂ = H₁ (1 + 0.2)

H₂ = H₁×1.2

H₂ =1.2 H₁

Hence, the larger boxes will be 1.2 times taller than old boxes.

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The explicit formula for the given geometric sequence is: [tex]a_n=2^n[/tex].

Now, Given sequence: 2, 4, 8, 16, ...

=> 2¹, 2², 2³, 2⁴, ....

Thus, the explicit formula for this geometric sequence will be given by:  [tex]a_n=2^n[/tex].

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The characteristic that justifies each assertion Property of substitution

The substitution property asserts that if a=b, then one can of replacing b in quite an expression or equation.

X Y+20=Y W and X Y+20=D T

then Y W=D T

The replacement property of equality states that "If a variable x is equal towards another variable y, then x may be substituted in place of y in whatsoever equation/expression and y can indeed be substituted throughout the place of x in any equation/expression."

Substitution connects many aspects of mathematics and hence aids in viewing mathematics as an entire discipline.

Three phases are involved in the substitution method: Solve this equation for a single of the variables. Substitute (plug-inin) this equation into a different equation and solve. Replace the value inside this original equation to obtain the equivalent variable.

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Answer:

B. Divide both sides by 26

Explanation:

When doing a one step equation you basically want to get the x alone. To do that you need to divide 26x by 26.

26x = 74

26 26

x = 2.8

Her consumption of x is mathematically given as

x=8

Generally, the equation for Slope  is  mathematically given as

u=x^2y^2 ....1

Therefore

[tex]$ slope=-\frac{m u x}{m v_y}=\frac{-2 x y^2}{2 x^2 y}$[/tex]

slope=-y/x

y=0.875 x

Substitute in (1)

[tex]u=x^2(0.875 x)^2=3136 \\[/tex]

[tex]0.875^2 x^4=3136 \\[/tex]

[tex]x^4=4096[/tex]

x=8

y=7

In conclusion,

x=8

y=7

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The equation of the circle (x + 5)^2 + y^2 = 18 has a radius of 3√2 and a center located at (-5 , 0).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 5)^2 + y^2 = 18, is in standard form, then

h = -5

k = 0

r = 3√2

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Answer:

10

Step-by-step explanation:

First write out the equation: 42 = 12 + 3x

42 - 12 = 12 - 12 + 3x

30 = 3x

30/3 = 3x/3

x = 10

The 7 days will he have to work per month to make either choice equal financially.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Adam can rent an apartment in the city and walk to work for $615 per month.

He can rent for $500 per month and take the train to work for $5 per day.

According to given question we have

Total rent =$615 per month.

Rent an apartment in the suburbs = $500 per month

train to work= $5 per day

train to work in a month=$5*30=  $150 per month

So, total Rent an apartment in the suburbs

=$500 per month+$150 per month

=$650 per month

Difference

=$650 per month- $615 per month.

=$ 35 per month

$5day==$ 35  month

1 day= $ 35 /5 = $ 7 per month

To work per month to make either choice equal financially in 7 days.

Therefore, the 7 days will he have to work per month to make either choice equal financially.

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Myra's distance is increasing as time increases.

Given table showing the time (in minutes) and distance (in miles) :

Time (in minutes)    Distance (in miles)

 0                                        0.0

 2                                        0.4

 4                                        0.8

 6                                        1.2

 8                                        1.6

As we can see from the table, when there is an increase of 2 minutes in time, the distance is increasing by 0.4 miles.

So the distance covered by Myra is increasing with increase in time.

The question is incomplete. Find the complete question below:

The table shows the total distance that Myra runs over different time periods. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0. 0, 0. 4, 0. 8, 1. 2, 1. 6. Which describes Myra's distance as time increases? increasing decreasing zero constant.

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The solution of the given equation  x/2 + x/3 = 15 is x = 18

In this question,

We have been given an equation.

x/2 + x/3 =15

We need to find the solution of given equation.

First we simplify the LHS of given equation.

x/2 + x/3

= (3x + 2x) / (2)(3)

= 5x / 6

So given equation  would be,

⇒ x/2 + x/3 = 15

⇒ 5x / 6 = 15

⇒ 5x = (15)(6)

⇒ 5x = 90

⇒ x = 18

We need to check above solution.

Substitute x = 18 in LHS of given equation.

= 18/2 + 18/3

= 9 + 6

= 15

= RHS

Therefore, the solution of the given equation  x/2 + x/3 = 15 is x = 18

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Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.

The term triangular coordinates can refer to at least three related systems of coordinates in the Euclidean plane: a special case of barycentric coordinates for a triangle, also known as a ternary plot or areal coordinates, among other things.

Because this is a right triangle, two of its sides can be found on the axes. Placing the triangle's right angle at the origin will allow the two legs to be parallel to the x- and y-axis.

Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.

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The algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]

Given

The word phrase

"The quotient of the sum of 2 and a number b and 3"

Sum off 2 and a number b = 2+b

Then the quotient of the sum of 2 and a number b and 3 = [tex]\frac{2+b}{3}[/tex]

Hence ,the algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]

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The amount in the savings account after 2 years, 5 years and 8 years is respectively $13.6, $34, $54.4.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't really compound, therefore the creditor only has to pay more interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.

Principle=3400

Rate of interest=0.2

Time period=2, 5 and 8 years

To calculate simple interest I= PRT/100

=> To find the amount in the savings account after 2 years

=(3400×0.2×2)/100

=13.6

So the amount in the savings account after 2 years is $13.6.

=> To find the amount in the savings account after 5 years

=(3400×0.2×5)/100

=34

Therefore the amount in the savings account after 5 years is $34.

=> To find the amount in the savings account after 8 years

=(3400×0.2×8)/100

=54.4

Hence the amount in the savings account after 8 years is $54.4.

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Answer:

2 years: 3413.60 or 3,413.60

5 years: 3434, 3,434.00, 3,434, or 3434.00

8 years: 3454.40 or 3,454.40

(the other persons is wrong)

It should be noted that Zahraa saying that the first division to perform is determining how many whole times 289 divides into 5,437 is incorrect.

It should be noted that based on the information, Zahraa is calculating the quotient of 54,379÷289 and she set up the long division with the numbers in the correct places.

She said that first division to perform is determining how many whole times 289 divides into 5,437. This is incorrect.

It should be noted that the first thing to do is to find the number of times that 28 will go in 54 and then bring the remainder down and solve till she gets the final value.

In this case, 54,379÷289 will be 188 47/289

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Answer:

la correcta es verdadero

Multiplicative Identity Property

Using math properties like the multiplicative identity property we can solve different expressions and equations.

Definition of Multiplicative Identity Property

The multiplicative identity property states that any number multiplied by 1 equals itself. This means that 18 x 1 = 18. Of course, since this is a property we can apply this idea to any equation.

All of the statements above are true because of the multiplicative identity property.

Uses of the Multiplicative Identity Property

While being able to do simple operations with this property is helpful, there are other uses as well. One of the most prominent uses is finding a great common factor. When adding or subtraction fractions, you must have a GCF. We can use the multiplicative identity property to do this.

Take the expression

To solve this we must multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{2}{2}[/tex]. The multiplicative identity property tells us that since 2/2 = 1, this will not affect the value of the expression (remember that anything times 1 is still equal to itself).

Then, we can solve the expression.

The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width of the rectangle. The area is 85 yd², hence:

xy = 85

If both the length and the width of the rectangle are doubled:

new length = 2x; new width = 2y

new area = 2x * 2y = 4xy = 4(85) = 340 yd²

The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²

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The equation of the line y = 6x has 0 and 0 as its x- and y-intercept, respectively.

The equation of a line is an equation containing variable(s) and constant(s) and can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The x-intercept of a line is the value of x when y = 0 while the y-intercept of a line is the value of y when x = 0.

For an equation written in standard form ax + by = c, the x- and y-intercept is as follows:

x-intercept = c/a

y-intercept = c/b

If the equation of the line is y = 6x, then its x- and y-intercept is as follows:

x-intercept = c/a = 0/6 = 0

y-intercept = c/b = 0/1 = 0

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The inverse of a function is a mirror image of a graph around y = x thus graph in (A) will be the inverse of a function y = m(x).

The inverse of a function is basically a reverse function or undo of the function.

It means in the inverse function we need to interchange x and y.

Let's consider a function y = 2x + 3

The inverse of y is ⇒ y = (x - 3)/2

Now,

If we draw both graphs, both are mirror images of each other about x = y (as shown below).

Therefore y = m⁻¹(x) will be the mirror image of y = m(x) about y = x.

In option (A) the graph is the only mirror image of graph y = m(x).

Hence "The graph in option (A) shows the inverse of function y = m(x)".

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The slope of the line is - 2 / 5

The equation in standard form is as follows:

2x + 5y = -15

The slope of the line can be found as follows;

using (0, - 3)(5, - 5)

m = -5 + 3 / 5 - 0

m = -2 / 5

slope = -2 / 5

The slope intercept form representation of an equation is as follows:

y = mx + b

where

Therefore,

y = -2 / 5 x + b

using (0, -3),

-3 = - 2 / 5 (0) + b

b = -3

Hence,

y = - 2 / 5 x - 3

The standard form is as follows:

Ax + By = C

Therefore, the equation in standard form is as follows:

2 / 5 x + y = - 3

2x + 5y = -15

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Katty rode the roller coaster four times after riding the slide eight times.

Let R be the number of times she rode the roller coaster

Let S be the number of slides

The following mathematical equation can be created using the information provided:

R + S = 12. ........(i)

25R + 10S = 180 .......(ii)

From equation i, R = 12 - S.

Therefore, 25(12 - s) + 10s = 180

300 - 25s + 10s = 180

300 - 15s = 180

15s = 300 - 180

15s = 120

S = 120/15

S = 8 ,

Therefore R = 12 - S = 12 - 8 = 4

Katty rode the roller coaster four times after riding the slide eight times.

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The nth term of the given geometric sequence, 3, 12, 48, 192, . . . , is a(n) = 3[4^(n - 1)], where a(n) is the nth term.

A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.

a(n) = a r^(n-1)

Where:

a(n) = nth term

a = first term

r = ratio

Given the geometric sequence 3, 12, 48, 192, . . .

Find the ratio,

r = a(n)/a(n-1)

r = a(2)/a(1)

r = 12/3

r = 4

Notice that the ratio between two succeeding terms is always 4.

Substitute the value or r and the first term to the formula to determine expression for the nth term.

a(n) = a r^(n-1)

a(n) = 3[4^(n - 1)]

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Answer:

Thus, the length of the arc AB will be 5/18 of the circumference of the circle, which equals 2πr, according to the formula for circumference. length of arc AB = (5/18)(2πr) = (5/18)(2π(18)) = 10π. Thus, the length of arc AB is 10π.

Step-by-step explanation:

Answer:

  204 °C

Step-by-step explanation:

You want the predicted temperature of a pizza that has cooled for 20 minutes, as predicted by the formula ...

  log(temp) = 2.39 -0.004·time

where temp is in degrees Celsius, and time is in minutes.

Using time = 20 in the formula, we find ...

  log(temp) = 2.39 - 0.004·20 = 2.39 -0.08 = 2.31

Taking the antilog, we find the temperature to be ...

  temp = 10^2.31 ≈ 204.2 . . . . . degrees C

The predicted temperature of the pizza is 204 °C.

Answer:

EF = 10

Step-by-step explanation:

DE + EF = DF

So, x + 22 + x + 23 = 21

2x + 47 = 21

2x = -26

x = -13

EF = x + 23

EF = 10

Answer:

X€R or x€(-&, +&)......

The value of the variable 'x' shown in th the geometrical figure is equal to 2cm

What is line bisector?

A line bisector divides the line into two equal parts. For a line of length ' L ', the bisector divides the line into two equal parts of length L/2 each.

Given is a geometrical figure in which RS is bisector of AB at point T and RS = 36.

RS bisects AB at point T. Therefore, we can say that T is the mid-point of AB. So, we can write -

AT = TB

25 - 3x = 2y - 5

- 3x - 2y = - 5 - 25

-(3x + 2y) = - 30

3x + 2y = 30             ...[1]

RS = 36

RT + TS = 36

2y - 6 + 18 = 36

2y + 12 = 36

2y = 24

y = 12

Substitute y = 12 in [1], we get -

3x + 2 x 12 = 30

3x + 24 = 30

3x = 6

x = 2

Therefore, the value of x = 2

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