What’s the answers to b,c and d for 20 points.

If 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, then the cost of renting the pool is the same for both plans for 4 hours.

The number of hours for which the cost of renting the pool will be the same for both plans can be calculated by using an algebraic expression.

An algebraic expression is a type of equation that consists of both numbers and letters.

An algebraic expression for this problem can be given as,

30(x) = 20(x) + 40

Where x is equal to the number of hours.

The value of x can be calculated by rearranging the equation,

30(x) - 20(x) = 40

10(x) = 40

x = 40 ÷ 10

x = 4

Thus, the number of hours for which the cost of renting the pool same for both plans is 4 hours.

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The solution of the system of equations involving 3x + 5y = 13 and 2x + y = 4 is (1 , 2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

3x + 5y = 13     (equation 1)

2x + y = 4     (equation 2)

Using the second equation, find the value of one variable, lets say y, in terms of the other.

2x + y = 4     (equation 2)

y = 4 - 2x

Substitute the equation of y to the first equation.

3x + 5y = 13     (equation 1)

3x + 5(4 - 2x) = 13

3x + 20 - 10x = 13

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.

3x + 20 - 10x = 13

3x - 10x = 13 - 20

-7x = -7

x = 1

Substitute the value of x in the equation of y.

y = 4 - 2x

y = 4 - 2(1)

y = 4 - 2

y = 2

Hence, the solution of the given system of equations is (1 , 2).

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Answer:

Step-by-step explanation:

32 / 4 = 8 = length or width (because it is a square both are the same)

8 + 2 = 10

10 + 10 + 10 + 10 = 40 (perimeter of outer fence)

32(1.18) + 40(1.18) = $84.96

The arithmetic mean a n of the given terms a n₋₁ = 4, a₊₁ = -3 is [tex]a_{n}[/tex] = 1/2.

an=a1+d(n−1)   by using this formula the arithmetic mean a n of the given terms are

[tex]a_{n}[/tex] = (-3 + 4)/2

[tex]a_{n}[/tex] = 1/2

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.

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The entrance fee in the water park for the adult $37 and for the child are $24.

The maximum power of a variable in a linear equation of two variables is one.

Now, for the question's given condition;

Let the cost for the adult is 'x'.

Let the cost for the child is 'y'.

The total cost for entrance fee is $220.

The group of 4 adults and 3 children costs 220.

4x + 3y = 220     ........equation 1

The group of 2 adults and 1 child costs $98.

2x + y = 98           .........equation 2

Use elimination method to solve the equations;

x = 37 and y = 24.

Therefore, the entrance fee in the water park for the adults is $37 and for the child us $24.

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If x is doubled then the value of y is also doubled.

A sort of proportionality known as "direct variation" occurs when one quantity immediately changes in response to a change in another variable. This suggests that if one number increases, the other quantity will also rise proportionately. Similar to the last example, if one quantity declines, the other amount likewise declines. The link between direct variation and the graph will be linear, resulting in a straight line.

As y varies directly with x,

Using direct variation,

which implies y = kx

if x is doubled,

y = 2kx,

This implies that if x is doubled then the value of y is also doubled.

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The forecast for the next period when the actual demand turned out to be 278 will be 294 units.

The method of forecasting entails creating assumptions based on historical and current data. These might then be contrasted with what transpires.

Ft = 290, Tt = 8, α = 0.40, δ = 0.50, At = 278. Then the forecast for the next period will be

FITt = Ft + Tt

       = 290 + 8

       = 298 units

Ft + 1 = FITt + α(At − FITt)

        = 298 + 0.40(278 − 298)

        = 298 − 8

        = 290 units

Tt + 1 = Tt + δ(Ft + 1 − FITt)

         = 8 + 0.50(290 − 298)

         = 8 − 4

         = 4 units

FITt + 1 = Ft + 1 + Tt + 1

            = 290 + 4

            = 294 units

The forecast for the next period will be 294 units.

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Subtraction Property of Equality and Addition Property of Equality are two different approaches to resolving a real-world problem that can be depicted by an equation.

When the identical quantity is added to the both sides of an equation, it generates an equivalent equation, according to the addition property of equality.

To maintain equality, if we deduct a number from one side of the equality, we must subtract the very same number from the opposite side of the equality.

Thus, Subtraction Property of Equality as well as Addition Property of Equality are two different ways of solving a real-world problem that may be represented by an equation.

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The equation of the circle that passes through the point (√3 , 0) and has a center at the origin is x^2 + y^2 = 3.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (√3 , 0).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(√3 - 0)^2 + (0 - 0)^2

radius= √3

The standard form of the equation of the 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.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

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

where (h , k) = (0 , 0)

r = √3

(x - 0)^2 + (y - 0)^2 = (√3)^2

x^2 + y^2 = 3

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We have given the expression -13y + 7 -11 - 4y to write as sum which is

-13y + 7 +(-11) + (-4y).

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. (Number/variable, Math Operator, Number/variable) is the order in which an expression is composed.

Arithmetic operators and numbers make up a mathematical numerical expression. No equality or inequality symbols, or unidentified variables, are present.

Indeterminate variables, integers, and arithmetic operators make up an algebraic expression. Neither equality nor inequality symbols can be found in it.

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Answer:43

Step-by-step explanation:

(9+17)x2

The point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).

A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).

given that

the coordinates points are (1, 10) and (5,42)

(x1,y1) = (1,10)

(x2, y2) = (5,42)

The formula of point-slope is

(y - y1) = m(x - x1)

Here,

x1 = 1 and y1 = 10 but we don't know the value of m.

now,find the value of m using the following formula

[tex]m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]

now, substitute the values, we get

[tex]m = \frac{(42 - 10)}{(5 - 1)} [/tex]

[tex]m = \frac{30}{4} [/tex]

m = 8

so, the value of m is 8.

substitute these values into the point-slope formula

(y - 10) = 8(x - 1)

Hence, the point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).

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In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

WE have been given graph that titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000.

The line graph showed that:

The U.S. population was under 50 million in 1800

It increased exponentially after 1880

It reached around 300 million in 2000

The U.S. has seen its population rise exponentially over the last century such that; over 300 million and it was around the year 2000 that this milestone was reached.

Therefore U.S. population in 2000 was around 300 million.

In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.

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Answer:

300 million is ur answer:)

Step-by-step explanation:

Answer:

x= -6/5

Step-by-step explanation:

-6=3x+2x

-6=5x

x=-6/5

Answer:

x = - [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

- 2x = 3x + 6 ( subtract 3x from both sides )

- 5x = 6 ( divide both sides by - 5 )

x = - [tex]\frac{6}{5}[/tex]

I can't answer it but i hope someone else does :)

Maybe the answer - But there are limits depending on whether you donate the funds to a “50% charity” or a “30% charity.” As the name implies, the total deduction for gifts to 50% charities cannot exceed 50% of a taxpayer's adjusted gross income (AGI). Accordingly, donations to 30% charities are limited to 30% of AGI.

Answer:26

Step-by-step explanation:it's 26

Answer:

26

Step-by-step explanation:

You add 24 + 2 = 26 ( SUM means to ADD )

The sum of the infinite geometric series 6+5+ 25/6 + . .  is S = 36

The given geometric series is:

  6 + 5 +  25/6 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 6

a(2) = 5

a(3) = 25/6

Hence, the common ratio is

   r = a(2) / a(1) = 5/6

Since 0 < r < 1, the series is convergent and the sum exists.

Use the sum formula:

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

Substitute a(1) 6 and r = 5/6 into the formula:

S = 6 / (1 - 5/6)

   = 6 / (1/6)

   = 36

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Answer: 78 pounds

Step-by-step explanation:

10.4/4 = 2.6

2.6 * 30 = 78

10in × 20in  is size paper should she use. That is, option J . 10in × 20in  is the correct answer.

What are examples of linear equations?

The given size of the painting is 3 feet wide and 6 feet long.

The value of 1 foot in inches,

1 foot  = 12inches.

The size of the painting is 36 inches wide and 72 inches long.

width is, ( 0.25 × 36 ) = 9 inches. So option F . 4in × 8 in is not the answer and

the length is, ( 0.25 × 72 ) = 18 inches. So option G 6in × 12in and  H. 8inch × 16 in are not the possible choices.

So, the reduced dimensions of the dilated painting are 9 inches wide and 18 inches long.

That is, option J . 10in × 20in is the correct answer.

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Answer: 49

Step-by-step explanation:

A=πr^2

A=π(7)^2

A=49π in^2

Answer: 49

Answer:

154 Inches square.

r=7

area= πr^2

= 22/7* 49

= 154

The perimeter of the triangle is 37.86

Given,

The ratio of the measure of the angles of triangle = 1:2:3

Let the angles be taken as x, 2x, 3x.

Total angle of a triangle is 180°.

We can now find x.

x + 2x + 3x = 180°

6x = 180°

x = 180°/6 = 30°

x = 30°

2x = 2 × 30° = 60°

3x = 3 × 30° = 90°

Let the sides of the triangle be a, b, c.

The length of the shortest side is given = 8

Lets take a as 8.

We can use Trignometric Formulas here:

Trignometric Formulas:

sin θ = [tex]\frac{opposite side}{hypotenuse}[/tex]

cos θ = [tex]\frac{adjacent side}{hypotenuse}[/tex]

tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]

By using sin rule we can find other sides.

That is,

sin 30° = opposite side / hypotenuse

sin 30° = a/b

sin 30° = 8/b

b = 8 × sin 30°

b = 16

Next,

sin 60° = opposite side / hypotenuse

sin 60° = c/16

c = sin 60° × 16

c = 13.86

Now we can find the perimeter of the triangle = a + b + c

= 8 + 16 + 13.86

= 37.86

The perimeter of the triangle is 37.86

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Using the concept of the or operation, the solution of the given inequality in the number line is given at the graph in the end of the answer.

The or operation between sets has as a result all the elements that belong to at least one of the sets.

For this problem, we have two inequalities:

Then we solve the inequality then apply the or operation between them.

The solutions to the inequalities are given as follows:

The or operation will involve both the numbers to the left of k = -7 and the numbers to the right of k = 3 being plotted on the number line, as shown in the graph at the end of the answer.

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Answer: 25/2

Step-by-step explanation:

coverting the mixed numbers into improper fractions we get

17/5+91/10

getting a common denominator and adding the numerators we get 125/10

then we can simplify, which gets 25/2

  The algebraic expression or sigma (summation) notation is given by:

∑ = 10(100 + 10)/2

And its value is ∑ = 550

 The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

  The equation for this type of problem is:

∑ = n(a1 + an)/2

  Our values are:

100+90+80+ . . . . . . +10

∑ = 10(100 + 10)/2

∑ = 10(110)/2 = 5(110)

∑ = 550

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Simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.

As given in the question,

Given equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex]

Simplify the given equation,

x/ 3(x+3) - 8/x(x+3)

= (x² - 24) / 3x(x+3)

Restriction on the variables for the above equation is,

x≠ 0 , x≠ -3

Therefore, simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.

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Answer:

43.57

Step-by-step explanation:

subtract 6.43 from 50

Answer: 43.57

Step-by-step explanation:  50 dollars minus 6 dollars and 43 cents and it gives you 43.57

If there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.

Given that the element X decays radioactively with a half life of 15 minutes.

We are required to find the time that would take the 420 grams of element X would take the element to decay to 4 grams.

Radioactive decay is basically the emission of energy in the form of ionizing radiation.

4=420*[tex](1/2)^{x/15}[/tex]

x=15* [tex]log_{2}[/tex] (105)

x=15*log (105)/log (2)

x=15*2.0212/0.3010

x=30.318/0.3010

x=100.72

After rounding it will be 100.7 of a minute.

Hence if there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.

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Answer:

(5+10)u

= 15u

is the solution

Limit the domain to x > 0 for it to be one to one

The function is given as:

f(x)= x^4

The above function is an even function

This means that

f(x) = f(-x)

So, for the function to be one to one, we have to limit the function to only the positive x values

Hence, limit the domain to x > 0 for it to be one to one

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