A bowling alley and a skating rink both offer birthday party rentals. The bowling alley costs $5 per person plus a $15 room rental fee. The skating rink costs $3 per person plus a $20 room rental fee. You have $50. If you want to invite as many people as possible, which location should you choose?

Follow the steps to decide on the party location.

1. Write an expression for the amount you would spend on a birthday party at the bowling alley. Let x represent the number of people you invite. (2 points)















2. Write an expression for the amount you would spend on a birthday party at the skating rink. (2 points)















3. How many people could you invite to the bowling alley? Show how you found your answer. (2 points)















4. How many people could you invite to the skating rink? Show your work. (2 points)















5. To which location could you afford to invite more people? (2 points)

Drake needs 144 ft² (squared feet) of fabric to make the 8 ft long and 18 ft tall sail.

The area (square units) of two lengths is the product of the multiplication of the two lengths.

The area refers to the space occupied by a two-dimensional object or structure.

Areas are stated in square feet to show the squared units occupied by such objects.

The length of a sail = 8 feet

The height of the sail = 18 feet

The square area = 144 ft² (8 x 18)

Thus, Drakes requires a fabric measuring 144 ft² (squared feet) to make the sail.

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Step-by-step explanation:

10 + x = 30

or, x = 30 - 10

x = 20

The Fourier series representation of the output y(t) is;

(a) y(t) = 0.097 cos(3πt - 67)

(b) y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

Given;

A causal continuous-time LTI system whose input x(t) and output y(t) are related by the following differential equation;

[tex]\frac{d}{dt}y(t) + 4y(t) = x(t)[/tex]

By taking Laplace's Transform;

sY(s) + 4Y(s) = X(s)

Y(s)/X(s) = H(s) = 1/(s + 4)

(a) When input x(t) = cos3πt

∵ ω = 3π

H(jω) = 1/(jω + 4)

H(jω₁) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.097

∠H(jω) = -tan⁻¹(ω/4) = -67° = Ф₁

y(t) = H(jω₁)*cos(3πt + Ф₁)

→ y(t) = 0.097 cos(3πt - 67)

(b) When input x(t) = sin3πt + cos(6πt + π/4)

∵ ω = 6π

H(jω) = 1/(jω + 4)

H(jω₂) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.051

∠H(jω) = -tan⁻¹(ω/4) = -78° = Ф₂

y(t) = H(jω₁) * sin(3πt + Ф₁) +  H(jω₂) * cos(6πt + π/4 + Ф₂)

→  y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

The Fourier series representation of the output y(t) is;

y(t) = 0.097 cos(3πt - 67)

y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

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Answer:

Slope = - 2

Explanation step by step:

Answer: [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

The two points found on the graph are:

The slope can be calculated as:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-3-4}{-1-2} =\frac{-7}{-3} =\frac{7}{3}[/tex]

As per given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

As given in the  question,

Number of copies of 26 pages article print by printing center is equal to 1,233 copies

Number of copies of 12 page article print by printing center is equal to 658 copies

Total number of pages print by printing center during this one week is equal to

= ( 1233 × 26 ) + ( 658 × 12 )

= 32,058 + 7896

=39,954 pages

Therefore, for the given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

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Answer:

1/2

Step-by-step explanation:

Because the y is going up by 0.5 which in a fraction form is 1/2 and it isn't negative 1/2 because the number is growing and is not decreasing.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

1) Find the difference between  and y

2) Find the pattern between the numbers

As we can see there is a pattern of subtract [tex]\frac{1}{2}[/tex] between every number

To find this just subtract each number by the other

As 0.5 is equal to [tex]\frac{1}{2}[/tex] the answer to the solution would be [tex]\frac{1}{2}[/tex]

Hope this helps, have a great day!!

Answer:

$47.76

Step-by-step explanation:

77 : 100 = x : 207.65

x = (207.65 * 77)/100

x = 159.8905

final price = 207.65 - 159.8905 = 47.7595= $47.76

1. The number of sides of the polygon is of: 12 sides.

2. The missing exterior angles are of: α = 48.5º.

3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.

A regular polygon is a polygon in which all the sides have the same length.

The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:

Measure of each angle = 360º/number of sides.

For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:

24º = 360º/number of sides.

24n = 360

n = 360/24

n = 12 sides.

The sum of the measures of the external angles of a polygon is always of 360º.

Hence, for item 2, the missing angles are obtained as follows:

2α + 90 + 55 + 40 + 78 = 360

2α + 263 = 360

2α = 97

α = 97/2

α = 48.5º.

An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:

Exterior angle = 180º - 160º = 20º.

Then the number of sides of  the polygon is obtained as follows:

20n = 360

n = 360/20

n = 18 sides.

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Answer:

slope = 10

Step-by-step explanation:

Solve the equation for "y". In other words, isolate "y":

y + 7 = 10(x - 4)

y = 10(x - 4) - 7

y = 10x - 40 - 7

y = 10x - 47

Above is a linear expression in slope-intercept form "y = mx + b", where "m=slope" and "b=y-intercept". "m=10", so 10 is the slope

The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

Given that,

p = $2,000, r = 3%, and t = 2 yr.

We have to find the i when i=prt.

Here,

i is interest amount.

p is principal amount.

r is rate of interest per year.

t is time period.

So,

Formula for finding interest amount is

i=prt

So,

i=2000(3/100)(2)

i=20×3×2

i=120

Therefore, The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

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Answer:

3 feet

Step-by-step explanation:

All 4 sides are equal so 12/4=3

Answer:

Step-by-step explanation:

define function fg(x) :

Fg(x)  = f(g(x))

         = [tex]\frac{5}{x}[/tex] (4-2x)-1

         = [tex]\frac{20}{x}[/tex] - [tex]\frac{10x}{x}[/tex] - 1

         = 20 - 10x -1

         = 20 - 1 - 10x

         = 19 - 10x

The original price of the guitar is $120

From the question, we have

guitar is on sale for 3/4 of the original price (p).

3/4*p = $90

p = (90*4)/3

p= $120

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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No, because it is plausible that she would make 3 or fewer shots by chance alone.

What is convincing evidence?

The proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent.

if our test statistic is: positive and greater than the critical value, then we have sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. positive and lower than or equal to the critical value, we must accept the null hypothesis.

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Answer:

$5

Step-by-step explanation:

Since $10 for 6 avocados and 3 = half of 6,

You would half $10 too = $5

Answer:

$5

Step-by-step explanation:

divide both numbers by 2 and there is your answer

The amount after four years is £2649.79 .

Now we know that we need to obtain the rate for the compounding of the money and we need to recall that for the amount, we have;

A = P(1 +r/n)^nt

A = amount

P = principal

r = rate

n = number of times compounded

t = time

For one year in which the interest is compounded annually;

2496.96 = 2448(1 + r)^1

2496.96/ 2448 = (1 + r)

1.02 = 1 + r

r = 1.02 - 1

r = 0.02 or 2%

Now after four years;

A = 2448(1 +  0.02)^4

A = £2649.79

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Standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.

As given in the question,

Given set of data is equal to :

{ 6,7,8,9,10}

[tex]x_{i}[/tex] = { 6,7,8,9,10}

Here total number of observation 'N' is equal to 5.

Mean [tex]\bar{x}[/tex] = ∑x / n

            = ( 6+ 7+ 8 + 9 + 10 ) / 5

            = 40 /5

            = 8

[tex]\sum (x_{i} -\bar{x})^{2}[/tex] = ( 6- 8)² + (7-8)² + (8 - 8)²+ ( 9 -8)² + (10 - 8)²

                 = 4 + 1+ 0 + 1+ 4

                 = 10

Standard deviation = [tex]\sqrt{ \frac{\sum (x_{i} -\bar{x})^{2}}{N}[/tex]

                                = √10/5

                                = √2

Therefore, standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.

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Answer:

x= 2.7,-11.7 (sorry if im wrong) :'C

The ratio of green apples to all apples in the basket is 5:14 and the ratio of red apples to all apples in the basket is 9:14.

According to the question,

We have the following information:

There are five green apples and nine red apples in a basket.

Now, total apples in the basket are (5+9) which is 14.

Now, the ratio of green apples to all apples in the basket:

Number of green apples : total apples in the basket

5:14

Now, the ratio of red apples to all apples in the basket:

Number of red apples : total apples in the basket

9:14

Hence, the ratio of green apples to all apples in the basket is 5:14 and the ratio of red apples to all apples in the basket is 9:14.

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Answer:

x= -3/5

Step-by-step explanation:

2x+21/5=3

2x+21/5-21/5=3-21/5           (subtract 21/5 from both sides)

2x=3-21/5                            (L.C.M=5)

2x= 15-21/5

2x= -6/5

2x/2=-6/5/2                        (divide both sides by 2)

x= -6/5x1/2                          (reciprocal)

x= -6/10

simplify:

x= -3/5

Answer:

B

Step-by-step explanation:

1.20x + 3.60 < 9.60

1.20x < 9.60 - 3.60

1.20x < 6

x < 6 ÷ 1.20

x < 5

Answer:

5 whole laps + 1/4 of a lap. Or, 5.25 laps

Step-by-step explanation:

We can solve this 2 ways.
First, we can continuous add 4/3rds to itself until we reach 7 miles.

4/3 + 4/3 = 2 2/3
+ 4/3 = 4
+ 4/3 = 5 1/3
+ 4/3 = 6 2/3
Then you see that we are almost at 7. We have 1/3 left until we reach 7. 1/3 is 0.25% of 4/3, so its only 25% of a lap. That plsu the 5 other laps we did would equal 5.25 laps.

An easier way is 7 divided by (4/3), which is 5.25.

Good Luck! Hope this helps.

Answer:

B. -x^2-2

Step-by-step explanation:

-x^2 would max out at 0, so you need to shift it down by 2 (hence the -2) to have the correct function.

Hope this helped!

Answer:

Subtract 3 3/4 from 10 1/2.  Note that the LCD is 4, so 10 1/2 = 10 2/4.

What is    10 2/4

              -  3 3/4

-------------------------

                    ?

Since 2/4 is smaller than 3/4, you must borrow 1 from that 10.

Now your problem looks like   9 6/4

                                              -3 3/4

                                            ----------

                                                6 3/4   (answer)

The remnant of the board is 6 3/4 feet long.

Step-by-step explanation:

The total bill that will be paid by the friends is $88.27.

Cost of meal = $72.50

Sales tax = 6.75%

The amount on tax will be:

= 6.75% × $72.50

= $4.89

Tip = 15% × $72.50

Tip = $10.88

The total bill will be:

= Cost of bill + Tax + Tip

= $72.50 + $4.89 + $10.88

= $88.27

The cost is $88.27.

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-691 is the value of the expression −||6c−16b||+1 when a=−12, b=34, and c=−23.

An expression is combination of variables, numbers and operators.

The given expression is −||6c−16b||+1

The values of c is minus twenty three, the value a is minus twelve and the value of b is thirty four.

−||6c−16b||+1

-||6(-23)-16(34)||+1

-||-138--55||+1

-||-692||+1

-692+1

=-691

Hence -691 is the value of the expression −||6c−16b||+1 when a=−12, b=34, and c=−23.

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