Tickets for a basketball game cost $20 for upper-level seats and $30 for lower-level seats. Tickets at the same venue for an ice hockey game cost $15 for upper-level seats and $35 for lower-level seats. If tickets for all seats are sold, the venue generates $7000 in revenue for a basketball game and $6500 for a hockey game. How many upper and lower-level seats does the venue have?

Let x represent the number of upper-level seats.

Let y represent the number of lower-level seats.

20x + 30y = 7000
15x + 35y = 6500

The venue has
upper-level seats and lower-level seats.

Answer:

The dimensions of the dilated image are 60 cm by 32 cm

Step-by-step explanation:

we know that

The scale factor is equal to 4

The scale factor is > 1 -----> therefore the dilation is an enlargement

To find the dimensions of the dilated image, multiply the original dimensions by the scale factor

New Length=(15)(4)=60 cm

New Width=(8)(4)=32 cm

The dimensions of the dilated image are 60 cm by 32 cm

Answer:

70

Step-by-step explanation:

14*100/20

14* 100= 1400

1400/20= 70

The percentage is a certain proportion of a number. 14 is 20[tex]\%[/tex] of 70.

Percentage is a way of expressing a fraction or proportion out of 100. It is represented by the symbol "%". The word "percent" comes from the Latin phrase "per centum," which means "per hundred."

Percentages are commonly used to describe ratios, rates, or proportions in various fields such as mathematics, finance, statistics, and everyday life. They allow us to compare quantities or express relative changes easily.

Let x be the number whose 20[tex]\%[/tex] is 14.

Then,

20[tex]\%[/tex] of x = x [tex]\times \ \frac{20}{100}[/tex] = 14,

x [tex]\times \ \frac{1}{5}[/tex] = 14,

x = 14 [tex]\times\ 5[/tex],

x = 70.

So, 20[tex]\%[/tex] of 70 is 14.

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Answer:

Answer C. 4 to 7

Step-by-step explanation:

32 muffins to 56 donuts.

32/8=4 and 56/8=7

So it reduces to 4 to 7

4 to 7

i just divided each number by the smallest common factor which was 8

Answer:

The rate 37.5 miles per hour

The distance 150 miles

Step-by-step explanation:

∵ 1 mile = 1.6 kilometer

∵ The rate is 60 km/h

∴ The rate = (60 × 1) ÷ 1.6 = 37.5 miles per hour

∵ The car will travel for 4 hours

∴ The distance = 37.5 × 4 = 150 miles

Answer:

Step-by-step explanation:

the rectangle side is 9.3 yd.

the front side is 27.9

the back is 26.35

the top is 12.75 and so is the bottom. then add them

9.3 + 27.9 + 26.35 + 12.75 + 12.75

= 89.5 Yards of area space

Answer:

h - 145 = 457

602 meters

Step-by-step explanation:

The original height of the helicopter is unknown.

Let h = original height of the helicopter.

The helicopter was originally at height h.

The helicopter descended 145 m.

Descending means going down, so it lost height, so we subtract 145 from the original height.

The helicopter is now at a height of h - 145.

The new height is 457 meters.

That means that h - 145 must equal 457.

The equation is

h - 145 = 457

This is a subtraction equation since the only operation is the subtraction on the left side.

To solve the equation, we want h alone on the left side. 145 is being subtracted from h. The opposite operation to subtraction is addition. If we add 145 to the left side, we get h - 145 + 145 which is just h. That's what we want. We must do the same operation to both sides of an equation, so we add 145 to both sides.

h - 145 + 145 = 457 + 145

h = 602

Since h stands for the original height, now we answer that the original height was 602 meters.

Answer:

50(0.6)

Step-by-step explanation:

There are 5 coolers at the event - 3 popsicles, and 2 ice cream. If randomly selecting a cooler, that means there's a 3 in 5 chance you will get a popsicle, which simplifies to 0.6. So simply multiply the probability (0.6) by the amount of football players (50) to get the answer, which is that 30 football players will get a popsicle.

Answer: Close to 30 but not 30 will get a popsicle.

Step-by-step explanation:

Here 3 coolers so if it pick the 3 out of 5 so 3/5= 0.6

and 50 players so 50*0.6= 30 but its probability will be 30 but not exactly 30.

Answer:

1363.2 / 16

=85.2  

Answer:

85.2

Step-by-step explanation:

first, you need to bring up the decimal. then go through the numbers and see how many times 16 can go into 1 or 13 or 136, so on and so forth. after u do the continue to figure out what 16 goes into with the answers that you get from subtracting until you get your answer of 85.2

Answer:

The value of a is 1

Step-by-step explanation:

* Lets talk about some facts in the circle

- If two chords equal in length, then they are equal in measure

 or if they are equal in measure, then they are equal in length

- All the radii of the circle are equal

* Lets look to the figure

∵ The measure of arc WV = 86°

∵ The measure of arc XY = 86°

∴ The two arcs equal in measure, then they are equal in length

∴ WV = XY

∵ WV = 28

∵ XY = 4a + 24

∴ 4a + 24 = 28 ⇒ subtract 24 from the both sides

∴ 4a = 4 ⇒ divide two sides by 4

∴ a = 1

* The value of a is 1

Answer:

B

Step-by-step explanation:

There is one input for every output, so it is a function.

And since a relation = function, it is also a relation.

Answer:

The correct answer option is B. both a function and a relation.

Step-by-step explanation:

From the given graph, we can see that for each input we have an output.

It means that we have a function because each element in the domain is matched with exactly one element in the range.

And it is also a relation since each input related to the out put in some way.

Therefore, the correct answer option is B. both a function and a relation,

The supplement of a 9 degree angle is 171 degrees.

Final answer:

The measure of the supplement of a 9 degree angle is 171 degrees, which is found by subtracting 9 degrees from 180 degrees.

Explanation:

The measure of the supplement of a 9 degree angle is the amount you would need to add to 9 degrees to reach a straight line, which is 180 degrees. This is calculated by subtracting the given angle from 180 degrees.

To find the measure of the supplement of a 9 degree angle:

Start with a straight line, which measures 180 degrees.

Subtract the given angle from 180 degrees: 180 degrees - 9 degrees.

This results in a supplement of 171 degrees.

Therefore, the supplement of a 9 degree angle is 171 degrees.

I think the answer is 27 square feet.

18 square feet, I believe.

slope =6, y-intercept =10

Answer:

The rate of change is 6

Step-by-step explanation:

The rate of change (which is also known as slope), is always the coefficient of x, when written in slope-intercept form. Therefore, in this case, it is 6.

least 3/3 3/6 3/7 greatest3/9

Answer:

Step-by-step explanation:

The order will be:

3/3, 3/6, 3/7, 3/9

When the fractions have the same numerator, the minor will be the greatest denominator.

Best regards

Answer:

I think the answer is -25

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

This notation basically means "putting the function f into g and then evaluating that at 3".

Let's do this.

[tex](gof)(x)=-(|x+2|})^2\\(gof)(3)=-(|(3)+2|})^2\\(gof)(3)=-(|5|})^2\\(gof)(3)=-(5})^2\\(gof)(3)=-25[/tex]

Thus, A is the correct answer.

You can describe them by Charts and lines or if it has a single peak

The shape of graphs can vary and be influenced by the number of bars. Understanding general graph shapes is key to interpreting data.

The shape of a graph can vary depending on the data being represented. It could have a V shape, a hump in the middle or at either end, or go straight across.

Increasing the number of bars in a graph could affect the shape by making it appear smoother and more continuous or by providing more detailed information.

General shapes of graphs for different types of motion can help in understanding and explaining the data being presented.

I think the answer is 0.62

Answer:

D. 0.53

Step-by-step explanation:

From the given picture, the number of persons from California and prefers brand A = 90

The total numbers of persons prefer brand A = 170

The probability that the person is from California, given that the person prefers brand A will be :-

Hence, The probability that the person is from California, given that the person prefers brand A = 0.53

Answer:

Step-by-step explanation:

Three

Sum of all numbers beginning at 0 up to 2200 that are divisible by 3

a = 3

d = 3

L = 2199

Now we need to find out how many there are.

L = a1 + (n - 1)*d

2199 = 3 + (n-1)*3             Subtract 3

2199 - 3 = (n - 1)*3            Divide by 3          

2196/3 = n - 1

732 = n - 1                        Add 1 to both sides

733 = n                    

Sum = (a + L)*n /2            Substitute the values

Sum = (3 + 2199)*733/2   Combine and Divide by 2

sum = (1101)*733               Multiply

Sum = 807033

Five

Go through exactly the same steps.

a = 5

L = 2195  ( below 2200. You can't include 2200)

d = 5

L = a + (n-1)*d

2195 = 5 + (n-1)*5

2190 = (n - 1)*5

438 = n - 1

439 = n

Sum = (a + L ) * n

Sum = (5 + 2195)*439/2

Sum = 1100 * 439

Sum = 482900

===============

The problem is ambiguous, so I'm going to leave the two answers that are there.

Here's the problem.

What do you do with the numbers that are divisible by both? I counted them in both sums, but that may not be correct.

As it stands your answer should 965800 + 482900

Nor does it seem right to count them only in 1 sum. So the answer is given by adding the two numbers above.

Answer:

See attachment.

Step-by-step explanation:

The given equation is

[tex] {y}^{2} = - 4x[/tex]

We solve for x to obtain:

[tex]x = - \frac{1}{4} {y}^{2} [/tex]

This is a horizontal parabola that has its vertex at the origin.

The graph of this parabola opens in the direction of the negative x-axis because of the negative coefficient.

The focus is (-1,0) and the directrix is x=1

See diagram in the attachment.

Answer:

The answer is A

Step-by-step explanation:

Its just the other persons longer answer but simplified I guess..

Answer:

Part a) The equation that represent the depreciation is [tex]y=18,000(0.88)^{x}[/tex]  

Part b) The value of the car in 8 years is [tex]\$6,473.42[/tex]  

Step-by-step explanation:

Part a)

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]y=P(1-r)^{x}[/tex]  

where  

y is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$18,000\\r=12\%=0.12[/tex]

substitute in the formula

[tex]y=18,000(1-0.12)^{x}[/tex]  

[tex]y=18,000(0.88)^{x}[/tex]  ------> equation that represent the depreciation

Part b) Find the value of the car in 8 years

Substitute the value of [tex]x=8\ years[/tex] in the equation and solve for y

[tex]y=18,000(0.88)^{8}=\$6,473.42[/tex]  

Each drill takes $44 in materials and $36 in labor.  So it costs the company ($44+$36)= $80 to MAKE one drill.  THEN they're ready to sell it.  

At the same time, the company has to pay $4,000 just to use the building to make the drills.

I can see at least two different questions here:

Question #1). How much does it cost the company if they MAKE 330 drills in one month ?

Materials and labor:  330 x ($80)  =  $26,400

Rent the building space:  $4,000

Total for the month:  $30,400

Question #2).  How many drills do they have to SELL just to pay back the amount they already spent to manufacture those drills ?

We can't answer that right now, because we don't know the PRICE they charge for each drill when somebody buys it.

The polynomial that correctly combines the like terms and to express in standard form is Option (D) [tex]3x^{4} + x^{3}y - 8x^{2}y^{2} + 9xy^{3} - 13y^{4}[/tex] .

Given polynomial is -

=  [tex]9xy^{3} - 4y^{4} -10x^{2}y^{2} + x^{3}y + 3x^{4} + 2x^{2}y^{2} - 9y^{4}[/tex]

Separating the like terms from the above polynomial -

=  [tex]9xy^{3} + (-10x^{2}y^{2} + 2x^{2}y^{2})+ x^{3}y + 3x^{4}+( - 9y^{4} - 4y^{4})[/tex]

Expressing the polynomial in standard form -

=  [tex]3x^{4} + x^{3}y - 8x^{2}y^{2} + 9xy^{3} - 13y^{4}[/tex]

Therefore the polynomial that correctly combines the like terms and to express in standard form is Option (D) [tex]3x^{4} + x^{3}y - 8x^{2}y^{2} + 9xy^{3} - 13y^{4}[/tex] .

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Answer: There are 21 slices of  [tex]\dfrac{3}{8}[/tex]  inch.

Step-by-step explanation:

Since we have given that

Length of one cucumber = 3 inches

Length of another cucumber = 5 inches

Total length would be

3 + 5 = 8 inches

According to question,  She cuts the cucumbers into [tex]\dfrac{3}{8}[/tex] inch slices and adds them to a salad.

so, Number of [tex]\dfrac{3}{8}[/tex]  inch thick slices would be

[tex]\dfrac{8}{\dfrac{3}{8}}\\\\=\dfrac{8\times 8}{3}\\\\=\dfrac{64}{3}\\\\=21.33\\\\\approx 21[/tex]

Hence, there are 21 slices of  [tex]\dfrac{3}{8}[/tex]  inch.

Answer:

4 hours

Step-by-step explanation:

30(4)+65= 185

Answer: 4.5 hours.

Step-by-step explanation:

Hi, to answer this question we have to write an inequality with the information given;

Cost: 30h+65 (h= hours)

So, the cost must be less or equal to the money that Brianna can spend.(200)

Mathematically speaking:

30h+65 ≤ 200

Solving for h

30h≤ 200 -65

30h ≤ 135

h ≤ 135/30

h≤ 4.5

She can rent the boat for 4.5 hours.

Answer:  1.58 hours

Step-by-step explanation:

[tex]5400=1800(2)^t\\\\3=2^t\\\\ln\ 3=ln\ 2^t\\\\ln\ 3=t\cdot ln\ 2\\\\\dfrac{ln\ 3}{ln\ 2}=t\\\\1.58=t[/tex]

Answer:

Let

x = number 8043

y = number  9

z = the product of 8043 and 9

z = x*y

We substitute

z = (8043)*(9)

z = 72387

Answer:

50 yards

Step-by-step explanation:

Yards are 3 feet. This is a simple question, all you have to do is 150 divided by 3 and you shall receive 50 yards. Hope this helps!

50 individuals bought single tickets and 65 couples bought couple tickets.

Let's define our variables first:

Let [tex]x[/tex] be the number of individuals who bought single tickets.
Let [tex]y[/tex] be the number of couples who bought couple tickets.

From the problem, we have two pieces of information:

We can use these pieces of information to create the following system of equations:

[tex]x + 2y = 180[/tex]

[tex]3x + 5y = 475[/tex]

First, solve equation 1 for [tex]x[/tex]:

[tex]x = 180 - 2y[/tex]

Now, substitute this expression for [tex]x[/tex] in equation 2:

[tex]3(180 - 2y) + 5y = 475[/tex]

Simplify and solve for [tex]y[/tex]:

[tex]540 - 6y + 5y = 475[/tex]

[tex]540 - y = 475[/tex]

[tex]-y = 475 - 540[/tex]

[tex]-y = -65[/tex]

[tex]y = 65[/tex]

So there were 65 couples at the dance.

To find the number of individuals who bought single tickets, substitute [tex]y[/tex] back into the expression for [tex]x[/tex]:

[tex]x = 180 - 2(65)[/tex]

[tex]x = 180 - 130[/tex]

[tex]x = 50[/tex]