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4 years ago

7.5% of the box office reciepts on a friday night are $270. What are the total box office reciepts

1 answer:

6 0

Hello there! To solve for the total box office receipts, we can write and solve a proportion. Set it up like this:

270/x = 7.5/100

We do that, because we are looking for the total and 270 is the part of the whole. 270 makes up 7.5% of the box office receipts.
Now, we cross multiply. 270 * 100 is 27,000. 7.5 * x is 7.5x. Divideeach side by 7.5 to isolate the "x". 7.5x/7.5 cancels out the "x". 27,000/7.5 is 3,600. There. x = 3,600. The total box office receipts are $3,600.

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A baker can make 120 cupcakes in 2 hours. At that rate, how many cupcakes can he make in 3.5 hours? *

Valentin [98]

Answer:

210

Step-by-step explanation:

first I took 120 and divided by four to show how many cupcakes he can make in thirty minutes (.5 of an hour). this was 30. the reason we divided by four is because in two hours theres four halves.

120÷4=30 for half an hour

30x2=60 this is how many cupcakes he can make in one hour

since we already know how many he makes in two hours we're going to use that

120+60=180 (three hours)

120+60=180 (three hours)180+30 (half an hour) =210

4 0

3 years ago

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GarryVolchara [31]

Answer:

PQ = 1/2BC

Step-by-step explanation:

6 0

3 years ago

According to a 2013 study by the Pew Research Center, 15% of adults in the United States do not use the Internet (Pew Research C

Pavel [41]

Answer:

a) For this case we can use the binomial model since we assume independent events and the same probability for each trial is the same p =0.15

b) $P(X=0)=(10C0)(0.15)^0 (1-0.15)^{10-0}=0.1969$

c) $P(X=3)=(10C3)(0.15)^3 (1-0.15)^{10-3}=0.1298$

d) $P(X \geq 1)= 1-P(X$

And using the result from part a we got:

$P(X \geq 1)= 1-P(X$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n p)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

Part a

For this case we can use the binomial model since we assume independent events and the same probability for each trial is the same p =0.15

Part b

For this case we want this probability:

$P(X=0)$

And replacing we got:

$P(X=0)=(10C0)(0.15)^0 (1-0.15)^{10-0}=0.1969$

Part c

For this case we want this probability:

$P(X=3)$

And replacing we got:

$P(X=3)=(10C3)(0.15)^3 (1-0.15)^{10-3}=0.1298$

Part d

For this cae we want thi probability:

$P(X \geq 1)$

And we can use the complment rule and we got:

$P(X \geq 1)= 1-P(X$

And using the result from part a we got:

$P(X \geq 1)= 1-P(X$

4 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

miss Akunina [59]

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid. When we rotate it about x = 1, we get a hollow cylinder shape. We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part. If we use shell method, we only need one integral. So let's use shell method.

Cut a thin, vertical slice of the region. The width of this slice is dx. The height of the slice is y₂ − y₁ = x − 0 = x. The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]

V = 2π (72⅔ − 12)

V = 121⅓ π

V ≈ 381.18

The volume is approximately 381.18 cubic units.

6 0

3 years ago

The Carr School Band purchases pizza and drinks for their end-of-year celebration. Each pizza costs $10 and each drink costs $2.

Advocard [28]

Answer:

4n + 100 = C

7n = C

by elimination 7n - 4n - 100 = 0

3n = 100

n = 100/3 (33.33)

*need to sell 34 pizzas

n= number of pizzas

c= cost

Step-by-step explanation:

6 0

3 years ago

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