A play is performed for a crowd of 400 people. Adult tickets cost $22 each, student tickets cost $15 each, and tickets for children cost $13.50 each. The revenue for the concert is $7840. There are 40 more children at the concert than students. How many of each type of ticket are sold?

To solve this problem, one would need to use the binomial probability formula, substituting different values of 'x' into the formula depending on the requirement of the question. To calculate probabilities for specific numbers of people saying cashews are their favorite, substitute those numbers into the formula and solve, adding appropriate probabilities together for situations with ranges of people.

The subject of this question is probability. We can use the binomial probability formula, which is P(X=x) = C(n, x) * (p^x) * ((1-p)^(n-x)), where 'p' is the probability of success, 'n' is the number of trials, and 'x' is the number of successful outcomes.

(a) For exactly 3 people loving cashews, substitute x=3, p=0.32 (32%), and n=12 into the formula to calculate the probability.
(b) For at least 4 people loving cashews, calculate the probability for x=4, x=5,....x=12 and add these probabilities together as this is an 'or' condition.
(c) For 2 or fewer people loving cashews, calculate the probability for x=0, x=1, x=2 and add them, because it says 'at most two' which includes 0 to 2 people.

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Hi the answer is:

y = IxI + 6

The probability of drawing a red gumdrop is [tex]\( \frac{2}{5} \)[/tex] and butterscotch candy is [tex]\( \frac{3}{5} \)[/tex]. Combined, it's [tex]\( \frac{6}{25} \)[/tex]. Answer: A.

To find the probability that Craig will draw a red gumdrop and a piece of butterscotch candy, we need to find the probability of each event separately and then multiply them together because the events are independent.

1. Probability of drawing a red gumdrop:

[tex]\[ P(\text{red gumdrop}) = \frac{\text{number of red gumdrops}}{\text{total number of gumdrops}} \][/tex]

[tex]\[ P(\text{red gumdrop}) = \frac{2}{2 + 3} = \frac{2}{5} \][/tex]

2. Probability of drawing a piece of butterscotch candy:

[tex]\[ P(\text{butterscotch candy}) = \frac{\text{number of butterscotch candies}}{\text{total number of candies}} \][/tex]

[tex]\[ P(\text{butterscotch candy}) = \frac{3}{3 + 2} = \frac{3}{5} \][/tex]

Now, multiply the probabilities together:

[tex]\[ P(\text{red gumdrop and butterscotch candy}) = P(\text{red gumdrop}) \times P(\text{butterscotch candy}) \][/tex]

[tex]\[ P(\text{red gumdrop and butterscotch candy}) = \frac{2}{5} \times \frac{3}{5} \][/tex]

[tex]\[ P(\text{red gumdrop and butterscotch candy}) = \frac{6}{25} \][/tex]

So, the probability that Craig will get a red gumdrop and a piece of butterscotch candy is [tex]\(\frac{6}{25}\)[/tex], which corresponds to option A.

The correct question is:

Here are 2 red gumdrops and 3 green gumdrops in a small jar. Also, 3 pieces of butterscotch candy and 2 pieces of cinnamon candy are in another jar. If Craig draws one piece of candy from each jar without looking, what's the probability that he will get a red gumdrop and a piece of butterscotch candy? The Answer choices are

A. 6/25

B. 1/2

C. 4/25

D. 1/5

It's 21. You just divide one by the other.

The quotient is 2.

A quotient is the result of division. In division, the dividend Divided by the Divisor = the Quotient, in your question 14 is the Dividend and 7 is the Divisor,

Hope this Helps :D

Jenny's total earnings:

total earnings = (hours worked on design)*40 + (hours worked on maintenance)*35

average earnings = total earnings / hours worked

So far she has

total earnings = 18*40 + 20*35 = $1420

which is an average per hour = $1420/38hr = $37.37

How many more hours on webdesign: x

so that

($1420+x*$40)/(38+x)=38

Now solve for x - this I let you do. My results is x=12 (you can verify by plugging it iback into the equation).

The answer is Jenny needs to work 12 more hours to claim an average earnings of $38/hr. Lmk if you have questions.

g = 152.98 - 114.78 = 38.2

Final answer:

Explanation of how the orbital period increases when a planet's distance from the sun is increased using Kepler's third law.

Explanation:

The factor by which the orbital period is increased when planet Y is k times the mean distance from the sun as planet X can be calculated using Kepler's third law:

Given the equation 72 = a3, the relationship between a planet's orbital period T and mean distance from the sun A in AU is established.

If planet Y is k times the mean distance from the sun as planet X, the orbital period is increased by k1.5 times due to Kepler's third law.

10:00 will show trhe corect tiem

To factorize the expression completely, we use the difference of squares formula and simplify the expression to get 6x.

The given expression is (2x+1)^2 -(x-1)^2. To factorize it completely, we can use the difference of squares formula, which states that (a^2 - b^2) = (a + b)(a - b). Applying this formula, we have:

(2x+1)^2 -(x-1)^2 = [(2x+1) + (x-1)][(2x+1) - (x-1)]

Simplifying further, we get:

(2x+1+x-1)(2x+1-x+1) = (3x)(2) = 6x.

Answer:  C looks like the best fit.

Answer:

C

Step-by-step explanation:

A scatterplot best fit line looks as thought the distance of the points above the line are the same as the points below the line in this case. See the comment under d for more.

A

All the points are above the line

B

Only a very few points come close to the line. Left right is more at work here rather than up and down.

C Answer

D

The average of those above the line might be the same as below the line, but the symmetry is a left right symmetry; all the downs are on the left and all the ups are on the right.. They might average out to be 0 but it is not what is meant. The x and y values both have something to do with the answer. D is the second best answer.

Hello,

The speed was .67 mph

Hope this helps!

Answer:

6 1/4

Step-by-step explanation:

First

Multiply 20in. by 15in.

Second

Multiply 12 by 8

Third

Multiply the sum of 8 and 12 to 3

The answer would be yes because the sum of 12, 8, and 3 is 288 and 20 by 15 is 300 so you'd have some left over.

Yes, the rectangular piece of wrapping paper can cover the shirt gift box.

To determine if the rectangular piece of wrapping paper can cover the shirt gift box, we need to compare the dimensions of the paper to the dimensions of the box.

The dimensions of the paper are 20 in. by 15 in. The dimensions of the box are 12 in. long, 8 in. wide, and 3 in. deep.

To cover the box completely, the paper needs to have enough surface area to cover the top and all four sides of the box.

Since the dimensions of the paper are greater than or equal to the corresponding dimensions of the box, the rectangular piece of wrapping paper can cover the shirt gift box.

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Ok so if the agent spend 1,500$ on advertising then thats -1,500 for his wallet eg.

WALLET:

-1,500$

Now if the house sells in 3 months that's 9,000 in wallet but since there is only a 40% chance then we need to work out 40% of 9000 we can do that by doing 9000 x 0.40 which = 3,600 so 3,600 in wallet on average

-1,500

+3,600

now if we combine these we get 2,100 so the answer is on average 2,100

Answer:

B edge

Step-by-step explanation:

It would be a closed circle or "dot" since it is a less than or equal to sign.

Answer:

2e-7 or 2x10^-7

Step-by-step explanation: correct me if i'm wrong

[tex]4(px+1)=64\qquad|\text{divide both sides by 4}\\\\px+1=16\qquad|\text{subtract 1 from both sides}\\\\px=15\qquad|\text{divide both sides by}\ p\neq0\\\\\boxed{x=\dfrac{15}{p}}[/tex]

D. the final one, the one you currently have answered is the correct one, this is because a parallelogram, like this one, requires that the triangles on either side must be congruent in order for this to be true.

Triangles BPA and DPC are congruent, which implies that opposite sides AB and CD are parallel, thus making quadrilateral ABCD a parallelogram.

The statement Triangles BPA and DPC are congruent is used to prove that quadrilateral ABCD is a parallelogram.

Given that diagonals AC and BD bisect each other, we have:

[tex]$\angle BAP = \angle CDP$[/tex]  (vertically opposite angles)

[tex]$AP = CP$[/tex] and BP = DP  (given)

Therefore, triangles BPA and DPC are congruent by SAS (side-angle-side) congruence. This means that [tex]$\angle ABP = \angle CDP$[/tex] and [tex]\angle BPA = \angle DPC$.[/tex]

Since [tex]$\angle ABP$[/tex] and [tex]$\angle CDP$[/tex]  are alternate interior angles formed by transversal BD intersecting parallel lines AB and CD, we have:

AB \parallel CD

Similarly, since [tex]$\angle BPA$[/tex]  and [tex]$\angle DPC$[/tex] are alternate interior angles formed by transversal AC intersecting parallel lines AB and CD, we have:

AB \parallel CD

Therefore, quadrilateral ABCD is a parallelogram.

Proof:**

1. Given:[tex]$\angle BAP = \angle CDP$ and $AP = CP$ and $BP = DP$[/tex]

2. Prove:[tex]$AB \parallel CD$[/tex]

SAS Congruence**

1.[tex]$\triangle BAP \cong \triangle DPC$ (SAS)[/tex]

Alternate Interior Angles**

2. [tex]$\angle ABP = \angle CDP$[/tex](alternate interior angles)

3. [tex]$\angle BPA = \angle DPC$[/tex] (alternate interior angles)

Therefore, $AB \parallel CD.

For similar question on quadrilateral.

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Quick Answer: Yes

If you reduce both to their lowest terms each becomes 1/2

Divide the numerator and denominator by 7 for the first one

(7 ÷ 7)/(14 ÷ 7) = 1/2

And numerator and denominator by 3 for the second one

(3 ÷ 3)/ (6 ÷ 3) = 1/2

For this case we have:

Cost of manufactures of T-shirts [tex]C(x)=10.5x[/tex]

where x represents the number of T-shirts

Part A:

Substituting [tex]x = 8[/tex] in the total cost equation you have to:

[tex]C (8) = (10.5) (8)\\\\C (8) = 84\\[/tex]

Thus, the cost of 8 shirts will be [tex]C (8) = 84\\[/tex]

Part B:

If [tex]x = 12[/tex] then

[tex]C (12) = (10.5) (12)\\\\C (12) = 126\\[/tex]

Thus, the cost of 12 shirts will be [tex]C (12) = 126\\[/tex]

Answer:

[tex]C (8) = 84\\\\C (12) = 126\\\\[/tex]

The cost function c(x) = 10.5x, when applied for 8 and 12 t-shirts, indicates that 8 t-shirts will cost $84 and 12 t-shirts will cost $126.

The function c(x) = 10.5x represents the cost to manufacture t-shirts, where x is the number of t-shirts.

Part A: If a club needs 8 t-shirts, we substitute x=8 into the function. Therefore, c(8) = 10.5*8 = 84. Thus, it will cost $84 to manufacture 8 t-shirts.

Part B: If c(12), we substitute x=12 into the function. Therefore, c(12) = 10.5*12 = 126. This means that 12 t-shirts will cost $126.

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We know that [tex]\sqrt(4)[/tex] and [tex]\sqrt(9)[/tex] are 2 and 3 respectively. Therefore, [tex]/sqrt(5)[/tex] is between 2 and 3, approximately 2.2.

It would cost $37.50.

Answer:

Volume increasing rate = [tex]62831.85 mm^3/s[/tex]

Explanation:

We rate of change of radius of sphere, [tex]\frac{dr}{dt} =2mm/s[/tex]

Diameter of sphere = 100 mm

Radius of sphere = 50 mm

Volume of sphere, V = [tex]\frac{4}{3} \pi r^3[/tex]

Rate of change of volume = [tex]\frac{dV}{dt}[/tex]

[tex]\frac{dV}{dt}=\frac{d}{dt} (\frac{4}{3} \pi r^3)=\frac{4}{3} \pi\frac{d}{dt}(r^3)=\frac{4}{3} \pi*3r^2*\frac{dr}{dt}[/tex]

Substituting known values

     [tex]\frac{dV}{dt}= \frac{4}{3}* \pi*3*50^2*2=62831.85 mm^3/s[/tex]

Volume increasing rate = [tex]62831.85 mm^3/s[/tex]

the answer would be 374.00

the original value before any increase or decrease is 340.00

so...

340.00 X 1.10 = 374.00

Answer:

New Wage after 10% increase =£374

Step-by-step explanation:

Let us assume  Carol's initial weekly wage be £ x

Now there is 10% decrease in weekly wage

10 %  of weekly wage = 10 % of x

                                    =  [tex]\frac{10x}{100} = 0.1x[/tex]

New wage after 10% decrease =  initial weekly wage - 10% of x

                                                   =  [tex]x- 0.1x = 0.9x[/tex]

It is given that new weekly wage is £ 306

so we equate £306 and 0.9x , so we have

[tex]0.9x=306[/tex]

[tex]x=\frac{306}{0.9}[/tex] ( divide both sides by 0.9)

[tex]x= 340[/tex]

So we got

Initial weekly wages = £ 340

Now Let us find weekly wage when there is 10% increase,

10% of initial weekly wage = [tex]10% of 340[/tex]

                                            =[tex]\frac{10}{100}[/tex]×[tex]340[/tex]

                                            = [tex] 34[/tex]

New Wage after 10% increase = [tex]340+34[/tex]

                                                  =£ 374

1000 would be the answer

The rounding number to the nearest thousand will be 1,000.

What is Rounding number?

To making a number simpler but keeping its value close to what it was, is called Rounding.

Given that;

The number is;

1348

Now, To round a number to the nearest thousand, look at the hundreds digit. If the hundreds digit is 5 or more, then round up.

If the hundredth digit is 4 or less, then round down.

So, Here the hundreds digit is 3, which is less than 5.

Then, we round down.

Thus, The rounding number = 1,000

So, The rounding number to the nearest thousand will be 1,000.

Learn more about the rounding number visit:

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54 x .50 = $27

54 x .25 = 13.5

50% = $27.00

25% = $13.50

The correct evaluation for the expression 2⋅(36⋅3−5) under the order of operations is 206, which is not one of the provided options A: 2/3, B:3, C:6, D:18.

The subject is Mathematics and the question belongs to the Middle School grade. The problem given is to evaluate the expression: 2⋅(36⋅3−5). Here, we will use the order of operations, also known as BIDMAS or PEMDAS, which stands for Brackets, Indices (or exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

First, we evaluate the operation in the parentheses: 36 times 3 minus 5, which simplifies to 108-5 = 103. Next, this value is multiplied by 2 according to the expression, resulting in a final answer of 2*103= 206. Hence, the correct evaluation of the expression 2⋅(36⋅3−5) is 206. The options provided in the question A: 2/3, B:3, C:6, D:18 do not match the correct answer.

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zero days, 3 hours + 20 min + 1 hour + 48 min = 308 min which is about 5 hours.

3 hours 20 minutes + 1 hour 48 minutes = 0.2139 days

Let’s calculate the total time in hours and minutes:

Now, let’s convert the total time to days:

First, convert the minutes to hours:

[tex]68 \text{ minutes} = \frac{68}{60} \text{ hours} = 1.1333 \text{ hours}[/tex]

Next, add the converted hours to the original 4 hours:

[tex]4 \text{ hours} + 1.1333 \text{ hours} = 5.1333 \text{ hours}[/tex]

Now, divide the total hours by 24 to find the equivalent days:

[tex]5.1333 \text{ hours} \div 24 = 0.2139 \text{ days}[/tex]

Therefore, 3 hours 20 minutes + 1 hour 48 minutes equals approximately 0.2139 days

Answer:

Use the distance formula.  Result:  sqrt [ (a-c)^2 + (b-d)^2 ]

Step-by-step explanation:

distance = d = sqrt [ (a-c)^2 + (b-d)^2 ]

Answer:

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Step-by-step explanation:

We are given two points (a, b) and (c, d)

We need to find the distance between two points.

It is coordinate of two points. Using coordinate formula of distance.

[tex]d=\sqtt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where,

[tex]x_2\rightarrow c[/tex]

[tex]x_1\rightarrow a[/tex]

[tex]y_2\rightarrow d[/tex]

[tex]y_1\rightarrow b[/tex]

Substitute into formula

Distance between two points is

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Hence, The formula of distance between two points  (a, b) and (c, d) is [tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Janet: x + 3

Julie: x

brother: x - 8

Janet + Julie + brother = sum

x + 3  +   x     +   x - 8    =  55

3x - 5 = 55

    +5   +5

3x      = 60

[tex]\frac{3x}{3} = \frac{60}{3}[/tex]

x = 20

Janet: x + 3   ⇒   (20) + 3   = 23

brother: x - 8   ⇒   (20) - 8   = 12

Answer: Janet=23, Julie=20, brother=12