A store sells prepackaged popcorn in two sizes
The package for the small size can be modeled by a cone with a height of 6 inches and a diameter of 4 inches
The package for the larger size can be modeled by a cone with a height of 9 inches and a diameter of 5 inches

Which of the following are true?
Select all that apply

A. The small popcorn has a volume of about 25.13 cubic inches
B. The small popcorn has a volume of about 75.40 cubic inches
C. The volume of two small popcorn is less than the volume of one large popcorn
D. The volume of two small popcorns is greater than the volume of one large popcorn
E. The volume of a large popcorn is about 135.09 cubic inches greater than the volume of the small popcorn

​

Answer:The value of x is 15 units.

Step-by-step explanation:

In the given triangle RSQ and ΔRST it is given that

∠RTS ≅ ∠SRQ ≅ 90°

∠RSQ is common in two triangles Δ RSQ and Δ RST.

Therefore two angles are equal so both the triangles are common.

From this property we opposite sides of the corresponding angles will be in the same ratio.

SR/SQ = ST/SR

x/(9 + 16) = 9/x

By cross multiplication on each side of the equation

x² = 25×9 = 225

x = √225 = 15

Therefore measurement of x is 15 units.

We can fill in the Venn diagram since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.

Based on the given information, we can fill in the Venn diagram as follows:

n(A) = 33, n(B) = 36, n(C) = 24, n(B ∩ C) = 14, n(A ∩ C) = 9, n(A ∩ B ∩ C) = 5

n(A ∩ B) = n(A) + n(B) - n(A ∩ B) = 33 + 36 - 17 = 52

Now we can fill in the Venn diagram:

Region I: n(A ∩ B ∩ C) = 5

Region II: n(A ∩ B) - n(A ∩ B ∩ C) = 52 - 5 = 47

Region III: n(B ∩ C) - n(A ∩ B ∩ C) = 14 - 5 = 9

Region IV: n(B) - n(B ∩ C) - n(A ∩ B) = 36 - 14 - 17 = 5

Region V: n(A) - n(A ∩ C) - n(A ∩ B) = 33 - 9 - 17 = 7

Region VI: n(C) - n(A ∩ C) - n(B ∩ C) = 24 - 9 - 14 = 1

Region VII: n(U) - n(A) - n(B) - n(C) + n(A ∩ B) + n(A ∩ C) + n(B ∩ C) + n(A ∩ B ∩ C) = 70 - 33 - 36 - 24 + 52 + 9 + 14 + 5 = 57

Region VIII: n(U) - (n(I) + n(II) + n(III) + n(IV) + n(V) + n(VI) + n(VII)) = 70 - (5 + 47 + 9 + 5 + 7 + 1 + 57) = -4

Since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.

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According to the question the value of x in the right triangle with a 30-degree angle and hypotenuse of 15 is 7.5.

We can use trigonometric ratios to find the value of x in a right triangle with a 30-degree angle and hypotenuse of 15.

First, we can use the fact that in a 30-60-90 triangle, the length of the shorter leg is half the length of the hypotenuse. So, we know that:

x/15 = 1/2

Multiplying both sides by 15 gives:

x = 7.5

Therefore, the value of x in the right triangle with a 30-degree angle and hypotenuse of 15 is 7.5.

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Answer:

Step-by-step explanation:

To find the distance they traveled, we can use the formula:

distance = rate × time

In this case, the rate is 65 miles per hour and the time is 3 hours.

So, the distance they traveled is:

distance = 65 × 3 = 195 miles

Therefore, Lily's family traveled 195 miles from Chicago to Wisconsin Dells.

The subject of this question is Mathematics and it involves counting and working with coins.

The subject of this question is Mathematics as it involves counting and working with coins.

Tia has 12 coins in total, consisting of 6 pennies, 3 nickels, and 3 dimes. Will has 15 coins, with an equal number of pennies, nickels, and dimes. Ana has a total of 9 coins, with 2 pennies, 4 nickels, and 3 dimes.

In summary, the question involves counting the number of coins each person has, which can be solved using basic arithmetic and understanding of coin values.

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Answer:

z = 1

Step-by-step explanation:

-z + 7 = 6

    -7    -7

             -1    

So, basically add -7 on both side (or the kcf method) which cancels out on on the right side but makes -1 on then notice how the -z/-1 = a positive because a negative divided by a negative is a positive so its positive one.

How to check?

just replace -z with -1 and put -1 + 7 = 6 which makes this answer correct.

Debt is usually expected in all of the following cases except for option A, which is the purchase of a house.

Debt refers to an amount of money that is owed by one party (the borrower) to another party (the lender). It can be incurred through borrowing money, using credit cards, or other forms of financing. Debt can take many different forms, including personal loans, mortgages, credit card balances, student loans, and other types of financial obligations.

Debt is usually expected in all of the following cases except for option A, which is the purchase of a house. Purchasing a house with a mortgage involves taking on debt, but it is often considered a necessary and responsible investment for many people. The other options - credit card purchases, purchasing a car, and educational loans - often involve taking on debt as well, but they are not typically seen as long-term investments like a house.

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The total surface area of the triangular prism is 1008cm² with dimensions 13cm, 5cm, 12cm, 9cm, 15cm, and 20cm.

To find the total surface area of a triangular prism with dimensions 13cm, 5cm, 12cm, 9cm, 15cm, and 20cm, we first need to identify the different faces of the prism. The triangular prism has two triangular faces and three rectangular faces.

The area of one triangular face can be calculated as

(1/2) x base x height, where the base is 12cm and the height is 9cm. Therefore, the area of one triangular face is

(1/2) x 12cm x (9+5)cm = 84cm²

Since there are two triangular faces, the total area of the triangular faces is 2 x 84cm² = 168cm².

The area of one rectangular face can be calculated as length x width, where the (length, width) is (13cm, 20cm), (14cm, 20cm) and (15cm, 20cm) = 15 × 20 + 13 × 20 + 14 × 20

= 840cm²

Thus, the total surface area of the triangular prism is the sum of the areas of the two triangular faces and three rectangular faces, which is

168cm² + 840cm² = 1008cm²

Therefore, the total surface area of the triangular prism is 1008cm².

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Answer:

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Answer: If I'm correct, an equivalent expression to v could be (2y)+10+2(5x+3)

Sorry I don remember how to do the other 2.

Step-by-step explanation

PEMDAS

2x + 10 + 2(5y + 3)

2x = 2

5y = 5

2+10=12 12+16

2 x (5+3=8) = 16

12+16= 28

x=1 y=1

An equivalent algebraic expression could be

(2y)+10+2(5x+3) if I'm correct because the

The answer is equal to the previous answer

60$

if you add $25.50 + $32.75 + 1.75 you get a sum of 60 (this being with no tax)

Answer:

f(x)=2x+x2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

2x→1

x^2→2

The largest exponent is the degree of the polynomial.

2

Step-by-step explanation:

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Answer: - 6

Step-by-step explanation:

Since n is c in [tex]ax^{2}[/tex] + bx + c, that means that n is the y - intercept of the graph. The y - intercept in the graph is -6 which means that n = -6.

Answer:

x=7 y=14

Step-by-step explanation:

2x-x=11-4

x=7

y-4=x+3

y-4=7+3

y=7+3+4

y=14

Answer:

[tex]\textsf{D.}\quad f(x)=\dfrac{(x-1)}{x(x-3)}[/tex]

Step-by-step explanation:

An asymptote is a line that the curve gets infinitely close to, but never touches.

Vertical asymptotes of a rational function occur when the denominator equals zero.

From inspection of the given graph, the vertical asymptotes are:

Therefore, for the denominator to equal zero, it must include the factors:

Since the only answer option that has the factors x and (x - 3) is option D, the graphed rational function is:

[tex]f(x)=\dfrac{(x-1)}{x(x-3)}[/tex]

The team was provided 10 gallons of water.

Answer:

8$ is the answer so chose that one

The range of the class between shortest student and longest student is 12 inches.

Range is the difference between highest and lowest possible values.

R= (higest value)-(lowest value)

Tallest student= 63 inches

Shortest student= 51 inches

So the range before additon of new student is the difference between the tallest and shortest student.

R= 63(tallest student) - 51(shortest student) = 12inches

Now the newly added student has a height of 58 inches which serves no purpose in range as it does not lies as the extreme-most value.

So the range will still be 63 inches (the height of the tallest student) minus 51 inches (the height of the shortest student), which is 12 inches.

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The function that models the total attendance a (in thousands) at NCAA women's basketball games and the number t of NCAA women's basketball teams over a period of time can be expressed as:

a = 5t + 200 thousands.

The total attendance a (in thousands) at NCAA women's basketball games and the number t of NCAA women's basketball teams over a period of time can be modeled by a function of the form a = kt + b.

where k and b are constants.

Let's determine the slope and y-intercept using the given information: a = kt + b

Given: a = 200 thousand and t = 5 teams

Substitute these values into the equation: a = kt + b200 thousand = 5k + b

The equation can be rewritten as: b = 200 thousand - 5k

We know that b represents the y-intercept,

so when t = 0, the attendance is given by b (in thousands).

Therefore, b represents the initial attendance at the start of the period of time in question.

To find the value of b, substitute t = 0 into the equation:

b = 200 thousand - 5(0) = 200 thousand.

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Answer:

Growth

3.8%

Step-by-step explanation:

Look at the number raised to a power.

In this case it is 1.038

If the number raised to a power is greater than 1, it is growth.

If that number is less than 1 it is decay.

Here, it is growth since 1.038 > 1.

Also, 1.038 = 1 + 0.038 = 1 + 3.8%

The rate of growth is 3.8%.

(a)The probability that a call is answered during the first two minutes is 50%.

(b)The probability that a customer waits more than four minutes is infinite.

(a)The probability that a call is answered during the first two minutes is 50%. This is because, if the average waiting time is four minutes, then the call is equally likely to be answered during the first two minutes as it is during the last two minutes. Therefore, the probability of being answered within the first two minutes is 50%.

(b)The probability that a customer waits for more than four minutes can be calculated by assuming that the waiting time follows the same continuous uniform distribution from 0 to 4 minutes. The probability density function (PDF) for this distribution is:

f(x) = 1/4 0 <= x <= 4

The probability that a customer waits more than four minutes is the area under the PDF from 4 to infinity:

P(x > 4) = integral from 4 to infinity of f(x) dx

= integral from 4 to infinity of 1/4 dx

= [1/4 * x] evaluated from 4 to infinity

= lim(x -> infinity) (1/4 * x) - (1/4 * 4)

= infinity

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The perimeter of the figure is approximately 32.6 units

What is perimeter ?

Perimeter is a term used in geometry to describe the total length of the boundary or outer edge of a two-dimensional shape. In other words, it is the sum of the lengths of all the sides of a shape.

The concept of perimeter is most commonly used with polygons, which are shapes with straight sides. To find the perimeter of a polygon, we simply add up the lengths of all its sides. For example, the perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

where length and width are the dimensions of the rectangle.

According to the question:
To find the perimeter of the figure, we need to add up the lengths of all its sides.

First, let's find the circumference of each semicircle. The diameter of each semicircle is 4, so the radius is 2. The circumference of each semicircle is:

C = πr = π(2) = 2π

Since there are two semicircles, the total length of their circumferences is:

2(2π) = 4π

Now let's find the length of the sides of the rectangle. One side has length 6, and the other side is the diameter of the semicircles, which is also 4. So the length of the other side of the rectangle is 4. Therefore, the perimeter of the rectangle is:

2(6 + 4) = 20

Finally, we can add up the lengths of all the sides to find the perimeter of the figure:

Perimeter = 4π + 20

Using a calculator to approximate π as 3.14 and rounding to the nearest tenth, we get:

Perimeter ≈ 4(3.14) + 20 ≈ 32.6

Therefore, the perimeter of the figure is approximately 32.6 units.

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Answer: The answer is 32.6

Answer:

18

Step-by-step explanation:

here,

circumference of the circle = 90

[tex]S = r\theta[/tex]

in above equation, S is the length of arch, r is the radius and theta is the angle formed by arc at the center,

As you can see, in a circle of given radius,

[tex]S \propto \theta[/tex]

therefore,

[tex]\dfrac{S_1}{S_2} = \dfrac{\theta_1}{\theta_2}[/tex]

we have the arc length for angle 360 (circumference of the circle).

let S1 be the length of minor arc, S2 be the arc formed by full circle (360 degree),

[tex]\dfrac{S_1}{90} = \dfrac{72}{360}[/tex]

solving the above equation, we get

[tex]S_1 = 18[/tex]

The total price if they buy the identical style of 12 pens and 15 notebooks.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence total cost

= Rs ( 300 + 120 )

= Rs 420

The cost of 15 notebooks

= Rs ( 15 × 20 )

= Rs 300

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Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be

Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.

Answer:

[tex]- 8 {g}^{15} {h}^{6} [/tex]

Step-by-step explanation:

[tex] {( - 2 {g}^{5} \times {h}^{2} )}^{3} [/tex]

Use the property of exponents (raise each term by a degree separately):

[tex] {( - 2 {g}^{5} \times {h}^{2} )}^{3} = ( { - 2})^{3} \times {( {g}^{5} })^{3} \times {( {h}^{2}) }^{3} = - 8 \times {g}^{15} \times {h}^{6} = - 8 {g}^{15} {h}^{6} [/tex]

Answer:

-108

Step-by-step explanation:

We know b is -7 so we have to plug it in.
6(2(-7)-4)

Simplify: 6(-14-4)

Simplify again: 6(-18)

Simplify: -108

Final answer -108

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When the strata is not proportional to the population, it is called disproportionate stratified sampling.

The sampling method used in this case is a stratified sampling method. What is Stratified Sampling? Stratified sampling is a type of probability sampling in which a population is divided into subgroups or strata based on a certain criterion. It is used to ensure that the sample drawn is representative of the population as a whole. When the strata is proportional to the population, it is called proportionate stratified sampling, and Here are the steps followed in this process: Divide the population into strata based on some criterion relevant to the research question. Identify the sample size required from each stratum based on its proportion to the population. Draw a random sample from each stratum to arrive at the final sample.

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \sf \large{↣ \frac{2}{3} + \frac{2}{5} }[/tex]

[tex] \: [/tex]

[tex] \sf \large{ ↣\frac{2 \times 5 + 3 \times 2}{3 \times 5} }[/tex]

[tex] \: [/tex]

[tex] \sf \large{ ↣\frac{10 + 6}{15} }[/tex]

[tex] \: [/tex]

[tex] \large{↣\boxed{ \sf{ \purple{ \: \frac{16}{15} \: }}}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

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