Each marble bag sold by jenny's marble company contains 3 yellow marbles for every 5 orange marbles. if a bag has 15 yellow marbles, how many orange marbles does it contain?

Answer

300

Step-by-step explanation:

The volume of the first cylinder is 300π cm³. The height of the second cylinder is 5 cm. The volume of the third cylinder is [tex]45\pi \rm\; m^3[/tex]. The volume of the fourth cylinder is 5889.95 cubic feet. The volume of the fifth cylinder is 89438997.08 cubic feet.

We have a right circular cylinder with a radius of 5 cm and a height of 12 cm.

It is required to calculate the volume of the cylinder.

So, the volume of the cylinder will be,

[tex]V=\pi r^2h\\V=\pi\times 5^2\times 12\\V=300\pi \rm\; cm^3[/tex]

The volume of a cylinder is 225π cm³ and its height is 9 cm. It is required to calculate the radius of the cylinder.

So, the radius of the cylinder will be,

[tex]V=\pi r^2h\\225\pi=\pi\times r^2\times 9\\r^2=\dfrac{225}{9}\\r=\dfrac{15}{3}=5\rm\;cm[/tex]

We have a right circular cylinder with a diameter of 6 m and a height of 5 m.

It is required to calculate the volume of the cylinder.

So, the volume of the cylinder will be,

[tex]V=\pi r^2h\\V=\pi\times 3^2\times 5\\V=45\pi \rm\; m^3[/tex]

We have a right circular cylinder with a diameter of 17.5 ft and a height of 24.5 ft.

It is required to calculate the volume of the cylinder.

So, the volume of the cylinder will be,

[tex]V=\pi r^2h\\V=3.14\times (\dfrac{17.5}{2})^2\times 24.5\\V=5889.95 \rm\; ft^3[/tex]

A right circular cylinder has a height of ​ [tex]20 \dfrac{1}{2}[/tex] ​ ft and a diameter ​ 115 ​ times its height.

The diameter of the cylinder will be,

[tex]d=115\times 20\dfrac{1}{2}\\d=2357.5\\r=1178.75\rm\; ft[/tex]

It is required to calculate the volume of the cylinder.

So, the volume of the cylinder will be,

[tex]V=\pi r^2h\\V=3.14\times (1178.75)^2\times 20.5\\V=89438997.08 \rm\; ft^3[/tex]

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Answer: The answer is 68

The above answer is incorrect.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The radius of a circle with a circumference of 27 inches can be calculated using the formula for the circumference of a circle which is 2πr. Calculating this, the radius is approximately 4.3 inches.

The subject of this question is Mathematics, more specifically, Geometry which deals with shapes, sizes and properties of figures. In this case, we are being asked to find the radius of a circle given its circumference. The circumference of a circle is calculated as 2πr, where r represents the radius and π is approximately equal to 3.14.

To find the radius (r), you would divide the circumference by 2π. Given that the circumference of the circle is 27 inches, we divide 27 by 2π (approximately 6.28). This can be further simplified to approximately 4.3 inches.

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Identify

strategize

set up

solve

check

1) Identify ------> Mrs. Grey's time is the unknown

2) Strategize

Let

x--------> Mrs. Grey's time in minutes

3) set up

we know that

[tex]12*50=x*60[/tex]

4) solve

[tex]12*50=x*60\\ x=(12*50)/60\\x=10\ minutes[/tex]

5) check

[tex]12*50=10*60\\600=600[/tex]

therefore

the answer is

-Identify

-strategize

-set up

-solve

-check

Answer:

Option (b) is correct.

The slope of line shown in given graph is [tex]\frac{9}{7}[/tex]

Step-by-step explanation:

Given: A graph with an equation of line having two points (1,6) and  (-6, -3)

We have to find the slope of the given line in graph and choose the correct from the given options.

Consider the two points (1,6) and  (-6, -3).

Slope between two points can be calculated using the formula as,

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex]\left(x_1,\:y_1\right)=\left(1,\:6\right),\:\left(x_2,\:y_2\right)=\left(-6,\:-3\right)[/tex]

Thus, Slope is

[tex]m=\frac{-3-6}{-6-1}=\frac{9}{7}[/tex]

Thus, The slope of line shown in given graph is [tex]\frac{9}{7}[/tex]

The simplified form of the square root of 27a is [tex]3\sqrt{3a}[/tex]. In other words, the required answer is  [tex]3\sqrt{3a}[/tex]

To simplify the square root of 27a, we can break it down into its prime factors.

Step 1: Prime factorize the number inside the square root:

27 = 3 * 3 * 3

a = a (since 'a' is already in its simplest form)

Step 2: Rewrite the square root using the prime factors:

[tex]\sqrt{27a} = \sqrt{(3 * 3 * 3 * a)}[/tex]

Step 3: Group the prime factors into pairs:

[tex]\sqrt{(3 * 3 * 3 * a)} = \sqrt{(3^2 * 3 * a)}[/tex]

Step 4: Simplify the square root:

[tex]\sqrt{(3^2 * 3 * a) }= 3 * \sqrt{(3 * a)}[/tex]

Therefore, the simplified form of the square root of 27a is [tex]3\sqrt{3a}[/tex]. In other words, the required answer is  [tex]3\sqrt{3a}[/tex].

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Final answer:

The ice cream factory can make 936 quarts in 36 hours and the rate per day is 624 quarts.

Explanation:

To find out how many quarts of ice cream can be made in 36 hours, we can set up a proportion based on the rate of production. The rate of production is 260 quarts of ice cream in 10 hours. We can set up the proportion:

260 quarts / 10 hours = x quarts / 36 hours

Cross-multiplying, we get:

10x = 260 * 36

Simplifying, we find:

x = (260 * 36) / 10 = 936

Therefore, 936 quarts of ice cream can be made in 36 hours.

To find the rate per day, we need to calculate how many quarts can be made in 24 hours. We can set up the proportion:

260 quarts / 10 hours = y quarts / 24 hours

Cross-multiplying, we get:

10y = 260 * 24

Simplifying, we find:

y = (260 * 24) / 10 = 624

Therefore, the rate per day is 624 quarts of ice cream.

The value of v is v > -1.16.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given linear inequality is

−42v + 33 < 8v + 91

We have to take like terms on one side.

-42v and 8v are like terms and 33 and 91 are like terms.

Subtracting 8v from both sides,

−42v + 33 - 8v < 8v + 91 - 8v

-50v + 33 < 91

Subtracting 33 from both sides,

-50v + 33 - 33 < 91 - 33

-50v < 58

Dividing both sides by -50, the inequality sign changes.

v > -58 / 50

v > -1.16

Hence the solution for the inequality is v > -1.16.

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The domain and range of the function will be D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option second is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

M(g) = 17g

g = amount of gas.

M(g) = number of miles that Danny's truck travels on g gallons of gas

Maximum fuel capacity = 20 gallons

So the domain D will be:

D: 0 ≤ g ≤ 20

If g = 0, M(g) = 0

If g = 20, M(g) = 340

So the range:

R: 17 ≤ M(g) ≤ 340

Thus, the domain and range of the function will be D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option second is correct.

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Answer:

0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option

Step-by-step explanation:

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The domain and range of the function will be D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option second is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

M(g) = 17g

g = amount of gas.

M(g) = number of miles that Danny's truck travels on g gallons of gas

Maximum fuel capacity = 20 gallons

So the domain D will be:

D: 0 ≤ g ≤ 20

If g = 0, M(g) = 0

If g = 20, M(g) = 340

So the range:

R: 17 ≤ M(g) ≤ 340

Final answer:

To have $175 in your bank account, starting with $85 and depositing $23 weekly, solve the equation 175 = 85 + 23w. It takes approximately 3.913 weeks, so you will need to round up to 4 weeks to reach at least $175.

Explanation:

To find out how many weeks it will take to have $175 in your bank account, we can use the equation given: b = 85 + (15 + 8)w. We know the initial amount b is the goal of $175, and from the equation, we understand that every week you add $23 to your account ($8 from the allowance and $15 from the paycheck). Now, we set up the equation with the known values: 175 = 85 + 23w.

To solve for w, which represents the number of weeks, we follow these steps:

Since we cannot have a fraction of a week, we'll round up to the next whole number, which means it takes 4 weeks to have at least $175 in your bank account.

Therefore, it will take 4 weeks to reach or surpass the goal of $175 in your bank account.

Answer:

C. 2x^3-11x^2+16x-3

The measure of two vertical angles is same. So , the measure of angle A and angle B will be each equal to 20°.

What are the vertical angles ?

Vertical angles are the angles which are opposite to each other. A pair of vertically opposite angles are always equal to each other.

It is given that there are two vertical angles , which are ∠A and ∠B, The measure of the angles is given which is : m ∠A = x° and m ∠B = (5x - 80)°.

We know that the property of vertical angles states that two angles if they are vertical and opposite to each other then they have equal measures.

So , solving for the value of x :

x° = (5x - 80)°

Reordering the like terms :

5x  - x = 80°

4x = 80°

or

x = 20°

or

The measure of angle A i.e., m ∠A is 20°.

And the measure of angle B will be :

= (5 × 20°) - 80°

= 20°

Therefore , the measure of two vertical angles is same. So , the measure of angle A and angle B will be each equal to 20°.

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It is not advisable to produce an item due to high production costs compared to its value.

This situation is known as allocative inefficiency, where the costs outweigh the benefits to society.

For instance, if the cost of producing gold eyeglass frames is more than what customers are willing to pay for them due to their high production costs, it would not make economic sense to produce them.

In such cases, producers would opt to reduce production or not produce the item at all to avoid incurring losses.