A cone-shaped container has a height of 240 in. And a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week. How many weeks will it take for all of the chemical to evaporate?.

Answer:

ljj

Step-by-step explanation:

llk

Yes , the series is an arithmetic sequence of common difference 2

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the number of terms n = 20

The number of tiles in the first row = 10 tiles

The number of tiles in the second row = 2 more than first row

The number of tiles in the second row = 12 tiles

The number of tiles in the third row = 14 tiles

So , the sequence will be , 10 , 12 , 14 , 16 ...

The number of terms n = 20

The first term a = 10

The common difference d = second term - first term

The common difference d = 12 - 10 = 2

The series is an arithmetic sequence and the 20th term of the sequence will be

a₂₀ = a + ( n - 1 )d

a₂₀ = 10 + ( 19 ) 2

a₂₀ = 10 + 38

a₂₀ = 48 tiles

Hence , the series is an arithmetic sequence

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Answer: 1/2 cups

Step-by-step explanation:

Given that:

Every 1/4 cup of tuna has 1/2 gram of fat

How many cups of tuna are there for every gram of fat:

Let cup of tuna for 1 gram of fat = t

Hence, If

1/4 cup of tuna = 1/2 cup of fat

t tuna = 1 cup of fat

Cross multiply :

1/2 t = (1/4 * 1)

1/2 t = 1/4

t = 1/4 ÷ 1/2

t = 1/4 * 2/1

t = 2/4

t = 1/2

Hence, 1/2 cups of tuna for every gram of fat

I only agree with the first student strategy of multiplying the area of the base with the height.

A cylinder is made up of two circles at the top and the base.

The volume of the cylinder can be expressed as:

V = Bh

where
B is the base area

h is the height of the cylinder

V = πr²h

HEnce I only agree with the first student strategy of multiplying the area of the base with the height.

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Answer:

8.55 × \(10^{11}\)

Step-by-step explanation:

Answer:

8/50 × 100 = 16%

Answer:

Step-by-step explanation:

Answer:

$1.50

Step-by-step explanation:

9/6=1.5

1.5=1.50

One hotdog cost $1.50

Answer:

$1.50

Step-by-step explanation:

$9 > 6h

? > 1h

9/6 = $1.50

For one hotdog, the price is $1.50

$2.10 for the 6 pack

11.20 / 32 = 0.35

0.35 x 6 = 2.10

2.10 x 5 = 10.5

10.5 + 0.70 = $11.20

Answer:yes

Step-by-step explanation:Bc I am right and right

Answer:

2.32

Step-by-step explanation:

multiply 57.84 x 4 = 231.36

divide 231.36 / 100 = 2.31 but if you estimate then its 2.32

Answer:

The test statistic is Z = 1.157

Step-by-step explanation:

Given that:

The sample size n = 1200

The sample proportion of those that will vote for the Republican candidate is represented by \(\hat p = \dfrac{x}{n}\)

\(\hat p = \dfrac{620}{1200}\)

\(\hat p =0.5167\)

The null and the alternative hypothesis can be computed as:

\(H_o: P=0.50 \\ \\ H_a :P>0.50\)

The formula for the one-sample Z-test for the population proportion can be expressed as:

\(Z = \dfrac{\hat p - P_o}{\sqrt{\dfrac{P_o(1-P_o)}{n}}}\)

\(Z = \dfrac{0.5167 - 0.5}{\sqrt{\dfrac{0.5(1-0.5)}{1200}}}\)

\(Z = \dfrac{0.0167}{\sqrt{\dfrac{0.5(0.5)}{1200}}}\)

\(Z = \dfrac{0.0167}{\sqrt{\dfrac{0.25}{1200}}}\)

\(Z = \dfrac{0.0167}{\sqrt{2.08333333\times10^{-4}}}\)

Z = 1.157

Testing the hypothesis, from the information given, it is found that the test statistic is z = 1.157.

The null hypothesis is:

\(H_0: p = 0.5\)

The alternative hypothesis is:

\(H_1: p > 0.5\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

For this problem, the parameters are: \(p = 0.5, n = 1200, \overline{p} = \frac{620}{1200} = 0.5167\)

Hence, the value of the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.5167 - 0.5}{\sqrt{\frac{0.5(0.5)}{1200}}}\)

\(z = 1.157\)

The test statistic is z = 1.157.

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Answer:

x = 5

Step-by-step explanation:

x = 40 - (9 + 6 + 10 + 8)

x = 40 - 35

x = 5

Answer:

B, negative

Step-by-step explanation:

579 MPa is 0.1446.

The probability that a randomly chosen sample of glass will break at less than 579 MPa can be found using the Normal Distribution. Using the mean and standard deviation given, we can calculate the probability that a randomly chosen sample will have a fracture strength of less than 579 MPa. This is calculated using the formula P(X < 579) = 1 - P(X > 579) = 1 - 0.8554 = 0.1446.

Therefore, the probability that a randomly chosen sample of glass will break at less than 579 MPa is 0.1446.

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The marginal revenue at the output level 4 is 24, marginal revenue at the output level 4 is 41, and marginal profit at the output level 4 is 17.

It is defined as the cost showing an increase in the cost when the number of units produced increases, In simple words it is the ratio of the cost to quantity.

We have a cost function of a product:

C(Q) = 3Q² +8

a) To find the marginal cost to differentiate it with respect to Q and plug

Q = 4:

C'(Q) = 6Q

C'(4) = 6(4) = 24

b) R(Q) = P×Q

\(\rm R(Q) = (\dfrac{1}{3} Q^2 - 10Q + 105)Q\)

\(\rm R(Q) = \dfrac{1}{3} Q^3 - 10Q^2 + 105Q\)

R'(Q) = Q² - 20Q + 105

Plug Q = 4

R'(Q) = (4)² - 20(4) + 105

R'(Q) = 41

c) Marginal profit:

MP(Q)  = R(Q) - C(Q)

After calculating:

\(\rm MP(Q) = \dfrac{1}{3}Q^3-13Q^2+105Q-8\)

MP'(Q) = Q² - 26Q + 105

Plug Q = 4

MP'(Q) = 16 - 104 + 105 = 17

Similar, we can find the maximum profit.

Thus, the marginal revenue at the output level 4 is 24, marginal revenue at the output level 4 is 41, and marginal profit at the output level 4 is 17.

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Answer:

A'(-3,-2) B'(-1,-4) C'(-5,-3)

Step-by-step explanation:

im pretty sure that's right

hopes this helps

Answer:

\(A( - 2, \: 3) = > A'( 2, \: - 3) \\ B( - 4, \: 1) = > B'( 4, \: - 1) \\ C( - 3,\: 5) = > C'( 3, \: - 5)

\)

'

The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

the last one

Step-by-step explanation:

substitute both equation

\(y = 2(4 + y) + \frac{3}{2} \\ y = 2y + 8 + \frac{3}{2} \\ y = - 9.5\)

\(x = 4 + y \\ x = 4 - 9.5 \\ x = - 5.5\)

Answer:

magnitude of a shown vector is

\(4 \sqrt{5} \)

Answer:

The answer is located in the image below.

Answer:

b

Step-by-step explanation:

There are 250,000 different completed answer sheets possible using counting principle.

For part a, there are 2 choices for each of the 5 questions, so there are a total of 2^5 = 32 ways to complete part a.

For part b, there are 5 choices for each of the 4 questions, so there are a total of 5^4 = 625 ways to complete part b.

For part c, there are 6 choices for the first question, 5 choices for the second question (since one of the answers has already been used), 4 choices for the third question, and so on. So there are a total of 6 x 5 x 4 x 3 x 2 x 1 = 720 ways to complete part c.

To find the total number of possible completed answer sheets, we need to multiply the number of choices for each part. However, since part b and part c are mutually exclusive (you can only choose one of them), we need to add their totals together. Therefore, the total number of possible completed answer sheets is:

32 x (625 + 720) = 70,240

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The probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

To calculate the probability of rolling all six numbers at least once when rolling a six-sided die 12 times, we can use the concept of permutations.

The total number of possible outcomes when rolling a six-sided die 12 times is 6^12 since each roll has six possible outcomes. This represents the denominator of our probability calculation.

Now, let's calculate the numerator, which represents the number of favorable outcomes where we get all six numbers at least once. We can use the concept of derangements (or the principle of inclusion-exclusion) to determine this.

A derangement is a permutation in which none of the elements appear in their original position. In our case, we want to find the number of derangements for a set of six elements (the six numbers on the die).

The formula to calculate the number of derangements for a set of n elements is given by n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).

Using this formula, we can calculate the number of derangements for six elements:

Number of derangements = 6! * (1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!) = 265

Therefore, the numerator of our probability calculation is 265.

Finally, we can calculate the probability by dividing the numerator by the denominator:

Probability = Number of favorable outcomes / Total number of possible outcomes = 265 / 6^12

Calculating this value:

Probability ≈ 0.0263

So, the probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

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The angles in the figure are:

∠PQR = 45°

∠POR = 90°

Given : O is the centre of circle, ∠OPQ = 25° and ∠ ORQ = 20°

To Find : ​values of ∠ POR and ∠ PQR.

OP = OQ  = Radius

⇒ ∠OPQ = ∠OQP  

⇒ ∠OQP = 25°

OR = OQ  = Radius

⇒ ∠OQR = ∠ORQ

⇒ ∠OQR = 20°

∠PQR = ∠OQP + ∠OQR

⇒ ∠PQR =   25° + 20°

⇒ ∠PQR =   45°

∠POR = 2∠PQR

⇒ ∠POR = 2*45°

⇒  ∠POR = 90°

Hence we get the two angles as 45° and 90° respectively.

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The largest population to which the results can be generalized is in option C i.e. All student-athletes at the college.

Population: A population can be described as a complete group with at least one characteristic in common and a sample of the population can be used to get the features of the population.

We were told that a random sample of 50 student-athletes from all the student-athletes at a college, even though the population can be used to have an idea about how the consumption of beetroot juice enhances exercise performance, and it can not be used to get the results that can be generalized as more than 50 students-athletes is required which is chosen randomly.

All the other options are wrong because of this reason.

Therefore, option C is correct.

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1) Since in this pie chart, we have a budget. Let's locate the sectors for Housing, Insurance, and utilities

2) Enlisting them:

Housing: 24.8%

Insurance: 26.7%

Utilities: 12.9%

\%

So we can add them up:

The Gram-Schmidt process is not unique, and the order in which the vectors are processed can affect the result. In this case, we followed the given order: v₁ = (6, 8) and v₂ = (2, 0).

To convert the basis {(6,8), (2,0)} into an orthonormal basis in ℝ² using the Gram-Schmidt process, we follow these steps:

1. Start with the first vector, v₁ = (6, 8).
  Normalize v₁ to obtain the first orthonormal vector, u₁:
  u₁ = v₁ / ||v₁||, where ||v₁|| is the norm of v₁.
  Thus, ||v₁|| = √(6² + 8²) = √(36 + 64) = √100 = 10.
  Therefore, u₁ = (6/10, 8/10) = (3/5, 4/5).

2. Proceed to the second vector, v₂ = (2, 0).
  Subtract the projection of v₂ onto u₁ to obtain a new vector, w₂:
  w₂ = v₂ - projₐᵤ(v₂), where projₐᵤ(v) is the projection of v onto u.
  projₐᵤ(v) = (v · u)u, where (v · u) is the dot product of v and u.
  So, projₐᵤ(v₂) = ((2, 0) · (3/5, 4/5))(3/5, 4/5) = (6/5, 8/5).
  Therefore, w₂ = (2, 0) - (6/5, 8/5) = (2, 0) - (6/5, 8/5) = (2, 0) - (6/5, 8/5) = (2 - 6/5, 0 - 8/5) = (4/5, -8/5).

3. Normalize w₂ to obtain the second orthonormal vector, u₂:
  u₂ = w₂ / ||w₂||, where ||w₂|| is the norm of w₂.
  Thus, ||w₂|| = √((4/5)² + (-8/5)²) = √(16/25 + 64/25) = √(80/25) = √(16/5) = 4/√5.
  Therefore, u₂ = (4/5) / (4/√5), (-8/5) / (4/√5) = (√5/5, -2√5/5) = (√5/5, -2/√5).

Now, we have an orthonormal basis for ℝ²:
{(3/5, 4/5), (√5/5, -2/√5)}.

Please note that the Gram-Schmidt process is not unique, and the order in which the vectors are processed can affect the result. In this case, we followed the given order: v₁ = (6, 8) and v₂ = (2, 0).

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