Kate surveyed 16 politicians from her state about their views on certain issues. is this sample of citizens of the state likely to be representative?

The equation that can be used to find x, the amount of the 60% mixture used to create the 65% mixture is:

0.60*x + 0.80*(100 - x) = 0.65*(100).    

First, let's define two variables:

We know that we want to make 100 lb of 65% copper brass, then we must have that:

x + y = 100

And the percentage of copper before and after mixing must be the same, so we can write:

0.60*x + 0.80*y = 0.65*(x + y).

(where the percentages are written in decimal form).

Then we have a system of equations:

x + y = 100

0.60*x + 0.80*y = 0.65*(x + y).

To get a single equation, we can isolate the variable "y" on the first equation:

y = 100 - x

Now we replace that in the other equation:

0.60*x + 0.80*(100 - x) = 0.65*(100).      

This is what we wanted to get, an equation that can be used to find x, the amount of the 60% mixture used to create the 65% mixture.

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When 120 hours shared in the ratio it gives 50 hours : 70 hours

Lets add up the ratio= 5 + 7 =12

Now for 5/12 of the time =  5/12 × 120

                                        = 50 hours

And for 7/12 of the time  =  7/12 × 120

                                        = 70 hours

A ratio in mathematics describes the amount of times one number is present in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). The proportions of oranges to the overall amount of fruit are 8:14 for oranges and 6:8 (or 3:4) for lemons (or 4:7).

The quantities in a ratio can be of any form, including counts of people or things, measures of lengths, weights, or times, etc. Both numbers must be positive in the vast majority of situations.

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Answer:

(a) The percent of students who passed the exam is:

Percent passed = (number of students who passed ÷ total number of students) × 100

Percent passed = (80 ÷ 110) × 100

Percent passed = 72.73%

Rounded to the nearest percent, 73% of the students passed the exam.

(b) The percent of students who did not pass the exam is:

Percent did not pass = 100% - percent passed

Percent did not pass = 100% - 72.73%

Percent did not pass = 27.27%

Rounded to the nearest percent, 27% of the students did not pass the exam.

Answer:

x = 4, y = 5.

Step-by-step explanation:

4x-2=3y-1

y+3=3x-4

Rearranging:

4x - 3y =  1       (A)

-3x + y = -7      (B)

Multiply  B by 3:

-9x + 3y = -21   (C)
Adding A and C:

-5x = -20

x = 4

Substitute for x in equation A:

4(4) - 3y = 1

3y = 15

y = 5.

a. The composite scores for each location are as follows: Location A: 84.34, Location B: 81.05, Location C: 82.63 (b)  Based on the composite scores, Location A should be chosen for the clothing store.

To determine the composite score for each location, we need to calculate the weighted sum of the factor ratings.

a. The composite score for each location is calculated as follows:

Location A:

Composite score = (Convenience of access * Weight) + (Parking facility * Weight) + (Frontage * Weight) + (Shopper traffic * Weight) + (Operating cost * Weight) + (Neighbourhood * Weight)

Composite score = (0.10 * 92) + (0.15 * 91) + (0.19 * 96) + (0.31 * 79) + (0.10 * 70) + (0.15 * 69)

Composite score = 84.34

Location B:

Composite score = (0.10 * 70) + (0.15 * 73) + (0.19 * 89) + (0.31 * 95) + (0.10 * 95) + (0.15 * 81)

Composite score = 81.05

Location C:

Composite score = (0.10 * 72) + (0.15 * 75) + (0.19 * 74) + (0.31 * 80) + (0.10 * 92) + (0.15 * 96)

Composite score = 82.63

b. Based on the composite scores, we can see that Location A has the highest score of 84.34, followed by Location C with a score of 82.63, and Location B with a score of 81.05. Therefore, Location A should be chosen for the clothing store.

After calculating the composite scores for each location based on the factor ratings and weights, it is determined that Location A has the highest composite score and should be chosen for the clothing store.

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324πh is the required value of the integral.

The given solid hemisphere, represented by the inequality x² + y² + z² ≤ 36, z ≥ 0, can be expressed in spherical coordinates as follows: r = 6, ρ = 6 cos φ, and 0 ≤ θ ≤ 2π.

The integral for h(8 - x² - y²)dv using spherical coordinates can be written as: h(8 - ρ² sin² φ)ρ² sin φ dρ dφ dθ.

The bounds for the integral are as follows: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π/2, and 0 ≤ ρ ≤ 6 cos φ.

Substituting the values in the integral, we can evaluate it as follows:

∫(0 to 2π) ∫(0 to π/2) ∫(0 to 6 cos φ) h(8 - ρ² sin² φ)ρ² sin φ dρ dφ dθ = h∫(0 to 2π) ∫(0 to π/2) [∫(0 to 6 cos φ) (8ρ² sin φ - ρ^4 sin³ φ) dρ] dφ dθ.

Simplifying further:

= h∫(0 to 2π) ∫(0 to π/2) [4(6cos φ)^4/4 - 2(6cos φ)^2/2] sin φ dφ dθ.

Continuing the calculation:

= h∫(0 to 2π) [6^4/4] [1/3 - (1/2) cos² φ] dθ.

Integrating again:

= h(6^4/4) [θ/3 - (1/6) sin 2θ] from 0 to 2π.

Simplifying further:

= h(6^4/4) [(4π)/3] = 324πh.

Hence, the required value of the integral is 324πh.

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Answer:

36

Step-by-step explanation:

Let's let n be any number.

If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n must be even. Therefore, let 2n be our first number.

So, the consecutive even number will be (2n+2) followed by (2n+4).

We know that their sum must be 114. Therefore, we can write the following equation:

\((2n)+(2n+2)+(2n+4)=114\)

Solve for n. Combine like terms on the left:

\(6n+6=114\)

Subtract 6 from both sides:

\(6n=108\)

Finally, divide both sides by 6. Therefore, the value of n is:

\(n=108/6=18\)

Therefore, our first even number is 2n or 2(18) which equates to 36.

And the consecutive even numbers will be 38 and 40.

So, the smallest of them, the first term, is 36.

Let the three consecutive even numbers be x, x + 2 and x + 4 .

\( \longrightarrow \rm x + x + 2 + x + 4 = 114\)

\( \longrightarrow \rm 3x + 6 = 114\)

\( \longrightarrow \rm 3x = 108\)

\( \longrightarrow \bf x = 36\)

Smallest number = 36

Answer:

\(2ba\)

Step-by-step explanation:

Given the following question:

\(4b\times0.5a\)
Simplify by multiplying:
\(4b\times0.5a\)
\(4\times0.5=2\)
\(=2ba\)
\(2ba\)

Since the variables are not the same, we do not combine like terms. Your answer is "2ba."

Hope this helps.

Answer:

2ab

Step-by-step explanation:

4b × 0.5a

= 2ab

Answer:

4.2

Step-by-step explanation:

4  1/2

1 4/5 = 9/5

2 1/3 = 7/3

---------------------------

9/5 · 7/3  = 21/5 OR 4 1/2

Answer:

I think it's 10-x because that would give you a negative number

The fastest speed reached by the lorry is 40 km/h (to 2 decimal places) between the points (2, 20) and (4, 100).

To find the fastest speed reached by the lorry, we need to determine the steepest slope on the distance-time graph. The slope represents the rate of change of distance with respect to time, which corresponds to the speed.

Looking at the given data points, we can calculate the speed between each pair of consecutive points. The speed can be determined by dividing the change in distance by the change in time.

Between (0, 0) and (2, 20):

Speed = (20 - 0) / (2 - 0) = 20 / 2 = 10 km/h

Between (2, 20) and (4, 100):

Speed = (100 - 20) / (4 - 2) = 80 / 2 = 40 km/h

Between (4, 100) and (6, 140):

Speed = (140 - 100) / (6 - 4) = 40 / 2 = 20 km/h

Between (6, 140) and (8, 140):

Speed = (140 - 140) / (8 - 6) = 0 / 2 = 0 km/h

From the calculations, we can see that the fastest speed reached by the lorry is 40 km/h (to 2 decimal places) between the points (2, 20) and (4, 100).

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The value of the given expression will be 3√5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression c² = 45 will be solved as below:-

c² = 45

Take the square root of the number 45.

c = √45

c = √ 9 x √5

c = 3√5

Therefore, the value of the given expression will be 3√5.

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Answer:

Delia pays $4,680 in 4 months

Step-by-step explanation:

Equation:

18,000 * 6.5% = 1170

4680 ÷ 4 = 1170

So, the answer is 4 months this is the equation.

Hope this helps! :)

Frequency distribution  is a way to organize qualitative data into categories and record the number of observations in each category.

Differentiate between frequency distribution and relative frequency ?

A frequency distribution lists how frequently each category of data occurs, but a relative frequency analysis lists how frequently each types of information occurs.

One approach to organise data is to use a "frequency distribution," which can be done by listing the data, placing it in a table, or displaying it in a graph. Then, the list's entries (distinct values) are counted in terms of how frequently they have occurred.

Define relative frequency distribution

A "relative frequency distribution," on the other hand, refers to the percentage of the total number of observations that fall into a certain group. Divide each frequency by the total amount of data in the sample to obtain this.

what is qualitative data ?

Quantitative data are counts or measures, whereas qualitative data describe categories. Examples of qualitative data include eye colours and shoe brand names in a consumer survey. Examples of quantitative data are student heights and test results.

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Answer:

the equation of line parallel to y=-3x+2

is y=-3x+k---(1)

Since,line(1) passes through point (4,3).

3=-3(4)+k

or,3=-12+k

or,k=3+12

:.k=15

Putting value of k in line (1), we get

y=-3x+15,which is the required eqn.

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Answer:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle

Answer:

13.5

Step-by-step explanation:

If x is the number,

then,  6(x-9) =27

x-9 = 4.5

x=13.5

Answer:

27/2

Step-by-step explanation: 6*(n-9)=27 Distribute 6(n-9)=27 6n-54=27 add 54 to both side of the equation 6n-54+54=27+54 simplify (add the numbers) 6n=81 divide both sides of the equation by the same term 6n/6=81/6 simplify (cancel terms that are both the numerator and the denominator) (divide the numbers) n=27/2 or 13.5

B) "Some goat was eaten by a wolf" is a correct interpretation of the statement, because it means that there exists at least one goat that was eaten by a wolf.

The given statement can be translated as: "For all goats z, if z is eaten by a wolf, then there exists a wolf w such that w has eaten z."

A) "Every goat is eaten by a wolf" is not a correct interpretation of the statement. The correct interpretation is that if a goat is eaten by a wolf, then there exists at least one wolf that has eaten a goat.

B) "Some goat was eaten by a wolf" is a correct interpretation of the statement, because it means that there exists at least one goat that was eaten by a wolf.

C) "There is a wolf who has eaten every goat" is not a correct interpretation of the statement. The correct interpretation is that for each goat that is eaten, there exists at least one wolf that has eaten it.

D) "Every goat has eaten a wolf" is not a correct interpretation of the statement. The correct interpretation is that if a goat is eaten by a wolf, then there exists at least one wolf that has eaten a goat, but it does not imply that every goat has eaten a wolf.

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the determinant of the matrix is e1e4-e3e2

The determinant of a matrix is a scalar value that is a function of the entries. It characterizes some properties of the matrix and the linear map represented by it. The determinant is nonzero if and only if the matrix is invertible and an isomorphism exists.

Determinants are only defined for square matrices and encode certain properties of the matrices.

The determinant of a matrix is defined by the difference betweern the product of the right diagonal to the the product of the left diagonal

From the given question. the determinant of the matrix is e1*e4 -e3-e2 = e1e4-e3e2

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Therefore, the ratio of girls to boys in the auditorium is 8:11.

The ratio of girls to boys in the auditorium can be calculated by dividing the number of girls by the number of boys. In this case, there are 16 girls and 22 boys.

Ratio of girls to boys = Number of girls / Number of boys

Ratio of girls to boys = 16 / 22

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2 in this case.

Ratio of girls to boys = 8 / 11

This means that for every 8 girls, there are 11 boys in the auditorium

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When x = 90, ΔC = $5.31 and C'(x) = 2.2.
Given the total-cost function C(x) = 0.01x^2 + 0.4x + 50, we'll first find the change in cost (ΔC) and then the derivative of the cost function (C'(x)) when x = 90 and Δx = 1.

To find ΔC when x = 90 and ΔΧΖ = 1, we need to use the formula:
ΔC = C(x + ΔΧΖ) - C(x)
Substituting the values, we get:
ΔC = C(90 + 1) - C(90)
ΔC = C(91) - C(90)
ΔC = [0.01(91)^2 + 0.4(91) + 50] - [0.01(90)^2 + 0.4(90) + 50]
ΔC = 91.31 - 86
ΔC = $5.31
To find C'(x), we need to take the derivative of the total-cost function C(x):
C(x) = 0.01x^2 + 0.4x + 50
C'(x) = 0.02x + 0.4
Substituting x = 90, we get:
C'(90) = 0.02(90) + 0.4
C'(90) = 1.8 + 0.4
C'(90) = 2.2
Therefore, when x = 90, ΔC = $5.31 and C'(x) = 2.2.
Given the total-cost function C(x) = 0.01x^2 + 0.4x + 50, we'll first find the change in cost (ΔC) and then the derivative of the cost function (C'(x)) when x = 90 and Δx = 1.
1. To find ΔC, evaluate C(x + Δx) - C(x) when x = 90 and Δx = 1:
ΔC = C(90 + 1) - C(90) = C(91) - C(90)
2. Now, let's find the derivative of the cost function C(x):
C'(x) = d(0.01x^2 + 0.4x + 50)/dx = 0.02x + 0.4
3. Evaluate C'(x) when x = 90:
C'(90) = 0.02(90) + 0.4 = 1.8 + 0.4 = 2.2
So, ΔC = C(91) - C(90), and C'(x) when x = 90 is 2.2.

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TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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The h'(3) = h'(x)|x=3 = 22. We can see from the calculation that the value of h'(3) depends on the slopes of both f(x) and g(x) at x=3, as well as their values at x=3.

To evaluate h'(3) for h(x) = f(x) * g(x), we will use the product rule. The product rule states that if h(x) = f(x) * g(x), then h'(x) = f'(x) * g(x) + f(x) * g'(x).
Given the graphs of f(x) and g(x), we need to find the values of f(3), g(3), f'(3), and g'(3).
1. Locate the point x = 3 on the graph of f(x) and determine the value of f(3).
2. Locate the point x = 3 on the graph of g(x) and determine the value of g(3).
3. Determine the slope of the tangent line at x = 3 on the graph of f(x), which represents f'(3).
4. Determine the slope of the tangent line at x = 3 on the graph of g(x), which represents g'(3).
Once you have the values of f(3), g(3), f'(3), and g'(3), plug them into the product rule formula:
h'(3) = f'(3) * g(3) + f(3) * g'(3)
After calculating, you'll get the value of h'(3). Please refer to the graphs of f(x) and g(x) to obtain the necessary values and complete the evaluation.

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Answer:

70

Step-by-step explanation:

63+47=110

180-110=70

Answer: x= 70

Step-by-step explanation:

A triangle=180 degrees

We know 2 of these degrees

Add them together

63+47=110

Now subtract 110 from 180

180-110=70 degrees

The JMGK Board of Directors has requested a review of the operations of the Billy Fontaine School of Profit Inc. (BFS) after discovering an overdrawn bank account.

As a CPA, you are tasked with determining the expected cash flow for the year, conducting an audit of the financial statements, discussing the appropriate accounting treatment for enrollment fees, and explaining the role of an Audit Committee.

The initial situation reveals a financial discrepancy at the BFS, with an overdrawn bank account despite full session enrollment and minimal expenses. The review aims to identify the reasons behind this situation and suggest improvements to address any weaknesses. The audit plan will include a comprehensive examination of the BFS financial statements for the year ending December 31, 2022, in accordance with Accounting Standards for Private Enterprises. This plan will outline the scope and objectives of the audit, as well as the key areas to be assessed.

Regarding enrollment fees, it is important to discuss the appropriate accounting treatment. This involves determining whether the fees should be recognized as revenue upon receipt or deferred and recognized over the duration of the art sessions. The decision will depend on the specific terms and conditions of the enrollment contracts and the revenue recognition principles applicable to the BFS.

The establishment of an Audit Committee is being considered by the JMGK Board. The role of the Audit Committee would involve overseeing the BFS financial statement audit, ensuring the integrity and reliability of financial reporting, and monitoring compliance with relevant regulations and policies. The committee would provide an independent and objective review of the audit process, enhance internal controls, and strengthen corporate governance practices.

By conducting a thorough review of the BFS operations, implementing necessary improvements, and involving an Audit Committee, the JMGK Board aims to ensure transparency, accountability, and sound financial management within the organization.

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The probability of rolling a number that is both even and greater than 3 on a standard 6-sided die is 1/3 or approximately 0.3333 (33.33%).

To determine the probability of rolling a standard 6-sided die and getting a number that is both even and greater than 3, we first need to identify the outcomes that meet these criteria.

The even numbers on a standard 6-sided die are 2, 4, and 6. However, we are only interested in numbers that are greater than 3, so we eliminate 2 from the list.

Therefore, the favorable outcomes are 4 and 6.

Since a standard die has 6 equally likely outcomes (numbers 1 to 6), the probability of rolling an even number greater than 3 is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Probability = (Number of favorable outcomes) / 6

In this case, the number of favorable outcomes is 2 (4 and 6).

Probability = 2 / 6

Simplifying the fraction gives:

Probability = 1 / 3

So, the probability of rolling a number that is both even and greater than 3 on a standard 6-sided die is 1/3 or approximately 0.3333 (33.33%).

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Answer:

Its A i took this question

Step-by-step explanation: