half of a number is 16. What is the number?
A. 8
B. 4
C. 64
D. 32

Answer: Step 2 : Additive

              Step 4 : Multiplicative

Step-by-step explanation:

Also, if you could hook me up into Passione, that'd be cool

The nearest integer 136,043 people. To find the total population within a 3-kilometer radius of the city center, we need to integrate the population density function (∂(x, y)) over the circular region with a radius of 3 kilometers.

Given that the population density (∂) is defined as 7000 (x^2 + y^2)^-0.2 people per square kilometer, we can express the population density as a function of the distance from the origin (r).

Let's perform the integration using polar coordinates, where x = rcos(θ) and y = rsin(θ):

∂(r) = 7000\((r^2)^-0.2\)

∂(r) = 7000\(r^(-0.4)\)

Now, we need to integrate this population density function (∂(r)) over the circular region with a radius of 3 kilometers.

To do this, we integrate from 0 to 2π for the angle (θ), and from 0 to 3 kilometers for the radius (r).

Total population = ∫∫R ∂(r) r dr dθ

Total population = ∫[0 to 2π] ∫[0 to 3] 7000 \(r^(-0.4)\) r dr dθ

Simplifying the integral:

Total population = 7000 ∫[0 to 2π] ∫[0 to 3] \(r^(0.6)\) dr dθ

Total population = 7000 ∫[0 to 2π] [(\(r^(1.6)\))/(1.6)]|[0 to 3] dθ

Total population = 7000 \((1.6)^(-1)\)∫[0 to 2π] [(\(3^(1.6))\)/(1.6)] dθ

Total population = (7000/1.6) \((3^(1.6))\) ∫[0 to 2π] dθ

Total population = (7000/1.6) \((3^(1.6)\)) (θ)|[0 to 2π]

Total population = (7000/1.6) (\(3^(1.6)\)) (2π)

Now, let's evaluate this expression:

Total population ≈ (7000/1.6) (\(3^(1.6)\)) (2π)

Total population ≈ 136042.195 people

Rounding up to the nearest integer, the total population within a 3-km radius of the city center is approximately 136,043 people.

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Answer: C=250S+4500

C=250(17) + 4500    

C=4250+4500

C=8750

Step-by-step explanation:

As an equation, 250 would be the slope because it is multiplying by the ton and 4500 is the y intercept. If you substitute in 17 for S, then multiply 17 by 250, you get 4250 then add the 4500 and you get 8750 so if S=17, C=8750

The cost of transporting 17 tons of sugar is $8750.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

The given information can be related as,

C = 250S + 4500.

Now, when tons of sugar is 17 we'll simply replace S with 17.

∴ C = 250(17) + 4500.

C = 4250 + 4500.

C = 8750.

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The polynomial with zeros 2, -3, and 5 and a degree of 3 is x³ - 4x² - 7x + 30.To form a polynomial with given zeros and degree, we need to use the concept of factoring and the zero-product property.

The zero-product property states that if a product of factors equals zero, then at least one of the factors must be zero.

Here's how you can form a polynomial with given zeros:

1. Start with the given zeros. Let's say we have zeros x = a, x = b, x = c, and so on.

2. Use the zero-product property to write the factors. For each zero, write a factor in the form (x - zero). For example, if a = 2 is a zero, then the corresponding factor is (x - 2).

3. Multiply all the factors together to form the polynomial. Each factor represents a term in the polynomial.

For example, let's say the zeros are 2, -3, and 5, and we want to form a polynomial of degree 3. The steps would be:

1. Zeros: a = 2, b = -3, c = 5.

2. Factors: (x - 2), (x + 3), (x - 5).

3. Polynomial: (x - 2)(x + 3)(x - 5).

Expanding this polynomial would give us the final form. It would look like:

(x - 2)(x + 3)(x - 5) = x³ - 4x² - 7x + 30.

Therefore, the polynomial with zeros 2, -3, and 5 and a degree of 3 is x³ - 4x² - 7x + 30.

Remember to substitute the given zeros and adjust the degree accordingly to form the desired polynomial.

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Answer:

The equation of a line passing through the points (2, 3) and (4, 6) is 3x - 2y = 0.

Step-by-step explanation:

The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.

The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.

Given, the double integral ∫∫yA and the region y = x-6 and x = y²

y = x-6

x = y²

y² = y +6

y² - y - 6 = 0

y² - 3y +2y - 6 = 0

(y-3) (y+2) = 0

y = 3 and y = -2

\(\int\int\limits_\triangle {y} \, dA\\ \\\)

= \(\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}\)

The value for the double integral is 125/12.

Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.

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Since there are only 4 terms in the sum, it's not too much work to expand it as

\(\displaystyle \sum_{n=0}^3 (2n-3) = -3 + (-1) + 1 + 3 = \boxed{0}\)

Alternatively, we can use the well-known formulas

\(\displaystyle \sum_{n=1}^N 1 = \underbrace{1 + 1 + \cdots + 1}_{N \text{ 1s}} = N\)

\(\displaystyle \sum_{n=1}^N n = 1+2+\cdots+N = \frac{N(N+1)}2\)

These sums start at n = 0, so in our given sum we will keep track of the 0-th term separately:

\(\displaystyle \sum_{n=0}^3 (2n-3) = -3 + \sum_{n=1}^3 (2n-3) = -3 + 2 \sum_{n=1}^3 n - 3 \sum_{n=1}^3 1 = -3 + 3\times4 - 3\times3 = 0\)

as expected.

The value of MO is 28.

Two or more triangles are said to be similar, though not congruent, when on comparing their properties, some common relations holds.

Considering the diagram given in the question, on comparing the two triangles. Let MO be represented by x;

MN/ MK = MO/ ML

But, MK = 21 + 9 = 30, and ML = x + 12

Thus,

21/ 30 = x/ (x+ 12)

cross multiply to have;

30x = 21 (x + 12)

30x = 21x + 252

30x - 21x = 252

9x = 252

x = 252/ 9

  = 28

x = 28

Therefore, MO = 28

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Answer:

(150*85)*0.9

=12750*0.9

=11475

Answer:

11475

Step-by-step explanation:

((50+50+50)*85)*0.9=

(150*85)*0.9=

12750*0.9=

11475

∠6 and ∠8 are vertical angles.

∠2 and ∠7 are same side exterior angles

∠3 and ∠ 5 are alternate interior angles

∠1 and ∠2 are supplementary angles

Transversal angles are angles that are formed when a transversal line intersects two other lines in a plane. A transversal is a line that intersects two or more other lines, which are called the base lines.

When a transversal intersects two parallel lines, it creates eight angles. These angles can be classified into three types:

Corresponding angles: Pairs of angles that are on the same side of the transversal and in corresponding positions relative to the parallel lines. Corresponding angles are congruent when the parallel lines are cut by the transversal.

Alternate interior angles: Pairs of angles that are on opposite sides of the transversal and between the parallel lines. Alternate interior angles are congruent when the parallel lines are cut by the transversal.

Alternate exterior angles: Pairs of angles that are on opposite sides of the transversal and outside the parallel lines. Alternate exterior angles are congruent when the parallel lines are cut by the transversal.

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Answer:

All real numbers would be the correct answer.

Step-by-step explanation:

First of all, add 6n to -2n which now the equation would be 4n+3 < 4n+8.

Now, subtract 4n to both sides and subtract 3 to both sides. Now you will have 0n < 5 which will be all real numbers.

The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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Answer:

D. x^2-x-9-12/x-2

Step-by-step explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

    2 |   1   -3   -7    6

       |______2___-2__-18

       | 1   -1   -9  -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).

Answer:

637.50

Step-by-step explanation:

7,650.00 per year divided by 12 months equals 637.50

Answer:

The answer is 3⁴

Step-by-step explanation:

3² • 3² = 3²⁺² = 3⁴

Thus, The answer is 3⁴

-TheUnknownScientist

Answer:

The answer is C

Step-by-step explanation:

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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If a hypothesis test is performed that rejects the null hypothesis, the decision would be interpreted as there being enough evidence to support the alternative hypothesis.

In this case, it would mean that there is enough evidence to support the claim that the gestation period for a fox is different from 50.3 weeks, but it does not specify whether it is longer or shorter. In hypothesis testing, the null hypothesis (H0) represents the default position or the claim to be tested, while the alternative hypothesis (Ha) represents the opposing claim. In this case, the null hypothesis would be that the mean gestation period for a fox is 50.3 weeks. If the hypothesis test rejects the null hypothesis, it means that there is enough evidence to suggest that the true mean gestation period is different from 50.3 weeks. However, the test does not provide information on whether the gestation period is longer or shorter than 50.3 weeks. The alternative hypothesis does not specify a direction, so the interpretation would be that there is enough evidence to support the claim that the gestation period is different from the claimed value of 50.3 weeks.

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On solving the provided question, we can say that By the help of trigonometry the angle elevation is 45.

The area of mathematics known as trigonometry looks at how triangle side lengths and angles relate to one another. In the Hellenistic era, roughly in the third century BC, the region had its initial appearance due to the use of geometry in astronomical study.

Exact mathematics focuses on specific trigonometric functions and how calculations could employ them. There are six well-known trigonometric functions in trigonometry.

They go by a variety of names and abbreviations, including sine, cosine, tangent, cotangent, secant, and cosecant (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. In geometry, the characteristics of every geometric figure are explored.

Let the pole's height be denoted by AB = h.

A pole's shadow will create the base BC.

Let the elevation angle be 9,

By the help of trigonometry

tan x = AB/BC

tan x = h/h = 1

x = tan^(-1)

x = 45

Hence, the angle elevation is 45

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Answer:

We know that Billy caught total 4+10=14 fishes including trout and catfish.

P(catching the catfish):

10/14

Step-by-step explanation:

Simplify that into 5/7. As a result, the probability that the next fish that Billy catches will be a catfish is 5/7. Hope it help!

Answer with step-by-step explanation:

Let us find the perfect cubes between 1 to 100.

We know that, 1

3

=1,2

3

=8,3

3

=27,4

3

=64 and the rest numbers i.e. 4,5,6,.... have their cubes greater than 100.

So, only these four numbers have their cubes between 1 to 100.

Thus, there are 4 perfect cubes from 1 to 100.

Now, let's find the cubes between −100 to 0

We know, 0

3

=0,(−1)

3

=−1,(−2)

3

=−8,(−3)

3

=−27,(−4)

3

=−64 and the rest numbers have their cubes less than −100

So, only these 5 numbers have their cubes between −100 to 0 and 4 perfect cubes are there from 1 to 100.

Thus, there are 9 perfect cubes from −100 to 100.

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Answer:

Step-by-step explanation:

3

=1,2

3

=8,3

3

=27,4

3

=64

The rest numbers i.e. 4,5,6,.... have their cubes greater than 100.

So, only these four numbers have their cubes between 1 to 100.

Thus, there are 4 perfect cubes from 1 to 100.

Now, let's find the cubes between −100 to 0

3

=0,(−1)

3

=−1,(−2)

3

=−8,(−3)

3

=−27,(−4)

3

=−64 and the rest numbers have their cubes less than −100

So, only these 5 numbers have their cubes between −100 to 0 and 4 perfect cubes are there from 1 to 100.

Thus, there are 9 perfect cubes from −100 to 100.

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.

In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.

The given function is f'(x) = 3x^3.

No integrating on both side,

f(x) = \(\int3x^3dx\) + C

f(x) = 3x^4/4 + C

As given, the line 81x + y = 0 is tangent to the graph of f.

So, slope at point of tangent; f'(x) = -81

So, 3x^3 = -81

Divide by 3 on both side, we get

x^3 = -27

Taking cube root on both side, we get

x = -3

So putting the value of x in 81x + y = 0, we get

y = 243

Thus, f(x) passes through (-3, 243).

So, 243 = 3/4(81) + C

Multiply by 4 on both side, we get

972 = 243 + 4C

Subtract 243 on both side, we get

4C = 729

Divide by 4 on both side, we get

C = 729/4

So, f(x) = 3x^4/4 + 729/4

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The required expression for

\(log_5(\frac{x}{4} )^2\) = 2 \(log_5\) x - 2 \(log_5\) 4.

Given,

In the question:

The expression is given as:

Log subscript 5 baseline (startfraction x over 4 endfraction) squared

To find the which expression is equivalent?

Now, According to the question:

The expression is given as:

\(log_5(\frac{x}{4} )^2\).

We know that from the properties of logarithm, the following identities

\(log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)\)

Now,  \(log_5(\frac{x}{4} )^2\) = 2 log \(\frac{x}{4}\) (using 1 identity)

Again, Using (2) identity we get,

\(log_5(\frac{x}{4} )^2\) = 2 \(log_5\) x - 2 \(log_5\) 4.

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.