HELP!
Name the relationship between the two angles 'a' and 'b'.

Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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Answer:

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Step-by-step explanation:

To decide by virtue of what many age it will love trio person engaged in private ownership of business, we can use the rule of 72 for plain interest. The rule of 72 states that you can approximate the number of age it takes for an expenditure to double by separating 72 apiece annual interest. In this case, we ask about by virtue of what long it takes to trio person engaged in private ownership of business, so we'll separate 72 for one interest (5%).72 / 5 = 14.4According to the rule of 72, it would take nearly 14.4 age to double person engaged in private ownership of business at a 5% annual interest. Since we be going to trio person engaged in private ownership of business, we need to double it two times.14.4 age x 2 = 28.8 ageTherefore, it would take nearly 28.8 age to trio person engaged in private ownership of business at a 5% natural interest.In Spanish:Para determinar cuántos años tomará triplicar el money, podemos utilizar la regla del 72 para el interés plain. La regla del 72 establece que puedes aproximar el número de años que se tarda en duplicar una inversión dividiendo 72 entre la tasa de interés anual. En este caso, queremos weapon cuánto tiempo tomará triplicar el money, así que dividiremos 72 entre la tasa de interés (5%).72 / 5 = 14.4Según la regla del 72, tomaría aproximadamente 14.4 años duplicar el money a una tasa de interés anual del 5%. Como queremos triplicar el money, necesitamos duplicarlo do veces.14.4 años x 2 = 28.8 añosPor lo tanto, tomaría aproximadamente 28.8 años triplicar el money a una tasa de interés natural del 5%. La respuesta correcta es 28.8 años.

The value of the function at x = 4 is 8.79.

Tangent line approximation is the approximation of any function using a linear function. It is also called as linear approximation.

It allows us to approximate the value of a general function with a more simpler linear function.

Given that,

f(1) = 2

f'(x) = \(\sqrt{x^{2} +2cos x + 3}\)

We have the formula for linear approximation as,

f(x) = f(a) + f'(a) (x - a)

Here x = 4 and a = 1

f(a) = f(1) = 2

f'(a) = f'(1) = \(\sqrt{1^{2} +2cos 1 + 3}\) = 2.254

Substituting,

f(4) = 2 + (2.254) (4 - 1)

     = 8.762 ≈ 8.79

Hence the value of f(4) is 8.79.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

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In linear equation, 57 cents per cubic foot  should clint charge for a cubic foot .

What are a definition and an example of a linear equation?

cubic meter =  [3.28 ft ]^3  ≈ 35.29 cubic feet

So,

 price [ in cents] / 35.29  cubic feet  = 2000 / 35.29  ≈  57 cents per cubic foot

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The absolute value of y, and the square root of (xy to the power of z) is \(xy^{z}\)

Floats are a type of number representation that allows us to store very large or very small numbers with a high degree of precision. In computer programming, it is often used to represent real numbers, such as decimals.

In this problem, we are given three float numbers x, y, and z and asked to perform various mathematical operations with them.

Let's start with the first operation: x to the power of z. This means that we want to find x raised to the power of z. This can be written mathematically as xᵃ.

The next operation is x to the power of (y to the power of z). This means that we want to find x raised to the power of y raised to the power of z. This can be written mathematically as x(yᵃ).

The third operation is the absolute value of y. The absolute value of a number is its magnitude, or distance from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. Mathematically, it can be written as |y|.

Finally, we have to find the square root of (xy to the power of a). The square root of a number is the value that, when multiplied by itself, gives the original number.

The square root of 25 is 5 because 5 * 5 = 25. This can be written mathematically as

=> √(xyᵃ).

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In the ANOVA test, factors don't directly explain variation, levels don't account for external variation, and the blocking factor's significance should be considered despite a significant main factor for accurate interpretation.

1. A factor in an ANOVA test that does not necessarily describe the cause of the variation in the data is False. A factor represents a categorical variable or an independent variable that is believed to have an effect on the dependent variable. It is used to explain the observed differences among groups or treatments, but it does not directly explain the cause of the variation.

2. A level in an ANOVA test does not account for the variation outside of the main factor is False. A level refers to the different values or categories within a factor. It represents the specific groups or treatments being compared within a factor.

Levels do not account for variation outside of the main factor; rather, they help analyze the variation within the factor and assess the differences between the levels.

3. The significance of the blocking factor is still important even if the main factor is statistically significant in a randomized block ANOVA is False. A blocking factor is included to account for potential sources of variation that are not of primary interest but might affect the outcome variable.

It helps control for confounding variables or other sources of variation, and its significance should be considered in interpreting the results accurately. Both the main factor and the blocking factor need to be evaluated to understand the overall significance and impact of different factors on the outcome variable.

Therefore, all the answers are false.

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Note: The question would be as

1. A Factor In An ANOVA Test Describes The Cause Of The Variation In The Data. True Or False?

2. A Level In An ANOVA Test Accounts For The Variation Outside Of The Main Factor. True Or False?

3. As Long As The Main Factor Is Statistically Significant With Randomized Block ANOVA, There Is No Concern About The Significance Of The Blocking Factor. True

13) SSS

14) SAS

15) ASA

16) AAS

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The solutions to the systems of equations graphically are (-2, 3) and (3, 8)

From the question, we have the following parameters that can be used in our computation:

f(x) = x + 5

g(x) = x² - 1

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (-2, 3) and (3, 8)

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Question

Estimate the solution to the following system of equations by graphing.

f(x) = x + 5

g(x) = x² - 1

Therefore , the problem of equation comes out to be Four is the solution when transformed into an equation.

An equilibrium is a rule that shows two expressions are equal by using the equals sign.The connotations of the measures the overall and its cognates might differ slightly among languages. For example, whereas in English an equation is really any well-formed formula made up of two expressions connected by the equals sign, an equation in French is defined as comprising one or more variables.

When attempting to solve a variable equation, the first step is to identify the variables with values that lead to equality.

The equation's solutions are the values of the unknown variables that satisfy the equality as well as the unknown variables that the equation should be solved.

Here,

8N+2N-6=34

10N-6=34

10N=40

N=4

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Answer:

p = 43

Step-by-step explanation:

Here, we have it that;

(x^22) * (x^7)^3 = x^p

From law of indices

(y^a)^b = y^ab

and also;

y^a * y^b = y^(a + b)

applying these, we have it that;

(x^7)^3 = x^(7* 3) = x^21

Thus, we have it that;

x^22 * x^21 = x^(22 + 21) = x^43

So we have it that the value of p is 43

Answer:

13p

Step-by-step explanation:

because the P it have 1 hidden there

12p + 1p = 13p

The number of hours Jackson worked washing cars last week is 8 hours

The number of hours Jackson worked landscaping cars last week is 6 hours

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

Jackson worked a total of 14 hours

x + y = 14

Jackson earned a total of $152

$10 per hour washing cars and $12 per hour landscaping

10x + 12y = 152

The simultaneous equation

x + y = 14

10x + 12y = 152

using calculator to solve the equation  we have that

x = 8 and y = 6

hence hours of washing cars is 8 hours while hour s of landscaping is 6 hours

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The length of BP is 14.4 meters.

To find the length of BP, we can use the property that states that when two chords intersect inside a circle, the product of the segment lengths on one chord is equal to the product of the segment lengths on the other chord.

Using this property, we can set up the equation:

AP * PC = BP * DP

Substituting the given values:

12 m * 6 m = BP * 5 m

Simplifying:

72 m^2 = BP * 5 m

To solve for BP, divide both sides of the equation by 5 m:

72 m^2 / 5 m = BP

Simplifying:

14.4 m = BP

Therefore, the length of BP is 14.4 meters.

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It would take 20 seconds for both coolers to contain the same amount of water.

To determine the number of seconds it would take for each cooler to contain the same amount of water, we can use the formula:

amount of water = rate of change x time

For the first cooler, we know that it is initially empty and filling at a rate of 0.1 gallons per second. Let's say it takes t seconds for this cooler to contain the same amount of water as the second cooler, which initially contains 7 gallons of water and is draining at a rate of 0.25 gallons per second.

Using the formula above for the first cooler, we can write:

amount of water in first cooler = 0.1t

For the second cooler, we know that it is initially containing 7 gallons of water and draining at a rate of 0.25 gallons per second. So, after t seconds, the amount of water in the second cooler would be:

amount of water in second cooler = 7 - 0.25t

To find the time it would take for both coolers to contain the same amount of water, we can set the two equations above equal to each other and solve for t:

0.1t = 7 - 0.25t

0.35t = 7

t = 20

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The 30th term a30 of the sequence is -1445

The definition of the function is given as

arithmetic sequence of 1,-4,-9,-14

The above definitions imply that we simply subtract 5 from the previous term to get the current term

Using the above as a guide,

so, we have the following representation

First term, a = 1

Common difference, d = 5

An arithmetic sequence is represented as

a(n) = a + (n - 1)d

For the 30th term, we have

a(30) = a + 29d

So, we have

a(30) = 1 + 29 * -5

Evaluate

a(30) = -144

Hence, the value of a30 is -144

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The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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It would take 12 men 18 days to complete the job.

1) g ∝ h

g = kh; where k is the constant of variation.

g = 64, h = 8, hence:

64 = 8k

k = 8

g = 8h

2) j ∝ 1/h

j = k/h; where k is the constant of variation.

j = 190, h = 7, hence:

190 = k/7

k = 1330

j = 1330/h

When h = 70:

j = 1330/70

j = 19

3) y represent number of men and x represent the days

y ∝ 1/x

y = k/x

9 = k/24

k = 216

y = 216/x

For 18 days:

y = 216/18 = 12 men

Hence it would take 12 men 18 days to complete the job.

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Answer:

6/50

Step-by-step explanation:

0.12 as a fraction is 6/50.

Answer:

3/25

Step-by-step explanation:

12/100=6/50=3/25 .

The speed of bullet just before the impact would be 1.28 x 10^3 meter per second.

Let the speed of the bullet before impact be 'V₀.'

According to the question, we are given the mass of the rod 'M' = 4 kg. Length of the rod 'l' = 0.5 meter. The angle of the bullet's path 'Θ' = 60 degree and the angular velocity 'ω' = 10 rad/s.

   For bullet, the mass 'M' = 3 g = 3 x 10^3 kg. and the velocity is V₀.

  According to the law of conservation of momentum, we get

L(bullet) = l (bullet + rod)

mV₀ (l/2 sinΘ) = Iω

mV₀ x (l/2 sinΘ) = [ ml²/ 12 + m (l/2) ²] x ω

By cancelling the like terms, we get the equation as,

V₀ = (m +3m) x l/6m sin Θ

  By calculating the above equation, we get,

V₀ = 1.28 x 10^3 meter per second.

  Therefore, the speed of bullet before the impact is 1.28 x 10^3 meter per second.

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The answer is (d) no, because grade level is a lurking variable which may well be confounded with the variables under consideration.

The experimental design described in the scenario is not ideal for determining a cause-and-effect relationship between reading and academic performance. The design lacks proper control and fails to address the potential influence of lurking variables, specifically grade level. Grade level could be a confounding variable, meaning it may be associated with both the amount of reading and the academic performance of the students.

In this experiment, different grade levels are assigned to different conditions: eighth graders with extra reading time, seventh graders with extra reading time, and sixth graders with no extra reading time (control group). The issue arises because each grade level could have different levels of academic readiness, maturity, or other factors that could impact their performance. Therefore, any differences in the mean academic performance observed among the groups could be attributed to grade level rather than the intervention itself.

To address this, the experiment could be improved by randomly assigning students from each grade level to the different conditions. This randomization would help ensure that any differences observed in academic performance are more likely to be due to the extra reading time rather than the inherent differences between grade levels.

Overall, the experimental design needs to account for the potential confounding effect of grade level to establish a stronger cause-and-effect relationship between reading time and academic performance.

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Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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Answer:

549.8 inches³

Step-by-step explanation:

Volume of Cylinder = height × base, where base = \(\pi\)r².

The radius (r) is given, 5 inches, and so is the height, 7 inches.

We simply substitute these values into the equation.

V(volume)  = 7 × \(\pi\) × 5²

                  = 175\(\pi\)

                  = 549.77871437821...

when we round that to the nearest tenth,

                  ≈ 549. 8

Answer:

real numbers

Step-by-step explanation:

f = 8.1432

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer:

the iqr is 3 , and the range is 7

Step-by-step explanation:

The percent decrease in the travel time after getting a new job is 36%.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.

decrease in time = 48 - 30.72

decrease in time = 17.28

Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.

percent decrease = (17.28 / 48) x 100

percent decrease = 36%

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