Find an equation of the plane parallel to the plane −3x−2y−8z=−14 which passes through the point (−10,−8,−1)(−10,−8,−1).
Answer in the form ax+by+cz=d with a=3

\( \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } \)

let the denominator x² - 3x - 10 is f(x),

• Setting this factor equal to 0,

→ x² - 3x - 10 = 0

• By using Middle term splitting method,

→ x² - 5x + 2x - 10 = 0

→ (x² - 5x) + (2x - 10) = 0

• Taking common,

→ x( x - 5 ) + 2( x - 5 ) = 0

→ ( x - 5 ) ( x + 2 ) = 0

• Again, setting these factors equal to 0,

( x - 5 ) = 0 and ( x + 2 ) = 0

→ x = 5 → x = -2

Hence, the values that would make the fraction undefined is x = 5,-2...

The values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

To find the values that would make the fraction undefined, we need to identify any values of x that would make the denominator equal to zero.

The denominator of the fraction is (\(x^2 - 3x - 10\)). We need to solve the equation:

\(x^2 - 3x - 10 = 0\)

To factorize the quadratic equation, we look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

(x - 5)(x + 2) = 0

Now, we can set each factor equal to zero and solve for x:

x - 5 = 0 => x = 5

x + 2 = 0 => x = -2

Therefore, the values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

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a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

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Answer:

39°

Step-by-step explanation:

A triangle always equals 180° so you have to subtract the other two angles from 180 to find the measure of J

180°-88°-53°= 39°

The probability of choosing an American having Type O blood is  \(0.40\), the probability of choosing an American with Type A or Type B blood is \(0.17\), and the probability of choosing an American with neither Type O nor Type A blood is \(0.48\).

Human blood types are classified into four major types: A, B, AB, and O. A person's blood type is determined by the presence of specific antigens (proteins) on the surface of red blood cells. The percentage of Americans with each blood type is listed in the problem as 40% Type O, 12% Type A, 5% Type B, and 43% Type AB or other types. To find the probability of selecting a person with a certain blood type from the US population, the percentage of people with that blood type is divided by 100.

a. The probability that a randomly chosen American has Type O blood is 0.40 (40%).
b. The probability that a randomly chosen American has Type A or Type B blood is 0.12 + 0.05 = 0.17 (12% + 5%).
c. The probability that a randomly chosen American does not have Type O or Type A blood is \(1 - (0.40 + 0.12) = 0.48\).

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Answer:

11^5/3

Step-by-step explanation:

when you move the 5 over to the right, it always goes above the other exponent. if that makes sense? I use this shortcut.

another way of showing is:

\(x\frac{a}{b} = \sqrt[b]{x^a}\)

Answer:

\(11^{\frac{3}{5} }\)

Step-by-step explanation:

Proof:

The power of a fraction is:

\(x^{\frac{a}{b} } =\sqrt[b]{x^{a} }\)

Step-by-step explanation:

always remember, equations and inequalities are like a scale with 2 pans (left and right).

a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.

for an equation the scale has to stay balanced all the time.

and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.

A

so, in our case here

2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.

2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?

2×5 - 5 >= 3

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = 5 is also a valid solution.

what else ?

let's simplify the inequality

2x - 5 >= 3

2x >= 8

x >= 4

so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.

B

-2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.

-2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?

-2×-5 - 5 >= 3

remember, -×- = +

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = -5 is also a valid solution.

what else ?

let's simplify the inequality

-2x - 5 >= 3

-2x >= 8

x <= -4

a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.

so, really every value of x that is less or equal to -4 is a valid solution for the inequality.

a) Ninety percent is not a trustworthy estimate of the percent of all students who are outraged.

It is important to note that a sample of 5000 responses, while large, may not necessarily be representative of the entire population of students. The sample may have biases or limitations that affect the results of the survey. For example, the survey may have only been distributed to certain groups of students or there may have been a higher response rate from students who are particularly passionate about the issue.
In order to accurately estimate the percent of all students who are outraged, a representative sample of the entire population of students would need to be surveyed, and the survey would need to be designed and administered in a manner that minimizes biases and limitations.

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Complete question:

The university newspaper posts a survey question to its readers asking for opinions on the recently approved increase in fees for parking in a garage. The newspaper receives more than 5000 responses and reports that 90% of students are outraged over the approval of the garage parking fee. Which of the following is true?

a) Ninety percent is not a trustworthy estimate of the percent of all students who are outraged.

b) Ninety percent is an accurate estimate of the percent of all students who are outraged, since the sample size is so large.

there are approximately 2.18 billion license plates that can be generated using this format.

There are 22 letters and 6 digits that can be used on the license plates. Since each license plate has four letters and two digits, there are a total of 6 slots to be filled. For each slot, there are 22 + 6 = 28 possible characters that can be used. Since the characters can be repeated, we can use the fundamental counting principle and multiply the number of possibilities for each slot. Therefore, the total number of license plates that can be generated using this format is:
28 x 28 x 28 x 28 x 28 x 28 = 28^6
This is equivalent to 28 multiplied by itself six times. Using a calculator, this is approximately equal to 2.176782 x 10^9 or 2.18 billion.

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Answer:

For 21: The first option (the uppermost) is correct for question 21. When it is no greater than, it implies that it can be equal to the number.

For 22: x+637 ≤ 2000, let x be the money he can spend for everything else.

Let me know if this helps!

Answer:

well when he buys the ticket he is left with 1,363 dollars

Step-by-step explanation:

The value of  \(\sqrt{0.9}\) is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.

The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.

The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.

Since, 3*3*0.1

= 9*0.1

= 0.9

\(\sqrt{3*3*0.1} \\\)

= 3(\(\sqrt{0.1}\))

\(\sqrt{0.9}\) ≈ 0.94868329805

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Correct Question:

What is the value of  \(\sqrt{0.9}\)

You have the following operation:

6x9

To solve the previous operation you consider that the expression means 6 times 9, that is, that is the sum of six 9s:

6x9 = 9 + 9 + 9 + 9 + 9 + 9 = 54

Hence, the simplied operation is 6x9 = 54

Answer:

Jonathans car can go 15 miles per gallon of gas

Step-by-step explanation:

Do 45 divided by 3

Answer:

15 miles

Step-by-step explanation:

Take the number of miles and divide by the number of gallons

45 miles / 3 gallons

15 miles per gallon

Answer:

1x2 = 2, 32 + 2= 34

Step-by-step explanation:

Answer: There are 198 different combinations.

Step-by-step explanation:

To solve this type of problem, first, we need to identify the selections.

We have 3 selections.

Baby doll, Jigsaw puzzle, and a stuffed dog.

Now, we need to count the numbers of options for each case:

Baby doll: 11 options.

Jigsaw Puzzle: 6 options.

Stuffed dog: 3 options.

To find the total number of different combinations, we need to multiply all the numbers of options together, this is:

Combinations = 11*6*3 = 198

There are 198 different combinations.

Answer:

5cm

Step-by-step explanation:

i dont know maybe I'm right

have a nice day

Answer:

Step-by-step explanation:

A kite is symmetrical about its vertical axis, so

if it is a kite, P is the reflection of  (b,0), so its coordinates are

(-b,0) by reflection about the y-axis.

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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The fish population will be the same as on January 1, 2002 on January 1, 2017 and all the fish in the lake will have died by 2019

The function is given as:

F(t) = 1000(30 + 15t - t^2)

Start by calculating F(0) --- population in 2002

So, we have:

F(0) = 1000(30 + 15(0) - 0^2)

F(0) = 30000

Substitute 30000 for F(t) in F(t) = 1000(30 + 15t - t^2)

1000(30 + 15t - t^2) = 30000

Divide by 1000

30 + 15t - t^2 = 30

Simplify

t^2 - 15t = 0

Divide through by t

t - 15 = 0

Solve

t = 15

This means that

Year = 2002 + 15

Year = 2017

Hence, the fish population will be the same as on January 1, 2002 on January 1, 2017

This means  that F(t)= 0

So, we have:

1000(30 + 15t - t^2) = 0

Divide by 1000

30 + 15t - t^2 = 0

Rewrite as

t^2 - 15t - 30 = 0

Using a graphing calculator, we have

t = 17 (approximated)

This means that

Year = 2002 + 17

Year = 2019

Hence, all the fish in the lake will have died by 2019

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Answer:A

Step-by-step explanation:

The phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.

"Adjusted gross income, or AGI, is your gross income minus certain adjustments. The IRS uses this number as a basis for calculating your taxable income. AGI can also determine which deductions and credits you may qualify for."

Since, Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.

It can be described broadly as adjusted gross income (AGI) minus allowable itemized or standard deductions.

Taxable income includes wages, salaries, bonuses, and tips, as well as investment income and various types of unearned income.

Hence, the phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.

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The correct choice is (e) All of the above is a property for all LP problems.

All Linear Programming (LP) problems have a linear objective function that is to be maximized or minimized (property a), a set of linear constraints (property b), and decision variables (property c). Additionally, LP problems require variables that are all restricted to nonnegative values (property d). Therefore, all of the given properties are true for all LP problems, making option (e) the correct choice.

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Answer:

Option A would be the best option, as the payment would not change. Option B has a lower payment, but that payment is expected to rise and eventually be a bigger payment. Option C would require them to pay it off in 8 years, which would be too much based on their income and they would end up having to get another mortgage. Option C would be better if they wanted to live their temporarily, but Demarco and Tanya would like to live in their house permanently. This makes option A the best option because it is an affordable payment that will not change.

Step-by-step explanation:

The best option will be option A which will be chosen by Demarco and Tanya.

Finance deals with the study of money, management, creation, and investments. Also, finance is divided into the following board of categories such as personal finance, corporate finance, and public finance.

The best option will be option A which will be chosen by Demarco and Tanya as the payment plan would not change in this situation.

Option B has a lower payment, but the payment is expected to increase with time and eventually be a bigger payment.

Also, option C would require them to pay it off in 8 years but both of them want to live permanently not separately. Therefore, the best option to choose will be option A.

So, The best option will be option A which will be chosen by Demarco and Tanya.

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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

Yes it will

Step-by-step explanation:

A circular coin has circumference 32 pi millimeters. Will the coin fit through a slot that is 35 millimeters long? Explain.

The formula for the circumference of a circle = πD

Where D = Diameter which can also be referred to as the length of the circle

Circumference =32π mm

Hence:

32π = πD

Cancel out the π

D = 32 mm

The diameter of the coin = 32 mm

The length of the slot = 35 mm hence, the coin with a diameter of 32 mm can fit into the slot

We are given the equation for f(x), f(x)=1.5x².We are also given the point P(x, y), where

y=f(x) and y=-3.

So, -3 = 1.5x²Or, x² = -2So, x does not exist in R, since there is no real square root of a negative number. Hence, there is no value of x for which P(x, -3) exists. Given that f(x) = 1.5x²Let us determine x such that P(x, y) exists where y = -3.Now, we know that for P(x, y) to exist, y should be equal to f(x). So, y = -3, then,-3 = 1.5x²Or,

x² = -2Now, since the square root of a negative number does not exist in real numbers, there is no value of x for which P(x, -3) exists. Hence, the answer is that there is no such value of x.

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The square root of a negative number does not exist in real numbers, there is no value of x for which P(x, -3) exists.

Here, we have,

We are given the equation for f(x), f(x)=1.5x².

We are also given the point P(x, y), where y=f(x) and y=-3.

So, -3 = 1.5x²Or, x² = -2

So, x does not exist in R, since there is no real square root of a negative number. Hence, there is no value of x for which P(x, -3) exists.

Given that

f(x) = 1.5x²

Let us determine x such that P(x, y) exists where y = -3.

Now, we know that for P(x, y) to exist, y should be equal to f(x).

So, y = -3,

then,-3 = 1.5x²

Or, x² = -2

Now, since the square root of a negative number does not exist in real numbers, there is no value of x for which P(x, -3) exists.

Hence, the answer is that there is no such value of x.

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Answer:

A =338.56 units ^2

Step-by-step explanation:

The area  is now

A = (SF)^2 * s^2

where s is the side length and SF is the scale factor

A = (4)^2 (4.6)^2

A =338.56

Option A is the correct answer. Ellora wants to accumulate 150,000 in an RRSP by making annual contributions of 5,000 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.

First, we have to find the interest rate per quarter, which will be
\(5.5% / 4\)= 1.375%.
The formula for the future value of an annuity is: 
\(FV = (C * [(1 + r)^n - 1] / r)\),

For Ellora, \(FV = $150,000, C = $5,000, and r = 1.375%.\)
Substituting these values into the formula gives:
\(150,000 = 5,000 * [(1 + 0.01375)^n - 1] / 0.01375\)
Simplifying this equation gives:
\(30 = [(1.01375)^n - 1]\)

We can solve this using logarithms:
\(ln 30 = ln [(1.01375)^n - 1]\)
\(ln 30 = n * ln 1.01375 - ln 1.01375e^(ln 30) / e^(-ln 1.01375) = n18.202125 = n\)

Therefore, it will take Ellora 18.202125 years to accumulate 150,000 in her RRSP through \($5,000\)annual contributions made at the beginning of each year with interest of \(5.5%\) compounded quarterly.

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