What is the answer to this, I’m doing an assignment that i forgot to do over spring break

1) i)No solutions in natural numbers. ii) Solution set for integers is x ≤ -20 or x ≥ 31. iii) Solution set for real numbers is x ≤ -20 or x ≥ 31. 2) He bought 1 mathematics book and 15 biology books. 3) f is a function. g is not a function. 4) a) Dom(f) = Dom(g) = R, b)  Dom(f±g) = R, Dom(fg) = R \ {0} = (-∞,0) U (0,∞), c) no function is given d) Dom(fog) = R \ {0}. e)  Dom(gof) = R \ {0}. 5) The roots are x = -1, x = 3, x = -1/2 + √3/2 i, and x = -1/2 - √3/2 i.

1) i) N: Since the quadratic inequality -x²+x+620 has a negative leading coefficient, it does not have any solutions in natural numbers.

ii) Z: To find the solution set in integers, we can factor the quadratic as -x(x-1) + 620 < 0. The roots are x = -20 and x = 31. We can test the intervals (-∞,-20), (-20,0), (0,1), (1,31), and (31,∞) to determine where the inequality is negative. The solution set is x ≤ -20 or x ≥ 31.

iii) R: To find the solution set in real numbers, we can use the same factored form and test the intervals (-∞,-20), (-20,0), (0,1), (1,31), and (31,∞) to determine where the inequality is negative. The solution set is x ≤ -20 or x ≥ 31.

2) Let x be the number of mathematics books and y be the number of biology books. Then we have the system of equations

x + y = 16 (total number of books)

120x + 80y = 1560 (total cost of books)

We can use the first equation to solve for y in terms of x:

y = 16 - x

Substituting this into the second equation gives:

120x + 80(16-x) = 1560

Simplifying and solving for x gives:

40x = 840

x = 21

Substituting this back into y = 16 - x gives:

y = 16 - 21

y = -5

This doesn't make sense, so we made a mistake. Let's check the problem again.

The problem statement says he bought 16 books total. Therefore, it must be that he bought 15 biology books and 1 mathematics book, or vice versa. The total cost is:

120(1) + 80(15) = 1560

Therefore, he bought 1 mathematics book and 15 biology books.

3) We need to show that for every (a,b) in N x N, the ordered pair (ab, a+b) is unique. Suppose we have (a,b) and (c,d) such that ab = cd and a+b = c+d. Then we have:

a = (c+d-b) / b

Substituting this into ab = cd gives

(c+d-b) / b * b * c = c+d

(c+d-b) * c = b(c+d)

c² + cd - bc - bd = 0

(c-b)(c+d) - bd = 0

Since c+d = a+b, this gives:

(c-b)(a+b) - bd = 0

cb + bd - bd = 0

cb = 0

Since a,b,c,d are all positive, this implies that c = b = 0, which contradicts the assumption that (c,d) is in N x N. Therefore, the ordered pair (ab, a+b) is unique for every (a,b) in N x N, and f is a function.

We need to show that there exists an ordered pair (a,b) in R x R such that (a,b) and (a,c) are both in g for some c ≠ b. Let's choose a = b = 0 and c = 1. Then we have:

g(0,0) = 0

g(0,1) = 1

Since (0,0) and (0,1) are both in g but c ≠ b, this implies that g is not a function.

4) a) Dom(f) is the set of all values of x for which f(x) is defined. Here, f(x) = 2x² - 5x + 6 is defined for all real numbers x. Therefore, Dom(f) is the set of all real numbers, or Dom(f) = R.

Similarly, we can find Dom(g) by determining the set of all values of x for which g(x) is defined.

b) For Dom(f±g), we need to find the set of all values of x for which both f(x) and g(x) are defined. Since Dom(f) = R and Dom(g) = R, the intersection of these two sets is also R. Therefore, Dom(f±g) = R.

For Dom(fg), we need to find the set of all values of x for which both f(x) and g(x) are defined and non-zero.

Since f(x) is defined for all real numbers and g(x) is defined for all non-zero real numbers, the set of all values of x for which both f(x) and g(x) are defined and non-zero is the set of all non-zero real numbers. Therefore, Dom(fg) = R \ {0} = (-∞,0) U (0,∞).

c) There is no function, so we cannot find the value.

d) Here, we have f(x) = 2x² - 5x + 6 and g(x) = Since the domain of g is all real numbers except 0, we can solve for the values of x that make g(x) = 0

x² - 4x + 4 = 0

(x-2)² = 0

x = 2

Therefore, the set of all values of x for which g(x) is defined is R \ {2}. Substituting g(x) into f(x), we get:

f(g(x)) = 2(g(x))² - 5(g(x)) + 6

= 2(1/x²) - 5(1/x) + 6

= (2 - 5x + 6x²) / x²

This function is defined for all values of x except 0. Therefore, Dom(fog) = R \ {0}.

e) Since f(x) is defined for all real numbers and the range of f is R, we know that g(f(x)) is defined for all values of x in the domain of g, so it is real except 0. Therefore, Dom(gof) = R \ {0}.

5) To factor the quadratic x² - 2x - 3, we can use the quadratic formula or completing the square

x² - 2x - 3 = 0

x = (2 ± √16) / 2 = 1 ± √4 = 1 ± 2

So the roots of x² - 2x - 3 are x = -1 and x = 3.

To factor the quadratic x² + x + 2, we can use the quadratic formula or completing the square

x² + x + 2 = 0

x = (-1 ± √-7i) / 2

Since the discriminant is negative, the roots are complex conjugates

x = -1/2 + √3/2 i and x = -1/2 - √3/2 i.

Therefore, the roots of the polynomial x⁴ - x³ - 5x² - x - 6 are x = -1, x = 3, x = -1/2 + √3/2 i, and x = -1/2 - √3/2 i.

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The total correction angle needed to converge on your destination is approximately 19.62 degrees.

To determine the total correction angle needed to converge on your

destination, we can consider the off-course distance and the remaining distance to be flown.

Given:

Distance flown: 52 miles

Off-course distance: 6 miles

Remaining distance to fly: 118 miles

To calculate the correction angle, we can use the concept of similar triangles. The ratio of the off-course distance to the total distance flown should be equal to the ratio of the correction angle to the total correction angle.

Let x represent the total correction angle.

Based on the given information, we have the following relationship:

6 miles / 52 miles = x / (52 miles + 118 miles)

Simplifying the equation, we have:

6/52 = x/170

To find x, we can cross multiply:

52x = 6 * 170

52x = 1020

Dividing both sides by 52:

x ≈ 19.62 degrees

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Let's solve your system by substitution.

2x−2y=−4;2x+y=11

Rewrite equations:

2x+y=11;2x−2y=−4

Step: Solve2x+y=11for y:

2x+y=11

2x+y+−2x=11+−2x(Add -2x to both sides)

y=−2x+11

Step: Substitute−2x+11foryin2x−2y=−4:

2x−2y=−4

2x−2(−2x+11)=−4

6x−22=−4(Simplify both sides of the equation)

6x−22+22=−4+22(Add 22 to both sides)

6x=18

6x/6 = 18/6

(Divide both sides by 6)

x=3

Step: Substitute3forxiny=−2x+11:

y=−2x+11

y=(−2)(3)+11

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

Answer:

y=-7/4x +10

Step-by-step explanation:

that the graph, you can plug the equation in desmos,

hope it helps! :)

The missing length is 7.5 cm.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Let the missing length be x cm.

The formula for the surface area of a rectangular prism is:

SA = 2lw + 2lh + 2wh

We are given that the height and width are both 9 cm, so we can substitute those values and simplify:

432 = 2(x)(9) + 2(x)(9) + 2(9)(9)

432 = 18x + 18x + 162

432 - 162 = 36x

270 = 36x

x = 270/36

x = 7.5

Hence, the missing length is 7.5 cm.

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Answer:

the value of M(2) would be 43

Step-by-step explanation:

M(2) mean y

y = 9t+25

= y=9(2) + 25

y = 18 + 25

y = 43

Answer:

Step-by-step explanation:

M(2) = 43; If Hazel mows 2 yards, she will earn $43.

Answer:

\(13 \frac{2}{11} \)

Step-by-step explanation:

Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

11•13=143

1a) The domain is a set of all real numbers not equal to 5

1b) The domain is a set of all real numbers not equal to 4

Domain of a function is the set of all possible input values that make the function defined.

1a) We are given the function;

C(x) = -3²/(x - 5)

The domain will be a set of values that makes the denominator not equal to zero. Thus;

The domain is a set of all real numbers not equal to 5

1b) The function is; R(x) = 4x/(3x - 12)

The domain will be a set of values that makes the denominator not equal to zero. Thus;

The domain is a set of all real numbers not equal to 4

2a) Function is;

f(x) = (x + 8)/(2x - 1)

f(2) = (2 + 8)/(2(2) - 1)

f(2) = 10/3

f(0) = (0 + 8)/(2(0) - 1)

f(0) = -8

f(-1/2) = (-1/2 + 8)/(2(-1/2) - 1)

f(-1/2) = -15/4

2b) Function is;

r(t) = (t² + 8)/(t³ - 25t)

r(3) = (3² + 8)/(3³ - 25(3)) = -17/48

r(2) = (2² + 8)/(2³ - 25(2)) = -12/42 = -2/7

r(-1) = ((-1)² + 8)/((-1)³ - 25(-1))  = 9/24 = 3/8

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The independent quantity for the given situation is time.

We are given that the factory produces 125 bags in every 10 seconds.

Because the number of bags is dependent on the time it takes to make bags, the dependent quantity in this case is the number of bags.

But time is an independent quantity.

Let us understand by taking examples;

It can be seen that in 20 seconds, the company will produce 250 bags.

It can also be seen that in 0 seconds, the company will produce 0 bags.

So, as time increases or decreases, the number of bags increases and decreases respectively.

Therefore, time is the independent quantity.

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A'C' = CD = 150. So, the answer is D) 150.

In asymptotic triangles, corresponding angles are equal. We are given that ∠BAC = ∠B'A'C' = 70° and ∠ACD = ∠A'C'D' = 80°.

Since ∠BAC = ∠B'A'C', it follows that ∠A'B'A = ∠B'AC'. Therefore, ∠A'B'AC' is an isosceles triangle with base angles of 70° each.

In an isosceles triangle, the base angles are congruent. So, ∠B'AC' = ∠A'AC' = 70°.

The sum of the angles in a triangle is 180°. Therefore, ∠B' = 180° - 70° - 70° = 40°.

Now, consider the triangle A'AC'. We know that ∠A'AC' = 70° and ∠AC'A' = 40°. The sum of the angles in a triangle is 180°, so ∠AA'C' = 180° - 70° - 40° = 70°.

Since ∠A'C'D' = ∠ACD = 80°, it follows that ∠A'C'D' + ∠AA'C' = 80° + 70° = 150°.

In the triangle A'C'D', the sum of the angles is 180°. Therefore, ∠DA'C' = 180° - 150° = 30°.

Now, we have an isosceles triangle A'CD with ∠DA'C' = ∠ACD = 30°.

In an isosceles triangle, the base angles are congruent. So, ∠A'CD = ∠ACD = 30°.

We know that AC = 150. Since A'CD is an isosceles triangle with base angles of 30° each, the triangle is symmetric. Therefore, A'C' = CD = 150.

So, the answer is D) 150.

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Given question is incomplete, the complete question is below

Let Δ(AB,CD) = Δ(A'B', C'D') be two asymptotic triangles such that m(∠BAC) = m(B'A'C') = 70° and m(ACD) = m(∠A'C'D') = 80°.Then, if AC = 150 then A'C' = ?

A) 70, B) 80, C) 10, D) 150

Answer:

More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.

I hope this helps you

Step-by-step explanation:

Answer:

Do you take screen shoot otherwise we cannot understand your question

Step-by-step explanation:

Answer:

-21z+238

Step-by-step explanation:

Use distributive property

Based on the calculations, the sample standard deviation is equal to 4.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{\bar x\;-\;u}{\delta}\)

Where:

In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:

Note: Variance, δ² = 16

Taking the square root of the variance, we have:

Standard deviation, δ = √16

Standard deviation, δ = 4.

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Complete Question:

A sample of n=225 scores has \(\bar x\) = 103 and δ² = 16. What is the sample standard deviation?

The length of one side of the pool if the pool has an area of 121 square feet is 11 feet

The formula for calculating the area of the square pool is expressed as:

\(A_s=L^2\)

L is the length of one side of the pool

If the area of the square pool is 121 square feet, hence;

\(121 = L^2\)

Take the square root of both sides;

\(\sqrt{121}= \sqrt{L^2}\\ \sqrt{121}=L\\11=L\\Swap \ sides\\L = 12ft\)

Hence the length of one side of the pool if the pool has an area of 121 square feet is 11 feet.

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The amount of interest would be $3076.51 in the account after 4 years.

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A = P(1+r/100)ⁿ

Where:

A = the future value of the investment or loan

P = the principal investment or loan amount

r = the interest rate (decimal)

n = the number of compound periods

Given that Rafi has $6,629 in an account that earns 10% interest compounded annually.

p = $6,629

r = 10%

t = 4 years

A = P(1+r/100)ⁿ

Substitute the values of p,r, and t in the formula,

A = 6,629 (1 + 10/100)⁴

A = 6,629 (1 + 0.10)⁴

A = 6,629 (1.1)⁴

A ≈ 9705.51

Now, C.I. = A - P

So C.I. = 9705.51 - 6,629 = $3076.51

Therefore, the amount of interest would be $3076.51 in the account after 4 years.

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A list of steps, in order, that will solve the following equation include the following:

In order to create a list of steps and determine the solution to the equation, we would have to add 5 to both sides and divide both sides by 2 in order to open the parenthesis as follows;

2(x + 3) – 5 = 123

2(x + 3) – 5 + 5 = 123 + 5

2(x + 3) = 128

By dividing both sides of the equation by 2, we have the following:

2(x + 3)/2 = 128/2

x + 3 = 64

By subtracting 3 from both sides of the equation, we have the following:

x + 3 - 3 = 64 - 3

x = 61

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The monthly payment is obtained with the following equation:

\(A = 6960\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The monthly payment formula is defined as follows:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

For this problem, the lone parameter given is P = 6960, hence the equation is:

\(A = 6960\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The problem is incomplete, hence the formula used to obtain the monthly payment was presented.

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The Department of Zoology at Virginia Tech conducted a study to compare the density of organisms at two different stations on Cedar Run, a secondary stream in the Roanoke River drainage basin. The study aimed to determine if there was a significant difference in the variances of the number of organisms per square meter of water at the two locations.

To test the hypothesis at the 0.05 level of significance that sigma^2_1 = sigma^2_2 against the alternative that sigma^2_1 ≠ sigma^2_2, we will perform an F-test. Here are the steps:

1. Calculate the sample variances (s^2) for both sets of density measurements.
2. Find the ratio of the larger sample variance to the smaller sample variance: F = (s^2_1) / (s^2_2), where s^2_1 > s^2_2.
3. Determine the degrees of freedom for both sets of data: df1 = n1 - 1 and df2 = n2 - 1, where n1 and n2 are the sample sizes.
4. Find the critical F values for a two-tailed test at the 0.05 level of significance using the F-distribution table, with df1 and df2 as the row and column indexes.
5. Compare the calculated F value to the critical F values. If the calculated F value is between the lower and upper critical F values, then we fail to reject the null hypothesis (sigma^2_1 = sigma^2_2). If the calculated F value is less than the lower critical F value or greater than the upper critical F value, we reject the null hypothesis and accept the alternative hypothesis (sigma^2_1 ≠ sigma^2_2).
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Answer:

A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42

Step-by-step explanation:

Answer:

a+b=-34

Step-by-step explanation:

a and b represent the two unknown numbers, which we know to sum to -34

Answer: in correct and the answer is 360 or 720

The expression for 4k - 9 in terms of t such that the sum starts from 0 is -9.

Given expression is 2(4k - 9). We are supposed to write an expression for 4k - 9 in terms of t such that the sum starts from 0.

To write the expression for 4k - 9 in terms of t such that the sum starts from 0, we need to find the value of k.Let the value of k be 'x'.

Now, putting x in the given expression, we have;

2(4x - 9) = 8x - 18

This means that the sum of 8x - 18 has to start from 0.

Now, if we add 18 to both sides of this expression, we have;

8x - 18 + 18 = 8x0 = 8x

Hence, the value of x is 0.

So, putting x = 0 in the expression 4k - 9,

we have;4k - 9 = 4(0) - 9= -9

Therefore, the expression for 4k - 9 in terms of t such that the sum starts from 0 is -9.

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Answer:

x = 3

Step-by-step explanation:

By tangent secant segment theorem:

\(x \times 12 = 4 \times 9 \\ \\ \implies \: 12x = 36 \\ \\ \implies \: x = \frac{36}{12} \\ \\ \implies \: x = 3\)

Answer:

x=3

Step-by-step explanation:

Answer:

3x³ - 15x² + 18x

Step-by-step explanation:

Given

3x(x² - 5x + 6) ← distribute the parenthesis by 3x

= 3x³ - 15x² + 18x ← in standard form

The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Answer:

I believe its 17.

Step-by-step explanation:

If you count the dots above 8, 9, 10, 11 and 12 you will get your answer.

Answer:

131560.072

Step-by-step explanation:

Because it is increase so we add humdred to the percent and then divide by hundred - 18+100/100 = 1.18

eight years - 1.18 raised to the pwer of 8

worth - 35000

hence it will be - 1.18 raised to the power of 8 x 35000

thank you