For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.

Answer:

it would be option C)  (x – 10)(x + 2)(x + 6)

Step-by-step explanation:

You have to divide x^3 -2x^2 -68x -120 by x + 2 to get x^2 - 4x -60 and then factor

The factors of the function are  (x + 2)(x - 10)(x + 6).

Any expression which is formed by using constants, variables, and exponents is polynomial, it is solved with the help of mathematical operators. Polynomial is made by the parts "poly" and "nominal"  here "poly" means many and "nomial" means terms.

Given f(-2) = 0

f(x) = x³ - 2x² - 68x - 120  .........(1)

one factor of function is x + 2

divide the function by x + 2

multiply x² by x +2

x²(x + 2) = x³ + 2x²

subtract the term from equation 1 we get,

x³ - 2x² - 68x - 120 - x³ - 2x²

= -4x² - 68x -120 ......(2)

now multiply -4x by x + 2

-4x(x + 2) = -4x² - 8x

subtract the term from equation 2 we get

-4x² - 68x -120 - (-4x² - 8x)

-60x - 120 ........(3)

again multiply -60 by (x + 2)

-60(x + 2) = -60x - 120

subtract from equation 3

-60x - 120 - (-60x - 120) = 0

The quotient we get from the division is,

x² - 4x - 60

here are the factors of x² - 4x - 60 = (x - 10)(x + 6)

Hence, the factors of polynomials are (x + 2)(x - 10)(x + 6).

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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\(m\angle ABC=24^{\circ}\) by the inscribed angle theorem.

Answer:= 24

Step-by-step explanation:

by the inscribed angle theorem.

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

What is independent event ?

In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.

Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:

P(A and B) = P(A) x P(B)

If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.

According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.

We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.

If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.

This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.

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Answer:

(3x+2)(x-5)

Step-by-step explanation:

Factor by grouping

\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)

Answer:

70.06

Step-by-step explanation:

Given the mean = 1217

Standard deviation = 51

And sample size = 80

Mean of bar x = 1217

Sd/√n

= 51/√80

= 5.7060

P(bar x<1220)

P(z < 1220-1217/5.7020)

= P(z<0.5261)

= 0.7006

Therefore the level of confidence in response to this question is 0.7006.

This statement can be made with 70.06% level of confidence.

Answer:

it looks good

Step-by-step explanation:

Answer:

2508

Step-by-step explanation:

We are given that

Principal ,P=2200

Rate of interest, r=7%

Time, t=2 year

We have to find the final account balance after two years.

\(S.I=\frac{P\times r\times t}{100}\)

Using the formula

\(S.I=\frac{2200\times 7\times 2}{100}=308\)

Amount=P+S.I

Amount=2200+308

Amount=2508

Hence,  the final account balance after two years=2508

Answer:

4/5 = 8/10

Step-by-step explanation:

x/5 = 8/10

x = 8/10 × 5

x = 4

Answer: a- (7,7) (4,19) b- m=-12/3=-4/1=-4 c- y=4x+35 d- 48min, it increases by 12min a day

Step-by-step explanation:

i did the assignment

Mr. Waxman's delivery is an illustration of a linear function.

(a) Two points on the graph

The points are: (4,19) and (6,11)

(b) The slope of the graph

The slope (m) is calculated as:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m = \frac{11 - 19}{6- 4}}\)

\(\mathbf{m = \frac{-8}{2}}\)

\(\mathbf{m = -4}\)

The slope of the graph is -4

(c) The equation of the graph

In point-slope form, we have:

\(\mathbf{y -y_1 = m(x - x_1)}\)

So, we have:

\(\mathbf{y -4 = -4(x -19)}\)

In slope intercept form, we have:

\(\mathbf{y = -4(x -19) + 4}\)

Open brackets

\(\mathbf{y = -4x +76 + 4}\)

\(\mathbf{y = -4x +80}\)

The equation of the graph is: \(\mathbf{y = -4x +80}\)

(d) The value of the function at day 0

This means that x = 0

So, we have:

\(\mathbf{y = -4(0) +80}\)

\(\mathbf{y = 0 +80}\)

\(\mathbf{y = 80}\)

Hence, it will take 80 minutes to deliver the package on day 0

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The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

We have,

The angle between the tangent and the radius of a circle is 90.

So,

∠1 = 90

∠2 = 90

And,

48 + 90 + 90 + ∠3 = 360 ______(1)

Solve for ∠3 from (1).

48 + 90 + 90 + ∠3 = 360

48 + 180 + ∠3 = 360

∠3 = 360 - 228

∠3 = 132

Thus,

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

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40 pounds of salami are purchased by a deli for its renowned grinder sandwiches. An illustration of an intermediate good is salami.

Given fill-in-the-blank;

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.

The answer for this case is Intermediate.

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of Intermediate goods.

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Answer: t _(α/2) = 2.060

Step-by-step explanation:

Given that;

sample size n = 26

confidence interval = 95%

level of significance α = ( 1 - 95/100 ) = 0.05

but from the question the salaries (26) are use to estimate the mean of the population so, its a two tail test

therefore our level if significance α will be divided by 2 = 0.05/2 = 0.025

now our degree of freedom df = 26 - 1 = 25

FROM standard t-table value

the critical value of t for the level of significance 0.025

and 25 degree of freedom is 2.060

therefore, t _(α/2) = 2.060

The calculation of the required financial ratios for Sunland Company is as follows:

The return on assets is 6%.

The Asset Turnover is 2.06 times.

The profit margin is 2.9%.

Financial ratios express the numerical relationships of two or more financial statement elements.

Financial ratios are used to make comparisons of the financial performance or position of companies from one year to another (trend analysis) and between companies or the industry average.

Net sales $11,257.9

Net earnings $327.9

Total assets, ending = $5,560.0

Total assets, beginning = $5,370.0

Average assets = (Beginning total assets + Ending total assets) ÷ 2

= $5,465 ($5,560 + $5,370)/2

Return on assets = Net earnings/Average total assets x 100

= 6% ($327.9/$5,465 x 100)

Asset Turnover = Net Sales/Average total assets

= 2.06x ($11,257.9/$5,465)

Profit margin = Net earnings/Net Sales x 100

= 2.9% ($327.9/$11,257.9 x 100)

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Therefore by making a line through following points we can make graph which is parabola in shape

Two things are equal, according to an equation. Like this: 9 + 2 = 11 . It will have an equivalent sign "=". According to that equation, "this equals that" is expressed as "what is on the left (9 + 2) is equal to what is on the right (11).

Here,

Given Equation : x² = 8y

Given Equation agrees with conventional equation of parabola on positive y-axis

x² = 4ay

Comparison of the two equations yields,

4a = 8 ⇒ a = 2

Focus of parabola = ( 0 , 2 ) ( 0 , 2 )

Parabola vertex equals ( 0 , 0 )

Axis of Symmetry = y-axis

To sketch its, we find some points

with x = 4 or -4 we get

4² = 8y ⇒ 16 = 8y ⇒ y = 2

So, points are ( 4 , 2 ) and ( -4 , 2 ) ( -4 , 2 )

we obtain when x = 8 or -8.

(-8)² = 8y ⇒ 64 = 8y ⇒ y = 8

So, points are ( 8 , 8 ) and ( -8 , 8 ) ( -8 , 8 )

Therefore by making a line through following points we can make graph which is parabola in shape

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The correct question is :-

Which graph represents the equation x2 = 8y?

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Answer:

4.5 hours

Step-by-step explanation:

fbdjdbercyTxxivdu

Answer:

Basically You are asking how many hours we need to reach 7:00, if we are at 2:30, so: we need 4hours, to reach 6:30, and and extra 30minutes to reach 7:00pm. The answer is 4hours and 30minutes.

Answer:

F

Step-by-step explanation:

x-9=15 will equal to 24 so x=24

if Allison is 15 but she is 9 years younger then Pam, Pam is x, so all you have to do is count up from 15, so 15+9 which equals 24 Pam is 24 making F the right choice

Answer:

5.58

Step-by-step explanation:

Answer:

I believe the answer is 5.35

Answer:

6(x + 4)

opening brackets

=6x+24 is the answer

Step-by-step explanation:

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

The LCM of 4 and 6 is 12.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, common multiples of 4 and 6 are 12, 24 and 36, but the lowest of those is 12; therefore, the lowest common multiple of 4 and 6 is 12.

Given:

4: 2 x 2

6: 2 x 3

Now, as there is one 2 common in both then it will be written for one time.

and the rest uncommon numbers are written as same as well.

So, LCM( 4, 6)= 2 x 2 x 3 = 12

Hence, the LCM of 4 and 6 is 12.

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Answer: Qualititative, Nominal and Categorical

Explanation:

The variable is qualitative since it does not involve numerical data (i.e. numbers). Rather we're dealing with names or labels.

Since names or labels are involved, and there isn't really inherent order to them, we consider this qualitative data to be nominal.

We can also consider it categorical since each label is a category.

Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

A black bear's average adult weight is 4000 kilograms, or 250 pounds.

Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined. For instance, the sum for 2, 3, 3, 5, 7, & 10 is equal to 30 split by 6, which equals 5.

If a male black bear's birth weight to adult weight ratio is 3:1000, the following sentence can be written:

weight at birth to adult weight is 3 to 1 000.

Let's calculate the normal adult weight using the information provided. Given that the typical birth is 12 ounces, we can establish the following ratio:

weight at birth to adult weight is 3 to 1 000.

Weight of an adult is 12: 3: 1000.

Cross-multiplying results in:

3 x adult weight is equal to 12,000

By multiplying both halves by 3, we obtain:

4000 ounces for an adult.

Divide by 16 to convert teaspoons to pounds:

Adult weight is equal to 4000 / 16 pounds, or 250 pounds.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: slope is (9-(-3))/(25-5)

12/20=0.6

point slope formula y-y1=m(x-x1), m slope (x1, y1) point

y-9=0.6(x-25)

y=0.6x-15+9

y=0.6x-6, x months and y profit.

for 60 months, y=0.6*60-6 or 36-6=$30000 profit

Answer:

Step-by-step explanation:

\((x - 3)2 = 49 \\ \frac{(x - 3)2}{2} = \frac{49}{2} \\ x - 3 = 24.5 \\ x - 3 + 3 = 24.5 + 3 \\ x = 27.5 \\ \)

Answer:

\(x = -4\\\\x = 10\)

Step-by-step explanation:

\(~~~~~(x-3)^2 = 49\\\\\implies (x-3)^2 -49 = 0\\\\\implies (x-3)^2 -7^2 = 0\\\\\implies (x-3+7)(x-3-7) = 0\\\\\implies (x+4)(x-10) = 0\\\\\implies x = -4,~ x = 10\)