Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question,

The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__

from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .

Since velocity is the rate of change of displacement of a body, then;

VELOCITY = DISPLACEMENT/TIME

displacement is measured in metres while time in seconds.

expressing the formula in terms of its fundamental unit,

v = metre/secs

Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;

V = L/T

V = L * 1/T

V = L * T⁻¹

V = LT⁻¹

Hence the dimension of b is  LT⁻¹.

Note that the dimension of a body is written in terms of its fundamental quantities.

The dimensions of b from the given equation are; B: LT⁻¹

The complete question is;

The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__

Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;

Velocity = Distance/Time

Now, distance is also called Length and represented by L in basic parameters units while Time is represented by T.

Thus, the dimensions of b are; L/T or expressed as LT⁻¹

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Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

Answer:

Step-by-step explanation:

If all 21 coins were dimes, she'd have $2.10. But she has 90 more cents than that. Now for each coin that's a quarter, not a dime, she has 15 cents more. 90/15= 6. So there are 6 quarters, and 21-6 = 15 dimes.

Now we do it backwards to see if it's right. 6 quarters is $1.50, 15 dimes is $1.50, add those together and you get $3. So it's right. 6 quarters, 15 dimes.

Beverley has quarters and dimes in her pocket.

There are 15 dimes and 6 quarters in her pocket.

1 Dime = $ 0.1

1 Quarter = $0.25

Let there be "D" dimes and "Q" Quarters.

So according to the given situation as there are  total 21 coins which can be formulated in equation (1)

\(\rm Q + D = 21 .......(1) \\\)

Also the total value of money is $3 which can be formulated in equation (2)

\(\rm 0.1 D + 0.25 Q = 3 .............(2)\)

Equations (1) and (2) represents two linear equations with two variables

On solving equation (1) and (2) for Q and D we can get

D = 15  and Q = 6

So we can conclude that there are 15 dimes and 6 quarters in Beverley's   pocket.

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Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

35°

Step-by-step explanation:

If BCD is 75, then BCA is 105.

105+40=145

180-145=35

So ABC is 35°

Answer:

4:14  2:7    8:28

Step-by-step explanation:

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Answer:

\(h(x)=-5x^2+10x-2\)

Step-by-step explanation:

\(h(x) = -5 (x - 1)^2 + 3\\\\\implies h(x) = -5 (x - 1)^2 + 3\\\\\implies h(x)=-5(x^2-2x+1)+3\\\\\implies h(x) = -5x^2+10x-5+3\\\\\implies h(x)=-5x^2+10x-2\)

Answer:

Try A

Step-by-step explanation:

382.4cm

Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.

Fixed costs: $34,000

Variable costs per widget: $5.00

Total costs = Fixed costs + (Variable costs per widget × Number of widgets)

Total costs = $34,000 + ($5.00 × 7,000)

Total costs = $34,000 + $35,000

Total costs = $69,000

Average cost per widget = Total costs / Number of widgets

Average cost per widget = $69,000 / 7,000

Average cost per widget ≈ $9.86

Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.

Step-by-step explanation: :)

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

The amount you earn each month before taxes and other deductions is referred to as your monthly gross income. In other words, it's your annual salary divided by 12. It's only a simple metric to aid in budgeting and other routine financial computations.

Annual Salary Amount / Number of Pay Periods = Gross Pay.

Gross pay equals the number of hours worked in a pay period multiplied by the hourly rate (+ overtime hours multiplied by the hourly overtime rate).

Given,

Tax rate=6.2%

=64000(6.2/100)

=3968

And also given another tax rate is 1.45%

=64000(1.45/100)

=92.8

Total=3968+928

=$4896

Therefore, the total gross salary for FICA taxes is $4896.

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

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The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

We have,

We see that there are 10 marbles.

Now,

Number of blue marbles = 2

Number of green marbles = 4

Now,

The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.

After picking a blue marble, there will be 9 marbles left in the bag.

The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.

Now,

P(blue marble and green marble) = P(blue marble) x P(green marble)

= (2/10) x (4/9)

= 8/90

= 4/45.

Therefore,

The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

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Answer:

2:3:5 is already in simplest form

Step-by-step explanation:

Answer:it is 2/15

Step-by-step explanation:

Yeah

Answer:

a) 070°

b) 145°

c) 234°

Step-by-step explanation:

Identify bearing of B from A.

This means you have to start at North arrow at A.

When calculating bearings, they must be in clockwise direction. So the direction you are moving from A to B must be clockwise.

Bearings must also be written with three digits as stated above.

a) The bearing is 70° but since it needs to be written in three digits, it becomes 070°.

b) The bearing is 145°.

c) The bearing is 234°.

Answer:

the answer is A ofcrose

Step-by-step explanation:

The Average total cost per class if a studio member takes 50 classes per year will be 17.8$

The average can be calculated by dividing the sum of observations by the number of observations.

Average = Sum of observations/the number of observations

Given that A yoga studio charges a $140 yearly fee for membership plus 15 dollars for each class.

Yearly charge = 140  $

Charge per class = 15 $

The Number of classes attended by; studio members per year = is 50

We want to find the average total cost per class for this member for a year.

The Total charge = Yearly charge + Number of classes attended x Charge per class

Total charge = 140 + 50 x 15

Total charge = 140 + 750

Total charge = 890$

Than the Average total cost per class =890/ 50

= 17.8

Therefore, the Average total cost per class, if a studio member takes 50 classes per year, will be 17.8$

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The printer that has the better rate of cost per page is B.

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Printer A prints 100 pages for $23.99. The rate is:

= $23.99 / 100

= $0.2399 per page

Printer B prints 275 sheets for $63.99. The rate is:

= $63.99 / 275

= $0.2327

Therefore, based on the above calculations, we can see that $0.2327 is a cheaper and better rate. The printer that has the better rate of cost per page is B.

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Printer A has the better rate of cost per page compared to Printer B. Here's how we can determine that:

To calculate the cost per page for each printer, we need to divide the total cost by the number of pages.

For Printer A, it prints 100 pages for $23.99. So, the cost per page for Printer A is $23.99 / 100 pages = $0.2399 per page, which is approximately $0.24 per page.

For Printer B, it prints 275 sheets for $63.99. Since a sheet usually has two pages (one on each side), we need to consider that. So, the number of pages printed by Printer B would be 275 sheets * 2 pages per sheet = 550 pages.

Therefore, the cost per page for Printer B is $63.99 / 550 pages = $0.11635 per page, which is approximately $0.23 per page.

Comparing the cost per page for both printers, we can see that Printer A has a lower cost per page ($0.24) compared to Printer B ($0.23).

Therefore, the correct answer is: Printer A, because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

Answer:

(From left to right) negative, negative, positive, positive, negative, positive, negative, positive

Answer:

16/81-3/4[

=[16×4-3×81]/[81×4]=-179/324 is your answer

Given

number of years, n = 8

common difference, d = 2250

starting salary, a = 32200

Find

Earnings after 8 years

Explanation

We know sum of n terms is given by

Final Answer

Earnings after 8 years is $320600

Answer:

Hello There!!

Step-by-step explanation:

The answer is 47 as (18+7)×2-3=47.

hope this helps,have a great day!!

~Pinky~

An expression is defined as a set of numbers, variables, and mathematical operations. The solution for the statement "add 8 and 17, double the sum, and then subtract three​" is 47.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The solution for the statement "add 8 and 17, double the sum, and then subtract three​" can be done as,

2(8+17) - 3

= 47

Hence, The solution for the statement "add 8 and 17, double the sum, and then subtract three​" is 47.

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liter

its pretty easyyyyyyyyyy

volume is the measurement of how much space something takes

Answer:

1/6

Step-by-step explanation:

0.333 - 1/3

0.6667 - 1/6

0.2 - 2/10

0.2857 - 2/7

Answer:

3 pieces

Step-by-step explanation:

Key skills needed: Division

1) Rudolph has a \(9\frac{1}{2}\) ft. long piece of wood.

2)He want to divide it into  \(2\frac{3}{4}\) ft. pieces.

3) To find out the maximum number of piece he can make you have to do:

\(9\frac{1}{2}\) ÷ \(2\frac{3}{4}\) --> Convert both to improper form --> ( 9 1/2 is 9x 2 + 1 = 19/2) & (2 3/4 is 2 x 4 + 3  = 11/4) This means it would be: \(\frac{19}{2}\) ÷ \(\frac{11}{4}\).

Dividing by a fraction is the same multiplying by it's reciprocal (The reciprocal of 11/4 is 4/11) so it would be \(\frac{19}{2}\) x \(\frac{4}{11}\)  = \(\frac{76}{22}\) ---> \(3\frac{10}{22}\)

The answer above means Rudolph can cut only 3 pieces, and then he will be left with a little chunk of wood, but that is not big enough to be counted as a whole piece.

Therefore, the answer is 3 pieces

Hope you understood and have a nice day!! :D

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

\(n(A\ u\ B) = 10\)

\(n(A'\ u\ C) = 10\)

\(n(A\ n\ B)' = 6\)

Step-by-step explanation:

Given

\(n(U) = 12\)

\(n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6\)

\(n(A\ n\ B\ n\ C)=4\)

\(n(A\ u\ B\ u\ C)=10\)

Required

Solve a, b and c

There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)

Solving (a):

\(n(A\ u\ B)\)

This is calculated as:

\(n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)\)

From the attachment

\(n(A) = 0+2+4+2 = 8\)

\(n(B) = 0+2+4+2 = 8\)

\(n(A\ n\ B) = 4 +2 = 6\)

So:

\(n(A\ u\ B) = 8 + 8 - 6\)

\(n(A\ u\ B) = 10\)

Solving (b):

\(n(A'\ u\ C)\)

This is calculated as:

\(n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)\)

From the attachment

\(n(A) = n(U) - n(A) = 12 - 8 = 4\)

\(n(C) = 0+2+4+2 = 8\)

\(n(A'\ n\ C) = 2\)

So:

\(n(A'\ u\ C) = 4 + 8 - 2\)

\(n(A'\ u\ C) = 10\)

Solving (c):

\(n(A\ n\ B)'\)

This is calculated as:

\(n(A\ n\ B)' = n(U) - n(A\ n\ B)\)

\(n(A\ n\ B)' = 12- 6\)

\(n(A\ n\ B)' = 6\)

The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.

For the stated question.

The volume of the sphere is modeled by the power function with respect to the radius as;

V = f(r) = 4/3πr³

As, r is independent of any of the coordinate axis.

Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.

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By definition of proportion, the value of x is,

⇒ x = 80

We have to given that;

In a triangle,

Perpendicular = 60

Now, By Pythagoras theorem we get;

60² = 36² + y²

3600 = 1296 + y²

y² = 3600 - 1296

y² = 2304

y = 48

Hence, By definition of proportion;

⇒ x / 48 = 60 / 36

⇒ x = 80

Thus, By definition of proportion, the value of x is,

⇒ x = 80

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