Find prime factors of
48

Answers

Answer 1

So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.


Related Questions

Refer to the table summarizing service times​ (seconds) of dinners at a fast food restaurant. How many individuals are included in the​ summary? Is it possible to identify the exact values of all of the original service​ times?
Time (sec) Frequency
60 to 119 7
120 to 179 24
180 to 239 14
240 to 299 1
300 to 359 4

Answers

Answer:

Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:

7 + 24 + 14 + 1 + 4 = 50

Therefore, there are 50 individuals included in the summary.

Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.

Determine the period.
NAV
8 10 12 14
3
2
1
-1
-2
-3
2

Answers

Answer:

7

Step-by-step explanation:

V looking shape has ends at 1 & 8

8 - 1 = 7

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En un terreno rectangular que mide 64 cm por 18 cm, van a construir en el 50 % una casa ¿Cuál es el área construida?

Answers

The built area of 50% of the house on the rectangular piece of land measures 576 cm^2.

To find the built area of 50% of a house on a rectangular piece of land, we need to calculate the area of the rectangular piece of land and then determine 50% of that area.

The rectangular piece of land has dimensions of 64 cm by 18 cm. To calculate the area, we multiply the length by the width:

Area = Length * Width

Area = 64 cm * 18 cm

Area = 1152 cm^2

The total area of the rectangular piece of land is 1152 cm^2.

To find the built area, which is 50% of the total area, we multiply the total area by 50% (or 0.5):

Built Area = Total Area * 50%

Built Area = 1152 cm^2 * 0.5

Built Area = 576 cm^2

Therefore, the built area of 50% of the house on the rectangular piece of land measures 576 cm^2.

It's important to note that this calculation assumes that the built area is uniformly distributed on the land and represents half of the house's total area. The actual shape and distribution of the house may vary, but this calculation provides an estimate of the built area based on the given information.

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Note the translate question is:

On a rectangular piece of land that measures 64 cm by 18 cm, they are going to build 50% of a house. What is the built area?

Answer:

Step-by-step explanation:

waza skibidi domo dom yes yes  insanito free fire

A race car driver won a 200 mile race with a speed of 159.5 miles per hour. Find the driver's time.

Answers

Answer:

1.255 seconds

Step-by-step explanation:

We can use the formula:

time = distance ÷ speed

to find the driver's time. Here, the distance is 200 miles and the speed is 159.5 miles per hour. Substituting these values into the formula, we get:

time = 200 miles ÷ 159.5 miles per hour

time = 1.255 seconds

Find the area of the parallelogram

Answers

The area of the parallelogram is  189 square units

How to determine the area

First, we have the determine the length of the base and height.

The distance between the lines x = 9 and f(x) = 9 + 2x is the height

We have that the line parallel to f(x) passes through (4, 11)

The equation in point-slope form is;

y - 11 = 2(x - 4

y = 2x + 3

Substitute x = 9 in the equation,  y = 2x + 3.

y = 2(9) + 3 = 21

The  points are then (9, 21) and (9, 0).

The distance between the y-axis and the line x = 9 is the base.

Base = 9 units.

The formula for calculating area of a parallelogram is given by ;

= base × height

= 9 × 21

= 189 square units.

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H
6:00 PM
What is a frostbite?

Answers

Its a skin injury that occurs when exposed to extreme low temperatures, causing the freezing of the skin or other tissues, commonly affecting the fingers, toes,nose, ears, cheeks and chin areas.

Ayesha is the marketing manager for Superior Stationery Suppliers, a company that supplies a variety of stationery items to its customers, mostly businesses. Ayesha has started a process to understand the key buying motivations for customers. Ayesha must consider each of the following variables in the process, except...

Answers

where are the choices? we cant answer

c) A company is considering expanding its business. The expansion will cost 350million initially for the premises and a further sh150 million to refurbish the premises with new equipment. Cash flow projections from the project show the
following cash flows over the next six years.

Year Net cash flows
Sh 000
1 70000
2 70000
3 80000
4 100000
5 100000
6 120000

The equipment will be depreciated to a zero resale value over the same period and after the sixth year, it is expected that the new business could be sold for sh350 million.

Required:

Calculate:

i. The payback period for the project. (5 marks)

ii. The accounting rate of Return (ARR) , using the average investment method.
(5 marks)

iii. The net present value (NPV) of the project. Assume the relevant cost of capital is 12%.
(5 marks)

iv. The internal Rate of Return (IRR) of the project. (5 marks)

Answers

i. The payback period for the project is 6 years.

ii. The accounting rate of return (ARR) using the average investment method is 21.18%.

iii. The net present value (NPV) of the project is -165,143.

iv. The internal rate of return (IRR) of the project is approximately 19.61%.

i. The payback period for the project:

To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.

Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.

Cumulative Cash Flow:

Year 1: 70,000

Year 2: 70,000 + 70,000 = 140,000

Year 3: 140,000 + 80,000 = 220,000

Year 4: 220,000 + 100,000 = 320,000

Year 5: 320,000 + 100,000 = 420,000

Year 6: 420,000 + 120,000 = 540,000.

The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.

So, the payback period for the project is 6 years.

ii. The accounting rate of return (ARR) using the average investment method:

ARR = Average Annual Profit / Average Investment

Average Annual Profit = Sum of Net Cash Flows / Number of Years

Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6

Average Annual Profit = 540,000 / 6

Average Annual Profit = 90,000

Average Investment = (Initial Investment + Residual Value) / 2

Average Investment = (500 million + 350 million) / 2

Average Investment = 425 million.

ARR = 90,000 / 425,000 = 0.2118 or 21.18%

iii. The net present value (NPV) of the project:

To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.

NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex]  + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.

[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)

Calculating each term and summing them up:

NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million

NPV = -165,143

Therefore, the net present value (NPV) of the project is -165,143.

iv. The internal rate of return (IRR) of the project:

To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.

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Which of the following is the prime factorization of 15?
01x15
03x5
02x2x5
05x2

Answers

Answer: The second one, 3×5

Step-by-step explanation:

We can use a factor tree to determine the prime factorization of 15. We first choose factors of 15, and the only factors we can use besides 1 and 15 are 3 and 5.

                                                             15

                                                            3×5

That is all, because the final numbers listed are prime and we cannot perform any further actions. The prime factorization of 15 is 3×5, or in exponential form, [tex]3^1[/tex]×[tex]5^1[/tex].

Note: You may notice with other numbers that there are several factors to choose from. That's okay, because in the end it will give you the same result.

Hope this helps!

A grain su nas a cylindrical shape. Its diameter is 19 ft, and
its height is 50 ft.
Answer the parts below. Make sure that you use the correct
units in your answers. If necessary, refer to the
list of geometry formulas.
(a) Find the exact volume of the silo. Write your answer in terms of
Exact volume:
Approximate volume:
(b) Using the ALEKS calculator, approximate the volume of the silo.
To do the approximation, use your answer to part (a) and the button on the calculator. Round
your answer to nearest hundredth.

Answers

a. The exact volume is V = π(9.5 ft)²(50 ft) = 225π ft³.

b. Rounding the answer to the nearest hundredth, the approximate volume of the silo is 706.50 ft³.

(a) The exact volume of the silo can be found using the formula for the volume of a cylinder, which is V = πr²h,

where r is the radius and h is the height.

Since the diameter is given, we can divide it by 2 to find the radius.

The radius of the silo is 19 ft / 2 = 9.5 ft.

The height of the silo is 50 ft.

Using these values, the exact volume of the silo is:

V = π(9.5 ft)²(50 ft) = 225π ft³.

The approximate volume can be found using the ALEKS calculator, which is not available in this text-based interface.

However, you can use the exact volume calculated above to manually approximate the volume to the nearest hundredth by evaluating the expression using the value of π as approximately 3.14 or 22/7.

(b) Approximate volume using the ALEKS calculator: [Please use an online calculator or a scientific calculator to approximate the value to the nearest hundredth].

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Find the average rate of change of each function over the interval (0, 3). Match each representation with its respective average rate of change.
-1
-2
X
0
6
= 2² + 2x - 5
1
3
2
3 4
-3

Answers

The correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

To match the representations with their respective average rates of change, we need to calculate the average rate of change for each function over the interval (0, 3) and compare it to the given values.

Let's calculate the average rate of change for each function:

Function: 2² + 2x - 5

To find the average rate of change, we need to calculate the difference in function values divided by the difference in x-values:

Average rate of change = (f(3) - f(0)) / (3 - 0)

Average rate of change = ((2² + 2(3) - 5) - (2² + 2(0) - 5)) / 3

Average rate of change = (13 - (-1)) / 3

Average rate of change = 14 / 3

Match: X = 14/3

Function: -1

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 3

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -3

Since the function is constant, the average rate of change is 0.

Match: 0

Therefore, the correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

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The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.
The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.

Answers

The Hernandez family bought 3 large pizzas and cut them into equal slices.
The total number of slices they got was 24.
Therefore, each pizza was cut into 8 slices.
On the other hand, the Wilson family ordered several large pizzas.
They also cut the pizzas so that each pizza had the same number of slices.
The relationship between the number of pizzas and the total number of slices is given by y = 10x, where x is the number of pizzas and y is the total number of slices.
This means that each pizza was cut into 10 slices.
The Hernandez family got a total of 24 slices, while the Wilson family's total number of slices depends on the number of pizzas they ordered.
The pizzas bought by both families were large, and they both cut their pizzas into equal slices.

a sphere with radius r and a cylinder with radius r and a height of r are shown below. how do the surface areas of these solid figures compare?

which statements are correct? check all that apply

A: the surface area of the sphere in terms of r is 4(pi)r^2 square units

B: the surface area of the cylinder in terms of r is 4(pi)r^2 square units

C: the surface area of the cylinder in terms of r is 6(pi)d^2 square units

D: the surface area of the cylinder and sphere are the same

E: the surface area of the cylinder and sphere are NOT the same

Answers

The correct statements are A and B, while C, D, and E are incorrect.

The correct statements are:

A: The surface area of the sphere in terms of r is 4(pi)r^2 square units. This is true. The formula for the surface area of a sphere is given by A = 4(pi)r^2, where r is the radius.

B: The surface area of the cylinder in terms of r is 4(pi)r^2 square units. This is true. The formula for the lateral surface area of a cylinder is given by A = 2(pi)rh, where r is the radius and h is the height. Since the height of the cylinder is also r, the formula simplifies to A = 2(pi)rh = 2(pi)r(r) = 2(pi)r^2. Additionally, the two circular bases of the cylinder also contribute to the surface area, each with an area of (pi)r^2. Therefore, the total surface area of the cylinder is A = 2(pi)r^2 + 2(pi)r^2 = 4(pi)r^2.

C: The surface area of the cylinder in terms of r is 6(pi)d^2 square units. This statement is incorrect. The formula provided is incorrect. The correct formula for the surface area of a cylinder is A = 2(pi)rh, not 6(pi)d^2.

D: The surface area of the cylinder and sphere are the same. This statement is incorrect. The surface areas of a cylinder and a sphere are different. The surface area of a sphere is given by A = 4(pi)r^2, while the surface area of a cylinder is given by A = 2(pi)r^2 + 2(pi)rh. The presence of the curved surface in the cylinder makes its surface area different from that of a sphere.

E: The surface area of the cylinder and sphere are NOT the same. This statement is correct. As mentioned above, the surface areas of a cylinder and a sphere are different, so they are not the same.

In summary, the correct statements are A and B, while C, D, and E are incorrect.

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Is the expression quadratic 3x+5y-2

Answers

No, the expression 3x + 5y - 2200 is not a quadratic expression.

A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.

It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.

"3x + 5y - 2" is a linear expression, not a quadratic expression.

In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.

The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.

It is a first-degree polynomial, meaning that the highest power of the variable is 1.

Linear expressions often have a graph that is a straight line.

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No. The expression, 3x + 5y - 2, is not quadratic.

What are quadratic expressions?

The expression "3x+5y-2" is a linear expression, not quadratic.

Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.

The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.

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Jennifer Aniston bought a property for $2,000,000. One year later, she sold it for $2,200,000. Jennifer invested only $1,000,000 of her own money and borrowed the rest interest-free from her friend, Brad Pitt. What was her return on this investment?

Answers

This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.

To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:

ROI = (Net Profit / Initial Investment) * 100

First, let's calculate the net profit. The net profit is the selling price minus the initial investment:

Net Profit = Selling Price - Initial Investment

Net Profit = $2,200,000 - $2,000,000

Net Profit = $200,000

Next, we calculate the ROI:

ROI = (Net Profit / Initial Investment) * 100

ROI = ($200,000 / $1,000,000) * 100

ROI = 0.2 * 100

ROI = 20%

Jennifer Aniston's return on investment for this property is 20%.

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What does 13 round to the nearest thousandth

Answers

13 rounded to the nearest thousandth is 13.000.

A minibus was purchased for R241 000. The rate of depreciation 22% p.a. on a reducing balance basis. The cost of a new minibus inflates at a rate of 15% p.a.

Calculate the replacement cost of the minibus in 4 years’ time if the old minibus is used as a trade-in.

A fixed amount is deposited into a sinking fund at the end of each month for the purchase of a new minibus in 4 years’ time. Calculate the required monthly payment if interest is earned at the rate of 8,6% p.a. compounded monthly, and the first payment is only made three months after the original bus was purchased.

Answers

Replacement cost of the minibus in 4 years' time, considering the trade-in of the old minibus, is R9,411.70.

1. Calculate the depreciation of the minibus over 4 years:

  Depreciation = Original cost * (1 - Rate of depreciation) Number of years

  Depreciation = R241,000 * (1 - [tex]0.22)^4[/tex]

  Depreciation = R241,000 * [tex]0.78^4[/tex]

  Depreciation ≈ R91,073.17

2. Calculate the remaining value of the minibus after 4 years:

  Remaining value = Original cost - Depreciation

  Remaining value = R241,000 - R91,073.17

  Remaining value ≈ R149,926.83

3. Calculate the inflated cost of a new minibus in 4 years:

  Inflated cost = Original cost * (1 + Rate of inflation) Number of years

  Inflated cost = R241,000 * (1 + [tex]0.15)^4[/tex]

  Inflated cost = R241,000 * [tex]1.15^4[/tex]

  Inflated cost ≈ R421,731.04

4. Calculate the replacement cost by subtracting the remaining value and adding the inflated cost:

  Replacement cost = Remaining value + Inflated cost

  Replacement cost = R149,926.83 + R421,731.04

  Replacement cost ≈ R571,657.87

5. Calculate the trade-in value by subtracting the depreciation from the replacement cost:

  Trade-in value = Replacement cost - Depreciation

  Trade-in value = R571,657.87 - R91,073.17

  Trade-in value ≈ R480,584.70

6. Therefore, the replacement cost of the minibus in 4 years' time, considering the trade-in, is approximately R480,584.70.

For the second question:

1. Determine the number of months until the first payment is made:

  Number of months = 4 years * 12 months/year - 3 months

  Number of months = 48 months - 3 months

  Number of months = 45 months

2. Use the formula for the future value of a series of payments to calculate the required monthly payment:

  Monthly payment = (Future value * Interest rate) / ((1 + Interest rate) Number of periods - 1)

  Monthly payment = (Replacement cost * Monthly interest rate) / ((1 + Monthly interest rate) Number of months - 1)

  Monthly payment = (R480,584.70 * 0.086/12) / ((1 + [tex]0.086/12)^4^5[/tex] - 1)

  Monthly payment ≈ R9,411.70

3. Therefore, the required monthly payment to the sinking fund for the purchase of a new minibus in 4 years' time, with the first payment made three months after the original bus was purchased, is approximately R9,411.70.

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the base of a square pyramid is 229 meters long, each slant height is 186 meters. what is the surface area​

Answers

Answer:

The total surface area is given by: base area + 4 * triangular face area

Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.

Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.

The total surface area is given by: base area +
4 * triangular face area
Substituting the values we calculated: 52441 +
4 * 10424.4 ~ 91588.4 square meters.
Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.

Which of the following gives the correct range for the piecewise graph?

A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.

Answers

The correct range for the piecewise graph is [-4, 2].

To solve this problem

We need to find the minimum and maximum values of the y-coordinates.

The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.

The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.

We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.

Therefore, the correct range for the piecewise graph is [-4, 2].

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How many gallons of a 50​% antifreeze solution must be mixed with 70 gallons of ​10% antifreeze to get a mixture that is 40​% ​antifreeze?

Answers

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

SOLUTION:

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

[tex]{\implies 0.5x + 0.1(70) = 0.4(70 + x)}[/tex]

Simplifying the equation:

[tex]\qquad\implies 0.5x + 7 = 28 + 0.4x[/tex]

[tex]\qquad\quad\implies 0.1x = 21[/tex]

[tex]\qquad\qquad\implies \bold{x = 210}[/tex]

[tex]\therefore[/tex] We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

A video posted on social media is gaining views among female users aged 25-30. The number of views, in thousands, is modeled by f(t)=70001+35000e−0.2t where time, t, is measured in hours.

How many views, in thousands, are predicted among this demographic after 24 hours? Round your answer to the nearest whole number.

Answers

Answer:

After 24 hours 24 thousand views are predicted.

Step-by-step explanation:

To find the number of times the video is predicted to be viewed after 24 hours, we evaluate f(24) for the function f(t)=7000/1+35000e−0.2t

f(24)=7000/1+35000e^(−0.2⋅(24))

f(24)=7000/1+35000e^−4.8

f(24)≈24.21800522

After 24 hours, 24 thousand views are predicted.

The number of views that the video would get after 24 hours based on the function is 24 thousand

What is an exponential function?

An exponential function is a mathematical function of the form:

f(x) =[tex]a^x[/tex]

where "a" is a positive constant called the base, and "x" is the exponent, representing the power to which the base is raised. The exponent "x" can be any real number, making exponential functions quite versatile in describing a wide range of phenomena.

We have that;

=7000/1+35000[tex]e^{-0.2t[/tex]

Where t = 24 hours

=7000/1+35000[tex]e^{-0.2 * 24[/tex]

= 24

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Can someone help me with this question?

Answers

Answer: - 27

Step-by-step explanation:

Plug in for x = 3 and y = -6

I'll start with x to make it easier.

Plugging in x =3

[tex]\sqrt{x^4}[/tex]

Means that first we find x^4, and take the square root of that result.

1. Find x^4

x = 3

3^4 = 3 * 3 * 3 *3  = 81

2. Take the square root of x^4

Square root of 81 = 9

So [tex]\sqrt{x^4}[/tex]  = 9

Plugging in y = -6

Let's move onto plugging in y, which appears in the expression  as

y = -6

so y²  = -6 * -6 = 36

Putting this together into the expression

[tex]\sqrt{x^4}[/tex] - y²

9 - 36 = -27

What percent of 50 is 20?

Answers

Answer:

40% of 50 is 20

Step-by-step explanation:

[tex]50x=20\\x=\frac{20}{50}=0.4=40\%[/tex]

Answer: 20 is 40% of 50.

Step-by-step explanation:

We can simply divide 20/50

20/50 = 0.4

Now multiply it by 100 to get the percent: 0.4×100 = 40%

Hope this helps!

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.



Which statements about the function are true? Select three options.

The vertex of the function is at (–4,–15).
The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where
x > 1.
The graph is negative on the interval x < –4.

Answers

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of [tex]f(x)=(x-1)(x+7)[/tex] has clear zeroes at [tex]x=1[/tex] and [tex]x=-7[/tex], showing that [tex]f(x) > 0[/tex] when [tex]x < -7[/tex] and [tex]x > 1[/tex]. To determine where the vertex is, we can complete the square:

[tex]f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16[/tex]

So, we can see the vertex is (-3,-16), meaning that where [tex]x > -3[/tex], the function will be increasing on that interval

Based on a Comcast​ survey, there is a 0.8 probability that a randomly selected adult will watch​ prime-time TV​ live, instead of​ online, on​ DVR, etc. Assume that seven adults are randomly selected. Find the probability that fewer than three of the selected adults watch​ prime-time live.
A. 0.00430
B. 0.00467
C. 0.000358
D. 0.0512

Answers

Answer:

B. 0.00467

Step-by-step explanation:

This is a binomial probability problem. The probability of fewer than three adults watching prime-time TV live is the sum of the probabilities of 0, 1, and 2 adults watching prime-time TV live.

Let X be the number of adults watching prime-time TV live. The probability mass function of X is given by:

P(X=k)=(kn​)p^k(1−p)^n−k

where n is the number of trials (7 in this case), k is the number of successes, and p is the probability of success on a single trial (0.8 in this case).

So, the probability that fewer than three of the selected adults watch prime-time TV live is:

P(X<3) = P(X=0) + P(X=1) + P(X=2)

=(7  0)(0.8)^0(0.2)^7 + (7  1​)(0.8)^1(0.2)^6 + (7  2​)(0.8)^2(0.2)^5

=1/78125 + 28/78125 + 336/78125

=73/15625

=0.004672

A marble is rolling up an inclined plane. The distance (in cm) the marble has rolled after t seconds is given by s(t)=100t/t+1

a. What is the initial velocity of the marble?
b. How fast is the marble rolling at time 4 seconds?
c. At what time is the velocity 50 cm/s?
d. How fast is the marble rolling when it is 90 cm from its starting point?
e. Find and interpret lim s(t) t-> infinity and lim v(t) lim t-> infinity. Do you think this model is valid for large values of t?

Explain.

Answers

a. The initial velocity of the marble is 0 cm/s.

b. The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.

e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.

a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:

lim (t->0) s(t) = lim (t->0) (100t / (t + 1))

By substituting 0 into the expression, we get:

lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.

Therefore, the initial velocity of the marble is 0 cm/s.

b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):

s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s

The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:

s'(t) = 50

[tex](100 / (t + 1))^2 = 50[/tex]

100 / (t + 1) = ±√50

100 = ±√50(t + 1)

±√50(t + 1) = 100

t + 1 = 100 / ±√50

t + 1 = ±2√2

Since time cannot be negative, we take t + 1 = 2√2:

t = 2√2 - 1

The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:

100t / (t + 1) = 90

100t = 90(t + 1)

100t = 90t + 90

10t = 90

t = 9

The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.

e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:

lim (t->∞) (100t / (t + 1))

≈ lim (t->∞) (100t / t)

= lim (t->∞) 100

= 100

Therefore, lim s(t) as t approaches infinity is 100 cm.

Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:

[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]

lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]

≈ lim (t->∞)[tex](100 / t^2)[/tex]

= lim (t->∞) [tex](100 / t^2)[/tex]

= 0.

The limit of v(t) as t approaches infinity is 0 cm/s.

As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.

However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.

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The wholesale price for a chair is $114 A certain furniture store marks up the wholesale price by 33% Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.

Answers

Answer:

Step-by-step explanation:

144*33/

simplify 1200×1260÷800 leaving your answer in standard form ​

Answers

The simplified form of the expression 1200 × 1260 ÷ 800 in standard form is 1890.

To simplify the given expression, we perform the multiplication and division operations according to the order of operations (PEMDAS/BODMAS).

First, we perform the multiplication: 1200 × 1260 = 1,512,000.

Next, we perform the division: 1,512,000 ÷ 800 = 1890.

The result, 1890, is in standard form.

In standard form, a number is expressed as a product of a number between 1 and 10 (inclusive) and a power of 10. In this case, 1890 is already in the appropriate format and does not require any further modification.

Therefore, the simplified form of the expression 1200 × 1260 ÷ 800 is 1890 in standard form.

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2) Looking at your average from question 1, with an expected weight of 4 ounces, what is the % error in actual weights? (Assume you think the answer is 10%. Find 10% of 4 ounces to check to see if that answer is reasonable!) Do not round!

A) 17.5%
B) .128%
C) 10%
D) 0.175%

Answers

The calculated percentage error with the assumed answer of 10%

To find the percentage error in actual weights, we can use the formula:

Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%

In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:

Measured Value = Expected Value + (10% of Expected Value)

              = 4 ounces + (10/100) * 4 ounces

              = 4 ounces + 0.4 ounces

              = 4.4 ounces

Now we can calculate the percentage error:

Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%

               = [(0.4 ounces) / 4 ounces] * 100%

               = (0.4/4) * 100%

               = 0.1 * 100%

               = 10%

Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.

The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%

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if you borrow $1,000 for 4 years at an annual interest rate of 8% what is the total amount of money you will pay back

Answers

1000 - (1000 x (8% x 4 years) )
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