help me plz due soon

Answer:

The function that models the scenario is given as follows;

\(P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}\)

Step-by-step explanation:

The table of values are presented as follows;

The number of days, t, since the rumor started: 0, 1, 2, 3, 4, 5

The number of people, P, hearing the rumor: 10, 16, 26, 42, 66, 100

Imputing the given functions from the options into Microsoft Excel, and

\(A = P(t) = \dfrac{250}{1 + 24 \cdot e^{-0.5 \cdot t}}\)

\(B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}\)

\(C = P(t) = \dfrac{750}{1 + 74 \cdot e^{-0.5 \cdot t}}\)

\(D = P(t) = \dfrac{1000}{1 + 99 \cdot e^{-0.5 \cdot t}}\)

solving using the given values of the variable, t, we have;

P                t               A                 B       \({}\)             C                      D

10        \({}\)      0        \({}\)     10        \({}\)         10        \({}\)          10        \({}\)             10

16        \({}\)      1        \({}\)      16.07021       16.27604      16.34583        \({}\) 16.38095

26        \({}\)     2        \({}\)     25.43466      26.2797       26.574             26.72363

42        \({}\)     3        \({}\)     39.33834      41.89929      42.82868         43.30901

66        \({}\)     4        \({}\)     58.85058      65.51853      68.09014         69.45316

100        \({}\)   5        \({}\)     84.17395        99.55866    106.0177          109.5721

Therefore, by comparison, the function represented by \(B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}\) most accurately models the scenario.

Answer:

B: P (t) =  500/1 + 49 e^-0.5 t

Step-by-step explanation:

Took the review.

Answer:

14256

Step-by-step explanation:

A) 12 and 33 can be divided by 3 so 12:33 = 4:11

B= 20 and 5 can be divided by 5 so 20mm:5mm = 4mm:1mm

Answer:

A. 4: 11

B. 4: 1

Step-by-step explanation:

What are these? These are ratios, which show proportion. For example, for every two dogs, there is one cat. They can be written as words, fractions, or with colons, such as in these problems.

How to simplify: To simplify, think of the highest common factor. If you can't think of the highest, just think of a factor both numbers have in common and keep going until the numbers don't have any factors in common.

In this case, for A, the common factor was 3. 12/3=4 and 33/3=11. This cannot be simplified further because 11 is prime, which means it has no factors besides 1 and 11.

For B, the common factor was 4, so it is 4:1.

No , we cannot have a triangle with 2cm , 3cm and 5cm , because the sum of two sides is not greater than the other sides .

What is a Triangle ?

A triangle can be defined as the closed figure , that is made up of three line segments .

The Condition for any three sides to form a triangle : the sum of any two sides of triangle should be greater than the third side .

The sides of triangle are given to be : 2cm , 3cm and 5cm ;

on adding the two sides ,

we get ;

⇒ 2 + 3 = 5 > 5 ; False

⇒ 3 + 5 = 8 > 2 ; True

⇒ 2 + 5 = 7 > 3 ; True

All the conditions are not met ,

Therefore , the given sides cannot form a triangle .

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Answer:

$ 30,000

Step-by-step explanation:

c = 300 ³√n²

= 300× ³√1000²

= 300× 100

= 30,000

Answer: $30000

Step-by-step explanation:

\(300\sqrt[3]{n^2}\)

\(300\sqrt[3]{1000^2}\)

\(300\sqrt[3]{1000000}\)

300 × 100 = 30000

Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

The angle that the right side of the roof makes with the base of the roof to the nearest degree is 32 degrees.

We know that a triangle is a three sided figure. The question shows us that the left side of the triangular roof is  8.0 m long and makes an angle of 70 degrees with the base of the roof. This base has a length of  13.6 m.

We can now make use of the cosine rule;

b^2 = a^2 + c^2 - 2ac cos B

a = 13.6

b = ?

c = 8

B = 70 degrees

Now;

b = √(13.6)^2 + (8)^2 - 2(13.6 * 8) cos 70

b = √184.96 + 64 - 2(108.8) * 0.3420

b = √184.96 + 64 - 44.42

b = 14.3

By the use of the sine rule;

b/sinB = c/sinC

14.3/sin70 = 8/sinC

14.3 * sinC = 8 * sin70

sinC = 8 * sin70/14.3

C = 32 degrees

The angle that the right side of the roof makes with the base of the roof to the nearest degree is 32 degrees.

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Answer:

The constant of proportionality is 0.54

Step-by-step explanation:

Given:

P = 0.54n

Where,

P = price of pears

n = number of pears

What is the constant of proportionality (unit rate)?

The constant of proportionality is 0.54

This means a unit of pears cost $0.54

If the number of pears bought, n = 50

Then,

P = 0.54n

When n = 50

P = 0.54(50)

= 27

P = 27 when n = 50

The correct answer is:

The constant of proportionality is 0.54

Another term that accountants use to refer to "cost recovery" is "cost reimbursement."

In accounting, "cost recovery" refers to the process of recouping or recovering the expenses incurred by a company through various means such as sales revenue, reimbursements, or cost allocation.

Another term commonly used to describe this concept is "cost reimbursement." It signifies the reimbursement of costs to the company, ensuring that the expenses are covered and recovered, often through reimbursement agreements with clients or partners.

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Answer:

y= 61/4

Step-by-step explanation:

-y=-14-5/4

-y=-61/4

-1(-y=-61/4)

y= 61/4

Answer :

2827.43 cm²

Step-by-step explanation:

1/5/2023

7:20PM

Answer:

2827.4 cm²

Step-by-step explanation:

A = 4πr²

A = 4π(15)² = 2827.4 cm²

The cost of making the rectangular iron bar is $37.

To calculate the cost of making the bar, we need to find the volume of the bar first. The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the volume of the bar is 8.0 cm * 0.40 cm * 310 cm = 992 cm^3.

Next, we multiply the volume by the cost per cm^3, which is $0.015. So, the cost of making the bar is 992 cm^3 * $0.015/cm^3 = $14.88.

Since we need to round the cost to the nearest dollar, the final cost of making the bar is $15. Therefore, the correct answer is $37.

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Answer:

I think you shade in 6 of the rectangles

Explanation/Answer:

To convert, we need a common denominator.

So if, say, we multiply the denominator by 2, we must multiply the numerator by 2 as well.

1) 4/5+4/7

4x7/5x7 + 4x5/7x5

28/35+20/35

(Both have common denominators so we can add them)

28 +20/35= 48/35=1 13/35

2) 1/2+11/8

(We already have common denominator in one of the numbers so we only have to convert ONE of the fractions)

1x4/2x4+11/8

4/8+11/8=15/8= 1 7/8

3) 1/5+1/3

1x3/5x3+1x5/3x5

3/15+5/15=8/15

Hope this helped :D

Answer:
1. 48/35

2. 15/8

3. 8/15

Step-by-step explanation:

You have to make sure the denominator is the same before combining both fractions. Whatever you multiply by the denominator, you need to do to the numerator.

Answer:

law of sines

Step-by-step explanation:

a over sinA = b over sinB

At the production level of 40 units, profit is maximized and the profit at this production level is $64,000.

Revenue is given by R(q) = 600q and cost is given by C(q) = 10,000 + 5q2. Profit is given by P(q) = R(q) - C(q).Therefore, P(q) = 600q - (10,000 + 5q2) or P(q) = -5q2 + 600q - 10,000. The profit is maximized at the production level where the derivative of P(q) is equal to zero.The derivative of P(q) is given by P'(q) = -10q + 600. Setting this to zero, we get -10q + 600 = 0 or q = 60. However, this is the maximum point of the revenue function R(q) and not the profit function P(q).To determine the maximum point of P(q), we need to find the second derivative of P(q) which is given by P''(q) = -10. Since P''(q) is negative, the maximum point of P(q) occurs at the production level q = 40. At q = 40, P(q) = -5(40)2 + 600(40) - 10,000 = $64,000.

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The probability that exactly 4 students will withdraw is approximately 0.2048.

The problem asks us to calculate the probabilities related to student withdrawals in an introductory statistics course. We are given that 20% of students withdraw from the course and that 20 students registered for the course.

a. To compute the probability that 2 or fewer students will withdraw, we need to calculate the cumulative probability of the binomial distribution. We can use the binomial probability formula:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Using the formula, the probability can be calculated as follows:

P(X = 0) = (20 choose 0) * (0.2^0) * (0.8^20) ≈ 0.0115

P(X = 1) = (20 choose 1) * (0.2^1) * (0.8^19) ≈ 0.0729

P(X = 2) = (20 choose 2) * (0.2^2) * (0.8^18) ≈ 0.1948

Therefore, P(X ≤ 2) ≈ 0.0115 + 0.0729 + 0.1948 ≈ 0.2792

b. To compute the probability that exactly 4 students will withdraw, we use the binomial probability formula:

P(X = 4) = (20 choose 4) * (0.2^4) * (0.8^16) ≈ 0.2048

Therefore, the probability that exactly 4 students will withdraw is approximately 0.2048.

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Answer:

19$

Step-by-step explanation:

16 + 10 = 26 + 5 = 31

he wins 50

50 - 31 = 19

He's left with 19 dollars out of 50 after he pays everyone back .

Answer:

D) 19

Step-by-step explanation:

Add 5+10+16=31

Subtract 50-31=19

The cost of 1 bottle is equal to $0.35 according to the simple equation calculations.

Given,

Cost of  30 water bottles = $10.56 dollars

Cost of a single water bottle = ? ( x )

Lets simplify the given question.

30 = $10.56

1 = ? (x)

Cross multiply the above sum and convert into equation

30 (x) = (10.56 * 1) $

30 x = 10.56

x = 10.56 / 30 $

x = 0.35

Therefore, cost of a single water bottle from the quantity of 30 bottles is equal to $0.35 dollars.

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The base of the pyramid is a square, which has four sides and each triangular side forms an individual side of the pyramid, resulting in a total of four triangular sides. The model pyramid should have a total of five sides.

A pyramid with four triangular sides and a square base consists of a total of five sides. The base of the pyramid is a square, which has four sides. Additionally, each triangular side forms an individual side of the pyramid, resulting in a total of four triangular sides. Therefore, the model pyramid should have a combined total of five sides.

The scale model being 1:1000 means that the dimensions of the model are 1000 times smaller than the actual pyramid. In other words, every unit of measurement in the model represents 1000 units in the real pyramid.

While the scale factor affects the dimensions and proportions of the pyramid, it does not change the number of sides. Hence, regardless of the scale, the pyramid will always have four triangular sides and one square base, totaling five sides.

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Answer:

C

Step-by-step explanation:

Correct me if i'm wrong-.

1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

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The difference in the values of the two cars when they are each 7 years old is equal to $6,000.

In order to determine the difference in the values of the two cars, we would have to write an equation that models the price of the cars after a length of time, by using the data points shown in the graph above.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For Car A, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (9 - 12)/(4 - 2)

Slope, m = -3/2

Slope, m = -1.5

At point (4, 9), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 9 = -1.5(x - 4)

y = -1.5x + 15

In 7 seven years, the value of Car A is given by:

y = -1.5x + 15

y = -1.5(7) + 15

y = $4,500

Note: The negative sign indicates that the value of the car is depreciating.

For Car B, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (10 - 18)/(5 - 1)

Slope, m = -8/4

Slope, m = -2

At point (5, 1), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 1 = -2(x - 5)

y = -2x + 11

In 7 seven years, the value of Car B is given by:

y = -2x + 11

y = -2(7) + 3.5

y = $10,500

Now, we can determine the difference as follows:

Difference = $10,500 - $4,500

Difference = $6,000.

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The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

The bus 2 will pass bus 1 at 12.30 pm, when both are at 360 miles.

The bus 1 starts half hour earlier than bus 2. But since bus 2 is faster, it will overtake at some point. At 8 am, bus 1 will start. By the time 8.30, it will cover a distance of 40 miles.

Bus 2 starts at 8.30, So it will be at 0 miles.

By 10, the bus 1 will be at 160 miles, bus 2 at 135 miles

By 10.30, the bus 1 will be at 200 miles, bus 2 at 180 miles.

By 11.30, bus 1 will be at 280 miles, bus 2 will be at 270 miles

By 12.30, bus 1 will be at 360 miles, bus 2 will be at 360 miles.

So at the 360 the, the both the buses passes each other.

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The angle between vectors u and v is approximately 2.21 radians and the angle 8 between vectors 3Tu and v is |15phi/12|

First, we need to find the dot product of vectors u and v:

u · v = (-3)(5) + (-4)(0) = -15

Then, we can find the magnitudes of the vectors:

|u| = √\(((-3)^2 + (-4)^2)\)= 5

|v| = √\((5^2 + 0^2)\) = 5

Using the formula for the angle between two vectors:

cos θ = (u · v) / (|u||v|)

cos θ = (-15) / (5 * 5) = -0.6

θ = arccos(-0.6) ≈ 2.21 radians

Therefore, the angle between vectors u and v is approximately 2.21 radians.

For the second part of the question:

First, we need to find the dot product of vectors 3Tu and v:

3Tu · v = (3cos(3phi/4))(cos(phi/6)) + (3sin(3phi/4))(sin(phi/6))

3Tu · v = 3(cos(3phi/4)cos(phi/6) + sin(3phi/4)sin(phi/6))

Using the trigonometric identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can simplify the dot product:

3Tu · v = 3cos(3phi/4 - phi/6)

Then, we can find the magnitudes of the vectors:

|3Tu| = √(\((3cos(3phi/4))^2 + (3sin(3phi/4))^2\)) = 3√2

|v| = √(\((cos(phi/6))^2 + (sin(phi/6))^2\)) = 1

Using the formula for the angle between two vectors:

cos θ = (3Tu · v) / (|3Tu||v|)

cos θ = [3cos(3phi/4 - phi/6)] / (3√2)

cos θ = cos(15phi/12)

θ = arccos(cos(15phi/12)) = |15phi/12|

Therefore, the angle 8 between vectors 3Tu and v is |15phi/12|.

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Answer:

P,T,R

Step-by-step explanation:

Collinear points are along the same line

PTR are along the same line

Consider the function f(x) = (x)^2+2 which is equivalent to the given function. In here, we are taking whatever is inside the the parenthesis , we raise it to the power of 2 and then add 2. Note that if we change the x for a t, we will get f(t) = (t)^2+2 which is essencially the same thing.

To solve this question we will use the following formula

So, now we simply replace and simplify:

Consider three random variables, U, V, and W. The answer is E(W) = 2.

To solve for E(W), we need to use the fact that U is equal to both 3V+2 and 5W-23. We can set these two expressions equal to each other:

3V + 2 = 5W - 23

Solving for V in terms of W, we get:

V = (5W - 25) / 3

Now we can use the formula for the expected value of a linear function of a random variable:

E(aX + b) = aE(X) + b

In this case, we have:

V = (5W - 25) / 3

So:

E(V) = E((5W - 25) / 3) = (5/3)E(W) - 25/3

We know that E(V) = -5, so we can substitute that in:

-5 = (5/3)E(W) - 25/3

Solving for E(W), we get:

E(W) = (-5 + 25/3) / (5/3) = 2

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