what is the volume of a sphere with a radius of 2.5 ? answer in terms of pi

The critical points of f(x) are x = -3 and x = 4.

Derivative of 4y = sin(cos(8x)):
We can find the derivative of the given function using the chain rule of differentiation. Let u = cos(8x), then we have:
y = sin(u)
dy/du = cos(u) (derivative of sin(u))
du/dx = -8sin(8x) (derivative of cos(8x) using chain rule)
dy/dx = dy/du * du/dx = cos(cos(8x)) * (-8sin(8x))
Therefore, the derivative of 4y = sin(cos(8x)) is:
dy/dx = -32sin(8x)cos(cos(8x))
Critical points of f(x) = x√(x+6):
To find the critical points of f(x), we need to find where the derivative of the function is equal to zero or undefined.
f(x) = x√(x+6)
f'(x) = (√(x+6) + x/2√(x+6))
To find the critical points, we need to set f'(x) equal to zero and solve for x:
(√(x+6) + x/2√(x+6)) = 0
Multiplying both sides by 2√(x+6), we get:
2x + 6 = -x√(x+6)
Squaring both sides, we get:
4[tex]x^2[/tex] + 24x + 36 = [tex]x^3[/tex] + 6[tex]x^2[/tex]
Rearranging, we get:
[tex]x^3[/tex] + [tex]2x^2[/tex] - 24x - 36 = 0
We can solve this cubic equation using numerical methods or by factoring.

By testing values, we can see that x = -3 is a root of the equation. Dividing the equation by (x+3), we get:
[tex]x^2[/tex]- x - 12 = 0
This quadratic equation can be factored as (x-4)(x+3) = 0.
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Answer: f(t) = 2.4t - 500

Step-by-step explanation:

So first of all, we need how much she actually profits from each taco. She charges $3.25 per taco, but we cannot forget that it is not free to make a taco in the first place. It costs her $0.85 to make a taco. This means we have to subtract the 85 cents from the 3 dollars 25 cents, which means it ends up being $2.40, or as the answer choices have it, 2.4.

So now we know what the number of tacos is being multiplied by: 2.4.

2.4t is now the profit per taco multiplied by the number of tacos.

But we're not quite done yet.

She has a fixed expense of $500 a month, which means this has to be subtracted from her taco profits to find her true profit.

Putting all of this together, we get f(t)=2.4t - 500.

(t)= (profit per taco)(amount of tacos sold) - (fixed expenses)

The mean number of points Kathleen made is 38.

To calculate the mean number of points Kathleen made, we will use the following terms: mean, sum, and total number of assignments.

The mean is the average value of a set of numbers. To find the mean, we need to sum all the given values and then divide the sum by the total number of values in the set.

Kathleen's assignment scores are 29, 38, 45, 42, and 36 points. To find the sum, we add these numbers together: 29 + 38 + 45 + 42 + 36 = 190 points.

Now, we need to determine the total number of assignments. Kathleen has completed five assignments. So, we will divide the sum of her points (190) by the total number of assignments (5) to find the mean.

Mean = Sum / Total number of assignments
Mean = 190 / 5
Mean = 38

The mean number of points Kathleen made on her assignments is 38 points. This indicates that on average, she scored 38 points per assignment. Calculating the mean gives us a general idea of her performance across all assignments, allowing us to gauge her overall progress.

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Check the picture below.

To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:

7² + 2² = x²

Simplifying this equation, we get:

49 + 4 = x²

53 = x²

To find the value of x, we need to take the square root of both sides:

√53 = x

So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.

In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.

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Approximately 21.3 percent of the total items sold were baseball items.

Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:

300 - 5 = 295

We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:

0.20 * 295 = 59

Therefore, the total number of baseball and football items sold is:

59 + 5 = 64

The percentage of total items sold that were baseball items is:

(64 / 300) * 100% = 21.3%

Therefore, approximately 21.3 percent of the total items sold were baseball items.

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The mean number of people in passenger cars on the highway is 1.7 (approximately 2).

The mean of a probability distribution function is also known as Expectation of the probability distribution function.

The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.

Thus E(x) can be calculated as,

E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5

where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway

⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)

⇒ E(x) = 1.7

Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.

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The correct answer is C.

The cost of membership is fixed at $50 per year, and the cost of purchasing games is $60 each. If you purchase up to 6 games a year, the cost of each purchase will be $60, and the total cost of membership and games will be $50 + ($60 x number of games purchased).

The function that relates the number of games purchased to the total cost is:

Total cost = 50 + 60(number of games purchased)

Now, let's consider the options provided:

A. Domain: All real numbers

Range: All real numbers

This is not a valid option since the domain and range are not restricted to the given context.

B. Domain: {50, 110, 170, 230, 280, 340}

Range: {0, 1, 2, 3, 4, 5, 6}

This option does not represent the relationship between the number of games purchased and the total cost correctly.

C. Domain: {0, 1, 2, 3, 4, 5, 6}

Range: {50, 110, 170, 230, 290, 350, 410}

This option correctly represents the relationship between the number of games purchased and the total cost. The domain represents the number of games purchased (up to 6), and the range represents the total cost (membership fee + cost of games).

D. Domain: {0, 1, 2, 3, 4, 5, 6}

Range: {60, 160, 210, 270, 320, 380}

This option represents the cost of games purchased only, and does not include the cost of membership.

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She requires 55 consecutive successful throws to get a success rate of 60%

The number of successful throws she made is 8 out of 50

Now to calculate the percentage we will use the formula

[tex]\frac{8}{50} X 100 = 16[/tex]

According to the problem, she needs to make her success percentage 60% and for that, we need to estimate the number of consecutive successful throws. Hence the new equation will be

[tex]\frac{8+x}{50+x} X 100 = 60[/tex]

[tex]or, \frac{8+x}{50+x} = 0.6[/tex]

This is the equation concerned.

Now,to solve this, we will take the denominator on the other side will give us

[tex]or, 8+x = 0.6(50+x)[/tex]

[tex]or, 8+x = 30+ 0.6x[/tex]

[tex]or, x - 0.6x = 30 -8[/tex]

[tex]or, 0.4x= 22[/tex]

or, x = 55

Hence we see that she requires 55 consecutive successful throws to get a success rate of 60%

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Complete Question

A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.

(a) Write an equation to represent this situation.

(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?

Answer:

Locker and Phone number

Step-by-step explanation:

Gym student grouped together with no thought doesnt matter, lunch menu doesn't need order, and a classroom seating chart doesn't really matter

Answer:

Step-by-step explanation:

First, let's simplify the numerator:

3^6 - 3^8 = 729 - 6561 = -5832

Now, let's simplify the denominator:

9^4 - 9^2 = 6561 - 81 = 6480

So, the expression simplifies to:

(-5832) / 6480 = -0.9

1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²), the power and multiplication law is not used correctly.

2. (y⁵/x²)*(y¹⁰/x³), the power and multiplication law is not used correctly.

3.  y⁷/x⁴ * y¹⁰/x³,  the multiplication law is not used correctly.

The exponents are simplified as follows; (using power exponents)

1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²)

= (x⁻⁴y¹⁰)*(x⁻⁹y¹⁰)

= x⁻¹³y²⁰

2. (y⁵/x²)*(y¹⁰/x³) (simplify using multiplication and division rule)

(y⁵/x²)*(y¹⁰/x³)

= (y⁵x⁻²)*(y¹⁰x⁻³)

= y¹⁵x⁻⁵

3. y⁷/x⁴ * y¹⁰/x³ (simplify using multiplication and division rule)

y⁷/x⁴ * y¹⁰/x³

= (y⁷x⁻⁴)(y¹⁰x⁻³)

= y¹⁷x⁻⁷

4. y¹⁷/x⁷ (This expression is simplified correctly)

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a. The tube dilution in tubes 1, 3, and 5:
- Tube 1: 1:5 (1 ml serum + 4 ml saline)
- Tube 3: 1:125 (1:5 dilution from Tube 1 x 1:5 dilution from Tube 2 x 1:5 dilution from Tube 3)
- Tube 5: 1:3125 (1:125 dilution from Tube 3 x 1:5 dilution from Tube 4 x 1:5 dilution from Tube 5)

b. The solution dilution in tubes 1, 2, and 7:
- Tube 1: 1:5
- Tube 2: 1:25 (1:5 dilution from Tube 1 x 1:5 dilution from Tube 2)
- Tube 7: 1:78125 (1:3125 dilution from Tube 5 x 1:5 dilutions for Tubes 6 and 7)

c. The total volume and solution dilution in tube 10 before transfer:
- Total volume: 3 ml (2 ml saline + 1 ml transferred from Tube 9)
- Solution dilution: 1:1953125 (1:78125 dilution from Tube 7 x 1:5 dilutions for Tubes 8, 9, and 10)

d. The amount or volume of serum in tube 6 before transfer and after transfer:
- Before transfer: 0.00064 ml (2 ml x 1:3125 dilution from Tube 5)
- After transfer: 0.00032 ml (1 ml x 1:3125 dilution from Tube 5, as half the volume was transferred to Tube 7)

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2x+14=30

2x =30-14

2x=16

x =8

Answer:

8

Step-by-step explanation:

Twice means 2 so twice a number,n, means 2 times n thus 2n

sum means add so, 2n + 14

"is" means equal so 2n + 14 = 30

Solve for n:

2n=16

N=8

The exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].

To write an exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416), follow these steps:

1. Use the point (0, 13) to determine the value of a. Since the x-coordinate is 0, we have y = a * b⁰, which simplifies to y = a. Therefore, a = 13.

2. Use the point (5, 416) to determine the value of b. Plug in the values for x and y, as well as the value of a we just found: 416 = 13 * b⁵.

3. Solve for b: b⁵ = 416 / 13 = 32. Taking the fifth root of both sides, we get b = 2.

So, the exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].

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3.75 kg of meat will cost 712.50, The correct answer is option (c).To determine how much 3.75 kg of meat will cost at ?190.00 per kilogram, you'll need to perform a multiplication using the given weight and price per kilogram, we need to :

1. Identify the weight of the meat: 3.75 kg.
2. Identify the cost per kilogram: ?190.00.
3. Multiply the weight (3.75 kg) by the cost per kilogram (?190.00).

3.75 kg × ?190.00/kg = 712.50
So, 3.75 kg of meat will cost ?712.50, which corresponds to option (c) in your list of possible answers. Remember to always check your calculations and units when solving problems like this to ensure accuracy.

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The set of ordered pairs that does NOT represent a function is option B) (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)

  A function is a term that do not have two different outputs that is (y) for the same input(x).

Note that

For option A: The x values are {0,2,4,-2,5} Here none of the x values are repeated, So, it represents a function.

For option B: The input value 2 is linked with two different output values (2 and 7), so this set of ordered pairs does not stand a function.

Based on the explanation of the function given above, if x=2, the 'y' can not be equal to 2, 7. So, this is not a function.

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The calculated value of x in the right triangle is 6

from the question, we have the following parameters that can be used in our computation:

The right triangle

Where we have

x/6 = 6/x

To solve this equation, we can use the property of cross-multiplication.

So for the equation x/6 = 6/x, we can cross-multiply as follows:

x/6 = 6/x

x * x = 6 * 6

x^2 = 36

To solve for x, we need to take the square root of both sides of the equation:

√(x^2) = √36

x = 6

The value of x is 6

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Answer: No they are not

Step-by-step explanation:

Distribute the 4 from the left equation into the parenthesis.

you would get 20k - 12

that is not equivalent to 14k - 8

The perimeter of Rebakh's new mural is 9 meters.

Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.

So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.

Therefore, the perimeter of Rebakh's new mural is 9 meters.

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Answer:

  C = (-1, -2)

  D = (2, 0)

Step-by-step explanation:

You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).

The diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:

  E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC

  C = 2E -A = 2(0, 2) -(1, 6)

  C = (-1, -2)

and

  D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern

  D = (2, 0)

Answer:  B   g(x)=1/4f(x)    odd

Step-by-step explanation:

First Page:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Second Page:

Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).

lets test for even:  does f(x)=f(-x)   =>    f(1)=f(-1)  no   -2[tex]\neq[/tex]2

see image for plotted points

lets test for odd:  does f(x)= -f(-x)   =>    f(1) = -f(-1)  yes  -2 = -2

Answer:

[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\textsf{B)} \quad \textsf{odd}[/tex]

Step-by-step explanation:

Functions f(x) and g(x) are exponential functions.

From inspection of the given points on both graphs:

When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):

[tex]g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\hrulefill[/tex]

And even function is symmetric about the y-axis:

According to the table, f(3) = -4 and f(-3) = 4.

Therefore, as f(x) ≠ f(-x), the function is not even.

An odd function is symmetric about the origin:

According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.

Therefore, as f(-3) = -f(3), the function is odd.

[tex]\hrulefill[/tex]

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The expression for the area of the triangle is given as follows:

A = 6x² - 7x - 3.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the expression for the area of the triangle is given as follows:

A = 0.5(4x - 6)(3x + 1)

A = 0.5(12x² - 14x - 6)

A = 6x² - 7x - 3.

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The displacement of the man from Noth east of A from C is 12.2 km.

The displacement of the man is the distance between his initial position at A and final position at C.

The angle formed at position B is calculated as follows;

θ = 30⁰  + 90⁰

θ = 120⁰

The displacement of the man is calculated by applying cosine rule as follows;

d² = 8² + 6² - 2(8 x 6) cos (120)

d² = 148

d = √148

d = 12.2 km

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The surface area of the triangular prism is

The surface area of the triangular prism is

= area of the two side rectangles + area of the base rectangles + area of the 2 triangles

= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24

= 2160 + 1296 + 1296

= 5752 square millimeters

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In Option 1, the arrival rate remains constant at 13 customers per hour. This means that, on average, 13 customers arrive at the checkout lane every hour, following a Poisson probability distribution.

However, the service rate in Option 1 increases to 30 customers per hour. This improvement is achieved by hiring a second person to assist the cashier in bagging groceries while the main cashier is occupied with entering cost data and collecting money from the customer. This essentially speeds up the overall service process, allowing more customers to be served within the same time frame.

The service rate of 30 customers per hour indicates that, on average, the cashier and the assistant can complete the checkout process for 30 customers in an hour. The service times still follow an exponential probability distribution, but with a faster rate of service compared to the initial service rate of 20 customers per hour.

By implementing Option 1, the manager aims to reduce the waiting time prior to the checkout process to no more than five minutes, thereby improving overall customer satisfaction and efficiency at Pete's Market.

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Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.

Let x be the time (in minutes) that Norma and David spent crawling to the barn, and y be the time (in minutes) they spent hopping back to the house. We know that:

x + y = 7 (the total time they spent on the round trip was 7 minutes)

300x + 400y = distance to the barn and back (since their speeds are given in centimeters per minute, the product of their speeds and the time spent crawling or hopping gives the distance in centimeters)

We want to find x, the time they spent crawling to the barn. We can solve for x by rearranging the first equation as x = 7 - y, and substituting into the second equation:

300(7 - y) + 400y = distance to the barn and back

2100 - 300y + 400y = distance to the barn and back

100y = distance to the barn and back - 2100

y = (distance to the barn and back - 2100)/100

Now we need to find the distance to the barn and back. They crawled to the barn at 300 cm/min, so the distance they crawled is 300x cm. They hopped back to the house at 400 cm/min, so the distance they hopped is 400y cm. The total distance to the barn and back is:

distance to the barn and back = 300x + 400y

= 300x + 400[(distance to the barn and back - 2100)/100] (substituting the expression we found for y)

= 300x + 4(distance to the barn and back - 2100)

Simplifying and solving for distance to the barn and back, we get:

distance to the barn and back = 5400/7 cm

Finally, we can substitute this value into the expression we found for y, and solve for x:

y = (distance to the barn and back - 2100)/100

= (5400/7 - 2100)/100

= 24/7

x = 7 - y

= 7 - 24/7

= 37/7

Therefore, Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.

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Using given function 9(x) = ln(3x+11), gl (x) B) 3(-3x + 11)^-1.

We are given 9(x) = ln(3x+11) and we need to find gl(x).

First, we can use the chain rule to differentiate ln(3x+11):

d/dx [ln(3x+11)] = 1/(3x+11) * d/dx [3x+11] = 3/(3x+11)

Now, we can use the given equation 9(x) = ln(3x+11) to find d/dx [9(x)]:

d/dx [9(x)] = d/dx [ln(3x+11)] = 3/(3x+11)

Therefore, gl(x) = d/dx [9(x)] / 3(x) = 3/(3x+11) * 1/3 = (3(-3x+11))^-1.

Therefore, the correct answer is B) 3(-3x+11)^-1.

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