Given a sphere with a diameter of 6 cm, find its volume to the nearest wholenumber.

A. 905 cm^3
B. 85 cm^3
C. 113 cm^3
D. 37 cm^3

Answer:

The +1 in f(x) is the y intercept

The +1 in g(x) is the y coordinate of the vertex

Step-by-step explanation:

For f(x), plugging in x = 0 leads to

f(x) = 2x^2+5x+1

f(0) = 2(0)^2+5(0)+1

f(0) = 1

Showing that (0,1) is the y intercept of f(x).

The same is not true for g(x)

g(x) = 2(x+5)^2+1

g(0) = 2(0+5)^2+1

g(0) = 51

-------------------------------

The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is

y = a(x-h)^2+k

with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.

The values of the inverse functions are f-¹ (3) = -1 and f-¹ (8) = 7

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

x   f(x)

-1   3

1     6

2    5

3    7

7   8

Using the above as a guide, we have the following:

f-¹ (x) means that we calculate the value of x from the table when y = x in the function notation

So, we have

f-¹ (3) = -1 and f-¹ (8) = 7

Read more about inverse functions at

https://brainly.com/question/3831584

#SPJ1

Answer:

300

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

5!, called 5 factorial is the product of all positive intergers from 5 down though 1. by definition, 0! is 0.

Factorials are basically the number times itself-1 the 2 the 3 until it times it by itself-(itself-1). n!=n*(n-1)*n(n-2).....*n-(n-1).

For example 2!=2*1=2 and 6!=6*5*4*3*2*1=720

keep in mind that I am not an expert so the blanks I filled in might be wrong and the explanation might have errors

5!, called "5 factorial," is the product of all positive integers from 5 down through 1. By definition, 0! is equal to 1.

Factorial is a mathematical operation denoted by an exclamation mark (!). It represents the product of all positive integers from a given number down to 1. In the case of 5!, it is calculated as 5 × 4 × 3 × 2 × 1, resulting in the value of 120.

The exclamation mark notation allows us to represent the factorial of a number concisely. For example, 5! represents the factorial of 5. It is important to note that 0! is defined to be equal to 1. This is a special case in factorial calculations. While it may seem counterintuitive, it is defined this way to maintain consistency and enable certain mathematical calculations and formulas.

Therefore, 5! is the product of all positive integers from 5 down through 1, equaling 120, and 0! is defined to be 1.

Learn more about Factorial here:

https://brainly.com/question/30136880

#SPJ11

The weight of Bill's pack is a quantitative variable, so the weight can take on any numerical value within a certain range (in this case, likely between 0 and 100 lbs or so).

The type of variable for the weight of Bill's pack is a continuous variable, and the corresponding level of measurement is the ratio level of measurement.

Continuous variable: A continuous variable is a variable that can take on any value within a given range. In this case, the weight of Bill's pack can take on any value within a certain range (e.g., from 0 lb to 100 lb or more), making it a continuous variable.
Ratio level of measurement: The ratio level of measurement has a true zero point and allows for meaningful comparisons and calculations, such as multiplication and division. Since the weight of Bill's pack has a true zero point (0 lb) and allows for meaningful comparisons (e.g., one pack can be twice as heavy as another), it falls under the ratio level of measurement.

Hence,  The weight of Bill's pack (48.3 lb) is a continuous variable, and its corresponding level of measurement is the ratio level of measurement.

learn more about quantitative variable click here:

https://brainly.com/question/14037311

#SPJ11

22 ml of rboh is titrated with 35 ml of 0.9 m hf. The concentration of the base is 1.43M.

Titration is a method of chemical analysis in which the amount of a sample's ingredient is determined by adding an exact known amount of a different substance to the measured sample in which the desired constituent interacts in a specific, known proportion. Titrating reagent, or titrant, is often added to a standard solution (i.e., a solution of known concentration) using a burette, which is essentially a long, graduated measurement tube with a stopcock and a delivery tube at its bottom end. When the equivalence point is achieved, the addition is terminated.

To learn more about titration, visit:

https://brainly.com/question/13307013

#SPJ4

Answer:

18

Step-by-step explanation

:

Answer: (C)

6,2,2,2

Step-by-step explanation:

A mean is an arithmetic average of a set of observations. The set of population data that is the least dispersed from its mean is {6, 2, 2, 2}.

A mean is an arithmetic average of a set of observations. it is given by the formula,

\(\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}\)

To solve the problem we will find the mean of each population set and then add the difference between the mean and each data point.

A.)

\(Mean = \dfrac{2+3+2+9}{4} = \dfrac{16}{4} =4\)

Dispersion of each point from the mean,

\(\rm |Mean - data\ point|\\|4-2|=2\\|4-3|=1\\|4-2|=2\\|4-9|=5\)

Thus, the dispersion of the population from the means is 10 (2+1+2+5).

B.)

\(Mean = \dfrac{4+0+4+0}{4} = \dfrac{8}{4} =2\)

Dispersion of each point from the mean,

\(\rm |Mean - data\ point|\\|2-4|=2\\|2-0|=2\\|2-4|=2\\|2-0|=2\)

Thus, the dispersion of the population from the means is 8 (2+2+2+2).

C.)

\(Mean = \dfrac{6+2+2+2}{4} = \dfrac{12}{4} =3\)

Dispersion of each point from the mean,

\(\rm |Mean - data\ point|\\|3-6|=3\\|3-2|=1\\|3-2|=1\\|3-2|=1\)

Thus, the dispersion of the population from the means is 6 (3+1+1+1).

D.)

\(Mean = \dfrac{9+3+5+3}{4} = \dfrac{20}{4} =5\)

Dispersion of each point from the mean,

\(\rm |Mean - data\ point|\\|5-9|=4\\|5-3|=2\\|5-5|=0\\|5-3|=2\)

Thus, the dispersion of the population from the means is 8 (4+2+0+2).

Hence, the set of population data that is the least dispersed from its mean is {6, 2, 2, 2}.

Learn more about Mean:

https://brainly.com/question/16967035

Answer:

Step-by-step explanation:

A=12

1.) The cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.

2.) The number of necklace Janet can make in 1 hour = 2.4 to the nearest tenth.

But the cost of a pound weight= 1.5/2 = $0.75

Therefore, the cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.

The number of necklace made in 20 minutes= 4/5

The number of necklace made in 60mins(1hr) = X

Make X the subject of formula,

X= (60* 4/5) ÷ 20

X= 48/20

X= 2.4 to the nearest tenth.

Learn more about equations here:

https://brainly.com/question/13763238

Answer:

y = (1/2)x

Step-by-step explanation:

Lets look for an equation of the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = zero).  We can find the slope by calculating the Rise/Run between the two given points:

Going from (0,0) to (8,4):

Rise = (4-0) = 4

Run = (8-0) = 8

Slope = Rise/Run   (4/8) or (1/2)

The equation becomes y = (1/2)x + b

We need a value of b that forces the line through both points.  The point (0,0) actually tells us that b is 0, since b is the value of y when x=0.  If we weren't ask lucky to get a point where x is zero, we could cacalute b by putting either point in the above equation and solving for b:

y = (1/2)x + b

4 = (1/2)*(8) + b  for (8,4)

b = 0

The equation is y = (1/2)x

See the attached graph.

A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.

Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.

The diameter of the semicircle is also the length of the rectangle, so it is 3x.

The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.

The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:

3x^2 + (9/8)πx^2 = 750

(21/8)πx^2 = 750

x^2 = 750/(21/8)*π

x = √(750/(21/8)*π)

To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:

x = √(750/(21/8)*3.14)

= √(750/6.71)

= √(112.64)

= approximately 10.65 inches.

The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.

Read more about rectangle

https://brainly.com/question/29123947

#SPJ1

Answer:

$162.94

Step-by-step explanation:

Because 20% off of 192.15 = $162.94 and

$153.72  + (6.0%) $9.22  = $162.94

We first calculate the difference between each pair (y-x) which gives 3, -6, 5, 0, -1. We then calculate the sample mean of these differences which is 1.02.

To compute the test statistic, we need to calculate the standard error of the mean difference, which is the standard deviation of the sample differences divided by the square root of the sample size. Using the sample differences, we can calculate the sample standard deviation to be approximately 3.24. With a sample size of 5, the standard error of the mean difference is approximately 1.45.

The test statistic is calculated as the sample mean difference minus the hypothesized population mean difference divided by the standard error of the mean difference. Substituting the values, we get (1.02 - 0) / 1.45 = 0.70. This is our test statistic.

The interpretation of this result depends on the significance level chosen for the test. If we use a significance level of 0.05, which is a commonly used value, we compare the test statistic to the critical value from the t-distribution with four degrees of freedom (one less than the sample size). Using a t-table, we find the critical value to be approximately 2.78. Since our test statistic of 0.70 is less than the critical value, we fail to reject the null hypothesis that the mean difference is 0.

In summary, to test the claim that the paired sample data come from a population for which the mean difference is Ud=0, we calculated the test statistic using the provided data. The test statistic was 0.70, and using a significance level of 0.05 and a t-distribution with four degrees of freedom, we failed to reject the null hypothesis that the mean difference is 0. This suggests that there is not enough evidence to conclude that the mean difference is different from 0.

In simpler terms, we used the given data to see if there is enough evidence to suggest that the average difference between the paired samples is not 0. By calculating the test statistic and comparing it to a critical value, we determined that we cannot reject the null hypothesis that the mean difference is 0. This means that there is not enough evidence to conclude that the mean difference is different from 0, and we cannot say that there is a significant difference between the paired samples.

To learn more about standard error  click here, brainly.com/question/31941158

#SPJ11

A prism has two congruent parallel bases and the number of sides on the base determine the number of faces. A base with 13 sides is a 13-gon, so the prism has 2 faces from the 13-gon bases and 13 faces from the rectangular sides. In total the prism has 2+13 = 15 faces.

A prism is a three-dimensional geometric shape that has two congruent and parallel bases, and a set of rectangular faces connecting the bases. The bases are typically polygonal in shape, and the rectangular faces are perpendicular to the bases. The distance between the bases is known as the height of the prism. Prisms are named based on the shape of their bases, for example, a triangular prism has triangular bases, and a rectangular prism has rectangular bases. There are different types of prisms like regular prism, triangular prism, pentagonal prism, hexagonal prism etc.

Learn more about prism visit:

brainly.com/question/23963432

#SPJ1

Answer:

1/4

Step-by-step explanation:

Well see how far each points are from each other.

Start at the red triangle and go up 1, go to the right 4.

Thus,

the rise/run is 1/4.

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

To find the rise/run, you first need to pick two points from the line.  You can pick whichever points you want, and you will get the right answer.  I will pick (-8, -3) and (8, 1).

Divide the difference of the y's by the difference of the x's.

-3 - 1 = -4

-8 - 8 = -16

-4/-16 = 1/4

The rise/run is 1/4.

Answer:

6 tacos and 3 drinks

Step-by-step explanation:

taco =  3x

drink = y

= 3(3x+y)

= 6x+3y

Answer:

Step-by-step explanation:

⅔n - 5 = ⅓n + 7

⅓n = 12

n = 36

Answer:

A= 695.3cm²

Step-by-step explanation:

(a, b) = (1, 2) and (c, d) = (6, -6)

(a, b) = (2, 0) and (c, d) = (5, -4)

(a, b) = (3, -2) and (c, d) = (4, -2).

1) Note that since the adjacent angles in a parallelogram sum up to 180°, thus,

∠BDE = 180 -115 = 65°

∠DEC = 180 - 60 = 120°

Also:

∠BED = 60° (Angles on a straight line.)

Since we know ∠BDE and ∠BED, thus:
∠DBE = 180 - ∠BDE - ∠BED (Sum of Angles in a triangle)

∠DBE = 180 - 65 - 60

Thus:
∠DBE = x = 55°

2 )We know that the midpoint of the line segment joining (a, b) to (c, d) is (3.5, -2).

The midpoint formula is:

Midpoint = ((a+c)/2, (b+d)/2)

We can use this formula to create two equations based on the coordinates given:

3.5 = (a+c)/2 ---- (1)

-2 = (b+d)/2 ---- (2)

We have two equations with two variables (a, b, c, d). We can solve for one of the variables and then use that solution to find the other variables.

Let's solve equation (1) for c:

7 = a + c

c = 7 - a

Substitute c = 7 - a into equation (2):

-2 = (b+d)/2

-4 = b + d

d = -4 - b

So, we have found two expressions for c and d in terms of a and b:

c = 7 - a

d = -4 - b

Therefore, the possible coordinates for (a, b) and (c, d) are:

(a, b) = (1, 2) and (c, d) = (6, -6)

(a, b) = (2, 0) and (c, d) = (5, -4)

(a, b) = (3, -2) and (c, d) = (4, -2)

Learn more about Coordinates on:

https://brainly.com/question/16634867

#SPJ1

The point with polar coordinates (-5, 5π/3) can be converted to rectangular coordinates using the formulas:

x = r * cos(θ)

y = r * sin(θ)

where r represents the distance from the origin to the point and θ is the angle measured counterclockwise from the positive x-axis.

In this case, the distance from the origin is -5 and the angle is 5π/3. Plugging these values into the formulas, we get:

x = -5 * cos(5π/3)

y = -5 * sin(5π/3)

The rectangular coordinates of the point are (-5/2, -5√3/2).

To convert polar coordinates to rectangular coordinates, we use the formulas x = r * cos(θ) and y = r * sin(θ), where r represents the distance from the origin to the point and θ is the angle measured counterclockwise from the positive x-axis.

In this case, the distance from the origin is -5, indicating that the point lies 5 units away from the origin in the opposite direction. The angle is 5π/3, which corresponds to a counterclockwise rotation of 5π/3 radians from the positive x-axis.

By plugging these values into the formulas, we can calculate the rectangular coordinates as follows:

x = -5 * cos(5π/3)

y = -5 * sin(5π/3)

Evaluating the trigonometric functions, we find that cos(5π/3) = -1/2 and sin(5π/3) = -√3/2.

Therefore, the rectangular coordinates of the point (-5, 5π/3) are (-5/2, -5√3/2).

To learn more about polar coordinates click here :

brainly.com/question/31904915

#SPJ11

Answer:

A. 2x = 3x - x

E. x - 1 = 2x - (x + 1)

Step-by-step explanation:

To find out which linear equations have an infinitely many solutions, we must solve for the value of x:

A. 2x = 3x - x

Subtract 2x from both sides:

2x - 2x = 3x - x - 2x

0 = 3x - 3x

0 = 0  This is a true statement, which implies that any values of x will satisfy the given equation. Therefore, this linear equation has infinitely many solutions.

B. 3x = 3(2 + x)

Distribute 3 into (2 + x):

3x = 6 + 3x

Subtract 3x from both sides:

3x - 3x = 6 + 3x - 3x

0 = 6  This is a false statement.  Therefore, there is no solution.

C. 4x = x + 4

Subtract x from both sides:

4x - x = x - x + 4

3x = 4

Divide both sides by 3:

\(\frac{3x}{3} = \frac{4}{3}\)

x = 4/3  This is the solution to the given equation.

D. -2x = -x - 2

Add x to both sides:

-2x + x  = -x + x  - 2

-x = -2

Divide both sides by -1:

\(\frac{-1x}{-1} = \frac{-2}{-1}\)

x = 2  This is the solution to the given equation.

E. x - 1 = 2x - (x + 1)

Distribute -1 into (x + 1):

x - 1 = 2x - x - 1

Add 1 to both sides:

x - 1 + 1 = 2x - x - 1 + 1

x = x

Subtract x from both sides:

x - x = x - x

0 = 0  This is a true statement, which implies that any values of x will satisfy the given equation. Therefore, this linear equation has infinitely many solutions.

Given these calculations, we can see that options A and E have infinitely many solutions.

Please mark my answers as the Brainliest if my explanations were helpful :)

Answer:

the answer is B.  The inverse f the given statement is

"If a polygon is not a Pentagon, then it does not have five sides".

Step-by-step explanation:

If 6 square feet weighs half a pound, the 10 square feet weigh is 5/6 pounds.

The weight of a certain material varies directly with the surface area of that material.

So if surface area is A and weight of a certain material is w.

Then A ∝ w

After removing the varies the constant k is added.

A = kw

From the question A = 6 and w = 1/2 pounds.

So 6 = k × 1/2

Multiply by 2 on both side we get

k = 12

Since A = 10

So 10 = 12 × w

Divide by 12 on both side, we get

w = 10/12

On simplifying

w = 5/6 pounds

To learn more about weight link is here

brainly.com/question/29076184

#SPJ4

Answer:

It is not possible.

Step-by-step explanation:

The triangle inequality theorem states that any 2 sides of a triangle must be greater than or equal to the other side. If you add 3 and 1, you get 4, and that is less than 5, so the triangle cannot exist.

Answer:

1. No

2. Yes

3. No

4. Yes

5. Yes

Step-by-step explanation:

These are the answers for edge 2021

The correct statement is b. If the firm produced, the firm's losses would have been higher than $100. The firm will choose to shut down production if the market price is lower than $100 because it would not be able to cover its total cost of production.

In the short run, a profit-maximizing firm will shut down production if the total revenue it can earn from selling its output is not enough to cover its variable costs. In this case, since the total fixed cost of production is $100, the firm will shut down production if its total variable cost is higher than $100. If the firm produced, it would have to pay its variable costs, which would be in addition to the fixed cost of $100.

The decision to shut down production in the short run is based on the concept of the shutdown point, which is the output level at which a firm's total revenue is just enough to cover its variable costs. If a firm cannot cover its variable costs at a given output level, it will choose to shut down production. The shutdown point is determined by comparing the marginal revenue (MR) of the firm's output with its marginal cost (MC). If MR is lower than MC, the firm will reduce its output level until MR equals MC, which is the profit-maximizing level of output. In this case, the firm has a fixed cost of $100, which is a sunk cost that cannot be recovered in the short run. The only decision the firm can make is whether to continue producing or to shut down production. If the firm decides to produce, it will have to pay its variable costs, which are costs that vary with the level of output. The firm's total cost of production will be the sum of its fixed cost and its variable cost. If the market price is lower than the total cost of production, the firm will incur losses.

To know more about market price visit :-

https://brainly.com/question/31964955

#SPJ11

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).