Find the volume of the sphere. Use 3.14 for Pi. Round your answer to the nearest thousandth. A sphere with diameter 7 inches. a. 51.287 cu. in. b. 1436.027 cu. in. c. 100.971 cu. in. d. 179.503 cu. in.

After testing all the possible rational roots, we can see that x = 3 is an actual root of the equation.

a. To find all possible rational roots of the given equation x^4 - 2x^3 - 10x^2 + 18x + 9 = 0, we can use the Rational Zero Theorem. According to the theorem, the possible rational roots are all the factors of the constant term (9) divided by the factors of the leading coefficient (1).

The factors of 9 are ±1, ±3, and ±9.

The factors of 1 (leading coefficient) are ±1.

Combining these factors, the possible rational roots are:

±1, ±3, and ±9.

b. Now let's use synthetic division to test several possible rational roots to identify one actual root. We'll start with the first possible root, x = 1.

1 | 1 -2 -10 18 9

| 1 -1 -11 7

|------------------

1 -1 -11 7 16

The result after synthetic division is 1x^3 - 1x^2 - 11x + 7 with a remainder of 16.

Since the remainder is not zero, x = 1 is not a root

Let's try another possible root, x = -1.

-1 | 1 -2 -10 18 9

| -1 3 7 -25

|------------------

1 -3 -7 25 -16

The result after synthetic division is 1x^3 - 3x^2 - 7x + 25 with a remainder of -16.

Since the remainder is not zero, x = -1 is not a root.

We continue this process with the remaining possible rational roots: x = 3 and x = -3.

3 | 1 -2 -10 18 9

| 3 3 -21 57

|------------------

1 1 -7 39 66

-3 | 1 -2 -10 18 9

| -3 15 -15

|-----------------

1 -5 5 3 -6

After testing all the possible rational roots, we can see that x = 3 is an actual root of the equation.

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Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

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Answer:

18-2x=4x is given

18=6x is addition property of equality

3=x is I think division property of equality bc you divided to get x=3

The minimum marginal cost occurs at q = 30.

The lowest average cost is 7.

The marginal cost at q = 30 is 16.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To find the total cost of producing q goods, we need to multiply the average cost by the number of goods produced:

C(q) = a(q) * q

Substituting a(q) = 0.01q² - 0.6q + 13, we get:

C(q) = (0.01q² - 0.6q + 13) * q

= 0.01q³ - 0.6q² + 13q

To find the minimum marginal cost, we need to take the derivative of the average cost function:

a'(q) = 0.02q - 0.6

Setting a'(q) = 0 to find the critical point, we get:

0.02q - 0.6 = 0

q = 30

Therefore, the minimum marginal cost occurs at q = 30.

To find the production level at which the average cost is a minimum, we need to find the minimum point of the average cost function. We can do this by taking the derivative of the average cost function and setting it equal to zero:

a'(q) = 0.02q - 0.6 = 0

q = 30

Therefore, the production level at which the average cost is a minimum is q = 30.

To find the lowest average cost, we can substitute q = 30 into the average cost function:

a(30) = 0.01(30)² - 0.6(30) + 13

= 7

Therefore, the lowest average cost is 7.

To compute the marginal cost at q = 30, we need to take the derivative of the total cost function:

C(q) = 0.01q³ - 0.6q² + 13q

C'(q) = 0.03q² - 1.2q + 13

Substituting q = 30, we get:

C'(30) = 0.03(30)² - 1.2(30) + 13

= 16

Therefore, the marginal cost at q = 30 is 16.

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Rosie, this is the solution to the system of equations:

___________________________________________

2x - 3y = 6

2x - 6y = 9

___________

Step 1: Let's multiply by -1 the second equation, therefore we have:

2x - 3y = 6

-2x + 6y = -9

___________

Step 2: We eliminate x and solve for y, as follows:

-3y + 6y = 6 - 9

3y = -3

Dividing by 3 at both sides:

3y/3 = -3/3

y = -1

_______________________

Step 3: We substitute y and solve for x in the first equation, this way:

2x - 3 (-1) = 6

2x + 3 = 6

Subtracting 3 at both sides:

2x + 3 - 3 = 6 - 3

2x = 3

Dividing by 2 at both sides:

2x/2 = 3/2

x = 3/2

_________________________

Step 4: Now, let's prove x = 3/2 and y = -1 are right, replacing in the second equation, as follows:

2x - 6y = 9

2 (3/2) - 6 (-1) = 9

3 + 6 = 9

9 = 9

We proved that x = 3/2 and y = -1 are correct.

Considering that the square root of 9 is of 81 and of 10 is of 100, we have that the expression that has a value between 9 and 10 is given by:

B.) √89

E.) \(\sqrt[3]{750}\)

F.) \(\sqrt[3]{999}\)

We suppose numbers n and m, with square roots given, respectively, by n² and m².

Then, the square roots of all numbers between n² and m² have values between n and m.

In this problem, the square roots are given by:

Hence, the square root of all values between 82 and 99 are values between 9 and 10, thus option B is correct.

As for the cubic root, we apply the same logic and have that:

Hence options E and F are also correct, as the values between 730 and 999 have cubic roots between 9 and 10.

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There must exist an orange node in G that has both a purple neighbor and a yellow neighbor.

Suppose to the contrary that there is no orange node in G that has both a purple neighbor and a yellow neighbor. Let's consider the connected component of G containing an arbitrary vertex v. Since G is connected, this connected component contains all the vertices of G.

Since x(G) = 3, we know that this connected component contains a vertex of degree at most 2. Let's call this vertex u.

Since u has degree at most 2, it can have at most one neighbor that is colored purple and at most one neighbor that is colored yellow. Without loss of generality, assume that u has a purple neighbor but no yellow neighbor. Then, all other neighbors of u must be colored orange.

Consider the two cases:

Case 1: u has only one neighbor that is colored purple.

Then, this neighbor of u has no orange neighbor because u only has orange neighbors. Therefore, we can recolor u with the purple color, and the purple neighbor of u with the orange color. This new coloring is also a proper 3-coloring, but now u has both a purple neighbor and an orange neighbor, which contradicts our assumption.

Case 2: u has two neighbors that are colored purple.

Let's call these neighbors p and q. Since u has no yellow neighbor, both p and q must be colored orange. But then, p and q have no yellow neighbors, which contradicts the assumption that G is properly 3-colored.

Therefore, in both cases, our assumption that there is no orange node with both a purple neighbor and a yellow neighbor leads to a contradiction. Therefore, there must exist an orange node in G that has both a purple neighbor and a yellow neighbor.

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The decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.

To determine the decimal value of the 2 in the hexadecimal number F42AC16, we need to understand the positional value system of hexadecimal numbers. In hexadecimal, each digit represents a power of 16. The rightmost digit has a positional value of 16^0, the next digit to the left has a positional value of 16^1, the next digit has a positional value of 16^2, and so on.

In the given hexadecimal number F42AC16, the 2 is the fifth digit from the right. Its positional value is 16^4. Calculating the decimal value: 2 * 16^4 = 2 * 65536 = 131,072. Therefore, the decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.  None of the provided options (a) 409610, b) 51210, c) 25610, d) 210) matches the correct decimal value of 131,072.

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Answer: 4

Step-by-step explanation:

10+3+2+5+0=20

20/5=4

Answer:

The mean number of points your basketball team scored for all 5 games is 4 points per game.

Step-by-step explanation:

To find the mean or average number of points scored by the team for all 5 games, we need to add up the total number of points and then divide by the number of games played.

Total number of points scored in 5 games = 10 + 3 + 2 + 5 + 0 = 20

Mean number of points scored per game = Total number of points scored / Number of games played

= 20 points / 5 games

= 4 points

Therefore, the mean number of points your basketball team scored for all 5 games is 4 points per game.

The correct answer is (b) the system {Ty>0, Ty=0,y≥0} is feasible.

To understand why, let's first look at the given linear system {x = , x ≤ 0}. This system consists of one equation and one inequality.

The equation states that x is equal to something (we don't know what), and the inequality states that x must be less than or equal to 0.

Now, let's try to solve this system. Since we only have one equation, we can't directly solve for x. However, we do know that x ≤ 0. This means that any feasible solution for x must be less than or equal to 0.

But since we don't know what x is equal to, we can't say for sure whether or not there are any feasible solutions.

So, how do we determine if there are feasible solutions? We can use the concept of duality.

Duality tells us that if we take the transpose of the matrix in our original system (T), and create a new system using the rows of T as the columns of a new matrix, then we can determine the feasibility of this new system.

In this case, the transpose of our matrix is simply the vector [1 0].

To create a new system, we take the rows of this vector as the columns of a new matrix:
| 1 |
| 0 |

Our new system is:
Ty > 0
Ty = 0
y ≥ 0

Notice that the first row of this system (Ty > 0) corresponds to the inequality in our original system (x ≤ 0). The second row (Ty = 0) corresponds to the equation in our original system (x = ).

And the third row (y ≥ 0) is a new inequality that ensures that all variables are non-negative.

Now, we can use this new system to determine the feasibility of our original system. If this new system has feasible solutions, then our original system has no feasible solutions.

If this new system has no feasible solutions, then our original system may or may not have feasible solutions.

Let's look at each of the answer choices:

(a) The system {Ty<0, Ty=0,y≥0} is feasible.

This means that our original system has no feasible solutions. But why is this? The first row (Ty < 0) tells us that the first variable in our original system must be negative.

But we don't know what this variable is, so we can't say for sure whether or not this is feasible.

The second row (Ty = 0) tells us that the second variable in our original system must be 0. But we also don't know what this variable is, so we can't say for sure whether or not this is feasible.

The third row (y ≥ 0) ensures that all variables are non-negative, so this doesn't add any new information. Overall, we can't determine the feasibility of our original system based on this new system.

(c) The system {Ty > 0, Ty ≤ 0, } is feasible.

This means that our original system has no feasible solutions.

The first row (Ty > 0) tells us that the first variable in our original system must be positive.

But we know from our original system that this variable must be less than or equal to 0, so there are no feasible solutions.

The second row (Ty ≤ 0) tells us that the second variable in our original system must be non-positive.

But we don't know what this variable is, so we can't say for sure whether or not this is feasible.

Overall, we can't determine the feasibility of our original system based on this new system.

(d) The system {Ty < 0, Ty ≤ 0, } is feasible.

This means that our original system has no feasible solutions. The first row (Ty < 0) tells us that the first variable in our original system must be negative.

But we don't know what this variable is, so we can't say for sure whether or not this is feasible.

The second row (Ty ≤ 0) tells us that the second variable in our original system must be non-positive. But we don't know what this variable is, so we can't say for sure whether or not this is feasible.

Overall, we can't determine the feasibility of our original system based on this new system.

(b) The system {Ty>0, Ty=0,y≥0} is feasible.

This means that our original system may or may not have feasible solutions.

The first row (Ty > 0) tells us that the first variable in our original system must be positive.

But we know from our original system that this variable must be less than or equal to 0, so there are no feasible solutions.

The second row (Ty = 0) tells us that the second variable in our original system must be 0. But we also don't know what this variable is, so we can't say for sure whether or not this is feasible.

The third row (y ≥ 0) ensures that all variables are non-negative, so this doesn't add any new information.

Overall, we can't determine the feasibility of our original system based on this new system.

Therefore, the correct answer is (b) the system {Ty>0, Ty=0,y≥0} is feasible.

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Answer:

because they are both in the circle

Step-by-step explanation:

Answer:

C 10^-3

Step-by-step explanation:

because the other options are the same as 10^ -3/5

Answer:

It would be  10^-3

Step-by-step explanation:

A

Either divide each by one fourth or multiply each by 0.25. Then turn the answer to a fraction.

Answer:

y = -3x + 1

Step-by-step explanation:

Since we already know the slope, we just need to find the y-intercept.

y = mx+b   (the slope is m)

y = -3x + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

The equation is y = -3x + 1

Answer:

y = -3x + 1

Explanation:

Answer:

f(x)=(2.5)x

Step-by-step explanation:

x equals the number of years after 2010, and every year after 2010 their total corn harvest increases by 2.5%, so you would have 2.5 multiplied by however many years after 2010 it is

The exponential function f(x) that models the number of bushels of corn produced x years after 2010 is f(x) = 175000(1.025)^x

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P(1 +\dfrac{R}{100})^T - P\)

The final amount becomes:

\(A = CI + P\\A = P(1 +\dfrac{R}{100})^T\)

We can use compound interest formula whenever there is compounding (increment or decrement) per unit time.

Here, the initial amount of  production farm was doing in 2010 is 175000 bushels of corn.

This value increases by 2.5% per year.

We need the final number of bushels of corn that will be produce x years after 2010.

So, here, we can take P = 175000, R = 2.5, and T = x

Then, we get:

\(f(x) = A = 175000\left(1 + \dfrac{2.5}{100}\right)^x\\\\f(x) = 175000(1.025)^x\)

Thus, the exponential function f(x) that models the number of bushels of corn produced x years after 2010 is \(f(x) = 175000(1.025)^x\)

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Answer:

\(8v^{3} +27=(2v)^{3} +3^{3}=(2v+3)(4v^{2} -6v+9)\\\)

Step-by-step explanation:

from  formula a³ – b³ = (a – b) (a² + ab + b² )

Answer:

two are correct:  side ED is equal to DC, and ABCDE is a pentagon

Step-by-step explanation:

pentagon is a polygon having 5 sides

You can find the length of BC by using the distance formula

Answer:

a, d to make it simpler

Step-by-step explanation:

Answer:

Because it had hay fever.

False. When conducting a cluster sample, it is typically preferable to have more heterogeneous clusters with fewer individuals.

This is due to the fact that when clusters are diverse, it is crucial to appropriately represent the population by capturing its diversity.

In such situations, the danger of sampling bias is increased by having fewer clusters with more individuals because a larger number of people from a single heterogeneous cluster would not fairly represent the overall community. Incorrect estimates and conclusions may result from this.

Having fewer clusters with more individuals, on the other hand, can assist raise the precision of the estimates when clusters are homogeneous by lowering the variance associated with sampling from a single cluster. In general, to achieve a precise representation of the population and to lessen the chance of sampling bias, the number of clusters and the size of each cluster should be balanced.

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Answer:

Each axis has a label. The axis label shows the name of the variable and its unit. The data points are the values plotted on the graph. Each point is plotted using a pair of values for the variables (the x-coordinate and the y-coordinate).

The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).

To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.

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Answer: Simplifying a square root just means factoring out any perfect squares from the radicand, moving them to the left of the radical symbol, and leaving the other factor inside the radical symbol. If the number is a perfect square, then the radical sign will disappear once you write down its root. hope this helps can u give me brainliest or use this link it can help u

Step-by-step explanation:

There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

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Answer:

295/72

Step-by-step explanation:

Answer:

60 Sq in

Step-by-step explanation:

14×6= 84

4×6=24

84-24= 60