Apply the distributive property to factor out the greatest common factor.
75+20=

The rational function representing the graph is \(f(x) = \dfrac{x}{(x-5)(x+2)}\). The correct option is C.

Any function that can be expressed mathematically as a rational fraction an algebraic fraction in which both the numerator and the denominator are polynomials is referred to as a rational function.

One curve is at x = 5 and the second curve is at x = -2. The numerator value is x = 0.

The function can be written as,

\(f(x) = \dfrac{x}{(x-5)(x+2)}\)

The graph of the function is attached with the answer below.

Therefore, the correct option will be C, for the given graph in the image.

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Answer: positive

Step-by-step explanation:

Answer:

Adding two functions is like plotting one function and taking the graph of that function as the new x-axis. Points of the second function are then plotted with respect to the new axis. For example, (2, 3) becomes "over 2," "up 3 from the new axis," or (3, f + 2).

Another Example:

To add or subtract functions, just add or subtract the values at each point where it makes sense. If the functions are given by formulas, you can just add or subtract the formulas (it doesn't matter whether you plug in values before or after).

Step-by-step explanation:

Hope this helps.      :)

Answer:

The mode is 9 letters: True

The median is 7.5 letters: True

The mean is 7 letters: False

The graph is skewed right with an outlier of 2: False

Step-by-step explanation:

1) The mode is 9 letters. (True)

The mode is the value that shows up the most. 9 letters shows up the most as the length of a child's last name.

2) The median is 7.5 letters. (True)

The median is one of the middle points of a data set. This can be found by writing out all of the results from least to greatest, and crossing out each number starting from the ends.

2, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9

Once you meet in the middle, you should be left with 7 and 8. In this case, we find the mean of the two numbers, which is 7.5. (In cases where the data set has an odd amount - if there were 13 children instead of 12), you'd just use the middle piece of data.

3) The mean is 7 letters. (False)

The mean is also a middle point of a data set. However, this one is different. The mean can be found by adding up all of the numbers in the data set (\(2+6+6+7+7+7+8+8+9+9+9+9\)) and then dividing that number by the amount of numbers are in the data set. Setting this up as an expression would look like: \(\frac{2+6+6+7+7+7+8+8+9+9+9+9}{12}\). By plugging this into a calculator you'd get 7.25 instead of just 7.

4) The graph is skewed right with an outlier of 2.

Although the outlier of 2 part of the statement is correct, the graph is not skewed right; it is skewed left.

By using Dijkstra's algorithm, it can be concluded that-

It will loop forever.

Third option is correct

What is Dijkstra's algorithm?

Dijkstra's algorithm is used to find the shortest path between the nodes of a graph.

Here, a node is fixed which is called the source node and the distance from the source node to all other nodes are calculated.

The minimum distance gives the shortest path.

For the first option,

The first option is incorrect because the shortest path will not be obtained. There does not exist path between every pair of vertices

For the second option

The second option is incorrect because all the conditions of Dijkstra's algorithm are fulfilled but here, infinite looping takes place.

For the fourth option

The fourth option is incorrect because there exist a path between the point M and every other vertex in the graph.

So the third option is correct

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Complete Question

The complete question has been attached

Answer:

1. The data show that skipping breakfast is associated with earning lower exam grades.

2. There is an increase in B's for those who do eat breakfast before the exam.

Answer:

$0.25

Step-by-step explanation:

2.99/12 aprrox. equals 25 cents

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

8 units

Step-by-step explanation:

Area of square:

length * width

2 * 3

= 6  units

Area of triangle:

1/2 * base * height

1/2 * 2 * 2

= 2 units

Area of entire shape:

6 + 2

= 8 units

So, the area of the shape is 8 units.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Check the picture below.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:34.5

Step-by-step explanation:trust me

Answer:

b

Step-by-step explanation:

The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

54

Step-by-step explanation:

\(A=\frac{1}{2}bh \\A=\frac{1}{2}*12*9\\A= 54\)

A proof by exhaustion of the theorem must prove that for every positive integer x less than 4, (x +1)^3 is greater than or equal to 4^x.

To prove the theorem by exhaustion, we must prove that for all positive integers x less than 4, (x + 1)^3 is greater than or equal to 4^x.

First, we start with x = 0. We must show that (0 + 1)^3 is greater than or equal to 4^0. We can calculate that (1)^3 = 1, which is greater than 4^0 = 1.

Next, we move to x = 1. We must show that (1 + 1)^3 is greater than or equal to 4^1. We can calculate that (2)^3 = 8, which is greater than 4^1 = 4.

Next, we move to x = 2. We must show that (2 + 1)^3 is greater than or equal to 4^2. We can calculate that (3)^3 = 27, which is greater than 4^2 = 16.

Finally, we move to x = 3. We must show that (3 + 1)^3 is greater than or equal to 4^3. We can calculate that (4)^3 = 64, which is greater than 4^3 = 64.

The complete question: Select the value for x that is a counter-example to the following statement: For every integer , < ^2 . a. x = 1/2 b. x = -1/2 c. x = -1 d. x = 1 6. Theorem: If x is a positive integer less than 4, then ( + 1) ^3 ≥ 4^ . Which set of facts must be proven in a proof by exhaustion of the theorem? a. 1^3 ≥ 4^0 2^3 ≥ 4^1 3^3 ≥ 4^2 4^3 ≥ 4^3 b. 2^3 ≥ 4^1 3^3 ≥ 4^2 4^3 ≥ 4^3 c. 2^3 ≥ 4^1 3^3 ≥ 4^2 4^3 ≥ 4^3 5^3 ≥ 4^4 d. 3^3 ≥ 4^2 4^3 ≥ 4^3

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Keep in mind that without the population standard deviation, it is impossible to provide an exact sample size. However, this formula will give you a good starting point.

To find the sample size needed for a 99.5% confidence interval with a margin of error of 1.5, we can use the formula:

n = (Z * σ / E)^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the margin of error.

For a 99.5% confidence interval, the Z-score is approximately 2.807 (from a standard normal distribution table). Since we do not have the population standard deviation (σ), we will need to estimate it using a sample standard deviation or use a conservative approach by assuming the maximum possible value. For now, let's assume we have an estimated standard deviation.

n = (2.807 * σ / 1.5)^2

Solve for n by plugging in the estimated standard deviation (σ) and then round up to the nearest whole number, as you cannot have a fraction of a sample.
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Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.

Answer: Banana has the lowest value, and habanero has the greatest value

Step-by-step explanation:

there. :)

after i put the answer first but its fine it is JUST a app

:|

Answer:

72

Step-by-step explanation:

principal (P)=1800

time(T)=2yrs

rate(R)=2%

SI=?

now,

SI=PTR÷100

= 1800×2×2÷100

=7200÷100

=72

so interest is 72.

hope this will help you :D

He would have saved $87,221.02  after 1 year

He would have saved $268,335.90   after 3  years

What is an ordinary annuity?

An ordinary annuity means a fixed amount invested at specific intervals, in this case, $7,185.51 is invested monthly, which means that its future value can be computed using the future value formula of an ordinary annuity as shown below:

FV=PMT*(1+r)^N-1/r

FV=future value of an ordinary annuity

PMT=monthly payment invested every month

r=monthly interest rate=annual interest/12

N=number of months that monthly payments were

FV after 1 year:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in 1 year=12

FV=$7,185.51*(1+0.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*(1.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*0.02528845698324970/0.00208333333333333

FV=$87,221.02

FV after 3  years:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in  3 years=36

FV=$7,185.51*(1+0.00208333333333333)^36-1/0.00208333333333333

FV=$268,335.90

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Answer:

A

Step-by-step explanation:

bc thats the one that makes more sense to me

Answer:

A

Step-by-step explanation:

It’s a, because equiangular triangle means having an equal angles

Answer:

\(\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)\)

Step-by-step explanation:

Given dimensions:

Given value of π :

To find:

Solution:

Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.

\( \pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}\)

where,

Plug/substitute them onto the formulae,then simplify it using PEMDAS.

\( \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3\)

\( \rm \: Volume_{(Cylinder)} = \pi(49)(3)\)

\( \rm \: Volume_{(Cylinder)} = 147\pi \: \)

\( \rm \: Volume_{(Cylinder)} = 147 \times 3.14\)

\( \rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3} \)

\( \boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \: \)

Hence, we can conclude that:

The volume of the cylinder is approximately

461.6 m³.

\( \rule{225pt}{2pt}\)

Answer:

2,3,5,7,11,13,17,19,23,29

Step-by-step explanation:

Answer: Mrs. Somner is correct.

Step-by-step explanation: In a triangle, the angles add up to 180 degrees. Since we know that Triangle ABC is equal to Triangle RST, we can assume that their angle values are equal as well. Angle A is 41 degrees, and Angle B is 74 degrees. This adds up to 115 degrees. If we subtract 115 from 180, we get 65. Therefore, Mrs. Somner is correct.

Answer:

y= -4

Step-by-step explanation:

To find the value of y when x = 6, we can substitute x = 6 into the equation and solve for y:

4(6) + y = 20

24 + y = 20

y = 20 - 24

y = -4

Therefore, when x = 6, y is equal to -4.

Answer:21,700

Step-by-step explanation: