determine the length of line AB and line AC in the right triangle. You may give your answer in radical form

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Answer:

coefficent=21,9,7

constant=x,y,z

Answer:

tell me more info

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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Answer: x≤-6 or 0<x≤6.Option D.

Step-by-step explanation:

Given:

Subtract   from both sides,

0

Simplifying by taking common denominator:

0

Factoring numerator:

0

Computing the signs and selecting that one satisfies ≤ 0:

x≤ -6,0<x≤6.

Option D is the right answer.

The radius of the given circle is 2 units.

Here, we are given an equation of a circle as follows-

\(x^{2}+ y^{2} + 8x - 6y + 21 = 0\)

The general form of the equation of a circles is -

\((x- h)^{2}+ (y-k)^{2} = r^{2}\)

where (h, k) are the coordinates of the center of the circle and r is the radius of the circle.

Let us convert the given equation into the general form by completing the squares as follows -

\(x^{2}+ y^{2} + 8x - 6y + 21 = 0\)

\(x^{2}+ (2*4)x+ y^{2} - (2*3)y + 21 = 0\)

\(x^{2}+ (2*4)x+ 16 -16+ y^{2} - (2*3)y + 9 - 9+ 21 = 0\)

\([x^{2}+ (2*4)x+ 16] -16+ [y^{2} - (2*3)y + 9] - 9+ 21 = 0\)

\((x+4)^{2} -16+ (y - 3)^{2} - 9+ 21 = 0\)

\((x+4)^{2} + (y - 3)^{2} = 16 + 9 - 21\)

\((x+4)^{2} + (y - 3)^{2} = 4\)

\((x+4)^{2} + (y - 3)^{2} = 2^{2}\)

Thus, we have obtained the equation of the circle in the general form. From this, we can observe that the center coordinates will be (-4, 3) and the radius of the circle will be 2 units.

Therefore, the radius of the given circle is 2 units.

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Answer:

Step-by-step explanation:

|x-3|=x-3,if x-3≥0,or x≥3

|x-3|=-(x-3),if x-3<0 ,or x<3

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Step-by-step explanation:

\( = ({4p}^{2}) ( {2p}^{5}) \)

\( = 8 {p}^{(2 + 5)} \)

\( = {8p}^{7} \)

Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.

To compose the two functions, we substitute g(x) into f(x) in place of x:

f(g(x)) = 2(g(x)) - 8

= 2(1/2x + 4) - 8

= x + 8 - 8

= x

Therefore, composing the two functions results in the identity function, f(g(x)) = x.

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Answer:

Step-by-step explanation:

The domain is all x-values.

The range is all y-values.

Domain: 3, 5, -3, 2, 1

Range: 4, 7, 8, 0, 3

Best of Luck!

Answer:

.0725

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

7 1/4 divided by 10

then you do same change flip the fraction

7 1/4 X 0/10 = 0

Answer:

A - As the length increases, the wingspan increases.

Very sorry if I got it wrong but I think it is A.

Answer:

I think it's A

Step-by-step explanation:

As the length increases the wingspan increases

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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ANSWER

My answer is in the phograph above

The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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CFI refers to cash flows from investing activities, which includes the purchase of computer equipment, while CFO refers to cash flows from financing activities, which includes interest expense paid to bondholders.

To calculate the cash flows from investing activities using the indirect method, start by calculating the net income for the period. Then, adjust the net income by adding back non-cash expenses and subtracting non-cash income items such as depreciation, amortization, and deferred taxes. Next, add the change in accounts receivable and subtract the change in accounts payable to calculate the cash generated from operating activities. Finally, add the purchase of capital assets and subtract the sale of capital assets to calculate the cash flows from investing activities.

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Answer:

the answer of the question is 77

Ruth and Josie will each have collected 117 signatures in one minute.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The slope and the intercept for this problem are given as follows:

Hence the functions are given as follows:

They will have the same amount when:

R(x) = J(x)

113 + 4x = 116 + x

3x = 3

x = 1 minute.

The amount is of:

J(1) = 116 + 1 = 117 signatures.

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Answer:

13th term

Step-by-step explanation:

41 = 7n - 50

41 + 50 = 7n

91 = 7n

7n = 91

n = 91/7

n = 13

13th term has value 41

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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The statement that a clock that is set fifteen minutes fast is less precise than an identical clock that keeps correct time is false

When a time is set away from the correct time, the time on the clock would be incorrect.

However, this has nothing to do with the precision of the clock.

This is so because precision deals with closeness of the time measurement to the original time

Since the time is ten minutes fast, it would not be less precise

Hence, the statement is false

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answer 60°

solve:180°-(60°+60°)

180°-120°

60°##

The charge of each company will be the same at 40 miles.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let us suppose the miles travelled as x.

Given that:

Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:

C = 0.10(x) + 40

Carnuba's Car rental charges $.15 per mile and has a service of $20.

D = 0.15(x) + 20

The charge of both the companies would be equal when C = D:

0.10(x) + 40 = 0.15(x) + 20

40 -20 = 0.15x = 0.10x

20 = 0.5x

x = 20/ 0.5

x = 40

Hence, the charge of each company will be the same at 40 miles.

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