If n is an integer and n > 1, then n! is the product of n and every other positive integer that is less than n. For example, 5! =5 • 4 • 3 • 2 • 1.

a. Write 6! in standard factored form.

b. Write 20! in standard factored form.

c. Without computing the value of (20!)2 determine how many zeros are at the end of this number when it is written in decimal form. Justify your answer.

Answer:

Multiplied by -5

Step-by-step explanation:

-8 X -5 = 40

40 X -5 = -200

Answer:B costs less than A

Step-by-step explanation:

i am not quite sure but i think,

A)8----2,89

  1------x

x=0.38

B)12----4,19

1---------y

y=0.35

To sketch the angle θ in standard position, you can start by plotting the point ( -3, 4 ) on the coordinate plane. Next, you draw a line from the origin ( 0, 0 ) to the point ( -3, 4 ), which represents the terminal side of the angle.

Now, you can use the six trigonometric functions to find the exact values for θ:

Cosine ( cos θ ) = x / r = -3 / 5

Sine ( sin θ ) = y / r = 4 / 5

Tangent ( tan θ ) = y / x = 4 / -3

Secant ( sec θ ) = 1 / cos θ = -5 / 3

Cosecant ( csc θ ) = 1 / sin θ = -5 / 4

Cotangent ( cot θ ) = 1 / tan θ = -3 / 4

Here, r represents the distance from the origin to the point ( -3, 4 ), which is 5 units. Note that these values are for the least positive measure of the angle, which is in the second quadrant.

place g(x) as the value x, into p(x)

to gain p(g(x)) = (1 / SqrRt(x) )² - 4

simplify = ( 1 / x ) - 4

find domain

x =/= 0 (undefined) & (1/4)

Answer: The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).

In this case, the function s(x) = 6/25 - x^2 has no restrictions on the input values for x, so the domain of the function is all real numbers.

Therefore, the domain of the function s(x) = 6/25 - x^2 is:

(-∞, ∞)

This means that the function can be evaluated for any real value of x.

Step-by-step explanation:

The number of rotational symmetries that the figure has would be C. 1 at 360 degrees.

The number of times the geometric figure is similar to the original figure after undergoing a full revolution is known as the order of rotational symmetry. The order of rotational symmetry is determined by how many times the rotated figure perfectly fits within the original figure.

When the Figure F is rotated, the only times that it can be rotated to be able to give the same figure of F, is once, and that once has to be a full revolution of 360 degrees.

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Answer:

C

Step-by-step explanation:

An irrational number cannot be shown as a simple fraction. If the number has decimals that are non-repeating (so not 7.85555555... or. 9.121212121...), cannot be shown as fractions (not 1.50000000... as it can be written as 3/2), and does not terminate (aka end).  C is the answer you're looking for, as it cannot be shown as a fraction, the numbers after the decimal go on indefinitely,  and the number's don't follow a noticeable repeatable pattern.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine which option is faster, we need to determine the total number of nights required for each option.

First, let's find the number of pages Nora still needs to read by subtracting the number of pages she's already read from the total number of pages: 280 pages * 30% = 84 pages

So, Nora still needs to read 280 pages - 84 pages = 196 pages.

For Option 1, Nora would read 25% of the remaining pages each night, so the number of pages she reads each night would be: 196 pages * 25% = 49 pages

The total number of nights required would be 196 pages / 49 pages/night = 4 nights.

For Option 2, Nora would read 28 pages each night, so the total number of nights required would be 196 pages / 28 pages/night = 7 nights.

Since 4 nights is less than 7 nights, Nora should choose Option 1 to finish reading the book in the least amount of time.

Answer:

-$48.39

Step-by-step explanation:

The new tuition 4 years from now is $6962.68.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$6691, rate of interest=1% and time period=4 years.

Now, A=6691(1+1/100)⁴

=6691(1+0.01)⁴

=6691(1.01)⁴

= 6691×1.04060401

= $6962.68

Therefore, the new tuition 4 years from now is $6962.68.

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Answer:

Base: 8. Height: 3.

Step-by-step explanation:

Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.

Answer:

Step-by-step explanation: Option A is correct.

Answer: TASK 1: The answer to how much more of the atmosphere is nitrogen than all other gases combined can be found by measuring the atmospheric composition. Nitrogen makes up the largest fraction of the Earth's atmosphere, at around 78%. Oxygen makes up around 21%, while all other gases make up the remaining 1%. So, nitrogen makes up around 77% more of the atmosphere than all other gases combined.

TASK 2: I'm sorry, but there seems to be a typo in your prompt. Can you please clarify what you meant by "in the Tronosphere was separated out from"?

Step-by-step explanation:

Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:

lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞

As x approaches negative infinity, the square root of x approaches 0, so the function approaches:

lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7

Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.

Step-by-step explanation:

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

Answer: Function

Step-by-step explanation:

The vertex of the given function is (0,4)  

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

identify the coefficients a and b of the quadratic function

y =ax² +bx+c-------(1)

a=2, b=0

x-coordinate of the vertex is x= -b/2a = -(0)/(2(2)) = 0

Substitute  x=0 into given equation  to get y-coordinate of the vertex

y= 2(0)² + 4 = 0+4 = 4

Vertex= (x,y) = (0,4)

The vertex of the given function is (0,4)

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In the given figure angle CBF and angle CEF are supplementary angles. So Option C is correct.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Given that,

A figure which contains one trapezium BCEF

And in this portion angle CBF and angle BCE are  opposite angles

and opposite angles are supplementary angles,

Hence, the pairs of angles are ∠CBF & ∠CEF

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Answer:

The answer is 112ft

Step-by-step explanation:

32+16+8+8+16+8+8+16 = 112ft

Answer:

112ft

Step-by-step explanation:

The length of the little rectangle jutting out is the only unmarked length, so once we find that we can just add up all the sides to find the perimeter.

We see the overall length of the shape is 24ft and the length of the top of the shape, minus the unmarked length, is 16ft. This means the unmarked length is 24ft-16ft=8ft

Now add up each side to get to the perimeter:

32ft + 16ft + 16ft + 8ft +8ft +8ft +8ft +16ft = 112ft

The number of Caroline's textbook is 8

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.

Represent the Notebook bought by Bert as q

q = p-5

p-2= 2q

p = 2q +2

substitute 2q +2

q = 2q+2-5

2q-q = 3

q = 3

substitute 3 for q

3 = p-5

p = 5+3

p= 8

Therefore Caroline's number of notebook is 8

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Answer:

8.25 gallan=33 quart

Step-by-step explanation:

The correlation coefficient of the data-set in this problem is given as follows:

C. r² = 0.931.

The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.

The points from the table in this problem are given as follows:

(3,2), (4,4), (5,5), (7,6), (10,20).

Inserting these points into a calculator, the correlation coefficient is obtained as follows:

r² = 0.931.

Meaning that the correct option is given by option C.

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The combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

The volume of a cube is calculated by cubing the length of its side.

here,

Let's denote the length of the sides of the 4-foot and 6-foot cubes as "a" and "b", respectively. Then the length of the side of the 10-foot cube is "c", and we know that:

a³ + b³ = c³

We want to confirm if the combined volume of a 4-foot cube and a 6-foot cube is equal to the volume of a 10-foot cube. We can calculate the volumes of the cubes as follows:

Volume of 4-foot cube: a³ = 4³ = 64 cubic feet

Volume of 6-foot cube: b³ = 6³ = 216 cubic feet

Volume of 10-foot cube: c³ = 10³ = 1000 cubic feet

The sum of the volumes of the 4-foot and 6-foot cubes is:

64 + 216 = 280

Therefore, the combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

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Answer:

Step-by-step explanation:

For part a:

Mean: Use the AVERAGE function to find the mean of the "Number" column.

Median: Use the MEDIAN function to find the median of the "Number" column.

Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.

Maximum: Use the MAX function to find the maximum value in the "Number" column.

Minimum: Use the MIN function to find the minimum value in the "Number" column.

For part b:

Mean: Use the AVERAGE function to find the mean of the "Percent" column.

Median: Use the MEDIAN function to find the median of the "Percent" column.

Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.

Maximum: Use the MAX function to find the maximum value in the "Percent" column.

Minimum: Use the MIN function to find the minimum value in the "Percent" column.

For part c:

The statistics on children whose parents do not have secure employment provide important insights into the state of the economy. In this case, the mean and median of the number of children in each state seem to be around 450,000. The mode cannot be determined since there are no repeated values in the "Number" column. The maximum number of children is 678,000 in Ohio, while the minimum number is 141,000 in Iowa.

Comparing the states, Indiana has a slightly higher mean and median percent of children whose parents do not have secure employment at 27%, compared to the other surrounding states which range from 20% to 31%. However, there is no clear state with the best or worst data as the range of the percent values is not too wide.

In terms of comparison, the number of children may provide a more comprehensive understanding of the extent of the problem, as it gives a clearer picture of the actual number of children affected. However, the percentage provides a more relative comparison between the states, allowing for easier comparison and a clearer understanding of the proportion of children affected in each state.

Answer:

Step-by-step explanation:

5 times -4 is -20, so the equation becomes -20 - r + 1 = -37

-20 plus 1 equals -19, so the equation is now -19 - r = -37

Then you add 19 to both sides to isolate r

-r = -18

To get a positive r, divide or multiply both sides by -1, and you get r = 18

[tex]5(-4)-r+1=-37[/tex]

Simplify:

[tex]-20-r+1=-37[/tex]

Combine Like Terms:

[tex](-r)+(-20+1)=-37[/tex]

[tex]-r-19=-37[/tex]

Add 19 to both sides:

[tex]-r-19+19=-37+19[/tex]

[tex]-r=-18[/tex]

Divide both sides by -1:(To remove the negative from the variable r)

[tex]\dfrac{-r}{-1}=\dfrac{-18}{-1}[/tex]

[tex]\boxed{r=18}[/tex]

Step-by-step explanation:

for z -> 3 (3z - 2) -> (3×3 - 2) = 7

Answer:

The correct formula that expresses the statement "when x is equal to the square root of another number, s, plus the square root of two" is:

x = √s + √2

This formula says that x is equal to the square root of s plus the square root of 2.

Answer:

-30

Step-by-step explanation:

Answer:

f(x)=3x^2+2

Step-by-step explanation:

use pm