Evaluate the factorial expression. 27!30!​ 27!30!​= In how many ways can five people line up at a single counter to order food at McDonald's? Five people can line up in ways. How many ways can a 3-person subcommittee be selected from a committee of 8 people? The number of ways is

Given, the indicated variable is: ab - ac = 2, We have to solve the given equation for a. So the answer is a = 2/(b - c).

Let's do this: Factor out the a from the left-hand side of the equation.

Using the distributive property, we get: a(b - c) = 2

Now, we'll isolate a by dividing both sides by (b - c).

Thus, we get: a = 2/(b - c)

Therefore, the value of the variable a is 2 divided by the quantity of (b - c).

Let's have a look at the steps: ab - ac = 2

a(b - c) = 2

a = 2/(b - c). Hence, we have obtained the value of the variable a by solving the given equation.

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Answer:

C

Step-by-step explanation:

x4(x4-5)+5(x4-5)

=x8-5x4+5x4-25

x8-25

Answer:

x=60

Step-by-step explanation:

this is an isosceles triangle. so angle D and F are equal. D= x and F=x. so 58+x+x=180

2x+58=180

2x=122

x=60

The given series diverges. The condition not satisfied is that the magnitude of the terms does not decrease.

In the Alternating Series Test, one condition is that the magnitude of the terms must decrease as the series progresses. However, in the given series Σ(-1)^(k+1) / (2k + 1), the magnitude of the terms does not decrease. If we evaluate the series, we can observe that the terms alternate in sign but their magnitudes actually increase. For example, the first term is 1/2, the second term is 1/3, the third term is 1/4, and so on. Therefore, the series fails to satisfy the condition of the Alternating Series Test, which states that the magnitude of the terms should decrease. Consequently, the series diverges.

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Answer:

i believe it’s 7.9 miles

Step-by-step explanation:

if there’s no specific location of the house then 7.9 must be the answer

Answer: 16/20

Step-by-step explanation:

If ur asking for the sine of angle C

Answer: 18

Step-by-step explanation:

To get the answer you need to divide 12 by 2 to see what it was multiplied by. (6) Now that you know what the first part of the ratio was multiplied by, you can multiply the other part of it as well.

3 x 6 = 18

You can fact-check it by simplifying the fraction 12/18 which is 2/3.

Answer:

18

Step-by-step explanation:

12 drops of blue would be 6 sets of colouring, meaning you need to do the number of sets multiplied by the drops, giving us 6x3

And 6x3 is 18

Answer:

Mean: 10.7

Median: 11

Mode: 12

Hope you find this helpfull:)

Answer:

96Km

Step-by-step explanation:

l wrote 90/60 because the speed is given in hours.

so I had to deal with hours only not hours and minutes.

that's why I wrote 90/60 .

you can also choose to divide.

I mean to change the minutes to hours so that the formula can work.

good day.

Answer:

x = 33

Step-by-step explanation:

Sum of the interior angles of a 5-sided polygon = 540°

Therefore all the interior angles of the given polygon would all be equal to 540°.

Thus:

(4x - 25)° + (3x + 25)° + (2x - 3)° + (4x)° + (3x + 15)° = 540°

Solve for x

4x - 25 + 3x + 25 + 2x - 3 + 4x + 3x + 15 = 540

Combine like terms

4x + 3x + 2x + 4x + 3x - 25 + 25 - 3 + 15 = 540

16x + 12 = 540

16x = 540 - 12

16x = 528

Divide both sides by 16

x = 33

Answer:

4 sigfig is 164.4

3 sigfig is 164.

1 sigfig is 200

hope that answers your question

comment for more explanation

Answer:

67

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

x + 55 = 90 (Right angle triangle)

x = 90 - 55

x = 35

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Given:

1.75 cups per batch

That is

\(\frac{1.75}{1.75}\) Cups per \(\frac{1}{1.75}\) batch = 1 cup per \(\frac{1}{1.75}\) batch

Therefore, 5.25 cups will make

\(5.25 *\frac{1}{1.75}\) Batches = \(\frac{5.25}{1.75}\) = 3 Batches

ANSWER being: 3 batches

The function g(x) is a transformation of the cube root parent function f(x) = ∛x will be g(x) = ∛(x - 4) - 3. Then the correct option is D.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function g(x) is a transformation of the cube root parent function that will be given below.

f(x) = ∛x.

If we subtract h in the variable of the function then the function shifts toward the left by h units.

And if we subtract k in the function then the function shifts downward by k units.

Then the function g(x) will be

g(x) = ∛(x - 4) - 3

Then the correct option is D.

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Answer:

answer is x=-1/10 is the answer

Answer:

1) true

2) false

hope it worked

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Divide the numerator by the denominator.

When a letter like a, b, x or y pops up in a mathematical expression, it's called a variable, but really it's a placeholder that represents a number of unknown value. You can perform all the same mathematical operations on a variable that you'd perform on a known number. That fact comes in handy if the variable pops up in a fraction, where you'll need tools like multiplication, division and canceling of common factors to simplify the fraction.

Combine like terms in both the numerator and the denominator of the fraction. When you first start handling fractions with variable, this may be done for you. But later on, you might encounter "messier" fractions like the following:

(a + a) / (2_a_ - a)

When you combine like terms, you end up with a much more civilized fraction:

2_a_/a

Factor the variable out of both numerator and denominator of the fraction if you can. If the variable is a factor in both places, you can then cancel it. Consider the simplified fraction just given:

2_a_/a

As a quick aside, any time you see a variable by itself, it's understood to have a coefficient of 1. So this could also be written as:

2_a_/1_a_

Which makes it more obvious that when you cancel the common factor a from both the numerator and denominator of the fraction, you're left with the following:

2/1

Which, in turn, simplifies to the whole number 2.

What if you have a fraction like 3_a_/2? You can't factor a out of both the numerator and the denominator of the fraction, but because it's in the numerator, you can treat it as a whole number. To make sense of this, first write the fraction out thusly:

3_a_/2(1)

You can insert the 1 in the denominator thanks to the multiplicative identity property, which states that when you multiply any number by 1, the result will be the original number you started with. So you haven't changed the value of the fraction at all; you've just written it a little differently.

Next, separate the factors thusly:

a/1 × 3/2

And simplify a/1 to a. This gives you:

a × 3/2

Which can be simply written as the mixed number:

a (3/2)

What if you end up with a messy fraction like the following?

(b2 - 9) / (b + 3)

At first glance there's no easy way to factor b out of both numerator and denominator. Yes, b is present in both places, but you'd have to factor it out of the entire term in both places, which would give you the even messier b(b - 9/b) in the numerator and b(1 + 3/b) in the denominator. That's a dead end.

But if you've been paying attention in your other lessons, you might notice that the numerator can actually be rewritten as (b2 - 32), also known as "the difference of squares," because you're subtracting one squared number from another squared number. And there's a special formula that you can memorize to factor the difference of squares. Using that formula, you can rewrite the numerator as follows:

(b - 3)(b + 3)

Now, take a look at that in the context of the entire fraction:

(b - 3)(b + 3) / (b + 3)

Thanks to that standard formula you either memorized or looked up, you now have the identical factor (b + 3) in both the numerator and the denominator of your fraction. Once you cancel that factor, you're left with the following fraction:

(b - 3) / 1

Which simplifies to just:

(b - 3)

In calculus, dx is a symbol used to represent a small change or increment in the variable x.

It is commonly used in derivative and integral expressions to indicate the variable of differentiation or integration.

For example, if we have the function f(x) and want to find its derivative, we would write it as df/dx, which represents the change in f with respect to the change in x.

Similarly, if we want to find the integral of a function g(x), we would write it as ∫g(x)dx, which represents the sum of all the small changes in g(x) multiplied by the corresponding small changes in x.

In short, dx is used to indicate the variable of differentiation or integration in calculus.

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Answer:

No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.

Step-by-step explanation:

In case when ben wants to save $15 for a week and the total number of weeks is 10 so the total saving amount is $150. Now if the cost of a stereo is less than the total of saving amount so he is confident to purchase the stereo.

Now if the amount that required to be saved is represented by a is more than $150 so he is unable to purchase a stereo

Hence, the correct option is a.

Answer:

Step-by-step explanation:

Using the equation, A + 212 ≥ 365

No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.

The area of triangle PQR is 336 square units.

First, we can find the length of PM using the midpoint formula:

PM = (PQ) / 2 = 36 / 2 = 18

Next, we can use the angle bisector theorem to find the lengths of PX and QX. Since PX bisects angle QPR, we have:

PX / RX = PQ / RQ

Substituting in the given values, we get:

PX / RX = 36 / 26

Simplifying, we get:

PX = (18 * 36) / 26 = 24.92

RX = (26 * 18) / 26 = 18

Now, we can use the Pythagorean theorem to find the length of AX:

AX² = PX² + RX²

AX² = 24.92² + 18²

AX² = 621 + 324

AX = √945

AX = 30.74

Since Y lies on the perpendicular bisector of PQ, we have:

PY = QY = PQ / 2 = 18

Therefore,

AY = AX - XY = 30.74 - 8

                      = 22.74

Finally, we can use Heron's formula to find the area of triangle PQR:

s = (36 + 22 + 26) / 2 = 42

area(PQR) = sqrt(s(s-36)(s-22)(s-26)) = sqrt(42*6*20*16) = 336

Therefore, the area of triangle PQR is 336 square units.

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Answer:

8 inches

Step-by-step explanation:

The area of a circle is:

A = π\(r^{2}\)

We know the area is 16π

16π = π\(r^{2}\)

16 = \(r^{2}\)

Taking the square root of both sides.

4 = r

The diameter is 2 times the radius.

D = 2r.

D = 2(4) = 8 inches

Answer:

pi r *2 = 16 pi

r*2=16

r= squre root of 16 = 4

diameter = 2r = 8 units

$13608

Amount saved by Bao per month = $179

Amount saved by Bao per month = Ada's savings - 179

Amount saved by Ada = $179 + $145

Amount saved by Ada per month = $324

time = three and a half years

We convert years to months:

12 months = 1 year

time = 3(12) + 1/2(12) = 36 + 6

time = 42 months

Amount Ada saved = $324 × number of months

Amount Ada saved = $324 × 42

Amount Ada saved = $13608

Answer:

A, C, E

Step-by-step explanation:

A function cannot have an x-value that produces more than y-value.  Examples would be {(2, 2), (2,3)} and {(1,0), (1,5)}.

A - This could be a function because it follows the above rule.

B - This can not be a function because it has an x-value that has two y-values.

C - This could be a function because it follows the rule.

D - This can not be a function because it has an x-value that has two y-values.

E - This could be a function because it follows the rule.

Answer:

AB=5

Step-by-step explanation:

Triangle TAB is similar to triangle TWE. This can be proven through AA congruency. Because line AB is parallel to line segment WE, angle TAB is congruent to angle TWE (corresponding angles) and angle TEW is congruent to angle TEW(corresponding angles). Now, having proved that triangle TAB is similar to triangle TWE, we know that similar triangles have proportional sides. We can do \(\frac{TB}{AB} = \frac{TE}{WE}\), plug in values for \(\frac{4}{AB} = \frac{16}{20}\)  , simplify   \(\frac{4}{AB} = \frac{4}{5}\), both fractions have a four in the numerator and must be equal to each other so AB=5.

This is False in light of the stated statement. Due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

How is regression calculated?

Y = mX + b, where X is the predictive (independent) factor, m is really the approximately slope, and b is the expected intercept, is the methodology for simple linear regression.

The relationship between scattered data points in any set is shown by a regression line. When there is a linear pattern, it displays the relationship between the dependent y variable and independent x variables.

The correlation between the independent variables (IVs) and the dependent variable is described by a linear regression equation (DV). The DV for the IV values you indicate can also be predicted for new values.

Hence we get the required answer.

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Answer:

i think its reflection over the x-axis up 1 unit

Step-by-step explanation:

The words savage and savory are neither similar nor contradictory.

Contradiction is a term used to indicate mutually opposite things. It is commonly used in statements where both the statements cannot be true.

Savage is a word the meaning of which is wild or non cultivated in a context as an adjective. In another context, savage can be used as a noun to define an uncivilized or a brutal human.

On the other hand, savory is a completely different term which is used to define the taste of the dishes, typically in a positive way.

Hence the terms savage and savory are neither similar nor contradictory words.

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Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

-2(-1/2) + 3 = 4(1/2) + 2

1 + 3 = 2 + 2

4 = 4

6(1/2) + 4(-1/2) = 1

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

Step-by-step explanation:

I'm assuming you mean:

(4 - 2) / (-5 - 2)

First, simplify the numerator:

4 - 2 = 2

Next, simplify the denominator:

-5 - 2 = -7

Now, substitute the simplified numerator and denominator into the expression:

(4 - 2) / (-5 - 2) = 2 / (-7)

This fraction can be simplified by dividing numerator and denominator by their greatest common factor, which is 1 in this case:

2 / (-7) = -2/7

Therefore, (4 - 2) / (-5 - 2) = -2/7.