write the expression useing exponents 4×4×4×4​

9514 1404 393Answer:

  21·a^5·b^2

Step-by-step explanation:

The k-th term is ...

  C(7, k)·a^(7-k)·b^k . . . . . where k counts from 0 to n

Then k=2 for the third term. The coefficient of it is ...

  C(7, 2) = 7!/(2!(7-2)!) = 7·6/(2·1) = 21

The third term is ...

  21·a^5·b^2

Option 1's airfare will set you back $2600.

The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired. See.

We have been given that

For option 1

Airfare = $x

Hotel = $600

For option 2

Airfare = $0.75x

Hotel = $800

Only 10 family members can attend if they choose Option 1.

10x + $600 .........eq 1.

12 family members can attend the reunion if they choose Option 2.

12(0.75)x + $800

9x + $800 ........eq 2.

By using Eq (1) and Eq (2)

10x + $600 = 9x + $800

10x - 9x = $800 - $600

x = $200

Put the value of x in the eq (1)

Then we get 10x + $600

= 10 x 200 + $600

= 2000 + $600

=  $2600

Hence ,  the cost of airfare for Option 1 is  $2600.

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Answer:

60

step-by-step explanation:

Answer: 60

Step-by-step explanation: Basically just multiply the whole number by 2 :)

Whenever you see something times 0.5, just know that its going to be that number times 2 (like another half of that number if you understand)

Why? Because 0.5 is basically like a one half (1/2) and you flip the stuff. since 0.5 is a half, here's a tip. Whenever you're dividing with decimals, use the formula KCF (keep, change, flip) (what my teacher taught me before)          

Here's a drawing to better explain:

The following area tagged expression or sentence as;

1. Expression

2. Expression

3. Sentence

4. Sentence

5. Expression

Algebraic expressions are described as expressions that are composed of variables, terms, coefficients, factors and constants.

These expressions are also identified with various mathematical or arithmetic operations, such as;

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Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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Answer:

Of the 500 parents surveyed 275 would be expected to spank their​ children.

Step-by-step explanation:

Let the random variable X represent the number of parents who spank their children.

It is provided that, from previous studies, p = 55​% of parents spank their children.

A random sample of n = 500 adults were selected.

The event whether a parent spank their children is independent of other parents.

The random variable X thus follows a Binomial distribution with parameters n = 500 and p = 0.55.

The expected value of a Binomial random variable is:

\(E(X)=np\)

         \(=500\times 0.55\\=275\)

Thus, of the 500 parents surveyed 275 would be expected to spank their​ children.

From the 500 parents surveyed, the number of parents that will be expected to spank their​ children is 275 parents.

Number of parents surveyed = 500

Percentage of parents that spank their children = 55%

Therefore, from the 500 parents surveyed, the number of parents that will be expected to spank their​ children  will be:

= 55% × 500

= 0.55 × 500

= 275

Therefore, the number of parents will be 275 parents.

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Answer:

cos 60 degrees=1/2 and sin 60 degrees = square root 3/2

The answer it's true.

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

hello! :) have a good day!

1). 24

2). 27

3). 5

PICTURE 1:

The answer is 24: (13 7/10) Rounded To The Nearest Whole Number is: (14)

\(13 \frac{7}{10} = 14\)

AND,

(10 1/8) Rounded To The Nearest Whole Number is: (10)

\(10 \frac{1}{8} = 10\)

So, 14 + 10 = 24

______________________________________

PICTURE 2:

The answer is 5: (8 1/5) Rounded To The Nearest Whole Number is: (8)

\(8 \frac{1}{5} = 8\)

AND,

(2 7/8) Rounded To The Nearest Whole Number is: (3)

\(2 \frac{7}{8} = 3\)

So, 8 - 3 = 5

______________________________________

PICTURE 3:

The answer is 27: (58 5/12) Rounded To The Nearest Whole Number is: (58)

\(58 \frac{5}{12} = 58\)

AND,

(30 5/7) Rounded To The Nearest Whole Number is: (31)

\(30 \frac{5}{7} = 31\)

So, 58 - 31 = 27

______________________________________

HERE ARE ALL THE ANSWERS:

PICTURE 1: 24

PICTURE 2: 5

PICTURE 3: 27

HOPE THIS HELPS!! :)

Answer:

the answer is 17x+20

Step-by-step explanation:

7x+10x+20

17x+20

hope it helps

mark me brainliest pls

Answer:

17x+20

Step-by-step explanation:

like terms= 7x and 10x so add= 17x

unlike term 20 it remains as it is.

so 17x+20 further cannot be simplified as both are unlike terms

Using the triangle inequality theorem, the possible values for the third side of the triangle are: 5 < x < 35.

The Triangle Inequality Theorem asserts that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Stated differently, the difference between the lengths of any two sides must be less than the length of the third side.

Thus, if you have the lengths of two sides of a triangle, as 20 and 15, we have:

20 - 15 < x < 20 + 15

5 < x < 35

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Answer:

  $766.23

Step-by-step explanation:

The amortization formula is appropriate for this. (Better, use a financial calculator or spreadsheet.)

  A = P(r/12)/(1 -(1 +r/12)^-(12t))

where P is the amount borrowed (25,000), r is the annual rate (0.065), and t is the number of years (3).

Putting the given numbers into the formula, we have ...

  A = $25,000(0.065/12)/(1 -(1 +0.065/12)^(-36))

  A = $25,000(.00541667)/(1 -1.00541667^-36)

  A = $25,000(0.00541667)/(0.1767322)

  A = $766.23

The monthly payment is $766.23.

_____

Comment on tools

A graphing or scientific calculator is useful for these. Something like a TI-84, or any of the equivalents, will have financial calculations like this built in. There are also numerous apps available for phone or tablet that will do financial calculations.

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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Answer:

The probability that none of the households are tuned to 50 Minutes is 0.04398.

Step-by-step explanation:

We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.

A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.

The above situation can be represented through binomial distribution;

\(P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........\)

where, n = number of samples (trials) taken = 14 households

r = number of success = none of the households are tuned to 50 min

p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%

Let X = Number of households that are tuned to 50 Minutes

So, X ~ Binom(n = 14, p = 0.20)

Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)

               P(X = 0)  =  \(\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}\)

                              =  \(1 \times 1 \times 0.80^{14}\)

                              =  0.04398

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

x is all real numbers

Step-by-step explanation:

5(x-7) + 42 = 5x+7

Distribute

5x - 35 +42 = 5x+7

Combine like terms

5x +7 = 5x+7

Subtract 5x from each side

7=7

This is always true, so x can be any number

Answer:

Hey there!

5(x-7)+42=5x+7

5x-35+42=5x+7

7=7

Infinite solutions.

Hope this helps :)

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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Answer:

A

Step-by-step explanation:

iTS JUST a

Answer:

Step-by-step explanation:

i cant see it

Answer:

circumference =2×3.14

circumference =6.28 m

Answer:

square root of 25

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

the square root of 25 is 5, and thats the only rational number there

I hope I was helpful! :D

Answer:

$677.25

Step-by-step explanation:

Money deposited: $375.45 + 614.20 + $187.60 = $1177.25

Money withdrawn: $500.00

Total deposit: $1177.25 - $500.00 = $677.25

Answer: $677.25

Answer:

Option C: -$1500 is the correct answer.

Step-by-step explanation:

Given that:

Total amount invested in business = $24,000

Loss suffered in first quarter = $4500

As the amount is shared by Brian, Steve and Rita equally, therefore,

Loss of each person = \(\frac{Loss}{Number\ of\ people}\)

Loss of each person = \(\frac{4500}{3} = \$1500\)

As loss is defined by decrease in the investment,

Loss of each person = -$1500

Hence,

Option C: -$1500 is the correct answer.

Answer:

-$1,500

I hope this helps

The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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Answer:

Step-by-step explanation:

So, first they spend $100

The next week, they spend 20% less than $100, so they spent $80 that week.

The 3rd week, they spend 3/4 of $80, so they spend $60 that week.

Finally, we add the spent money from the 3 weeks (100 + 80 + 60) and get $240. I hope this helps!

Answer:

  GPA ≈ 2.67

Step-by-step explanation:

Grade points are weighted by credit hours:

  GPA = ∑(grade points×credit hours) / ∑(credit hours)

  GPA = (3×2 +2×4 +4×3 +2×3)/(2 +4 +3 +3)

  = (6 +8 +12 +6)/12 = 32/12 = 2 2/3

  GPA ≈ 2.67

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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3. We want to solve using properties;

It simply involve trying to reduce numbers to their simpliest form to make multiplication and addition easy without using calculator.

like; 21=20+1, 39=40-1 etc.

4. Given;

Answer: Do you need hel

Step-by-step explanation:

Answer:

The horizontal line test.

Step-by-step explanation:

If you do the test, the horizontal line will intersect at 2 points.