There are 10 people waiting on standby at an airport to get on the next flight when 2 seats open up. One
of the seats is in first class, and the other is in coach. What error is made in the work shown below to
calculate the number of ways to choose the passengers to fill the seats?
101
10.9.8
(10-2)!21 81.2.1
10.9 90
2.
17 = 45
The correct formula for 10C2 was not used.
There is a multiplication error in the numerator.
The solution is for combinations, but the situation calls for permutations,
8! was incorrectly divided out of the numerator and the denominator.

Answer:

2

Step-by-step explanation:

f'(x) is an odd function (symmetrical about the origin), therefore f(x) is an even function (symmetrical about the y-axis).  So f(x) = f(-x).

Since f(-4) = 2, f(4) = 2.

We can also show this using integrals:

f(-4) = ∫₀⁻⁴ f'(x) dx + C

2 = ½ (-4)(-2) + C

2 = 4 + C

C = -2

f(4) = ∫₀⁻⁴ f'(x) dx − 2

f(4) = ½ (4)(2) − 2

f(4) = 4 − 2

f(4) = 2

Answer:

Each of the pieces will be 0.5 feet long

Step-by-step explanation:

In this question, we are asked to calculate the individual length Anita will cut a ribbon 6 feet long into to ensure that each of the piece has the same length.

To calculate this, since we don not know what length each of the piece would be, we can say let the length of each of the pieces be x feet

Now, we know that there are 12 pieces that are equal in length. The length of all these 12 pieces would be 12 * x = 12x feet

Now what do we know again?

We also know that these 12x feet equals a total of 6 feet

mathematically therefore;

12x = 6

x = 6/12

x = 0.5 feet

Answer: Each piece will be 1/2 feet long.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given.

We simply have to divide the length of the ribbon (6) by the number of pieces that she wants to cut (12).

Mathematically speaking:

6 /12 = 1/2  

In conclusion, each piece will be 1/2 feet long.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

1.00 and 0.65

Step-by-step explanation:

:D

To find two decimals with a difference of 0.35, you can start with any decimal and add or subtract 0.35 from it.

To find two decimals with a difference of 0.35, we can start with any decimal and add or subtract 0.35 from it. Here are two examples:

These decimals have a difference of 0.35 between them.

It should look like the photo I've attached.

The points that represent the data are of the form (age, height), and the graph can be seen below.

Here we have the table:

Age (years) Height (cm)

11                   140

12                  145

12                   151

13                   160

14                   155

14                    161

15                    170

15                    179

16                    175

16                    179

Then the points that represent the data are of the form (age, height).

So we have 10 points:

(11, 140), (12, 145), (12, 151), (13, 160), (14, 155), (14, 161), (15, 170), (15, 179), (16, 175), (16, 179).

The graph of these 10 points can be seen below:

If you want to learn more about graphing:

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Answer:

Tenth term=14

Step-by-step explanation:

The nth term of a sequence=2n-6

Find the 10th term

If 2n-6= nth term

Then,

Tenth term=2(10)-6

=20-6

=14

Therefore,

Tenth term =14

Answer: 0.6 meters cubed.

Step-by-step explanation:

To find the answer to this, first find the volume of the cube.

Volume is equal to the side cubed. In this case, 1 cubed is 1, so the area of the cube is 1 meter cubed.

The depth of the water is 0.4 meters, so the water makes a shape of a rectangular prism, where the length and width are 1 meter, and the height is 0.4 meters.

The volume of a rectangular prism is l*w*h, so the volume of this rectangular prism is 0.4 * 1 * 1, or 0.4 meters cubed.

As such, the volume of the air in the tank is 1 - 0.4, or 0.6 meters cubed.

Answer:

0.6 meters CUBED

Step-by-step explanation:

hope it helps

The length of the side of a cube with a surface area of 390 sq cm is approximately 8.06 cm.

The student's question relates to finding the length of a side of the cube, given the total surface area of the cube. In the case of a cube, all sides are equal in length. Furthermore, a cube has six equal sides. Therefore, to find the length of one side, we can use the formula of the surface area of a cube, which is 6 * side² = Total Surface Area. For our problem, side² = 390 / 6 = 65. Hence, the length of the side would be the square root of 65, which is approximately 8.06 cm.

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The best description of the length of the side of the cube is Option C. between 8 and 9.

To determine the length of the side of a cube given its surface area, we first recall the formula for the surface area (SA) of a cube:

SA = 6s²

where s is the length of one side. We are given a surface area of 390 cm². We substitute this value into the formula and solve for s:

390 = 6s²

s² = 390 / 6

s² = 65

s = √65

To find the exact value of √65, we use a calculator:

√65 ≈ 8.06

Therefore, the length of the side of the cube is approximately 8.06 cm, which falls between 8 and 9. Hence, the correct answer is:

Option C. between 8 and 9

Complete question:

If the surface area of a cube is 390 cm^2. Which best describes the length of the side of the cube?

A. less than 7

B. between 7 and 8

C. between 8 and 9

D. greater than 9

Answer:

96

Step-by-step explanation:

Multiply 8 and 12.

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

97=29+17x

subtract 29 from both sides

68=17x

divide both sides by 17

4=x

Answer:

30% off

Step-by-step explanation:

63 is 70% of 90 which means that 30 percent of the price is off.

Please mark me brainliest. I need it. Hope this helps

Answer:

4

Step-by-step explanation:

6 + 3 + 9 + 2 + 4 + 3 + 1 =

9 + 11 + 7 + 1 =

20 + 8 =

28

28 / 7 =

4

The required mean number is 4 miles that Kiki cycled every day.

Given that,
The number of miles that Kiki cycled in a seven-week period Is shown: 6, 3, 9, 2, 4, 3, 1. What is the mean number of miles Kiki cycled is to be determined.

The average of the values is the ratio of the total sum of values to the number of values.

Mean = total sum of the reading/number of readings
Mean = (6 + 3 + 9 + 2  + 4 + 3 + 1) / 7

Mean = 28 / 7
Mean = 4

Thus, the required mean number is 4 miles that Kiki cycled every day.

Learn more about average here:

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Answer:

3/5

Step-by-step explanation:

Perimeter is the sum of the outside dimensions:

4 + 5 + 1 + 5 + 9 = 24 inches.

Answer:

9.19

Step-by-step explanation: please give brainliest

Answer:

[tex]-18\cdot h^{2} + 85\cdot h - 18[/tex]

Step-by-step explanation:

The polynomial in standard form is:

[tex](-2\cdot h + 9) \cdot (9\cdot h - 2)[/tex]

[tex]-18\cdot h^{2} + 81\cdot h +4 \cdot h - 18[/tex]

[tex]-18\cdot h^{2} + 85\cdot h - 18[/tex]

Answer:

14

Step-by-step explanation:

In mathematics, sum can be defined as the result or answer we get on adding two or more numbers or terms.

(-4)-10=14

The solution to the system of equations is (x, y) = (0, 2).

To solve the system of equations using the elimination method, we'll eliminate one of the variables by adding or subtracting the equations. Let's proceed:

Given the system of equations:

3x - y = -2

-2x + y = 2

We'll add the two equations together to eliminate the variable y:

(3x - y) + (-2x + y) = (-2) + 2

This simplifies to:

3x - y - 2x + y = 0

x = 0

Now, substitute x = 0 into one of the original equations to solve for y. Let's use the first equation:

3(0) - y = -2

-y = -2

y = 2

So, the solution to the system of equations is (x, y) = (0, 2).

Answer:

x=-2

Step-by-step explanation:

2+3x=-20-8x

22=-11x

x=-2

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex]2 + 3x = - 4(5 + 2x) \\ 2 + 3x = - 20 - 8x \\ 3x + 8x = - 20 - 2 \\ 11x = - 22 \\ \frac{11x}{11} = \frac{-22}{11} \\ x =- 2[/tex]

Answer:

Yes.

Step-by-step explanation:

The number 3 is a natural number, and all of these types of numbers are rational.

Another way to look at it is if a number can be written as a fraction, the number is rational.

Answer:

in fact yes

Step-by-step explanation:

it is since it's actually a normal number

Final answer:

After 30 years of monthly $250 contributions to a 401(k) with a 2% annual growth rate, the interest earned on the account is approximately $65,961.73.

Explanation:

To calculate the amount of interest earned in the 401(k) after 30 years with a 2% annual growth rate, we first need to figure out the future value of the account. We use the formula for the future value of an annuity, as the investments are made at regular intervals (monthly).

The formula is: FV = P *rac{(1 + r)^n - 1}{r}

Where:

FV is the future value of the annuity.

P is the payment amount per period.

r is the interest rate per period.

n is the total number of payments.

Since contributions are made monthly, the annual interest rate (2% or 0.02) is divided by 12 to get the monthly rate, and the total number of contributions is multiplied by 12 to account for monthly contributions over 30 years.

For an investment of $250 per month at a monthly rate of 0.02/12, over 360 months (30 years), we get:

FV = $250*  rac{(1 + 0.02/12)^{360} - 1}{0.02/12}

Now we calculate the future value:

FV ≈ $250 *  rac{(1 + 0.0016667)^{360} - 1}{0.0016667}

FV ≈ $250 *  rac{(1.0016667)^{360} - 1}{0.0016667}

FV ≈ $250 *  rac{2.0398873 - 1}{0.0016667}

FV ≈ $250 * 623.8469386

FV ≈ $155,961.73

The total amount invested over 30 years is $250 * 12 *30 = $90,000.

The interest earned is therefore:

Interest = FV - Total amount invested

Interest ≈ $155,961.73 - $90,000

Interest ≈ $65,961.73

So the interest earned on the account after 30 years is approximately $65,961.73.

Answer:

3.08mm

Step-by-step explanation:

use Pythagorean Theorem. 1.3^2 + 2.8^2 = 9.53 sqrt of 9.53 = 3.08

Answer:

3.087

Step-by-step explanation:

[tex] = \sqrt{ {1.3}^{2} + {2.8}^{2} } \\ = \sqrt{1.69 + 7.84} \\ = \sqrt{9.53} \\ = 3.087[/tex]

Answer:

$120.1355

Step-by-step explanation:

We can model this as an exponencial function:

P = Po * (1+r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

For this case, we have that Po = 900, r = -25% = -0.25 and t = 7, so we can find the value of P

P = 900 * (1 - 0.25)^7 = $120.1355

The price after 7 years will be $120.1355.

To calculate the value of Dan's computer after 7 years of 25% annual depreciation, we use the exponential decay formula. The approximate value of the computer after 7 years is $120.14.

To calculate the approximate value of Dan's computer after 7 years with a depreciation rate of 25% per year, we can use the formula for exponential decay:

[tex]V = P(1 - r)^t[/tex]

Plugging in the values, we get:

[tex]V = $900(1 - 0.25)^7[/tex]

[tex]V = $900(0.75)^7[/tex]

V = $900 * 0.1334838867

Therefore, the approximate value of the computer after 7 years is:

V = $120.14

Dan can expect the computer to be worth approximately $120.14 after 7 years.

Answer:

dependent

Step-by-step explanation:

This question assumes that we're working with a standard full deck of cards.  There are 52 unique cards in such a deck.

If David picks a card at random and doesn't put it back, then the number of unique cards left in his deck is 51.

These two events are dependent because the withdrawal of 1 card changes the probability of drawing any other of these 51 cards

Answer:

9 /16 cups

Step-by-step explanation:

Take the number of cups and divide by the number of servings

2 1/4 ÷ 4

Change to an improper fraction

9/4 ÷4

Copy dot flip

9/4 * 1/4

9 /16

Answer: 9/16

Step-by-step explanation: First, take the number of cups and divide by the number of servings. So we have 2 and 1/4 ÷ 4.

Now, rewrite 2 and 1/4 as the improper fraction 9/4 an 4 as 4/1.

So we have 9/4 ÷ 4/1.

Now, dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. So 9/4 ÷ 4/1 can be rewritten as 9/4 × 1/4.

Now, multiply across the numerators and denominators to get 9/16.

So there are 9/16 cup of raisins in each serving.

Answer:

1.5 GPH.

Step-by-step explanation:

Hello there!

Since we are given the amount that leaked out in half an hour, we can multiply it by 2 to get the final amount in gallons per hour (GPH).

:)

Answer: [tex]\frac{3}{2}[/tex] gallons of water per hour

Step-by-step explanation:

If [tex]\frac{3}{4}[/tex] of a gallon of water are leaked in half an hour, I conclude that if I multiply that by 2, it will give the result of gallons of water leaking per hour.

[tex]\frac{3}{4}*2=\frac{3}{2}[/tex]

Answer:

m+5=7

"A number m" will be a unknown nmber known as a variable. So it will be m.

"Increased by 5" is addition. So you are adding 5.

"Is 7" is equal to 7. it will be =7.

So when you put this together it will give you m+5=7

Answer:

8

Step-by-step explanation:

Ok here's the solution. I'm typing this to get 20+ characters:

2^3 = 2 x 2 x 2

= 8

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{z = 2^3}[/tex]

[tex]\mathsf{2^3 = z}[/tex]

[tex]\mathsf{2^3}[/tex]

[tex]\mathsf{= 2 \times 2 \times 2}[/tex]

[tex]\mathsf{= 4 \times2}[/tex]

[tex]\mathsf{= \bf 8}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: z = \bf 8 (Option A)}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

Answer:

  2

Step-by-step explanation:

For a linear function, the rate of change is the same everywhere. It is the same between points C and D as it is between points A and B: 2.

The rate of change between points C and D is 2.

Answer:

D

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Cost of 1 can = $18.95

Cost of x cans = 18.95x

Cost of paintbrushes = $55

Total cost = 18.95x+55

Let y be the total cost

y=18.95x+55

So, Equation that can be used : y=18.95x+55

We are given that Martina can use the equation x = 18.95y + 55 to find the total cost, y, of her order.

So, It is False