MATHEMATICS HIGH SCHOOL

Write the number of permutations in factorial form. Then simplify, how many different ways can you and six of your friends sit in your assigned seats in math classA)6!; 120
B)6!;720
c)7!;2,520
D) 7!;5,040

Answers

Answer 1

Answer:

Answer: D) 7!;5,040

Step-by-step explanation:

Given: The number of friends = 7

Permutations says that the number of different ways of arranging r objects out of n objects is given by ;-

$^nP_r=(n!)/((n-r)!)$

By permutations the number of different ways they can sit is given by :-

$^7P_7=(7!)/((7-7)!)=(7!)/(0!)\n\n=7*6*5*4times3*2*1\n\n=5,040$

Therefore, the different ways can you and six of your friends sit in your assigned seats in math class = 5,040.

Answer 2

Answer: You and 6 of your friends. Total of 7 people.

The answer is D.) 7! ; 5,040

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The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100 meters, what is the width of the rectangle?a. 13 meters b. 12 meters c. 11 meters
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2 Which of the following functions best represents the graph? f(x) = x3 + x2 − 4x − 4 f(x) = x3 + 4x2 − x − 4 f(x) = x3 + 3x2 − 4x − 12 f(x) = x3 + 2x2 − 4x − 8
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(3x+8)+x>3x-12 can someone tell me how to solve it because already know the answer which is x>-20

Find the Surface Area and Volume of Sphere with radius 12 cm.

Answers

$Radius:r=12cm\n\nSurface\ area:\nA=4\pi r^2\to A=4\pi\cdot12^2=4\pi\cdot144=576\pi\ (cm^2)\n\nVolume:\nV=(4)/(3)\pi r^3\to V=(4)/(3)\pi\cdot12^3=(4)/(3)\pi\cdot1728=4\pi\cdot576=2304\pi\ (cm^3)$

The surface area of a sphere is 4 pi R² = 576 pi = 1,809.6 cm² (rounded)

The volume of a sphere is 4/3 pi R³ = 2,304 pi = 7,238.2 cm³ (rounded)

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.a. 8/9
b. 2

Answers

Hello,

Answer B
$a_(0)=-5\na_(9)=a_(0)+9*r\n13=-5+9*r\nr= (18)/(9)=2$

Question: Find the x-intercepts for the parabola defined by this equation:y = 2x²
- 8x + 10
Write your answer as two ordered pairs:
(x1, y1), (×2, y2)
Separate the values with a comma.
Round, if
necessary, to the nearest hundredth.

Answers

Answer:

To find the x-intercepts of the parabola defined by the equation y = 2x² - 8x + 10, you need to set y equal to zero (because x-intercepts occur when y is zero) and solve for x.

So, you have:

0 = 2x² - 8x + 10

Now, you can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 2, b = -8, and c = 10. Plug these values into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Since the discriminant (the value inside the square root) is negative, there are no real solutions, which means this parabola does not have x-intercepts in the real number system.

So, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts because there are no x-intercepts for this parabola in the real number system.

Step-by-step explanation:

Certainly, let's find the x-intercepts step by step for the equation:

y = 2x² - 8x + 10

Step 1: Set y to zero because x-intercepts occur when y equals zero:

0 = 2x² - 8x + 10

Step 2: Now, we want to solve this equation for x. We can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this formula:

a is the coefficient of the x² term (which is 2 in this case).

b is the coefficient of the x term (which is -8).

c is the constant term (which is 10).

Step 3: Plug the values of a, b, and c into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

Step 4: Simplify the equation inside the square root:

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Step 5: Now, notice that we have a square root of a negative number (√(-16)). In the real number system, we can't take the square root of a negative number. This means there are no real solutions for x.

Step 6: Since there are no real solutions, there are no x-intercepts for this parabola in the real number system. Therefore, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts in this case.

How much would $100 invested at 8% interest compounded continuously be worth after 15 years? Round your answer to the nearest cent.

Answers

Answer:

On Apex it is $332.01

Step-by-step explanation:

A(t)=P*e^rt

A(15)=100*e^0.08(15)

A(15)= 332.01

What multiplies to 3969 and adds to 126. Please help. I tried 49 and 81 but that did not work.

Answers

Factors of 3969:
1,3,7,9,21,27,49,63,81,147,189,441,567,1323,3969
-1,-3,-7,-9,-21,-27,-49,-63,-81,-147,-189,-441,-567,-1323,-3969 is this what you mean

Final answer:

In this Mathematics problem, you're searching for two numbers that, when multiplied, equal 3969 and, when added, equal 126. By factoring 3969, we find that the numbers 63 and 63 meet both criteria.

Explanation:

This Mathematics problem falls under factoring in Algebra. You are trying to find two numbers that multiply to 3969 (the product) and add up to 126 (the sum). The numbers you're looking for are 63 and 63. Let's see why.

First, factor 3969. The factors of 3969 are 1, 3, 9, 27, 81, 147, 441, 1323, and 3969. Looking at these factors, we see that only 63 and 63 multiply together to give 3969.

Now, check if they also add up to 126. Indeed, 63 + 63 equals 126, confirming that these are the two numbers you're looking for.