MATHEMATICS HIGH SCHOOL

If the area of a rectangle is 16s^2t and the length is 8st^2, what would be the width of the rectangle, given that width is found by dividing area by length? Simplify the answer.2st

2 over the quantity s times t

the quantity of 2 times s all over t

t over the quantity 2 times s

Answers

Answer 1
Answer: Given:
Area = 16s²t
Length = 8st²
Width = ?

Width = Area / Length
Width = 16s²t / 8st²
Width = 2s/t ⇒ the quantity of 2 times s all over t.
Answer 2
Answer:

Answer:

(2s)/(t)

Step-by-step explanation:

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an indicator variable x takes value 0 with probability 1/4 and 1 with probability 3/4, what is e[(1 x)(1-x)]?

Answers

The expected value E[(1-x)(1-x)] is 1/4. This represents the average value of the function (1-x)(1-x) for the given probability distribution of x values.

We are given an indicator variable x with values 0 and 1. The probability of x = 0 is 1/4 and x = 1 is 3/4. We need to find the expected value E[(1-x)(1-x)].

Step 1: Determine the function we are working with.
We have the function (1-x)(1-x), which simplifies to (1-2x+x^2).

Step 2: Find the probabilities for each value of x.
For x = 0, the probability is 1/4.
For x = 1, the probability is 3/4.

Step 3: Compute the function values for each x value.
For x = 0, (1-2(0)+0^2) = 1.
For x = 1, (1-2(1)+1^2) = 0.

Step 4: Calculate the expected value.
E[(1-x)(1-x)] = (1)(1/4) + (0)(3/4) = 1/4.

For more about probability distribution:

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The circumference of a circle is 60pie cm what is the length of an arc of 140 degrees

Answers

Find the diameter, the radius, and the length of an arc of 140? 8. The circumference of a circle is 60 cm. Find the diameter, the radius, and the length of an arc of 140°. a. 120 cm; 30 cm; 160 cm b. 30 cm; 60 cm; 11.7 cm c. 60 cm; 30 cm; 23.3 cm d. 60 cm; 120 cm; 11.7 cm 9. A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a... show more

E=mc
e = mc {}^(2)

solve for c​

Answers

e = mc
e/m = mc/m
e/m = c
c = e/m
i think it’s c = e / m

Two angles that can be trisected with a straightedge and compass are a 90angle and a _____ angle.A. 9
B. 75
C. 45
D. 90

Answers

The correct answer is:

C) 45.

Explanation:

An angle of measure (2\pi)/(N) can be trisected if and only if N is not divisible by 3.

A 45° angle in radians is (\pi)/(4). Setting up a proportion, we can find the value of N to determine if this fits:

(\pi)/(4)=(2\pi)/(N)

Cross multiply:

\pi * N = 4 * 2\pi \n N\pi = 8\pi
 
This means N = 8, and is not divisible by 3; thus the 45 degree angle is trisectible.

the answer on apex is 45°

What are the solutions of this quadratic equation? x^2+13=8x+37

Answers

The solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.

What is a quadratic equation?

The quadratic equation is defined as a function containing the highest power of a variable is two.

The given equation as:

x² - 8x + 13 = 37

Subtracting 37 from both sides, we get:

x² - 8x - 24 = 0

Now, we have the equation in standard form, so we can use the quadratic formula to find the solutions:

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 1, b = -8, and c = -24.

Substitute these values into the quadratic formula, and we get:

x = (-(-8) ± √((-8)² - 4(1)(-24))) / 2(1)

x = (8 ± √(64 + 96)) / 2

x = (8 ± √160) / 2

x = (8 ± 4√10) / 2

Simplifying, we get:

x = 4 ± 2√10

Therefore, the solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.

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Answer:

              x\in\left\{4-2√(10)\ ,\ \,4+2√(10)\,\right\}

Step-by-step explanation:

x^2+13=8x+37\n\nx^2-8x-24=0\n\na=1\,,\ \ b=-8\,,\ \ c=-24\n\nx_1=(-(-8)-√((-8)^2-4\cdot1\cdot(-24)))/(2\cdot1)=\frac{8-√(64+96)}2=\frac{8-√(160)}2 =\n\n=\frac{8-4√(10)}2=\frac{2(4-2√(10))}2=4-2√(10) \n\nx_2=(-(-8)-√((-8)^2-4\cdot1\cdot(-24)))/(2\cdot1)=\frac{8+4√(10)}2=4+2√(10)

What are the real imaginary solutions of the polynomial equation?
x^3=216

Answers

When you look at it, you would wonder why this equation is considered to be a polynomial where in fact there is only one factor. The only reason to explain this is that the other factors have zero as the coefficient. On another note, to answer this problem, we need to get the cube root of 216 which is 6, which is also the answer to this problem. 
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