A triangle has one angle that measures 35°. which values could be the measures of the other two angles?

Answer:

  c)  36√15 cm³

Step-by-step explanation:

We can compute the volume of the pyramid if we know the area of its base, and its height.

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A regular quadrilateral is a square. If one side of the square is 6 cm, its area will be ...

  A = s² = (6 cm)² = 36 cm² . . . . area of the pyramid base

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Each triangular face will have a slant height that makes its area the same as that of the base.

  A = 1/2bh

  36 cm² = (1/2)(6 cm)h

  (36 cm²)/(3 cm) = h = 12 cm  . . . . .  divide by the coefficient of h

The slant height of a face is the hypotenuse of a right triangle whose short leg is half the side length, and whose long leg is the height of the pyramid. If that height is represented by h, the Pythagorean theorem tells us ...

  (6 cm/2)² +h² = (12 cm)²

  h² = (144 -9) cm²

  h = 3√15 cm . . . . . height of the pyramid

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The volume of the pyramid is given by ...

  V = 1/3Bh . . . . . . base area B, height h

Using the values we found above, we compute the volume to be ...

  V = (1/3)(36 cm²)(3√15 cm) = 36√15 cm³

Answer:

length: 6 inches

width: 7 inches

Step-by-step explanation:

Let n represent the number. Then the length is (n+2) and the width is (2n-1). The product of these dimensions is the area:

42 = (n+2)(2n -1) = 2n^2 +3n -2

2n^2 +3n -44 = 0 . . . . subtract 42

(n -4)(2n +11) = 0 . . . . . factor

n = 4 . . . . . . . . we aren't interested in the negative solution

Length = 4+2 = 6 . . . inches

Width = 2·4 -1 = 7 . . . inches

Final answer:

The dimensions of the rectangle given that its area is 42 square inches, the length is 2 inches more than a number, and the width is 1 inch less than twice the same number, are 6 inches by 7 inches.

Explanation:

To solve this problem, let's define the unknown number as

x. According to the problem, the length of the rectangle is 2 inches more than x (so it's x + 2), and the width is 1 inch less than twice the number x (which makes it 2x - 1).

Now, we'll use the formula for the area of a rectangle, which is length times width: (x + 2) * (2x - 1) = 42.

Solve this equation by expanding the parentheses (2x^2 + 4x - x - 2 = 42), simplifying (2x^2 + 3x - 2 - 42 = 0), and rearranging (2x^2 + 3x - 44 = 0).

Using the quadratic formula, we find that the possible values of x are 4 and -5.5. However, a negative size doesn't make sense in this context, so x = 4 inches. That makes the length = 4 + 2 = 6 inches, and the width = 2*4 - 1 = 7 inches. Therefore, "the dimensions of the rectangle are 6 inches by 7 inches".

Learn more about Algebra here:

brainly.com/question/24875240

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Final answer:

In a queueing system with customer arrivals every 3 minutes and service times of 2 minutes, the average number of customers in the system is calculated to be approximately 0.667

Explanation:

To calculatethe average number of customers in the system, we can use Little's Law, which states that the average number of customers in a stable queueing system is equal to the average arrival rate multiplied by the average time spent in the system.

First, we need to calculate the average arrival rate. Since customers arrive once every 3 minutes, the arrival rate is 1 customer per 3 minutes or 1/3 customers per second.

The total service time is 2 minutes, and the standard deviation is 6.3. Therefore, the average service time is 2 minutes.

Using Little's Law, we multiply the average arrival rate (1/3 customers per minute) by the average service time (2 minutes) to obtain the average number of customers in the system.

Average number of customers in the queue = (1/3) × 2 = 2/3 ≈ 0.667

Read more about standard deviaton at:

brainly.com/question/32836450

Answer:

The answer is: 20

Step-by-step explanation:

Significant figures are the meaningful digits that contribute to the precision and accuracy of the given number.

The given number: 24.67 has four significant figures because all the non-zero digits are significant.

Rounding off refers to the method of expressing the given number to the nearest whole number or nearest thousand, hundred, ten, etc.

Now, rounding off the given number (24.67) to one significant figure gives 20, which has only one significant figure. As the trailing zero is not significant.

Answer: 233.33

Step-by-step explanation:

350/3 = 116.66 (this is 1/3)

116.66 x 2 = 233.33  (this equals 2/3rds)

Hope this helps.

pd :)

Answer:

Option B is correct.

Step-by-step explanation:

We have been given that  3 lottery games have decided to play

So, here we have total possibility of numbers s between 0 and 9 which is total of 10 numbers

And number can be chosen more than once.

So, the probability will be

On simplification we will get

the probability of winning

Therefore, option B is correct.