QuestionCalculate the arc length for a circle whose radius is 6 with a central angle θ=135°. S=

Answers

Answer 1
Answer:

9514 1404 393

Answer:

  S = 4.5π ≈ 14.14 units

Step-by-step explanation:

The arc length is given by ...

  s = rθ . . . . . r = radius; θ = central angle in radians

The angle 135° is ...

 135° = 135°(π/180°) = 3π/4 radians

The arc of interest has length ...

  s = 6×3π/4 = 9/2π ≈ 14.14 . . . units


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two sides of an equilateral triangle measure (y+10) and (y^2(-2)). if the perimeter of the triangle is 21 units what is the value of y?

Answers

Answer:

  y = -3

Step-by-step explanation:

Each side of an equilateral triangle will have a length that is 1/3 the perimeter. This triangle has sides of length 21/3 = 7, so ...

  y + 10 = 7

  y = 7 - 10

  y = -3

This is consistent with the other given side measure ...

  y^2 -2 = (-3)^2 -2 = 9 -2 = 7

Lena is on a two week bicycle trip. After 5 days she had ridden 212 miles. Express Lena’s rate as a unit rate

Answers

Answer:

42.4 miles per day

Step-by-step explanation:

212 miles ÷ 5 (days) = 42.4 miles

which means Lena can go at the rate of

42.4 miles per day

Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 70% want a used copy. Consider randomly selecting 15 purchasers.The bookstore has 10 new copies and 10 used copies in stock.
If 15 people come in one by one to purchase this text, what is the probability that all 15 will get the type of book they want from current stock?

Answers

Answer:

The probability that all 15 will get the type of book they want from current stock is 0.4838.

Step-by-step explanation:

Denote the random variable Xas the number of students who want to buy new copy.

The probability of a student wanting to buy a new copy is, P (X) = p = 0.30.

A random sample of n = 15 students is selected.

The random variable X follows a Binomial distribution.

The probability function of a Binomial distribution is:

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

It is provided that the bookstore has 10 new copies and 10 used copies in stock.

All the 15 students get their desired copy, then this can happen if at most 10 want to buy new copy and at least 5 wants to buy used copy.

Compute the probability of (5 ≤ X ≤ 10) as follows:

P (5 ≤ X ≤ 10) = P (X = 5) + P (X = 6) + P (X = 7) + P (X = 8) + P (X = 9) + P (X = 10)

                     ={15\choose 5}(0.30)^(5)(1-0.30)^(15-5)+{15\choose 6}(0.30)^(6)(1-0.30)^(15-6)\n+{15\choose 7}(0.30)^(7)(1-0.30)^(15-7)+{15\choose 8}(0.30)^(8)(1-0.30)^(15-8)\n+{15\choose 9}(0.30)^(9)(1-0.30)^(15-9)+{15\choose 10}(0.30)^(10)(1-0.30)^(15-10)\n=0.2061+0.1472+0.0811+0.0348+0.0116+0.0030\n=0.4838

Thus, the probability that all 15 will get the type of book they want from current stock is 0.4838.

A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.

Answers

Answer:

Due to the higher z-score, he did better on the SAT.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = (X - \mu)/(\sigma)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Determine which test the student did better on.

He did better on whichever test he had the higher z-score.

SAT:

Scored 1070, so X = 1070

SAT scores have a mean of 950 and a standard deviation of 155. This means that \mu = 950, \sigma = 155.

Z = (X - \mu)/(\sigma)

Z = (1070 - 950)/(155)

Z = 0.77

ACT:

Scored 25, so X = 25

ACT scores have a mean of 22 and a standard deviation of 4. This means that \mu = 22, \sigma = 4

Z = (X - \mu)/(\sigma)

Z = (25 - 22)/(4)

Z = 0.75

Due to the higher z-score, he did better on the SAT.

Let x = 20. Which expression has a value greater than 4x−10 ? 5x−100 8(x−10) 5(2x−26) 5x−30

Answers

Answer:

  8(x-10)

Step-by-step explanation:

When the calculation is repetitive, I like to let a calculator or spreadsheet do it. The value of the given function is

  4·20 -10 = 70

Only the expression 8(x-10) = 8(20-10) = 80 has a larger value for x=20.

_____

Comment on this solution

It is actually fewer keystrokes to copy the numbers into a calculator, but getting a record of results can be difficult.

Answer:

Step-by-step explanation:

10x - 8y =4-5x + 3y = -9

Please solve with elimination i really need the help!!
please show work

Answers

Answer:

x = 6

y = 7

Step-by-step explanation:

Here, (10x - 8y = 4) and (- 5x + 3y = - 9) are two given equation

Now, Name the equation

10x - 8y = 4

take 2 as common we get

2(5x - 4y = 2)

5x - 4y = 2 ...(1)

- 5x + 3y = - 9 ...(2)

Now, Subtract (1) from (2)

5x - 4y = 2

- 5x + 3y = - 9

————————

- y = - 7

y = 7

Now,Put the value of y in equation (1) we get

5x - 4y = 2

5x - 4(7) = 2

5x - 28 = 2

5x = 28 + 2

5x = 30

x = 30÷5

x = 6

Thus,The value of xis6and yis7

FORVERIFICATIONONLY:

5x - 4y = 2

5(6) - 4(7) = 2

30 - 28 = 2

2 = 2

- 5x + 3y = - 9

- 5(6) + 3(7) = - 9

- 30 + 21 = - 9

-9=-9

Hence,L.H.S = R.H.S

-TheUnknownScientist