What is the square footage of a 13 foot by 14 foot circle?

Name the correct angles 5 and 7

Alex787 [66]

Answer:

Acute angle.

Right angle.

Obtuse angle.

Straight angle.

Reflex angle

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so th

Reptile [31]

Answer:

The least number of items to produce is 41

Step-by-step explanation:

Average Cost

Given C(x) as the cost function to produce x items. The average cost is:

$\displaystyle \bar C(X)=\frac{C(x)}{x}$

The cost function is:

$C(x) = -20x+1681$

And the average cost function is:

$\displaystyle \bar C(X)=\frac{-20x+1681}{x}$

We are required to find the least number of items that can be produced so the average cost is less or equal to $21.

We set the inequality:

$\displaystyle \frac{-20x+1681}{x}\le 21$

Multiplying by x:

$-20x+1681 \le 21x$

Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.

Adding 20x:

$1681 \le 21x+20x$

$1681 \le 41x$

Swapping sides and changing the sign:

$41x \ge 1681$

Dividing by 41:

$x\ge 41$

The least number of items to produce is 41

8 0

3 years ago

Show that the sum of the reciprocals of three different positive integers is greater than 6 times the reciprocal of their produc

Montano1993 [528]

If a,b,c are the 3 positive integers
1/a +1/b +1/c > 6/abc
(bc+ac+ab)/abc >6/abc so
(bc+ac+ab)>6
The lowest positive integers that are different are 1,2,3 so the lowest value that (bc+ac+ab) could have is 1•2+2•3+1•3=2+6+3= 11 therefore
1/a +1/b +1/c > 6/abc is true

8 0

3 years ago

Find the unit rate 6 and 2/5 revolutions in 2 and 2/3 in seconds

Makovka662 [10]

Step 1

Convert mixed fractions into fractions

6 2/5 = (6*5)+2) / 5 = 32/5

2 2/3 = (2*3)+2) / 3 = 8/3

Step 2

32/5 ÷ 8 / 3 ; where 32/5 is the 1st fraction and 8/3 is the 2nd fraction

Step 2 (A)

Get the reciprocal of the 2nd fraction:

From 8/3 to 3/8

Step 2 (B)

Multiply 1st fraction to the reciprocal of the 2nd fraction

32/5 * 3/8 = (32*3) / (5*8) = 96/40

Step 2 (C)

Simplify the fraction

96/40 divide by 4 will become 24/10

24/10 divide 2 will become 12/5. The simplest fraction of 96/40

The unit rate is 12/5 = 2 2/5 revolutions per second

3 0

3 years ago

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive pr

LenKa [72]

Answer:

(a) The correct option is: H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b) Explained below.

(c) The better value of α will be 0.10.

Step-by-step explanation:

An automobile manufacturer is considering using robots for part of its assembly process only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers.

To test whether the proportion of defective installations is less for the robots than for human assemblers use a single-proportion z-test.

(a)

The hypothesis can be defined as:

H₀: The proportion of defective installations is same for both the robots and human assemblers, i.e. p = 0.02.

Hₐ: The proportion of defective installations is less for the robots than for human assemblers, i.e. p < 0.02.

The alternate hypothesis is the claim or the statement that is being tested.

In this case we need to test whether the proportion of defective installations is less for the robots than for human assemblers or not, so that the manufacturer can decide whether they want to apply the conversion.

Thus, the correct option is:

H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b)

A type I error occurs when we discard a true null hypothesis and a type II error is made when we fail to discard a false null hypothesis.

In this case a type I error will be committed if conclude that the proportion of defective installations is less for the robots than for human assemblers when in fact it is not.

And a type II error will be committed if we fail to conclude that proportion of defective installations is less for the robots than for human assemblers.

(c)

The power of the test is the probability of rejecting a false null hypothesis.

The power of the test sis affected by the significance level of the test (α).

Lesser the significance level of the test the lesser is the power of the test.

If the value of α is reduced from 0.05 to 0.01 then the region of acceptance will increase. This implies that there is low probability of rejecting the null hypothesis even when it is false.

So higher the value of α the higher is the probability of making a correct decision.

Thus, the better value of α will be 0.10.

3 0

3 years ago