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2 years ago

CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already

Mathematics

1 answer:

Ratling [72]2 years ago

6 0

Answer:

15.7 in

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

$\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}$

It checks.

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Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by model

Ann [662]

Answer:

(1) The degrees of freedom for unequal variance test is (14, 11).

(2) The decision rule for the 0.01 significance level is;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The value of the test statistic is 0.3796.

Step-by-step explanation:

We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.

The following is the amount ($000) earned per month by a sample of 15 Claiborne models;

$3.5, $5.1, $5.2, $3.6, $5.0, $3.4, $5.3, $6.5, $4.8, $6.3, $5.8, $4.5, $6.3, $4.9, $4.2 .

The following is the amount ($000) earned by a sample of 12 Klein models;

$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.

(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;

$\text{F}_(_n__1-1, n_2-1_)$

Here, $n_1$ = sample of 15 Claiborne models

$n_2$ = sample of 12 Klein models

So, the degrees of freedom = ( $n_1-1, n_2-1$ ) = (15 - 1, 12 - 1) = (14, 11)

(2) The decision rule for 0.01 significance level is given by;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The test statistics that will be used here is F-test which is given by;

T.S. = $\frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }$ ~ $\text{F}_(_n__1-1, n_2-1_)$

where, $s_1^{2}$ = sample variance of the Claiborne models data = $\frac{\sum (X_i-\bar X)^{2} }{n_1-1}$ = 1.007

$s_2^{2}$ = sample variance of the Klein models data = $\frac{\sum (X_i-\bar X)^{2} }{n_2-1}$ = 2.653

So, the test statistics = $\frac{1.007}{2.653 } \times 1$ ~ $\text{F}_(_1_4,_1_1_)$

= 0.3796

Hence, the value of the test statistic is 0.3796.

3 0

2 years ago

A truck stops at a gas station where diesel fuel costs $3.99 per gallon. The truck needs 8.8 gallons of diesel for the driver to

Dmitry [639]

36.00 will be enough to pay for fuel because if you multiply the 8.8 gallons of diesel needed by the fuel cost per gallon you get 35.112

6 0

2 years ago

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estimate the total weight of two boxes that weigh 9.4 lb and 62.6 lb using rounding and compatible numbers. which estimate is cl

Scorpion4ik [409]

<span><span>1. </span>We have 2 boxes weighs:
=> 9.4 lb and 62.6 lbs.
Now, let’s estimate the total weight of this 2 boxes using rounding and compatible numbers.
For 9.4 lbs , the rounded and compatible number is 9 lbs
And for 62.6 lbs, the rounded and compatible number is 63 lbs
=> now, let’s try adding both numbers if we get a close answer
=> 9 +63
=> 72 = the estimated and rounded answer is 72.
Let’s check if we have close answer
=> 9.4 + 62.6
=> 72</span>

5 0

2 years ago

Let ∠D be an acute angle such that cosD=0.33. Use a calculator to approximate the measure of ∠D to the nearest tenth of a degree

kotegsom [21]

To approximate the measure of angle D, we will need to use the inverse cosine function on our calculator. All calculators vary, so I am not sure where you would find the button for it on your calculator. However, I know many calculators have it so you click the second button, then cos.

cos(D) = 0.33

D = cos^-1 (0.33)

D = 70.7 degrees

Hope this helps!! :)

5 0

2 years ago

Sandy evaluated the expression below. (negative 2) cubed (6 minus 3) minus 5 (2 + 3) = (negative 2) cubed (3) minus 5 (5) = 8 (3

nasty-shy [4]

Answer:

should be - 8

Step-by-step explanation:

-2*-2=4 4*-2=-8

4 0

2 years ago

Read 2 more answers