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quester [9]
1 year ago
11

Please help with all of question 5 ​

Mathematics
1 answer:
musickatia [10]1 year ago
7 0

Volume of a right cone with base radius r cm and height h cm :

V = 1/3 π r² h cm³

Surface area :

A = (π r² + π r √(h² + r²)) cm²

Volume of a sphere with radius r cm :

V = 4/3 π r³ cm³

Surface area :

A = 4 π r² cm²

Volume of a cuboid with dimensions r cm × r cm × h cm :

V = r² h cm³

Surface area :

A = 2 r² + 4 r h

a. If the cone and sphere have the same volume, then

1/3 π r² h = 4/3 π r³   ⇒   h = 4r

b. If the area of the cuboid is 98 cm², then

2 r² + 4 r h = 98   ⇒   r (r + 2 h) = 49

c. Since h = 4r, substituting this into the equation from (b) gives

r (r + 8 r) = 9 r² = 49   ⇒   r² = 49/9   ⇒   r = 7/3

d. With r = 7/3, we have

h = 4 × 7/3 = 28/3

and so the volume of the cuboid is

V = (7/3 cm)² (28/3 cm) = 1372/27 cm³

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Marizza181 [45]

Answer:

The company should take a sample of 148 boxes.

Step-by-step explanation:

Hello!

The cable TV company whats to know what sample size to take to estimate the proportion/percentage of cable boxes in use during an evening hour.

They estimated a "pilot" proportion of p'=0.20

And using a 90% confidence level the CI should have a margin of error of 2% (0.02).

The CI for the population proportion is made using an approximation of the standard normal distribution, and its structure is "point estimation" ± "margin of error"

[p' ± Z_{1-\alpha /2} * \sqrt{\frac{p'(1-p')}{n} }]

Where

p' is the sample proportion/point estimator of the population proportion

Z_{1-\alpha /2} * \sqrt{\frac{p'(1-p')}{n} } is the margin of error (d) of the confidence interval.

Z_{1-\alpha /2} = Z_{1-0.05} = Z_{0.95}= 1.648

So

d= Z_{1-\alpha /2} * \sqrt{\frac{p'(1-p')}{n} }

d *Z_{1-\alpha /2}= \sqrt{\frac{p'(1-p')}{n} }

(d*Z_{1-\alpha /2})^2= \frac{p'(1-p')}{n}

n*(d*Z_{1-\alpha /2})^2= p'(1-p')

n= \frac{p'(1-p')}{(d*Z_{1-\alpha /2})^2}

n= \frac{0.2(1-0.2)}{(0.02*1.648)^2}

n= 147.28 ≅ 148 boxes.

I hope it helps!

3 0
3 years ago
A set of 6 number cards contains the numbers 2,5,7,8,9, and 11. Which ratio of odd number cards to total cards in the set?
Harlamova29_29 [7]
The ratio would be 4:6 because there are 6 number in total and 4 of them are odd numbers.
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Answer:

2 hrs and 32 mins

Step-by-step explanation:

Step 1. Because Inez worked more we are going to start by subtracting the the minutes. 23-51= -28.

Step 2. Now we move on to the hours. 7-4= 3. Know we know that the hour time is going to be three. But wait!

Step 3. Because we can't have negative numbers, we need to subtract some more. 60-28= 32. Now I know that my minutes will be 32.

Step 4. But because we used a negative number we have to subtract another hour from our time.

Answer: 2 hrs and 32 mins

Hope this helps!

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Answer:

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