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Advocard [28]
3 years ago
12

I need help with this equation. 9q - 14 + 3(q - 8) = 7 I looked it up and the answer was 3.75, however I don't understand how it

works.
Mathematics
1 answer:
coldgirl [10]3 years ago
8 0
Parentheses first

9q-14+3q-3(8)=7
9q-14+3q-24=7

Combine like terms

9q + 3q - 14 - 24 = 7
12q -38=7

add 38 to both sides

12q - 38 + 38 = 7 + 38

12q = 45

divide both sides by 12

q = 45/12
q = 3.75


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A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data
LuckyWell [14K]

Answer:

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

Step-by-step explanation:

The margin of error of a confidence interval is given by:

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.

In this question:

The narrower C.I. is the 95%, and the wider is the 99%. So

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

4 0
3 years ago
. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum
Drupady [299]

Answer:

r=1.05\ \text{ft}

h=2.12\ \text{ft}

20.91\ \text{ft}^3

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = 7.35\ \text{ft}^3

V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}

Surface area is given by

A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}

Differentiating with respect to radius we get

\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}

Equating with zero we get

0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05

\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0

So, the value of the function is minimum at r=1.05

h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3

The minimum surface area is 20.91\ \text{ft}^3.

8 0
3 years ago
In the equation x + y = 8, find the value of x if y = 3<br><br> 3<br> 5<br> 7<br> 11
snow_lady [41]

Answer:

11

Step-by-step explanation:

x+y=8     y=3

x+3=8

-3     -3

x=11

7 0
3 years ago
Read 2 more answers
Find the value of x in the triangle shown below.
oee [108]

Answer: x = 5

Step-by-step explanation:

Use Pythagorean's Theorem

a^2+b^2=c^2\\12^2+x^2=13^2\\144+x^2=169\\x^2=25\\x=5

8 0
2 years ago
Nvm i got it lol sorry!
Dima020 [189]
Lol that’s good to hear I’m glad
4 0
2 years ago
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