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Phantasy [73]
3 years ago
9

Need a problem answered pls help

Mathematics
2 answers:
vfiekz [6]3 years ago
8 0
The formula for the volume of a cone is V =PI x r^2 x h/3

r is given as as 8 and h is given as 63.

V = PI x 8^2 * 63/3

V = PI x 64 x 21

V = PI x 1344

Volume = 1344 PI cu. units.
 The answer is D.

insens350 [35]3 years ago
7 0
I think the answer is B
You might be interested in
Jane wants to estimate the proportion of students on her campus who eat cauliflower. after surveying 39 ​students, she finds 4 w
stellarik [79]

Let x be the number of students who eat cauliflower.

Therefore, x=4.

Let n be the total number of students surveyed.

Therefore, n=39

Thus, \hat p=\frac{4}{39} =0.10256

Now, for 90% confidence level, from the table we know that Z=1.645.

The formula for the interval range of proportion of students is :

p= \hat p\pm Z\sqrt{\frac{\hat p(1-\hat p)}{n}}

Plugging in the values we get:

p=0.10256\pm 1.645\sqrt{\frac{0.10256(1-0.10256)}{39}}=0.10256\pm 0.04858=0.15114, 0.05398

Thus, Jane is 90% confident that the population proportion p, for students who eat cauliflower in her campus is between 5.398% and 15.114% (after converting the answer we got to percentage).

7 0
3 years ago
Calculate the pH of a buffer solution made by mixing 300 mL of 0.2 M acetic acid, CH3COOH, and 200 mL of 0.3 M of its salt sodiu
Lesechka [4]

Answer:

Approximately 4.75.

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of  \rm CH_3COOH and \rm CH_3COO^{-} are equal.

{\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}

Since \rm CH_3COONa is a salt soluble in water. Once in water, it would readily ionize to give \rm CH_3COO^{-} and \rm Na^{+} ions.

Assume that the \rm CH_3COOH and \rm CH_3COO^{-} ions in this solution did not disintegrate at all. The solution would contain:

0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol of \rm CH_3COOH, and

0.06\; \rm mol of \rm CH_3COO^{-} from 0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol of \rm CH_3COONa.

Accordingly, the concentration of \rm CH_3COOH and \rm CH_3COO^{-} would be:

\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}.

\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}.

In other words, in this buffer solution, the initial concentration of the weak acid \rm CH_3COOH is the same as that of its conjugate base, \rm CH_3COO^{-}.

Hence, once in equilibrium, the \rm pH of this buffer solution would be the same as the {\rm pK}_{a} of \rm CH_3COOH.

Calculate the {\rm pK}_{a} of \rm CH_3COOH from its {\rm K}_{a}:

\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}.

7 0
3 years ago
What is the slope of a line that is perpendicular to the line whose equation is 2y = 3x - 1?
alexandr1967 [171]

Answer:

The slope of the line is -\frac{2}{3}

Step-by-step explanation:

For any line y=mx+b, a line that is perpendicular to it is y_\perp =-\frac{1}{m} x+b.

Therefore the slope of the perpendicular line is -\frac{1}{m}.

For our case y=\frac{3}{2}x-\frac{1}{2} therefore the slope of the prependicular is the reciprocal of \frac{3}{2} multiplied by -1.

\therefore\:slope=-\frac{2}{3}.

4 0
3 years ago
The area of a circle is 30.8m2.<br> Find the length of the diameter rounded to 1 DP.
andre [41]
Area of a circle = pi • r^2

We need to isolate for r.

A/pi = r^2

r = sqrt(A/pi)

r = sqrt(30.8/pi)

r = 3.1311251164

Diameter = 2r

Diameter = 6.26225023

Diameter = 6.3 m
8 0
2 years ago
You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 3% or the interest on $100,00
valentinak56 [21]

Answer:

Step-by-step explanation:

the simple interest formula= principal* interest rate*time

simple interest : 100000*%2*2 years

simple interest= 4000 dollars

compound quarterly : A=principal(1+r/4)^t

since it is quarterly and have 4 quarters in a year, and 8 in two years.

compound quarterly: 100000(1+0.03/4)^8=106159.88

it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.

the difference between the interest: 6159.88-4000=2159.88

5 0
3 years ago
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