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antoniya [11.8K]
2 years ago
13

Find the volume of a right circular cone that has a height of 17.5 m and a base with a circumference of 19.4 m

Mathematics
1 answer:
Oxana [17]2 years ago
4 0

Answer: Volume = 174.71 cubic meters

Step-by-step explanation:

Hi, to answer this, first, we have to apply the formula for the circumference (C) of a circle.

C= 2πr

Substituting with c=19.4 in the formula, and solving for the radius (r)

19.4= 2πr

19.4/ 2π =r

r= 3.09

Finally we apply the formula:

Volume of a right circular cone: 1/3 π r^2 h

Where h is the height of the cone and r is the radius of the base.

Replacing with the values given and calculated:

V=1/3 π (3.09)^2 (17.5)

V = 174.71 cubic meters

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Answer:

72

Step-by-step explanation:

For Q 1 : 25 % of the scores are below this value. The area under the bell-shaped curve of the normal distribution is 0.25. And since we have 288 electricians that took a certification test:

0.25 * 288 = 72.

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A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card ho
valkas [14]

Answer:

c) t-test of population mean

Explanation:

The t-test statistic is used in hypothesis testing. Here we would use a one sample t test to test our hypothesis. The one sample t test measures the statistical difference between the hypothesized mean and the sample mean. In a one sample t test or single sample t test, a test variable is measured against a test value.

Example we compare our test variable to the hypothesized mean value $75 above.

The t test is used instead of z score when standard deviation is unknown.

Using the t test, we either accept or reject the null hypothesis given alternative hypothesis.

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2 years ago
Given that α and β are the roots of the quadratic equation <img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B6x-7%3Dp" id="Tex
siniylev [52]

Answer:

\large \boxed{\sf \ \ \ p=-11 \ \ \ }

Step-by-step explanation:

Hello,

\alpha \text{ and } \beta \text{ are the roots of the following equation}

   2x^2+6x-7=p

It means that

   2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\

And we know that

\alpha= 2\cdot \beta

So we got two equations

   2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\6\beta^2+6\beta =0\\\\\beta(\beta+1)=0\\\\ \beta =0 \ or \ \beta=-1

For \beta =0, \ \ \alpha =0, \ \ p = -7

For \beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11

I assume that we are after two different roots so the solution for p is p=-11

b) \alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1

So a quadratic equation with the expected roots  is

x(x-1)=x^2-x

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

3 0
2 years ago
Use the alternative form of the dot product to find u · v.
vodka [1.7K]

Answer:

Step-by-step explanation:

u = 45

v = 30

Angle between them, θ = 5π / 6 = 150°

(a) The formula for the dot product is given by

\overrightarrow{u}.\overrightarrow{v}= u v Cos\theta

\overrightarrow{u}.\overrightarrow{v}= 45 \times 30 \times Cos150

\overrightarrow{u}.\overrightarrow{v}= -1169.13

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\overrightarrow{v}=Cos\frac{2\pi }{3}\widehat{i}+Sin\frac{2\pi }{3}\widehat{j}

\overrightarrow{v}=-0.707\widehat{i}+0.707\widehat{j}

Let the angle between them is θ

The formula in terms of the dot product is given by

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u=\sqrt{0.5^{2}+0.866^{2}}=1

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Cos\theta =\frac{0.5 \times (-0.707) + 0.866 \times 0.707)}{1\times 1}

Cos\theta=0.2587

θ = 75°

(c) \overrightarrow{u}=1\widehat{i}+4\widehat{j}+8\widehat{k}

u=\sqrt{1^{2}+4^{2}+8^{2}}=9

Cos\alpha =\frac{1}{9}

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3 years ago
In a survey, 10% of the people said they live in a city. If 70 people
ddd [48]
700 people were surveyed.

SOLUTION
70/10%
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7 x 10^2
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