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3 years ago

Find the volume of the sphere need help

Mathematics

1 answer:

Ivanshal [37]3 years ago

4 0

Answer:

36pi

Step-by-step explanation:

volume = (4/3) · π · r3

in this case r = 3

4/3 x pi x r^3

3 cubed = 27

27 x pi x 4/3

27 x 4/3 = 36

36 $\pi$ is the answer

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Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

Answer

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

3 years ago

A simple random sample of n measurements from a population is a subset of the population selected in a manner such that which of

Ierofanga [76]

Answer:

a) sample of size n from the population has an equal chance of being selected.

b) Every member of the population has an equal chance of being included in the sample.

Step-by-step explanation:

Simple random sampling:

It is a type of probabilistic sampling.
It is an unbiased representation of population.
The probability of selection is equal for every observation.
A sample is taken in such a way that each member has an equal probability of being selected.
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
Thus,the correct interpretation is given by,

a) sample of size n from the population has an equal chance of being selected.

b) Every member of the population has an equal chance of being included in the sample.

c) The simplest method of selection is used to create a representative sample.

The statement is false.

There is no pattern or technique used for selection. The selection is purely random.

d) Each subset of the population has an equal chance of being included in the sample.

The statement is false.

Each object of the population has an equal chance of being included in the sample. and not each subset.

e) Every sample of size n from the population has a proportionally weighted chance of being selected.

The given statement is false.

8 0

3 years ago

Help! Use trigonometric ratios to determine whether or not it is possible to construct triangle ABC if b = 3, c = 5, and B = 45°

elena-s [515]

No its not posible because the sine is 1.5 and it cant be higher then 1

7 0

3 years ago

Read 2 more answers

Ten(10) adults and 3 children attend a local concert for $59. Four(4) adults and 3

gladu [14]

Answer:

$5 per adult and $3 per kid

Step-by-step explanation:

5x10=50

3x3=9

50+9=59

4x5=20

3x3=9

20+9=29

4 0

3 years ago

What is 4 and 2/3 written as a radical?

TEA [102]

Answer:

14/3

Step-by-step explanation:

4 and 2/3 = 4 2/3 = 4 + 2/3 = 4/1 + 2/3 = 12/3 + 2/3 = 14/3

7 0

3 years ago