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3 years ago

Solve the problem as directed.

Mathematics

1 answer:

Alex17521 [72]3 years ago

4 0

The algebraic equation for the given statement is $v = cd^3$

<h3><u>Solution:</u></h3>

Given that The volume (v) of a sphere varies directly as the cube of its diameter (d)

To find: statement in algebraic language using an equation with the variables c, v, and d

Let "v" be the volume of sphere

Let "d" be the diameter of sphere

From given information,

volume of sphere varies directly as the cube of its diameter

$\text{ volume of sphere } \alpha \text{ cube of its diameter}$

$\text{ v} \alpha d^3$

$v = cd^3$

Where "c" is the constant of proportionality

Then the algebraic equation for the given statement will be :-

$v=cd^3$ , where c is the proportionality constant.

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Please help and explain please !!!!!!

weeeeeb [17]

The answer for number one is 4.

How do you simplify the square root of 4? It's simple. What times itself equals 4? The answer would be 2! And because its √4×√4 it is simplified into 2×2=4

For number 2 the same thing applies. What times itself equals 12?

This one is a little tricky because it is not a perfect square (like how √4 is.)

But the square root of 12 is 3.46, which we can round to about 3.5.

Now what is the square root of 6? Once agian it is not a perfect root so the answer will be a decimal. 2.44 or rounded to 2.45.

Now what is 3.5 × 2.45? Answer is the answer is about 8.57 or rounded
8.60.

For the third question what is the square root of 7? The answer would be about 2.65.
Remember PEMDAS. Parenthesis, exponents, multiply, divide, add, subtract. (yeah you know this:)
First comes parenthesis. SO 1 minus 2.65 is equal to - 1.65.
Next set of parenthesis is 1+ the square √7 so it would be the opposite of what we just did. So 1 plus 2.65. That equals 3.65.

Now when there are 2 sets of parenthesis next to eachother )(
That means we need to MULTIPLY the two sides.
So
-1.65 × 3.65 ≈ - 6.

Last but not least Number 30. It might look scary but its not.

What is the square root of 2?
Its about 1.5.
The fraction is just another form for this 3÷1.5
The answer is 2.

Hope this was Helpful, sorry it was a little long but you needed an explanation :)

6 0

3 years ago

from a survey involving 1000 University students market research company found that 780 students on laptops 460 on cars and 380

aliina [53]

Considering the definition of probability:

the probability that the student owns either a car or laptop is 86%.
the probability that the student owns neither a car nor a laptop is 14%.

<h3>Definition of Probabitity</h3>

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:

$Probability=\frac{number of favorable cases}{total number of possible cases}$

<h3>Union of events</h3>

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

<h3>Complementary event</h3>

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

<h3>Events and probability in this case</h3>

In first place, let's define the following events:

A: The event that a student owned a laptop.

B: The event that a student owned a car.

Then you know:

P(A)= $\frac{780}{1000}$ = 0.78
P(B)= $\frac{460}{1000}$ = 0.46
P(F and R)= P(F∩R)= $\frac{380}{1000}$ = 0.38 [The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.]

In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.78 + 0.46 -0.38

P(A∪B)= 0.86= 86%

Then, the probability that the student owns either a car or laptop is 86%.

On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:

P [(A∪B)']= 1- P(A∪B)

P [(A∪B)']= 1 - 0.86

P [(A∪B)']= 0.14= 14%

Finally, the probability that the student owns neither a car nor a laptop is 14%.

Learn more about probability:

brainly.com/question/25839839

brainly.com/question/26038361

#SPJ1

5 0

2 years ago

The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrator

Nana76 [90]

Step-by-step explanation:

4 administrator are eligible and the student relations committee has only 2 administrator there are C (4,2) ways of choosing the administrators for the student relations committee

similarly for faculty members ways (8,3) and for students C (20,5)

the number of possible committee = 4!/2!2! × 8!/3!5! ×20!/5!15!

= 6 ×56 ×15504

= 5,209,344

6 0

3 years ago

Great britain developed a huge debt from fighting the what war

Brilliant_brown [7]

For the answer to the question above asking, Great Britain developed a huge debt from fighting the what war? The to this question is that at Britain developed a huge debt from fighting the French and Indian War or it is also known as Seven Years War

3 0

3 years ago

Which set of values are equivalent. ,

Gnoma [55]

3/10, 30%, 0.3

because 3/10 basically means 3 out of 10. that's 30%. 0.3 is just 3/10 in decimal form.

3 0

3 years ago