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ruslelena [56]
3 years ago
12

What is the volume of a rectangular prism with the dimensions: base 2

Mathematics
1 answer:
White raven [17]3 years ago
7 0
Assuming the base is the width, V = 6
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Sir Ving Spoon earned $5,436 on his $7,550 certificate of deposit. If he had the CD for 12 years, what simple interest rate did
Lilit [14]

6% or 0.06 is the simple interest rate the bank pays him.

<u>Step-by-step explanation:</u>

Sir Ving Spoon earned $5,436 on his $7,550 certificate of deposit.

From this given information,

It can be determined that the Principal amount is $7550 and the interest amount is $5436.

The CD is for 12 years. Therefore, the number of years is 12.

<u>To find the interest rate (r) :</u>

Using the simple interest formula,

Interest = P×r×t

where,

  • P is the principal amount = $7550
  • r is the rate of interest.
  • t is the number of years = 12

⇒ 5436 = 7550 × r × 12

⇒ 5436 = 90600 × r

⇒ r = 5436 / 90600

⇒ r = 0.06

Multiply by 100 to represent in rate %

⇒ r = 0.06 × 100

⇒ r = 6%

∴ 6% or 0.06 is the simple interest rate the bank pays him.

5 0
3 years ago
What is the inverse function of g(x)=1/x-2
kkurt [141]
Assuming it's g(x)=\dfrac{1}{x-2}

y=\dfrac{1}{x-2}\\ x-2=\dfrac{1}{y}\\ x=\dfrac{1}{y}+2\\ g^{-1}(x)=\dfrac{1}{x}+2
3 0
3 years ago
In a string of 12 Christmas tree light bulbs, 3 are defective. The bulbs are selected at random and tested, one at a time, until
Juliette [100K]

Using the hypergeometric distribution, it is found that there is a 0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

In this problem, the bulbs are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

In this problem:

  • There are 12 bulbs, hence N = 12.
  • 3 are defective, hence k = 3.

The third defective bulb is the fifth bulb if:

  • Two of the first 4 bulbs are defective, which is P(X = 2) when n = 4.
  • The fifth is defective, with probability of 1/8, as of the eight remaining bulbs, one will be defective.

Hence:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,12,4,3) = \frac{C_{3,2}C_{9,1}}{C_{12,4}} = 0.2182

0.2182 x 1/8 = 0.0273.

0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

More can be learned about the hypergeometric distribution at brainly.com/question/24826394

8 0
2 years ago
Which inequality is the solution to 20 + 2 &lt; x/3 - 8?
pychu [463]

Answer:

x > 90, C

Step-by-step explanation:

20 + 2 < x / 3 - 8

x / 3 - 8 > 22

x / 3 > 30

x > 90

4 0
2 years ago
Read 2 more answers
12<br> Using side lengths only, could the triangles be similar?<br> 0.5<br> m05 1 1.5
Murljashka [212]

Answer:

\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}

Step-by-step explanation:

\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/

\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}

\text{Despite this, let's check the ratios}

\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5

\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}

8 0
3 years ago
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