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3 years ago

Determine if the following statement is true or false:

1 answer:

5 0

It is a completely false statement that 12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two. The correct option among the two options that are given in the question is the second option. I hope that this is the answer that has actually come to your help.

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I like to help in this problem: in the course of Juan 2/9 of the students are children of 13 years, 1/4 have 14 years and the re

taurus [48]

Rest are 19/36

it is 1 -(1/4) - (2/9)
= 1-9/36 - 8/36
= (36-9-8)/36
= 19/36.

3 0

3 years ago

Please apply the properties of rational exponents to simplify expressions with radical or rational exponents. Explain the steps

schepotkina [342]

Step-by-step explanation:

Product property

If the bases are the same, you don't multiple them. However, if they are the same, you do multiple for example : (2³ * 2¹ = 2⁴.when the bases are the same) (2³ * 3¹ =6⁴. When the bases are not the same
We add the index.

Quotient property

Same here, if the bases are the same, they stay the way they were
We subtract the index

Power property

Here we multiple the index because of the bracket for example : (9²)²= 9⁴

Negetive exponent property

When ever the index has a negative sign its convected to a fraction, for instance : 9¯² = 1 /9²
Note, when it turns to a fraction th index becomes positive

6 0

3 years ago

25+ -8 equals I really need help

Nimfa-mama [501]

Answer:

Step-by-step explanation:

Saying 25+ -8 is basically saying 25-8, and since 25 is the bigger number and it's positive, you get positive 17

7 0

3 years ago

Read 2 more answers

I need help on this aswell

Katena32 [7]

Answer:

Graph C

Step-by-step explanation:

Hi there!

The given linear equations are organized in slope-intercept form: $y=mx+b$ where m is the slope of the line and b is the y-intercept, or the value of y when the line crosses the y-axis.

y = 2x + 4

Here, the b value is 4. Therefore, the y-intercept of this line is 4.

y = -3x - 2

Here, the b value is -2. Therefore, the y-intercept of this line is -2.

To identify the graph that models these equations, we just have to look for the graph where the lines cross the y-axis at 4 and -2.

The only graph that does this is graph C.

I hope this helps!

8 0

3 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection.

This means that,

Probability that at least one of them needs replacement at the first inspection =

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago