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3 years ago

Desperately need help

Mathematics

1 answer:

maxonik [38]3 years ago

8 0

$\begin{cases} x=-5\implies &x+5=0\\ x=3\implies &x-3=0 \end{cases}\qquad \implies \underline{a(x+5)(x-3)~~ = ~~\stackrel{0}{y}} \\\\\\ \stackrel{\textit{we also know that}}{P(0)=-30}\implies \begin{cases} x=0\\ y=-30 \end{cases}\implies a(0+5)(0-3)~~ = ~~-30 \\\\\\ a(5)(-3)=-30\implies -15a=-30\implies a=\cfrac{-30}{-15}\implies \boxed{a=2} \\\\[-0.35em] ~\dotfill\\\\ 2(x+5)(x-3)=y\implies 2(\stackrel{F~O~I~L}{x^2+2x-15})=y\implies \underline{2x^2+4x-30=y}$

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Suppose it is known that 60% of radio listeners at a particular college are smokers. A sample of 500 students from the college i

vladimir1956 [14]

Answer:

The probability that at least 280 of these students are smokers is 0.9664.

Step-by-step explanation:

Let the random variable X be defined as the number of students at a particular college who are smokers

The random variable X follows a Binomial distribution with parameters n = 500 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

$np=500\times 0.60=300>10\\n(1-p)=500\times(1-0.60)=200>10$

Thus, a Normal approximation to binomial can be applied.

So,

$X\sim N(\mu=600, \sigma=\sqrt{120})$

Compute the probability that at least 280 of these students are smokers as follows:

Apply continuity correction:

P (X ≥ 280) = P (X > 280 + 0.50)

= P (X > 280.50)

$=P(\frac{X-\mu}{\sigma}>\frac{280-300}{\sqrt{120}}\\=P(Z>-1.83)\\=P(Z$

*Use a z-table for the probability.

Thus, the probability that at least 280 of these students are smokers is 0.9664.

8 0

3 years ago

What is the volume of this rectangular prism?

Ainat [17]

L x b x h
1 1/2 x 3/12 x 2/12
13 1/8. I THINK

6 0

3 years ago

Read 2 more answers

What is the answer for -6n-2n=16

djverab [1.8K]

Answer:

n=-2

Step-by-step explanation:

-6n-2n=16

-8n=16

n=16/-8

n=-2

8 0

4 years ago

Read 2 more answers

Select all the expressions which are equivalent to –3(0.15 – 0.2 + 0.25p)

Sergio [31]

Answer:

–3(0.15 – 0.2 + 0.25p) = –3(0.15) + (–3)(0.2) + (–3)(0.25p)

Because the 2nd experssion is taking -3 times each number in the ( ).

hope this helps.

Step-by-step explanation:

4 0

3 years ago

Tom simplified an expression in three steps, as shown: x to the power of negative 2 multiplied by y to the power of 4, over y mu

ss7ja [257]

Answer:

Step 1, all the exponents are increased by 4

Step-by-step explanation:

The three steps are

(x⁻² × y⁴ /y × x⁴ × x⁴ × y⁻²)⁴ =
x²×y⁸/y⁴×x⁸×x⁸×y² =
x²×y⁸/y⁶×x¹⁶

Correct solution should be:

(x⁻² × y⁴ /y × x⁴ × x⁴ × y⁻²)⁴ = all powers inside the parenthesis should be multiplied by 4 as per power of the power (xᵃ)ᵇ = xᵃᵇ

This would give next steps:

x⁻⁸×y¹⁶/y⁴×x⁸×x⁸×y⁻⁸ =
x⁻⁸×y¹⁶/x¹⁶×y⁻⁴ =
y²⁰/x²⁴

Answer options:

Step 1, all the exponents are increased by 4

There should be multiplication of powers. (It is close option but is not fully correct as not all the exponents increased by 4, for example y became y⁴)

Step 2, the exponents of the same base are added during multiplication

It was done correctly

Step 3 wasn't performed yet, there was step 1 and 2.

So answers about step 3 are irrelevant

5 0

3 years ago