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4 years ago

Simplify 8^ -5 over 8^ -3 <-- this is a fraction

1 answer:

8 0

Ok, 8^(-5) divided by 8^(-3) would be 8^(-5-(-3)), because when you divide numbers with the same base, you subtract the exponents. That would be 8^(-2), which I suppose is A

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Current estimates are that about 25% of all deaths are due to cancer, and of the deaths that are due to cancer, 30% are attribut

Aliun [14]

Answer:

(a) P (T|C) = 0.30, P (T|D) = 0.40 and P (O|C) = 0.30

(b) The probability that a death is due to cancer and tobacco is 0.075.

Step-by-step explanation:

Let us denote the events as follows:

C = death is due to cancer

T = cause of cancer was tobacco

D = cause of cancer was diet

O = cause of cancer was other issue

The provided information is:

P (C) = 0.25

P (T|C) = 0.30

P (T|D) = 0.40

P (O|C) = 0.30

(a)

The conditional probability of an event <em>A</em> given that another event <em>B</em> has already occurred is denoted by, P (A|B).

This implies that the occurrence of event B is affected by the previously occurred event A.

Causes of cancer are tobacco, diet and other issues. If a death is caused by cancer then the probability that the cause of cancer was tobacco or diet or something else are conditional events.

The conditional probabilities are:

0.40 for diet, 0.30 for tobacco and 0.30 for other causes.

(b)

Conditional probability formula is:

$P (A|B)=\frac{P(A\cap B)}{P(B)}$

Compute the probability that a death is due to cancer and tobacco as follows:

$P (T|C)=\frac{P(C\cap T)}{P(C)}\\P(C\cap T)=P(T|C)\times P(C)\\=0.30\times0.25\\=0.075$

Thus, the probability that a death is due to cancer and tobacco is 0.075.

8 0

3 years ago

How do I find the missing side length to the nearest tenth of a millimeter.

iogann1982 [59]

Answer:

11.5

Step-by-step explanation:

5 0

3 years ago

List all integers between −100 and 100 that are congruent to −1 modulo 25.

777dan777 [17]

"-1 modulo 25" is "1 less than a precise multiple of 25".
So what are the exact or precise multiples of 25 in the appropriate interval?
It is -75, -50, -25, 0, 25, 50, 75, and 100.
Now just subtract 1 from each of them.

So the answers are -76, -51, -26, -1, 24, 49, 74, and 99.

4 0

4 years ago

Need help pls thx..........

S_A_V [24]

Answer:

170 degree. is the answer

3 0

3 years ago

I need help with pre calculus.

otez555 [7]

Question 1

<h3>Answer: Choice A) -7</h3>

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Explanation:

To compute f(g(2)), we'll first need to find g(2).

Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4

This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) = -9

Overall, we can say f(g(2)) = -9

We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2

Lastly, we subtract the results we got:

f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7

==============================================

Question 2

<h3>Answer: Choice B) 0</h3>

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Explanation:

If you were to graph each equation, you should get what you see below.

The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.

==============================================

Question 3

<h3>Answer: Choice B</h3><h3> $-2x^2+250x-2000$ </h3>

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Explanation:

x = number of scooters made and sold

Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression $150x+2000$

The cost function is $C(x) = 150x+2000$ . We'll subtract this from the revenue function R(x) to get the profit P(x)

$\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\$

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Question 4

<h3>Answer: Choice B</h3>

$\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}$

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Explanation:

$g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\$

I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.

So we start off with the real number line, and poke holes at x = -2 and x = 1.

The notation $x \in \mathbb{R}$ means x is a real number. Then we tack on $x \ne -2, x \ne 1$

Overall, the domain is $\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}$

Let's see what happens if we tried plugging x = -1 into this composite function:

$(g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\$

We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.

4 0

2 years ago