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3 years ago

Can this be simplified?

Mathematics

2 answers:

Airida [17]3 years ago

7 0

You can divide al the terms in the numerator by 4 and rewrite as:

$\frac12x^4 + x - \frac54$

Then you could factor out an x and write:

$x(\frac12x^3 + 1) - \frac54$

Not sure if this is any simpler. I'd go for the top one as the cleanest form.

liraira [26]3 years ago

6 0

No Nothing Further Can Be Done

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Tayâ€“Sachs Disease Tayâ€“Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carri

BARSIC [14]

Answer:

a) 0.0156 = 1.56% probability that all children will develop the disease.

b) 0.4219 = 42.19% probability that only one child will develop the disease.

c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The probability that their offspring will develop the disease is approximately .25.

This means that $p = 0.25$

Three children:

This means that $n = 3$

Question a:

This is P(X = 3). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156$

0.0156 = 1.56% probability that all children will develop the disease.

Question b:

This is P(X = 1). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219$

0.4219 = 42.19% probability that only one child will develop the disease.

c. The third child will develop Tayâ€“Sachs disease, given that the first two did not.

Third independent of the first two, so just multiply the probabilities.

First two do not develop, each with 0.75 probability.

Third develops, which 0.25 probability. So

$p = 0.75*0.75*0.25 = 0.1406$

0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

6 0

2 years ago

Which statements are true? Check all that apply.

mariarad [96]

Answer:

A, B, and C

Step-by-step explanation:

A) We can see if this is a horizontal line if its slope is 0. Slope is change in y divided by change in x, so: slope = $\frac{7-7}{3-(-2)} =\frac{0}{5} =0$ . Thus, this is a horizontal line and the statement is correct.

B) Any equation of the form x = k, where k is a constant, will always be a straight line. Let's see if it goes through (-8, 3) by plugging in the values of -8 in for x and 3 in for y in the equation.

Clearly, we don't have a y, so we just put in the -8 for the x: -8 = -8. Since this is a true statement, we know that x = -8 does go through (-8, 3). So, this is a true statement.

C) We can see if this is a vertical line if its slope is undefined (for example, if the denominator is 0, it's undefined). Slope = $\frac{5-(-7)}{0-0} =\frac{12}{0}$ = undefined. So, this is a vertical line and the statement is true.

D) As a basic fact, any point on a horizontal line will have the same y coordinate. However, their x coordinates may vary. Thus, the statement is false.

So, the answers are A, B, and C.

Hope this helps!

4 0

2 years ago

Read 2 more answers

A truck is leaving a post office and heading out to deliver mail. The table shows the truck's distance d from the post office at

zalisa [80]

Answer:

eliver mail. The table shows the truck's distance d from the post office at time t. Calculate the average rate of change over the interval from 8 to 15 minutes. t(min) d (km) 0 0 8 7 11 11 15 14 22 16 (1 point) The rate of change is about 0.8 kilometers per minute. The rate of change is 7 kilometers

7 0

2 years ago

kherson [118]

Answer:

$25.57

Step-by-step explanation:

First, you have to multiply $5.29 by 2 because she wants to spend $5.29 on 2 pairs of socks.

5.29 * 2 = $10.58

Then you want to add $10.58 and $14.99 together.

$10.58 + $14.99 = $25.57

3 0

3 years ago

1. A professional basketball used for league play has a diameter of 25 cm. Which of the following is closest to the volume of th

yKpoI14uk [10]

Answer:

V = 8,181.23 $cm^{3}$

Step-by-step explanation:

Unfortunately, we are not given any answer choices to choose from but using the information provided we can find the actual volume of the basketball. A basketball is made in the shape of a sphere and the formula for the volume of a sphere is the following...

V = $\frac{4}{3} * \pi * r^{3}$

radius of a circle/sphere is half of it's diameter. Since we are provided the diameter size we simply divide it by 2 which would give us 12.5cm. Now we simply plug this value into the formula and solve for V.

V = $\frac{4}{3} * \pi * 12.5^{3}$

V = $\frac{4}{3} * \pi * 1953.125$

V = 8,181.23 $cm^{3}$

5 0

2 years ago