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3 years ago

Simplify the following expression

Mathematics

1 answer:

Kay [80]3 years ago

6 0

Answer:

$\frac{98p^{6}}{q}$

Step-by-step explanation:

Distribute the exponents

$(\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}$

$(\frac{q}{98p^{6}} )^{-1}$

Distribute the -1

$\frac{98p^{6}}{q}$

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If two lines are parallel which statement must be true? A.Their slopes are zero. B.Their slopes are negative reciprocals. C. The

stepan [7]

Answer:

Step-by-step explanation:

Parallel lines have the same gradient.

A line with a slope of zero is a horizontal line. Although two lines that have a slope of zero will result in two parallel lines, not all parallel lines are horizontal lines. Since the question is asking for which statement <u>must</u> be true, option A is incorrect.

If the slopes of two lines are negative reciprocals, they are perpendicular to each other. This is because the product of the gradients of 2 perpendicular lines is -1. Let the gradient of the first line be A and the other be B.

AB= -1

$A = - \frac{ 1}{B}$

$B = - \frac{1}{A}$

Thus, option B is incorrect too.

Undefined slopes gives vertical lines. Like option A, if two lines have an undefined slope, they will be parallel to each other. However since parallel lines are nit necessarily vertical lines, option C is also incorrect.

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2 years ago

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Question 4 of 10, Step 1 of 1 1/out of 10 Correct Certify Completion Icon Tries remaining:0 The Magazine Mass Marketing Company

erastovalidia [21]

Answer:

0.0105 = 1.05% probability that no more than 3 of the entry forms will include an order.

Step-by-step explanation:

For each entry form, there are only two possible outcomes. Either it includes an order, or it does not. The probability of an entry including an order is independent of any other entry, 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 Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes.

This means that $n = 16$

They know that the probability of receiving a magazine subscription order with an entry form is 0.5.

This means that $p = 0.5$

What is the probability that no more than 3 of the entry forms will include an order?

At most 3 including an order, which is:

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

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

$P(X = 0) = C_{16,0}.(0.5)^{0}.(0.5)^{16} \approx 0$

$P(X = 1) = C_{16,1}.(0.5)^{1}.(0.5)^{15} = 0.0002$

$P(X = 2) = C_{16,2}.(0.5)^{2}.(0.5)^{14} = 0.0018$

$P(X = 3) = C_{16,3}.(0.5)^{3}.(0.5)^{13} = 0.0085$

Then

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0002 + 0.0018 + 0.0085 = 0.0105$

0.0105 = 1.05% probability that no more than 3 of the entry forms will include an order.

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3 years ago

How do you solve the equation:

Molodets [167]

Copy and paste the answer on quizlet

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3 years ago

Answer the question

cluponka [151]

The unit rate in this problem is one payment per month. Since Martha has made 86 payments, that means it has been 86 months. Because of that, we can simply multiply 3335*86 to get 286810.

So she so far has paid $286,810 for her house payment

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3 years ago

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About what percent of gyms in shanesville have fewer than 56 gym members

Jet001 [13]

Answer:

25%

Step-by-step explanation:

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3 years ago