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4 years ago

4. A local DVD rental machine rents

Mathematics

1 answer:

Mrrafil [7]4 years ago

3 0

It takes 16 movie rentals for both options to be the same price

<u>Solution:</u>

Given that, A local DVD rental machine rents movies out to customers for $5.75 per movie.

A digital movie company allows you to rent movies for $3.25 but requires a membership fee of $40.

We have to find how many movie rentals will it take for both options to be the same price?

Now, let the number of movies rented be "n"

Then, according to the given information,

$\begin{array}{l}{5.75 \times n=3.25 \times n+40} \\\\ {5.75 n=3.25 n+40} \\\\ {5.75 n-3.25 n=40} \\\\ {2.50 n=40} \\\\ {n=\frac{40}{2.5}=16}\end{array}$

Hence, it takes 16 movies to be the same price for both options.

You might be interested in

Which polygon has four sides, two sets of parallel sides, and sides that are not all equal?

Dmitriy789 [7]

A polygon that has 4 sides and two sets of parallel sides is a parallelogram. In a parallelogram, each set of opposite sides is congruent, but all four sides do not have to be congruent.

7 0

4 years ago

Read 2 more answers

Simplify the following: (-8z)²

Cloud [144]

Answer:

64z^2

Step-by-step explanation:

Here's why, it's actually very simple we use exponent rule when raising something to a power. In this case we're raising the term to the second power. So we raise both -8, and z. As so: (-8)^2 x (z)^2

Which equals 64z^2.

4 0

3 years ago

A presidential candidate's aide estimates that, among all college students, the proportion who intend to vote in the upcoming el

inessss [21]

Answer:

$z=\frac{0.529 -0.6}{\sqrt{\frac{0.6(1-0.6)}{240}}}=-2.24$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the proportion college students expressed an intent to vote is not higher than 0.6

Step-by-step explanation:

Assuming the following question: A presidential candidate's aide estimates that, among all college students, the proportion p who intend to vote in the upcoming election is at least 60% . If 127 out of a random sample of 240 college students expressed an intent to vote, can we reject the aide's estimate at the 0.1 level of significance?

Data given and notation

n=240 represent the random sample taken

X=127 represent the college students expressed an intent to vote

$\hat p=\frac{127}{240}=0.529$ estimated proportion of college students expressed an intent to vote

$p_o=0.6$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that at least 60% of students are intented to vote .:

Null hypothesis: $p \geq 0.6$

Alternative hypothesis: $p < 0.6$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.529 -0.6}{\sqrt{\frac{0.6(1-0.6)}{240}}}=-2.24$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(z$

7 0

3 years ago

8 - 3(k + 2) = 2-3k

Rus_ich [418]

Answer:

Any value of k makes the equation true.

All real numbers

Interval Notation:

( − ∞ , ∞ )

5 0

3 years ago

There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are the

zlopas [31]

Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

For the above questions we apply that combination formula

(a) How many are there to select 2 pairs of gloves?

There are 5 pairs of gloves according to the question above, hence:

5C2 = 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/2 × 1 × 3 × 2 × 1

= 10 ways.

Therefore, there are 10 ways to select 2 pairs of gloves

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

i) A way to select 4 gloves out of 10 gloves =

10C4 = 10!/4! ×(10 - 4)!

= 10!/ 4! × 6!

= 210 ways

ii) In order for 2 of the 4 gloves selected to be a pair, note that we have 5 pairs of gloves hence:

5 × 2⁴

= 80 ways.

Therefore, the number of ways which we can select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.) = 210 ways - 80 ways

= 130 ways

4 0

3 years ago