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2 years ago

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You have at most $3.65 to make copies for a school project. Each copy costs $0.25. Write and solve an inequality that represents

the number of copies you can make.

1 answer:

slamgirl [31]2 years ago

5 0

The equation for the problem is $0.25x$ ≤ $3.65$

Hope it helps!

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Al purchases a speedboat costing $24,500. State taxes are 5.5% and federal excise tax is 13%. What is the total purchase price?

trapecia [35]

Answer: The total purchase price is $ 29,032

Step-by-step explanation:

Hi, to solve this problem you have to solve the percentages of each taxes first.

So :

state taxes =$24,500 × 5.5% = $1,347.5

federal tax = $24,500 × 13% = $3,185

The next step is adding the taxes results to the speedboat cost.

so:

speedboat = $24,500

speedboat + taxes = $24,500 + $1,347.5 +$3,185 = $29,032

The total purchse price for the speedboat is $29,032.

8 0

2 years ago

−7x−50≤−1 AND−6x+70>−2

fgiga [73]

Answer:

$-7\geq x$ and $[-7,12)$ in interval notation.

Step-by-step explanation:

We have been given a compound inequality $-7x-50\leq -1\text{ and }-6x+70>-2$ . We are supposed to find the solution of our given inequality.

First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.

$-7x-50\leq -1$

$-7x-50+50\leq -1+50$

$-7x\leq 49$

Dividing by negative number, flip the inequality sign:

$\frac{-7x}{-7}\geq \frac{49}{-7}$

$x\geq -7$

$-6x+70>-2$

$-6x+70-70>-2-70$

$-6x>-72$

Dividing by negative number, flip the inequality sign:

$\frac{-6x}{-6}$

$x$

Upon merging both intervals, we will get:

$-7\geq x$

Therefore, the solution for our given inequality would be $-7\geq x$ and $[-7,12)$ in interval notation.

7 0

2 years ago

A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website re

nataly862011 [7]

Answer:

The 90% confidence interval would be given by (57.006;62.994)

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

$\bar X=60$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=10$ represent the population standard deviation

n=30 represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=10)$

The sample mean $\bar X$ is distributed on this way:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

The confidence interval on this case is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The next step would be find the value of $\z_{\alpha/2}$ , $\alpha=1-0.90=0.1$ , $\alpha/2 =0.05$ and $z_\alpha/2=1.64$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=1.64$

Since we have all the values we can replace:

$60 - 1.64\frac{10}{\sqrt{30}}=57.006$

$60 + 1.64\frac{10}{\sqrt{30}}=62.994$

So on this case the 90% confidence interval would be given by (57.006;62.994)

5 0

2 years ago

The angle \theta_1θ

enyata [817]

Answer:

$sin\theta_1 = \dfrac{\sqrt{217}}{19}$

Step-by-step explanation:

It is given that:

$cos\theta_1 = -\dfrac{12}{19}$

And we have to find the value of $sin\theta_1 = ?$

As per trigonometric identities, the relation between $sin\theta\ and \ cos\theta$ can represented as:

$sin^2\theta + cos^2\theta = 1$

Putting $\theta_1$ in place of $\theta$ Because we are given

$sin^2\theta_1 + cos^2\theta_1 = 1$

Putting value of cosine:

$cos\theta_1 = -\dfrac{12}{19}$

$sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}$

It is given that $\theta_1$ is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

$\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}$

8 0

2 years ago

John made a small rectangular table for his workroom. If the sides of the table are 32 inches and 26 inches, what should the tab

matrenka [14]

Answer:

The table should measure diagonally about 41.23 inches.

Step-by-step explanation:

To find the diagonal of a rectangle we use the formula :

$a^{2}$ + $b^{2}$ = $c^{2}$

A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.

$32^{2}$ + $26^{2}$ = $c^{2}$

1024 + 676 = $c^{2}$

1700 = $c^{2}$

The square root of 1700 is (rounded to the hundreth's place) = 41.23

6 0

1 year ago