The original cost is $25. The item has a discount of 20% off. What is the discount amount?

David has a bag of coins. The bag contains 7 dimes, 2 nickels, and 6 pennies. He will randomly select 2 coins from the bag one a

julia-pushkina [17]

7 out of 17 coin in the bag

7 0

2 years ago

Solve for u:−14u+32=−6.

zubka84 [21]

Answer:u=19/7 or 2.714286 or 2 5/7

Step-by-step explanation:

−14u+32=−6

Step 1: Subtract 32 from both sides.

-14u+32-32=-6-32

-14u=-38

Step 2: Divide both sides by -14.

-14u/-14=-38/-14

U=19/7

3 0

2 years ago

Peter is buying office supplies he is able to buy three packages of paper in for staplers for $40 or he is able to buy five pack

Damm [24]

<u>Answer:</u>

Cost of package of paper = 4$

Cost of stapler = 7$

<u>Explanation:</u>

Consider the cost of package of paper = x and that of stapler = y.

Now, we are given that cost of 3 paper packages and 4 staplers = 40$

Hence we get, 3x + 4y = 40 as 1st equation.

we are also given, cost of 5 paper packages and 6 staplers = 62$

Hence, the second equation is 5x + 6y = 62

Now, solving the two equations by method of elimination, we first equate coefficients of any one variable say x by multiplying 1st equation by 5 and second by 3 we get ->

15x + 20y = 200

15x + 18y= 186

Subtracting the two we get y = 7 and substituting this value of y in first equation we get x = 4

which gives the required cost of one paper package = x = 4$

and one stapler = y = 7$

7 0

3 years ago

HELP, Prove: (cos(x))/(sin(x)tan(x))=cot^2x

Mice21 [21]

Answer:

Steps shown below

Step-by-step explanation:

We will simplify this using definitions and identities. Let's start.

$\frac{cos(x)}{sin(x)tan(x)}$

Using $tanx=\frac{sinx}{cosx}$ , we have:

$\frac{cos(x)}{sin(x)\frac{sin(x)}{cos(x)}}\\=\frac{cos^2(x)}{sin^2(x)}$

Using $cot(x)=\frac{cos(x)}{sin(x)}$ , we have:

$\frac{cos^2(x)}{sin^2(x)}\\=cot^2(x)$

Hence, proved.

7 0

2 years ago

Read 2 more answers

A study of pollutants showed that certain industrial emissions should not exceed 2.3 parts per million. You believe a particular

Musya8 [376]

Answer:

$t=\frac{3.3-2.3}{\frac{0.4}{\sqrt{9}}}=7.5$

The degrees of freedom are given by:

$df=n-1=9-1=8$

And the p value would be:

$p_v =P(t_{(8)}>7.5)=0.0000346$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 2.3 ppm the safe limit

Step-by-step explanation:

Information provided

$\bar X=3.3$ represent the sample mean in ppm

$s=0.4$ represent the sample standard deviation

$n=9$ sample size

$\mu_o =2.3$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to verify if the true mean is higher than 2,3 ppm, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.3$

Alternative hypothesis: $\mu > 2.3$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{3.3-2.3}{\frac{0.4}{\sqrt{9}}}=7.5$

The degrees of freedom are given by:

$df=n-1=9-1=8$

And the p value would be:

$p_v =P(t_{(8)}>7.5)=0.0000346$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 2.3 ppm the safe limit

6 0

3 years ago