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3 years ago

Colin buys a box of pasta that contains 823 cups of pasta. He uses 212 cups to make dinner. How much pasta is left?

Mathematics

1 answer:

inessss [21]3 years ago

4 0

Given that,

Colin buys a box of pasta that contains 823 cups of pasta.

He uses 212 cups to make dinner.

To find,

How much pasta is left?

Solution,

Left pasta = Total cups of pasta - used cups of pasta

= 823 - 212

= 611

Hence, 611 cups of pasta is left.

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Raul is saving up to buy a used motorcycle for $700. He can save $50 per month. How

Margarita [4]

14 months.

$50 x 14months = $700

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4 years ago

Twice a number plus twice a second number is 310. The difference between the numbers is 55

agasfer [191]

Answer:

x = 105

y = 50

Step-by-step explanation:

To solve this, try writing it out as an equation/expression first.

When you do, you should get something like this:

2x + 2y = 310

x - y = 55

This is a system of equations. To solve this, we're going to multiply the second equation [x - y = 55] by 2.

2(x - y = 55) = 2x - 2y = 110

Now, subtract your new equation from the first one [2x + 2y = 310]

2x + 2y = 310

-2x + 2y = -110

//If you're wondering why I changed the signs of the new equation, I multiplied our new equation [2x - 2y = 110] by -1 since we're subtracting//

When you're done subtracting, the "2x" and "-2x" cancel out, so you're left with:

4y = 200

Now, simply solve for "y" by dividing both sides by 4.

4y = 200

y = 50

Now that we know y's value, substitute it into one of our original equations to solve for x.

//I'm gonna plug y into the second equation [x - y = 55] just because it's easier, but you can plug it into the first one as well and get the same answer//

When we plug it in, we get:

x - (50) = 55

To solve for "x," we must get rid of "-50." To do this, add 50 to both sides.

x - 50 = 55

x = 105

So, x = 105 and y = 50

4 0

3 years ago

A rectangular balcony has an area of 32 square feet. its perimeter is 24 feet. what are the dimensions of the balcony?

Paul [167]

Answer:

Step-by-step explanation:

8 ft by 4 ft

8ft x 4ft = 32 ft

8ft + 8 ft = 16 ft 4 ft + 4 ft = 8 ft

16ft + 8 ft = 24 ft

5 0

3 years ago

c. Debbie and Jan are both in the 28% tax bracket. Since the interest is deductible, how much would Debbie and Jan each save in

alisha [4.7K]

Step-by-step explanation:

Let's assume Debbie paid $1700 in interest, while Jan paid $9000.

Debbie Saves = $1700* 0.28

Jan Saves = $9000 * 0.28

Debbie Saves $476 in taxes

Jan Saves $2520 in taxes

7 0

3 years ago

Men are believed to have a slightly longer average length of short hospital stays than women; 5.2 days versus 4.5 days respectiv

Georgia [21]

Answer:

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of singificance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

Step-by-step explanation:

1) Data given and notation

$\bar X_{1}=5.2$ represent the mean for group men

$\bar X_{2}=4.5$ represent the mean for group women

Assuming these values for the remaining data:

$\sigma_{1}=1.2$ represent the population standard deviation for the sample men

$\sigma_{2}=1.5$ represent the population standard deviation for the sample women

$n_{1}=32$ sample size for the group men

$n_{2}=30$ sample size for the group women

z would represent the statistic (variable of interest)

$p_v$ represent the p value

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for men it's higher than the mean for women, the system of hypothesis would be:

H0: $\mu_{1} \leq \mu_{2}$

H1: $\mu_{1} > \mu_{2}$

If we analyze the size for the samples both are higher than 30, and we know the population deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We have all in order to replace in formula (1) like this:

$z=\frac{5.2-4.5}{\sqrt{\frac{1.2^2}{32}+\frac{1.5^2}{30}}}=2.02$

4) Find the critical value

In order to find the critical value we need to take in count that we are conducting a right tailed test, so we are looking on the normal standard distribution a value that accumulats 0.01 of the area on the right and 0.99 of the area on the left. We can us excel or a table to find it, for example the code in Excel is:

"=NORM.INV(1-0.01,0,1)", and we got $z_{critical}=2.33$

5) Statistical decision

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of significance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

6 0

3 years ago