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klio [65]
4 years ago
13

Beth and Sarah are selling candy for a school fundraiser. Customers can buy small boxes of candy and large boxes of candy. Beth

sold 9 small boxes of candy and 10 large boxes of candy for a total of $297. Sarah sold 8 small boxes of candy and 5 large boxes of candy for a total of $194.
What is the cost of one small box of candy, and what is the cost of one large box of candy?

Hint: Solve a system of two equations using the elimination method.
Mathematics
1 answer:
Scrat [10]4 years ago
6 0

Answer:

Cost of small box = $13

Cost of large box = $18

Step-by-step explanation:

Let the cost of small box of candy = $s

And the cost of large candy box = $b

Beth sold 9 small and 10 large boxes of candies for $297.

9s + 10b = 297 -----(1)

Sarah sold 8 small and 5 large boxes of candies for $194.

8s + 5b = 194 -------(2)

Multiply equation (2) by 2 then subtract equation (1) from (2).

2(8s + 5b) - (9s + 10b) = (2×194) - 297

16s + 10b - 9s - 10b = 388 - 297

7s = 91 ⇒ s = $13

From equation (2),

(8×13) + 5b = 194

104 + 5b = 194

5b = 90

b = $18

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A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the un
ss7ja [257]

Answer:

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

Step-by-step explanation:

Previous concepts

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".  

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".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.112 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

3 0
3 years ago
Drew's car weighs 1,344 kilograms. His car weighs 7 times as much as his motorcycle. How many grams does his motorcycle weigh? N
Alona [7]

Answer:

192,000 grams

Step-by-step explanation:

turn 1,344 kilograms to grams, which gives u 1344000 grams

divide 1344000 by 7 and you get 192,000 grams. Hope this helped :)

7 0
3 years ago
Write the standard form of an equation with p= sqrt 3, phi= 150 degrees. Please explain.
kupik [55]

Answer:

I'm sorry but i don't know, but I do know the answer is <em>NOT B</em>

Step-by-step explanation:

6 0
3 years ago
A new Community Center is being built in Oak Valley. The perimeter of the rectangular playing field is 382 yards. The length of
vesna_86 [32]

Answer:

The width is 50 yards and the length is 141 yards.

Step-by-step explanation:

Let's call: L the length of the field and W the width of the field.

From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:

2L + 2W = 382

Because the perimeter of a rectangle is the sum of two times the length with two times the width.

Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:

L = 3W - 9

So, replacing this last equation on the first one and solving for W, we get:

2L + 2W = 382

2(3W - 9) + 2W = 382

6W -18 +2W = 382

8W - 18 = 382

8W = 382 + 18

8W = 400

W = 400/8

W = 50

Replacing W by 50 on the following equation, we get:

L = 3W - 9

L = 3(50) - 9

L = 141

So, the width of the rectangular field is 50 yards and the length is 141 yards.

3 0
3 years ago
Nathan took his car in for service and repairs. He had a coupon for 10% off. Original Prices • Labor $218.97 • Parts $303.47 • O
Dmitry_Shevchenko [17]

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

218.97 + 303.47 + 77.78 = $600.22

600.22 x .10 = 60.02 (amount of discount)

600.22 - 60.02 = $540.20 (amount he owes)

Answer is C

7 0
3 years ago
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