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brilliants [131]
3 years ago
14

To raise money for new uniforms, the band boosters sell t-shirts and hats. The cost and sale price of each item is shown. The bo

osters spend a total of $2,000 on T-shirts and hats. They sell all of the merchandise, and make $3375. How many T-shirts did they sell?
Mathematics
1 answer:
Mila [183]3 years ago
5 0
Found the problem:
Item     Cost       Sales Price
T-shirt    6                10
hats       4                  7

Let x = t-shirts, y = hats

6x + 4y = 2,000
10x + 7y = 3,375

4y = 2000 - 6x
y = 2000/4 - 6x/4
y = 500 - 3x/2

10x + 7y = 3,375
10x + 7(500 - 3x/2) = 3,375
10x + 3500 - 21x/2 = 3,375
10x - 10.5x = 3,375 - 3500
-0.5x =  -125
-0.5x / -0.5 = -125/-0.5
x = 250 shirts

They will need 250 shirts.
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Answer:

\frac{2}{3}

Step-by-step explanation:

Calculate the scale factor, using the ratio of corresponding sides, image to original.

Using the vertical line image = 4 and original = 6 , then

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4 0
3 years ago
The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a
patriot [66]

Answer:

Step-by-step explanation:

Hello!

Your study variable is X: "number of ColorSmart-5000 that didn't need repairs after 5 years of use, in a sample of 390"

X~Bi (n;ρ)

ρ: population proportion of ColorSmart-5000 that didn't need repairs after 5 years of use. ρ = 0.95

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sample proportion ^ρ: x/n = 303/390 = 0.776 ≅ 0.78

Applying the Central Limit Theorem you approximate the distribution of the sample proportion to normal to obtain the statistic to use.

You are asked to estimate the population proportion of televisions that didn't require repairs with a confidence interval, the formula is:

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Z_{1-\alpha /2} = Z_{0.995} = 2.58

0.78±2.58* √[(0.78(1-0.78))/390]

0.0541

[0.726;0.834]

With a confidence level of 99% you'd expect that the interval [0.726;0.834] contains the true value of the proportion of ColorSmart-5000 that didn't need repairs after 5 years of use.

I hope it helps!

7 0
3 years ago
What is the lcm of 4 and 5
timama [110]

Answer:

20

Step-by-step explanation:

4 * 1 = 4        5 * 1 = 5

4 * 2 = 8        5 * 2 = 10

4* 3 = 12        5 * 3 = 15

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Find P on AB that is 2/3 of the distance from A(-3,-5) to B(9,4).
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A line segment can be divided into ratios.

<em>The coordinate of P on line segment AB is (5,1)</em>

Given

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B = (9,4)

The position of P from A to B is:

P_A = \frac 23

So, from P to B would be:

P_B =1 -  \frac 23

P_B = \frac 13

So, the ratio is:

m : n = \frac 23 : \frac 13

Simplify

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<u>The coordinate of point P is:</u>

P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})

So, we have:

P = (\frac{2 \times 9 + 1 \times -3}{2 + 1},\frac{2 \times 4 + 1 \times -5}{2 + 1})

P = (\frac{15}{3},\frac{3}{3})

P = (5,1)

<em>Hence, the coordinate of P is (5,1)</em>

Read more about line ratios at:

brainly.com/question/8847082

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umka2103 [35]
The first thing you need to do is add and then subtract
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3 years ago
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