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Mashutka [201]
3 years ago
8

To get a 100 kilograms of a 48% fat content chocolate how many kilograms of a 30% and 50% mix should be used

Mathematics
1 answer:
wlad13 [49]3 years ago
8 0
A kilogram %30 chocolate,
b kilogram %50 chocolate,
a+b = 100 kilogram chocolate,

48.(a+b) = 30.a + 50.b
48a + 48b = 30a + 50b
18a = 2b
b = 9a

a+b = a + 9a = 10a = 100 kg
a = 10 kg
b = 9.a = 90 kg

You should use,

10 kg %30 chocolate,
90 kg %50 chocolate
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Answer:

a) The point estimate of the proportion of items returned for the population of

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b) The 95% confidence interval for the proportion of returns at the Houston store = [0.0718 < p < 0.2282].

c) Yes.

We set an hypothesis and construct a test statistics. The test statistics result gives us:

Z calculated  = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

Step-by-step explanation:

a) Point estimate of the proportion = number of returned items/ total items sold = 12/80 = 0.15.

b) By formula of confident interval:

CI(95%) = p ± Z*\sqrt{\frac{p*(1-p)}{n} }  =  0.15 \pm 1.96 *\sqrt{\frac{0.15*(1-0.15)}{80} },

CI(95%) = [0.0718 < p < 0.2282]

c) The hypothesis:

H_{0}: The proportion of returns at the Houston store is not significantly different from the returns  for the nation as a whole.

H_{a}: The proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

The test statistics:

Z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p*(1-p)}{n} }}, where p_{0} is the proportion of nation returns.

Z calculated  = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

6 0
3 years ago
Let z = 5. What is the value of (10 + 25) ÷ z?
Murrr4er [49]

Answer:

<h2>A. 7</h2>

Step-by-step explanation:

Put z = 5 to the expression (10 + 25) ÷ z:

(10 + 25) ÷ 5 = 35 ÷ 5 = 7

5 0
3 years ago
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Ostrovityanka [42]
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3 0
3 years ago
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Suppose f(x)=2×+5 find the value of -2f(x+1)
loris [4]
F(x) = 2x + 5 

-----------------------------------
Find f(x + 1) :
-----------------------------------
f(x +1) = 2(x + 1) + 5
f(x +1) = 2x + 2 + 5
f(x + 1) = 2x + 5

-----------------------------------
Find -2f(x+1):
-----------------------------------
-2(fx+1) = -2(2x + 5)
-2(fx+1) = -4x - 10

----------------------------------------------------------------------
Answer: -2(fx+1) = -4x - 10
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Answer:

point form: (3,-6)

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Step-by-step explanation:

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2 years ago
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