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Sonja [21]
3 years ago
8

8 kg of potatoes and 5 kg of carrots cost $28 whereas 2 kg of potatoes and 3 kg of arrot cost $11.20.what is the cost of 1 kg of

each item
Mathematics
1 answer:
kow [346]3 years ago
5 0
1 kg of potatoes costs  x, 1 kg <span>of carrots costs y.

8x+5y=28 | :(-4)
2x+3y=11,2

-2x-1,25y=-7
2x+3y=11,2

3y-1,25y=11,2-7
1,75y=4,2
y=2,4

</span><span>1 kg of carrots costs $2,4.
</span>
<span>1 kg of potatoes costs:
</span>2x+3*2,4=11,2
2x+7,2=11,2
2x=11,2-7,2
2x=4
x=2
1 <span>kg of potatoes costs $2</span>

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A sample size 25 is picked up at random from a population which is normally
Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 100 and variance of 36.

This means that \mu = 100, \sigma = \sqrt{36} = 6

Sample of 25:

This means that n = 25, s = \frac{6}{\sqrt{25}} = 1.2

(a) P(X<99)

This is the pvalue of Z when X = 99. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{99 - 100}{1.2}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

Z = \frac{X - \mu}{s}

Z = \frac{100 - 100}{1.2}

Z = 0

Z = 0 has a pvalue of 0.5

X = 98

Z = \frac{X - \mu}{s}

Z = \frac{98 - 100}{1.2}

Z = -1.67

Z = -1.67 has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0
2 years ago
At highland falls pumpkin growing contest, the prize winning pumpkin contains 360 seeds. The proud farmer plans to sell his seed
saul85 [17]
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3 years ago
In the triangle,sum of two angles is 90° which is the measure of the third angle. Also,the difference of these 2 angle is 10°, f
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3 years ago
Mr. Larson is debating between investing $10,000 into an account that pays 4% interest compounded daily or 4.9% compounded weekl
AVprozaik [17]

9514 1404 393

Answer:

   4.9% weekly

Step-by-step explanation:

The compound interest formula is ...

  A = P(1 +r/n)^(nt)

where A is the account balance that results from investing P at rate r compounded n times per year for t years.

Filling in the values for the two scenarios, we find ...

  A = 10,000(1 +0.04/365)^(365·3) ≈ 11,274.89

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The higher interest rate will earn Mr. Larson the most money in three years. (4.9% weekly)

5 0
2 years ago
Given △ABC≅△JKL, m∠B=55°, and m∠L=25°, what is the measure of ∠J?
8_murik_8 [283]
For the answer to the question above, 
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</span><span>because they are similar they have the same angles
</span>The two triangles are similar, so they must have corresponding angles. Thats one way to define similarity, it can dilate (zoom in /zoom out) , but the angles are preserved. You can also define similarity in terms of the proportionality of the sides. 

"Given △ABC≅△JKL"

The order of the letters counts. 
<A = <J
<B = <K
<C = <L

<span>now you can draw two generic triangles, which have the same three angles, but label the angles accordingly, so they match up.
</span>
<span>then by correspondance we can fill in
</span>nightowlthe third angle can be found by the fact that 
the three angles must add up to 180.
6 0
3 years ago
Read 2 more answers
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