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JulijaS [17]
3 years ago
15

Solve the system of equations.

Mathematics
1 answer:
Slav-nsk [51]3 years ago
8 0
13x - 6y = 2......multiply by 2
3x - 4y = -10....multiply by -3
------------------
26x - 12y = 4 (result of multiplying by 2)
-9x + 12y = 30 (result of multiplying by -3)
-----------------add
17x = 34
x = 34/17
x = 2

now sub 2 in for x into either of the original equations to find y
3x - 4y = -10
3(2) - 4y = -10
6 - 4y = -10
6 + 10 = 4y
16 = 4y
16/4 = y
4 = y

solution is (2,4)
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Christopher bought 4 pens that cost the same amount of money and a marker that cost $3. He spent a total of $11. Which statement
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The pens cost $2 each.
2*4+3=11
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3 years ago
Y = 2x + 3<br><br><br> y = 1/2 x – 3<br><br><br> y = –2x – 3<br><br><br> y = 1/2 x + 3
vodka [1.7K]

Answer:

y = 1/2 x + 3

Step-by-step explanation:

the positive 3 is the y intercept and the positive 1/2 is rise over run up-1 & 2 to the right

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The volume of a right square prism is 588 cubic centimeters and its height is 12 cm. What is the length of each side of the base
Sauron [17]

Answer:

7cm

Step-by-step explanation:

588 / 12 = 49

\sqrt{49} = 7 * Since 7 times 7 equals 49

6 0
2 years ago
Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A samp
shutvik [7]

Answer:

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

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 20, standard deviation of 5:

This means that \mu = 20, \sigma = 5

Sample of 170:

This means that n = 170, s = \frac{5}{\sqrt{170}}

What is the probability that a sample of 170 steady smokers spend between $19 and $21?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.

X = 21

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

By the Central Limit Theorem

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

Z = \frac{21 - 20}{\frac{5}{\sqrt{170}}}

Z = 2.61

Z = 2.61 has a p-value of 0.9955

X = 19

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

Z = \frac{19 - 20}{\frac{5}{\sqrt{170}}}

Z = -2.61

Z = -2.61 has a p-value of 0.0045

0.9955 - 0.0045 = 0.9910

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

3 0
3 years ago
The function f(x) = 40sin(0.1x + 12) + 50 represents the number of items, f(x), made in a factory each day for x days. The data
Sladkaya [172]

Answer:

its 11 and 31

Step-by-step explanation:

got it right on test

7 0
3 years ago
Read 2 more answers
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