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3 years ago

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Mathematics

2 answers:

Lana71 [14]3 years ago

8 0

Answer:

x=7

Step-by-step explanation:

63˚+70˚ = 133˚

180˚ - 133˚ = 47˚

(8x-9)˚ = 47˚

8x7=56

56-9=47˚

Furkat [3]3 years ago

3 0

Answer:

x = 7

Step-by-step explanation:

(8x - 9)° = 180° - ( 70° + 63° )

8x - 9 = 47

8x = 47 + 9

x = 56 ÷ 8

x = 7

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.

lora16 [44]

First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.

The sum $x^2+y^2$ can be written as: $x^2+y^2=(x+y)^2-2xy$ ,

from the binomial expansion formula: $(x+y)^2=x^2+2xy+y^2$ .

Thus, substituting y=-3x+18 and simplifying we have

 $x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)$ $=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x$ $=10x^2-108x+18^2$ .

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.

At x=5.4, the expression $10x^2-108x+18^2$ , which is equivalent to $x^2+y^2$ , takes it smallest value.

Substituting, we would find $10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324$ =32.4 This is the smallest value of the expression.

For x=5.4, y=-3x+18=-3(5.4)+18=1.8.

Answer: (5.4, 1.8)

8 0

2 years ago

if pentagon abcd was reflected over the axis y-axis, reflected over the x-axis, and rotated 180, where would be point A' lie

frez [133]

A reflection over the x axis coupled with another reflection over the y axis leads to a rotation of 180 degrees.

In other words,

Start with point A. Reflect over the x axis to get point B. Reflect B over the y axis to get point C. To go from A to C, we can rotate A 180 degrees about the origin.

----------------

So this means that if we do those reflections and then do the rotation, then we end up back where we started. Wherever point A is located, the point A' will also be located at the same position with the same coordinates.

4 0

2 years ago

Please solve 5/5 ÷ 1/2 =

Gala2k [10]

5/5 ÷ 1/2 =
5/5 is the same as 1 so 1/2 of 1 = 1/2

5 0

2 years ago

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t

skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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 establishes 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.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that $\mu = 273, \sigma = 100$

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 30, s = \frac{100}{\sqrt{30}}$

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}$

$Z = 0.88$

$Z = 0.88$ has a p-value of 0.8106

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}$

$Z = -0.88$

$Z = -0.88$ has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 50, s = \frac{100}{\sqrt{50}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}$

$Z = 1.13$

$Z = 1.13$ has a p-value of 0.8708

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}$

$Z = -1.13$

$Z = -1.13$ has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 100, s = \frac{100}{\sqrt{100}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}$

$Z = 1.6$

$Z = 1.6$ has a p-value of 0.9452

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}$

$Z = -1.6$

$Z = -1.6$ has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0

2 years ago

What inequality is represented by the graph?

lyudmila [28]

Answer:

Step-by-step explanation:

i can not see the pic

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3 years ago