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3 years ago

What is the value of x? x =

Mathematics

1 answer:

forsale [732]3 years ago

8 0

Answer:

141

Step-by-step explanation:

It is a 7 sided shape

first find the sum of interior angles

7-2 x 180 = 900

so 122 +125 +131 +107+ x-15+x+x+7 = 900

477 +3x =900

3x= 423

x=141

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A math teacher gets a starting salary of $30,000. IF she gets a 1.5% increase in salary each year, what will her total income be

kolezko [41]

No it is not base e. It is 1.015.

An increase of 1.5 % = 1.015

Year     1,   2,   3,.........................., 30.
   30000, 3000(1.015), 30000(1.015)²,........... 30000(1.015)²⁹

Her Total Income is sum over the thirty 30 year period:

Sn = a(r^n - 1) / (r - 1); a = 30000, r = 1.015, n = 30

Sn = 30000 ( 1.015^30 - 1) / (1.015 - 1)

      = 30000 (1.56308022 - 1) / (0.015) = 1126160.44

Total = $ 1 126 160.44

5 0

3 years ago

Find the inverse of f(x)=(x−5)/(−4x−2)

uysha [10]

Answer:

${f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}$

Step-by-step explanation:

The given rational function is

$f(x) = \frac{x - 5}{ - 4x - 2}$

Let

$y = \frac{x - 5}{ - 4x - 2}$

Interchange x and y

$x= \frac{y- 5}{ - 4y - 2}$

Cross multiply

$x( - 4y - 2)= y- 5$

Expand

$- 4xy - 2x= y- 5 \\ - 4xy - y= 2x - 5 \\y( - 4x - 1)= 2x - 5$

Solve for y;

$y= \frac{ 2x - 5}{ - 4x - 1}$

$y= \frac{ 5 - 2x }{ 4x + 1}$

Therefore

${f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}$

7 0

3 years ago

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

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

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0

3 years ago

Determine a polynomial that represents the area of the parallelogram. A=

sp2606 [1]

Answer:

4b² - 16

Step-by-step explanation:

The formula to find the area of a parallelogram equals $bh$ , where b = base and h - height. We're given the base as 2b + 4 and the height as 2b - 4.

$(2b+4)*(2b-4)=(2b+4)(2b-4)$
$(2b+4)(2b-4)=(2b)(2b)+(2b)(-4)+(4)(2b)+(4)(-4)$
$4b^2-8b+8b-16$
$4b^2-16$

Therefore, the answer is 4b² - 16.

6 0

2 years ago

Christian's bill at a restaurant is $840.If Christian's wants to leave a 17% tip, how much tip should he leave?

Ilya [14]

Hey there!

840 = 100%

x = 17%

840/x = 100%/17%

(840/x) * x = (100/17) * x 840 = 5.8823529411765

= 840/5.8823529411765 = 142.80

The correct answer to your question is option C.

The tip Christian should leave is $142.80.

Hope this helps you.
Have a great day!

5 0

3 years ago