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2 years ago

118° (10x+2)° solve for x and z

Mathematics

1 answer:

Ghella [55]2 years ago

6 0

Answer:

Simplifying

10x + -2 = 118

Reorder the terms:

-2 + 10x = 118

Solving

-2 + 10x = 118

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.

-2 + 2 + 10x = 118 + 2

Combine like terms: -2 + 2 = 0

0 + 10x = 118 + 2

10x = 118 + 2

Combine like terms: 118 + 2 = 120

Combine like terms: 118 + 2 = 12010x = 120

Combine like terms: 118 + 2 = 12010x = 120Divide each side by '10'.

Combine like terms: 118 + 2 = 12010x = 120Divide each side by '10'.x = 12

Combine like terms: 118 + 2 = 12010x = 120Divide each side by '10'.x = 12Simplifying

Combine like terms: 118 + 2 = 12010x = 120Divide each side by '10'.x = 12Simplifyingx = 12

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2 years ago

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A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25

GREYUIT [131]

Answer:

The upper limit of a 95% confidence interval for the population mean would equal 83.805.

Step-by-step explanation:

The standard deviation is the square root of the variance. Since the variance is 25, the sample's standard deviation is 5.

We have the sample standard deviation, not the population, so we use the t-distribution to solve this question.

T interval:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of 0.95( $t_{95}$ ). So we have T = 1.761

The margin of error is:

M = T*s = 1.761*5 = 8.805.

The upper end of the interval is the sample mean added to M. So it is 75 + 8.805 = 83.805.

The upper limit of a 95% confidence interval for the population mean would equal 83.805.

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2 years ago

Which rational exponent represents a square root? A. 1 / 2 B. 3/2 C. 1/3 D. 1/4

Fofino [41]

Answer:

1/2 rational exponent represents a square root.

Therefore, option A is correct.

Step-by-step explanation:

As we know that raising to the one-half power i.e. $\frac{1}{2}$ is the same

as taking the square root.

so $x^{\frac{1}{2}}$ is the same as the square root of $x$ .

For example, taking the square root of 4 will determine:

$4^{\frac{1}{2}}$

$\mathrm{Factor\:the\:number:\:}\:4=2^2$

$4^{\frac{1}{2}}=\left(2^2\right)^{\frac{1}{2}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0$

$\left(2^2\right)^{\frac{1}{2}}=2^{2\cdot \frac{1}{2}}$

so the expression becomes

$4^{\frac{1}{2}}=2^{2\cdot \:\frac{1}{2}}$

$=2^1$

$=2$ ∵ $\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a$

so, 1/2 rational exponent represents a square root.

Therefore, option A is correct.

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1 year ago

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