All categories

3 years ago

Simplify fully, does anyone know ?

Mathematics

2 answers:

Misha Larkins [42]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

$\frac{a^{m} }{a^{n} }$ = $a^{(m - n)}$ , then

(a)

$\frac{x^{7} }{x^{3} }$ = $x^{(7-3)}$ = $x^{4}$

(b)

$\frac{y^{5} }{y^{4} }$ = $y^{(5-4)}$ = $y^{1}$ = y

Julli [10]3 years ago

6 0

Here's an explanation! :)

You might be interested in

Use the distributive property to write an equivalent expression. 6(x+y+z)

DENIUS [597]

Answer: no I pooped on my head :)

Step-by-step explanation:

6 0

2 years ago

Construct a 95% confidence interval for the population mean, mu. Assume the population has a normal distribution. A random sam

aniked [119]

Given Information:

Number of lithium batteries = n = 16

Mean life of lithium batteries = μ = 645 hours

Standard deviation of lithium batteries = σ = 31 hours

Confidence level = 95%

Required Information:

Confidence Interval = ?

Answer:

$CI = 628.5 \: to \: 661.5 \: hours$

Step-by-step explanation:

The confidence interval is given by

$CI = \mu \pm t_{\alpha/2} (\frac{\sigma}{\sqrt{n}})$

Where μ is the mean life of lithium batteries, σ is the standard deviation, n is number of lithium batteries selected, and t is the critical value from the t-table with significance level of

tα/2 = (1 - 0.95) = 0.05/2 = 0.025

and the degree of freedom is

DoF = n - 1 = 16 - 1 = 15

The critical value (tα/2) at 15 DoF is equal to 2.131 (from the t-table)

$CI = 645 \pm 2.131(\frac{31}{\sqrt{16}})$

$CI = 645 \pm 2.131(7.75})$

$CI = 645 \pm 16.515$

$CI = 645 - 16.515 \: and \: 645 + 16.515$

$CI = 628.5 \: to \: 661.5 \: hours$

Therefore, the 95% confidence interval is 628.5 to 661.5 hours

What does it mean?

It means that we are 95% confident that the mean life of 16 lithium batteries is within the interval of (628.5 to 661.5 hours)

6 0

3 years ago

A spiral staircase turns $270^\circ$ as it rises 10 feet. The radius of the staircase is 3 feet. What is the number of feet in t

Anastaziya [24]

The number of feet in the length of the handrail is 17.3 ft.

The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle

The bottom side of the rectangle is just the arc length of a circle with a radius of 3 ft turned through 270°= (3/4) of a whole revolution

(3/4) (2pi) (3) = (9/2)pi ft = 4.5 pi ft

The side of the rectangle will be the rise of the staircase = 10ft

And the diagonal of the rectangle will be the length of the handrail

We can use the Pythagorean Theorem to solve this

Handrail length = √ [ (4.5 pi)^2 + 10^2 ] ≈ 17.3 ft

Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Learn more about the Pythagorean theorem here: brainly.com/question/343682

#SPJ4

3 0

1 year ago

Draw a point that shows the value of the 2020th dvddvd. label it 1. draw a point that shows the willingness to pay for the 1010t

Elina [12.6K]

Very hard question. .....

6 0

3 years ago

Now, determine a general rule for what happens when we have two exponential

fomenos

Y=mx+b so this means you’ll get the correct answer

3 0

3 years ago