2^4 X 4^-2 please help give step by step

NISA [10]

The maximum number of shrubs (x) = a(area) divided by 15.9

a(area)=37.1*15
37.1*15= 556.5
556.5/15.9=x
556.5/15.9=35
35=x

6 0

4 years ago

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

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:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

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

$Z = \frac{34 - 20.76}{4.14}$

$Z = 3.2$

$Z = 3.2$ has a pvalue of 0.9993

X = 21

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

$Z = \frac{21 - 20.76}{4.14}$

$Z = 0.06$

$Z = 0.06$ has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0

4 years ago

The sum of two numbers is 10 and their product is 24. Find the<br>numbers.

irina [24]

Answer:

Step-by-step explanation:

$x,\ y-\text{the numbers}\\\\(1)\qquad x+y=10\\\\(2)\qquad xy=24\\\\==================\\\\(1)\qquad x+y=10\qquad\text{subtract}\ y\ \text{from both sides}\\(*)\qquad x=10-y\\\\\text{Substitute to (2):}\\\\(10-y)y=24\qquad\text{ue the distributive property:}\ a(b+c)=ab+ac\\10y-y^2=24\qquad\text{subtract 24 from both sides}\\-y^2+10y-24=0\qquad\text{change the signs}\\y^2-10y+24=0\\y^2-6y-4y+24=0\\y(y-6)-4(y-6)=0\\(y-6)(y-4)=0\iff y-6=0\ or\ y-4=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6\\\\y-4=0\qquad\text{add 4 to both sides}\\y=4$

$\text{Put the values of}\ y\ \text{to (*)}:\\\\\text{for}\ y=6:\\x=10-6=4\\\\\text{for}\ y=4:\\x=10-4=6$

8 0

4 years ago

An object is traveling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what

arsen [322]

Usually, Δ stands for a difference: if you have two quantities a₂ and a₁, their difference a₂-a₁ can be shortened as Δa.

This said, your formula is not set up correctly: the linear speed can be found with the formula:
v = ω·r
where r is the radius and <span>ω is the angular frequency, which is given by:
</span>ω = Δα / Δt
Substituting this into the one above, you find the correct formula:
<span>v = (Δα / Δt) · r

The problem gives you directly </span>Δα, which is 1/3 rad, because does not say at what angle the point started moving and at what angle it stopped.
Similarly, for the time you have Δt, which is 20 s.

Therefore, plugging in the numbers you get:
v = (Δα / Δt) <span>· r = (1/3 </span>÷ 20) × 10 = 1/6 = 0.167 cm/s

3 0

3 years ago

The length of a rectangular garden is 8 feet longer than it’s width. The garden is surrounded by a sidewalk that is 4 feet wide

Westkost [7]

Answer:

The length = 20
The width = 12

Explanation:

Let the Length of the garden be L and the Width W
Therefore the area of the garden = L*W
But we know that L = W + 8
Therefore the area of the garden can be expressed as W*(W + 8)
When the brackets are expanded this equals W^2 + 8W

The area of the recctangle which includes the path and garden will have a length of L + 8 (ie the length of the garden + 4 feet at the top and 4 feet at the bottom)
The width will be W + 8 (width of garden + 4 feet at the left and 4 feet at the right)
Therefore the area will be (W + 8)*(L +8)
Once again we know that L = W + 8
Therefore the area of the path/garden = (W +8)(W +8 +8)
=(W +8)(W +16)
=W^2 +24W + 128

We know that the path alone has an area of 320 square feet. Therefore if we subtract the area of the garden (W^2 + 8W) from the area of the path/garden the area left is the area of the path only

Therefore W^2 + 24W + 128 - (W^2 + 8W) = 320
W^2 + 24W + 128 - W^2 - 8W = 320
Simplify
16W + 128 = 320
Subtract 128 from both sides of the equation
16W = 192
divide both sides of the equation by 16
W = 12
As L = W + 8
L = 12 + 8 = 20

7 0

3 years ago