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2 years ago

Assume that X has a normal distribution, and find the indicated probability.

Mathematics

1 answer:

GrogVix [38]2 years ago

6 0

Answer: 0.6827

Step-by-step explanation:

I believe it is 0.6827

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What fraction is shown on the number line? 5/6 5/5 1/6 1/5 Pls help

icang [17]

5/6 as there is 6 jumps and the dot is placed on the fifth therefore being 5/6

3 0

2 years ago

A sample of bacteria is growing at an hourly rate of 14% according to the exponential growth function. The sample began with 7 b

tatiyna

Answer:

125

Step-by-step explanation:

x(t) = x0 × (1 + r) t

where:

x(t) = the amount of some quantity at time t

x0 = initial amount at time t = 22

r = the growth rate

t = time

3 0

3 years ago

A recent survey of 128 high school students indicated the following information about release times from school.

Delicious77 [7]

Answer:

A) Interval estimate for those that want to get out earlier = (35%) ± (4%) = (31%, 39%)

Interval estimate for those that want to get out later = (39%) ± (4%) = (35%, 43%)

B) The group that wants to get out of school earlier can win after all the votes are counted if their true population proportion takes on a value that is higher than the closest true population proportion (for the group that wants to get out of school later)

That is, in the (31%, 39%) and (35%, 43%) obtained in (a), a range of (35.1%, 39%) and (35%, 38.9%) show how possible that the group that wants to get out of school earlier can win after all the votes are counted.

Step-by-step explanation:

The Interval estimate for the proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Interval estimate = (Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the proportion.

a) Find the interval estimates

i) for those that want to get out earlier and

ii) those that want to get out later.

i) Sample proportion of those that want to get out earlier = 35%

Margin of Error = 4%

Interval estimate for those that want to get out earlier = (35%) ± (4%) = (31%, 39%)

ii) Sample proportion of those that want to get out later = 39%

Margin of Error = 4%

Interval estimate for those that want to get out later = (39%) ± (4%) = (35%, 43%)

b) Explain how it would be possible for the group that wants to get out of school earlier to win after all the votes are counted.

Since the interval estimates represent the range of values that the true population proportion can take on for each group that prefer a particular option, the group that wants to get out of school earlier van have their proportion take on values between 31% and 39%. If their true population takes on a value that is highest (which is very possible from the interval estimate), and the group with the highest proportion in the sample, (the group that wants to get out of school later, whose true population proportion can take between 35% and 43%) has a true population proportion that is less than that of the group that wants to get out of school earlier, then, the group that wants to get out of school earlier can win after all the votes are counted.

Hope this Helps!!!

3 0

3 years ago

Remember to show work and explain. Use the math font.

MrMuchimi

Answer:

$\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}$

Step-by-step explanation:

$\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================$

$1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}$

$\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)$

$--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)$

$--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}$

6 0

3 years ago

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29

melomori [17]

Answer:

3280 square inches

Step-by-step explanation:

The surface area of square pyramid = 4* the area of the triangular side + the area of the square base.

TRIANGULAR SIDE

The pyramid has an isosceles triangular side of size, a=40 inches, b= 29 inches, c = 29 inches.

Surface area = sqrt{ s(s-a)(s-b)(s-c) }

Where s= (a+b+c)/2

S= (40+29+29)/2 = 49

Surface area = sqrt{ 49(49-40)(49-29)(49-29)}

Surface area = 420 square inches

SQUARE BASE

Area of a square = a²

Area = 40² = 1600 square inches

Surface area of the pyramid = 4*420 + 1600 = 1680 + 1600

Surface area = 3280 square inches.

8 0

2 years ago

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