For what values of b will F(x) = logbx be an increasing function?

8.23 A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators

Kitty [74]

Answer:

The 95% confidence interval estimate for the population mean force is (1691, 1755).

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally.

The sample selected here is <em>n</em> = 30.

Thus, the sampling distribution of the sample mean will be normal.

Compute the sample mean and standard deviation as follows:

$\bar x=\frac{1}{n}\sum x=\frac{1}{30}\times 51702=1723.4\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{30-1}\times 232561.2}=89.55$

Construct a 95% confidence interval estimate for the population mean force as follows:

$CI=\bar x\pm z_{\alpha /2}\times\frac{s}{\sqrt{n}}$

$=1723.4\pm 1.96\times\frac{89.55}{\sqrt{30}}\\\\=1723.4\pm 32.045\\\\=(1691.355, 1755.445)\\\\\approx (1691, 1755)$

Thus, the 95% confidence interval estimate for the population mean force is (1691, 1755).

3 0

3 years ago

Write an equation for converting the number of meters to kilometers

oee [108]

Y= X divided by 1000

Y= X/1000

Hope it works! Good luck!

7 0

2 years ago

Read 2 more answers

Need help ASAP, I do not understand this one.

taurus [48]

2y+20=100
2y=80
y=40

The explanation for this would because because the two base angles of an isosceles triangle are equal so since the both equal to 40 degrees, in total would be 80 degrees.

Since the total degrees of a triangle is 180 and you know the base angles make up for 80 percent you subtract that from the total of the angle your trying to find, which is 2y+20.

6 0

3 years ago

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Which number line represents the solution set for the inequality 3(8-4x)<6(x-5)?

djverab [1.8K]

we have

$3(8-4x) 54\\ x > (54/18)\\x > 3$

the solution is the interval -------> (3,∞)

therefore

the answer in the attached figure

3 0

3 years ago

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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago