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2 years ago

12

Given a 10 foot length of tree trunk with a radius of 3 feet, what is the weight of the tree trunk section if it has a density o

f 45 lb/ft3? (to the nearest whole integer)

1 answer:

Soloha48 [4]2 years ago

3 0

You will use the formula for the mass of a cylinder. Since the trunk forms like a cylinder.

It is Mcylinder = density x pi x radius x height

So the given in our problem is:

Density = 45 lb/ft^3

Radius = 3ft

Height = 10 ft

Plugging that in our equation:

M cylinder = 45 lb/ft^3 * pi * 3ft^2 * 10 ft

= 5771.26 kgs

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Toyota advertises that their Toyota Highlander Hybrid provide 28 MPG. To test this, an experiment involving a sample of 20 Toyot

klemol [59]

Answer:

We accept the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 28.8 miles per gallon

Sample size, n = 120

Alpha, α = 0.01

Sample standard deviation, σ = 6.89 miles per gallon

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 28\text{ miles per gallon.}\\H_A: \mu \neq 28\text{ miles per gallon.}$

We use Two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n-1}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.8 - 28}{\frac{6.89}{\sqrt{19}} } = 0.5061$

Now, $t_{critical} \text{ at 0.01 level of significance, 19 degree of freedom } =\pm 2.8609$ Since,

$-2.609 < t_{stat} < 2.8609$

We fail to reject the null hypothesis and accept it.

We accept the null hypothesis and the population mean MPG of Toyota Highlander Hybrid vehicles is equal to 28 miles per gallon.

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2 years ago

The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor?

PtichkaEL [24]

Answer:

$\left(y-8\right)$

Step-by-step explanation:

$y^2-10y+16$

$=\left(y^2-2y\right)+\left(-8y+16\right)$

$y^2-2y$

$=yy-2y$

$=y\left(y-2\right)$

$-8y+16$

$=-8y+8\cdot \:2$

$=-8\left(y-2\right)$

$=y\left(y-2\right)-8\left(y-2\right)$

$=\left(y-2\right)\left(y-8\right)$

The other factor is:

$\left(y-8\right)$

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2 years ago

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Suppose that demand in period 1 was 7 units and the demand in period 2 was 9 units. Assume that the forecast for period 1 was fo

Zepler [3.9K]

Answer:

Step-by-step explanation:

Forecast for period 1 is 5

Demand For Period 1 is 7

Demand for Period 2 is 9

Forecast can be given by

$F_{t+1}=F_t+\alpha (D_t-F_t)$

where

$F_{t+1}=Future Forecast$

$F_t=Present\ Period\ Forecast$

$D_t=Present\ Period\ Demand$

$\alpha =smoothing\ constant$

$F_{t+1}=5+0.2(7-5)$

$F_{t+1}=5.4$

Forecast for Period 3

$F_{t+2}=F_{t+1}+\alpha (D_{t+1}-F_{t+1})$

$F_{t+2}=5.4+0.2\cdot (9-5.4)$

$F_{t+2}=6.12$

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2 years ago

What is the area of the shaded region?

azamat

Answer:

$(25\pi\ -24)\ cm^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of the two isosceles triangles

so

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

where r is the radius of the circle

In this problem we have

$r=5\ cm$

substitute

$A=\pi (5)^{2}$

$A1=25\pi\ cm^{2}$

Find the area of the two triangles

The area of the two isosceles triangles is equal to

$A=2[\frac{1}{2}bh]=bh$

we have

$b=6\ cm$

$h=5-1=4\ cm$

substitute

$A2=6*4=24\ cm^{2}$

Find the area of the shaded region

$A1-A2=(25\pi\ -24)\ cm^{2}$

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2 years ago

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Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent th

oksian1 [2.3K]

Equation represents the difference in the number of foreign and domestic stamps Malik collected: X-34=y

equation represents the total number of stamps Malik collected:
212 = X-34-y
so,
245= X-Y

Situation :
Y= X-34
X-Y= 245

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2 years ago

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