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3 years ago

Translate this sentence into an equation. 48 is the product of Greg’s score and 3. Use the variable g to represent Greg’s score

Mathematics

1 answer:

wolverine [178]3 years ago

3 0

Answer:

3*g = 48

Step-by-step explanation:

Greg's score multiplied by 3 is equal to 48 (the product).

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A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

3 years ago

Solve for x<br> x+4/3 = 6

VladimirAG [237]

Answer:

x= 4 2/3

Step-by-step explanation:

Subtract 4/3 from 6 to get X! Hope this helped!

5 0

3 years ago

Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at t

olga_2 [115]

Answer:

a) The critical value on this case would be $t_{crit}=1.325$

b) The critical value on this case would be $t_{crit}=-1.345$

c) The critical values on this case would be $t_{crit}=\pm 2.201$

Step-by-step explanation:

Part a

The system of hypothesis on this case would be:

Null hypothesis: $\mu \leq \mu_0$

Alternative hypothesis: $\mu > \mu_0$

Where $\mu_0$ is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, on this case that is given df=20. Since its an upper tailed test we need to find a value a such that:

$P(t_{20}>a) = 0.1$

And we can use excel in order to find this value with this function: "=T.INV(0.9,20)". The 0.9 is because we have 0.9 of the area on the left tail and 0.1 on the right.

The critical value on this case would be $t_{crit}=1.325$

Part b

The system of hypothesis on this case would be:

Null hypothesis: $\mu \geq \mu_0$

Alternative hypothesis: $\mu < \mu_0$

Where $\mu_0$ is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since its an lower tailed test we need to find b value a such that:

$P(t_{14}$

And we can use excel in order to find this value with this function: "=T.INV(0.1,14)". The 0.1 is because we have 0.1 of the area accumulated on the left of the distribution.

The critical value on this case would be $t_{crit}=-1.345$

Part c

The system of hypothesis on this case would be:

Null hypothesis: $\mu = \mu_0$

Alternative hypothesis: $\mu \neq \mu_0$

Where $\mu_0$ is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, given by:

$df=n-1=12-1=11$

Since its a two tailed test we need to find c value a such that:

$P(t_{11}>c) = 0.025$ or $P(t_{11}$

And we can use excel in order to find this value with this function: "=T.INV(0.025,11)". The 0.025 is because we have 0.025 of the area on each tail.

The critical values on this case would be $t_{crit}=\pm 2.201$

5 0

3 years ago

What is the equation of a line that is perpendicular to 2x+3y=9 and passes through the point (8,5)

pochemuha

For
ax+by=c
slope=-a/b

perpendiculare lines have slopes that multiply to -1

so

2x+3y=9
slope=-2/3
-2/3 times what=-1
what=3/2

point slope form
the equation of a line that passes through the point (x1,y1) and the slope is m is
y-y1=m(x-x1)
slope=3/2
point i (8,5)

equation is
y-5=3/2(x-8)
converted to standard form
2y-10=3x-24
-3x+2y=-14
3x-2y=14

7 0

3 years ago

Read 2 more answers

Hugh made a list to show all the factore of 60. what are the factors.

elena55 [62]

1,2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

6 0

3 years ago

Read 2 more answers