Solve for x 5x 2^3x = 21

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When car

fenix001 [56]

Answer:

Now, to answer the question, we need to add the weight of (58-42) = 16 gallons of fuel to the weight of the plane

carrying 42 gallons of fuel, 2331 pounds.

So, the answer is 2331 + 16*5.5 = 2419 pounds.

7 0

2 years ago

Solve this inequality

8090 [49]

X is greater than or equal to -5

4 0

3 years ago

Read 2 more answers

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally

Dafna1 [17]

Answer:

a) 0.0869 = 8.69% probability that the thickness is less than 3.0 mm

b) 0.0668 = 6.68% probability that the thickness is more than 7.0 mm

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

$\mu = 4.9, \sigma = 1.4$

(a) the thickness is less than 3.0 mm

This is the pvalue of Z when X = 3.

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

$Z = \frac{3 - 4.9}{1.4}$

$Z = -1.36$

$Z = -1.36$ has a pvalue of 0.0869

0.0869 = 8.69% probability that the thickness is less than 3.0 mm

(b) the thickness is more than 7.0 mm

This is 1 subtracted by the pvalue of Z when X = 7. So

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

$Z = \frac{7 - 4.9}{1.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% probability that the thickness is more than 7.0 mm

5 0

3 years ago

A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

2 years ago

A cyclist rides her bike at a speed of 30 kilometers per hour. What is this speed in kilometers per minute? How many kilometers

Nata [24]

Step-by-step explanation:

The answer is mentioned above.

3 0

2 years ago