Solve the polynomial equation x3 + 7x2 − 16x −112 = 0 and select the correct answer below.

A normal population has mean =μ7 and standard deviation =σ5. (a) What proportion of the population is less than 18?

marshall27 [118]

Answer:

P(x< 18) = 0.986

Step-by-step explanation:

Step 1: find the z-score using the formula, z = (x - µ)/σ

Where,

x = randomly chosen values = 18

µ = mean = 7

σ = standard deviation = 5

Proportion of the population that is less than 18 = P(x < 18)

Plug in the values into z = (x - µ)/σ, to get z-score.

z = (18 - 7)/5

z = 11/5 = 2.2

Step 2: Find P(x< 18) = P (z<2.2) using z-table.

The probability that corresponds with z-score calculated is 0.986.

Therefore,

P(x< 18) = 0.986

4 0

3 years ago

Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced

Sati [7]

Answer:

$\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\$

$W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}$

Step-by-step explanation:

$\text{If an urn contains two blue balls} (denoted \:B_1 \:and \:B_2) \text{and three white balls}$ , $(denoted \:W_1, W_2, \:and\: W_3)$

If One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.

The 25 Possible outcomes of this experiment are listed below:

$\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\$

$W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}$

The tree diagram of this event is also attached.

6 0

4 years ago

Find the given angle to the nearest degree.

Darina [25.2K]

Answer:

$\alpha=44\°$

Step-by-step explanation:

By definition, the tangent of an angle is the quotient between the side opposite the angle and the side adjacent to the angle

In other words:

$tan(\alpha) = \frac{opposite}{adjacent}$

In this triangle, the length of the side adjacent to the desired angle is 50, and the length of the opposite side is 48

So:

$tan(\alpha) = \frac{48}{50}\\\\tan(\alpha)= 0.96$

Finally

$\alpha =arctan(0.96)\\\\\alpha=44\°$

7 0

3 years ago

Read 2 more answers

5/14 - - 1/14 I will provide a picture

m_a_m_a [10]

Answer:

$\frac{3}{7}$

Step-by-step explanation:

Simplify: $\frac{5}{14} - (-\frac{1}{14}) = \frac{5}{14} + \frac{1}{14}$
$\frac{5}{14} + \frac{1}{14} = \frac{6}{14}$
$\frac{6}{14} = \frac{3}{7}$

I hope this helps!

3 0

3 years ago

How long would a rock that weighs 2 pounds take to fall 99 feet

miv72 [106K]

Answer:

When you are calculating the amount of mechanical energy used to exert force and move something, you are talking about work being done by a force at a distance. You can describe this in terms of foot-pounds. For example, you want to calculate the energy used to tighten a nut when using a wrench, or to lift a weight from the floor. Mechanical force takes place in time, so to describe the power requirement, you use foot-pounds per second.

Step-by-step explanation:

3 0

4 years ago