If the measure of angle 2 is 120 degrees, find the measure of angle 4.

I can quite figure out how to go about this problem l, we are writing equations by defining a variable, writing an equation, the

galben [10]

Answer:

14 ft

Step-by-step explanation:

Let x represent the number of segments of the divided wood beam

Let y represent the total length of the wood beam.

Given that each segment measures 3.5, the equation to express this scenario is given as

y = 3.5x

Thus, to find the length of the wood beam, substitute x = 4 into the equation.

We would have:

y = 3.5(4)

y = 14

Length of the wood beam = 14 ft

3 0

3 years ago

What is 17-4x=1-4x+12-2x

SIZIF [17.4K]

17-4x = 1-4x+12-2x

17-4x = 13-6x | +4x

17 = 13-2x | -13

4 = -2x | :(-2)

-2 = x

5 0

3 years ago

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard devia

olga_2 [115]

Let X be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

P(X ≤ 0.37) = P((X - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(Z ≤ -2)

where Z follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform X to Z using the rule Z = (X - mean(X))/sd(X).)

Given the required precision for this probability, you should consult a calculator or appropriate z-score table. You would find that

P(Z ≤ -2) ≈ 0.0228

You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,

P(-2 ≤ Z ≤ 2) ≈ 0.95

which means

P(Z ≤ -2 or Z ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(Z ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

4 0

3 years ago

Julie wrote the rate $108 in 6 weeks as a unit rate. Find her mistake and correct it.

Goshia [24]

Julie wants to express $108 in 6 weeks as a unit rate.

Her errors are:
$108 = $54 (Not true)
6 weeks = 3 weeks (Not true).

Instead,
$\frac{\$108}{6\,weeks} \\ = \frac{\$54 \times 2}{3\,weeks \times 2} \\ = \frac{\$54}{3\,weeks} \\ =18 \, \frac{\$}{week}$

The correct unit rate is 18 $/week.

6 0

3 years ago

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation ℎ(

maw [93]

The irrigation system is positioned 9.5 feet above the ground to start.
The spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.
The spray reaches all the way to the ground at about 10.87 feet away

<h3>How to determine the position?</h3>

Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

<h3>How to determine the maximum height?</h3>

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

Read more on maximum height here: brainly.com/question/24288300

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Complete Question:

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away

8 0

2 years ago