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Dennis_Churaev [7]
3 years ago
15

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

Mathematics
1 answer:
Alla [95]3 years ago
8 0

Answer:

60 degrees

Step-by-step explanation:

1+<2=180

<1+120=180

<1=180-120

<1=60

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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 <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

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

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

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

P(<em>Z</em> ≤ -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 ≤ <em>Z</em> ≤ 2) ≈ 0.95

which means

P(<em>Z</em> ≤ -2 or <em>Z</em> ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(<em>Z</em> ≤ -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]
  1. The irrigation system is positioned 9.5 feet above the ground to start.
  2. The spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.
  3. 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 <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> 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

#SPJ1

<u>Complete Question:</u>

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
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