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borishaifa [10]
2 years ago
12

Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (

3x – 4) feet, (x2 – 1) feet, and (2x2 – 15) feet. What is the perimeter of the triangle if x = 4?
Mathematics
2 answers:
matrenka [14]2 years ago
8 0

Answer:

40 feet

Step-by-step explanation:

Serggg [28]2 years ago
7 0
Given:
edge 1 = 3x - 4
edge 2 = x² - 1
edge 3 = 2x² - 15

perimeter if x = 4

edge 1 = 3(4) - 4 = 12 - 4 = 8
edge 2 = 4² - 1 = 16 - 1 = 15
edge 3 = 2(4²) - 15 = 2(16) - 15 = 32 - 15 = 17

Perimeter = 8 + 15 + 17 = 40 feet.
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Suppose r(t)= cos(t)i+sin(t)j+(2t)k represents the position of a particle on a helix, where Z is the height of the particle abov
Gwar [14]

Answer:

The parametric equations for the tangent line are :

x = Cos(10) - t×Sin(10)

y = Sin(10) + t×Cos(10)

z = 20 + 2t

Step-by-step explanation:

When Z=20:

Z=2t=20 ⇒ t=10

The point of tangency is:

r(10)= Cos(10) i + Sin(10) j + 20 k

We have to find the derivative of r(t) to get the tangent line:

r'(t)= -Sin(t) i + Cos(t) j + 2 k

The direction vector at t=10 is:

r'(10)= -Sin(10) i + Cos(10) j + 2 k

So, the equation of the tangent line is given by:

x = cos 10 -t×Sin(10)

y = sin 10 + t×Cos(10)

z = 20 + 2t

4 0
2 years ago
A study was conducted on the effects of long-term marriage (more than 10 years). Researchers gathered data from a random sample
True [87]

Answer:

The correct option is;

We cannot infer a cause and effect relationship because the multiple variables were included

Step-by-step explanation:

The criteria required in order to establish a cause and effect relationship includes the following;

1) There must be a temporal precedence between the cause and the effect such that the cause must take place before the effect

In the question, it is not clearly stated weather there was a divorce (the likely cause) takes place before the event

2) In the vent that the cause occurs, the effect must occur

Therefore, all those who are not married are expected to be deceased for there to be a cause and effect relationship

3) The cause and effect relationship must not be explicable by other factors

In the question, it is stated that those who were married were more likely to be active physically, maintain an healthy weight and were nonsmokers, which are factors that contribute to longevity.

8 0
2 years ago
The average time an individual reads online national news reports is 49 minutes. Assume the standard deviation is 16 minutes and
Alexus [3.1K]

Answer:

11.70% probability someone will spend no more than 30 minutes reading online national news reports.

Step-by-step explanation:

Problems of normally distributed samples can be 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 = 49, \sigma = 16

What is the probability someone will spend no more than 30 minutes reading online national news reports?

This is at most 30 minutes, so 30 or less minutes. This is the pvalue of Z when X = 30.

So

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

Z = \frac{30 - 49}{16}

Z = -1.19

Z = -1.19 has a pvalue of 0.1170.

So there is a 11.70% probability someone will spend no more than 30 minutes reading online national news reports.

4 0
2 years ago
Describe any domain restrictions that make sense for each of these scenarios: The price of a stock fluctuates several times thro
mrs_skeptik [129]

Answer:

  • a) Restriction: days of the year (a discrete time)

  • b) The time the ball is on the air: t = 0, until the balls touchs the ground (any real value from t = 0 to t when the ball hits the ground)

  • c) Any positive real value: x ≥ 0

Explanation:

The <em>domain </em>is the set of elements that can be inputs of the <em>function</em>.

<u><em>1. The price of a stock fluctuates several times throughout the year as a function of time.</em></u>

The input variable is the time through out the year.

If you assume that the fluctuaion is recorded once a day, and not every second, the logical assumption is that the time is a day of the year.

Thus, the restricion is the days of the year.

You could represent them in different forms, like DD/MM/YY, or even as a number from 1 to 365 if it covers just one year.

<u><em></em></u>

<u><em>2. A ball is hit into the air by a baseball player, rises until it reaches its highest point, and then falls into left field.</em></u>

The domain is the time the ball is on the air, which may be any real value from t = 0, until the balls touchs the ground.

It is not restricted to integer numbers.

<u><em>3. The volume of a spherical balloon increases as the balloon is blown up and decreases as air is let out of it.</em></u>

The inputs of the function are amounts of air, which may be measured as number of moles.

The number of moles can be any real value equal or greater than zero.

Thus, the domain is the positive real values x ≥ 0.

8 0
2 years ago
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erastovalidia [21]
35 degree swing. 20 to -15 is 35
4 0
2 years ago
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