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3 years ago

Solve for x. -1+14x 12+17

Mathematics

1 answer:

tino4ka555 [31]3 years ago

8 0

Answer:

x=9

Step-by-step explanation:

These two angles are equal since they are alternate exterior angles

-1 +14x = 12x+17

Subtract 12x from each side

-1 +14x-12x = 12x-12x+17

-1+2x= 17

Add 1 to each side

-1+1+2x = 17+1

2x = 18

2x/2 = 18/2

x =9

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Alan hikes 4.5 miles in 3 hours. Determine whether quantities (distance and time) vary directly or inversely and find the consta

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V = x/t = 4.5 mil / 3 h = 1.5 mph
Since, v = 1.5 mph (or we can say that v is constant), distance and time vary directly and the constant of variation is 1.5 mph.

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3 years ago

Find the perimeter of a square with side a. Are the perimeter of the square and the length of its side directly proportional qua

inna [77]

The perimeter of a square with side a = 7.2 cm is 28.8 cm. Yes there exists a direct proportional relationship between Side length and Perimeter of square

<h3>Solution:</h3>

Given that side of square "a" = 7.2 cm

We have to find the perimeter of square

The perimeter of square is given as:

Perimeter of square = 4a

Where "a" represents the length of side of square

Substituting the given value a = 7.2 cm in above formula, we get perimeter of square

Perimeter of square = 4(7.2) = 28.8 cm

Are the perimeter of the square and the length of its side directly proportional quantities?

$\begin{array}{l}{\text { perimeter of square }=4 a=4 \times \text { length of side }} \\\\ {\frac{\text { perimeter of square }}{\text { length of side }}=4}\end{array}$

The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.

Two values are said to be in direct proportion when an increase in one results in an increase in the other.

So when length of sides increases, perimeter also increases

Hence perimeter and length of side of square are directly propotional quantities

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3 years ago

the mean sale per customer for 40 customers at a grocery store is $23.00, with a standard deviation of $6.00. Apply Chebyshev's

Lunna [17]

The answers is 75%x40=0.75x40=30

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3 years ago

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35° above the horiz

klemol [59]

Answer:

Step-by-step explanation:

Given:

Angle, θ = 35°

Vertical distance, Δx = 6 m

Diameter, d = 1.9 cm

= 0.019 m

When the water leaves the sprinkler, it does so at a projectile motion.

Therefore,

Using equation of motion,

(t × Vox) = 2Vo²(sin θ × cos θ)/g

= Δx = 2Vo²(sin 35 × cos 35)/g

Vo² = (6 × 9.8)/(2 × sin 35 × cos 35)

= 62.57

Vo = 7.91 m/s

Area of sprinkler, As = πD²/4

Diameter, D = 3 × 10^-3 m

As = π × (3 × 10^-3)²/4

= 7.069 × 10^-6 m²

V_ = volume rate of the sprinkler

= area, As × velocity, Vo

= (7.069 × 10^-6) × 7.91

= 5.59 × 10^-5 m³/s

Remember,

1 m³ = 1000 liters

= 5.59 × 10^-5 m³/s × 1000 liters/1 m³

= 5.59 × 10^-2 liters/s

= 0.0559 liters/s.

For the 4 sprinklers,

The rate at which volume is flowing in the 4 sprinklers = 4 × 0.0559

= 0.224 liters/s

Area of 1.9 cm pipe, Ap = πD²/4

= π × (0.019)²/4

= 2.84 × 10^-4 m²

Volumetric flowrate of the four sprinklers = 4 × 5.59 × 10^-5 m³/s

= 2.24 × 10^-4 m³/s

Velocity of the water, Vw = volumetric flowrate/area

= 2.24 × 10^-4/2.84 × 10^-4

= 0.787 m/s

7 0

3 years ago

Read 2 more answers

Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, nor

iren2701 [21]

Answer:

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,0.08)$

Where $\mu$ and $\sigma=0.08$

Since the distribution for X is normal then the we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE= \frac{0.08}{\sqrt{24}}= 0.0163$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,0.08)$

Where $\mu$ and $\sigma=0.08$

Since the distribution for X is normal then the we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE= \frac{0.08}{\sqrt{24}}= 0.0163$

8 0

3 years ago