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3 years ago

Graph each piecewise function. Then identify the properties.

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

7 0

Answer:

Domain: (-∞, 0] U (0, ∞): All real numbers.

Range: (-∞, ∞)

Step-by-step explanation:

This function is composed of two polynomial functions, a quadratic whose domain is all real numbers and a negative slope whose domain is all real numbers.

Observe in the attached graph that the function is continuous for the whole domain, it does not have any jump. In addition, the parabolic function comes from ∞, then it has a minimum value in y = 1 it grows up to y = 4. Finally it joins with the equation of the line and it extends to -∞.

Then we can conclude that for this piecewise function:

Domain: (-∞, 0] U (0, ∞): All real numbers.

Range: (-∞, ∞)

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What is the value of x in the equation 3x – 4y = 65, when y = 4?

xz_007 [3.2K]

27 because 4*4=16. 65+16=81 and 81 divided by 3=27

5 0

4 years ago

The math club needs to raise more than $552. $.50 for a trip to state competition. The club has raise 12% of the funds which is

ratelena [41]

Each of the members must raise at least $69.46.

To start they need to raise $552.50. However, they have already raised 12% of it. They only need to raise 88% of it.

552.50 x 0.88 = 486.2

Divide the remaining amount by 7 to determine how much each individual must raise.

486.2 / 7 = 69.46

4 0

3 years ago

The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 m

Zinaida [17]

Answer:

$G = 0.007523$

The number of cars the highway patrol officer would watch before a car that is seen is $E(X) = 1.6027$

The standard deviation is $s = 0.9829$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 71.5 \ miles/hour$

The standard deviation is $\sigma = 4.75 \ miles/hour$

The speed limit is $x = 70 \ miles /hour$

Generally the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as

$p =P(X > x ) = P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})$

=> $p= P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})$

=> $p= P(X > 70) = P(\frac{X - \mu }{\sigma } > -0.31579 )$

Here

$\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of X )$

=> $p= P(X > 70) = P(Z > -0.31579 )$

From the z-table

$p = P(Z > -0.31579 ) = 0.62392$

$p = P(X > 70) = 0.62392$

Generally the probability of getting a car that is not moving with speed greater than the speed limit is mathematically represented as

$q = 1 - p$

=> $q = 1 - 0.62392$

=> $q = 0.37608$

Generally the probability of getting 5 cars that are not speeding is mathematically represented as

$G = q^5$

=> $G = (0.37608)^5$

=> $G = 0.007523$

Generally the number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten is mathematically represented as

$E(X) = \frac{1}{p}$

=> $E(X) = \frac{1}{0.62392}$

=> $E(X) = 1.6027$

Generally the standard deviation is mathematically represented as

$s = \sqrt{\frac{1 - p }{ p^2} }$

=> $s = \sqrt{\frac{1 -0.62392 }{ (0.62392)^2} }$

=> $s = 0.9829$

8 0

3 years ago

Alkena and Hsu together earn $84,369 per year, If alkena earns $12,468 more per year than Hsu, the how much of them earn per yea

scoray [572]

Answer:

Hsu makes $35,950.50 and Alkena makes $48,418.50

Step-by-step explanation:

Create a system of equations, where h is the amount Hsu makes and a is the amount Alkena makes:

a + h = 84,369

a = h + 12,468

Solve by substitution by plugging in h + 12,468 as a:

h + 12,468 + h = 84,369

2h + 12,468 = 84,369

2h = 71,901

h = 35,950.50

Plug this into the equation, a = h + 12,468 , to solve for a

a = 35,950.50 + 12,468

a = 48,418.50

So, Hsu makes $35,950.50 and Alkena makes $48,418.50

3 0

3 years ago

Find the equation of line (use exact numbers)

maw [93]

Answer:

$y=3x+3$

Step-by-step explanation:

Use the slope-intercept form:

$y=mx+b$

m is the slope and b is the y-intercept. The y-intercept is the place where x is equal to 0, and the slope is the change in the y-axis over the change in the x-axis, otherwise known as rise over run ( $\frac{rise}{run}$ ).