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2 years ago

Simplify the expression -4^2(3x - 7)

Mathematics

1 answer:

maxonik [38]2 years ago

3 0

Answer:

−48x+112

Step-by-step explanation:

evatulate: −16 (3−7)

-48+112

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Given the function f(x) = 4 - 2x: If the domain is {-4, 0, 5}, find the range. A) {-4, 4, -6} B) {-4, 4, 14} C) {12, 4, -6} D) {

Ivenika [448]

F(x) = 4 - 2x Domain = x = -4, 0, 5

f(x) = 4 - 2(-4) = 4 - (-8) = 12

f(x) = 4 - 2(0) = 4 - 0 = 4

f(x) = 4 - 2(5) = 4 - 10 = -6

f(x) = 12, 4, -6

The range is C.

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2 years ago

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The system shown has _____ solution(s).

yulyashka [42]

The answer is B because it has one solution

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2 years ago

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Rockport had 5,620 residents at the time of its founding. Currently there are 3,934 residents. What is the percent of decrease i

adell [148]

Answer:

30%

Step-by-step explanation:

percent decrease = (new - old) / old * 100 = (3934-5620)/5620 * 100 = 30%

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1 year ago

An automobile travels past the farmhouse at a speed of v = 45 km/h. How fast is the distance between the automobile and the farm

yulyashka [42]

Answer:

$\frac{ds}{dt} = 39.586 km/h$

Step-by-step explanation:

let distance between farmhouse and road is 2 km

From diagram given

p is the distance between road and past the intersection of highway

By using Pythagoras theorem

$s^2 = 2^2 +p^2$

differentiate wrt t

we get

$\frac{d}{dt} s^2 = \frac{d}{dt} (4 + p^2)$

$2s \frac{ds}{dt} =2p \frac{dp}{dt}$

$\frac{ds}{dt} = \frac{p}{s}\frac{dp}{dt}$

$\frac{ds}{dt} = \frac{p}{\sqrt{p^2 +4}} \frac{dp}{dt}$

putting p = 3.7 km

$\frac{ds}{dt} = \frac{3.7}{\sqrt{3.7^2 +4}} 45$

$\frac{ds}{dt} = 39.586 km/h$

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3 years ago

The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (according to GolfWeek). Assume th

Usimov [2.4K]

Answer:

a) $f(x) = \frac{1}{25.9}$

b) 0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

The probability density function of the uniform distribution is:

$f(x) = \frac{1}{b-a}$

The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards.

This means that $a = 284.7, b = 310.6$ .

a. Give a mathematical expression for the probability density function of driving distance.

$f(x) = \frac{1}{b-a} = \frac{1}{310.6-284.7} = \frac{1}{25.9}$

b. What is the probability the driving distance for one of these golfers is less than 290 yards?

$P(X < 290) = \frac{290 - 284.7}{310.6-284.7} = 0.2046$

0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards

3 0

2 years ago