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3 years ago

[2x+4] -[-x+5 ]subtract linear expressions

Mathematics

1 answer:

Olin [163]3 years ago

6 0

(2x +4 ) - (x+5)

when we open the brackets the sign (-) will change to (+) so,

2x+4 - x-5

x+4-5

x-1

<h3>Hope this helps you mate </h3>

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Line AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to

amid [387]

parallel means "same slope (m)"

m = $\frac{y2 - y1}{x2 - x1}$ = $\frac{0 - 5}{-3 - (-6)} = \frac{-5}{-3 + 6} = \frac{-5}{3}$

Now, input the point (0, 0) and the slope $(\frac{-5}{3})$ into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - 0 = $\frac{-5}{3}$ (x - 0)

y = $\frac{-5}{3}x$

3y = -5x multiplied both sides by 3

0 = -5x - 3y subtracted 3y from both sides

Answer: C

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2 years ago

Write and expression for 7 divided by c

Over [174]

Answer:

7/c

Step-by-step explanation:

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2 years ago

In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre

Veseljchak [2.6K]

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that $p = 0.09$

41 people arrested for DUI in Illinois are selected at random.

This means that $n = 41$

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158$

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ .

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791$

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

$E(X) = np = 41*0.09 = 3.69$

d. What is the standard deviation of the number of repeat offenders?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83$

4 0

2 years ago

If C ( x ) = 11000 + 500 x − 3.6 x 2 + 0.004 x 3 is the cost function and p ( x ) = 1700 − 9 x is the demand function, find the

Bess [88]

Answer:

Step-by-step explanation:

The cost function = C(x)

The demand function = P(x)

C(x) = 11000 + 500x - 3.6x^2 + + 0.004x^3

P(x) = 1700 - 9x

Differentiate C(x) with respect to x

C'(x) = 500 - 7.2x + 0.012x^2

C'(x) is the marginal cost

Revenue = x. P(x)

R(x) = x( 1700 -9x)

= 1700x - 9x^2

Differentiate R(x) with respect to x

R'(x) = 1700 - 18x

R'(x) is the marginal revenue

Profit is maximized when R'(x) = C'(x)

1700 - 18x = 500 - 7.2x + 0.012x^2

Collect like terms

0 = 500 - 1700 - 7.2x +18x +0.012x^2

0 = -1200 + 10.8x +0.012x^2

0 = 0.012x^2 + 10.8x - 1200

Using x=( -b +_ √b^2 - 4ac) /2a

a = 0.012 , b= 10.8 , c= -1200

x= (-10.8 +_ √(10.8^2) - 4*0.012*(-1200)) /2*0.012

= ( -10.8 +_√116.64 + 57.6) / 0.024

= (-10.8 +_ √174.24) / 0.024

= (-10.8 +_13.2) / 0.024

= (-10.8+13.2)/0.024 or (-10.8 - 13.2)/0.024

= 2.4/0.024 or -24/0.024

x= 100 or -1000

Since our profit cannot be negative, the profit = $100

5 0

2 years ago

Explain how you simplfy 5(4i - 3m) + 2m

Galina-37 [17]

Answer:

20i - 13m. look at the picture

5 0

2 years ago