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3 years ago

Which of the following is equivalent to 7-2(x+2)<-4-3(1 - x)?

Mathematics

1 answer:

Artemon [7]3 years ago

7 0

Answer:

2 < x

Step-by-step explanation:

7-2(x+2)<-4-3(1 - x)

Distribute

7 - 2x-4 < -4 -3 +3x

Combine like terms

3 -2x < -7 +3x

Add 2x to each side

3-2x +2x< -7+3x+2x

3< -7+5x

Add 7 to each side

3+7 <-7+7+5x

10 <5x

Divide each side by 5

10/5 <5x/5

2 < x

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You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die an

ASHA 777 [7]

Answer:

Yes

$P(1 \& 5) = \frac{1}{36}$

$P(5 \& 1) = \frac{1}{36}$

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

Step-by-step explanation:

From the question we are told that

Two fair dice, one green and one red were rolled

Generally the outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the probability of getting a 1 on a dice rolled is $P(1) = \frac{1}{6}$

the probability of getting a 5 on a dice rolled is $P(5) = \frac{1}{6}$

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

$P(1 \& 5) = \frac{1}{6} *\frac{1}{6}$

$P(1 \& 5) = \frac{1}{36}$

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

$P(5 \& 1) = \frac{1}{6} *\frac{1}{6}$

$P(5 \& 1) = \frac{1}{36}$

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

$P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}$

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

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3 years ago

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3 years ago

How do you solve this ?

quester [9]

3x + 7 > 4x + 3

subtract 3x from both sides

7 > x + 3

7 - 3 > x

x < 4

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3 years ago

Camille's Cupcakes spends $032 to make one cupcake. They sell each cupcake for $1.40. How much profit will the shop make if they

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6 0

3 years ago

A line includes the points (-39,49) and (0,0). What is its equation in slope-intercept form?

malfutka [58]

Answer:

The equation in the slope-intercept form will be:

$y=-\frac{49}{39}x+0$

Step-by-step explanation:

Given the points

(-39,49)

(0,0)

Finding the slope between the points using the formula

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-39,\:49\right),\:\left(x_2,\:y_2\right)=\left(0,\:0\right)$

$m=\frac{0-49}{0-\left(-39\right)}$

$m=-\frac{49}{39}$

We know that the point-slope of the line equation is

$y-y_1=m\left(x-x_1\right)$

substituting $m=-\frac{49}{39}$ and (-39,49) in the equation

$y-y_1=m\left(x-x_1\right)$

$y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)$

Now writing the equation in slope-intercept form

$y=mx+b$

where m is the slope and b is the y-intercept

$y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)$

$y-49=\frac{-49}{39}\left(x+39\right)$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$y-49=-\frac{49}{39}\left(x+39\right)$

$\mathrm{Add\:}49\mathrm{\:to\:both\:sides}$

$y-49+49=-\frac{49}{39}\left(x+39\right)+49$

$y=-\frac{49}{39}x+0$ ∵ $y=mx+b$

Where

$m=-\frac{49}{39}$ and the y-intercept i.e. $b=0$

Therefore, the equation in the slope-intercept form will be:

$y=-\frac{49}{39}x+0$

5 0

3 years ago