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3 years ago

Solve the inequality. 6x + 3 > 3x + 30

Mathematics

1 answer:

LekaFEV [45]3 years ago

6 0

6x+3>3x+30

The thing about solving inequalities, you just need to treat the symbol, which is the less than symbol in this case, as an equal sign.

So our problem becomes: 6x+3=3x+30

Now we solve this like a normal algebra problem.

First, get all the variables on one side. Since 3x is smaller than 6x, we'll get rid of that by subtracting it from each side.

3x+3=30 is what we end up with.

Now to get the variable alone and get rid of that constant. To do that, we are going to subtract 3 from each side.

We end up with 3x=27

Now, to get the 'x' alone, we need to divide each side by 3.

x=9 is what we end up.

BUT WE FORGOT TO DO SOMETHING

We started this as an inequality problem, so we need to end it as an inequality solution.

Since there wasn't any negatives we need to worry about (Which is something else entirely) we just need to transfer the symbol we started with down.

x>9

Any Questions?

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3 years ago

assume that when adults with smartphones are randomly selected 15 use them in meetings or classes if 15 adult smartphones are ra

Tanzania [10]

Answer:

The probability that at least 4 of them use their smartphones is 0.1773.

Step-by-step explanation:

We are given that when adults with smartphones are randomly selected 15% use them in meetings or classes.

Also, 15 adult smartphones are randomly selected.

Let X = <em>Number of adults who use their smartphones</em>

The above situation can be represented through the binomial distribution;

$P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; n = 0,1,2,3,.......$

where, n = number of trials (samples) taken = 15 adult smartphones

r = number of success = at least 4

p = probability of success which in our question is the % of adults

who use them in meetings or classes, i.e. 15%.

So, X ~ Binom(n = 15, p = 0.15)

Now, the probability that at least 4 of them use their smartphones is given by = P(X $\geq$ 4)

P(X $\geq$ 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= $1- \binom{15}{0}\times 0.15^{0} \times (1-0.15)^{15-0}-\binom{15}{1}\times 0.15^{1} \times (1-0.15)^{15-1}-\binom{15}{2}\times 0.15^{2} \times (1-0.15)^{15-2}-\binom{15}{3}\times 0.15^{3} \times (1-0.15)^{15-3}$

= $1- (1\times 1\times 0.85^{15})-(15\times 0.15^{1} \times 0.85^{14})-(105 \times 0.15^{2} \times 0.85^{13})-(455 \times 0.15^{3} \times 0.85^{12})$

= <u>0.1773</u>

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3 years ago

Devon rented a U Haul truck for $48 for 4 hours plus $13.50 per each hour you go over. At the end of the day, his total bill was

Rasek [7]

Answer:

You need to write an equation to find the answer to this:

h = hours

48 + 13.5h = 112.50 -First you need to subtract 48 from both sides

48 - 48 + 13.5h = 112.50 - 48

13.5h = 64.5 -Now divide both sides by 13.5

13.5h / 13.5 = 64.5 / 13.5

h = 4.77777778

However, I would just round to 5.

I hope this helps!

-Mikayla

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3 years ago

Car A, traveling at a constant 10 m/s, crosses the start line 3 seconds before Car B, who is traveling at a constant 15 m/s. At

Margaret [11]

The distance between Car A and car B,When Car A crosses the start line is:
distance =speed car B* time
distance=(15 m/s)(3 s)=45 m

Distance traveled by car A =x, (when the car B is at the same distance from the start line)
time of car A=t

x=10 m/st ⇒ x=10t (1)

Distance traveled by car B=x
time of car B=t-3

x=15(t-3) (2)

With the equations (1) and (2) we make a system of equations:

x=10t
x=15(t-3)

We solve this system of equations:

10t=15(t-3)
10t=15t-45
-5t=-45
t=-45 / -5
t=9

t-3=9-3=6

x=10 t=10 (9)=90

Answer: The time would be 9 seconds for Car A and 6 seconds for car B and the distance would be 90 meters.

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3 years ago