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3 years ago

Use the table to solve the inequality −3x ≤ 3.The solution of the inequality is .

Mathematics

2 answers:

lions [1.4K]3 years ago

7 0

Answer:

x $\geq$ -1

Step-by-step explanation:

First, we divide each side by -3. Since the number that we are dividing by is negative we have to flip our inequality symbol.

I hope this helps!

ohaa [14]3 years ago

5 0

Answer:4

)

Step-by-step explanation:

See a solution process below:

Explanation:

First, subtract

from each segment of the system of inequalities to isolate the

term while keeping the system balanced:

−

≤

−

≤

−

≤

Now, divide each segment by

−

to solve for

while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators:

−

≥

−

≥

−

≥

−

and

≥

−

Or, in interval notation:

[

−

)

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h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does h hh have a negative

Semenov [28]

Answer:

(C)−3 ≤ x ≤ 1

Step-by-step explanation:

The average rate of change of function h over the interval $a \leq x\leq b$ , is given by this expression:

$\dfrac{h(b)-h(a)}{b-a}$

Given the function $h(x)=x^2-1$ on the interval:− 3 ≤ x ≤ 1

$h(1)=1^2-1=0\\h(-3)=(-3)^2-1=9-1=8$

The average rate of change:

$\dfrac{h(b)-h(a)}{b-a}=\dfrac{0-8}{1-(-3)}=\dfrac{-8}{4}=-2$

Therefore, the function has a negative average rate of change over the interval − 3 ≤ x ≤ 1.

CHECK:

(A)Average rate of change of h(x) over the interval − 3 ≤ x ≤ 5=2

(B)Average rate of change of h(x) over the interval 1 ≤ x ≤ 4=5

(D)Average rate of change of h(x) over the interval − 1 ≤ x ≤ 5=4

5 0

3 years ago

You deposit $300 in a savings account. The account earns 2% simple interest per year.

Sholpan [36]

Answer:

Answer:

a. ----> $10

b. ----> $110

Step-by-step explanation:

principle ( p ) = $100

time ( t ) = 10 years

rate ( r ) = 11%

simple interest = (p × r × t)÷ 100

= ( $100 × 11 × 10 )÷ 100

= 11000 ÷ 100

= $110

interest = simple interest - principle

interest = $110 - $100

= $10

8 0

3 years ago

Find the equation 3x-1=11

g100num [7]

Answer:

x = 4

Step-by-step explanation:

3x - 1 = 11

3x = 1 + 11

3x = 12

x = 12/3

x = 4

Thus, The value of x is 4

-TheUnknownScientist

8 0

3 years ago

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what is the area of a circle with radius of 7cm using 3.14 for pi and round to he nearest tenth plz hurry

Sophie [7]

Answer:153.9 cm

Step-by-step explanation:

The area of a circle is found by pi × radius squared and pi is aprox 3.14 so 3.15×7² = 153.86 then round off to the nearest tenth you get 153.9

5 0

3 years ago

Read 2 more answers

Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w

Shtirlitz [24]

Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so $p = 0.6$

The week has 5 days, so $n = 5$

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

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

$P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102$

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

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

$P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768$

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

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

$P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304$

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

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

$P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456$

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

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

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so $P(X = 5)$ .

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

$P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778$

7.78% probability of spending 12 dollars on coffee over the course of a five day week

8 0

4 years ago