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3 years ago

What is the solution to this inequality?

Mathematics

2 answers:

Sedbober [7]3 years ago

8 0

Answer:

Option D.

<h3>Why is this the case, though?</h3>

These equations prove it true.

$-4 * 2 - 8 = -16 > -20$

$-4 * 1 - 8 = -12 > -20$

The only reason these two equations are correct, is because on the number line it shows: Any negative number further to the right than the last negative number is greater than that number.

Black dot is the main point, Blue dot is solution 1, and Red dot is solution 2

Snezhnost [94]3 years ago

5 0

Answer:

$\boxed{\sf{D. \quad x < 3}}$

Step-by-step explanation:

It is necessary to isolate the term of x from one side of an inequality to find its solution.

First, add by 8 from both sides.

$\sf{-4x-8+8 > -20+8}$

Solve.

-20+8=-12

Rewrite the problem down.

$\sf{-4x > -12}$

Multiply by -1 from both sides.

(-4x)(-1)<(-12)(-1)

Solve.

Multiply the numbers from left to right.

(-12)(-1)=12

4x<12

Divide by 4 from both sides.

4x/4<12/4

Solve.

Divide the numbers from left to right.

12/4=3

x<3

Therefore, the correct answer is D. x<3 (last option).

I hope this helps you! Let me know if my answer is wrong or not.

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4 years ago

Kelsie works at a bicycle shop as a salesperson. She records the number of bicycles she sells daily. Here is the probability dis

Andru [333]

Answer:

a) $E(B)= \sum_{i=1}^n B_i P(B_i) =0*0.3+1*0.5+2*0.15+ 3*0.05=0.95$

b) $E(T)= \sum_{i=1}^n T_i P(T_i) =10*0.3+20*0.5+30*0.15+ 40*0.05=19.5$

c) $E(B^2)= \sum_{i=1}^n B^2_i P(B_i) =0^2 *0.3+1^2 *0.5+2^2 *0.15+ 3^2 *0.05=1.55$

And the variance is given by:

$Var(B) = E(B^2) -[E(B)]^2 = 1.55- [0.95]^2 =0.6475$

And the deviation would be $Sd(B) = \sqrt{0.6475}=0.8047$

$E(T^2)= \sum_{i=1}^n T^2_i P(T_i) =10^2 *0.3+20^2 *0.5+30^2 *0.15+ 40^2 *0.05=445$

And the variance is given by:

$Var(T) = E(T^2) -[E(T)]^2 = 445- [19.5]^2 =64.75$

And the deviation would be $Sd(T) = \sqrt{64.75}=8.047$

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

Solution to the problem

Part a

For this case we have the following info:

B 0 1 2 3

____________________________________

T 10 20 30 40

____________________________________

P 0.3 0.5 0.15 0.05

____________________________________

And we can calculate the expected value for the random variable B like this:

$E(B)= \sum_{i=1}^n B_i P(B_i) =0*0.3+1*0.5+2*0.15+ 3*0.05=0.95$

Part b

Similar to part a we can find the expected value for the random variable T like this:

$E(T)= \sum_{i=1}^n T_i P(T_i) =10*0.3+20*0.5+30*0.15+ 40*0.05=19.5$

Part c

In order to find the variance for B we need to calculate the second moment given by:

$E(B^2)= \sum_{i=1}^n B^2_i P(B_i) =0^2 *0.3+1^2 *0.5+2^2 *0.15+ 3^2 *0.05=1.55$

And the variance is given by:

$Var(B) = E(B^2) -[E(B)]^2 = 1.55- [0.95]^2 =0.6475$

And the deviation would be $Sd(B) = \sqrt{0.6475}=0.8047$

Similar for the random variable T we have:

$E(T^2)= \sum_{i=1}^n T^2_i P(T_i) =10^2 *0.3+20^2 *0.5+30^2 *0.15+ 40^2 *0.05=445$

And the variance is given by:

$Var(T) = E(T^2) -[E(T)]^2 = 445- [19.5]^2 =64.75$

And the deviation would be $Sd(B) = \sqrt{64.75}=8.047$

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4 years ago

On commencing employment a man is paid a salary of $7200 per annum and receives annual increments of $350. Determine his salary

Marina CMI [18]

Answer:

Step-by-step explanation:

From the question, we can form an equation like: S = 7200 + 350X

where S is the salary and X is year.

1. His salary in the 9th year, means X=9, so we substitute 9 into the equation to find S = 7200 +350 (9) = 10350

2. The total he will have in the first 12years, we have:

Sum of first n terms of an AP: S =(n/2)[2a + (n- 1)d] where a is the value of the 1st term, here a is 7200 and d = 350 the common difference between terms

=> S = (12/2)[2*7200 + (12- 1)350] = 109500

8 0

3 years ago