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3 years ago

Simplify 5.47+2.758+12.3

Mathematics

1 answer:

-Dominant- [34]3 years ago

8 0

Answer:

20.528

Step-by-step explanation:

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Help please explain as simple as possible

Virty [35]

Short answer: (-8)^2 + 8 x -8 = 0

Use PEMDAS

"Evaluate the expression" just means solve until you can't simplify anymore. You must solve it in a certain order according to PEMDAS: Parentheses, Exponents, Multiply, Divide, Add, Subtract.

What does the beginning of the expression look like? It is $(-8)^{2}$ .

According to PEMDAS, you must solve what is in the parentheses *first*. But, since there is only a number (-8), there is nothing to solve for and you can move on to exponents.

The squared symbol, the little 2, means you have to square what is *inside* the parentheses. $(-8)^{2}$ = 64, because -8 times itself is 64.

Next comes multiplication. Remember, we are not working from left to right. We must multiply the values on the far right before we do any adding, because multiplication comes *before* addition.

(64) + (8 times -8)

(64) + (-64)

Finally, we can add. In this case, because we are adding a negative number, we are really subtracting. 64 + -64 equals 0.

8 0

3 years ago

Easy :) solve any ones you want

liberstina [14]

Answer:

3. D, Additive Property of Equality

4. x < 2

5. attached graph

Step-by-step explanation:

3. Additive Property of Equality: this means that you can add/subtract a number from one side, as long as you can do it to the other. as shown in steps 4 and 5, this is what they have done in order to get x by itself.

4. to solve -3x + 8 > 2x - 2, we want to get x by itself on one side. we can treat the inequality sign as an equal sign to solve

-3x + 8 > 2x - 2 < -- subtract 8 from both sides to get -3x alone

-8 -8

-3x > 2x - 10 < -- subtract 2x from both sides to get 2x with the -3x

-2x -2x

-5x > -10 <-- divide both sides by -5 to get x alone

when we divide by a negative number in an inequality, we flip the sign. so > becomes < once we divide by -5. this is important to ensure we get the right answer

-5x/-5 = x

-10/-5 = 2

x < 2

this inequality means that any value for x has to be less than 2 in order for the inequality to be true

on a number line it would look like the following:

<---------------2) - - - - - - - - >

the numbers to the left of 2 would be shaded in, as those are less than 2. the number 2 would have either an open circle on top of it or a parentheses facing to the left, either one works.

5. to graph y < 2/5x - 4, we want to get this equation into slope intercept form which is y = mx + b, where mx is the slope and b is the y-intercept

again, treat the inequality symbol as an = sign in this case and solve to get y by itself

y = 2/5x - 4 <--- this is already in slope intercept form, so we do not need to solve for y in this case.

to graph this, we would need to start at the y-intercept which is (0, -4). i will attach a graph to make this a bit easier visually

from there, you would use the slope to find another point on the graph. the slope is rise/run which also means y/x.

so you would need to go 2 units up from (0, -4), and 5 units right from where you landed

since this is an inequality, we will need to find any answers on the graph that satisfy the inequality by shading in the region where those points are solutions.

to do this we need to find a test point. a test point tells us whether or not that point and anything in its section is included in the solution. if the inequality is true with the test point, that answer and anything in that section is included in the answer. if its false, that point and everything in that section is not included.

you can always use the origin (0,0) if its not graphed on the line. in this case, we will use the origin as a test point. so plug in the test point into the original inequality

y < 2/5x - 4

0 < 2/5(0) - 4

0 < -4 <-- this is false and (0,0) and anything in its section is not included as a solution, so you would shade below the line as (0,0) was above the line, and anything above the line cannot be used as a solution to the inequality

graph the line connecting the two points using a dotted line as the inequality symbol is <, meaning points on that line are not solutions to the inequality

with the graph i attached, shade in the entire dark blue area. the graph is a bit rough but your graph should look similar to that

4 0

2 years ago

Which expression is equivalent to(2^3)^-5

Nady [450]

Answer:

hope this helps if not im sorry

Step-by-step explanation:

(2^3)^5

=2^(3*5)

= 2^15

3 0

3 years ago

1t = 1000kg.

natka813 [3]

Answer:

i think ur question is wrong

4 0

3 years ago

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

EleoNora [17]

Answer:

a) $P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)$

And we can use the probability mass function and we got:

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

And adding we got:

$P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061$

b) $P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182$

c) $P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

$P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054$

And replacing we got:

$P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886$

d) $E(X) = 20*0.2= 4$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=20, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part a

We want this probability:

$P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)$

And we can use the probability mass function and we got:

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

And adding we got:

$P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061$

Part b

We want this probability:

$P(X=4)$

And using the probability mass function we got:

$P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182$

Part c

We want this probability:

$P(X>3)$

We can use the complement rule and we got:

$P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

$P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054$

And replacing we got:

$P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886$

Part d

The expected value is given by:

$E(X) = np$

And replacing we got:

$E(X) = 20*0.2= 4$

3 0

3 years ago