Answer:
0.97
Step-by-step explanation:
From the question:
If 58% = 58/100 of the people have been vaccinated, then;
1 - (58/100) = 42% = 42/100 of the people have not been vaccinated.
Now:
Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;
P( > 1 ) = 1 - P(0) -----------(1)
Where;
P(0) = probability that all of the four have not been vaccinated.
P(0) = P(1) x P(2) x P(3) x P(4)
Where;
P(1) = Probability that the first out of the four has not been vaccinated
P(2) = Probability that the second out of the four has not been vaccinated
P(3) = Probability that the third out of the four has not been vaccinated
P(4) = Probability that the fourth out of the four has not been vaccinated
Remember that 42/100 of the population have not been vaccinated. Therefore,
P(1) = 42/100
P(2) = 42/100
P(3) = 42/100
P(4) = 42/100
P(0) = (42/100) x (42/100) x (42/100) x (42/100)
P(0) = (42/100)⁴
P(0) = (0.42)⁴
P(0) = 0.03111696
Therefore, from equation (1);
P( > 1 ) = 1 - 0.03111696
P( > 1 ) = 0.96888304 ≅ 0.97
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.97
The probability will be "0.969".
According to the question,
Population,
P = 58%or,
= 0.58
Number of people,
n = 4In a Binomial distribution,
→ [tex]P(X=x )= n_C_x P^x q^{n-x}[/tex]
where,
→ [tex]q = 1-P[/tex]
[tex]= 0.42[/tex]
∴ X = at least one
hence,
→ [tex]P(x \geq 1) = 1-P(X<1)[/tex]
[tex]= 1-P(x=0)[/tex]
[tex]=1-4_C_0 (0.58)^0 (0.42)^4[/tex]
[tex]= 1-0.03112[/tex]
[tex]= 0.969[/tex]
Thus the answer above is right.
Learn more:
https://brainly.com/question/22160655
For what value of the constant c is the function f continuous on (−[infinity],[infinity]) ? f(x)={cx2+2xifx<3x3−cxifx≥3
Answer:
c = 6.25
Step-by-step explanation:
We are given the following piecewise function:
[tex]\left \{ {{cx^{2} + 2x, x < 3} \atop {3x^{3} - cx, x \geq 3}} \right[/tex]
Continuous function:
A function f(x) is continuous, at a point a, if:
[tex]\lim_{x \to a} f(x)[/tex] exists and [tex]\lim_{x \to a} f(x) = f(a)[/tex]
In this question:
Piece-wise function, so we have to verify if the limit exists.
The function changes at x = 3. So we verify at a = 3.
It will exist if:
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]
To the left:
Less than 3.
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{-}} cx^{2} + 2x = c*(3)^{2} + 2*3 = 9c + 6[/tex]
To the right:
Greater than 3.
[tex]\lim_{x \to 3^{+}} f(x) = \lim_{x \to 3^{+}} 3x^{3} - cx = 3*3^{3} - 3c = 81 - 3c[/tex]
f continuous:
They have to be equal:
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]
[tex]9c + 6 = 81 - 3c[/tex]
[tex]12c = 75[/tex]
[tex]c = \frac{75}{12}[/tex]
[tex]c = 6.25[/tex]
HELP! will give brainlest or whatever its called... Triangle ABC has vertices A(–2, 3), B(0, 3), and C(–1, –1). Find the coordinates of the image after a reflection over the x-axis. A’ B’ C’
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
=======================================================
Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]
Applying this rule to the three given points will mean....
Point A = (-2, 3) becomes A ' = (-2, -3)Point B = (0, 3) becomes B ' = (0, -3)Point C = (-1, -1) becomes C ' = (-1, 1)The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
Answer:
(-2,-3)...(0,-3)...(-1,1)
Step-by-step explanation:
Flora paid her supplier $0.75 a stem for roses to sell at her flower shop. She added an 80% markup. What is the amount of markup?
Answer:
$0.60
Step-by-step explanation:
the question ask us to find the amount of the markup on Flora’s roses. The amount of markup is given by:
markup rate x original price = amount of markup
the markup rate is in decimal form
since the original price was $0.05 and the markup price is 80% = 0.80, we have
0.80 x .075 = 0.60
thus, the amount of the markup on Flora’s roses was $0.60
find the area of the Triangle
6 ft
12 ft
Answer:
area = 36 ft²
Step-by-step explanation:
no figure has been given ..
therefore, area of a triangle = 1/2 * b * h
assume b = 6 ft
assume h = 12 ft
area = 1/2 * 6 * 12
area = 36 ft²
QUESTION 1 (ONLY ANSWER FOR ALL QUESTIONS) a) 2x/3 =8 (what is x=?) b)3x/2 =6 (what is x=?) QUESTION 2 a)x/3 -2 =6 (what is x=?) b )x/5 +1 = 5 (what is x=?) QUESTION 3 a) 5x/2 +1 =11 (what is x=?) b)2x/7 -3 = 2 (what is x=?)
Answer:
1 (a) x = 12
1 (b) x = 4
2 (a) x = 24
2 (b) x = 20
3 (a) x = 4
3 (b) x = 17.5
Step-by-step explanation:
1 (a)
2x/3 = 8
2x = 8 × 3
2x = 24
x = 24 ÷ 2
x = 12
1 (b)
3x/2 = 6
3x = 6 × 2
3x = 12
x = 12 ÷ 3
x = 4
2 (a)
x/3 - 2 = 6
x/3 = 6 + 2
x/3 = 8
x = 8 × 3
x = 24
2 (b)
x/5 + 1 = 5
x/5 = 5 - 1
x/5 = 4
x = 4 × 5
x = 20
3 (a)
5x/2 + 1 = 11
5x/2 = 11 - 1
5x/2 = 10
5x = 10 × 2
5x = 20
x = 20 ÷ 5
x = 4
3 (b)
2x/7 - 3 = 2
2x/7 = 2 + 3
2x/7 = 5
2x = 5 × 7
2x = 35
x = 35 ÷ 2
x = 17.5
Can someone help me do this? Me and my son are stuck
Hey there! :)
Answer:
Last option. (-1, 0) and (0, 6).
Step-by-step explanation:
Solve this system by setting the two equations equal to each other:
6x + 6 = -x² + 5x + 6
Rearrange the equation:
x² + 6x + 6 - 5x - 6 = 0
Combine like terms:
x² + x = 0
Factor out x:
x(x + 1) = 0
Set each factor equal to 0:
x = 0
x + 1 = 0
x = -1
These are the x values of the solutions. Plug these into an equation to solve for y:
y = 6(0) + 6
y = 6
-------
y = 6(-1) + 6
y = -6 + 6
y = 0
Therefore, the solutions to the equation are (-1, 0) and (0, 6).
I travelled at 60km/hour and took 2hours for a certain journey.How long would it have taken me if I had travelled at 50km/hour?
Answer:
if you would travel 50km/h then the time will be 2.4hours
Step-by-step explanation:
speed=v1=60km/h
time=t1=2h
speed=v2=50km/h
time=t2=?
as we know that
v1×t1=v2×t2
evaluating the expression
(v1×t1)/v2=t2
putting values
[tex]\frac{60km/h*2h}{50km/h}=t2[/tex]
[tex]\frac{120km/h^2}{50km/h}=t2[/tex]
2.4hours=t2
i hope this will help you :)
Identifying Additive Inverses
Try it
Match each polynomial expression to its additive inverse.
-6x²-x-2
6x²-x+2
6x2 + x-2
6x2 - X+2
622 - x + 2
622 + x + 2
1-6x²+x-2
6x²+x-2
Intro
Done
Answer:
he additive inverse of:
a) [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]
b) [tex]6x^2-x+2[/tex] is : [tex]-6x^2+x-2[/tex]
c) [tex]6x^2+x-2[/tex] is : [tex]-6x^2-x+2[/tex]
d) [tex]6x^2+x+2[/tex] is : [tex]-6x^2-x-2[/tex]
Step-by-step explanation:
You need to consider that the additive inverse of a polynomial is that polynomial that consists of the opposite of each term of the polynomial given.
Then, the additive inverse of:
a) [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]
b) [tex]6x^2-x+2[/tex] is : [tex]-6x^2+x-2[/tex]
c) [tex]6x^2+x-2[/tex] is : [tex]-6x^2-x+2[/tex]
d) [tex]6x^2+x+2[/tex] is : [tex]-6x^2-x-2[/tex]
A competition
took place in 1983
takes place every 6 years.
What is the first year after 2045 that it will also take place?
Answer:
2049.
Step-by-step explanation:
2045 - 1983 = 62 years.
So the competition will take place in 1983 + 60 = 2043.
After 2045 the competition takes place in 2049.
Coupons driving visits. A store randomly samples 603 shoppers over the course of a year and nds that 142 of them made their visit because of a coupon they'd received in the mail. Construct a 95% con dence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail.
Answer:
The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 603, \pi = \frac{142}{603} = 0.2355[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694[/tex]
The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)
What is the measure of PSQ?
Answer:
Do you have an image because I'm a bit confused with you just asking the measure of PSQ.
Step-by-step explanation:
Pluto's distance P(t)P(t)P, left parenthesis, t, right parenthesis (in billions of kilometers) from the sun as a function of time ttt (in years) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d. At year t=0t=0t, equals, 0, Pluto is at its average distance from the sun, which is 6.96.96, point, 9 billion kilometers. In 666666 years, it is at its closest point to the sun, which is 4.44.44, point, 4 billion kilometers away. Find P(t)P(t)P, left parenthesis, t, right parenthesis. \textit{t}tstart text, t, end text should be in radians.
Answer: P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65
Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:
y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D
where:
A is amplitude A=|A|
B is related to the period by: T = [tex]\frac{2.\pi}{B}[/tex]
C is the phase shift or horizontal shift: [tex]\frac{C}{B}[/tex]
D is the vertical shift
In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.
Amplitude:
a = [tex]\frac{largest - smallest}{2}[/tex]
At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:
a = [tex]\frac{6.9-4.4}{2}[/tex]
a = 1.25
b
A time period for Pluto is T=66 years:
66 = [tex]\frac{2.\pi}{b}[/tex]
b = [tex]\frac{\pi}{33}[/tex]
Vertical Shift
It can be calculated as:
d = [tex]\frac{largest+smallest}{2}[/tex]
d = [tex]\frac{6.9+4.4}{2}[/tex]
d = 5.65
Knowing a, b and d, substitute in the equivalent positions and find P(t).
P(t) = a.sin(b.t) + d
P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65
The Pluto's distance from the sun as a function of time is
P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65
Answer:
P(t) = 1.25.sin(.t) + 5.65
Step-by-step explanation:
HELP SNOG OR WHOEVER (x+3)(y-19)
Answer:
xy-19x+3y-57
Step-by-step explanation:
Once again, FOIL is the way to go!
First, Outside, Inside, Last
xy-19x+3y-57
Answer:
xy-19x+3y-57
Step-by-step explanation:
(x+3)(y-19)
FOIL
first: xy
outer: -19x
inner 3y
last -57
Add them together
xy-19x+3y-57
Bijan has agreed to run a half-marathon to raise money for charity. Each day before school, Bijan runs a 2.4-mile route around his neighborhood. Then, each day after school, he runs on a lakeside trail. After 4 days, Bijan has run a total of 14.8 miles. Suppose you want to find out the length of the lakeside trail, x. What expression would represent how far Bijan runs everyday? What is the equation that represents his total distance after 4 days?
Answer:
First one is (x+2.4)
Second one is 4(x+2.4)=14.8
Step-by-step explanation:
Answer:
What expression would represent how far Bijan runs everyday?
✔ (x + 2.4)
What is the equation that represents his total distance after 4 days?
✔ 4(x + 2.4) = 14.8
Step-by-step explanation: I TOOK THE TEST
Please answer this correctly
Answer:
1/7
Step-by-step explanation:
There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7
Answer:
1/7
Step-by-step explanation:
The number from the list that is less than 2 is 1.
1 number out of a total of 7 numbers.
= 1/7
I have no idea what this is
Answer:
B. -1.
Step-by-step explanation:
[tex]i^1[/tex] = i
[tex]i^2 = -1[/tex]
[tex]i^3 = -i[/tex]
[tex]i^4 = 1[/tex]
...And it keeps going in a pattern, from i to -1 to -i to 1. And so, we have four values.
34 / 4 = 8 with a remainder of 2. That means that the value of [tex]i^{34}[/tex] is the same thing as [tex]i^2\\[/tex], so it is B. -1.
Hope this helps!
Reflections over the X-Axis
Answer:
Domain : (-∞, ∞)
Range : (-∞, ∞)
Step-by-step explanation:
Parent function (y = [tex]\sqrt[3]{x}[/tex] ) of the given function y = -[tex]\sqrt[3]{x}[/tex] has been shown as the dotted line on the graph.
Solid curve represents the function,
y = [tex]-\sqrt[3]{x}[/tex]
Therefore, Domain of this function will be (-∞, ∞) Or x ∈ set of all real numbers.
And Range of the function will be (-∞, ∞) Or y ∈ set of all real numbers
if X= 2, Y=-2 and Z=3 find the value of 3 X + Y - Z
Answer:
1Given,
X=2
y=-2
z=3
Now,
[tex]3x + y - z \\ = 3 \times 2 + ( - 2) - 3 \\ = 6 + ( - 2) - 3 \\ = 6 - 2 - 3 \\ = 4 - 3 \\ = 1[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
1
Step-by-step explanation:
3X+Y-Z
Where X = 2, Y = -2 amd Z = 3
=> 3(2)+(-2)-(3)
=> 6-2-3
=> 4-3
=> 1
PLEASE HELP!!!! Find the common difference
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
Josh and Lucy share some money in the ratio 3:7. What fraction of the money does Josh receive?
Answer:
3/10ths of the money
Step-by-step explanation:
Add together the two numbers to get the total.
Josh gets 30 percent and Lucy gets 70 percent.
3/10
Answer:
3/10
Step-by-step explanation:
3+7=10
Josh=3
Lucy=7
Question 4
If Madeline wanted to know whether or not her sample results could be generalized to the population, she would use
Answer:
Inferential statistical methods
Step-by-step explanation:
Remember, Madeline had obtained sample results, but she wants to decide whether to apply the sample results to the entire population. To do this, she can use the following:
- estimate her research parameters or
- or perform a hypothesis test which answers her research objectives.
Based on the results she gets, Madeline, can to thus infer from the sample results and apply them to the population.
I need help please!!!!! Will give BRAINLIST !!
Answer:
0.65
Step-by-step explanation:
There are 65 student that do sports as 20+20+25=65. In total there are 100 student and you find this by adding up all the values. Now all you do is divide 65/100 and get 0.65 and that is the probability a random student plays sports.
Of 41 bank customers depositing a check, 22 received some cash back. Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
Answer:
CI: {0.4085; 0.6647}
Step-by-step explanation:
The confidence interval for a proportion (p) is given by:
[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]
Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:
[tex]p=\frac{22}{41}=0.536585[/tex]
Thus the confidence interval is:
[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}
Find the fourth term in the expansion of the binomial
(4x + y)^4
a) 16xy^3
b) 256x^4
c) 64y^4
d) 4xy^3
Answer:
a) 16xy³
Step-by-step explanation:
For a binomial expansion (a + b)ⁿ, the r+1 term is:
nCr aⁿ⁻ʳ bʳ
Here, a = 4x, b = y, and n = 4.
For the fourth term, r = 3.
₄C₃ (4x)⁴⁻³ (y)³
4 (4x) (y)³
16xy³
find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°
Answer:
(190-5a)°
Step-by-step explanation:
Sum of internal angles of a triangle equals to 180°
If the third angle is x, then we have:
(2a-32)°+(3a+22)° +x = 180°(5a- 10)° +x= 180°x= (180+10-5a)°x= (190-5a)°The third angle is: (190-5a)°
The function fx =-x^2-4x+5 is shown on the graph which statement is true
Answer:
Option (3)
Step-by-step explanation:
Given question is incomplete; here is the complete question.
The function f(x) = –x2 – 4x + 5 is shown on the graph. Which statement about the function is true?
The domain of the function is all real numbers less than or equal to −2.
The domain of the function is all real numbers less than or equal to 9.
The range of the function is all real numbers less than or equal to −2.
The range of the function is all real numbers less than or equal to 9
By using a graph tool we get a parabola opening downwards.
Since domain of a function is represented by x-values and range by y-values.
Domain of the given function will be (-∞, ∞)
Range of the function will be (-∞, 9] Or a set of all real numbers less thn equal to 9.
Therefore, Option (3) will be the answer.
A recipe requires 31 cup of milk for each 41 cup of water. How
many cups of water are needed for each cup of milk?
Step-by-step explanation:
here,
31 cup of milk require 41 cup of water.
1 cup of milk require 41/31 cup of water.
so, 41/31 cup of water is required for 1 cup of milk.
hope u get it..
if 7 is added to a number then it becomes at least 15 what is the number?
Step-by-step explanation:
yeah,when 15-7=8
the number is 8
Evaluate. Write your answer as a fraction or whole number without exponents. 6^–4 =
Answer:
The answer is 1/1296
Step-by-step explanation:
6^-4 can be written as 1/6⁴
And
1/6⁴ = 1/1296
Hope this helps you.
Study the steps used to solve the equation. Given: StartFraction c Over 2 EndFraction minus 5 equals 7 Step 1: StartFraction c Over 2 EndFraction minus 5 plus 5 equals 7 plus 5 Step 2: StartFraction c Over 2 EndFraction plus 0 equals 12 Step 3: StartFraction c Over 2 EndFraction equals 12 Step 4: 2 (StartFraction c Over 2 EndFraction) equals 12 (2) Step 5: c equals 24 Choose the property that justifies each step of the solution. Step 1: Step 2: Step 3: Step 4:
Answer:
addition property of equalityintegers are closed to additionidentity elementmultiplication property of equalitycommutative property of multiplication; reals are closed to multiplication; identity elementStep-by-step explanation:
Given:
c/2 -5 = 7
Step 1: c/2 -5 +5 = 7 +5
Step 2: c/2 +0 = 12
Step 3: c/2 = 12
Step 4: 2(c/2) = 12(2)
Step 5: c = 24
Find:
The property that justifies each step of the solution.
Solution:
Step 1: addition property of equality (lets you add the same to both sides)
Step 2: integers are closed to addition
Step 3: identity property of addition (adding 0 changes nothing)
Step 4: multiplication property of equality
Step 5: closure of real numbers to multiplication; identity property of multiplication
_____
It is hard to say what "property" you want to claim when you simplify an arithmetic expression. Above, we have used the property that the sets of integers and real numbers are closed to addition and multiplication. That is, adding or multiplying real numbers gives a real number.
In Step 5, we can rearrange 2(c/2) to c(2/2) using the commutative property of multiplication. 2/2=1, and c×1 = c. The latter is due to the identity element for multiplication: multiplying by 1 changes nothing.
Apart from the arithmetic, the other properties used are properties of equality. Those let you perform any operation on an equation, as long as you do it to both sides of the equation. The operations we have performed in this fashion are adding 5 and multiplying by 2.
Answer:
Step 1 ~ addition property of equality
Step 2 ~ additive inverses
Step 3 ~ additive identity
Step 4 ~ multiplication property of equality
Explanation:
Addition property of equality means that If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. In this problem, they added 5 to both sides to make the equation balanced.
Additive inverses means what you add to a number to get zero. The negative of a number. -5 + 5 = 0.
Additive identity means that the sum of a number and 0 is that number.
Multiplication property of equality states that when you multiply both sides of an equation by the same number, the two sides remain equal. In this problem, they multiplied 2 to both sides to get rid of the denominator in the fraction.