The population would be the name that is used to refer to the segmentation variables
What is population in research?
In research, population refers to the entire group of individuals or objects that share a common characteristic and are of interest to the researcher. The population is the group to which the researcher wishes to generalize their findings. For example, if a researcher is studying the effects of a new medication on blood pressure in adults, the population would be all adult individuals who have high blood pressure.
It is important to define the population accurately in research because the results of the study can only be generalized to the population being studied. If the population is not defined accurately, the results of the study may not be applicable or generalizable to other groups or populations.
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If 30% of all commuters ride to work in carpools, find the probability that if eight workers are selected, three will ride in carpools.
The probability that out of 8 workers, 3 will ride in carpools is 0.254.
What is probability?
The mathematical concept of probability is used to determine the likelihood of an event. It is solely useful for calculating the probability that an event will occur. From 0 to 1, where 0 represents impossibility and 1 represents a particular occurrence.
We are given that 30% of all commuters ride to work in carpools.
Now, if eight workers are selected, then the probability that three will ride in carpools is determined by using the following
P (X = 3) = [tex]n C_{x} p^{x} (1-p)^{(n-x)}[/tex]
We have n = 8, x = 3 and p = 0.3
So, using the formula, we get
⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (1-0.3)^{(8-3)}[/tex]
⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (0.7)^{(5)}[/tex]
⇒P (X = 3) = 56 * [tex](0.3)^{3} (0.7)^{(5)}[/tex]
⇒P (X = 3) = 56 * 0.027 * 0.16807
⇒P (X = 3) = 0.254
Hence, the probability that out of 8 workers, 3 will ride in carpools is 0.254.
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What is different about the Statue of Liberty
compared to other outdoor statues?
A its in a park
B its on a pedestal
C it is made of copper
D It is much bigger.
The difference between the Statue of Liberty compared to other outdoor statues is that it is made of copper which is option C.
Statue of liberty explained.
The Statue of Liberty is a colossal neoclassical sculpture located on Liberty Island in New York Harbor in the United States. It was a gift from the people of France to the people of the United States, dedicated on October 28, 1886, and has since become one of the most recognizable symbols of the United States and its ideals of freedom and democracy.
The statue was designed by French sculptor Frédéric-Auguste Bartholdi, with the help of engineer Gustave Eiffel. The statue depicts a female figure dressed in a flowing robe and holding a torch in one hand and a tablet in the other, upon which is inscribed the date of the American Declaration of Independence (July 4, 1776).
The Statue of Liberty is unique among outdoor statues in that it is made of copper sheets that have oxidized over time to form a green patina. This patina has become an iconic symbol of the statue and is a result of the natural process of copper corrosion. The statue was originally a shiny brown color, but the oxidation of the copper has gradually changed its appearance over time.
Therefore, while the Statue of Liberty is also located in a park and on a pedestal, and it is larger than many outdoor statues, these characteristics are not unique to the statue and can be found in other outdoor statues as well.
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Jorge Holland is having a new furnace installed. The furnace costs $3,500.00. The bank requires a down payment of 20 percent and 36 monthly payments of $85.18 each. What is the APR on his loan?
Answer:
Down payment = $3,500 x 0.20 = $700.00So the amount of the loan is:Loan amount = $3,500.00 - $700.00 = $2,800.00Now we can use the formula for the present value of an annuity to find the APR:PV = PMT x [(1 - (1 + r)^-n) / r]where PV is the present value (in this case, $2,800.00), PMT is the monthly payment ($85.18), r is the monthly interest rate, and n is the number of months (36).Solving for r, we get:r = 0.01301 or 1.301%Since the monthly interest rate is 1.301%, the APR is:APR = 12 x 1.301% = 15.61%Therefore, the APR on Jorge Holland's loan is 15.61%.
11. Which fraction has a value that's equal to ½?
O A. 568
O B. 15
O C. 4964
O D. 21/24
Answer: d is the answer
Step-by-step explanation: because if you do your math correctly it comes out to be 21/24
Solve the integral equation using the generalized power rule
Answer:
a = 4x with a small 3 at the top ( x with a small 4 at the top + 3x ) with a small 30 + 3
b = B = 6x with a small 17 at the top + 192x with a small 15 at the top + 2520x with a small 13 at the top + 17280x with a small 11 at the top + 64800x with a small 9 at the top + 124416x with a small 7 at the top + 93312 with a small 5 at the top
sorry but I don't know c
Step-by-step explanation:
Question 2: Stony opened a bank account with a particular bank! at the beginning of 2015. The bank pays 8% simple interent on a yearly basis. If Stony's initial is $1575, how much money would be in Stony's account by september of 2020.
There would be $2203.50 in Stony's account by September 2020 using simple interest formula.
As the bank charges an annual 8% simple interest, we may apply the following formula:
Simple interest is calculated as follows: Principle is the initial investment, Rate is the annual interest rate, and Time is the duration in years.
Here, the principal (P) is $1575, the interest rate (r) is 8%, and the time (t) is 5 since we need to know how much money Stony will have in his account by September 2020, which is five years from now.
We may calculate Stony's interest earnings over a five-year period using the simple interest formula:
Interest is calculated as follows: $1575 x 0.08 x 5 = $628.50
Stony's account will therefore have the following balance by September 2020: Total Amount = Principal + Interest = $1575 + $628.50 = $2203.50
Therefore by September 2020, Stony would have $2203.50 in his account.
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refers to the standard normal distribution find a z value such that the probability of obtaininig a large z value of 0.20?
Therefore , the solution of the given problem of probability comes out to be the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.
What is probability exactly?The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.
Here,
The z-value for a chance of 0.20 in the right tail of the distribution can be found using a calculator or a standard normal distribution table.
The probability number in the right tail that is
=> closest to 0.20 using a standard normal distribution table is 0.1995.
This probability's equivalent z-value is roughly 0.84.
As an alternative, we can calculate the z-value using a computer. With a chance of 0.20, a mean of 0, and a standard deviation of 1, and the inverse normal function—also known as the normal quantile function—we obtain:
=> Z=invNorm(0.20) 0.84
As a result, the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.
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Which solid figure could be formed from the net shown?
(A) cube
(B) triangular prism
(C) rectangular pyramid
(D) square pyramid
_______________________________
(reporting wrong/spam answers)
(giving brainliest to correct answers)
_______________________________
A) Cube
the two squares will form the top and one side.
Each square right, top and bottom of the square will form the sides
new food is designed to add weight to mature beef cattle. The weight in pounds is given by
W = 8xy(20 − x − 2y),
where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?
x=
y=
What is max weight?
The maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.
Describe Derivatives?In calculus, the derivative is a fundamental concept that measures the rate of change of a function with respect to its input variable. The derivative of a function at a particular point gives the instantaneous rate of change of the function at that point.
The derivative of a function f(x) with respect to its input variable x is denoted by f'(x) or df/dx. It is defined as the limit of the difference quotient as the change in x approaches zero:
f'(x) = lim (h → 0) [(f(x+h) - f(x)) / h]
Intuitively, the derivative of a function at a particular point gives the slope of the tangent line to the graph of the function at that point. This slope can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant at that point.
To find the maximum weight, we need to find the critical points of the function.
First, we find the partial derivatives of the weight function with respect to x and y:
∂W/∂x = 8y(20 - 2x - 2y)
∂W/∂y = 8x(20 - x - 4y)
Setting these partial derivatives equal to zero, we get:
8y(20 - 2x - 2y) = 0
8x(20 - x - 4y) = 0
Solving for x and y, we get two critical points:
x = 0, y = 0
x = 10, y = 5
To determine which of these critical points correspond to a maximum, we use the second partial derivative test.
The second partial derivatives of W with respect to x and y are:
∂²W/∂x² = -32y
∂²W/∂y² = -32x
At the critical point (0,0), both second partial derivatives are negative, which means that it is a maximum.
At the critical point (10,5), both second partial derivatives are positive, which means that it is a minimum.
Therefore, the maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.
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Please help!! No one answered my last question
Answer:
3 final songs
Step-by-step explanation:
Answer: There will be 3 songs on the final CD.
Step-by-step explanation: The band expects to put 12 songs on their next CD. They write and record 25% more songs than they expect, which means they wrote and recorded 12 + (0.25 x 12) = 15 songs. During the editing process, 80% of the songs are removed. 80% of 15 is (0.80 x 15) = 12 songs. Subtracting the removed songs from the recorded songs, we get 15 - 12 = 3 songs that will be on the final CD. Therefore, there will be 3 songs on the final CD.
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Screenshot 2023-03-06 9.
57.19 AM.pn
The relationship between the diameter of a circle and it's circumference is presented in this problem.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
[tex]C = 2\pi r[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:
r = 0.5 x 35
r = 17.5 in.
Then the circumference of the circle is given as follows:
C = 2 x pi x 17.5
C = 109.9 in.
Missing InformationThe problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.
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If ABCD is a rectangle, AD=9, AC=22
If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, the missing measures are m<ADC = 90°, m<BAC = 24°, m<CDB = 240°, and m<AEB = 132°.
What is the Pythagorean theorem?The Pythagorean theorem is a fundamental theorem in geometry that says that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
That is to say mathematically,
[tex]a^{2} + b^{2} = c^{2}[/tex]
where a and b are the lengths of the two sides of the triangle (the sides adjacent to the right angle), and c is the length of the hypotenuse.
Thus, substituting our values for this formula,
[tex]x^{2} +9^{2} =22[/tex]
[tex]x^{2} +81= 484[/tex]
[tex]x^{2} = 484-81[/tex]
[tex]x^{2} =403[/tex]
[tex]x=20.1[/tex] = AB
Thus,
BC = 9
AB = 20.1
BD= 22
EC = 11
m<ADC = 90°
m<BAC = 24° (90-66)
m<CDB = 240°
m<AEB = 132° (180-24-24)
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You asked an incomplete question. The complete question reads;
If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, find each missing measure. I also attached an image of the question.
PWSB has a deal where they give you $100.00 to start a savings account. In addition, you decide toput money in the bank for 5 weeks and finish with $50.00.
a. Assuming you save the same amount every week, write an equation where y is the total
money in the savings account and x represents the number of weeksyou saved money.
b. What do the slope and y-intercept represent in the context of the problem?
Someone please help me with this it is a linear equation I think and the formula is y=Mx+b
y = $100.00 - $10.00x is the equation for the total amount of money in the savings account after x weeks.
The y-intercept represents the initial deposit of $100.00 and the slope is -10
How to find the expressiona. Let's call the amount of money saved each week "s" and
let's call the total amount of money in the savings account after "x" weeks "y".
Since the amount saved each week is the same, we can express the total amount of money in the savings account as:
y = $100.00 + sx
We know that at the end of the 5th week, the total amount in the savings account is $50.00. So we can set up the following equation:
$50.00 = $100.00 + 5s
solving for s:
$50.00 - $100.00 = 5s
-$50.00 = 5s
-10 = s
So the equation for the total amount of money in the savings account after x weeks is:
y = $100.00 - $10.00x
b. In the context of this problem, the slope represents the amount of money that is saved each week.
In this case, the slope is -10, meaning that $10.00 is saved each week. The y-intercept represents the initial deposit of $100.00.
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Find x correct to 2 decimal places.
Answer:
216.49
Step-by-step explanation:
you have two right triangles, for the left one
[tex]tan(64)=\frac{113}{a}[/tex]
[tex]a=\frac{113}{tan(64)}[/tex]
for the one on the right
[tex]tan(35)=\frac{113}{b}[/tex]
[tex]b=\frac{113}{tan(35)}[/tex]
The total value of X is the sum
[tex]\frac{113}{tan(35)} +\frac{113}{tan(64)}=216.4945073[/tex]
so 216.4945073
What is
2+3(3x9)
Someone pls explain this to me
Answer:
83
Step-by-step explanation:
The expression follows the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, in that order.
First, simplify what is inside the parentheses: 3 x 9 = 27
Next, multiply 3 by 27: 3 x 27 = 81
Finally, add 2 to 81: 2 + 81 = 83
Therefore, the expression 2+3(3x9) equals 83.
The result of this expression is 83
Basic rules for expressionsTo solve them we have to start from the inside to out, that is, parentheses, brackets...
And proceed to signal resolution:
[tex]\begin{array}{l}\sf 2+3\tiny\text{$\times$}(3\times9)\\\sf 2+3\tiny\text{$\times$}(27)\\\sf 2+81\\\bf 83\end{array}[/tex]
We get the result 83
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Suppose that the dollar value (t) of a certain house that is ‹ years old is given by the following exponential function.
v(t) =427,500(1.08)^t
Can someone help with this?!
In AJKL, JK II MN. Given that MJ = 10, NK=25, and LN = 20, find LM.
M
Z
K
=0
LM=
Answer:
Please mark as brainliest
Suppose a = 5 and A = 75 degrees.
Find:
The side lengths of given triangle is;
a=5 units
b=18.72 units
c=18.99 units
What is triangle?A triangle is a closed, two-dimensional figure with three straight sides and three angles. It is one of the basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles, including equilateral triangles (where all three sides are of equal length and all three angles are 60 degrees), isosceles triangles (where two sides are of equal length), and scalene triangles (where all three sides and angles are different). Triangles are used in many different areas of mathematics and science, including trigonometry, geometry, and physics.
Here,
We can use the trigonometric ratios of sine, cosine, and tangent to find the values of b and c. First, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle C:
C = 180 - A - B = 180 - 75 - 90 = 15 degrees
Next, we can use the definition of the sine ratio:
sin(A) = opposite/hypotenuse
to find c:
sin(75) = 5/c
c = 5/sin(75) ≈ 18.99
Finally, we can use the Pythagorean theorem:
a² + b² = c²
to find b:
b² = c² - a²
= (18.99)² - 5²
≈ 350.66
b ≈ √350.66 ≈ 18.72
Therefore, a ≈ 5, b ≈ 18.72, and c ≈ 18.99.
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write a linear equation based on the given information.
through: (5,-1) and (2,2)
Answer:
y = (-1/3)x + 2/3
Step-by-step explanation:
We can use the slope-intercept form of a linear equation to find the equation of the line passing through the points (5, -1) and (2, 2). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points, we have:
slope = (2 - (-1)) / (2 - 5) = -1/3
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We can use the point-slope form of a linear equation to find the y-intercept.
Using the point (5, -1), we have:
-1 = (-1/3)(5) + b
Solving for b, we get:
b = -1 + 5/3 = 2/3
Therefore, the equation of the line passing through the points (5, -1) and (2, 2) is:
y = (-1/3)x + 2/3
The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8 $220
82.8 $280
Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth.
A) ŷ = 3.8x − 109.2
B) ŷ = −3.8xx − 109.2
C) ŷ = 6.5x − 279.1
D) ŷ = −6.5x − 279.1
The linear regression equation is defined as follows:
C. ŷ = 6.5x − 279.1
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given on the table as follows:
(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).
Inserting these points into a calculator, the line of best fit is given as follows:
ŷ = 6.5x − 279.1
Meaning that the correct statement is given by option C.
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After working through the suggested questions,Zanele realises that the questionnaire is not suitable.List two reasons why you that the given questionnaire is Not suitable
Below are some general reasons why a questionnaire might not be suitable:
Poorly constructed questionsLaslty Inadequate samplingWhat is the questionnaire about?Poorly constructed questions: If the questions in the questionnaire are not clear, ambiguous, leading, or biased, then the responses obtained may not be accurate or reliable. Poorly constructed questions may also lead to confusion, misunderstandings, and errors.
Lastly Inadequate sampling: If the sampling technique used to select respondents is not representative of the target population, then the results obtained may not be generalizable or applicable to the larger population. The sample size and composition may also affect the validity and reliability of the results.
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Help with math problems
Answer:
I think
Step-by-step explanation:
How many ways is there to answer 20-question multiple choice test if there are 5 choices for each question?
Answer:
95,367,431,640,625 (or approximately 9.5 x 10^13)
Step-by-step explanation:
If there are 5 choices for each question in a 20-question multiple-choice test, then there are 5 possible answers for each question. To find the total number of ways to answer the test, we need to multiply the number of choices for each question together.
Therefore, the total number of ways to answer the 20-question multiple-choice test is:
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
which is equal to 95,367,431,640,625 (or approximately 9.5 x 10^13) ways to answer the test.
can someone hel-p me
I NEED HELP ASAP
An athlete dives from the 3-meter springboard her height y, and horizontal distance x, can be approximated by the function y=-1.2x^2+3.12x +3. both the height and distance are in meters.
A:
how far has she traveled horizontally when she reaches her maximum?
B:
what is her maximum height, round to the nearest tenth of a meter
Part A: distance travelled by athlete when she reaches her maximum is 1.3 m.
Part B: her maximum height: 5 m.
Explain about the quadratic equation?In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where such a, b, and c are all numbers which can't be zero. All of these are examples of quadratic equations:Th equation is-
y = -1.2x² + 3.12x +3.
horizontal distance - x
Part A: distance travelled by athlete when she reaches her maximum:
Comparing given equation with standard form of quadratic equation:
x = -b/a
x = -3.12/2(-1.2) = 1.3
Thus, distance travelled by athlete when she traveled horizontally and reaches her maximum of 1.3 m.
Part B: her maximum height:
y = -1.2x² + 3.12x +3.
Put x = 1.3
y = -1.2(1.3)² + 3.12(1.3) +3.
On solving:
y = 5.028
y = 5 m
Thus, her maximum height, round to the nearest tenth of a meter is 5 m.
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22. A small coffee company claims to include 11 ounces of coffee in every bag of ground coffee it produces. Out of a random sample of 250 bags, 50 of the bags contain only 10.9 ounces. Which inferences from the results of the random sample are reasonable? Choose all that are correct.
A. It can be inferred that 5% of the bags from a second random sample will contain more than 11 ounces.
B. It is likely that a second random sample of bags will show a much lower percentage of bags with only 10.9 ounces.
C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
D. It is likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
E. It is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
The inferences from the results of the random sample that are reasonable is: C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
Which inferences from the results of the random sample are reasonable?From the sample of 250 bags, we know that 50 of them contain only 10.9 ounces of coffee. Let's calculate the percentage of bags in the sample that contain less than 11 ounces:
50/250 = 0.2 = 20%
Now let's consider each inference:
A. It cannot be inferred that 5% of the bags from a second random sample will contain more than 11 ounces. The sample only provides information about the bags in the sample, not the entire population.
B. It is possible that a second random sample of bags will show a lower percentage of bags with only 10.9 ounces, but it cannot be concluded with certainty based on the given information.
C. It is reasonable to estimate that the percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%. This is because out of a sample of 250 bags, 50 bags contained 10.9 ounces, which is 20% of the sample.
D. It is not necessarily likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.
E. It is not necessarily unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.
Therefore, the correct inferences from the given information are C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
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3.1. 1 Three friends Anna, Manna and Hanna are doing the decorations for matric farewell dance. Anna put up two - fifth of the decoration, Manna put up one-fourth and Hanna put up three-tenth of the decoration. Is this job complete at this stage? If not, what fractional amount of job is still left to do? Show all necessary calculations to prove your answer. [13]
Answer:
Step-by-step explanation:
To determine if the job is complete, we need to add up the fractions of the decoration that each person put up:
Anna: 2/5
Manna: 1/4
Hanna: 3/10
Now we can find the total fraction of the decoration that they put up by adding these fractions:
2/5 + 1/4 + 3/10 = 16/40 + 10/40 + 12/40 = 38/40
So they have completed 38/40 of the decoration. To find the fraction of the job that is still left to do, we can subtract this from 1:
1 - 38/40 = 2/40
Therefore, there is still 2/40 of the decoration left to do, or 1/20 of the total job.
I need help with this please
Answer:
Ricky is taller by 11 inches ( a)
Step-by-step explanation:
1 foot = 12 inches
5 feet= 60 inches
Ticky is 68 inches
Ricky is 79 inches
ricky-Ticky= 79- 68= 11 inchesss!
The elevation at ground level is O feet. An elevator starts 90 feet below
ground level. After traveling 15 seconds, the elevator is 20 feet below
ground level. Which statement describes the elevator's rate of change in
elevation during this 15 second interval?
Answer: there you go :)
Step-by-step explanation:
Its D, 90-20=70 ft traveled downwards
15. Maggie said that she could add 8 to both sides of the equation would still be equal. Do you agree? Explain
Answer:
It depends on the equation in question. If Maggie is referring to an equation in the form of x = y, then adding 8 to both sides would still result in the same value of x and y being equal. For example, if the equation is 2x - 5 = 7, then adding 8 to both sides would result in 2x - 5 + 8 = 7 + 8, which simplifies to 2x + 3 = 15. In this case, adding 8 to both sides would not maintain equality.
However, if the equation is in the form of an inequality such as x < y or x > y, adding the same value to both sides may not maintain the inequality. For example, if the inequality is 2x - 5 < 7, then adding 8 to both sides would result in 2x - 5 + 8 < 7 + 8, which simplifies to 2x + 3 < 15. In this case, adding 8 to both sides would still maintain the inequality.
Therefore, whether or not adding 8 to both sides of an equation would still result in equality depends on the equation in question and the mathematical operation being performed.
Yes. Yes I do.
If you think of an equation as a balance, where both sides have equal weight, then adding the same amount to both sides or taking away the same amount from both sides will still maintain that balanced weight.
We call this the addition property of equality:
If a = b, then a+c = b+c for any expression c.