Solve the following equation:
30= |- 4y + 2|
Answers
Suppose \(-4y+2\ge0\). Then by definition of absolute value,
\(|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}\)
On the other hand, suppose \(-4y+2<0\). Then
\(|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}\)
Recall the definition,
\(|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}\)
Related Questions
Using 50 random numbers given below, compute the mean and standard deviation. 0.937776 0.270012 0.243785 0.590701 0.824982 0.131805 0.879337 0.741998 0.254683 0.080259 0.419321 0.928220 0.958430 0.980182 0.263900 0.063119 0.762096 0.485612 0.662900 0.362242 0.724796 0.307736 0.305021 0.417052 0.054337 0.323357 0.069662 0.843387 0.353107 0.074262 0.735596 0.175095 0.390508 0.668932 0.029861 0.205228 0.387740 0.962169 0.646565 0.423914 0.754782 0.156719 0.773113 0.546335 0.323573 0.649740 0.214082 0.382383 0.383982 0.030539 Mean = (to 6 decimals) Standard deviation = (to 6 decimals)
Answers
The mean is 0.477514 (rounded to 6 decimal places).
The standard deviation is 0.288919 (rounded to 6 decimal places).
How to Solve the Problem?To calculate the mean and standard deviation, we will use the following formulas:
Mean = (sum of all values) / (number of values)
Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]
Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:
Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514
Therefore, the mean is 0.477514 (rounded to 6 decimal places).
Now we will calculate the standard deviation:
Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919
Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).
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Sorry but plz forgive me for you feeling like I’m using you guys :(
Question:Find the area of a rectangular prism whit a height of 4yards a length of 2.6 yards and with of 3.5 yards.
Answers
Step-by-step explanation:
67yd² is the answer...........
simplify 5m - m - m +3
Answers
Answer:
Brainliest!Step-by-step explanation:
5m-m-m+3
5m-2m+3
3m+3
Answer: 3m + 3
Explanation: If there's no coefficient in front of the variable, you can give it a coefficient of 1, so the -m can be thought of as -1m.
So our problem can be read as 5m - 1m - 1m + 3.
Now combine like terms.
Since 5m, -1m, and -1m are terms that contain an m, we can combine.
So 5m - 1m - 1m simplifies to 3m.
So our answer is 3m + 3
According to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,060. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $495. Use Appendix B.3. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,575 per year on reading and entertainment
Answers
Answer:
The answer is \(15.00\) %
Step-by-step explanation:
Let's start defining the random variable. We have the following variable :
\(X:\) '' The amount spent per year on reading and entertainment among adults in the 25- to 34- year age group ''
We assume that \(X\) follows the normal distribution. We can write :
\(X\) ~ N ( μ , σ )
Where μ is the mean of the distribution and σ is the standard deviation (both are parameters from the normal distribution). Using the data from the question :
\(X\) ~ \(N(2060;495)\)
In order to answer the question, we first must calculate the probability :
\(P(X>2575)\) (I)
We are going to calculate this probability by making a substitution. If we substract the mean to the variable \(X\) and then divide by the standard deviation, we obtain a new variable \(Z\) which can be modeled as a \(N(0;1)\). This is convenient because the cumulative distribution from \(Z\) is tabulated and can be found on any book or either in Internet.This process is called standardizing the variable :
[ (\(X\)-μ) / σ ] = \(Z\) ~ \(N(0;1)\) ⇒ If we apply this to the equation (I) ⇒
\(P(X>2575)=P(Z>\frac{2575-2060}{495})=P(Z>1.04)\)
Then,
\(P(Z>1.04)=1-P(Z\leq 1.04)\) (II)
Looking in any cumulative distribution table of \(Z\) ⇒ \(P(Z\leq 1.04)=0.85\)
If we replace this value in (II) ⇒
\(P(Z>1.04)=1-P(Z\leq 1.04)=1-0.85=0.15\)
Using percent we obtain \(15.00\) %
The annual rate, r, it takes for 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².
Find the rate necessary for a dollar to triple in 2 years.
Answers
The rate of interest is 73%.
What is the annual rate?
The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.
Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².
A dollar to triple in 2 years.
Thus putting X = 3 in X = (1+r) ²
3 = (1+r) ²
Take square root on both sides:
√3 = 1 + r
Subtract 1 from both sides:
r = √3 - 1
r = 0.73
r = 73%
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Study this table.
x
y
–3
–2
–2
0
0
4
4
12
Which best describes the function represented by the data in the table?
linear with a common ratio of 2
linear with a common first difference of 2
quadratic with a common ratio of 2
quadratic with a common first difference of 2
Answers
Consider a 3 x 3 matrix 0.000 0.000 0.000
A= 3.000 3.000 -3.000
0.000 0.000 0.000 Find three linearly independent eigenvectors 0.000 0.000 0.000 v1, v2, v3 and their eigenvalues λ1, λ2, λ3. In order to be accepted as correct, all entries of the vector Av; λivi must have absolute value smaller than 0.05. Your eigenvalues will only be correct if the corresponding vectors are eigenvectors with these eigenvalues.
v1 = -1 is an eigenvector of A to the eigenvalue λi = 0 1
0
v2 = -1 is an eigenvector of A to the eigenvalue λ2= 0
0
1
v2 = 0 is an eigenvector of A to the eigenvalue λ3= 0
1
0
Answers
As per the matrix, the three linearly independent eigenvectors are 0, 0.05 and 1.
Now let's consider the given matrix A. We are asked to find three linearly independent eigenvectors and their corresponding eigenvalues. Linearly independent eigenvectors are important because they allow us to represent any vector in the space as a linear combination of these eigenvectors.
The first eigenvector v1 is -1, and it corresponds to the eigenvalue λ1 = 0. To check if this is indeed an eigenvector, we multiply it by A and check if the resulting vector is a scalar multiple of v1. In this case, Av1 = 0v1, which means that v1 is indeed an eigenvector with eigenvalue λ1 = 0.
The second eigenvector v2 is also -1, and it corresponds to the eigenvalue λ2 = 0. Again, we multiply it by A and check if the resulting vector is a scalar multiple of v2. Av2 = 0v2, which means that v2 is an eigenvector with eigenvalue λ2 = 0.
The third eigenvector v3 is 0, and it corresponds to the eigenvalue λ3 = 1. We repeat the same process and check if Av3 is a scalar multiple of v3. In this case, Av3 = 0.05v3, which satisfies the given condition of having all entries with absolute value smaller than 0.05. Therefore, v3 is an eigenvector with eigenvalue λ3 = 1.
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The populations of two towns, town A and town B, are being compared. The population of town A is 4 x 10⁴ and the population of B is 2 x 10⁵. How many times greater is the population of town B than town A?
A. 0.2
B. 0.5
C. 2
D. 5
Answers
Type the correct answer in the box.
Fill in the missing term in the equation.
(1 + 2)(2+1) + blank
= 5(2+i)
Answers
(1 + 2)(2 + 1) + blank
= 3(3) + blank
= 9 + blank
Expanding the right side of the equation:
5(2 + i)
= 10 + 5i
Since the left side of the equation (9 + blank) is equal to the right side (10 + 5i), we can deduce that the missing term should be equal to 1i.
Therefore, the missing term in the equation is "1i".
Maria is taking a multiple-choice
exam in which
there are five possible answers for each question.
The instructions indicate that she will be rewarded
2 points for each correct response, that she will lose
half a point for each incorrect response and that no
points will be added or subtracted for answers left
blank.
A. If Maria does not know the correct answer to a
question, is it to her advantage or disadvantage to
guess at an answer?
B. If she can eliminate one of the possible choices, is it
to her advantage or disadvantage to guess at the
answer?
Answers
Since there is no expected value, there is neither a benefit nor a drawback to making an educated prediction.
Expected value (EV), which is based on a random variable's probability distribution, refers to the long-term overall average of that variable.The expected value of a company or even other investment is a crucial factor in investing and is taken into account while performing scenario analysis.To create optimum portfolios, modern portfolio theory combines anticipated value with the standard deviation of an investment's risk.Correct Probability P(Correct) Equals 1/5 = 0.20
P(Wrong) = 4/5 = 0.80.
Expected Value is equal to P(Correct) * Marks given for Correct Questions plus P(Incorrect) * Marks given for Incorrect Questions.
Value Expected Equals 0.20*2 + 0.80* (-0.50)
Value Expected = 0
Since there is no expected value, there is neither a benefit nor a drawback to making an educated prediction.
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Which of the expressions are equivalent to the one below check all that apply
Answers
Answer:
A , B and C
Step-by-step explanation:
evaluate the expressions following the order of operations as set out in PEMDAS
initial expression
note that • indicates multiplication
3 (2 + 6) + 4 × 5 ← evaluate parenthesis
= 3(8) + 20 = 24 + 20 = 44
A
5 × 4 + 3 × (6 + 2) ← evaluate parenthesis
= 5 × 4 + 3 × 8 ← perform multiplication
= 20 + 24 ← perform addition
= 44
B
(6 + 2) × 3 + 4 × 5 ← evaluate parenthesis
= 8 × 3 + 4 × 5 ← perform multiplication
= 24 + 20 ← perform addition
= 44
C
3 × 2 + 3 × 6 + 4 × 5 ← perform multiplications
= 6 + 18 + 20 ← perform addition
= 44
D
3 × 2 + (6 + 4) × 5 ← evaluate parenthesis
= 3 × 2 + 10 × 5 ← perform multiplication
= 6 + 50 ← perform addition
= 56
the expressions equivalent to the initial expression are A , B and C
What is the product of 5 x 2 1/3=
Answers
\(\huge\text{Hey there\bf!}\)
\(\mathtt{5\times2\dfrac{1}{3}}\)
\(\mathtt{= \dfrac{5}{1}\times2\dfrac{1}{3}}\)
\(\mathtt{= \dfrac{5}{1}\times\dfrac{2\times3 + 1}{3}}\)
\(\mathtt{= \dfrac{5}{1}\times\dfrac{6 + 1}{3}}\)
\(\mathtt{= \dfrac{5}{1}\times\dfrac{7}{3}}\)
\(\mathtt{= \dfrac{5\times7}{1\times3}}\)
\(\mathtt{= \dfrac{35}{3}}\)
\(\mathtt{= 11\dfrac{2}{3}}\)
\(\huge\text{Therefore your answer should be: }\)
\(\huge\boxed{\mathtt{11\dfrac{2}{3}}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
what does x+y=mb mean
Answers
Answer: The equation "x + y = mb" represents a linear equation in two variables, x and y. In this equation, m is a constant and b is another constant or a known value. The equation states that the sum of x and y is equal to the product of m and b.
This equation can be used to model a variety of real-world situations where two quantities are related and their sum is equal to a constant value. For example, it could represent the amount of money saved by two people, where x and y are the savings of the two people and mb is the total amount of money saved.
To solve for x and y, we can use either substitution or elimination method, or any other method for solving systems of linear equations. The values of x and y that satisfy the equation "x + y = mb" are called the solutions of the equation.
Step-by-step explanation:
Please help. 8th grade math homework
Answers
Completing the table using the rounded values showing the relative frequencies is as follows:
Column Relative Frequency Table
Men Women Total
January - June 25% 25% 25%
July - December 75% 75% 75%
Total 100% 100% 100%
What is the relative frequency?Relative frequency shows the quotient between the number of events and the total number of possible events occurring.
The quotient of relative frequency is expressed over 100 to show the result in percentage terms.
Frequency Table
Men Women Total
January - June 21 19 40
July - December 62 58 120
Total 83 77 160
Column Relative Frequency Table
Men Women Total
January - June 25% (21/83) 25% (19/77) 25% (40/160 x 100)
July - December 75% (62/83) 75% (58/77) 75% (120/160 x 100)
Total 100% 100% 100% (160/160 x 100)
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Julia leans a 18-foot ladder against a wall so that it forms an angle of 68° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest hundredth of a foot if necessary.
Answers
The length of the wall is approximately 16.7ft high.
To solve this problem, we would use trigonometric ratios.
The sine angle between any two body is the ratio between the opposite and hypotenuse.
Data given;
angle = 68 degreehypotenuse = 18 footopposite = ?Trigonometric Ratio\(sin x = \frac{opposite}{hypotenuse}\\sin 68 = \frac{opposite}{18}\\opposite = 18 sin68\\opposite = 16.68ft\)
From the above calculation, the length of the wall is approximately 16.7ft
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Mr. Martinez has a 16-ounce Starbucks drink. He drinks 10 ounces. What is the percent of ounces Mr. Martinez has left of his drink?
Answers
well, he has left only 6 oz.
now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5\)
Help fast Fast Fast Fast
Answers
Answer:
0,5
Step-by-step explanation:
Missing number 5 or it can be a 0
This is beacause a number that ends with 0 or 5 is divisible by 5. Divisibilitiy rules state that!
Ex: 5 x 5 = 25
5 x 4 = 20
calculate the Area of parallelogram GDEF if the base is 5m and the altitude is 3,2m
Answers
Step-by-step explanation:
the area of a parallelogram is
baseline × height = 5 × 3.2 = 16 m²
7.
(02.01 MC)
Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x axis and Age of Runner on the y axis. The x axis has a scale from 0 to 80 in increments of 10. The y axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6 and 60, 6 is drawn.
Which statement best describes the domain of the function represented in the graph? (1 point)
6 ≤ x ≤ 60, or x is from 6 to 60
6 ≤ x ≤ 20, or x is from 6 to 20
0 ≤ x ≤ 20, or x is from 0 to 20
20 ≤ x ≤ 60, or x is from 20 to 60
HELP
Answers
The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries.
A line segment is sometimes referred to as a section of a path that joins two places.
Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.
The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.
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Answer:
the correct option is D
Step-by-step explanation:
 Hey guys, I would really appreciate if one of you help me with this question
Answers
Answer: 28.25%
Step-by-step explanation:
113/400=0.2825=28.25%
Fill in this table as you work through the lesson.
Answers
The table can be filled with the following words.
1. Represent - to be an example or symbol of something.
2. Apex -the point (vertex) farthest from the base of a pyramid.
3. Height - the vertical distance from the base to the top of a plane figure or three-dimensional figure.
4. Lateral face - any face (side) of a prism or pyramid that is not a base.
5. Pyramid - a solid object whose base is a polygon, sides are straight and the triangles meet at the top.
6. Volume - the measure of the amount of space occupied by a three-dimensional solid object.
What is the meaning of an apex?An apex is the highest point that is measured from a base. For many pointed objects, it is usually easy to get the apex by determining the farthest point.
The height of an object is not to be confused with the apex because the height measures the distance from the base to the top of the object in question.
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help y’all this due at 11: 30 btw the code goes by 0-9
Answers
Answer and Step-by-step explanation:
Answer in picture.
Simply just convert the numbers given to what it says.
#teamtrees #PAW (Plant And Water)
Express the following in exponential notation:
(-13) X (-13).
35 times
Answers
Answer:
\((-13) * (-13) = (-13)^{2}\)
\(35 * 35 = 35^{2}\)
Step-by-step explanation:
Given
\((-13) * (-13)\)
Required
Express as an exponential notation
\((-13) * (-13)\)
Apply the following law of indices
\(x^a * x^b = x^{a+b}\)
This gives:
\((-13) * (-13) = (-13)^{1+1}\)
\((-13) * (-13) = (-13)^{2}\)
The second complete is incomplete; However, I'll assume it is: 35 times 35
\(35 * 35\)
Using the same law applied in (1) above:
\(35 * 35 = 35^{1+1}\)
\(35 * 35 = 35^{2}\)
NO LINKS!! URGENT HELP PLEASE!!!!
Please help me with #1 - 3
For each table, state if the model is linear or exponential and write an equation.
Answers
Answers:
Linear; equation is y = -5x+15Linear; equation is y = -x+4Exponential; equation is y = 80*2^x=====================================================
Explanation:
Problem 1
Each time x goes up by 1, y goes down by 5. This constant rate of change leads to the equation being linear. The slope is m = -5/1 = -5. You can use the slope formula for any two points in the table to confirm this is the correct slope.
The y intercept is b = 15 because we have x = 0 lead to y = 15.
Therefore, we go from y = mx+b to y = -5x+15
-----------------------------------
Problem 2
Each time x goes up by 3, the y coordinate goes down by 3. Therefore, we have another linear equation here. The slope is m = -3/3 = -1.
The y intercept is b = 4 because x = 0 leads to y = 4.
y = mx+b turns into y = -x+4
-----------------------------------
Problem 3
Each time x goes up by 1, y is NOT going up the same amount. The jump from 10 to 20 is +10. The jump from 20 to 40 is +20. And so on.
Therefore, this equation isn't linear. Instead it's exponential. Each y term doubles when x increases by 1, so that's why the b term is b = 2.
The initial term is a = 80 because x = 0 leads to y = 80.
We go from y = a*b^x to y = 80*2^x
-----------------------------------
You can use a tool like Desmos or GeoGebra to visually confirm each of the answers. Both also offer support for function tables.
Answer:
1. y = -5x + 15.
2. y = -x + 4.
3. y = 80(2^(x/3))
Step-by-step explanation:
1.
From the given data, we can see that as x increases by 1, y decreases by a fixed amount of 5. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.
To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).
Using the formula for slope:
m = (change in y) / (change in x)
m = (0 - 30) / (3 - (-3))
m = -5
Using the point-slope form of a linear equation:
y - y1 = m(x - x1)
y - 30 = -5(x - (-3))
y - 30 = -5x - 15
y = -5x + 15
So the equation for this linear relationship is y = -5x + 15.
2.
From the given data, we can see that as x increases by 3, y decreases by a fixed amount of 3. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.
To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).
Using the formula for slope:
m = (change in y) / (change in x)
m = (-5 - 13) / (9 - (-9))
m = -18 / 18
m = -1
Using the point-slope form of a linear equation:
y - y1 = m(x - x1)
y - 13 = -1(x - (-9))
y - 13 = -1(x + 9)
y = -x + 4
So the equation for this linear relationship is y = -x + 4.
3.
From the given data, we can see that as x increases by 1, y doubles. This means that the relationship between x and y is exponential.
To write the equation for an exponential relationship, we can use the general form of an exponential function:
y = ab^x
where a is the initial value, b is the base, and x is the exponent.
To find a and b, we can use the first and fourth data points since they have the smallest and largest values of y, respectively.
When x = -3, y = 10, so we have:
10 = ab^(-3)
When x = 0, y = 80, so we have:
80 = ab^(0)
From the second equation, we can see that a = 80. Substituting this into the first equation, we get:
10 = 80b^(-3)
Simplifying, we get:
b = 2^(1/3)
So the equation for this exponential relationship is:
y = 80(2^(1/3))^x
Simplifying further:
y = 80(2^(x/3))
The graph of g(x) is a transformation of the graph of f(x) = 2².
Enter the equation for g(x) in the box. g(x) =
Answers
3=k
G(x)=2^ˣ-k
Solution
G(x)=2ˣ - 3
which of the following is a good representation of what a typical worker in a particular group might make?
-salary representation
-income estimation
-median salary
-Income potential
Answers
plz answer!!!! Ill give brainly to first RIGHT person!!!!!
Answers
Answer:
D
Step-by-step explanation:
If it was 2/4, percent is 50% greater than 0, but less than 100
2/4 decimal 0.5 between 0 and 1
How many variables are in 10 - 3x + 4y - z?
Answers
Answer: 10
Step-by-step explanation:
Solve T=M(3+FG) for G.
G=?
Answers
My answer was wrong, delete this answer or disregard
The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Answers
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).