Answer:
A. |x| < 3
Step-by-step explanation:
The absolute value of a number is the value that a number has beyond its sign. This means that the absolute value is the numerical magnitude of the number regardless of whether its sign is positive or negative. Formally, the absolute value of any real number x, is defined by:
[tex]|x|=\left \{ {{x,\hspace{3}if\hspace{3}x\geq0} \atop {-x,\hspace{3}if\hspace{3}x<0}} \right.[/tex]
In this sense, to satisfy the inequality [tex]|x|<3[/tex], the domain of x must be:
[tex]-3<x<3\\\\or\\\\(-3,3)[/tex]
Because for [tex]x<-3[/tex] or [tex]x>3[/tex] the inequality is absurd. For example if x=-4
[tex]|-4|=4<3[/tex] which is not true.
and for x=4
[tex]|4|=4<3[/tex] which is not true.
On the other hand to satisfy the inequality [tex]|x|>3[/tex], the domain of x must be:
[tex]-3>x>3\\\\or\\\\(-\infty,-3)\cup(3,\infty)[/tex]
Because for [tex]x<3[/tex] the inequality is absurd. For example if [tex]x=2[/tex]
[tex]|2|=2>3[/tex] which is not true.
and for x=-1
[tex]|-1|=1>3[/tex] which is not true.
Therefore the correct statement is:
A. |x| < 3
The coordinate plane below represents a town. Points A through F are farms in the town.Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A.
(3 points)
Nonstandard dice can produce interesting distributions of outcomes. you have two balanced, six-sided dice. one is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. the other die has three faces with 0 spots and three faces with 6 spots. what are the possible values for the total number of spots y on the up-faces when you roll these two dice?
When rolling a standard die and another die with faces having either 0 or 6 spots, the possible total values y range from 1 to 12, excluding the numbers 5 and 6 twice due to the unique nature of the second die.
Explanation:The question asks about the possible values for the total number of spots y on the up-faces when you roll two nonstandard dice: a standard six-sided die with faces having 1, 2, 3, 4, 5, and 6 spots, and another die with three faces having 0 spots and three faces having 6 spots. To find y, we need to consider all the possible outcomes of rolling these two dice and summing the numbers of spots on the up-faces.
If the standard die shows a 1, y can be 1+0=1 or 1+6=7.If it shows a 2, y can be 2+0=2 or 2+6=8.If it shows a 3, y can be 3+0=3 or 3+6=9.If it shows a 4, y can be 4+0=4 or 4+6=10.If it shows a 5, y can be 5+0=5 or 5+6=11.If it shows a 6, y can be 6+0=6 or 6+6=12.Therefore, the possible values for y are 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 11, and 12.
I don't know how to do this
2(6-7x) = -8(x+6)
multiply the numbers inside the parenthesis with the numbers outside of them:
12 -14x = -8x-48
add 12 to each side:
-14x =-8x -36
add 8x to both sides
-6x = -36
divide both sides by-6
x = 6
Both 2 and 5 are common factors of a number. The number is between 101 and 118. What is the number
Enid got a job through an employment agency that charges a fee equal to 40% of the first five weeks’ pay. The job pays $315 per week. How much does Enid have to pay the employment agency?
Find the area of triangle.
-4=g+1
A. g=-4
B. g=4
C. g=-5
D. g=-3
Please help me with this graphing problem
A rectangular rug covers the floor in a living room one of the walls in the same living room is painted blue. Are the rug and the blue wall parallel
A professional baseball team will play 1 game Saturday and 1 game Sunday. A sportswriter estimates the team has a 60% chance of winning on Saturday but only a 35% chance of winning on Sunday. Using the sportswriter's estimates, what is the probability that the team will lose both games?
A) 14%
B) 21%
C) 25%
D) 26%
E) 39%
Final answer:
To find the probability of losing both games, multiply the probabilities of losing each game together. The probability is 26%.
Explanation:
To find the probability that the team will lose both games, we can multiply the probabilities of losing each game together.
The probability of losing on Saturday is 1 - 60%, or 40%. The probability of losing on Sunday is 1 - 35%, or 65%. Multiplying these probabilities gives us 40% × 65% = 26%.
Therefore, the correct answer is (D) 26%
What numbers below belong to the solution set of the inequality... x+16>51
38
35
16
80
55
34
Students reported volunteering at the animal shelter during the last 6 months for 25, 36, 31, and 32 hours. What is the mean absolute deviation for the number of hours students volunteered? Round to the nearest tenth.
Answer: the answer is 3
What is the equation of a horizontal line passing through the point (−3, 8)?
x = −3
y = 8
x = 5
y = −11
The equation of a horizontal line passing through the point (−3, 8) is y= 8
How to determine the equation of a horizontal line passing through the point (−3, 8)
From the question, we have the following parameters that can be used in our computation:
The point (−3, 8)
The equation of a horizontal line is of the form
y = c, where
c is a constant.
Since the line is horizontal, the value of y is constant for all points on the line.
In this case, the line passes through the point (−3,8), so the equation of the horizontal line is y = 8.
When can I apply the use of the cubic function (y= a( x - h ) ^3 + k) in a real life situation?
Did I do number 2 right?
(17+4) + 9 = 17 + (4+9)
Four times a number, x, plus 3 times a number, y, equals 75. Five times x minus 3 times y equals 6. Find the numbers by setting up a system of linear equations and solving the system using the elimination method.
What is 4 pi cubed divided by 3
A dependent variable is a. directly changed by the experimenter. b. manipulated by changes to the independent variable. c. a variable that is kept constant. d. a variable that is used as a control.
Answer:- Option b. is the right answer. A dependent variable is manipulated by changes to the independent variable.
Explanation:-
In mathematical modelling or scientific research a variable is defined as a term that has a quantity that varies. There are two kinds of variables:- 1) dependent variables 2) independent variables.
A independent variable can be change by the experimenter to check the effects on dependent variables which is observed by the him in a scientific experiment.
Thus, A dependent variable is manipulated by changes to the independent variable.
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f*g) (x)?
Answer: The required expression is [tex]3x^3+2x^2+3x+2.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=3x+2\\\\g(x)=x^2+1.[/tex]
We are to find the expression equivalent to [tex](f*g)(x).[/tex]
We know that
for any two functions p(x) and q(x), we have
[tex](p*q)(x)=p(x)\times q(x).[/tex]
Therefore, we get
[tex](f*g)(x)\\\\=f(x)\times g(x)\\\\=(3x+2)(x^2+1)\\\\=x^2(3x+2)+1(3x+2)\\\\=3x^3+2x^2+3x+2.[/tex]
Thus, the required expression is [tex]3x^3+2x^2+3x+2.[/tex]
Help please ! It’s practical math
Rhinestone Cowboy Dreadlock Holiday MacArthur Park Total Republican B 33 C 90 Democrat A 24 34 E Total 61 D 53 171 Which of the following can be determined from the table above? A. 2004-06-03-06-00_files/i0290000.jpg B. 2004-06-03-06-00_files/i0290001.jpg C. 2004-06-03-06-00_files/i0290002.jpg D. 2004-06-03-06-00_files/i0290003.jpg
B) On e2020 at least
Hope I helped!
The values that can be determined from the table are:
A = 23, B = 38, C = 19, D = 57 and E = 81
What are equations?Equations are expressions that have equal values, and they are represented by the "=" sign
How to determine the values of A to EThe table entries are given as:
Rhinestone Cowboy Dreadlock Holiday MacArthur Park Total
Republican B 33 C 90
Democrat A 24 34 E
Total 61 D 53 171
From the table, we have the following equations
[tex]B + 33 + C = 90[/tex]
[tex]A + 24 + 34 = E[/tex]
[tex]61 + D + 53 = 171[/tex]
The above equations become:
[tex]B + 33 + C = 90[/tex]
[tex]B + C = 57[/tex]
[tex]A + 24 + 34 = E[/tex]
[tex]A + 58 = E[/tex]
[tex]61 + D + 53 = 171[/tex]
[tex]D= 57[/tex]
Also from the table, we have the following equations
[tex]B + A = 61[/tex]
[tex]C + 34 = 53[/tex]
[tex]90 + E = 171[/tex]
Solve for C and E in the above equations
[tex]C + 34 = 53[/tex]
[tex]C = 19[/tex]
[tex]90 + E = 171[/tex]
[tex]E = 81[/tex]
Recall that:
[tex]A + 58 = E[/tex]
So, we have:
[tex]A + 58 = 81[/tex]
[tex]A = 23[/tex]
Recall that:
[tex]B + A = 61[/tex]
So, we have:
[tex]B + 23 = 61[/tex]
[tex]B = 38[/tex]
Hence, the values that can be determined from the table are:
A = 23, B = 38, C = 19, D = 57 and E = 81
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Find b given that p(b,2) is equidistant from a(5,4) and b(2,5)
Find two consecutive integers whose sum is 101
the table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012. What must the 2012 profit be (in hundreds of dollars) to break even over the five-year period?
The 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
It is required to find the profit in 2012.
What is break even point?The break-even point is the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. It tells an owner the amount of revenue needed to cover all expenses, including fixed costs.
Given:
The break-even point is the point in which a business makes no gain and no loss.
According to given question we have
Let the 2012 profit be x, then
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
4.25 - 3.3 - 1.4 + x = 0
-0.45 + x = 0
x = 0.45
Therefore, the 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
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P=21+2w the answer is w=p-21/2 I need the work to go along with it
Sammy and David were selling waterbottles to raise money for new football uniforms Sammy sold 5 for every 3 waterbottles David sold together they sold 160 waterbottles how many did each boy sell
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
Solve for a.
multiply both sides by 2 to get
2A = (a+b)*h
divide both sides by h
to get 2A/h = a+b
subtract b from both sides to get a = 2A/h -b
3rd choice is correct
Option C - a = [tex]$\frac{2A-bh}{h}[/tex] is the correct alternative.
We have the formula for a trapezoid that relates the area - A, the two bases - a and b and the height - h as follows -
[tex]$A=\frac{(a+b)}{2} h[/tex]
We have to solve for ' a '.
Solve for x : x ( 1 + 2 + 3 + .... + n) = πOn solving -
x( 1 + 2 + 3 + .... + n) = π
[tex]\frac{xn(n+1)}{2} =\pi[/tex]
[tex]x =\frac{2\pi }{n(n+1)}[/tex]
According to the question, we have -
[tex]$A=\frac{(a+b)}{2} h[/tex]
2A = (a + b)h
2A = ah + bh
2A - bh = ah
a = [tex]$\frac{2A-bh}{h}[/tex]
Hence, Option C is the correct alternative.
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At an annual salary of 55000 per year what is the amount of semi monthly paychecks
Which function below is the inverse of f(x)=x^2-25
f(x) = x^2-25
inverse:
y = x^2-25
x = y^2-25
y = sqrt(5 +25)
Answer is B