Recall the definition of absolute value:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
Then we have a few cases to consider:
• If [tex]4x-5\ge0[/tex] and [tex]-x+5\ge0[/tex], the equation simplifies to
[tex]4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}[/tex]
• If [tex]4x-5<0[/tex] and [tex]-x+5\ge0[/tex], we get
[tex]-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}[/tex]
• If [tex]4x-5\ge0[/tex] and [tex]-x+5<0[/tex], then
[tex]4x-5 = -(-x+5) \implies 3x=0 \implies x=0[/tex]
but we already have this solution.
• If [tex]4x-5<0[/tex] and [tex]-x+5<0[/tex], then
[tex]-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2[/tex]
which we also already found.
what is the least common factor between 9 8 and 7
Answer:
504
Step-by-step explanation:
Using LCM the common multiple is 504 as shown in the image above.
One third of number is four times eleven. What is half of that number
Answer:
One third of a number is four times eleven. What is the half of that number?
Explanation:
Four times 11 = 11 X 4 = 44
One third (1/3) of the number = 44
The number is = 44 X 3 = 132
Therefore half of the number 132 = 66
Answer:
66
Step-by-step explanation:
11 X 4 = 44
One third (1/3) of the number = 44
The number is = 44 X 3 = 132
Therefore half of the number 132 = 66
Work out the surface area of this solid quarter cylinder. give your answer in terms of pi. r:8cm h:15cm
Answer:
248 pi cm^2
Step-by-step explanation:
The surface area of a cylinder is given by
SA = 2 pi r^2 + pi rh where r is the radius and h is the height
= 2 pi( 8)^2 + pi (8)(15)
128 pi +120pi
248pi
You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?
Answer:
90 ml of the 25 percent mixture and 585 of pure alcohol
Step-by-step explanation:
Firstly, you should find the quantity of alcohol in the desired mixture.
675:100*90= 675*0.9= 607.5
Firstly, define all the 25 percents mixure as x, the pure alcohol weight is y.
1. x+y= 675 (because the first and the second liquid form a desired liquid).
Then find the equation for spirit
The first mixture contains 25 percents. It is x/100*25= 0.25x
When the second one consists of pure alcohol, it contains 100 percents of spirit, so it is x.
2. 0.25x+y=607.5
Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)
try 2-1 to get rid of y
x+y- (0.25x+y)= 675-607.5
0.75x= 67.5
x= 90
y= 675-x= 675-90= 585
It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol
Alice and Bob each choose a number uniformly (and independently) from the interval [0, 10]. What is the probability that the absolute value of the difference between their two numbers is less than 1/4
Answer:
The probability is zero (0)
Step-by-step explanation:
Given;
interval of numbers to be chosen = 0, 1, 2, 3 , 4, 5, 6, 7, 8, 9 , 10
total possible outcome = 11
The possible numbers whose absolute difference is greater than ¹/₄ includes the following;
(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,0)
The probability of this = 11 / 11 = 1
The probability that the absolute value of the difference between their two numbers is less than 1/4
[tex]P(less \ than \ \frac{1}{4} ) = 1 - P(greater \ than \ \frac{1}{4} )\\\\P(less \ than \ \frac{1}{4} ) = 1 - 1 \\\\P(less \ than \ \frac{1}{4} ) = 0[/tex]
A farmer plants the same amount every day, adding up to 4 1/3 acres at the end of the year. If the year is 5/8 over, how many acres has the farmer planted?
Answer:
5/6
Step-by-step explanation:
12/3 × 1/2 = 5/6
hope it helps
please mark Brainliest
Find the area of the circle around your answer to the nearest 10th
Answer:
A= π ( 3.8)^2
A= 45.36
OAmalOHopeO
Step-by-step explanation:
area is 2xr(times your answer)
help me with this please
There is a swimming pool which has a length of 15 m and a width of 12 m. There is a 2 m wide path around the pool. If the cost of the path is $5 per , what is the cost of the path? Use words, numbers, and/or symbols to justify your answer.
Answer:
15m+12m+15m+13m=54m
2m×12m=24m
Answer please answer!!
I need the answer asap
Answer:
35 cm
Step-by-step explanation:
is the correct answer
Which expression is equivalent to the following complex fraction?
-25
245 5
+
y
3 2
у
Step-by-step explanation:
[tex] \longrightarrow \sf{ \dfrac{ \cfrac{ - 2}{x} + \cfrac{ 5}{y}}{\cfrac{ 3}{y} -\cfrac{ 2}{x} }} \\ \\ \longrightarrow \sf{ \dfrac{ \cfrac{ - 2y + 5x}{xy}}{\cfrac{ 3x - 2y}{xy} }} \\ \\ \longrightarrow \sf{ \cfrac{ - 2y + 5x}{xy}} \times{\cfrac{ xy}{3x - 2y} } \\ \\ \longrightarrow \boxed{ \sf{ \cfrac{ - 2y + 5x}{3x - 2y}}}[/tex]
Option A is correct!
The expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
[-2/x + 5/y] / [3/y - 2/x]
This expression could also be given by;
[-2y + 5x /xy] / [3 x- 2y /xy]
Now, we know that x would cancel out;
[-2y + 5x ] / [3 x- 2y]
Hence, the expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]
Learn more about expression here;
brainly.com/question/14083225
#SPJ2
Question 3 of 10
Which angle in ABC has the largest measure?
2
С
A ZA
B. 8
C. 20
O O
D. Cannot be determined
Answer:
Option C
Angle C has the largest measure
PLEASE HELP THIS IS DUE ASAP!!!!!!!!!!
Answer:
1/36
Step-by-step explanation:
When you roll a die the possible outcomes are 1,2,3,4,5,6
P(1) = number of outcomes that are 1 / total outcomes
=1/6
The events are independent so we can multiply the probabilities
P(1,1) = 1/6*1/6 = 1/36
Please help me with this
9514 1404 393
Answer:
1+3x = -89x = -30Step-by-step explanation:
If we let x represent "a number", then "three times a number" is 3x. The usm of that and 1 is ...
1 +3x . . . . . . the sum of 1 and 3 times a number
That is said to be -89, so we have the equation ...
1 +3x = -89
__
To solve this equation, we can subtract 1 from both sides:
3x = -90
Then we can divide by 3 to find x.
(3x)/3 = -90/3
x = -30
a bus carry 53 passengar on a trif. how many passenger can 9 such carry if each dose 2 trif
Answer:
954 passengers
Step-by-step explanation:
(Assuming I read the question correctly)
1 bus can carry in 1 trip = 53 passengers
1 bus can carry in 2 trips : 106 passsengers
9 busses can carry in 2 trips = 106 x 9 = 954
Answred by Gauthmath
Fixed costs are $3,000, variable costs are $5 per unit. The company will manufacture 100 units and chart a 50% markup. Using the cost-plus pricing method, what will the selling price be? (2 pts)
Your company has fixed costs of $150,000 per year. The variable costs per unit in 2018 were $3 per unit, and 30,000 units were produced that year. Your company uses cost-based pricing and has a profit margin of $3 per unit. In 2019, production increased and your team had more experience—variable costs went down to $2 per unit because of your team’s higher skill and 65,000 units were produced that year. What is the change in selling price from 2018 to 2019? (2 pts)
Fixed Costs are $500,000. Per unit costs are $75, and the proposed price is $200. How many units must be sold to break even? How many units must be sold to realize a $200,000 target return? (2 pts)
Congratulations! You you just decided to become the proud owner of a new food truck offering traditional Mediterranean cuisine. Kitchen and related equipment costs are $100,000. Other fixed costs include salaries, gas for the truck, and license fees and are estimated to be about $50,000 per year. Variable costs include food and beverages estimated at $6 per platter (meat, rice, vegetable, and pita bread). Meals will be priced at $10.
Answer:
1. Using the cost-plus pricing method, the selling price = $5.25
2. The change in selling price from 2018 to 2019 is $3.69 or 33.5% reduction.
3. To break-even, unit sales = 4,000 units
To realize a target return of $200,000, the unit sales = 5,600 units
4. Units to break-even = 12,500 meals
Sales revenue at break-even point = $125,000
Step-by-step explanation:
a) Data and Calculations:
Fixed costs = $3,000
Variable costs per unit = $5
Units manufactured = 100 units
Total variable costs = $500 ($5 * 100)
Total costs = $3,500 ($500 + $3,000)
Cost per unit = $3.50
Markup percentage = 50%
Using the cost-plus pricing method, the selling price = $5.25 ($3.50 * 1.5)
b) Fixed costs per year = $150,000
Variable costs per unit = $3
Production units = 30,000
Total variable costs = $90,000 ($3 * 30,000)
Cost-based pricing with a profit margin = $3 per unit
Total costs = $240,000 ($90,000 + $150,000)
Cost per unit = $8 ($240,000/30,000)
Selling price per unit = $11 ($8 + $3)
Variable cost = $2 per unit
Production units = 65,000 units
Total costs = ($2 * 65,000 + $150,000)
= $280,000 ($130,000 + $150,000)
Unit cost = $4.31 ($280,000/65,000)
Selling price = $7.31 ($4.31 + $3)
Change in selling = $3.69 ($11 = $7.31) = 33.5%
c) Fixed costs = $500,000
Per unit costs = $75
Proposed price = $200
Contribution margin per unit = $125 ($200 - $75)
To break-even, unit sales = $500,000/$125 = 4,000 units
To realize a target return of $200,000, the unit sales = $700,000/$125 = 5,600 units
d) Kitchen and related equipment costs = $100,000
Other fixed costs per year = $50,000
Variable costs = $6 per platter
Price per meal = $10
Contribution margin per meal = $4 ($10 - $6)
Units to break-even = $50,000/$4 = 12,500 meals
Sales revenue at break-even point = $50,000/40% = $125,000
Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°
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Answer:
67.0 square units
Step-by-step explanation:
The formula for the area is ...
Area = 1/2ab·sin(C)
Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units
The area of the triangle is about 67.0 square units.
Deidre is planting tulips in her garden, and she has 44 red bulbs and 44 purple bulbs to plant in one row. What is the probability that she randomly plants the bulbs so that all 44 red bulbs are next to each other and all 44 purple bulbs are next to each other
Answer:
[tex]P=7.62*10^{-26}[/tex]
Step-by-step explanation:
From the question we are told that:
Available plants:
44 red bulbs
44 purple bulbs
Generally the equation for Total possible arrangement is mathematically given by
[tex]n= 88!/(44!*44!)[/tex]
[tex]n=2.6*10^{25}[/tex]
Since
Its either
All 44 red bulbs and All 44 purple bulbs next to each other in one row
OR
All 44 purple bulbs and All 44 Red bulbs next to each other in one row
Therefore
Probability is
[tex]P=\frac{2}{2.6*10^{25}}[/tex]
[tex]P=7.62*10^{-26}[/tex]
If X²+1=2x then what the value of x²?
Answer:
x² = 2x - 1
Step-by-step explanation:
x² + 1 = 2x
→ Minus 1 from both sides
x² = 2x - 1
x^2 + 1 = 2x
x^2 = 2x - 1
Also value of x = Root(2x -1)
Answered by Gauthmath must click thanks and mark brainliest
What is the quotient ? -4/2 divided by 2
Answer:
[tex]\frac{-\frac{4}{2} }{2} =-\frac{4}{2} *\frac{1}{2} =-\frac{4}{4} =-1[/tex]
six times the sum of a number and 4 is 5
The sum of 6 times a number and 4 equals 5
The sum (+) of 6 times (multiply by 6) a number (x) and 4 equals (=) 5
6 times (multiply by 6) a number (x) + 4 = 5
6x + 4 = 5
6x = 5 - 4
6x = 1
x = 1/6
Answer:
6(x+4) = 5
=> 6x + 24 = 5
=> 6x= -19
=> x = -19/6
=> x = -3.16666
Lets subtitute the value of x for proof
6(x+4)
6(-3.16666+4)
-18.999996+24
= 5.00004~ 5.00
Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola?
Answer:
The equation of the parabola is,
x²+4y-12=0
Question
Express all real numbers less than -2 or greater than or equal to 3 in interval notation.
Real numbers can be expressed using the following interval,
[tex]\mathbb{R}=(-\infty,\infty)[/tex]
Of course infinities are not just normal infinities but thats out of the scope of this question.
Real numbers less than two can be expressed with,
[tex](-\infty,\infty)\cap(-\infty,-2)=\boxed{(-\infty,-2)}[/tex]
The [tex]\cap[/tex] is called intersection ie. where are both intervals valid. First we took real numbers then we intersected them with real numbers valued less than -2 and we got real numbers which are less than -2.
Similarly we can perform with "greater than or equal to 3" real numbers,
[tex](-\infty,\infty)\cap[3,\infty)=\boxed{[3,\infty)}[/tex]
So we have one interval stretching from negative infinity to (but not including) -2, and another interval stretching from including 3 to positive infinity.
If we want numbers in both intervals we can express this two ways,
First way is to use [tex]\cup[/tex] union operator to denote we want numbers from two intervals,
[tex]\boxed{(-\infty,2)\cup[3,\infty)}[/tex]
The second way is to specify which numbers we do not want, we do not want -2 and everything up to but not including 3, which is expressed with the following interval
[tex][-2,3)[/tex]
Now we just take out the not wanted interval from real numbers and we will remain with all wanted numbers,
[tex]\boxed{(-\infty,\infty)-[-2,3)}[/tex]
Hope this helps.
The domain of a composite function (fog)(x) is the set of those inputs x in the domain of g for which g(x) is in the domain of f.
True
False
A basketball player averages 22.5 points scored per game with a standard deviation of 6.2 points. In one game, the athlete scored 10 points. What is the z-score for the points scored in this game?
–2.02
–1.63
1.63
2.02
Answer:
Step-by-step explanation:
Z -2.02
x 10
µ 22.5
σ 6.2
I need help thanks you!
I think its C: 2 hours. sry if its wrong
The graph of y= -2x + 10 is:
O A. a line that shows only one solution to the equation.
O B. a point that shows the y-intercept.
O C. a line that shows the set of all solutions to the equation.
O D. a point that shows one solution to the equation.
SUBM
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Answer:
C. a line that shows the set of all solutions to the equation.
Step-by-step explanation:
Any graph shows the set of all solutions to the equation being graphed.
The graph of a linear function is a straight line.
Given that ƒ(x) = 3^x, identify the function g(x) shown in the figure. A) g(x) = −3^-x
B) g(x) = −(1∕3)^x
C) g(x) = 3^−x
D) g(x) = −3^x
Answer:
Option (D)
Step-by-step explanation:
From the graph attached,
Function 'f' is the reflected across x-axis to get the graph function 'g'.
Therefore, by definition of reflection across x-axis,
g(x) = -f(x)
g(x) = [tex]-3^x[/tex]
Option (D) will be the answer.
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
3/5
Step-by-step explanation:
sin=opp/hyp
sinc=24/40=3/5
1. Find the value of the unknown angles in the following diagram.
Answer:
z= 40
y=140
x= 115
Step-by-step explanation:
look at the pics
