Answer:
(a) The inequality for the number of items, x, produced by the labor, is given as follows;
250 ≤ x ≤ 600
(b) The inequality for the cost, C is $1,000 ≤ C ≤ $3,000
Step-by-step explanation:
The total time available for production = 1000 hours per week
The time it takes to produce an item on line A = 1 hour
The time it takes to produce an item on line B = 4 hour
Therefore, with both lines working simultaneously, the time it takes to produce 5 items = 4 hours
The number of items produced per the weekly labor = 1000/4 × 5 = 1,250 items
The minimum number of items that can be produced is when only line B is working which produces 1 item per 4 hours, with the weekly number of items = 1000/4 × 1 = 250 items
Therefore, the number of items, x, produced per week with the available labor is given as follows;
250 ≤ x ≤ 1250
Which is revised to 250 ≤ x ≤ 600 as shown in the following answer
(b) The cost of producing a single item on line A = $5
The cost of producing a single item on line B = $4
The total available amount for operating cost = $3,000
Therefore, given that we can have either one item each from lines A and B with a total possible item
When the minimum number of possible items is produced by line B, we have;
Cost = 250 × 4 = $1,000
When the maximum number of items possible, 1,250, is produced, whereby we have 250 items produced from line B and 1,000 items produced from line A, the total cost becomes;
Total cost = 250 × 4 + 1000 × 5 = 6,000
Whereby available weekly outlay = $3000, the maximum that can be produced from line A alone is therefore;
$3,000/$5 = 600 items = The maximum number of items that can be produced
The inequality for the cost, C, becomes;
$1,000 ≤ C ≤ $3,000
The time to produce the maximum 600 items on line A alone is given as follows;
1 hour/item × 600 items = 600 hours
The inequality for the number of items, x, produced by the labor, is therefore, given as follows;
250 ≤ x ≤ 600
(a) The inequality for the number of items, x, produced by the labor, is given as follows;
250 ≤ x ≤ 600
(b) The inequality for the cost, C is $1,000 ≤ C ≤ $3,000
What is inequality?Inequality is a statement shows greater the, greater then equal to, less then,less then equal to between two algebraic expressions.
The total time available for production = 1000 hours per week
The time it takes to produce an item on line A = 1 hour
The time it takes to produce an item on line B = 4 hour
Therefore, with both lines working simultaneously, the time it takes to produce 5 items = 4 hours
The number of items produced per the weekly labor = 1000/4 × 5 = 1,250 items
The minimum number of items that can be produced is when only line B is working which produces 1 item per 4 hours, with the weekly number of items = 1000/4 × 1 = 250 items
Therefore, the number of items, x, produced per week with the available labor is given as follows;
250 ≤ x ≤ 1250
Which is revised to 250 ≤ x ≤ 600 as shown in the following answer
(b) The cost of producing a single item on line A = $5
The cost of producing a single item on line B = $4
The total available amount for operating cost = $3,000
Therefore, given that we can have either one item each from lines A and B with a total possible item
When the minimum number of possible items is produced by line B, we have;
Cost = 250 × 4 = $1,000
When the maximum number of items possible, 1,250, is produced, whereby we have 250 items produced from line B and 1,000 items produced from line A, the total cost becomes;
Total cost = 250 × 4 + 1000 × 5 = 6,000
Whereby available weekly outlay = $3000, the maximum that can be produced from line A alone is therefore;
$3,000/$5 = 600 items = The maximum number of items that can be produced
The inequality for the cost, C, becomes;
$1,000 ≤ C ≤ $3,000
The time to produce the maximum 600 items on line A alone is given as follows;
1 hour/item × 600 items = 600 hours
The inequality for the number of items, x, produced by the labor, is therefore, given as follows;
250 ≤ x ≤ 600
Hence the inequality for the number of items, x, produced by the labor, is 250 ≤ x ≤ 600 and the inequality for the cost, C is $1,000 ≤ C ≤ $3,000
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Sam starts his hike at an elevation of 311 feet above sea level. When
he reaches the end of the hike, he is 6371 feet above sea level. What
was the change in elevation from the start of his hike to the end?
label optional
Answer:
6060 feet
Step-by-step explanation:
6371-311=6060
What is the average rate of change for a
babysitter that earns $9 for 1hr and $36
for 4 hrs?
3
Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown. After each touchdown, the team can earn one point for the extra kick or two points for a 2-point conversion. The team scored one fewer 2-point conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were made during the game?
Answer:
Five touchdowns were made in the game
Step-by-step explanation:
Here, we want to know the number of touchdowns made during the game.
We proceed as follows;
Let the number of touch downs be x
So the total points earned through touchdowns is 6 * x = 6x
The number of scores is 10 times
Let the number of extra kick be y which means that the number of conversions will be (y-1)
So the total number of score times will be ;
x + y + y-1 = 10
x + 2y = 11 •••••••••(i)
Now let’s work with points
Touch down points = 6 * x = 6x
Points from extra kick = 1 * y = y
Points from 2-point conversions = 2(y-1) = 2y - 2
So;
6x + y + 2y -2 = 37
6x + 3y = 37 + 2
6x + 3y = 39
divide through by 3
2x + y = 13 •••••••(ii)
So now solve simultaneously
From ii, y = 13 - 2x
Put this into i
x + 2(13-2x) = 11
x + 26 - 4x = 11
x -4x = 11-26
-3x = -15
x = -15/-3
x = 5
There are five touchdowns in the game
Answer:
x = -15/-3
Step-by-step explanation:
Five touchdowns were made in the game
Step-by-step explanation:
Here, we want to know the number of touchdowns made during the game.
We proceed as follows;
Let the number of touch downs be x
So the total points earned through touchdowns is 6 * x = 6x
The number of scores is 10 times
Let the number of extra kick be y which means that the number of conversions will be (y-1)
So the total number of score times will be ;
x + y + y-1 = 10
x + 2y = 11 •••••••••(i)
Now let’s work with points
Touch down points = 6 * x = 6x
Points from extra kick = 1 * y = y
Points from 2-point conversions = 2(y-1) = 2y - 2
So;
6x + y + 2y -2 = 37
6x + 3y = 37 + 2
6x + 3y = 39
divide through by 3
2x + y = 13 •••••••(ii)
So now solve simultaneously
From ii, y = 13 - 2x
Put this into i
x + 2(13-2x) = 11
x + 26 - 4x = 11
x -4x = 11-26
-3x = -15
Solve the equation for all real solutions.
k^2+8k+22=6
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[tex] {k}^{2} + 8k + 22 = 6 [/tex]
Subtract sides 6
[tex] {k}^{2} + 8k + 22 - 6 = 6 - 6 [/tex]
[tex] {k}^{2} + 8k + 16 = 0[/tex]
[tex] ({k + 4})^{2} = 0[/tex]
Thus ;
[tex]k + 4 = 0[/tex]
Subtract sides 4
[tex]k + 4 - 4 = - 4[/tex]
[tex]k = - 4[/tex]
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Arnold puts $580 in a savings the account pays 3% simple interest. how much interest will he earn in 5 years
Answer:Arnold earns $87 of interest in 5 years.
Step-by-step explanation:
14
Bolve for the value of z:
5
Z
25
Answer:
The answer is 15
Step-by-step explanation:
Thats what I got
Find the GCF of 38 and 49.
Answer:1
Step-by-step explanation:
I found the factors and prime factorization of 38 and 49. The biggest common factor number is the GCF number. So the greatest common factor 38 and 49 is 1
Answer: The greatest common factor is 1
Step-by-step explanation:
49 is not even like 38 so the only one they have together in 1.
solve for c a(b-c)=d
Answer; c= -d/a + b
Step-by-step explanation:
Jasmine needs to solve the equation 9x + 12 = 3(x-8). Which
equations represent a first step Jasmine could use to solve the original
equation? Select all that apply.
Answer:
To find the value of x
1. Solve what it is in the parentheses
2. Combine like numbers on each side of the equation if is possible
3. Subtract 12 on both sides of the equation
4. Subtract 3x on both sides of the equation
5. Divide by 6 both sides of the equation
Step-by-step explanation:
9x + 12 = 3(x-8)
9x + 12 = 3x -24
-12 -12
9x = 3x -36
-3x -3x
6x = -36
6 6
x = -6
The equation that represent the first step that should be required is 9x + 12 = 3x -24.
Calculation of an equation:Since the equation is
9x + 12 = 3(x-8)
So
9x + 12 = 3x -24
6x = -36
x = -6
So based on this, we can say that The equation that represent the first step that should be required is 9x + 12 = 3x -24.
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Please help I don’t understand
Answer:
y = -2x+4
Exp:
Slope (m) =
ΔY
ΔX
=
-2
1
= -2
θ =
arctan( ΔY ) + 360°
ΔX
= 296.56505117708°
ΔX = 2 – 1 = 1
ΔY = 0 – 2 = -2
Distance (d) = √ΔX2 + ΔY2 = √5 = 2.2360679774998
Equation of the line:
y = -2x + 4
When x=0, y = 4
When y=0, x = 2
In the given figure QR ∥AB, RP∥ BD,CQ=x+2,QA=x,CP=5x+4,PD=3x.The value of x is
Answer:
where is the figure and without figure what to do
explain the slope rules
I need them for my notes.
many thanks <3
Answer:
Rules for Calculating the Slope of Line
Find two points on the line. Count the rise (How many units do you count up or down to get from one point to the next?) Record this number as your numerator. Count the run (How many units do you count left or right to get to the point?)
Step-by-step explanation:
Multi Step Problem (Show work!!)
-4 + -5 = 8
Answer:
the answer is -9 not 8
Step-by-step explanation:
What is the slope, the Y-intercept and the equation for this graph??
Answer:
equation of the line: y=1/2x-1
slope :1/2x
y intercept: -1
Step-by-step explanation:
using y1-y2/x1-x2:
-1-0/0-2= -1/-2=1/2
the slope is 1/2.
plug in the numbers from the given points to find the y intercept:
-1=1/2•0+b
b= -1
the y intercept is -1.
with that, you've gotten the slope and the y intercept, which means you just have to plug them into y=mx+b.
so, the equation of the line is y=1/2x-1
If 4x = 64,
find the value of 2x + 3.
Answer:
35
Step-by-step explanation:
4x=64
divide that: =16
x=16
2(16)+3
35
What’s the answer hurry
Answer:
y=12x
Step-by-step explanation:
According to the table
48=12(4) which is true
60=12(5) which is true
96=12(8) which is true
Answer:
12, 60/5 is 12, 48/4 is 12, 96/8 is 12
Martin uses 5/8 of a gallon of paint to cover 4/5 of a wall. What is the unit rate at which Martin paints in wall per gallon?
35/25
1 7/25
1/2
1 3/32
Answer:
Since your answer needs to be in walls per gallon I would assume you divide 4/5 by 5/8 since that would tell you how many walls he can paint in an hour.
4/5 walls÷5/8 gallons=1.28walls/gallon.
Step-by-step explanation:I hope this helps. Let me know if anything is unclear.
530, 6%, 1 year i dont think the answer is 3189 it told me i was wrong so yea please help
Answer:
6% of 530 is 31.8 hope this is what you ment
Answer this for 15 points
Answer:
A.
Step-by-step explanation:
y = mx + b
y = -2/3 x + b
(x, y) = (3, 0)
0 = -2/3 (3) + b
0 = -2 + b
b = 2
y = -2/3 x + 2
Answer: A.
Answer:
y = - 2/3 + 2
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
y = - 2/3x + b Input Slope
Step 3:
0 = - 2/3 ( 3 ) + b Input x and y
Step 4:
0 = - 2 + b Multiply
Step 5:
2 = b Add 2 on both sides
Answer:
y = - 2/3 + 2
Hope This Helps :)
find the area of a Semicircle whose radius is 3.5 cm (take pi as 22/7
Answer:
TSA=115.5cm²
Step-by-step explanation:
T.S.A=3πr²
Given r=3.5cm
eq.
3×22/7×3.5×3.5
=3×22×0.5×3.5
=115.5cm²
Answer:
[tex]19.25cm^{2} \\[/tex]
Step-by-step explanation:
Formula
[tex]\frac{\pi r^{2} }{2}[/tex]
Solve
[tex]\frac{(\frac{22}{7} )(3.5cm)^{2}}{2}= \frac{(\frac{22}{7} )(3.5cm)(3.5cm)}{2}=\frac{((\frac{22}{7} )(3.5cm))(3.5cm)}{2}=\frac{(\frac{77}{7}cm)(3.5cm) }{2}[/tex]=
[tex]\frac{(11cm)(3.5cm)}{2}=\frac{38.5cm^{2}}{2}=19.25cm^{2}[/tex]
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Use the information to answer the following question.
the table shows the relationship between the number of hours, h, jorge has been hiking
and the total distance, d,he has traveled in kilometers.
The graph shows the distance sara hiked over the same period of time.
who hikes faster?Explain.
Answer:
Step-by-step explanation:
Sara is faster she got a longer distance to Jorge
What is the domain of this quadratic function?
The graph goes on forever in both directions along the x axis. This indicates any x value can be plugged into the quadratic to get some y output. There are no restrictions. The domain is the set of all possible x inputs of a function.
A leather jacket is priced at $130. There is an 8% sales tax rate. What is the sales tax for the jacket in dollars and cents?
Answer:
$10.40
Step-by-step explanation:
Multiply $130 with 0.08 to get the sales tax. 0.08 is the same as 8%, just in decimal form.
$130 * 0.08 = $10.40
Which scatter plot shows a nonlinear association for the data?
10
8
6
10-
8
6-
4
2
2
092746810
0 246810
yt
10
8
6
4
2
y+
10
8
6
2
0 246810
0 249698 10x
Answer:
10, 8, 6, 4, 2
Step-by-step explanation:
-3x-4=-5y-8 what is the y-intercept and x-intercept
Answer:
3/5x + 4/5 = y
or
y = 3/5x + 4/5
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To find the y-intercept just need to put 0 instead of x in the equation.
[tex] - 3(0) - 4 = - 5y - 8[/tex]
[tex] - 4 = - 5y - 8[/tex]
Add sides 8
[tex] -4 + 8 = - 5y - 8 + 8[/tex]
[tex] 4 = - 5y[/tex]
Divide sides by -5
[tex] \frac{4}{ - 5} = \frac{ - 5}{ - 5} y \\ [/tex]
[tex]y = - \frac{4}{5} \\ [/tex]
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To find the x-intercept just need to put 0 instead of y in the equation.
[tex] - 3x - 4 = - 5(0) - 8[/tex]
[tex] - 3x - 4 = - 8[/tex]
Add sides 4
[tex] - 3x - 4 + 4 = - 8 + 4[/tex]
[tex] - 3x = - 4[/tex]
Negatives simplifies
[tex]3x = 4[/tex]
Divide sides by 3
[tex] \frac{3}{3} x = \frac{4}{3} \\ [/tex]
[tex]x = \frac{4}{3} \\ [/tex]
Done...
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Use the drop-down menu to complete the sentence.
Resistance is measured in units called _____.
Answer:
ohms
Step-by-step explanation:
Resistance is measured in units called ohms (symbol: Ω).
What is resistance?Resistance is a property of an electrical component that resists the flow of electric current through it.
We have,
Resistance is measured in ohms, which is the unit of electrical resistance. One ohm is the resistance value through which a current of one ampere will flow when a potential difference of one volt is applied across it.
Resistance is an important concept in electrical engineering and physics, as it is a fundamental property of electrical circuits and components.
Thus,
Resistance is measured in units called ohms (symbol: Ω).
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Can somebody help me please I needed this for the longest (3x+2) and (x-7)
Answer:
They intercept at (-4.5, -11.5)
Step-by-step explanation:
The Massachusetts Body of Liberties __________.Which shows two expressions that are equivalent to (Negative 7) (Negative 15) (Negative 5)?
Answer:
Step-by-step explanation:
The Massachusetts Body of Liberties were technically the first ever legal code system established by the colonists, and established a central court that had full rights and jurisdictions over the citizens.
I need help finding the slope, The y - intercept, and the equation?
Slope: -2/3
Y intercept: 5
Equation: y = -(2/3)x + 5
Hope this helped :)
Write an equation of a line that passes through the point (5,1) and is parallel to the line y= (-3/5)x -3
Answer:
y = (-3/5)x + 4
Step-by-step explanation:
Parallel lines have the same slope.
So the slope to the other line would be -3/5 as well.
Slope-intercept form is y = mx + b where m is the slope.
So you substitute the slope in making it y = (-3/5)x+b.
To find b, the y-intercept, you have to plug in the point for y and x in it. So you use the point (5,1) for it. That would get to 1 = (-3/5)5 + b.
To simplify that, it would get to 1 = -3 + b
Then you add 3 on both sides getting to b = 4.
Then you substitute b in, getting y = (-3/5)x + 4.
Hope this helped! If not, please let me know! <3
An equation of a line that passes through the point (5,1) and is parallel to the given line is y=-3/5 x+4.
Given that, a line that passes through the point (5,1) and is parallel to the line y= (-3/5)x -3.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
We know that, the slope of a line parallel to given line is m1=m2
By comparing y= (-3/5)x -3 with y=mx+c, we get m= -3/5
So, the slope of parallel line is -3/5
Now, put m= -3/5 and (x, y)=(5, 1), that is
1=-3/5 (5)+c
c= 4
So, equation with m=-3/5 and c=4, we have y=-3/5 x+4
Therefore, an equation of a line that passes through the point (5,1) and is parallel to the given line is y=-3/5 x+4.
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