In a factory, the production hours t and output y are having linear relationship. When the
factory operates for 5 hours per day, it may have the number of outputs of 2000 units and 3500
units for 8 hours of operation.
(a) Model an equation that gives the outputs, y, in terms of operation hours, t, per day.
(b) If the factory wants to have 4500 units of production per day, how long it should operate?
(c) Draw the graph in excel of the production against operation hours t up to first 20 hours.
Answers
Considering the linear relationship between the variables, we have that:
a) The function is: y = 500t - 500.
b) The factory should operate for 10 hours to have a production of 4500 units.
c) The graph for the first 20 hours of the function is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the given linear relationship, we have two points, as follows:
(5,2000) and (8,3500).
The slope is given by change in y divided by change in x, hence:
m = 1500/3 = 500.
Then:
y = 500t + b.
When t = 5, y = 2000, hence we solve for the intercept as follows:
2000 = 500(5) + b
b = -500.
Then the function is:
y = 500t - 500.
For 4500 units, the time is found as follows:
4500 = 500t - 500
500t = 5000.
t = 5000/500
t = 10 hours.
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Related Questions
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
How many squares will it take to fill up the large empty square?
A. 5
B. 10
C. 25
D. 50
Answers
You can use the Pythagorean theorem on the triangle formed in between the the squares to find that the large empty square has a length of 5 on each side.
To find the area, multiply length by with: 5 x 5=25.
HURRY Find all the solutions to 3x3 – 6x2 + 30x – 20 = –20.
0, 1 + 3i, 1 – 3i
0, 2 + 6i, 2 – 6i
0, –1 + 3i, –1 – 3i
0, –2 + 6i, –2 – 6i
Answers
Answer:
x= 0,1+3i, 1-3i
Step-by-step explanation:
So the first option
Find the unknown angle for the following right triangle:
Angle A Angle B Angle C
? 29 27°
Answers
The unknown angle for the given right triangle ABC which is angle A is: 63°
What is the angle in the right angle triangle?We are given the angles of a right angle triangle ABC as;
∠B = 90°
∠C = 27°
Now, it is pertinent to note that the sum of all angles in any given triangle is always 180°. This means that in our right angle triangle ABC, we can say that;
∠A + ∠B + ∠C = 180°
Thus;
∠A + 90 + 27 = 180
∠A + 117 = 180
∠A = 180 - 117
∠A = 63°
Thus, we conclude that the value of angle A is gotten as ∠A = 63°
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Complete question is;
Find the unknown angle for the following right triangle:
Angle A Angle B Angle C
? 90 27
[-17, 10] U (10, ∞)How to solve
Answers
1) Let's make use of pair of number lines to find the union between those intervals:
2) Note that in the first line the point 10 is included, while in the second one is not so the answer is:
[tex]\lbrack-17,\:∞)[/tex]Classify each polynomial by degree and number of terms 1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10THESE ARE THE OPTIONS Degree Name using degree 0 Constant1 Linear2 quadratic3 Cubic4 quartic5 quintic6 6th degree
Answers
1)
[tex]\begin{gathered} x^3\text{ + 5x} \\ \text{cubic , 2 terms} \end{gathered}[/tex]2) The term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree
[tex]\begin{gathered} x^2-2x-1 \\ \text{quadratic, 3 terms} \end{gathered}[/tex]3) of or relating to the fourth degree. a quartic polynomial or equation.
[tex]\begin{gathered} 5x^4 \\ \text{quartic, 1 term} \end{gathered}[/tex]4) quintic : a polynomial or a polynomial equation of the fifth degree.
[tex]\begin{gathered} 6x^5-3x^2\text{ + 7x + 9} \\ qu\text{intic , 4 terms} \end{gathered}[/tex]5)
[tex]\begin{gathered} =11x\text{ - 5} \\ L\text{inear , 2 terms} \end{gathered}[/tex]6)
[tex]\begin{gathered} 4x^2\text{ + 20} \\ \text{quadratic, 2 terms} \end{gathered}[/tex]What is the slope of the equation y – 3 = –4(x – 5)?
–4
–3
20
23
Answers
Answer: slope = -4
Step-by-step explanation:
y – 3 = –4(x – 5)
y - 3 = -4x + 20
y = -4x + 23
slope = -4
The area of a rectangle is 99 m2, and the length of the rectangle is 7 m more than double the width. Find the dimensions of the rectangle.
Answers
On the Left side is just an example.
On the paper is my answer to your question with explanation.
Hope this will help:)
true/false:1: you can keep mixed numbers when performing multiplication or division.2: numerators must be multiplied by numerators and denominators must be multiplied by denominators.3: You must convert mixed numbers into improper fractions before multiplying or dividing.4: The denominators MUST be the same.
Answers
1: you can keep mixed numbers when performing multiplication or division.-----> true
2: numerators must be multiplied by numerators and denominators must be multiplied by denominators.------>false
3: You must convert mixed numbers into improper fractions before multiplying or dividing. ------> false
4: The denominators MUST be the same. -----> false
The line below is the function y=-x+3. Identify the equation of a perpendicular line
Answers
The equation of the perpendicular line is y = x + 3
Perpendicular line:
The perpendicular line means a straight line that makes the right angle (90 degrees) with the other line.
Given,
Here we have the equation y = -x + 3.
Now, we need to find the equation of the perpendicular line.
In order to find the equation of a perpendicular line, first we need to find the negative reciprocal of the slope given.
Through the given equation we have identified the slope of the line is -1. so the slope of the perpendicular line will be 1.
While looking at the graph we have identified the y intercept of the equation is 3.
So now we know the values of y-intercept and slope.
We just put them together, and apply it one the standard form of the equation of line, then we get,
y = 1x + 3
y = x + 3.
Therefore, the equation of perpendicular line is y = x +3.
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Find the domain and the range
Answers
From the graph we can say that Domain : (-∞,-1) ∪(1,∞)
Range : (0,∞)
What is domain and range ?Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range. A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavor will be provided. As a result, the domain depicts the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a Coke machine won't give you a cheeseburger.
From the graph we can say that
Domain : (-∞,-1) ∪(1,∞)
Range : (0,∞)
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These box plots show the prices for two different brands of shoes.65 70 75 80 85Brand AHIH1550507085Brand B0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 e 90 95 100Price (5)Which statement is the most appropriate comparison of the spreads?O A. The interquartile range (IQR) for brand A, $10, is less than the IQRfor brand B, $20.O B. The interquartile ranges (IQRS) for brands A and B are both $20.O C. The median for brand A, $75, is greater than the median for brandB. $60.O D. The interquartile range (IQR) for brand A, $20, is less than the IQRfor brand B, $70.
Answers
Given:
Given the box plots of two different brands of shoes.
Required: Most appropriate comparison of the spreads
Explanation:
From the box plot of brand A,
Minimum value = 65
First quartile, Q1 = 70
Median = 75
Third quartile, Q3 = 80
Maximum value = 85
Also, from the box plot of brand B,
Minimum value = 15
First quartile, Q1 = 50
Median = 60
Third quartile, Q3 = 70
Maximum value = 85
The interquartile range is the difference between the upper quartile and the lower quartile
The interquartile range of brand A is
[tex]\begin{gathered} Q_3-Q_1=80-70 \\ =10 \end{gathered}[/tex]The interquartile range of brand B is
[tex]\begin{gathered} Q_3-Q_1=70-50 \\ =20 \end{gathered}[/tex]Option A is correct.
The median for brand A is $75, which is less than the median of brand B, $60.
Option C is correct.
Final Answer: The most appropriate
The profit from the expenditure of x thousand dollars on advertising is given by P(x)=930+15x-4x^2.
Find the marginal profit when the expenditure is x = 7.
Answers
The marginal profit is -41 dollars.
In accounting, a profit is an income that is given to the owner throughout a successful market producing process (business).
Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.When one more unit is manufactured and sold, a company or individual will make a profit known as marginal profit. The additional expense or profit made when producing the following unit is referred to as marginal. While marginal cost is the additional expense for producing one extra unit, marginal product is the additional income earned.The advertising is given by P(x) = 930 + 15x -4x².
The marginal profit at x = 7 is given by
P(x) = 930 + 15x -4x²
P'(x) = 15 - 8x
Now at x = 7 the marginal profit is
P'(7) = 15 - ( 8×7 )
or, P'(7) = -41
Hence there will be marginal profit of -41 dollars.
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write a quadratic equation that opens down and has vertex at (2,-8)
Answers
The quadratic equation that opens down and has vertex at (2,-8) is y = (-|a|)*(x - 2)² + (-8).
The graph of a quadratic function has the shape of a parabola. Although a parabola's "width" or "steepness" and direction of opening can differ, they all have the same basic "U" shape. If the leading coefficient is larger than zero, the parabola opens upward; if it is less than zero, it opens downward.
The quadratic equation's vertex form is y = a*(x - h)2 + k.
Given that (2,-8) or (h, k) is the vertex point (2,-8)
Since the graph starts out downward, a will have a negative value.
Since |a| is the magnitude of a, the quadratic equation will then be written as y = (-|a|)*(x - 2)2 + (-8).
Consequently, y = (-|a|)*(x - 2)2 + is a quadratic equation that opens downward and has a vertex at (2,-8). (-8).
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A center pivot irrigation system provides water to a sector shaped field, find the area of the field if 0=140 degrees and r= 40 yd
Answers
The area of the sector is approximately 1954.77 square yards.
A circular sector, also known as a circle sector or a disc sector (symbol:), is a piece of a disc (a closed region bordered by a circle) encompassed by two radii and an arc. The smaller area is known as the minor sector, and the bigger is known as the major sector.
Any point on the circle outside of the sector can be connected to the arc's endpoints to produce half of the central angle.
We know that the area of a circle is πr² and the area of the sector of a circle with angle θ is given by θ/360 πr² .
Area of the sector
= 140°/360° × π × 40²
= 1954.7687... square yards.
≈ 1954.77 square yards.
Therefore the area of the sector is approximately 1452.113 square yards.
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Which statement is true regarding the graphed functions?
9129
2
10-
19642
Of(0) = g(0)
Of(-2) = g(-2)
Of(0) = g(-2)
Of(-2) = g(0)
--6-5-4-3-2-1₂
2
74902
S
-6
-8
-10-
-12+
2 3 4 5 6 x
f(x)
Answers
Answer: The answer is -5559
Step-by-step explanation:
PLEASE PLEASE PLEASE!!!!!!!!!!HELP HELP HELP HELP HELP HELP!!!! IM CRYING IM STUCK
Answers
Answer:
[tex]y=\begin{cases}-\dfrac{7}{2}x-16&\text{for $-6\le x\le-4$}\\\\\dfrac{1}{5}x-\dfrac{6}{5}&\text{for $-4 < x < 1$}\\\\\dfrac{9}{4}x-\dfrac{13}{4}&\text{for $1\le x\le 5$}}\end{cases}[/tex]
Step-by-step explanation:
You want the piecewise function that describes the relation shown in the graph.
RelationThe relation shown consists of three line segments connecting the points ...
(-6, 5) and (-4, -2)
(-4, -2) and (1, -1)
(1, -1) and (5, 8)
LinesThe equations for the lines between the pairs of points can be written using the slope formula and the point-slope equation of a line.
The slope formula tells you the slope is ...
m = (y2 -y1)/(x2 -x1)
And the point-slope equation of a line is ...
y -y1 = m(x -x1)
If we add y1 to the equation of the line, and substitute the equation for m, we get ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . . . a 2-point formula for a line
ApplicationBetween x-values -6 and -4, the equation of the line will use the first pair of points:
y = (-2 -5)/(-4 -(-6))(x -(-6)) +5
y = -7/2(x +6) +5 = -7/2x -16
Between x-values -4 and 1, the equation of the line will use the second pair of points:
y = (-1-(-2))/(1 -(-4))(x -(-4)) +(-2)
y = 1/5(x +4) -2 = 1/5x -6/5
Between x-values 1 and 5, the equation of the line will use the last pair of points:
y = (8 -(-1))/(5 -1)(x -1) +(-1)
y = 9/4(x -1) -1 = 9/4x -13/4
Piecewise functionThe piecewise function uses the equation for the line that is applicable for the appropriate x-values. We have listed those sets of x-values above.
We need to make sure that the function has only one definition for any given value of x. When two segments have a point in common, we need to make sure only one segment includes it.
[tex]y=\begin{cases}-\dfrac{7}{2}x-16&\text{for $-6\le x\le-4$}\\\\\dfrac{1}{5}x-\dfrac{6}{5}&\text{for $-4 < x < 1$}\\\\\dfrac{9}{4}x-\dfrac{13}{4}&\text{for $1\le x\le 5$}}\end{cases}[/tex]
A triangle has side lengths of (5k-3) centimeters, (k+1) centimeters, and (m-7) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answers
The expression for the perimeter of the triangle is 6k + m -9.
How to calculate perimeter of the triangle?
In mathematics, the perimeter of any closed shape means addition of all the sides. Therefore, triangle has three sides and their addition represents the perimeter. It can be measured in different units like meters, centimeters, etc.
According to the question, the given parameters for the triangle is as written below:
The side lengths are: (5k - 3); (k + 1) and (m - 7)
Now, the perimeter of a triangle is addition of all the sides. That means,
Perimeter of a triangle = 5k - 3 + k + 1 + m - 7 = 6k + m - 9
Hence, the expression for the perimeter of the triangle is 6k + m -9.
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The mean output of a certain type of amplifier is 129 watts with a variance of 100.
If 96 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.9 watts? Round your answer to four decimal places.
Answers
The probability is given by -0.001, that the mean of the sample would differ from the population mean by less than 0.9 watts.
What is normal probability distribution?
Normal distribution also known as the Gaussian probability, ia a probability distribution that is symmetric about the mean, showing that data bear the mean are more frequent in occurrence than data far from the mean.
In a set with mean μ and standard deviation (which is the square root of the variance) σ , the z score of a measure X is given by:
Z =X-μ/σ
we have given μ =129
σ = [tex]\sqrt{100}[/tex] n = 96
This is the pvalue of Z when X = 129+1.7 =130.7 subtracted by the pvalue of Z when X = 129 - 1.7 = 127.3
When X = 130.7
Z =X-μ/σ
Z = 130.7-129/10
Z = 0.17 pvalue = 0.1699
When X = 127.3
Z =X-μ/σ
Z = 127.3-129/10
=-0.17 pvalue
0.1699 - 0.1700 = -0.001
Hence the probability is -0.001
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Enter the correct answer in the box.
Linear function g is shown in the graph. Write the slope-intercept form of the equation representing this function.
g
Answers
The equation in slope-intercept form that represents the function is: g(x) = -2x + 1.
How to Write the Slope-intercept Form of an Equation?To write the slope-intercept form of an equation that represents the linear function g, find the slope (m) of the line and determine the y-intercept (b) of the line, then substitute the values into g(x) = mx + b.
Slope of the line that represents function g = change in y/change in x = -6 units/3 units
Slope of the line (m) = -6/3
Slope of the line (m) = -2.
The line intercepts the y-axis at y = 1, therefore the y-intercept (b) of the linear function is b = 1.
To write the equation representing the function, substitute m = -2 and b = 1 into g(x) = mx + b:
g(x) = -2x + 1
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Decrease £50 by 60%
need help asap!! imma be posting a lot
Answers
When £50 is decreased by 60%, the remaining value is £20.
What is a percentage?A percentage refers to the ratio of a variable expressed as a fraction of 100.
Percentages show the proportional value contained in another.
We use the percent sign (%) to denote percentages, which may be increases or decreases.
Initial value = £50
Percentage decrease = 60%
Percentage change = 40% (1 - 60%)
In monetary terms, the final value after the percentage decrease = £20 (£50 x (1 - 60%).
Thus, when £50 is reduced by 60% the value left is only 40% of the former deal, which is £20.
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Must Find the Error in this problem
Answers
Answer:
They subtracted when they should have added
Step-by-step explanation:
You must do the opposite so if it says -17 you must add 17 to the other side the answer should be 32
Use the fact that
5x2 − y2 = c
is a one-parameter family of solutions of the differential equation
y
dy
dx
= 5x
to find an implicit solution of the initial-value problem
y
dy
dx
= 5x, y(3) = −8.
Answers
The required implicit solution to the initial-value problem would be 5x²- y² = 9.5 which is the equation of a hyperbola.
What is the hyperbola?Hyperbola is defined as a conic section, a two-branched open curve, produced by the intersection of a circular cone.
(x-h)²/b² - (y-k)²/a² = 1
We have been given that 5x²- y² = c is a one-parameter family of solutions of the differential equation.
To determine an implicit solution to the initial-value problem ydy/dx = 5x
⇒ y dy/dx = 5x
⇒ y dy = 5x dx
⇒ y²/2 = 5x²/2 + c
If y(3) = −8 which is the means that when substitute x = 3 then y = -8
⇒ (-8)²/2 = 5(3)²/2 + c
⇒ 64/2 = 5(9)/2 + c
⇒ 32 = 22.5 + c
⇒ c = 9.5
Substitute the value of c in the given function 5x²- y² = c
⇒ 5x²- y² = 9.5 which is the equation of a hyperbola.
Therefore, the implicit solution to the initial-value problem would be 5x²- y² = 9.5.
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Which inequality describes this situation?
SPEED
LIMIT
80
MINIMUM
75
75 ≥ x ≥ 80
75 ≤ x ≤ 80
75 >x> 80
75 < x < 80
Answers
the second one
Step-by-step explanation:
if 75 is the minum speed then you need to go more than 75 and less than 80 which is what the second one is showing
A line has a slope of 8 and passes through the point (0,5). What is its equation inslope-intercept form?Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
The form of the equation of the line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
The y-intercept is the value of the y-coordinate when the x-coordinate is equal to zero
Therefore in our case
m=8
b=5
We substitute the values
[tex]y=8x+5[/tex]ANSWER
y=8x+5
The coordinates of midpoint M and endpoint C or a segment are M(-2,-7) and C(12,-9). Find the coordinates of the other endpoint15 )
Answers
we have that the midpoint is (-2,-7)
and the endpoint is (12,-9)
We remember the midpoint formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where (x1,y1) are the coordinates of one endpoint and
(x2,y2) are the coordinates for the other endpoint.
Here, we are trying to find (x2,y2) given that
(x1, y1) ---> (12, -9)
[tex]\begin{gathered} x_1=12 \\ y_1=-9 \end{gathered}[/tex]And since we also know the midpoint M(-2, -7), making a comparison with this and the midpoint formula, we get two equations, the first one is:
[tex]\frac{x_1+x_2}{2}=-2[/tex]substituting x1 and solving for x2:
[tex]\frac{12+x_2}{2}=-2[/tex][tex]\begin{gathered} 12+x_2=4 \\ x_2=4-12 \\ x_2=-8 \end{gathered}[/tex]And now, with the second equation which is:
[tex]\frac{y_1+y_2}{2}=-7[/tex]we substitute y1 and solve for y2:
[tex]\frac{-9+y_2}{2}=-7_{}[/tex]solving for y2:
[tex]\begin{gathered} -9+y_2=-14_{} \\ y_2=-14+9 \\ y_2=-5 \end{gathered}[/tex]This the other endpoint (x2,y2) is at (-8,-5)
U.S. Customary area unit conversion with whole number values
A flower bed has the shape of a rectangle 21 feet long and 9 feet wide. What is its area in square yards?
Be sure to include the correct unit in your answer.
Answers
189cm²
Step-by-step explanation:
area is multiplication so it will be L×B
also because its a rectangle
Brandon is trying out for a junior bowling league. He bowled some extra games Friday and Saturday to practice. On Friday, he paid $7 to rent a pair of shoes and x dollars an hour to bowl. He went to a different bowling alley on Saturday, where he paid $5 to rent shoes and y dollars an hour to bowl. Brandon bowled 2 hours on Friday and 3 hours on
Saturday.
Answers
The equation for two different bowling alleys is 2x - 3y = -2
This is a problem from algebraic equations. We can solve this problem by following a few steps.
In the first case, he paid $7 to rent a pair of shoes and x dollars an hour to bowl and bowled for 2 hours on Friday.
Here, the cost to bowl for one hour is x dollars. So, the cost to bowl for 2 hours is ( 2× x ) = 2x
Now, the total expenditure for shoes and to bowl is, (2x + 7) dollars
In the second case, he paid $5 to rent a pair of shoes and y dollars an hour to bowl and bowled for 3 hours on Saturday.
Here, the cost to bowl for one hour is y dollars. So, the cost to bowl for 3 hours is (3 × y) = 3y
Now, the total expenditure for shoes and to bowl is, (3y + 5) dollars.
As the total expenditure is the same in these two cases. Therefore, we can conclude,
(2x + 7) = (3y + 5)
Or, 2x - 3y = -2
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Simplify 4 square root of 72
Answers
Simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.
As given in the question,
Given expression,
4 square root of 72
Prime factors of 72 are as follow:
72 = 2 × 2 × 2 × 3 × 3
Rewrite them into exponent form we get
72 = 2³ × 3²
Simplification of the given expression 4 square root of 72 is
4√72
= 4 × √ 2³ ×3²
= 4 × √ 2² × 2 × 3²
Calculate the square root
= 4 ×2 ×3 √2
= 24√2
= 24 ×1.414
= 33.94
Therefore, simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.
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Which of the following numbers represents the biggest risk of getting a disease? 1in 10, 1 in 1000, 1 in 100
Answers
Answer:
1 in 10
Step-by-step explanation:
Roland's farm land is assessed at 1.5 million dollars and the improvements for $500,000.
At a tax rate of 4 mills, how much are Rolan's monthly taxes?
Answers
At a tax rate of 4 mills, Rolan's monthly taxes are $667.00.
What is the mill rate?The amount of tax due per $1 of a property's assessed value is known as the mill rate. The word mill comes from the Latin millesimum, which means thousandth. In terms of property tax, 1 mill is the amount of property tax levied per $1,000 of the assessed value of a property. Divide the mill rate by 1,000 and multiply the assessed value of the property to determine the property tax.Given:
Assessed value = 1.5 million dollars
Amount for Improvements = $500,000
Tax rate = 4 mills
Total assessment of the property = Assessed value + Improvements
= 1,500,000 + 500,000
= $2,000,000
Multiply these 2 million by 4 mills then divide by 1000.
(2,000,000 × 4)/1000
= $8000 in annual taxes
To calculate the monthly tax amount divide by 12.
$8000/12 = $667.00
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