Answer:
1. Sometimes
2. Sometimes
3. Always
4. Sometimes
Step-by-step explanation:
1. Quadratic function : in which maximum power of [tex]x[/tex] is two.
The roots of quadratic function can be either equal or different.
For example:
[tex]x^{2} -2x+1[/tex] will have two equal roots i.e. 1 and 1.[tex]x^{2} -3x+2[/tex] will have two different roots i.e. 1 and 2.So, sometimes is the correct answer.
2. Cubic function has atleast 1 real root.
Cubic function has maximum power of [tex]x[/tex] as 3.
If the coefficients are real numbers then atleast 1 real root.
If the coefficients are imaginary in nature, then this is not true.
For example:
Cubic equation [tex]x^3 +i = 0[/tex] does not have any real root.
Cubic equation [tex]x^3 +1 = 0[/tex] has a real root x = -1.
So, it is sometimes true.
3. A function with degree 5 i.e. maximum power of [tex]x[/tex] as 5 will have 5 roots.
It is always true that a function will have number of roots equal to its degree.
4. Quadratic function can have only 1 complex solution.
Two complex solutions are also possible for a quadratic function.
For example:
[tex]x^{2} +1=0[/tex] will have two imaginary roots: [tex]x=i, -i[/tex]
It is also possible to have 1 complex solution,
For example:
[tex](x-1)(x-i) = 0[/tex] will have one complex root and one real root.
So, the statement is sometimes true.
Answer:
MY ANSWER IS CORRECT IN PLATO!!!
1. Sometimes
2. Always
3. Always
4. Never
Step-by-step explanation:
1. A quadratic function has 2 distinct roots SOMETIMES
2. A cubic Function has at least 1 root ALWAYS
3. A function with a degree of 5 has 5 roots ALWAYS
4. A quadratic function can have only 1 complex solution NEVER
I JUST GOT 100% on the quiz in PLATO
A) The perimeter of a rectangle is the sum of the lengths of its four sides. Write an expression for the perimeter of the rectangle and then evaluate when x=1/2 foot? B) The area of a rectangle is the product of its length and width. Write an expression for the area of the rectangle and then evaluate when x=1/2 feet?
Answer:
Below
Step-by-step explanation:
The length of this triangle is 3x+1 and the width is x.
The perimeter P is:
P= 2(3x+1)+2*x
P= 6x+2+2x
P= 8x+2
Let's evaluate it when x=1/2
●1/2 =0.5
P= 8*0.5+2 =4+2= 6 ft
●●●●●●●●●●●●●●●●●●●●●●●●
The area A is:
A = (3x+1)*x
A= 3x^2 +x
Let's evaluate it when x=0.5 feet
A= 3*0.5^2 +0.5
A= 3*0.25+0.5
A= 0.75 +0.5
A= 1.25 ft^2
Find the x-coordinates of the two points on the curve
y=x-1/x at which the tangent is parallel to the straight line 4y= x + 8. (4 marks)
Answer: x = {-2, 2}
Step-by-step explanation:
Tangent means it is touching. Find the intersection of the two equations.
Solve the linear equation for y, then set the two equations equal to each other.
[tex]4y=x+8\qquad \rightarrow \qquad y=\dfrac{x+8}{4}[/tex]
[tex]\dfrac{x-1}{x}=\dfrac{x+8}{4}\\\\\\\text{Cross multiply and solve for x:}\\4(x-1)=x(x+8)\\4x-4=x^2+8x\\.\qquad 0=x^2+4x+4\\.\qquad 0=(x+2)^2\\.\qquad 0=x+2\\.\qquad x=-2[/tex]
To find the next point that is parallel to the linear equation and tangent to the curve, we need to use the linear equation with slope (m) = [tex]\dfrac{1}{4}[/tex] and unknown b.
Let's try b = 0, then the equation of the linear equation is: [tex]y=\dfrac{1}{4}x[/tex]
Set the equations equal to each other and solve for x:
[tex]\dfrac{x-1}{x}=\dfrac{x}{4}\\\\\\4(x-1)=x^2\\4x-4=x^2\\.\qquad 0=x^2-4x+4\\.\qquad 0=(x-2)^2\\.\qquad 0=x-2\\.\qquad x=2[/tex]
This works!!! If it didn't work, we would have tried other values for b until we arrived at a solution.
Given: angle 1 congruent angle2 prove: p||q
Please hurry
Answer:
converse of alternate exterior angle theorem
Step-by-step explanation:
um im not sure if i should explain the full proof but
taking a test- Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]
Step-by-step explanation:
The surface area of a cone is given by
[tex]SA = \pi rl +\pi r^2[/tex]
r is the radius and l is the slant height.
The diameter is 12 inches, the radius is 12/2 = 6 inches.
The slant height is 10 inches.
[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]
Answer:
SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]
Step-by-step explanation:
Surface Area of cone = [tex]\pi rh+\pi r^2[/tex]
Where r = 6 inches (Diameter = 12 inches) , h = 8 inches (We'll not consider the slant height)
SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]
WILL GIVE BRAINLIEST IF CORRECT
A 10 ft ladder is propped up against a building at an angle of 39°. How far up the wall does the ladder go?
Answer:
6.3 ft
Step-by-step explanation:
The ladder lying on the wall with an elevation of 39° forms a right angled triangle.
Hypotenuse = length of ladder = 10 ft
Opposite = x = ?
θ = 39°
Use trigonometric ratio formula to find, x, which is how far the ladder goes up the wall.
The trigonometric ratio formula to use is:
sin(θ) = opposite/hypotenuse
Sin(39) = x/10
Multiply both sides by 10
10*sin(39) = x
x = 10*sin(39)
x = 6.29 ≈ 6.3 ft (to nearest tenth)
Answer:
6.3 ft
Step-by-step explanation:
did the quiz got it right
If a transversal is perpendicular to one of two parallel lines, then it's ________ to the other line. Question 16 options: A) perpendicular B) congruent C) parallel D) supplementary
Answer: Perpendicular.
Step-by-step explanation:
Suppose that you have two perpendicular lines:
Remember that a line is something like:
y = a*x +b
and two lines are parallel if they have the same slope (a) but a different y-intercept(b)
Then our lines can be:
y1 = a*x + b1
y2 = a*x + b2.
Now, if we have a line:
y = a*x + b
Then a perpendicular line will have a slope equal to -(1/a):
yp = (-1/a)*x + c
So this only depends on the slope, and we know that our two parallel lines have the same slope. So if we construct a transversal line that is perpendicular to one of our lines, it also must be perpendicular to the other line.
Answer:
A
Step-by-step explanation:
Solve the proportion below.
X =
A. 24
B. 49
c. 27
D. 6
Answer:
A. 24
Step-by-step explanation:
4/9 = x/54
x= 54*4/9 ===== multiplying both sides by 54
x= 24
Answer is 24, choice A is correct one
Example 2: The GPAs of 20 students are listed.
Make a stem-and-leaf plot for this data.
1.8 2.9 0.9 4.0 3.3
2.4 2.3 1.6 1.6 4.0
1.7 0.5 3.6 3.4 1.9
4.0 2.1 1.9 1.1 0.5
How do I make a stem and leaf plot for these numbers?
Answer/Step-by-step Explanation:
To create a stem-and-leaf plot for the GPAs of the 20 students that were listed in the above question, take the following steps:
Step 1: for easy plotting, write down the GPAs in an ordered manner, that is, from the smallest value to the largest.
0.5, 0.5, 0.9, 1.1, 1.6, 1.6, 1.7, 1.8, 1.9, 1.9, 2.1, 2.3, 2.4, 2.9, 3.3, 3.4, 3.6, 4.0, 4.0, 4.0
Step 2: divide each set of data into a stem and a leaf. For example, for a GPA, 0.5, 0 would be the stem, while 5 would be the leaf.
For a GPA listed, 2.9, 2 is the stem, 9 is the leaf. Same applies to all the other GPAs.
Step 3: All stems should be written in ascending order, vertically, from the smallest to the largest. From the listed GPAs, you would observe that the highest stem value would be 4, while the lowest would be 0.
Therefore, write down your stems vertically, in ascending order as shown below:
0 |
1 |
2 |
3 |
4 |
Step 4: All leaves should be written also in ascending order to their corresponding stem, from the smallest to the largest, as shown below:
Stem | Leaf
0 | 5 5 9
1 | 1 6 6 7 8 9 9
2 | 1 3 4 9
3 | 3 4 6
4 | 0 0 0
Thus,
0 | 5 5 9 represents => 0.5, 0.5, 0.9
*See attachment below for the stem-and-leaf plot.
I NEED HELP ASAP PLEASE 20 POINTS
Answer:
B.
Step-by-step explanation:
[tex]\sqrt[4]{2x^2} * \sqrt[4]{2x^3}[/tex]
= [tex]2^{1/4}x^{2/4} * 2^{1/4}x^{3/4}[/tex]
= B. [tex]2^{2/4}x^{5/4}[/tex].
Hope this helps!
Describe how to simplify the expression
3^-6
3^-4
Answer:
For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81
Step-by-step explanation:
ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...
3^-6
using law of indices x^-a = 1/x^a
So 3^-6 = 1/3^6
Now find the power of 3^6
which is the same as 3×3×3×3×3×3 = 729
therefore 1/3^6 = 729
For 3^-4
using the above method
3^-4 is same as 1/3^4
which is equal to
finding the nominator
3×3×3×3 = 81
so the answer is 81
The graphed line shown below is y = negative 4 x minus 12. On a coordinate plane, a line goes through (negative 3, 0) and (negative 2, negative 4). Which equation, when graphed with the given equation, will form a system that has no solution? y = 4 x + 12 y = negative 4 x y = negative 12 y = negative 4 (x + 3)
Answer:
y = -4x or the second option on edge.
This is because after you form it into the given equation, it equals y = -4x.
In order to clarify, edge also states that's the answer.
Answer:
2nd option
Step-by-step explanation:
Create a circle such that its center is point a and b is a point on the circle
Step-by-step explanation:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
Answer:
i think that this question is wrong
Step-by-step explanation:
YOU WILL GET 30 POINTS AND BRAINLIEST IF YOU GET THIS CORRECT AND ANSWER THIS IN 5 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 3x + 400 f(x) = 3x + 391 f(x) = −3x + 391 f(x) = −3x + 400
Answer:
f(x)= -3x + 400
Step-by-step explanation:
[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }[/tex]
[tex]\frac{x-3}{13-3} =\frac{y-391}{361-391}[/tex]
-3 ( x-3 ) = (y - 391 )
-3x + 400
Answer:
he is correct
Step-by-step explanation:
3+x=8 What would like match this answer
Answer:
x = 5
Step-by-step explanation:
x = 8 - 3
Thus, x = 5
Find the surface area of the solid shown or described. If necessary, round to the nearest tenth
7cm
10cm
14 cm
Answer:
616cm²or³
Step-by-step explanation:
SA = 2(lw)+2(lh)+2(hw)
SA=2(10×14) + 2(10×7) + 2(7×14)
SA= 2(140) + 2(70) + 2(98)
SA=280+140+196
SA=616cm²or³
Verify the Cauchy-Schwarz Inequality and the triangle inequality for the given vectors and inner product.
p(x)=5x , q(x)= -2x^2+1, (p,q)= aobo+ a1b1+ a2b2
Required:
a. Compute (p,q)
b. Compute ||p|| and ||q||
Answer:
To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||
(1,1,1) is not equal to (-10,5)
Step-by-step explanation:
a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)
Any algebra raised to the power of zero is equal to 1.
a°b° = 1 × 1 = 1
1 + ab + a^2b^2 < -10x^3 + 5x
The vectors:
(1,1,1) < (-10,5)
This verifies the Cauchy-Schwarz Inequality
Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.
PLEASE HELP HOW DO I TRANSLATE IT TO A PROPORTION!!
Answer:
See below.
Step-by-step explanation:
A proportion is setting two ratios equal to each other.
Look at the info you are given for price in $ and area in sq ft:
$385 for 70 sq ft
That allows you to write a ratio. The ratio of dollars to square feet is
385/70 (notice it's dollars divided by sq ft)
Now you look at the part of the problem that has an unknown, and you set up the same type of ratio (dollars to sq ft) using x for the unknown.
x dollars to 200 sq ft
The ratio is
x/200 (notice that, again, it's dollars divided by sq ft)
In both cases the ratios are dollars to sq ft.
To set up a proportion, you just set the ratios equal to each other.
385/70 = x/200
Now we solve the proportion. We can cross multiply.
385/70 = x/200
70x = 385 * 200
70x = 77,000
x = 1100
They would charge $1100 to install 200 sq ft of tile.
The unit price is obtained by dividing a cost by the corresponding area in sq ft. you can use either ratio.
unit price = ($385)/(70 sq ft) = $5.5/sq ft
($1100/200 sq ft also works since it is also equal to $5.5/sq ft)
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 kmh slower than the other. If the two buses are 1356 kilometers apart after 6 hours, what is the rate of each bus?
Answer:
106 km / hour
Step-by-step explanation:
Givens
Total time: 6 hours
Total distance: 1356 km
First bus rate: r
Second bus rate: r - 14
Formula
d = r * t
Solution
r*6 + (r - 14)*6 = 1356 Remove the brackets
6*r + 6*r - 84 = 1356 Add like terms
12r - 84 = 1356 Add 84 to both sides
12r + 84 - 84 = 1356-84 Combine
12r = 1272 Divide by 12
r = 1272/12
r = 106 km/hr
If an office is 12 feet by 16 feet with 8 foot ceilings and I have 4 feet by 8 feet paneling sheets for the walls, not the ceiling for 4 walls. How many panels do I need?
Answer:
14 panels
Step-by-step explanation:
Area of four walls is given by 2*(length + width)*height
_______________________________________
Given dimension
Length = 16 feet
width = 12 feet
height = 8 feet
Thus, area of four walls of office = 2(16+12)8= 448
_____________________________________________
dimension of paneling sheets
length = 8 feet
width = 4 feet
area of paneling sheets = 8*4 = 32 sq. feet
Let the number of paneling sheets required by n
thus, total area of n paneling sheets = n*area of paneling sheets = 32n
This, area of paneling sheets (32n) should be same as 448 area of four walls
as given " I have 4 feet by 8 feet paneling sheets for the walls"
thus,
32n = 448
n = 448/32 = 14
Thus, 14 panels are needed.
hhhelpp meeee!! I WILL GIVE BRAINLIEST
Answer:
We're solving for CD. If we look at ΔABD we notice that it's a 30-60-90 triangle which has a side length ratio of 1:√3:2 and in this case the 1 is 300 so side BD = 300√3. Similarly, ΔABC is also a 30-60-90 triangle but this time the √3 is 300 so side BC = 100√3. We know that CD = BD - BC using PWP so the answer is 300√3 - 100√3 = 200√3 = 346.4 feet.
Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).
Answer:
(-2,-3)
Step-by-step explanation:
Well in the system,
x−5y=13
4x−3y=1
We need to find x or y in either equation.
Let's do x - 5y = 13 for x.
+5y to both sides
x = 5y + 13
Now we substitute 5y + 13 for y in 4x - 3y = 1.
4(5y + 13) - 3y = 1
20y + 52 - 3y = 1
17y + 52 = 1
-52 to both sides
17y = -51
Divide all by 17
y = -3
Now we can substitute -3 for y in 4x - 3y = 1.
4x - 3(-3) = 1
4x + 9 = 1
-9 to both sides
4x = -8
Divide 4 to both sides
x = -2
Thus,
the solution is (-2,-3).
Hope this helps :)
Answer:
( - 2 , - 3 )Step-by-step explanation:
x - 5y = 13
4x - 3y = 1
Solve the equation for x
[tex]x - 5y = 13[/tex]
Move '5y' to R.H.S and change it's sign
[tex]x = 13 + 5y[/tex]
Substitute the given value of X into the equation
4x - 3y = 1
[tex]4(13 + 5y) - 3y = 1[/tex]
Solve the equation for y
distribute 4 through the parentheses
[tex]52 + 20y - 3y = 1[/tex]
Collect like terms
[tex]52 + 17y = 1[/tex]
Move constant to R.H.S and change it's sign
[tex]17y = 1 - 52[/tex]
Calculate
[tex]17y = - 51[/tex]
Divide both sides of the equation by 17
[tex] \frac{17y}{17} = \frac{ - 51}{17} [/tex]
Calculate
[tex]y = - 3[/tex]
Now, substitute the given value of y into the equation
x = 13 + 5y
[tex]x = 13 + 5 \times ( - 3)[/tex]
Solve the equation for x
Multiply the numbers
[tex] = 13 - 15[/tex]
Calculate the difference
[tex] = - 2[/tex]
The possible solution of the system is the ordered pair
( x , y )
( x , y ) = ( - 2 , - 3 )
-----------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex] - 2 - 5 \times ( - 3) = 15[/tex]
[tex]4 \times ( - 2) - 3 \times ( - 3) = 1[/tex]
Simplify the equalities
[tex]13 = 13[/tex]
[tex]1 = 1[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( - 2 , - 3 )Hope this helps..
Best regards!!
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. The probability is . (Round to three decimal places as needed.) b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters. The probability is . (Round to three decimal places as needed.) c. What do the preceding results suggest?
Answer:
Hello your questions is incomplete attached below is the missing part of the question
answer : A ) 0.647 , (B) 0.353, (C) students are more likely to spend the money than to have kept it
Step-by-step explanation:
from the attached table below
Given data :
Total number of students = Number of students who spent money + number of students who kept money
Total number of students = (33+13 ) + (18 + 27 ) = 91
p(Number of students given four quarters) = (33 +18 ) / 91 = 51/91
p( number of students who spent money ) = ( 33 +13 ) / 91 = 46/91
p( number of students who saved money ) = (18 +27 ) / 91 = 45 /91
p( number of students who spent money and given four quarters ) = 33/91
p( number of students who saved money and given four quarters ) = 18/91
A) The probability of randomly selecting a student who spent the money and also given four quarters
= p ( 33/91 | 51/91 )
= 33/91 * 91/51
= 33/51 = 0.647
B ) The probability of randomly selecting a student who kept the money and given that the student was given four quarters
= p ( 18/91 | 51/91 )
= 18/91 * 91/51
= 18 /51 = 0.353
C) students are more likely to spend the money than to have kept it
81^x^2=27^x solve for x
Step-by-step explanation:
81^x² = 27^x
(3^4)^x² = (3^3)^x
3^(4x²) = 3^(3x)
4x² = 3x
4x² − 3x = 0
x (4x − 3) = 0
x = 0 or ¾
Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For which of the following equations is the standard deviation of the y-values corresponding to all the x-values the greatest?
a) y = x/3
b) y = x/2+40
c) y = x
d) y = 2x + 50
e) y = 3x − 20
Answer:
Option E
Step-by-step explanation:
y = x /3
let x = 1, 2, 3
y = 0.333, 0.667, 1
y = x/2 + 40
let x = 1, 2, 3
y = 40.5, 41, 41.5
y = x
let x = 1, 2, 3
y = 1, 2, 3
y = 2x + 50
let x = 1, 2, 3
y = 52, 54, 56
y = 3x - 20
let x = 1, 2, 3
y = -17, -14, -11
The standard deviation is the spread of data, the data that is most spread is option E.
A line passes through the points (6, 10) and (4, -2). What is the equation of the line
Answer:
y = 6x - 26
Step-by-step explanation:
1. find slope: (y₂ - y₁) / (x₂ - x₁)
(-2 - 10) / (4 - 6) = -12 / -2 = 6
basic equation: y = 6x + b
2. plug in (x,y) value using one set of coordinates.
10 = 6(6) + b
10 = 36 + b
b = 10 - 36
b = -26
3. plug b in to find full equation.
y = 6x -26
Answer:
y = -1/6 x + 11
Step-by-step explanation:
In order to write an equation of a line you need slope (m) and y-intercept (b) or where the graph grosses the y- axis. since you are given two points (6, 10) and (4, -2). Slope when given two points is (y - y) / (x - x)
so (-2 - 10) / (6 - 4) = 6 / - 1 =- 6
use the equation y = mx + b and substitute either point (6, 10) or (4, -2) as a replacement for x and y respectively. (I chose (6, 10) because they are positive numbers. Substituting x = 6 and y = 10 and m = -6 into y = mx + b
10 = -6(6) + b
10 = -36 + b
b = 46 (add -36 to both sides)
so our equation: y = -6x + 46 :-)
Question 5 of 13, Step 1 of 1
3/15
Correct
2
The Chandlers are moving across the country. Mr. Chandler leaves 2.5 hours before Mrs. Chandler. If he averages 75 mph and she averages 85 mph, how many hours
will it take Mrs. Chandler to catch up to Mr. Chandler?
Answer:
It will take Mrs Chandler 18 hours 45 minutes or 18.75 hours to catch up Mr Chandler
Step-by-step explanation:
What we want to know here is that at how many hours will they have traveled same distance.
Let the total time taken by Mrs Chandler to catch up be x hours
Since Mr Chandler left 2.5 hours earlier , then the total time taken by him would be x + 2.5 hours
Now, we know that distance = speed * time
Since it’s same distance covered;
For Mr Chandler, his distance is calculated as 75(x + 2.5)
For Mrs Chandler, her distance is calculated as 85x
We equate both since they are equal;
75(x + 2.5) = 85x
75x + 187.5 = 85x
85x -75x = 187.5
10x = 187.5
x = 18.75 hours or 18 hours 45 minutes
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plan for production of the primer. Let x be the number of cans of paint produced during each production run, and let y be the number of production runs. Then the setup cost is 500y and the storage cost is 2.c, so the total storage and setup cost is C = 500y +2.c. Furthermore, .cy = 16,000 to account for the annual demand. How many times a year should the company produce this primer in order to minimize the total storage and setup costs?
A. The company should have 6 production runs each year.
B. The company should have 8 production runs each year.
C. The company should have 10 production runs each year.
D. The company should have 11 production runs each year.
Answer:
B. The company should have 8 production runs each year.
Step-by-step explanation:
From the given information:
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer
It costs $4 to store one can of paint for one year
$500 to set up the plan for production of the primer
Let x be the number of cans of paint produced during each production run
Let y be the number of production runs.
If the total storage and setup cost is C = 500y + 2c
and cy = 16000
Then c = 16000/y
From;
C = 500y + 2c
Replacing c with 16000/y, we have;
C = 500y + 2(16000/y)
C = 500y + 32000/y
in order to minimize the total storage and setup costs [tex]C_{min} = C[/tex]
Therefore [tex]\dfrac{dc}{dy}=0[/tex]
⇒ 500 - 32000/y² =0
y² = 32000/500
y² = 320/5
y² = 64
y = (√64)
y = 8
Therefore; The company should have 8 production runs each year in order to minimize the total storage and setup costs
I BEG OF YOU HELPPPP Twice last month, Judy Carter rented a car in Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 440 miles, and the rental cost her $286. On her second business trip she drove 190 miles in 3 days, and paid $165.50 for the rental. Find the daily fee and the mileage charge.
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
Step-by-step explanation:
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate the rate that the water is draining out of the pool. (Hint: remember this line is sloping down to the right) (3 marks) Rate=0-45000/70-20 Rate = (0 - 45000) / 70-20 Rate = -45000 / 50 Rate=-900/minute b) Calculate how much water was in the pool initially (at time 0). (2 marks)
Answer:
there were 63,000L of water initially in the pool
Step-by-step explanation:
do 900L times the first 20 minutes to find out how much water was drained during the first 20 minutes and you get 18,000L drained
then, add 18,000L plus the rest of the 45,000L of water drained from the pool to get 63,000L of water intially in the pool
find the slope for (-4,-2)(-3,-6)
Answer:
The slope is -4.
Step-by-step explanation:
The values -2 and -6 are 4 values apart.
The values -4 and -3 are 1 value apart.
Since the second coordinate is lower than the first one, the slope of this is negative.
4 / 1 = 1
Negating 1 gets us -1.
Hope this helped!
Answer:
[tex] \frac{y}{x} = \frac{ - 4}{1} = - 4[/tex]
Step-by-step explanation:
[tex]x = ( - 3) - ( - 4) = 1[/tex]
[tex]y = ( - 6) - ( - 2) = - 4[/tex]