The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.
For maximum r, r'(x) = 0
It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]
= [tex]10-0.5x=0[/tex]
[tex]x=\frac{10}{0.05}[/tex]
x= 200
Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]
Solving it we get,
r(200) = 1000
Hence, maximum revenue is $1000.
Please help!!!! I just need help with part c.
A pumpkin is being grown for a contest at the state fair. Its growth can be modeled by the equation P=25(1.56)^n, where P is the weight of the pumpkin in pounds and n is the number of weeks the pumpkin has been growing.
a. By what percentage does the pumpkin grow every week?
(my answer) The pumpkin grows 156% percent every week.
b. After how many weeks will the pumpkin be 80 pounds?
(my answer)The pumpkin will be 80 pounds after 3 weeks.
c. What if the growth percentage changed to 32, after how many weeks will the pumpkin be 80 pounds?
A) the growth is 56% per week. The 1.56 is multiplying the weight of the pumpkin now by the 56% to get the total weight after the 56% increase.
B) Replace P with 80 and solve for n:
80 = 25(1.56)^n
Divide each side by 25:
80/25 = 1.56^n / 25
3.2 = 1.56^n
Take the natural logarithm of both sides:
ln(3.2) = ln(1.56^n)
Remove the exponent:
ln(3.2) = n(ln(1.56)
Divide both sides by ln(1.56)
n = ln(3.2) / ln(1.56)
n = 2.6 weeks, round to 3 weeks.
C) Change 1.56 to 1.32 and redo the same calculation from B.
80 = 25(1.32)^n
80/25 = 1.32^n /25
3.2 = 1.32^n
ln(3.2) = ln(1.32^n)
ln(3.2) = n(ln(1.32)
n = ln(3.2) / ln(132)
n = 4.2, round to 4 weeks.
Graph the following lines and using the graph determine several values of x for which the graph is positive (negative):
y = -0.5x - 2
y is positive when BLANK
x is positive when BLANK
Answer:
Step-by-step explanation:
Given equation is,
y=-0.5x-2
when x=-2 , y=-0.5(-2)-2=1-2=-1
when x=0 , y=-0.5(0)-2=0-2=-2
when x=2 , y=-0.5(2)-2=-1-2=-3
So, we get the points (-2,-1) , (0,-2) , (2,-3)
Now, using the points on the graph and adding them, we will get the graph of given line.
Please check image for the graph.
Now for the second part- we have to find values of x , for which y is positive.
That means, y will be above the x-axis.
From the graph we can see that- when x<-4,
then the graph is above the x-axis.
So, for all values of x, which are less than -4,
we will get the positive graph.
Which of the following are ordered pairs for the equation y = -4x + 5?
(0,5) (1,1) (-1,9)
(0,5) (-1,-1) (-1,-9)
(0,5) (1,-1) (-1,9)
(0,5) (-1,1) (-1,-9)
The first one is your answer because if you plug into the cal it shows the x and y table and it shows that the first one is correct.
The correct ordered pairs for the equation y = -4x + 5 are (-1, 9) and (1, 1).
Explanation:The correct ordered pairs for the equation y = -4x + 5 are (-1, 9) and (1, 1).
To determine if an ordered pair is a solution to the equation, substitute the x and y values into the equation and check if the equation holds true. For example, for the ordered pair (-1, 9):
y = -4x + 5
9 = -4(-1) + 5
9 = 4 + 5
9 = 9
Since the equation is true, (-1, 9) is a solution to the equation.
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What does 1/4 of a can of coffee cost if 4 cans of coffee cost $1.60
We know that 4 cans of coffee cost $1.60. So, if we divide that number by 4, we get
[tex] 4\text{ cans of coffee} = 1.60 \iff \dfrac{4\text{ cans of coffee}}{4} = \dfrac{1.60}{4} \iff 1 \text{ can of coffee} = 0.4 [/tex]
Now we can simply repeat this process again: if we divide both sides by 4, we get
[tex] 1 \text{ can of coffee} = 0.4 \iff \dfrac{1 \text{ can of coffee}}{4} = \dfrac{0.4}{4} \iff \dfrac{1}{4}\text{ cans of coffee} = 0.1 [/tex]
joe has twelve more coins than brenda. together they have 64 coins. how many coins does each have
Which equation is an example of direct variation?
The equation of a direct variation: y = kx
Therefore your answer is [tex]D)\ y=\dfrac{2}{3}x[/tex]
Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 200 foreign coins.
x + 4x = 150
5x = 150
x = 30
John has x = 30 coins
Mary has 4x = 4*30 = 120 coins.Let the number of coins John has be "x".
The the number of coins Mary has is "4x"
John has 40 coin and Mary has 160 coins because 40 times 4 equals 160 and 160 plus 40 equals 200 so Mary has 160 and John has 40
I'd really appreciate it if anyone could help! :) I'll give Brainliest!
The graph of a function is shown below these choices.
Select ALL the statements that correctly describe this function.
The equation that represents this function is f(x)=−7x+1.
The equation that represents this function is f(x)=x−7.
The range of this function is increasing as the domain increases.
The range of this function is decreasing as the domain increases.
Answer:
The equation that represents this function is f(x)=x−7.The range of this function is increasing as the domain increases.Step-by-step explanation:
The line has a slope (m) of 1 and a y-intercept (b) of -7. Thus the equation in slope-intercept form is
... y = mx + b
... y = x - 7
For a linear function such as this, the size of the domain is equal to the size of the range (because the slope is 1). Thus when one increases, so does the other.
_____
Comments on the problem
It appears the first answer choice is a result of mixing up slope and intercept in the equation of the line. A slope (x-coefficient) of -7 is a pretty steep line going downward from left to right. The graph does not have that characteristic.
It is a bit unusual to talk about domain and range increasing or decreasing. The domain is the region over which the function is defined, so is generally fixed. The range is the corresponding set of values of the function, fixed once the domain is determined. Here, since the function is linear, if one were to define it over a larger region, the range of values produced by the function would also get larger.
Jake bought 4.08 pounds of apples he knows that 1.19 pounds are gala apples and the rest are cameo apples how many pounds of cameo apples did he buy?
Answer: He bought 2.89 pounds of cameo apples.
Step-by-step explanation:
Since we have given that
Total number of pounds of apples he bought = 4.08
Number of gala apples = 1.19 pounds
So, the rest are cameo apples.
As we know to get the remaining value we always use the subtraction operation,
Now,
[tex]4.08-1.19=2.89[/tex]
So, 2089 pounds of apple are cameo apples.
Final answer:
To find out how many pounds of cameo apples Jake bought, subtract the pounds of gala apples (1.19 pounds) from the total pounds of apples (4.08 pounds), resulting in 2.89 pounds of cameo apples.
Explanation:
Jake bought 4.08 pounds of apples. He knows that 1.19 pounds are gala apples and needs to find out how many pounds of cameo apples he bought. To find the weight of the cameo apples, we subtract the weight of the gala apples from the total weight of apples purchased.
So, the calculation will be as follows:
Total weight of apples - Weight of gala apples = Weight of cameo apples.
4.08 pounds - 1.19 pounds = 2.89 pounds.
Thus, Jake bought 2.89 pounds of cameo apples.
Ari walked 2 3/4 miles at a constant speed of 2 1/2 miles per hour. Beth walked 1 3/4 miles at a constant speed of 1 1/4 miles per hour. Cindy walked for 1 hour and 21 minutes at a constant speed of 1 1/8 miles per hour. List the three people in order of the times they spent walking from least to greatest.
The order of their time spent from least to greatest is; Ari, Cindy, Bety
What is the time spent for the distance covered?
Distance covered by ari = 2³/₄ miles
Speed of ari = 2¹/₂ miles per hour
Formula for time is;
time = distance/speed
Thus;
Time spent by ari = 2³/₄/2¹/₂
Time spent by ari = 1.1 hours
Distance covered by beth = 1³/₄ miles
Speed of beth = 1¹/₄ miles per hour
Formula for time is;
time = distance/speed
Thus;
Time spent by beth = 1³/₄/1¹/₄
Time spent by beth = 1.4 hours
Distance covered by cindy = 1 hour 21 minutes = 1⁷/₂₀ miles
Speed of cindy = 1¹/₈ miles per hour
Formula for time is;
time = distance/speed
Thus;
Time spent by cindy = 1⁷/₂₀/1¹/₈
Time spent by cindy = 1.35 hours
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long division x^3 - 6x^2 + 13x -12 over x - 3
Complete solution is given in attachment below.
Autumn is paying for college in monthly installments. The college requests that a $1000 down payment be made. Autumn will then continue to pay $500 per month to pay for her tuition. a) write an equation that represents Autumn’s payment to her college. b) after 4 months, how much will she have paid?
a. 500 X 12 =
b. 20,000
made a mistake when I last posted. can someone help me .
35 Centimeters Less than Triple the width:
190 cm. The Perimeter of the box:
W = Width of Box
L = Length of Box
Length = 3c - 35
2W + 2L = 190
Just solve to get your answer
Hope that helps!!!! : )
I need an expression for the area of the outer square, thanks
The area of a square is calculated suing the formula x^2, where x is a side length of the square. This is just like length times width because a square has equal side lengths.
Take the left side and add the two lengths together because they form one side length of the square. A side length of the square is x + 4.
To find the area using the side length x + 4, you would square the side length. Your answer is (x + 4)^2.
PLEASE HELP with vocabulary
This means to move a graph vertically and/or horizontally around the coordinate plane.
It’s NOT Shifting Or just translation by itself.
It’s 20 letters
Sweet t has 2 orange picks for every 5 green if there 21 picks in all ow many orange picks are there
I think the answer would be 6?
Which number is not divisible by either of the numbers 3 and 5?
A.
5000
B.
2374
C.
1203
D.
2505
Solve the equation.
9x2 + 4 = 0
Answer: [tex]x = \frac{2}{3}i , -\frac{2}{3}i[/tex]
Step-by-step explanation:
9x² + 4 = 0
-4 -4
9x² = -4
[tex]\frac{9x^{2} }{9} = \frac{-4}{9}[/tex]
x² = [tex]\frac{-4}{9}[/tex]
[tex]\sqrt{x^{2} } = \sqrt{-\frac{4}{9} }[/tex]
[tex]x = +/- \frac{2}{3}i[/tex]
Can someone explain step by step how to do this? thanks. I know some but not understanding what you do with the vto the power if 3
See the attached picture for the steps:
Find the length of the side of the square.
6x-1=4x+6
subtracting 4x from each side
2x-1=6
adding 1 to each side
2x=7
divide by 2
x=7/2 or 3.5
check: 6(7/2) -1 =4(7/2)+6
21-1 =14+6
20=20 correct
The length of a side of the square can be found using the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we find the length of a side of the square to be the square root of half of the square of the hypotenuse.
Explanation:To find the length of the side of the square, we are going to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
Consider a square with a hypotenuse labeled as 's'. If we bisect this square diagonally, we form two right triangles. Since the sides of the square are equal, we can denote the other two sides of the right triangle as 'D' and 'L'. So, the Pythagorean theorem becomes: D² + D² = s², since D = L. Solving this, we find that s² = 2D².
Therefore, the length of a side of the square 'D'= √(s²/2).
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In how many ways can the 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook?
Solution:
This problem is a permutation because the order matters here. This means that choosing A as King, B as Knight, C as Bishop and D as Rook results in a different arrangement from B as King, A as Knight, D as Bishop and C as Rook. We would count them both because in the first case A is King, but in the second case A is Knight.
Therefore, the possible number of ways are given below:
[tex]19P4=\frac{19!}{(19-4)!} =\frac{19 \times 18 \times 17 \times 16 \times 15!}{15!} =19 \times 18 \times 17 \times 16 =93024[/tex]
Hence there will be 93024 ways 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.
There are 19 members in the chess club, and they can fill the offices of King, Knight, Bishop, and Rook in 38760 ways.
In how many ways can the 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.
To determine the number of ways to fill the offices, we use the concept of permutations. Since each office must be filled by a different member, the number of ways is calculated as 19P4 = 19! / (19-4)! = 38760 ways.
what is 168 cm in feet
5.51181 in feet. Hope this helps
71.120-2.359 what is that answer please help m.
We could use the standard form of subtraction.
We put 71.120 on top and we put 2.359 at the bottom.
Then, we subtract the thousandths place. It involves a carry-over.
Then, we subtract and the answer is:
68.761
The subtraction of 71.120 and 2.359 equals 68.761.
Explanation:This question is asking for the subtraction of two decimal numbers, the first being 71.120 and the second being 2.359. To do this, you would stack the numbers on top of each other, aligning the decimal points, and subtract as you would with whole numbers.
So, your subtraction would look like this:
71.120
So, 71.120-2.359 equals 68.761.
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help cant do it? It's trigonometry
I think the answer to your problem is 69
The value of CD = AB = 6.5 cm. Angle CDA = 0 degrees.
To find the value of CD, we can use the fact that the opposite sides of a Trapezium properties are parallel and equal in length.
So, CD = AB = 6.5 cm.
Next, to find the size of angle CDA, we can use the fact that angles formed between perpendicular lines and the base of a trapezium are complementary.
Since BM is perpendicular to AD, angle CDA + angle BDM = 90 degrees.
We are given that angle BDM is 90 degrees, so angle CDA must be 0 degrees.
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The probable question may be:
ABCD is a trapezium
B draws a perpendicular line on segment AD as BM is 90 degree
AB=6.5 cm, AD=23 cm, BC=9 cm , BM is 6 cm
Find the value of CD. Work out the size of angle CDA
Use compatible numbers to find two estimates that the quotient is between 1045÷2
Answer: The two estimates of quotient is 522 and 523 .
Step-by-step explanation:
Compatible numbers are numbers which are close in value to the given numbers, and make it easy to calculate the answer for any given arithmetic problem .
To find two estimates that the quotient is between in 1045÷2
We now that 1045 is greater than 1044 and less than 1046 i.e.1044<1045<1046
Dividing 2 from all sides ,we get
1044÷2<1045÷2<1046÷2
⇒522<1045÷2<523
As the quotient of 1045÷2 is lying between 522 and 523.
Therefore, the two estimates of quotient is 522 and 523
To estimate the quotient of 1045 divided by 2 using compatible numbers, one can use 1040 (which gives an estimate of 520) and 1050 (which gives an estimate of 525) as they are easily divisible by 2. Hence, the quotient should fall between 520 and 525.
The student is asked to find two estimates that the quotient 1045 ÷ 2 falls between using compatible numbers. To estimate, we look for numbers that are easy to divide. Compatible numbers to 1045 that are close to it and divisible by 2 could be 1040 and 1050. So our two estimates for 1045 ÷ 2 are:
1040 ÷ 2 = 5201050 ÷ 2 = 525Therefore, the quotient of 1045 ÷ 2 should be between 520 and 525.
Which of the following is the correct expansion of (y + 2)(2y2 + y + 4)?
y3 + 5y2 + 6y + 4
2y3 + 10y2 + 5y + 4
y3 + 6y2 + 5y + 8
2y3 + 5y2 + 6y + 8
To expand the expression (y + 2)(2y^2 + y + 4), use the distributive property and multiply each term. Combine like terms to simplify the expression.
Explanation:The given expression is (y + 2)(2y^2 + y + 4). To expand this expression, we can use the distributive property. We multiply each term in the first expression (y + 2) by each term in the second expression (2y^2 + y + 4).
Using the distributive property, we get:
(y + 2)(2y^2 + y + 4) = y * 2y^2 + y * y + y * 4 + 2 * 2y^2 + 2 * y + 2 * 4
Simplifying this expression, we get:
2y^3 + y^2 + 4y + 4y^2 + 2y + 8
Combining like terms, we have:
2y^3 + 5y^2 + 6y + 8
Solve for d.
0.5(7d+4)=7-1.5d0.5(7d+4)=7−1.5d
ANSWER
[tex]d=1[/tex]EXPLANATION
We want to solve
[tex]0.5(7d+4)=7-1.5d[/tex]
Let us first multiply through by [tex]10[/tex] to clear the decimal.
[tex]10\times 0.5(7d+4)=7\times 10 -1.5d\times 10[/tex]
This implies that;
[tex]5(7d+4)=70 -15d[/tex]
We now expand to obtain;
[tex]35d+20=70 -15d[/tex]
We group like terms to obtain;
[tex]35d+15d=70 -20[/tex]
[tex]50d=50[/tex]
Dividing through by 50 gives;
[tex]d=1[/tex]
Answer:
The value of the equation for d is 1.
Step-by-step explanation:
Consider the provide equation.
[tex]0.5(7d+4)=7-1.5d[/tex]
We need to solve the equation for d.
Open the parentheses.
[tex]3.5d+2=7-1.5d[/tex]
Add 1.5d both sides.
[tex]3.5d+1.5d+2=7-1.5d+1.5d[/tex]
[tex]5d+2=7[/tex]
Subtract 2 from both sides.
[tex]5d+2-2=7-2[/tex]
[tex]5d=5[/tex]
Divide both the sides by 5.
[tex]d=1[/tex]
Hence, the value of the equation for d is 1.
Bill wants to put a large mural on a wall that is 9 1/3 feet long and 8 1/8 feet wide. Find the area of the wall. If the mural is 100 sq feet, will it fit on the wall?
The equation of a line is 4x−3y=−24.
What is the x-intercept of the line?
x-intercept → y = 0
substitute to 4x - 3y = -24:
4x - 3(0) = -24
4x - 0 = -24
4x = -24 |divide both sides by 4
x = -6
Select the equation that represents a line with a slope of 3 and that contains the point (-4,2).
A) y - 2 = 3(x+4)
B) y+2=3(x-4)
C) x-4=3(y+4)
D)x-4=3(y+2)
Answer:
A) y - 2 = 3(x+4)
Step-by-step explanation:
Given that the equation is a line with slope =m=3 and
a point on it (x1,y1) = (-4,2)
Any line having slope m and passing through (x1,y1) has equation in point slope form as
y-y1 = m(x-x1)
We are given here x1 =-4, y1 =2 and m =3
y-y1 = y-2 and x-x1 = x-(-4) = x+4
So equation is y-2 = 3(x+4)
Verify:
The line is y = 3x+12+2 = 3x+14
Hence slope =3 is verified
Substitute the point x =-4 and y =2
2 =3(-4)+14 = 2 is true
Thus verified
Answer:
A is correct option. Equation of line: y-2=3(x+4)
Step-by-step explanation:
Slope of line is 3 and passing point (-4,2).
If slope and passing point given then we have an equation of line
[tex]y-y_1=m(x-x_1)[/tex]
where,
[tex](x_1,y_1)\rightarrow (-4,2)[/tex]
Slope (m)=3
Equation of line:
y-2=3(x+4)
This equation match with option A
Thus. option A is correct.