Answer:
The number of units that must be produced and sold to maximize the profit is 30 units
[tex]30\text{ units}[/tex]The maximum profit is;
[tex]\text{ \$900}[/tex]Explanation:
Given that the profit P(x) obtained by manufacturing and selling x units of a certain product is given by;
[tex]P(x)=60x-x^2[/tex]The maximum point is at;
[tex]P^{\prime}(x)=0[/tex]Differentiating P(x);
[tex]\begin{gathered} P^{\prime}(x)=60-2x=0 \\ 60-2x=0 \\ 2x=60 \\ x=\frac{60}{2} \\ x=30 \end{gathered}[/tex]The number of units that must be produced and sold to maximize the profit is 30 units
Substituting x into p(x);
[tex]\begin{gathered} P(30)=60(30)-30^2 \\ P(30)=900 \end{gathered}[/tex]The maximum profit is;
[tex]\text{ \$900}[/tex]please helpFind the area between the graph of f(x) = ____ and the x-axis on the interval [4, 9]. Write the exact answer. Do not round.
Recall that the area between the graphs of two functions on the interval [a,b] is:
[tex]\int ^b_a|f(x)-h(x)|dx\text{.}[/tex]Therefore, the area between f(x)=4√x and the x-axis with equation y=0, on the interval [4,9] is:
[tex]\int ^9_4|4\sqrt[]{x}-0|dx=\int ^9_4|4\sqrt[]{x}|dx\text{.}[/tex]Notice that
[tex]4\sqrt[]{x}>0,[/tex]for all x in the given interval, therefore:
[tex]\int ^9_4|4\sqrt[]{x}|dx=\int ^9_44\sqrt[]{x}dx=4\int ^9_4x^{\frac{1}{2}}dx=4(\frac{2x^{\frac{3}{2}}}{3})|^9_4=\frac{8}{3}(9^{\frac{3}{2}}-4^{\frac{3}{2}})=\frac{8}{3}(19)=\frac{152}{3}.[/tex]Answer: 152/3.
A person is running a distance rate at a constant rate. What time will they finish the race? What information would i need to be able to dolve this problem?
We know
[tex]D=RT[/tex]Where
D is the distance
R is the rate (or speed)
T is the time
We would need to know ANY 2 variables to solve for the 3rd variable.
Since, we want to know the time (T), we MUST somehow know R (rate/speed) and D (distance).
This way, we will be able to solve the problem.
Dayna deposited $3,805 into savings account that pays a simple annual interest rateof 1.2%. How much interest will she earn after 3 months? Round answer to thehundredths place. If answer does not have a hundredths place then include zeros soit does.
ANSWER
$11.42
EXPLANATION
The equation for simple interest is,
[tex]i=P\cdot r\cdot t[/tex]Where P is the deposited amount, r is the interest rate, and t is the time in years. In this case, we have to find how much is the interest after 3 months, which is 1/4 of a year, so we have:
• P = 3805
,• r = 1.2% = 0.012
,• t = 1/4 year = 0.25 year
The interest earned is,
[tex]i=3805\cdot0.012\cdot0.25=11.415\approx11.42[/tex]Hence, the interest Dayna will earn in 3 months is $11.42.
Suppose the heights of women at a college are approximately Normally distributed with a mean of 66 inches and a population standard deviation of 1.5 inches. What height is at the 35thpercentile?
Given data:
Mean: 66 in
Standard deviation: 1.5in
Find height is at the 35th percentile
Use the formula to find the z-score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]z is the z-score corresponding to an area of 0.35 in the normal curve (35th percenlite)
μ is 66in
σ is 1.5in
Find the value of x corresponding to the given percentile:
1. Use a z-table to find the z score:
z=-0.39
2. Use the formula of z score and the given data to solve x:
[tex]\begin{gathered} -0.39=\frac{x-66}{1.5} \\ \\ 1.5(-0.39)=x-66 \\ \\ -0.585=x-66 \\ \\ -0.585+66=x \\ \\ x=65.415 \end{gathered}[/tex]Then, the 35th percentile is 64.4 inchesThe time, in years, that it takes an amount of money to double when invested at a simple interest rate can be approximated by dividing 0.72 by the interest rate expressed as a decimal. Approximately how many years would it take an investment of $1000 to be worth $2000 if the money were invested at a simple interest rate of 4%?
11)
The number of years for the investment to double = 0.72/interest
From the information given,
interest = 4% = 4/100 = 0.04
Therefore,
number of years for the investment to double = 0.72/0.04 = 18
Option 5 is correct
Which of the following is more likely to happen?Entering room A and room B simultaneously.Sending an e-card to your friend on Uranus.Your height will be reduced by half.Getting a promotion in the next year.
Most likely = more probability.
ANSWER
Getting a promotion in the next year.
6x - (5x + 5) = -8-2(x+12)
We need to isolate x and find the solution of the following equation:
[tex]\begin{gathered} 6x-(5x+5)=-8-2\cdot(x+12) \\ 6x-5x-5=-8-2x-2\cdot12 \\ x-5=-8-2x-24 \\ x+2x=-32+5 \\ 3x=-27 \\ x=-\frac{27}{3} \\ x=-9 \end{gathered}[/tex]The solution is x = -9.
Find the measure of arc BC, the measure of angle A, and the measure of arc AB.
Explanation
If we have the question as
Then, we will have the measure of arc BC as 45 degrees (An arc measure is an angle the arc makes at the center of a circle)
For the measure of angle A
[tex]Measure\text{ of angle A=}\frac{1}{2}\times45^0=22.5^0(Angle\text{ at center is twice that at the center})[/tex]To get the measure of angle AB
we will have
So that
[tex]\begin{gathered} x+x+45=360 \\ 2x=360-45 \\ 2x=315 \\ x=\frac{315}{2} \\ \\ x=157.5^0 \end{gathered}[/tex]Therefore, the measure of the arc AB is 157.5 degree
How much should you invest a 4.9% simple interest in order to earn $90 interest in 10 months?$ Round to 2 decimal places
$2212.93 should be invested
Explanations:Let the amount to be invested be the principal, P.
The interest rate, r = 4.9%
r = 4.9/100
r = 0.049
Time, t = 10 months
12 months = 1 year
10 months = 10/12
t = 10/12 years
t = 0.83
The interest in the next 10 months, I = $90
Interest, I, is given by the formula:
I = P x r x t
90 = P x 0.049 x 0.83
90 = P x 0.04067
P = 90 / 0.04067
P = $2212.93
Pete Smith found in his attic a woody woodpecker watch in its original box. It had a price tag on it for $4.80. The watch was made in 1947. Pete brought the watch to an antiques dealer and sold it for $37. What was the percent of increase in price?
We know that
• The watch value was $4.80 in 1947.
,• The watch value is $37 now.
To know the percentage of increase, we just have to divide
[tex]\frac{37}{4.80}\approx7.71[/tex]Then, we multiply by 100
[tex]7.71\cdot100=771[/tex]This means the new price represents 771% of the old price, that it's an increase of 671%.The length of a rectangular fish pond is 5 feet more than its width. The area of the fish pond is 143 squarefeet. Find the dimensions of the fish pond and its perimeter.What is the length of the fish pond? (Select]What is the width of the fish pond? Select]What is the perimeter of the fish pond? (Select]
We know that the length of the rectangle is 5 feet more than the width. Let x be the width of the rectangle, then its length is x+5. This can be see in the next picture
We also know that the area of the fish pond is 143 and that the area is given by
[tex]A=wl[/tex]Plugging the values we have that
[tex]143=x(x+5)[/tex]writting the equation in standard form we have that
[tex]\begin{gathered} 143=x(x+5) \\ 143=x^2+5x \\ x^2+5x-143=0 \end{gathered}[/tex]We know that any quadratic equation can be solve by
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]using it for our equation we have
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{(5)^2-4(1)(-143)}}{2(1)} \\ =\frac{-5\pm\sqrt[]{25+572}}{2} \\ =\frac{-5\pm\sqrt[]{597}}{2} \\ \text{then} \\ x_1=\frac{-5+\sqrt[]{597}}{2}=9.72 \\ \text{and} \\ x_2=\frac{-5-\sqrt[]{597}}{2}=-14.72 \end{gathered}[/tex]As we know the quadratic equation leads to two solutions. Nevertheless the negative solution is not right in this case, since the distances have to be positive. Then x=9.72.
Once we have the value of x we can know the width a lenght
[tex]\begin{gathered} l=9.72 \\ w=14.72 \end{gathered}[/tex]And the perimeter is
[tex]\begin{gathered} P=2w+2l \\ =2(14.72)+2(9.72) \\ =48.88 \end{gathered}[/tex]The perimeter is 48.88 ft.
15) A = 3x - 5 B = -4x + 2 What's A-B? What's B-A?
A = 3x - 5 B = -4x + 2 What's A-B? What's B-A?
Part 1
A-B
substitute
(3x-5)-(-4x+2)
remove the parenthesis
3x-5+4x-2
combine like terms
7x-7Part 2
B-A
(-4x+2)-(3x-5)
remove parenthesis
-4x+2-3x+5
combine like terms
-7x+7Write a translation rule that maps Point D(7,-3) onto point (2,5w
The given point is D(7,-3).
To map point D onto the point (2,5), we have to subtract 5 units to x-coordinate, and we have to sum 8 to y-coordinate.
Therefore, the translation rule is[tex](x,y)\rightarrow(x-5,y+8)[/tex]Let's prove it
[tex](7,-3)\rightarrow(7-5,-3+8)\rightarrow(2,5)[/tex]As you can see, the rule is correct.
So, if you look at number 17 I need to know how to do the strategy so I can wright it down and study it for my test tomorrow! Will give 5 stars if you do an amazing explanation!
Question:
What is:
[tex]51+5^2.31+18^2-9.7[/tex]Solution:
Consider the following expression:
[tex]51+5^2.31+18^2-9.7[/tex]By precedence in arithmetic operations, we will first perform the powers:
[tex]51\text{ + (25)(31)+(324)-(9)(7)}[/tex]now, by precedence in arithmetic operations, we will perform the multiplications:
[tex]51\text{ +775+324-}63[/tex]now, by precedence in arithmetic operations, we will perform the sums:
[tex](51\text{ +775+324)-}63[/tex]that is:
[tex]1150-63[/tex]Finally, we perform the respective subtraction:
[tex]1083[/tex]so that, we can conclude that the correct answer is:
[tex]1083[/tex]
Hello, I have a question with my algebra homework. we started learning about finding slope on a graph. last year I did this but they gave 2 points to find it from. how do you find slope on a line when there is no labled points. I will attach the assignment so you can better understand what I need help with.Thanks,Hunter
Verify Claire says
The line 3 is not visible in the figure
which fraction is equivalent to 35/50a) 25/45b 18/20c) 7/9d) 28/40
EXPLANATION:
To know which of all is the equivalent fraction, we must try with the same number, that is, divide the numerator and denominator by the same number;
Also in the opposite case, we must multiply the numerator and denominator by the same number.
So we have the following:
first step, check each fraction:
[tex]\frac{35}{50}\text{ divide }5=\frac{7}{10}[/tex]Find the value of x in the picture below using the provided 4 answer choices.
The second choice is the correct answer
What is the image of (-4, 8) after a dilation by a scale factor of centered at the
1/4
origin?
The image of the given point (-4, 8) is (1,-2).
The coordinates of the point are (4,-8).
Point is dilated by a scale factor of k centered at the origin.
When an image is subjected to dilation:
Upon dilation, with a scale factor of k centered at the origin, then the rule of dilation is defined as:
(x , y) → (kx , ky)
Using the above rule, we get
(-4 , 8) is dilated by a scale factor of 1/4 centered at the origin
(-4, 8) → (-4 x 1/4, 8 x 1/4)
(-4, 8) → (-1, 2)
Therefore, the image of the given point (-4, 8) is (1,-2).
To learn more about 'Dilation' refer here:
https://brainly.com/question/15590282
#SPJ9
Kaitlin sang 5 songs. Every song was 7/8 minutes long.For how much time did she sing in total?Write your answer in simplest form.
If Kaitlin sag 5 songs and each was 7/8 minutes long, then we can find the product to see for how much time did she sang
[tex]5\cdot\frac{7}{8}=\frac{35}{8}[/tex]35/8 cannot be simplified.
Kaitlin sang for 35/8 minutes.
An angle has a cosine of 4/5. What will its cosecant be?
Recall that the cosine ratio is determined by adjacent side, divided by the hypotenuse of a right triangle.
Given that cosine is 4/5, the opposite side is
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2+(4)^2=(5)^2 \\ a^2+16=25 \\ a^2=25-16 \\ a^2=9 \\ \sqrt{a^2}=\sqrt{9} \\ a=3 \end{gathered}[/tex]Now that we have solved for the opposite side, recall that cosecant is determined by the equation
[tex]\csc\theta=\frac{\text{hypotenuse}}{\text{opposite}}[/tex]Substitute
hypotenuse = 5
opposite = 3
and we get
[tex]\csc\theta=\frac{5}{3}\text{ \lparen final answer\rparen}[/tex]Eight times the result of subtracting 3 from a number is equal to the number increased by 25. What is the number? Write an equation that you could use to solve this problem. engagemy
Answer:
The number is 7.
[tex]x=7[/tex]Explanation:
Let us convert the sentences to a maths equation;
Let x represent the number.
"Eight times the result of subtracting 3 from a number"
[tex]8(x-3)[/tex]"the number increased by 25"
[tex]x+25[/tex]Since they are equal to each other, we have;
[tex]8(x-3)=x+25[/tex]Let's now solve the resulting equation;
[tex]\begin{gathered} 8(x-3)=x+25 \\ 8(x)+8(-3)=x+25 \\ 8x-24=x+25 \\ \text{add 24 to both sides} \\ 8x-24+24=x+25+24 \\ 8x=x+49 \\ \text{subtract x from both sides;} \\ 8x-x=x-x+49 \\ 7x=49 \\ \text{divide both sides by 7} \\ \frac{7x}{7}=\frac{49}{7} \\ x=7 \end{gathered}[/tex]Therefore, the number is 7.
[tex]x=7[/tex]
I need help with a question
we must replace the value of D
A.-11
[tex]\begin{gathered} 2(-3(-11)-8)\le98 \\ 2(33-8)\le98 \\ 2(25)\le98 \\ 50\le98 \end{gathered}[/tex]the option is right
B. -36
[tex]\begin{gathered} 2(-3(-36)-8)\le98 \\ 2(108-8)\le98 \\ 2(100)\le98 \\ 200\le98 \end{gathered}[/tex]the option is wrong
C.-19
2()
D.-29
1. Find the equation of the line of best fit. (y=mx+b) 2. Use the graph to predict what the correct mileage for a 7-year-old car should be. 3. Using your equation in 7d, calculate the mileage for a 25-year-old car.
From the graph
The two point ( 0, 35.8514 ) and ( 51.269, 0 )
[tex]\begin{gathered} \text{Slope m = }\frac{0\text{ - 35.8514}}{51.269\text{ - 0}} \\ \\ m\text{ = }\frac{-35.8514}{51.269} \\ m\text{ = -0.69928} \\ \\ \text{Intercept b on the y-a}\xi s\text{ = 35.8514} \\ b\text{ = 35.8514} \end{gathered}[/tex]1) y = mx + b
y = -0.69928x + 35.8514
2) Mileage for 7 years
y = -0.69928 ( 7) + 35.8514
y = -4.89496 + 35.8514
y = 30.9564
Mileage for 7 years = 30.9564
3) Mileage for 25 years
y = -0.69928 ( 25) + 35.8514
y = -17.482 + 35.8514
y = 18.3694
Mileage for 25 years = 18.3694
if a plane traveled 2100 miles in 210 minutes how many mph was it going?
First, let's convert 210 minutes to hours:
[tex]210\text{ minutes}=\frac{210}{60}\text{ hours}=3.5\text{ hours}[/tex]Now, to calculate the velocity in mph, let's divide the distance in miles by the time in hours:
[tex]velocity=\frac{2100}{3.5}=600\text{ mph}[/tex]A package for perfumed soap beads is in the shape of a triangular prism with equilateral triangle as it's bases. What is the total surface area of the soap beads package
Answer
Total Surface Area of the prism = 240 cm²
Explanation
The total surface area is the sum of all the area of the faces of this prism.
The prism has two triangular faces and three rectangular faces.
Area of one triangle = ½bh
b = base of the triangle = 8 cm
h = perpendicular height of the triangle = 3 cm
Area of one triangle = ½bh
Area of one triangle = ½ (8) (3) = 12 cm²
Area of two triangles = 2 (12) = 24 cm²
Area of rectangle at the base = LW
L = length of the triangle = 12 cm
W = width of the triangle = 8 cm
Area of rectangle at the base = LW
Area of rectangle at the base = (12) (8) = 96 cm²
For the two triangles at the side of the prism, we need to find the width using pythagoras theorem
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For the triangles,
a = Half of 8 = 4 cm
b = 3
hyp = W = ?
a² + b² = (hyp)²
4² + 3² = W²
16 + 9 = W²
W² = 25
Take the square root of both sides
W = 5
Area of rectangle at the side = LW
L = length of the triangle = 12 cm
W = width of the triangle = 5 cm
Area of rectangle at the side = LW
Area of rectangle at the side = (12) (5) = 60 cm²
Area of two rectangles at the side = 2 (60) = 120 cm²
Total Surface Area of the prism = (Area of the two triangles) + (Area of the two rectangles on the side) + (Area of the rectangle at the bottom)
Area of the two triangles = 24 cm²
Area of the two rectangles on the side = 120 cm²
Area of the rectangle at the bottom = 96 cm²
Total Surface Area of the prism = (Area of the two triangles) + (Area of the two rectangles on the side) + (Area of the rectangle at the bottom)
Total Surface Area of the prism = 24 + 120 + 96 = 240 cm²
Hope this Helps!!!
PROBLEM:how many cubic meters of gas will a cubical tank that has an edge of 4 m long? Need solutionQUESTION:What is the topic all about
Given:
edge of a cube - 4 meters
Find: volume of the cube
Solution:
The formula for getting the volume of the cube is:
[tex]V=s^3[/tex]where s = the length of one side of a cube
Let's plug into the formula above the length of the side of the cube or the edge length.
[tex]V=(4m)^3[/tex]Then, solve for the volume.
[tex]V=4m\times4m\times4m[/tex][tex]V=64m^3[/tex]Therefore, the cubical tank that has an edge of 4 m long can hold 64 cubic meters of gas.
The question is all about the volume of a cube.
3. Make Sense and Persevere In the equation 0.755s - 5/8= 44, how do you combine the like terms
The equation given is:
[tex]0.755s-\frac{5}{8}=44[/tex]"Like terms" are terms whose variables are the same. The coefficient (number in front of the variable) can be different. Also, constant (single numbers) are like terms with other constants.
In the equation given,
There is one term with the variable "s" and two "constant terms".
Thus, we combine the two constant terms and leave the "s" term as is because there isn't any other like term to combine it with.
So,
We have:
[tex]\begin{gathered} 0.755s-\frac{5}{8}=44 \\ 0.755s=44+\frac{5}{8} \\ 0.755s=44\frac{5}{8} \end{gathered}[/tex]Note that we added (5/8th) to the right hand side with "44". When we change sides, we change signs.
a pyramid has a base area of 29.4 cm squared and a height of 2 cmthe volume of the pyramid is ___ cubic centimeters. do not round your answer. (image not provided)
Given:
A pyramid has a base area = b = 29.4 square cm
And a height = h = 2 cm
The volume = V =
[tex]V=\frac{1}{3}\cdot b\cdot h=\frac{1}{3}\cdot29.4\cdot2=19.6[/tex]so, the answer will be:
The volume of the pyramid is 19.6 cubic centimeters.
65091/4562Long division This this is to solve how many brownies Joshua has. Help please and thank you.
Given:
[tex]\frac{65091}{4562}[/tex]Number of Brownies= 14.27
Number of Brownies=14 (approximately)
Consider the graph of f(x) = 5 ^ x + 1 1. Explain how to find the average rate of change between x = 0 and x = 4 . What is the average rate of change ?
1. To determine the average rate of change of a function "f(x)" between the points "x = a" and "x = b" we use the following formula:
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]2. In this case, we have the following function:
[tex]f(x)=5^x+1[/tex]And we have the points:
[tex]\begin{gathered} x=0 \\ x=4 \end{gathered}[/tex]Now we determine the value of f(b) by replacing x = 4 in the function:
[tex]\begin{gathered} f(4)=5^4+1 \\ f(4)=626 \end{gathered}[/tex]Now we determine f(0):
[tex]\begin{gathered} f(0)=5^0+1 \\ f(0)=1+1=2 \end{gathered}[/tex]Replacing in the formula for the average rate of change we get:
[tex]A=\frac{626-2}{4-0}[/tex]Solving the operations:
[tex]A=\frac{624}{4}=156[/tex]Therefore, the average rate of change is 156.