There are 49 ways to arrange the letters (if they aren't words)
A farmer finds that if she plants 50 trees per acre, each tree will yield 80 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?
Answer:
28
Step-by-step explanation:
From the given information:
Let x be the number of trees.
F(x) = (50 +x) (20 - 3x)
F(x) = 1000 - 150x + 20x - 3x²)
F(x) = -3x² - 130x + 1000
Differentiating F(x) with respect to x;
[tex]F'(x) = \dfrac{d}{dx}( -3x^2- 130x + 1000)[/tex]
[tex]F'(x) = ( -3(2x)- 130(1) +0)[/tex]
F'(x) = -6x -130
Now; we set F'(x) to be equal to zero to determine the critical value;
-6x - 130 = 0
x = - 130/6
Differentiating F''(x) with respect to x
[tex]F''(x) = \dfrac{d}{dx}( -6x- 130)[/tex]
[tex]F''(x) = ( -6(1))[/tex]
F''(x) = -6 (<0)
Thus; by the second derivative, the revenue function F(x) is maximum when x = -130/6
Therefore, the number of trees she should plant per acre to maximize her harvest is:
50 + x = 50 - 130/6
= 85/3
[tex]\simeq[/tex] 28
Therefore, the number of trees per acre to maximize the harvest is 28
Let h represent the number of hours it takes to fix a computer The expression shows the cost a cemputer repair center charges its customers How much does a 3.5 - hour repair cost?
Answer:
is this the full problem? you would just plug in 3.5 for h, but i dont see the equation
Step-by-step explanation:
Determine if the product CA is defined. If the product is defined, state its dimensions. Do not calculate the product.
Answer:
The product can be calculated.
The resulting matrix will have 3 rows and 3 columns.
Step-by-step explanation:
Matrix multiplication
To find the product of two matrices is only possible when the number of columns of the first matrix is equal to the number of rows of the second matrix.
If X is the first matrix with dimensions (n x m) and Y is the second matrix with dimensions (m x p), the product XY is possible and the dimensions of the resulting matrix are (n x p).
Matrix A has two rows and three columns (2x3)
Matric C has three rows and two columns (3x2)
If we wanted to calculate the product CA, the number of columns of C must be equal to the number of rows of A.
Since both numbers are 2, the product can be calculated.
The resulting matrix will have 3 rows and 3 columns.
Which expression is equivalent to this polynomial expression?
(2x^5 + 3y^4)(-4x^2 + 9y^4)
Answer:
A. -8x⁷ + 18x⁵y⁵ - 12x²y⁴ + 27y⁸
Step-by-step explanation:
Given:
(2x⁵ + 3y⁴)(-4x² + 9y⁴)
Required:
Find an equivalent polynomial
Solution:
(2x⁵ + 3y⁴)(-4x² + 9y⁴)
Using distributive property of multiplication
2x⁵(-4x² + 9y⁴) + 3y⁴(-4x² + 9y⁴)
-8x⁷ + 18x⁵y⁴ - 12x²y⁴ + 27y⁸
There are no like terms to add or combine, therefore:
(2x⁵ + 3y⁴)(-4x² + 9y⁴) = -8x⁷ + 18x⁵y⁵ - 12x²y⁴ + 27y⁸
Answer:
-8x^7 + 18x^5y^5 - 12x^2y^4 + 27y^8
Step-by-step explanation:
I took the test
find the missing value for each of the following 3 questions
1. 5% of 60 is _____
2. 40% of 500 is _____
3. 75% of 60 is ______
Answer:
1. 3
2. 200
3. 45
Step-by-step explanation:
The slope is the same as the unit rate and constant of a proportionality in a _______.
A. Prortional relationship
B. Slope
C. Rise
D. x2- x1
E. Run
F.y2 - y1
Answer:
I think the answer is B: Slope
Step-by-step explanation:
On a graph, proportional relationships are straight lines that extend through the origin. The relative steepness of the line is called slope; the slope of a graph is the same as the constant of proportionality of the equation.
Hope this helped, Have a Wonderful Day!!
The slope is the same as the unit rate and constant of proportionality in a slope. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The slope is the same as the unit rate and constant of proportionality in a slope. Then the correct option is B.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ5
Find the product. Enter your final answer as a simplified fraction.
1/4•4/5•5/6=
Answer:
I am sorry if I'm wrong, but I got 600 or 36000/60
Step-by-step explanation:
First I looked for the least common denominator,(LCM) it was 60. Then I multiplied the numerator by the number that was multiplied by the denominator to find the new numerator for each fraction.(Example: The denominator was 60, so I looked for what 60 divided by four was, because that was the denominator. It ended up being 15. now I multiplied the numerator, which was 1 by 15 to create the new numerator. Then I did that with the other two fractions.) After all the fractions have the same denominator, you can multiply them. To multiply fractions you multiply all the numerators together and leave the denominator the same. Then I just simplified it. From 36000/60 to 600. Hope this helped :)
Find an equation of the line containing the given pair of points.
(−5,−5) and (4,4)
Answer:
y = x - 9
Step-by-step explanation:
[tex]Slope=\frac{y^{2}-y^{1} }{x^{2}-x^{1} }=\frac{4-(-5)}{4-(-5)}=\frac{9}{9}=1[/tex]
[tex]y-intercept:y-y_{1}=m(x-x_{1} ) \\y-(-5)=1(x-4)\\y+5=x-4\\[/tex]
Subtract 5 from both sides;
y = x - 9
56) A tire retailer plans to sell
$100,000 worth of tires in
January. Planned reductions are
$15,000; planned inventory for
January Ist is $300,000 and for
January 31st is $350,000. As of
January 8th, the retailer has
ordered $15,000 for January
delivery. What is the open-to-
buy for the rest of the month?
Answer:
/
Step-by-step explanation:
A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Find the probability of getting exactly two heads out of three tosses.
Answer:
If a fair coin is tossed three times, sample = 2^3 = 8 (hhh, hht, hth, thh, htt, tht, tth, ttt) where h=head and t=tail.
Probability of getting one:
Outcomes with one head (h) = 3
P(1 h) = 3/8 = 0.375
Step-by-step explanation:
Answer:
2/8
Step-by-step explanation:
2/8 Because there is two answers that have two H's on them Ex: HHT, THH
Find the slope of the line passing through each pair of points. (9,4) and (5,-3).
Answer:
[tex]m=\frac{7}{4}[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDASSlope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
(9, 4)
(5, -3)
Step 2: Find slope m
Substitute: [tex]m=\frac{-3-4}{5-9}[/tex]Subtract: [tex]m=\frac{-7}{-4}[/tex]Simplify: [tex]m=\frac{7}{4}[/tex]2 What is the sum of 5x2 + 3x - 7 and 12x + 12? A. 5x2 + 15x + 5 B. 5x2 + 15x + 19 C. 17x2 + 3x + 5 D, 17x2 + 15x + 12 4 E. 20x" + 5
Question The average number of acres burned by forest and range fires in a county is 4,500 acres per year, with a standard deviation of 780 acres. The distribution of the number of acres burned is normal. What is the probability that between 3,000 and 4,800 acres will be burned in any given year? Round your answer to four decimal places. Provide your answer below:
Answer:
The probability that between 3,000 and 4,800 acres will be burned in any given year is 0.6206
Step-by-step explanation:
Given
Mean = μ = 4500 acres
SD = σ = 780 Acres
Two data points between which the probability has to be calculated are:
3000 and 4800
x1 = 3000
x2 = 4800
z-score will be found for both data points
z-score is given by the formula
[tex]z = \frac{x-mean}{SD}[/tex]
The z-scores are:
[tex]z_1 = \frac{x_1-mean}{SD} = \frac{3000-4500}{780} = \frac{-1500}{780} = -1.92\\z_2 = \frac{x_2-mean}{SD} = \frac{4800-4500}{780} = \frac{300}{780} = 0.3846[/tex]
Now we have to find probabilities for both z-scores using the z-score table
[tex]P(z_1<-1.92) =0.02743\\P(z_2<0.3846)= 0.6480[/tex]
Now for the probability between both values
[tex]P(-1.92<z<0.3846) = P(z_2) - P(z_1) = 0.6480-0.02743 = 0.62057[/tex]
Rounding off to four decimal places
0.6206
Hence,
The probability that between 3,000 and 4,800 acres will be burned in any given year is 0.6206
Does this graph represent a function? Why or why not?
A. No, because it fails the vertical line test.
B. No, because it is not a curve.
C. Yes, because it passes the vertical line test.
D. Yes, because it has two straight lines.
Nancy is checking to determine if the expressions x + 4 + x and 6 + 2 x minus 2 are equivalent. When x = 3, she correctly finds that both expressions have a value of 10. When x = 5, she correctly evaluates the first expression to find that x + 4 + x =14. What is the value of the second expression when x = 5, and are the two expressions equivalent? The value of the second expression is 8, so the expressions are not equivalent. The value of the second expression is 14, so the expressions are equivalent. The value of the second expression is 16, so the expressions are equivalent. The value of the second expression is 18, so the expressions are not equivalent.
Answer:
The value of the 2nd expression is 14, so the expressions are equivalent.
Step-by-step explanation:
6 + 2x - 2
6 + 2(5) - 2
6 + (10) - 2
16 - 2
14
Answer:
I believe is The value of the second expression is 14, so the expressions are equivalent.
Step-by-step explanation:
I took the test and got it right.
Find the volume of the cylinder 9 cm and 23 cm 
Complete the following statement:
12 orders in 2 days =
orders per day.???
Answer:
6 orders per day.
Step-by-step explanation:
12 divided by 2 is 6.
This means that in one day they can pack 6 orders.
Answer:
12 orders in 2 days = 6 orders per day
Step-by-step explanation:
In two days, 12 orders were completed. To find the amount of orders per day, we divide the number of orders by the number of days.
12÷2=6
Therefore, 6 orders per day.
PLEASE HURRY, ILL GIVE BRAINLIEST
A football player kicks a ball with a force of 50 N. Find the impulse on the ball if his foot stays in contact with the football for 0.01 second.
Answer:
I= f.t = (50) (0.01) = (0.5) kg.m15
Step-by-step explanation:
jesus loves you and cares for you
The tank of Miriams vehicle holds 12.1 gallons of gas.The current price for gasoline is $2.80 per gallon.How much will Miriam pay to full her tank
Answer:
$33.88
Step-by-step explanation:
12.1*2.8 is equal to $33.88
The Los Angeles area experiences many earthquakes. In 1994, the Northridge earthquake measured 6.7 on the Richter scale. In 2014, Los Angeles experienced an earthquake that measured 5.1 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.
Answer:
[tex]I_1=40I_2[/tex]
Step-by-step explanation:
[tex]M_1[/tex] = Magnitude of 1994 earthquake = 6.7
[tex]M_2[/tex] = Magnitude of 2014 earthquake = 5.1
[tex]I_1[/tex] = Intensity of 1994 earthquake
[tex]I_2[/tex] = Intensity of 2014 earthquake
[tex]I_0[/tex] = Zero-level earthquake the same distance from the epicenter = 0.001 mm
Magnitude is given by
[tex]M_1=\log(\dfrac{I_1}{I_0})\\\Rightarrow I_010^{M_1}=I_1\\\Rightarrow I_1=I_010^{6.7}[/tex]
[tex]M_2=\log(\dfrac{I_2}{I_0})\\\Rightarrow I_010^{M_2}=I_2\\\Rightarrow I_2=I_010^{5.1}[/tex]
Dividing the above intensities with each other we get
[tex]\dfrac{I_1}{I_2}=\dfrac{I_010^{6.7}}{I_010^{5.1}}\\\Rightarrow \dfrac{I_1}{I_2}=39.81\approx 40\\\Rightarrow I_1=40I_2[/tex]
The intensity of the earthquake in 1994 was 40 times stronger than the earthquake in 2014.
The sum of the two numbers is 37. The smaller number is 21 less than the larger number. What are the numbers?
Ashton is depositing money into a checking account. After 3 months there is $120 in the account. After 6 months, there is $240 in the account. Determine the constant rate of change of the account.
The constant rate of change of the account is $40 or Increasing by $40 per month.
Step-by-step explanation:
Consider the provided information.
Joanne is depositing money into a bank account. After 3 months there is $120 in the account. After 6 months there is $240 in the account.
Rate of change is known as how one quantity change in relation to other.
The rate of change can be calculated as:
y2-y1/x2-x1
Now use the above formula to calculated the rate of change.
240 - 120/6-3
120/3
40
Hence, the constant rate of change of the account is $40 or Increasing by $40 per month.
2p(9p − 1) pls help will give brainiest
Answer:
18p^2-2p
Step-by-step explanation:
You need to distribute
2*9= 18, p*p= p^2 so 18p^2
Then
2*-1= -2 and you need to include the p so -2p
In your own words how do you graph an equation that is in slope-intercept form?
Step-by-step explanation:
find the y intercept then graph using your slope
Name the values of the 5s in 5,500
Answer:
5 thousand and 5 hundred.
Step-by-step explanation:
Answer:
uno dos tres
Step-by-step explanation:
HELPPPPPP !!! I seriously don't know what to write.
Write a paragraph describing the business venture and what kind of algebra or other calculations and formulas might help someone in that endeavor. Also include ways in which the business might operate differently with those tools than without them.
Answer:
This question was previously answered on Brainly...
Be sure to put this into your own words.
Answer: check explanation for the solution
Step-by-step explanation:
A business that offers services to people by providing many amusement and fun with gate fees
The algebraic equations to be used is the general linear equation
Y = MX + C
Where
Y = total income or money realised
M = rate or price rate
X = number of goods or services
C = flat rate or gate fees
The business can also operate differently by using exponential equation
A = P(1 + R%)^t
Where
A = profit
P = capital
R = rate
t = time
A plane flies with a speed of 600 mph. What distance will it fly
in 3 /5 hours,11/12 hours, 4/15 hours?
Answer:
3/5=360 mph 11/12=550 4/15=160
Step-by-step explanation:
Calculate the monthly payment for a $2,500 loan at 9% annual interest for two years.
Given the function f(x) = 5(x+4) − 6, solve for the inverse function when x = 19.
Answer:
5.74
Step-by-step explanation:
fx=5(x+4)-6
f(19)=5(19+4)-6
19f=5(23)-6
19f=115-6
19f=109
f=109÷19
f=5.74 or 19 14/19
Is it correct to write "80.3°"?
Answer:
Yes! Temperature degrees are just like measurements.