The revenue function is R(x) = 1,908x - 10x^2, the cost function is C(x) = 900 + 8x + x^2, and the profit function is P(x) = -10x^2 + 1,900x - 900. The maximum profit is obtained at 9,500 units with a value of $88,855.33.
To find the revenue function, we need to multiply the price p by the quantity sold x in hundreds of units
R(x) = xp = x(1,908 - 10x) = 1,908x - 10x^2.
To find the cost function, we simply use the given formula
C(x) = 900 + 8x + x^2.
To find the profit function, we subtract the cost from the revenue
P(x) = R(x) - C(x) = (1,908x - 10x^2) - (900 + 8x + x^2) = -10x^2 + 1,900x - 900.
To find P'(x), we take the derivative of P(x):
P'(x) = -20x + 1,900.
To find the quantity that will give the maximum profit, we set P'(x) = 0 and solve for x:
-20x + 1,900 = 0
x = 95.
So the production quantity that will give the maximum profit is 9,500 units.
To find the maximum profit, we substitute x = 95 into P(x)
P(95) = -10(95)^2 + 1,900(95) - 900 = 88855.33.
Therefore, the maximum profit is $88,855.33 (rounded to the nearest cent).
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What is the slope of the line on the graph?
List the sample space for rolling a fair seven-sided die.
S = {1, 2, 3, 4, 5, 6, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8}
S = {1}
S = {7}
The sample space for rolling a fair seven-sided die is S = {1, 2, 3, 4, 5, 6, 7}.
Given that,
A fair seven sided die is rolled.
We have to find the sample space of the rolling.
A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.
The subset of the sample space are events.
The die has the numbers marked from 1 to 7.
So when we roll the die,
The possible numbers are 1, 2, 3, 4, 5, 6, 7
Sample space = {1, 2, 3, 4, 5, 6, 7}
Hence the sample space is {1, 2, 3, 4, 5, 6, 7}.
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In how many ways can a committee of five be selected from eight students if two particular students are to be included
There are 56 ways to choose a committee of students.
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
A committee of five be selected from eight students if two particular students are to be included.
Now,
Since, 2 members are must be included.
So, We have to choose 3 student from 8 student to form a committee.
Hence, The number of ways to choose 3 students from 8 students is,
= \(^{8} C_{3}\)
= 8! / (8-3)! 3!
= 8! / 5! 3!
= 8 x 7 x 6 / 3 x 2
= 56
Thus, There are 56 ways to choose a committee of students.
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consider a buffer made by adding 132.8 g of nac₇h₅o₂ to 300.0 ml of 1.23 m hc₇h₅o₂ (ka = 6.3 x 10⁻⁵)
The addition of 132.8 g of NaC₇H₅O₂ to 300.0 ml of 1.23 M HC₇H₅O₂ forms a buffer solution to maintain the pH of the solution
The addition of 132.8 g of NaC₇H₅O₂ to 300.0 ml of 1.23 M HC₇H₅O₂ (Ka = 6.3 x 10⁻⁵) results in the formation of a buffer solution.
In the given scenario, NaC₇H₅O₂ is a salt of a weak acid (HC₇H₅O₂) and a strong base (NaOH). When NaC₇H₅O₂ is dissolved in water, it dissociates into its ions Na⁺ and C₇H₅O₂⁻. The C₇H₅O₂⁻ ions can react with H⁺ ions from the weak acid HC₇H₅O₂ to form the undissociated acid molecules, maintaining the pH of the solution.
The initial concentration of HC₇H₅O₂ is given as 1.23 M. By adding NaC₇H₅O₂, the concentration of C₇H₅O₂⁻ ions in the solution increases. This increase in the concentration of the conjugate base helps in maintaining the pH of the solution, as it can react with any added acid.
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WILL GIVE BRAINLIEST IF POSSIBLE IF YOU ANSWER CORRECTLY AND WITH ALL STEPS
Answer:
Step-by-step explanation:
iasss
Answer:
Step-by-step explanation:
Each figure adds four boxes to the bottom.
(1) The preceding figure, figure zero would have no rows of four and would thus just have two boxes.
(2) Each figure adds four boxes and started with two so
y(x)=4x+2
(3)
y(22)=4(22)+2
y(22)=88+2=90
Describe a sequence of transformations that shows that Polygon A is
congruent to Polygon B.
Answer:
25
Step-by-step explanation:
Point K is located at
−
12
−12. Points L and M are each
6
6 units away from Point K. Where are L and M located?
Points M and N will be located on the number line as:
M is at -15
N is at 3.
Here, we have,
to Find the Coordinate of a Point on a Number Line:
The number line gives us an idea of how real numbers are ordered, where we have the negative numbers to the left, and the positive numbers to the right.
The distance between two points on a number line is the number of units between both points.
Given that point L is at -6 on a number line, thus:
Point M is 9 units away from point L = -6 - 9 = -15
Point N is 9 units away from point L = -6 + 9 = 3
Therefore, points M and N will be located on the number line as:
M is at -15
N is at 3.
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1 - (9 – 4) : 5 =
Please someone help
Answer:
-4 = 5
Step-by-step explanation:
9-4=5
1-5=-4
-4:5
how many phone numbers can be made if all the digits (that is, 10 digits) need to be lled in and any single digit number (0-9) can be used for any digit?
There are 10,000,000,000 unique phone numbers that can be made with 10 digits using any single digit number (0-9) for each digit using combinations.
To determine how many phone numbers can be made with 10 digits, where any single digit number (0-9) can be used for any digit, follow these steps:
1. Understand that there are 10 possible digits (0-9) for each digit in the phone number.
2. Since there are 10 digits in the phone number, you need to calculate the total number of combinations by multiplying the number of possibilities for each digit.
To calculate this, simply raise the number of possible digits (10) to the power of the number of digits in the phone number (10):
10^10 = 10,000,000,000
So, there are 10,000,000,000 unique phone numbers that can be made with 10 digits using any single digit number (0-9) for each digit.
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Question on a picture
Answer:
c = 0
Step-by-step explanation:
Step 1: Write equation
15 - 5(4c - 7) = 50
Step 2: Solve for c
Distribute -5: 15 - 20c + 35 = 50Combine like terms: -20c + 50 = 50Subtract 50 on both sides: -20c = 0Divide both sides by -20: c = 0Step 3: Check
Plug in c to verify it's a solution.
15 - 5(4(0) - 7) = 50
15 - 5(-7) = 50
15 + 35 = 50
50 = 50
can somebody please tell me how we can answer this
The final velocity and displacement after 5 seconds are 19.3m/s and 59m and the acceleration is 0.7m/s²
What are Equations of MotionThe equations of motion are a set of mathematical equations that describe the motion of an object in terms of its position, velocity, and acceleration. These equations are used in physics, engineering, and other fields to predict and analyze the motion of objects.
The equations are;
v = u + at ...eq(i)
v² = u² + 2as ...eq(ii)
s = ut + 1/2 at² ...eq(iii)
2.
From the first equation of motion;
v = u + at
v = 4.3 + 3(5)
v = 19.3m/s
The displacement after 5 minutes will be
From third equation of motion;
s = ut + 1/2 at²
s = 4.3 * (5) + 1/2(3)(5)²
s = 59m
1)
distance = 1.0 * 10²m
time = 12.11s
acceleration = ?
Acceleration = velocity / time
velocity = distance / time
velocity = 1.0×10² / 12.11
velocity = 8.23m/s
acceleration = velocity / time
acceleration = 8.23 / 12.11
acceleration = 0.7 m/s²
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HELP!! It’s due today
Answer:
B. 1 horse per 20 pounds hay
C. YEs, an equation that can represent this is y=20x where x is the number of horses and y is the hay. Because i can make an equation that works for any value in this table, it is proportional.
Step-by-step explanation:
Answer: a) 1 2 3 4 5 6 7
20 40 60 80 100 120 140
b) 20 pounds of hay/horse
c) Yes. An increase in 1 horse results to an equivalent increase of 20 pounds of hay.
Step-by-step explanation:
1. Determine whether the stress function = 50x² - 60xy - 70y² satisfies the conditions of compatibility for a two-dimensional problem. Obtain the stress distribution in the matrix plate. Also draw a sketch showing the boundary stresses on (tensor) form. [4+4+2 points]
The stress function satisfies the conditions of compatibility for a two-dimensional problem.
Given stress function is 50x² - 60xy - 70y²
To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.
Strain components are given as,
εx = ∂υ/∂x + (du/dx)
εy = ∂υ/∂y + (du/dy)
γxy = ∂υ/∂y + (du/dx)
Here,
υ = 50x² - 60xy - 70y²
du/dx = 100x - 60
ydu/dy = -60x - 140y
∂υ/∂x = 100x - 60y
∂υ/∂y = -60x - 140y
∂²υ/∂y² = -140
∂²υ/∂x² = 100
Now,εx = 100x - 60
yεy = -140y - 60
xγxy = -60y - 60x
Taking derivative of εy w.r.t x,
∂(εy)/∂x = -60
Similarly, taking derivative of εx w.r.t y,
∂(εx)/∂y = -60
∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.
Stress components are given as,
σx = (C11εx + C12εy)
σy = (C21εx + C22εy)
τxy = (C44γxy)
Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0
Therefore,
σx = 100(100x - 60y) - 60(-140y - 60x)
= 19600x - 8800
yσy = -60(100x - 60y) + 100(-140y - 60x)
= -19600y + 8800x
τxy = 0
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. Maggie is participating in her school reading challenge. She reads 40 books, 26 of which are fiction. What percent of the books that she read are fiction?
ASAP!!!
Answer:
65%
Step-by-step explanation:
26/40 x 100= 65%
hope this helps!
The degree of freedom to test if the coefficients on BDR and Age are statistically different from zero at the 5% level is The critical value for the preceding test using the Fm,wo distribution lable is (Enter your values exactly as they appear in the table ) The Fstatistic for omitting BDR and Age from the regression is F = 0.08. Are the coefficients on BDR and Age statistically different from zero at the 5% level? 0 A_ Because 0.08 is greater than the critica value the coefficients are jointly significant at the 5% level: Because 0.08 is less than the critical value, Ihe coefficients are jqintly significant at the 5% level: Because 0.08 less than the critical value, the coefficients are not jointly significant at the 59 level: Because 0.08 is greater Ihan the critical value the coefficients are not jointly significant at the 5% level.
This is because the F-statistic for omitting BDR and Age from the regression is 0.08, which is less than the critical value for the test using the F-distribution table.
To test if the coefficients on BDR and Age are statistically different from zero, we compare the F-statistic with the critical value from the F-distribution table. The F-statistic is a measure of the overall significance of the regression model when certain variables are omitted.
In this case, the F-statistic is given as 0.08. To determine if the coefficients are statistically different from zero at the 5% level, we compare this value with the critical value from the F-distribution table. The critical value represents the threshold beyond which we reject the null hypothesis.
Based on the statement provided, it states that 0.08 is "less than the critical value." Since the F-statistic is smaller than the critical value, we can conclude that the coefficients on BDR and Age are not jointly significant at the 5% level. In other words, we fail to reject the null hypothesis that the coefficients are equal to zero.
The use of the phrase "jointly significant" implies that the significance of the coefficients is considered together, rather than individually. The test assesses the overall impact of BDR and Age on the regression model, rather than their individual effects. Since the F-statistic falls below the critical value, we do not have sufficient evidence to conclude that BDR and Age have a significant impact on the model.
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The lengths of the diagonals of rectangle ABCD intersect at E. If AE =x+4 and CE= 3x-12. What is the length of BD?
SOMEONE HELP ME ASAP PLEASE
Answer:
DB = 24
Step-by-step explanation:
First, note that the diagonals of a rectangle are equal and bisect each other. In other words, DB = CA and CE = EA and DE = BE.
Also, AE + CE = CA
So, using this, we can write this equation:
AE = CE
x + 4 = 3x -12
Subtract 4 from both sides.
x = 3x -16
Subtract 3x from both sides.
-2x = -16
Divide both sides by -2
x = 8
Then, substitute this into AE + CE = CA
x + 4 + 3x - 12 =
8 + 4 + 24 - 12 = 24
Then, because CA = DB,
DB = 24
I hope this helps! Feel free to ask any questions! :)
Find the missing side lengths. Leave your answer as radicals in simplest form.
The values of the sides are;
41. x = 18√3. Option D
42. x = 6√3. Option A
How to determine the valuesUsing the different trigonometric identities, we have;
41. Using the tangent identity, we have;
tan 60 = 9√2/y
cross multiply the values
y =9√2 ×√3
y = 9√6
Using the sine identity;
sin 45 = y/x
1/√2 = 9√6/x
cross multiply the values, we have;
x = 9√2 ×√3 ×√2
x = 18√3
42. Using the cosine identity
cos 60 = 3√3 /x
cross multiply, we have;
x = 6√3
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Mrs. Smith has a total of 27 kids in her class. There are 6 more boys than there are girls. Write a system of equations to model this.
Some Equations:
6 + x = 27
x + 6 = 27
27 - 6 = x
27 - x = 6
27 = x + 6
27 = 6 + x
There are 11 girls
A system of equations to model this statement is x + (x + 6) = 27.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, There are 6 more boys than there are girls.
Assuming no. of girls to be x, therefore no. of boys is (x + 6).
Mrs. Smith has a total of 26 kids in her class.
∴ x + (x + 6) = 27.
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Starting from the initial trial solution (x1, x2) = (0,0), apply the gradient search procedure with e=0. 01 to find an approximate solution for the following problem: Maximize: f (x) = 6x1-2x^2-2x2-x^2+2x1x2
Using the gradient search procedure with e=0.01 and starting from the initial trial solution (x1, x2) = (0,0), the approximate solution for the given problem Maximize: f (x) = 6x1-2x^2-2x2-x^2+2x1x2 is (1.25, 0.625).
Explanation:
To use the gradient search procedure to find the maximum of the given function f(x), we first need to calculate its gradient, which is given by:
∇f(x) = [6-4x1+2x2, -2-2x1-2x2+2x1]
Next, we initialize the trial solution to (x1, x2) = (0,0) and set the value of e to 0.01. Then, we update the trial solution using the following formula until the value of the objective function f(x) no longer increases significantly:
(x1, x2) = (x1, x2) + e * ∇f(x)
Using this formula, we can iteratively update our solution until convergence. Applying this procedure, we get the following updates:
(x1, x2) = (0,0) + 0.01 * [6, -2] = (0.06, -0.02)
(x1, x2) = (0.06, -0.02) + 0.01 * [5.68, -1.96] = (0.1168, -0.0396)
(x1, x2) = (0.1168, -0.0396) + 0.01 * [5.344, -1.864] = (0.17128, -0.05524)
(x1, x2) = (0.17128, -0.05524) + 0.01 * [5.0152, -1.74744] = (0.223428, -0.0727144)
(x1, x2) = (0.223428, -0.0727144) + 0.01 * [4.69344, -1.63714] = (0.2733624, -0.0910854)
(x1, x2) = (0.2733624, -0.0910854) + 0.01 * [4.37913, -1.53358] = (0.3211587, -0.1104214)
(x1, x2) = (0.3211587, -0.1104214) + 0.01 * [4.07236, -1.43614] = (0.3678823, -0.130783)
(x1, x2) = (0.3678823, -0.130783) + 0.01 * [3.77302, -1.34423] = (0.4135973, -0.1523653)
(x1, x2) = (0.4135973, -0.1523653) + 0.01 * [3.48106, -1.2573] = (0.4583679, -0.1759383)
(x1, x2) = (0.4583679, -0.1759383) + 0.01 * [3.19644, -1.17484] = (0.5022553, -0.2016867)
(x1, x2) = (0.5022553, -0
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A house painter decides how many cans of paint to buy based on the total surface area of the house. The table below shows the surface area, o, in square meters, and the
number of cans of paint, P, used for three different houses
Answer:
Step-by-step explanation:p
a/p = 65
p = a/65 ≅ 0.015a
Please help on this thanks
\(2(n-2)<3n-6\)
↝ Multiply 2 inside (n-2) as we get 2n-4
\(2n-4<3n-6\)
↝ Inequality is almost the same as equation so you just do the same like equation.
\(2n-4-3n+6<0\\-n+2<0\\-n<-2\)
↝ Since it's Inequality. When the variable is negative, you have to make it positive.
\(n<\frac{-2}{-1}\\n<2\)
↝ BUT! n < 2 isn't the right answer.
↝ Because for Inequality. Taking out the negative/Move the negative variable to another side ( from -n to n and -2 to -2/-1 = 2).
↝ You have to swap the inequality symbol after taking the off the negative variable.
↝ For example, if it is -n < 2 then the answer will be n > -2
or -n < -3 then the answer will be n > 3
But if it is n>2-3 as we get n>-1, not n < -1 because the variable isn't negative at all.
Basically, we swap the inequality symbol when it's negative variable.
↝ Therefore, it's not n < 2 but it is n > 2
So the right choice is n > 2 also known as the ( D ) answer.
Drag the symbol > or < to compare each pair of decimal numbers
Answer:
1. <
2. <
3. >
Step-by-step explanation:
i think. probably. should be right.
yee.
Hello!
So to answer this question, we are comparing three different sets of numbers to one another, to see which is greater than the other.
For the first set, 0.15 and 0.8, the greater number is 0.8.
So, the answer for the first set is 0.15 < 0.8
For the second set, 0.308 and 0.380, the greater number is 0.380.
So, the answer for the second set is 0.308 < 0.380
Lastly, for the third set, 9.326 and 9.236, the greater number is 9.326.
So, the answer for the third set is 9.326 > 9.236
Hope this helps!
_________________ is the angle of tilt below the imaginary horizontal plane oriented 90-degrees to the _______________ direction.
The missing terms in the sentence are "Inclination" and "Vertical."
Inclination is the angle of tilt below the imaginary horizontal plane oriented 90-degrees to the vertical direction. It refers to the angle at which an object or surface deviates from being perfectly horizontal or flat. It measures the slope or tilt of the object or surface in relation to the vertical direction.
The vertical direction is the imaginary line or axis that points directly up or down, perpendicular to the horizontal plane. It is oriented at a 90-degree angle to the horizontal direction, which is typically considered the direction parallel to the ground or any other reference plane.
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the kona iki corporation produces coconut milk. they take coconuts and extract the milk inside by drilling a hole and pouring the milk into a vat for processing. they have both a day shift and a night shift to do this part of the process. they would like to know if the day shift and the night shift are equally efficient in processing the coconuts. a study is done sampling 9 shifts of the night shift and 16 shifts of the day shift. the mean number of hours to process 100 pounds of coconuts was measured for each shift. which statistical test would be used to determine if there is a difference in the mean amount of time for each shift to process 100 pounds of coconuts? question 11 options: 2 sample t-test (independent samples) one way anova randomized block anova paired t-test
A two-sample t-test (independent samples) would be used to determine if there is a difference in the mean amount of time for each shift to process 100 pounds of coconuts.
A t-test is a statistical test that compares the means of two groups or samples. It allows you to determine if there is a significant difference between the means of two sets of data.The most basic type of t-test is a two-sample t-test.
This is used when you want to compare the means of two independent groups. In this case, we have the day shift and night shift, which are independent groups. Hence, we would use a two-sample t-test (independent samples) to determine if there is a difference in the mean amount of time for each shift to process 100 pounds of coconuts.
The one-way ANOVA is used when you have more than two independent groups to compare, randomized block ANOVA is used when the samples are paired, and the paired t-test is used when you have two dependent samples.
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Part 4: solve a real-world problem using an absolute fraction
A transaction is a positive if there is a sale and negative when there is a return. Each time a customer uses a credit cards for a transaction,the credit company charges Isabel.The credit company charges 1.5% of each sale and a fee of 0.5% for returns.
Latex represent the amount of transaction and f(x) represent the amount Isabel is charged for the transaction.Write a function that expresses f(x).
a) A function that expresses f(x) is f(x) = 1.5x.
b) A graph of the function is shown in the image below.
c) The domain and range of the function are all real numbers or [-∞, ∞].
How to write a function that describes the situation?Assuming the variable x represent the amount of a transaction and the variable f(x) represent the amount Isabel is charged for the transaction, a linear function charges on each sale by the credit card company can be written as follows;
f(x) = 1.5x
Part b.
In this exercise, we would use an online graphing tool to plot the function f(x) = 1.5x as shown in the graph attached below.
Part c.
By critically observing the graph shown below, we can logically deduce the following domain and range:
Domain = [-∞, ∞] or all real numbers.
Range = [-∞, ∞] or all real numbers.
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Complete Question:
A transaction is positive if there is a sale and negative when there is a return. Each time a customer uses a credit card for a transaction, the credit company charges Isabel. The credit company charges 1.5% of each sale and a fee of 0.5% for returns.
a) Let x represent the amount of a transaction and let f(x) represent the amount Isabel is charged for the transaction. Write a function that expresses f(x).
b) Graph the function.
c) What are the domain and range of the function?
factorise 4px-3my-2pm-6xy
Answer:
E
Step-by-step explanation:
NO
In a basket of oranges , 20% of them are defective and 76 are in good condition.find the total number of oranges in the basket.
The total number of oranges in the basket is 95.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Of a basket of oranges,
20% of them are defective and 76 are in good condition.
Let x be the total number of oranges.
That means 80% = 76 oranges are in good condition.
20% in decimal form is 0.2.
Applying the percentage formula,
(1 - 0.2)x = 76
0.8x = 76
x = 95
And 20% of 95 = 19
Therefore, the total = 95.
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Find the difference of (-x^2 + 9xy) - (x^2 + 6xy - 8y^2)
Difference of (-x² + 9xy) and (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².
What is subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given expression,
(-x² + 9xy) - (x² + 6xy - 8y²)
Distributing negative sign
-x² + 9xy - x² - 6xy + 8y²
Adding like terms
- 2x² + 3xy + 8y²
Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).
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Your credit card limit is $5,000, and your current balance is $4,500. Your credit score will increase by 10 points for every $250 decrease in your balance. At the end of the year you have paid down your balance to $2,500. By how many points has your credit score increased?
a) 10
b) 25
c) 45
d) 80
Answer: 80
Step-by-step explanation:
4500-2500 is 2000 dollars reduction, or money paid off.
For every 250 dollars, there is a 10 points increase. 2000 divided by 250 is 8. There are 8 sets of 250 dollars. So, for every 250 dollars (you have 8 of them), 10 points increase. Therefore, you multiply 10 by 8.
10x8 = 80. Your credit score has increased by 80 points.
Luis has a pyramid shaped plant pot. It has a square base with a side length of
36
cm
36 cm36, start text, space, c, m, end text, and the height of the pot is
36
cm
36 cm36, start text, space, c, m, end text.
36
cm
36 cm
36
cm
36 cm
Luis wants to fill the pot with soil so that the soil takes up
75
%
75%75, percent of the pot's volume.
How far up the pot will the soil reach?
Round to the nearest tenth.
Answer:
The soil will occupy in 11664cm³ of the pot which is 3/4 or 0.75 of the squared based pyramid pot.
Step-by-step explanation:
The volume of a square based pyramid = V = a²h/3
a = base edge or side length = 36cm
h = height = 36cm
V = 36² × 36/3
V = 15552cm³
Luis wants to fill the pot with soil so that the soil takes up 75 % the pot's volume.
75% of the pot's volume =
75/100 × 15552cm³
= 11664cm³
The soil will occupy 11664cm³ of the pot which is 3/4 or 0.75 of the squared based pyramid pot.
Answer:
The soil will reach about 32.7 cm up the pot.
Step-by-step explanation:
Cause I took a test