The solution to the system of equations using matrices is x = 45, y = 15, and z = 30.
What is determinant of matrix?A scalar value that can be calculated from a matrix's elements is the determinant. When a square matrix is used to transform vectors, the determinant is a measurement of how much the matrix "stretches" or "shrinks" space. In linear algebra, the determinant is employed in a variety of operations, including as the computation of a matrix's inverse, the description of a matrix's eigenvalues and eigenvectors, and the resolution of linear equation systems. In specifically, the existence of a unique solution, the absence of a solution, or an unlimited number of solutions to a system of linear equations can be determined using the determinant of the coefficient matrix.
The given equation are:
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
Writing the equations in matrix form we have:
[tex]\begin{bmatrix} 2 & -1 & 3 \\ -4 & 2 & 3 \\ 3 & -4 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix}[/tex]
Multiplying the inverse of the coefficient matrix we have:
[tex]\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 2 & -1 & 3 \\ -4 & 2 & 3 \\ 3 & -4 & 0 \end{bmatrix}^{-1} \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix}[/tex]
Now,
[tex]\begin{bmatrix} 2/23 & 5/46 & -3/23 \\ 2/23 & 1/23 & 5/23 \\ -3/23 & -5/46 & 2/23 \end{bmatrix}[/tex]
Multiplying this by the vector on the right-hand side gives:
[tex]\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 2/23 & 5/46 & -3/23 \\ 2/23 & 1/23 & 5/23 \\ -3/23 & -5/46 & 2/23 \end{bmatrix} \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix} = \begin{bmatrix} 45 \\ 15 \\ 30 \end{bmatrix}[/tex]
Hence, the solution to the system of equations is x = 45, y = 15, and z = 30.
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ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?
A.
A'(0, 3), B'(2, 3), C'(1, 1)
B.
A'(0, -3), B'(3, -2), C'(1, -1)
C.
A'(-3, 0), B'(-3, 2), C'(-1, 1)
D.
A'(0, -3), B'(-2, -3), C'(-1, -1)
The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.
What are coordinates?Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.
We are to find the coordinates of the vertices of the image.
We know that
if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :
(a, b) ⇒ (-a, -b).
So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes
A(-3, 0) ⇒ (3, 0)
B(-2, 3) ⇒ (2, -3)
C(-1, 1) ⇒ (1, -1).
Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).
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LOOK AT THE PHOTO PLS
The next entry on the long division would be 0.054, and 0.0054
How to perform long divisionLong division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:
Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.
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Please Help ( Due today) ASAP
Question 6(Multiple Choice Worth 1 points)
(08.07 LC)
The table represents a quadratic function C(t).
t C(t)
−2 7
−1 4
0 3
1 4
2 7
What is the equation of C(t)?
C(t) = −(x − 3)2
C(t) = (x − 3)2
C(t) = −x2 + 3
C(t) = x2 + 3
C(t equation )'s is thus: [tex]C(t) = (t - 0)^2 + 3[/tex] or condensed, [tex]C(t) = t^2 + 3[/tex] as the vertical stretch or compression factor and (h, k) is the vertex.
what is parabola ?A parabola is a symmetry U-shaped plane curve. This graph represents a quadratic function using the formula y = ax2 + bx + c. The parabola's direction and shape are determined by the nonzero integers a and b in this equation, whereas the parabola's location on the x-axis is affected by the linear coefficient b and the constant coefficient c. A parabola has a vertex, or the location where the curve changes direction, and it can open upward or downward.
given
We can start by noting that since the vertex of a parabola always lies in the centre of the two x-intercepts for a quadratic function, the parabola's vertex must be at the coordinates (0, 3).
The equation can be expressed in the vertex form of a quadratic function as follows:
[tex]C(t) = a(t-h)^2 + k[/tex]
where "a" is the vertical stretch or compression factor and (h, k) is the vertex. Using the values from the table as inputs, we obtain:
[tex]C(t) = a(t - 0)^2 + 3[/tex]
We still need to determine what "a" is worth. To do this, we can utilise a different table row, for instance (1, 4):
[tex]4 = a(1 - 0)^2 + 3[/tex]
1 = a
C(t equation )'s is thus: [tex]C(t) = (t - 0)^2 + 3[/tex] or condensed, [tex]C(t) = t^2 + 3[/tex] as the vertical stretch or compression factor and (h, k) is the vertex.
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Use the graph to answer the questions for the questions
The vertex is (50, 630). The vertex is the peak and correspond with the coordinates of he maximum height of the arch.
The solutions is the base of the arch and this (20, 0) and (80, 0)
vertex form, y = -0.7(x - 50)² + 630
Quadratic equation factored form, y = -0.7 (x - 80) (x - 20)
The equations are the same when plotted on a graph and examined mathematically. physically it looks different.
the domain is (-∞, ∞)
The height of the monument 15 feet from the left side is 472.5 feet
How to find the quadratic equationsince the zeroes of the quadratic equation is (20, 0) and (80, 0), hence we have that
y = a(x - 20)(x - 80) and the equation pass points (50, 630)
630 = a(50 - 20)(50 - 80)
630 = a * 30 * -30
630 = -900a
a = -0.7
Quadratic equation has a standard vertex form, y = a(x - h)² + k
y = a(x - h)² + k
vertex (h, k) = (50, 630) and a = -0.7
plugging the values
y = -0.7(x - 50)² + 630
Quadratic equation has a standard factored form, y = a(x - h)² + k
y = a(x - r2)(x - r1)
where r2 and r1 are the roots r1 = 20 r2 = 80 an a = -0.7
plugging the values
y = -0.7 (x - 80)(x - 20)
The height of the monument 15 feet from the left side is gotten from the graph
this is 15 feet from 20 hence x = 35 feet
from the graph it can traced to be 472.5 feet
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Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y are y(y + 5) = 750, y² – 5y = 750 and y(y – 5) + 750 = 0
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
The equations that can be used to solve for y, the length of the room are:
1. y(y + 5) = 750
2. y² – 5y = 750
3. y(y – 5) + 750 = 0
Option 1 and 2 are quadratic equations that can be solved by factoring, completing the square, or using the quadratic formula. Option 3 is also a quadratic equation but it requires rearranging to the standard form before applying the same methods. The last option, (y + 25)(y – 30) = 0, is not a quadratic equation but it can be easily solved using the zero product property.
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You can afford a $1000 per month mortgage payment. You've found a 30 year loan at 5.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)
$
b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)
$
c) How much of that money is interest? (Round to the nearest cent, as needed.)
Answer:
a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).
In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.
Substituting these values into the formula, we get:
$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]
Simplifying and solving for P, we get:
P = $183,928.72
Therefore, you can afford a loan of approximately $183,928.72.
b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:
Total money paid = $1,000 x 360 = $360,000
Therefore, the total amount of money paid to the loan company will be $360,000.
c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:
Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28
Therefore, the amount of money paid in interest will be $176,071.28.
Determine the interval(s) on which the function Is constant.
Write your answer as an interval or list of intervals.
When writing a list of Intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None* if applicable.
The list of intervals on which the function is constant is:
A(-4,-3) and B(3,6).
What is a constant function?A constant function is a function that returns the same value regardless of the input. In other words, for every value of x, the output of the function is the same constant value. For example, the function f(x) = 2 is a constant function because no matter what value of x is plugged into the function, the output will always be 2. Constant functions are often represented by horizontal lines on a graph.
What does a list of intervals mean in the graph?A list of intervals in a graph typically indicates the range of values or intervals on a given axis. For example, on the x-axis of a graph, a list of intervals might represent the range of values from a lower bound to an upper bound, with each interval indicating a range of values that falls between two specific points on the axis. On the y-axis, the intervals might represent the range of possible values for the dependent variable or data being plotted. In general, the intervals on a graph provide a visual representation of the range of values being considered or plotted.
According to the given informationThe given function in the graph on intervals A(-4,-3) and B(3.6) is a horizontal line which means there is no change in output. So the function is constant.
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please answer in detail
Answer:
AB: y = 2x + 4
Step-by-step explanation:
Line AB is parallel to the line y = 2x + 3
When 2 lines are parallel they have the same coefficient of x.
=> AB: y = 2x + m (1)
Because line AB passes through the point (0, 4)
Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4
So AB: y = 2x + 4
A stack of books has a mass of 21 killagrams if each book in the stack has a mass of 3 kilograms how many books are in the stack
There are 7 books in the stack.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the number of books in the stack, we can divide the total mass of the stack by the mass of each book:
Number of books = Total mass of the stack / Mass of each book
In this case, the total mass of the stack is 21 kilograms, and the mass of each book is 3 kilograms.
Number of books = 21 kg / 3 kg/book
Simplifying the right side, we get:
Number of books = 7 books
Therefore,
There are 7 books in the stack.
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14. The local credit union is offering a special student checking account. The monthly cost of the account is $15. The first 10 checks are free, and each additional check costs $0.75. You search
the Internet and find a bank that offers a student checking account with no monthly charge. The first 10 checks are free, but each additional check costs $2.50.
a. Assume that you will be writing more than 10 checks a month. Let n represent the number of checks written in a month. Write a function rule for the cost c of each account in terms of n.
b. Write an inequality to determine what number of checks in the bank account would be more expensive than the credit union account.
c. Solve the inequality in part b.
Answer: a. c(n) = 15 + 0.75(n - 10)
b. 15 + 0.75(n - 10) = 2.50(n - 10)=
Simplifying and solving for n, we get:
n = 50
c. n > 50
Step-by-step explanation:
a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:
c(n) = 15 + 0.75(n - 10)
The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
The cost c of the bank account in terms of the number of checks written n can be expressed as:
c(n) = 2.50(n - 10)
The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:
15 + 0.75(n - 10) = 2.50(n - 10)
Simplifying and solving for n, we get:
n = 50
So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.
c. The solution to the inequality is:
n > 50
This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.
Which graph represents the hyperbola x2/52-y2/42 = 1?
For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.
What is a hyperbola?A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.
Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.
For the given equation of the parabola, the value of a and b = 5 and 4.
Thus, we have horizontal length of 5 and vertical width of 4 units
The graph that depicts this hyperbola is: Option B.
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The complete question is:
6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
40% of Canadians read at least 10 books a year.
Define percentageA percentage is a way of expressing a portion or a part of a whole as a fraction of 100. It is represented by the symbol "%". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific amount or group. For example, if you score 80 out of 100 on a test, your score can be expressed as 80%, meaning you got 80 out of 100 possible points.
If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:
2/5
We can multiply this fraction by 100 to turn it to a percentage:
(2/5) x 100 = 40%
Therefore, 40% of Canadians read at least 10 books a year.
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Oliver and Mike each place some apples and oranges into the same bowl.
• The ratio of apples to oranges Oliver places in the bowl is 2:3
• The ratio of apples to oranges Mike places in the bowl is 1:2
• They each place 6 oranges in the bowl.
Write the total number of apples and oranges they place in the bowl.
Answer: 5 * 5 = 20
20 divided by 1 = 20
If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.
Primary Level 2 3 4 5 6 7. 8 children/funny monkeys thin/rake strong/ox eagle/aeroplane my room/ clean/ whistle swimmer/fish Exercise 2 Read the story. Look for the simile (as/like) When Mr. Bumble is angry, he shouts as loud as thunder. His eyes look like fire. He bangs his hands which feel as heavy as lead. Mr. Bumble stamps his feet like an et All the pupils keep as quiet as lambs when Mr. Bumble behaves like e
The similes in the story are:
"shouts as loud as thunder""eyes look like fire""hands feel as heavy as lead""stamps his feet like an et""quiet as lambs"What is a Simile?A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.
Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.
Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.
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At a real estate agency, an agent sold a house for $377,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made $28,275 in commission on the house.
The agent earned $5,655 in commission on the sale of the house.
To calculate how much the agency made on the houseWe first need to calculate the amount of commission that the agency received.
The commission rate for the agency is 7.5%, so we can find the commission amount by multiplying the sale price of the house by 7.5% in decimal form:
Commission for the agency = $377,000 x 0.075 = $28,275
Therefore, the agency made $28,275 in commission on the house.
To calculate how much the agent earned in commission, we need to find 20% of the commission amount that the agency received:
Commission for the agent = $28,275 x 0.20 = $5,655
Therefore, the agent earned $5,655 in commission on the sale of the house.
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A solid glass cylinder is 31 centimeters high and has a diameter of 3 centimeters. What is the mass of the cylinder if the density of glass is 1.6 grams per cubic centimeter?
Answer:
the mass of the solid glass cylinder is approximately 350.67 grams.
Step-by-step explanation:
The diameter of the cylinder is 3 centimeters, which means that its radius is 1.5 centimeters (half the diameter). The area of the base of the cylinder is the area of a circle, calculated as pi (π) multiplied by the radius squared:
Base area = π x radius^2
Base area = π x (1.5 cm)^2
Base area = 7.07 cm^2 (approximately)
The volume of the cylinder is calculated by multiplying the area of the base by the height:
Cylinder Volume = Base Area x Height
Cylinder volume = 7.07 cm^2 x 31 cm
Cylinder volume = 219.17 cm^3 (approximately)
Now that we know the volume of the cylinder, we can calculate its mass using the density of the glass:
Mass = Density x Volume
Mass = 1.6 g/cm^3 x 219.17 cm^3
Mass = 350.67 grams (approximately)
A pianist plans to play 3 pieces at a recital from her repertoire of 25 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?
There are 13,800 different recital programs possible.
What is permutation?
In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.
The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:
25 x 24 x 23 = 13,800
There are 13,800 different recital programs possible.
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The most important of the Shinto gods is the sun goddess who gave light to the world, named ______.
Amaterasu
Susanoo
Tsukyomi
Izanagi
Answer: Amaterasu
Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.
if f(x)= -3, then f'(x)=?
Answer:
0
Step-by-step explanation:
0
Please help me solve and show my work
The degree measure of the angles are;
1. 5π/3 = 300°
2 3π/4 = 135°
3. 5π/6 = 150°
4. -3π/2 = 90°
What is degree and radian?A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.
A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.
therefore π = 180°
1. 5π/ 3 = 5×180/3 = 300°
2. 3π/4 = 3× 180/4 = 540/4 = 135°
3. 5π/6 = 5×180/6 = 150°
4. - 3π/2 = -3 × 180/2 = -270° = 90°
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13. What is the surface area of a dome (a half sphere) with a radius of 12 meters?
288 meters squared
48 meters squared
967 meters squared
576 meters squared
Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.
Plugging in the radius r = 12 meters, we get:
Surface area = 2π(12)^2
Surface area = 2π(144)
Surface area ≈ 904.78
Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.
So the answer is: 967 meters squared.
Step-by-step explanation:
The box plot displays data collected on the shoe sizes for a group of students. A box plot uses a number line from 3.5 to 11 with tick marks every one-half unit. The box extends from 6.5 to 8 on the number line. A line in the box is at 7. The lines outside the box end at 5 and 9. The graph is titled Students' Shoe Sizes, and the line is labeled Size Of Shoe. Which of the following represents the value of the median of the data?
A 6.5
B 7
C 8
D 8.5
Answer: it’s 8.25
Step-by-step explanation: because it’s in between 8 and 8.5. Thank god
2. Mrs. Cooper created a triangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 8m and a height of 10m, how much fertilizer will she need?
Answer:
40 m²
Step-by-step explanation:
Area of triangle:
To find the area of triangle, multiply the base and area and then divide it by 2.
base = b = 8 m
height = h = 10m
[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]
[tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]
Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
The total net amount the supermarket owes the wholesaler for the order is $231.31.
What does discount mean?A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.
According to the given informationTo find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.
The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:
Discounted cost = List price - (Discount rate x List price)
For the soup, the discounted cost per case is:
$18.90 - (0.39 x $18.90) = $11.51
For the baked beans, the discounted cost per case is:
$33.50 - (0.39 x $33.50) = $20.42
Now we can calculate the total net amount owed by the supermarket to the wholesaler:
Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)
Total net amount = (13 x $11.51) + (4 x $20.42)
Total net amount = $149.63 + $81.68
Total net amount = $231.31
Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.
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1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
a. How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
A. There are 9 sample spaces.
B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9
What is meant by sample spaces?
In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is used to define the space of events and calculate probabilities.
What is meant by probability?
Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.
According to the given information
A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.
B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.
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Identify the values of a, b, and c in the following quadratic equation: 2x^2 −3x−5
Explain why the empty set is a subset of every set
The empty set (also known as the null set) is a subset of every set because it does not contain any elements that are not in the set. In other words, if A is any set, then every element of the empty set is also an element of A, since the empty set contains no elements. This satisfies the definition of a subset, which states that for any two sets A and B, A is a subset of B if every element of A is also an element of B. Therefore, the empty set is a subset of every set.
~~~Harsha~~~
please help me
To begin a bacteria study, a petri dish had 2300 bacteria cells. Each hour since, the number of cells has increased by 12%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
The exponential function showing the relationship is y = 2300(1 + 0.12)^t
The exponential function showing the relationshipThe exponential function showing the relationship between y and t can be written as:
y = 2300(1 + 0.12)^t
where 2300 is the initial number of bacteria cells, 0.12 is the growth rate (12% expressed as a decimal), and t is the time in hours since the start of the study.
This function is obtained by using the formula for exponential growth, which is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is the time.
In this case, a = 2300, r = 0.12, and y represents the amount of bacteria cells after t hours.
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Lastly, let’s consider the alternative method of paying for college: paying with loans. You take out a loan in the amount of your tuition and fees cost for 5 years rounded up to the nearest thousand dollars (for example if the total cost is $55,787 the loan would be for $56,000). The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take 27.25 years to pay off the loan.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, the interest that is earned on both the principal amount and any previously accumulated interest. In other words, it is interest that is calculated not only on the original amount of money but also on any interest that has been earned previously. This can result in significant growth of an investment or loan balance over time, as the interest earned on the accumulated interest can compound exponentially. Compound interest can be calculated using a specific formula that takes into account the principal amount, the interest rate, and the compounding frequency.
Now,
First, we need to calculate the total amount of the loan. We round up the tuition and fees cost for 5 years to the nearest thousand dollars:
Total cost = $70,000
Rounded up to nearest thousand = $70,000
So, the amount of the loan is $70,000.
Next, we can use the formula N= (-log(1-i*A/P))/(log(1+i)) to calculate the number of monthly payments needed to pay off the loan.
N = (-log(1-0.0025*70000/250))/(log(1+0.0025))
N = (-log(1.75))/(log(1.0025))
N = 326.45
Rounding up to the nearest whole number, it will take 327 monthly payments to pay off the loan.
So, it will take 327/12 = 27.25 years to pay off the loan.
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HELP RAAHHHH
1. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 4 feet with an intal upward velocity of 72 feet per second
The T-shirt is caught 42 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
2. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 3 feet with an intal upward velocity of 80 feet per second
The T-shirt is caught 36 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
Answer:
1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:
h(t) = -16t^2 + 72t + 4
To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:
t = -b/2a = -72/(2(-16)) = 2.25 seconds
To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):
h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet
The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.
2. Using the same kinematic equation as before, we have:
h(t) = -16t^2 + 80t + 3
To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:
t = -b/2a = -80/(2(-16)) = 2.5 seconds
To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):
h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet
The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.
Step-by-step explanation: