Answer:
a. $1,240
b. $1,960
c. 9 years
d. 17 years
Step-by-step explanation:
For interest you multiply the percent with 1,000 and add the number you get for your answer. So 1,000 times 6% is 60. Each year the account earns $60 worth of interest. You multiply 60 by 4 and your result is 240. You add 240 to 1,000 and get your answer for a $1,240.
You repeat the same process for b. 16 times 60 is 960. You add 960 and 1,000 and your answer is $1,960.
So we know the account already has $1,000 so all that has to be done is to divide 500 by 60 and your result is 8.3. However you it is anual interest so you cannot but in a decimal so you round up to 9. Making it 9 years
Same process dividing 1,000 by 60 which gives you 16.6 rounding up to 17. Making it 17 years.
What are the domain and range of the function f(x)=-x+3-2? domain: -3 -2 domain: -3 -3 range: y<-2 domain: x>-3 range:y>-2
For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.
The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.
The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).
The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.
So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.
Correct option is D.
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Complete question is:
What are the domain and range of the function f(x)=-x+3-2?
A) domain: -3 -2
B) domain: -3 -3 range: y<-2
C) domain: x>-3 range:y>-2
D) domain : x>-3 range: y ≤ 2
Can anyone help me answer this question?
Find G(x) = sin^2(x) + 3cos(x), when x=
[tex]g(x)=\sin^2(x)+3\cos(x) \\\\[-0.35em] ~\dotfill\\\\ g(\pi )=\sin^2(\pi )+3\cos(\pi )\implies g(\pi )=[\sin(\pi )]^2+3\cos(\pi ) \\\\\\ g(\pi )=(0)^2+3(-1)\implies g(\pi )=-3[/tex]
A line passes through the points ( – 3, – 4) and (6, – 10). Write its equation in slope-intercept form.
The equation of the line in the slope-intercept form will be y = (-2/3)x - 2.
Given that:
Points, (-3, -4) and (6, -10)
The equation of the line in slope-intercept form is written as,
y = mx + b
The slope of the line is calculated as,
m = (y2 - y1) / (x2 - x1)
m = (-10 - (-4)) / (6 - (-3))
m = -6 / 9
m = -2/3
Now, to find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
y - (-4) = (-2/3)(x - (-3))
y = (-2/3)x - 2
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simplify the expression 4√ 2 + 2√ 32? 12/2 6/32 12/32 36/2
The solution is, simplification of the expression 4√ 2 + 2√ 32 is 12√2 .
We know that,
An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, given expression is,
4√ 2 + 2√ 32
=4√ 2 + 2√ 16 × 2
we know that,
√16 = 4
so, we get,
=4√ 2 + 2√2 × 4
=4√ 2 + 8√2
=12√2
Hence, The solution is, simplification of the expression 4√ 2 + 2√ 32 is 12√2 .
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Help please! Show all your work.
Answer:
If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.
To find the value of k, we can use the given values of y and x:
y = kx
24 = k(12)
k = 2
Now that we know k, we can use the equation to find the value of y when x=16:
y = kx
y = 2(16)
y = 32
Therefore, when x=16, y=32.
A pharmaceutical company develops a new generation of blood pressure medication that may also help with cholesterol. The research and development department advertises in the local papers and online seeking volunteers who already take blood pressure medication to participate in a study for the new medication. Two hundred people volunteer, and their current blood pressure along with their cholesterol levels are measured. They are randomly assigned to two groups, one that takes the new generation of blood pressure medication and one that takes the original medication. At the end of the study, the subjects’ blood pressure and cholesterol levels are measured. The group with the new medication is found to have a significantly lower overall blood pressure than the original medication group. It was also determined that the new medication did not significantly lower cholesterol levels. Which of the following is a valid conclusion? Inferences can be made about all blood pressure patients, and the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication. Inferences can be made about all blood pressure patients, but the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication. Inferences cannot be made about all blood pressure patients, and the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication. Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
The valid inference based on the information provided is:
Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
What's the information about?The study involved only 200 volunteers who were already taking blood pressure medication. This is a relatively small sample size and may not be representative of all blood pressure patients. Inferences about all blood pressure patients cannot be made from this limited sample.
While the group taking the new medication showed a significantly lower overall blood pressure than the group taking the original medication, it was also mentioned that the new medication did not significantly lower cholesterol levels.
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From the pharmaceutical company's test, we can conclude that the new medication is more effective than the original in lowering blood pressure for patients already taking blood pressure medication. However, this conclusion doesn't apply to all blood pressure patients.
Explanation:A valid conclusion from the scenario about the pharmaceutical company's testing of its new medication would be the following: Inferences cannot be made about all blood pressure patients, though the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients who are already taking blood pressure medication. The study has a specific sample population: people who are already taking blood pressure medication. We can't extrapolate this to all blood pressure patients, because the study didn't include those who don't take any medication. However, it was observed that the new medication was more effective in lowering blood pressure than the original one within this specific group.
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Solve for x. Please show all the work. Thank you.
[tex]\frac{5}{25} = \frac{9}{x +4}[/tex] when simplified, the value of x = 41
What is an Equation?Equation is a mathematical statement that is made up of two expressions connected by an equal value.It says that two things are equal and it expresses equality of two mathematical expressions.
How to determine this
[tex]\frac{5}{25} = \frac{9}{x +4}[/tex]
To find the value of x,
By cross multiplying
5(x+4) = 9(25)
Open bracket
5x + 20 = 225
Collect like terms
5x = 225 - 20
5x = 205
Divides through by 5
5x/5 = 205/5
x = 205/5
x = 41
Therefore, the value of x = 41
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Homework help?!?!?!
Answer:
1. The slope of the line is 3. The line goes up 3, over 1, and since slope is rise/run, the slope is 3.
2. The slope of the line is 4. The line goes up 4, over 1, and since slope is rise/run, the slope is 4.
3. The slope of the line is 2. The line goes up 2, over 1, and since slope is rise/run, the slope is 2.
4. The slope of the line is -4. The line goes down 4, over 1, and since slope is rise/run, the slope is -4.
The gradients of line equations are listed below:
m = 3m = 4m = 2m = - 3How to determine the gradient of a line
In this question we have four cases of line equations shown on Cartesian plane, whose gradients must be found. The gradient of each line can be computed by means of secant line formula and two points:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.Case 1: (x₁, y₁) = (- 1, - 4), (x₂, y₂) = (1, 2)
m = [2 - (- 4)] / [1 - (- 1)]
m = 3
Case 2: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (0, 3)
m = [3 - (- 1)] / [0 - (- 1)]
m = 4
Case 3: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (1, 3)
m = [3 - (- 1)] / [1 - (- 1)]
m = 2
Case 4: (x₁, y₁) = (0, 4), (x₂, y₂) = (2, - 2)
m = (- 2 - 4) / (2 - 0)
m = - 3
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Nicole made 10 dozen cupcakes. She made 20% with chocolate icing, 30% with vanilla icing, and 50% with powdered sugar. How many of each kind of cupcake did she make?
Answer:
2 Dozen Chocolate, 3 Dozen Vanilla, 5 Dozen Sugar.
Explanation:
0.5 x 10 = 5.
0.3 x 10 = 3.
0.2 x 10 = 2.
In a school, there are 4 boys to every 3 girls.
If there are 18 girls, how many boys are there? Show with great detail to every step
Sure, I'd be happy to help you with this problem!
Given that the ratio of boys to girls in the school is 4:3, we can say that for every 4 boys, there are 3 girls.
Let's start by finding the total number of students in the school, using the information that there are 18 girls.
If 3 girls represent a part of the whole, then we can find the total number of parts by dividing the total number of girls by 3:
18 girls ÷ 3 = 6 parts
So, there are 6 parts in the whole.
Now, since there are 4 boys for every 3 girls, we know that for every 7 parts (4 boys + 3 girls), there are 4 boys.
To find the total number of boys, we need to figure out how many groups of 7 parts there are in the whole.
6 parts ÷ 7 = 0 with a remainder of 6
This tells us that there are 0 groups of 7 parts in the whole, with 6 parts left over.
Since we know that for every 7 parts there are 4 boys, we can find the number of boys in the remaining 6 parts by multiplying 4 by the fraction of 6/7:
4 boys × 6/7 = 24/7 boys
This tells us that there are 24/7 boys in the remaining 6 parts.
To find the total number of boys in the school, we need to add the number of boys in the groups of 7 parts and the number of boys in the remaining 6 parts:
0 groups of 7 parts × 4 boys per group = 0 boys
6 parts × 4 boys per 7 parts = 24/7 boys
Total number of boys = 0 boys + 24/7 boys = 24/7 boys
So, there are 24/7 boys in the school. We can simplify this fraction by dividing both the numerator and the denominator by 3:
24/7 ÷ 3/3 = 8/7 boys
Therefore, there are 8/7 boys in the school, which is approximately 1.14 boys.
However, since we cannot have a fraction of a person, we can round this number to the nearest whole number, which is 1.
Therefore, there is 1 boy in the school for every 3 girls, making a total of:
1 boy × 18 girls = 18 boys
So, there are 18 boys in the school.
URGENT!! EQUIVALENT ALGEBRAIC EXPRESSIONS
Which expression is equivalent to (m^−3n^−5)^−3?
m−^9n^−15
m^−6n^−8
1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
m^9n^15
Using Laws of Exponents, the solution to the given algebraic expression is: m⁹n¹⁵
How to solve Laws of exponents?Some of the Laws of Exponents are:
1) When multiplying the like bases, ensure you keep the base the same and then add the exponents.
2) When raising a base that has a power to another power, ensure you keep the base the same and then multiply the exponents.
3) When dividing like bases, ensure you keep the base the same and then subtract the denominator exponent from the given numerator exponent.
We are given the expression:
(m⁻³n⁻⁵)⁻³
Using the second law of exponents above, we have:
m⁻³*⁻³ x n⁻⁵*⁻³
= m⁹n¹⁵
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A train running between two stations 50 Km apart arrives on time if it travels at an
average speed of 60 km/h. How late will it be if travels at an average speed of 50 Km/h?
If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.
How late will the train be if it travels at an average speed of 50 Km/h?Speed is simply referred to as distance traveled per unit time.
It is expressed as:
Speed = distance / time
Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.
The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:
Speed = distance / time
time = distance / speed
time = 50 km / 60 km/h
time = 5/6 hour
Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:
Speed = distance / time
time = distance / speed
time = 50 km / 50 km/h
time = 1 hour
Now, the difference in time between the two scenarios would be:
time difference = 1 hour - 5/6 hour
time = 1/6 hour
Convert to minutes
time = 1/6 × 60
time = 10 minutes
Therefore, the train would be late by 10 minutes.
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Correct answer gets brainliest!!!!
Answer:
D. It is a two-dimensional object.
The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.
Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.
Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.
Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.
Triangle Angles
Yes or No
The sum of 150, 20 , and 20 is more than 180 degrees, therefore, it is not possible to draw a triangle.
How to Determine if a Set of Angles will Form a Triangle?A triangle is simply a three sided polygon that has three sides and three interior angles. When all three interior angles are added together, the sum is equal to 180 degrees according to the triangle sum theorem.
If we have a set of angles with the measure of 150, 20, and 20 degrees, respectively, the sum of these is more than 180 degrees.
150 + 20 + 20 = 190 degrees.
Therefore, it is not possible to draw a triangle with those set of angles.
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Martin, wyatt , and adeyla were having a contest to see who could throw a softball the farthest. Martin threw the ball 9 feet. Wyatt threw the ball three times as far as Martin. Adeyla threw the softball 3 feet farther than Wyatt. How far did Adeyla throw the softball?
Answer: 30 Feet
Step-by-step explanation: Martin threw the ball 9 feet so we have Martins distance, next we know that Wyatt throws the ball 3 times as far which is 9x3 which is 27, Adeyla threw it 3 feet farther then Wyatt who threw it 27. 27+3=30
So the answer is 30 feet
An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different banks. The terms of each loan are:
Offer 1: 2.99% annual simple interest, with a total account balance of $81,353.75 after a 34-month term
Offer 2: 1.5% annual interest compounded monthly for a 38-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest penny.
O$1,718.99
O $2,001.57
O $2,707.62
O $2,489.68
Answer: 2,001.57
Step-by-step explanation:
there ya go!
Find the measure of angle 3. 90° 45° 120° 30°
Select the correct answer.
What is the value of x in the triangle?
a 30-60-90 triangle with long leg length x and shorter leg length of 7 times the square root of 3
The length of the hypotenuse is 7m.
Let the side opposite to 30° be the shortest leg.
The side opposite to 60° is the longest leg.
So, the side opposite to 90° is hypotenuse.
Length of the shortest side is x.
Length of longest side is [tex]\sqrt{3}x[/tex]
Length of the hypotenuse is 2x.
We know x = 7
So, [tex]\sqrt{3}(x)=\sqrt{3}(7)[/tex]
Thus, the length of the longer leg is [tex]\sqrt{3}(7)[/tex] m
Length of hypotenuse = 2x = 2(7) = 14m
[tex]x^{2} +(\sqrt{3} x)^2 =(2x)^2\\\\(7)^2+(\sqrt{3} (7))^2=(2x)^2\\\\49 + (3(49)) = (2x)^2\\\\49 + 147= (2x)^2\\\\(2x)^2=196[/tex]
Taking square root on both sides:
[tex]2x = \sqrt{196}[/tex]
2x = 14
x = 7
Therefore, the length of the hypotenuse is 7m.
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Help me… it’s so hard!
The solution of the each given equations:
(1) x = 9
(2) x = -2
(3) x = -2
(4) x = 26
(5) x = 3/5
(6) x = 13/12
(7) x = 15
(8) x = 26
(9) x = 7/3
(10) x = 5/8
We have to solve this given equation in on variable.
(1) Given equation is,
x - 7 = 2
x = 2 + 7 = 9
Hence, the solution is, x = 9
(2) Given equation is,
3x + 4 = -2
3x = -2 -4
3x = -6
x = -6/3 = -2
Hence, the solution is, x = -2
(3) Given equation is,
2x + 7 = x + 5
2x - x = 5 - 7
x = -2
Hence, the solution is, x = -2
(4) Given equation is,
x/2 = 13
x = 2*13 = 26
Hence, the solution is, x = 26
(5) Given equation is,
5(2 + x) = 13
10 + 5x = 13
5x = 13 - 10
5x = 3
x = 3/5
Hence, the solution is, x = 3/5
(6) Given equation is,
6(2x - 1) = 7
12x - 6 = 7
12x = 7 + 6 = 13
x = 13/12
Hence, the solution is, x = 13/12
(7) Given equation is,
2x/5 = 6
2x = 6*5 = 30
x = 30/2 = 15
Hence, the solution is, x = 15
(8) Given equation is,
x/2 = 13
x = 2*13 = 26
Hence, the solution is, x = 26
(9) Given equation is,
(x - 1)3 = 4
3x - 3 = 4
3x = 4 + 3 = 7
x = 7/3
Hence, the solution is, x = 7/3
(10) Given equation is,
(2x - 1)4 = 1
8x - 4 = 1
8x = 1 + 4
8x = 5
x = 5/8
Hence, the solution is, x = 5/8
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Pls help help its urgent!
The comparison of the function A(t) to the function H(t) is given as follows:
It is vertically stretched by a factor of 1.2.It is horizontally compressed by a factor of 3.How to interpret the transformations?The function A(t) in the context of this problem is given as follows:
A(t) = 1.2H(3t).
The transformations, compared to the function H(t), are then listed and explained as follows:
It is vertically stretched by a factor of 1.2, due to the multiplication by 1.2 on the range.It is horizontally compressed by a factor of 3, due to the multiplication by 3 on the domain.(multiplication by a value greater than 1 on the range stretches, on the domain it compresses).
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Given that cos(x) =
A.
B.
2/3 113
D.
C. 1
13
2/3
3'
Mark this and return
find sin (90-x).
Please select the best answer from the choices provided
Save and Exit
Next
Su
Answer:
C
Step-by-step explanation:
cos x and sin(90 - x) are cofunctions and are equal , then
cos x = [tex]\frac{1}{3}[/tex] , then sin(90 - x) = [tex]\frac{1}{3}[/tex]
Find the rank of the matrix [
2 − 1 − 3 − 1
1 2 3 − 1
1 0 1 1
0 1 1 − 1
]
The rank of the matrix is 3, since there are three linearly independent rows.
The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.
To find the rank of the matrix:
[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]
We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.
[tex]R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2[/tex]
This gives us the following matrix:
[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]
We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.
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Work out the angle of X
Answer:
x = 99
Step-by-step explanation:
Since x is on a straight line the adjacent angle and x must equal 180. We will call this adjacent angle B. The angle to the right of B also is on a straight line.
So,
180 - 123 = the inside angle Simplify
57
The addition of a triangles interior angles equals 180
180 = 42 + 57 + B Move variables to one side
180 - (42 + 57) = B Simplify
81 = B
Now we can solve for X
180 - 81 = x Simplify
99
a cylinder has a radius of 6 cm and height 7 cm. Calculate the volume of the cylinder. (pie=22/7) and (v=pie^r 2 h)
Answer: The volume of the cylinder is 924 cubic centimeters.
Step-by-step explanation:
The formula to calculate the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.
Given, radius (r) = 6 cm and height (h) = 7 cm.
Using the formula, we have V = (22/7) x 6^2 x 7 = 924 cubic centimeters.
Therefore, the volume of the cylinder is 924 cubic centimeters.
I need assistance please.
Your Assignment
Image displaying pentagon ABCDE in the third quadrant. Horizontal segment AB is at the bottom of the figure and vertex C is on the right. Pentagon A''B''C''D''E'', is in quadrant I. Segment A''B'' is at the top and vertex C'' is on the right.
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
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If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.
How to solveProblem 1
One method Olivia could have used is to reflect over the x axis and then translate 10 units to the right.
Let's apply this set of steps to point C.
C = (-2,-4)
C' = (-2,4) after reflecting over the x axis; y coordinate flips in sign
C'' = (8,4) after shifting to the right 10 units; add 10 to the x coordinate
Point C(-2,-4) moves to C''(8,4) which is shown in the diagram. I'll let you check the other four points.
-----------
Another method Olivia could have used is to shift to the right 10 units first, then reflect over the x axis. In this case, the order doesn't matter. Though for some other combinations of transformations, order does matter.
============================================================
Problem 2
Reflecting over the y axis will have the point (x,y) turn into (-x,y). Only the x coordinate changes, and we flip the sign here. The y coordinate stays the same.
A point like C(-2,-4) becomes C'(2,-4) after the y axis reflection. Shifting up 8 units means we add 8 to the y coordinate to arrive at C''(2,4) but this does not match what the diagram shows. Therefore, Angelica's method is incorrect.
You should find other inconsistencies for the other four points as well.
============================================================
Problem 3
Michael's method isn't correct either. He does not apply an x axis reflection and instead relies entirely on translations to move ABCDE to A''B''C''D''E''
At a quick glance, it looks like Michael may be correct. But upon a much closer look, you'll see that things don't line up perfectly.
Instead of point C, we'll pick on point D this time.
D is located at (-6,-2). If we shift up 8 units, then we add 8 to the y coordinate to get to D'(-6,6). Then add 10 to the x coordinate to shift 10 units to the right. This leads us to D''(4,6).
However, the diagram shows D'' is actually at (4,2)
Feel free to examine the remaining points. It will become apparent that merely C and E are accurately plotted; however, the others are not. This is, once again, due to Michael's failure in implementing an x-axis reflection.
The A''B''C''D''E'' diagram he produced is essentially inverted compared to its intended form.
============================================================
To summarize, the methods described in problem 1 are the correct way to get ABCDE to move to A''B''C''D''E''.
If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.
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Gable Supplies Ltd will commence trading in July 2018 with Share Capital of £55,000. The company will spend £80,000 on equipment.
They have arranged a loan of £110,000 repayable over five years. Repayments of capital and interest are £2,450 each month. The loan interest for the first three months included in the repayments is £2,367.
Sales are expected to be as follows:
July £120,000
August £130,000
September £150,000
40% of sales are for cash, and attract a discount of 5%.
The remainder of sales is on credit terms and collected 1 month later.
Opening inventory of £50,000 is paid for in July, further inventory is purchased at 45% of sales each month. Suppliers are paid one month in arrears.
Closing inventory should be £60,000.
Wages are forecasted to be £12,000 per month, payable in the month they are incurred. Overheads excluding depreciation are forecast to be £15,000 per month and paid in the month they are incurred.
Rent is £36,000 per year payable annually in advance.
Equipment will be depreciated at 10% of cost per year.
Required:
a) Forecast Monthly Cash Flow Statement for the 3 months to 30th September 2018.
(15 marks)
b) Forecast Income Statement for the period ending 30th September 2018.
(7 marks)
c) Forecast Statement of Financial Position as at the 30th September 2018.
(8 marks)
It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.
How to solveMonthly Cash Flow Statement for Gable Supplies Ltd for the three months ending on 30th September 2018:
Month: July August September
Opening Cash: £0 £3,550 £16,700
Cash Inflows:
Share Capital: £55,000
Loan: £110,000
Cash Sales: £45,600 £49,400 £57,000
Credit Sales: £0 £72,000 £78,000
Total Inflows: £160,600 £125,950 £135,000
Cash Outflows:
Loan Repayment: -£2,450 -£2,450 -£2,450
Equipment: -£80,000
Inventory: -£50,000 -£54,000 -£67,500
Wages: -£12,000 -£12,000 -£12,000
Overheads: -£15,000 -£15,000 -£15,000
Rent: -£36,000
Total Outflows: -£157,050 -£109,250 -£118,450
Closing Cash: £3,550 £16,700 £33,250
It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.
Additionally, credit sales to be accrued in the subsequent month from when the product was sold.
Inventory acquisition constitutes approximately 45% of revenue each month, whereas payments to suppliers get delayed by one month.
Rent, on the other hand, needs to be paid annually but paid beforehand instead of scheduled billing periods.
To note, the non-cash category of expenditures does not encompass depreciation according to the cash flow statement rules.
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Please can someone help me
The vector v can be decomposed into v₁ = -2i - 2j and v₂ = -6i + 6j.
What is the decomposition of the vectors?The decomposition of the vectors is calculated as follows;
v₁ = (v · w / |w|²) w
v₂ = v - v₁
The dot product of v and w is calculated as;
v · w = (-8)(1) + (4)(1)
v · w = -4
The magnitude of w is calculated as;
|w| = √1² + 1²)
|w|= √2
|w|² = 2
The value of v₁ is calculated as;
v₁ = (-4 / 2) (i + j)
v₁ = -2i - 2j
The value of v₂ is calculated as follows;
v₂ = v - v₁
v₂ = (-8i + 4j) - (-2i - 2j)
v₂ = -6i + 6j
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A tire is 22 inches in diameter and rests on a platform that is 4 inches above the ground. The six o’clock position on the tire is level with the platform. A piece of gum stuck to the three o’clock position of the tire completed 1 full revolution in 12 seconds. The function h(t) gives the height of the piece of gum in inches above the ground t seconds after the tire begins to turn. Find a formula for the height function h(t)
Answer:
h(t) = 11 * sin(π/6 * t) + 15
Step-by-step explanation:
To find the height function h(t) for the piece of gum, we'll use a sinusoidal function since the height of the gum changes in a periodic manner as the tire rotates. The general formula for a sinusoidal function is:
h(t) = A * sin(B * (t - C)) + D
where A is the amplitude, B is the angular frequency, C is the horizontal shift, and D is the vertical shift.
1. Amplitude (A): The amplitude is half the distance between the highest and lowest points of the gum. Since the diameter of the tire is 22 inches, the radius is 11 inches. Thus, the amplitude is 11 inches.
2. Angular frequency (B): Since the gum completes 1 full revolution in 12 seconds, the period of the function is 12 seconds. The angular frequency, B, is found by dividing 2π by the period: B = 2π / 12 = π/6.
3. Horizontal shift (C): Since the gum starts at the three o'clock position, and we want the height to be at its maximum at t = 0, there is no horizontal shift. So, C = 0.
4. Vertical shift (D): The platform is 4 inches above the ground, and the radius of the tire is 11 inches. Therefore, the midpoint of the gum's motion is 4 + 11 = 15 inches above the ground. So, D = 15.
Now we can write the height function h(t):
h(t) = 11 * sin(π/6 * t) + 15
In a class of 50 students, they had a chance to read novel,comics and textbook 21 read novel,24 read comics and 18 read textbook 3 read only novel 9 read only comics and 2 read only textbook 5 read all the 3. illustrate your information on a venn diagram. use your diagram to find the number of students who read a. comics and novel only b. textbook and novel only c. none of the 3
a. 3 students read comics and novel only.
b. 1 student read textbook and novel only.
c. 31 students read none of the three categories.
Here's a Venn diagram that shows the information given:
_________
/ \
/ \
/ \
/ \
/ A \
/ \
/__________\
| | |
| | |
| C | B |
| | |
|__________|__________|
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
|
|
|
D
The three circles represent the three categories: novel, comics, and textbook.
The overlap between the circles represents the number of students who read more than one category.
The letters A, B, C, and D represent the following regions:
A: Only comics and novel (not textbook)
B: Only textbook and novel (not comics)
C: Only textbook and comics (not novel)
D: All three categories
To answer the questions:
a. To find the number of students who read comics and novel only (region A), we need to add up the number of students who read both comics and novel (5) and subtract from it the number of students who also read textbook (2).
So, the number of students who read comics and novel only is 5 - 2 = 3.
b. To find the number of students who read textbook and novel only (region B), we follow the same process.
We add up the number of students who read both textbook and novel (3) and subtract from it the number of students who also read comics (2).
So, the number of students who read textbook and novel only is 3 - 2 = 1.
c. To find the number of students who read none of the three categories, we start with the total number of students (50) and subtract from it the number of students who read at least one category.
To find the latter number, we add up the number of students who read only novel (3), only comics (9), only textbook (2), and all three (5), which gives us 19. So, the number of students who read none of the three categories is 50 - 19 = 31.
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Verify that the given segments are parallel.
The verification of given segments in a triangle are parallel is as follow,
In triangle ABE, AC/ CE = BD/DE are in proportion ⇒ CD || AB.
In triangle RVS, VT/TR = VU/US are in proportion ⇒ UT || SR.
In the triangle ABE,
CD is the line segment divides AE and BE into equal parts.
AC = 1.5
CE = 1.5
BD = 1.5
DE = 1.5
AC/ CE = BD/DE
Line divides the two adjacent sides of a triangle are in proportion.
This implies ,
CD is parallel to AB.
In triangle RVS,
VT /TR = 90 /72
⇒VT /TR = 1.25
VU/US = 67.5/54
⇒VU/US = 1.25
This implies ,
VT/TR = VU/US are in proportion.
Hence , triangle proportionality theorem UT is parallel to RS.
Therefore, using triangle proportionality theorem in both the triangle that is,,
In triangle ABE , CD is parallel to AB and in triangle RVS , UT || RS.
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