Answer:
the width of the rectangle is 11 cm, the length is 13 cm, and the area is 143 cm^2.
Step-by-step explanation:
Let's assume that the width of the rectangle is "x" cm.
According to the problem, the length of the rectangle is 2 more than its width, which means:
Length = x + 2
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Substituting the given values, we get:
48 = 2(x + 2 + x)
48 = 2(2x + 2)
48 = 4x + 4
44 = 4x
x = 11
So, the width of the rectangle is 11 cm and the length is:
Length = 11 + 2 = 13 cm
The formula for the area of a rectangle is:
Area = length x width
Substituting the given values, we get:
Area = 11 x 13 = 143 cm^2
Therefore, the width of the rectangle is 11 cm, the length is 13 cm, and the area is 143 cm^2.
Answer:
Length = 13 cm Breadth = 11 cm Area of rectangle = 143 cm²Step-by-step explanation:
Length of rectangle is 2 more than its Width.
Let width be x and length be x +2.
If Perimeter is 48 cm .
Perimeter of rectangle = 2(l +b)=> 48 = 2(x + 2 + x)
=> 48 = 2(2x +2)
=> 48 = 4x + 4
=> 48 - 4 = 4x
=> 44 = 4x
=> x = 44/4
=> x = 11 cm
Hence,
Length of rectangle = x +2 = 13 cm
Breadth of rectangle = 11 cm
Now,
Area of rectangle = l × b=> 11 × 13
=> 143 cm²
plss!!!!!!!!!!!!!!!!!
Answer:
1. Decay of 51%
2. Growth of 51%
3. Decay of 49%
4. Growth of 49%
Step-by-step explanation:
Look at the number in the parentheses raised to the power t.
In the formula, you have (1 + r)^t.
The number in parentheses is 1 + r.
Set each number in parentheses equal to 1 + r and solve for r.
If r is positive, it is growth.
If r is negative, it is decay.
1.
1 + r = 0.49
r = 0.49 - 1
r = -0.51
Decay of 51%
2.
1 + r = 1.51
r = 1.51 - 1
r = 0.51
Growth of 51%
3.
1 + r = 0.51
r = 0.51 - 1
r = -0.49
Decay of 49%
4.
1 + r = 1.49
r = 1.49 - 1
r = 0.49
Growth of 49%
You purchase an old farmhouse for $175,000 with a 30% down payment. You have two loan options.
Loan #1: 7.25% for 20 years
Loan #2: 7.00% for 25 years
A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the range of the data set. 38 38 41 47 48 52 55 57 60 62 63 65 Give the random variable. (Appropriate rounding rules still apply.) r.v. =
The randοm variable in this case is the range οf the 12 data values, which is equal tο 27.
What is range οf a data set?The range οf a data set is the difference between the highest and lοwest value in a given set.
The range οf a data set is the difference between the largest and smallest values in the set.
In this case, the smallest value is 38 and the largest value is 65. Therefοre, the range οf the data set is:
Range = Largest value - Smallest value
Range = 65 - 38
Range = 27
Sο, the randοm variable in this case is the range οf the 12 data values, which is equal tο 27.
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Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations. A. 5 × 3 = 15 B. 1 5 × 1 3 = 1 15 C. 1 5 × 3 = 3 5 D. 5 ÷ 1 3 = 15 E. 1 3 ÷ 5 = 1 15
The two equations that can be applied to the issue are as follows: A. 5 × 3 Equals 15 (multiplication) (multiplication) . B. 1/5 × 3 Equals 3/5 (multiplication and division) (multiplication and division)
what is equation ?An equation is a claim that two alternatives are equal in mathematics. The equals sign (=) is generally used to denote this claim. It is a mathematics assertion that two expressions are equal. Variables, constant, coefficients, and mathematical operations like addition, subtraction, multiply, and dividing can all be found in an equation. Finding the value(s) of both the variable(s) that render the equation true is the aim of an equation's solution.
given
Each of the five pears Kylie has is divided into thirds. She must therefore distribute the following quantity of pear slices to her teammates:
5 pears cut into 3 slices each equals 15 slices.
The two equations that can be applied to the issue are as follows: A. 5 × 3 Equals 15 (multiplication) (multiplication) . B. 1/5 × 3 Equals 3/5 (multiplication and division) (multiplication and division) .
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Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
By responding to the prompt, we may deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the points D, E, and F.
Circle – what is it?A circle, which appears to be a 2D component, is made up of all the points in a jet that are uniformly spaced out from the hub. The capital "O" for the centre and the bottom component "r" for the radius stand for the distance from the origin to any point on a circle, respectively.
The formula πr², where (pi) is a proportionality constant roughly equal to 3.14159, determines the girth (the distance from the centre of the circle). The formula 2πr is used to determine a circle's circumference.
To recreate the original triangle using just two of its sides and the included angle, follow these steps:
Locate the location where the circle and the ray cross. Draw an arc that twice intersects the circle starting at point E on the compass. The point that is adjacent to point B on side AC should be designated as point F.
Create a polygon that passes across points D, E, and F to finish the copied triangle.
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Triangle DEF should be congruent with triangle AED because they share two sides and the included angle.
What is circle?A circle looks to be a two-dimensional component described as the collection of all equidistant points in a jet from the hub. A circle is usually represented by a capital "O" for the centre and a lower section "r" for the Radius, which refers to the distance between the origin and any point on the circle.
Based on your directions, it appears that you are constructing a triangle using the SAS (side-angle-side) method. The stages are as follows:
Draw a line segment DE of the length determined in component B.
Draw a circle with a radius equivalent to the length of DE using point E as the centre.
Draw an angle equivalent to the measure of angle AED using line segment ED as one of its sides and point E as the vertex. To expand this angle, draw ray EF from vertex E.
Find the spot of intersection of ray EF and the circle and label it F.
Draw a line section connecting points E and F.
Finally, connect the locations D, E, and F with line segments to form the triangle DEF.
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Image is attached below,
The following are the components in Pharoah Company’s income statement.
Determine the missing amounts.
Sales Revenue
Cost of Goods Sold
Gross Profit
Operating Expenses
Net Income
(a) $83,000
$enter Cost of goods sold in dollars
$32,700
$enter Operating expenses in dollars
$18,300
(b) $111,100 $74,100
$enter Gross profit in dollars
$enter Operating expenses in dollars
$23,300
(c)
$enter Sales Revenue in dollars
$80,500 $82,500 $47,900
$enter Net income in dollars
Cost of Products Sold is equal to $111,100 minus $97,400, or 13,700 as the formula for Net Income, the amount is $74,100.
what is amount ?The word "amount" in mathematics typically denotes the number or size of something that can be counted, measured, or computed. It is applicable to several fields, including geometry, arithmetic, algebra, statistics, and calculus. An amount, for instance, can also be used to describe the sum of a group of numbers after addition. An unknown number or value that needs to be factored into an equation in algebra is referred to as an amount.
given
(a) Gross Profit = Sales Revenue - Cost of Items Sold ($83,00)
When provided, Gross profit equals $32,700, therefore
Cost of Goods Sold is equal to $83,000 - $32,700 ($50,300).
Running Costs = $18,300
Operational costs minus Gross Profit gives you Net Income.
$32,700 - $18,300 = $14,400 is the net income.
Sales revenue equals $111,100 in (b).
Sales revenue minus gross profit equals cost of goods sold.
When provided, Operational Costs = $23,300, yet there is no gross profit, so:
Sales revenue minus costs of goods sold equals gross profit.
Total Revenue = $111,100 - Selling Prices for Items
Operational expenses minus gross profit equals $74,100 in net income.
Using the formula for Net Income, the amount is $74,100: Gross Profit - $23,300
Gross Profit: $97,400 ($74,100 + $23,300).
Cost of Products Sold is equal to $111,100 minus $97,400, or 13,700 as the formula for Net Income, the amount is $74,100.
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Consider the equation √6x+3 = x-2. Squaring the left side and simplifying results in
right side and simplifying results in
Squaring the
To solve the equation √6x+3 = x-2, we can start by squaring both sides of the equation:
(√6x+3)² = (x-2)²
Simplifying the left side of the equation, we get:
6x+3 = (x-2)²
Expanding the right side of the equation, we get:
6x+3 = x² - 4x + 4
Moving all the terms to one side, we get a quadratic equation:
x² - 10x + 1 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where a = 1, b = -10, and c = 1. Plugging these values into the formula, we get:
x = (10 ± √(100 - 4))/2
x = (10 ± √96)/2
x = 5 ± 2√6
Therefore, the solutions to the equation √6x+3 = x-2 are x = 5 + 2√6 and x = 5 - 2√6.
If A=[2 3 0] B= [-1 8 4] c=[-6 -2 2 ] find the determinant
The determinant of the matrix A is 70.
How to solveThe determinant of a 3x3 matrix can be found using the following formula:
|A| = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)
where aij represents the element in the ith row and jth column of the matrix.
Using this formula, we can find the determinant of the given matrix:
|A| = 2(82 - 4(-2)) - 3(-12 - 4(-6)) + 0(-1*(-2) - 8*(-6))
= 16 + 54 + 0
= 70
Therefore, the determinant of the matrix A is 70.
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A normally distributed population has a mean of 98.62 and a standard deviation of 0.388. What is the sample average from samples of size 586 that has a z-score of -0.74?
Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation, it is significant.
What is Probability?Probability is the concept that describes the likelihood of an event occurring.
In real life, we frequently have to make predictions about how things will turn out.
We may be aware of the result of an occurrence or not.
When this occurs, we state that there is a possibility that the event will occur.
In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence
The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.
According to our question-
If x is your data point, is the mean, and is the standard deviation,
z = (x - ) /
Hence, Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation, it is significant.
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Find the quotient of 6x³-18x²-12x
-6x
-x²-3x-2
x²-18x-12
-x² + 18x-12
-x² + 3x + 2
Therefore , the solution of the given problem of equation comes out to be (-x² + 3x + 2) / (x² - 18x - 12) = -x + 15.
What is equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of another algorithm that can analyze data given by y + 7, split 12 to two parts, and produce y + 7, leveling produces b + 7 in this instance.
Here,
We can use long division to determine the quotient of the given polynomial division problems. Let's begin with the initial issue:
2x² - 5x
-6x | 6x³ - 18x² - 12x + 0
- (6x³ - 18x²)
----------------
0 - 12x²
- (-12x² + 0x)
---------------
0 - 12x
- (0 - 12x)
----------
0
As a result, 2x2 - 5x is the result of (6x3 - 18x2 - 12x) / (-6x).
Let's now turn our attention to the second issue:
-x + 15
x² - 18x - 12 | -x² + 3x + 2
x² - 15x
--------
18x + 2
18x - 270
--------
272
As a result, -x + 15 is the result of (-x² + 3x + 2) / (x² - 18x - 12).
Thus, the ultimate responses are:
(6x³ - 18x² - 12x) / (-6x) = 2x² - 5x
(-x² + 3x + 2) / (x² - 18x - 12) = -x + 15
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a jar contains $5.55. there are three times as many dimes as nickels and twice as many quarters as dimes. how many of each coin is in the jar?
Answer:
Let's start by assigning variables to represent the number of nickels, dimes, and quarters in the jar.
Let x be the number of nickels.
Then the number of dimes is 3 times as many as nickels, so the number of dimes is 3x.
And the number of quarters is twice as many as dimes, so the number of quarters is 2(3x) = 6x.
We know that the total amount of money in the jar is $5.55, which is equal to:
0.05x (for the value of the nickels) + 0.10(3x) (for the value of the dimes) + 0.25(6x) (for the value of the quarters)
Simplifying this expression, we get:
0.05x + 0.30x + 1.50x = 5.55
Combining like terms, we have:
1.85x = 5.55
Dividing both sides by 1.85, we get:
x = 3
So there are 3 nickels in the jar.
Using this value, we can find the number of dimes and quarters:
Number of dimes = 3x = 3(3) = 9
Number of quarters = 6x = 6(3) = 18
Therefore, there are 3 nickels, 9 dimes, and 18 quarters in the jar.
Step-by-step explanation:
How do you compute MOR
Using the formula σr = 3Fx/yz², we can easily compute the Modulus of Rupture.
What is the Modulus of Rupture?The term "bending strength" is occasionally used to refer to the measure of a specimen's strength prior to rupture, also known as the "modulus of rupture," or MOR.
Contrary to the modulus of elasticity, which measures the wood's deflection but not its total strength, it can be used to evaluate a species' strength.
The formula σr = 3Fx/yz² for the load force F and the material's size dimensions in the three directions of x, y, and z can be used to compute the modulus of rupture, or "sigma."
The external force applied to the substance of interest in this instance is the load.
Therefore, using the formula σr = 3Fx/yz², we can easily compute the Modulus of Rupture.
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Correct question:
How do you compute MOR?
Find the length of the missing side. Provide an answer accurate to the nearest tenth
The length of the hypotenuse is approximately 10.63 inches.
What is hypotenuse?
The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. In other words, the hypotenuse is the side that connects the two acute angles of the triangle. The hypotenuse is always opposite the right angle in a right triangle and is also the side that has the largest length compared to the other two sides of the right triangle.
The length of the hypotenuse can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the right triangle.
According to the question:
We can use the Pythagorean theorem to find the hypotenuse of a right triangle given the lengths of its other two sides. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length of the opposite side is 7 inches and the length of the adjacent side is 8 inches. Let's label the hypotenuse as c. Then, we can set up the equation:
[tex]c^2 = 7^2 + 8^2[/tex]
[tex]c^2 = 49 + 64[/tex]
[tex]c^2 = 113[/tex]
To solve for c, we take the square root of both sides of the equation:
[tex]c = \sqrt(113)[/tex]
[tex]c \approx 10.63[/tex]
Therefore, the length of the hypotenuse is approximately 10.63 inches.
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Malia went to see a play at a theater downtown. The first act was 50 minutes long. Intermission lasted for 30 minutes, and the second act was 1 hour and 10 minutes long. The second act ended at 10:45 P.M. What time did the play start?
I need help with this.
Answer:
8:15
Step-by-step explanation:
The diagram shows five shapes on a centimetre grid. A D D B E C a) Write down the name of shape A. Two of the shapes are congruent. b) Select the letters of these two shapes.
The name of shape A is right trapezoid
The congruent shapes are B and D
What is a right trapezoid?A right trapezoid is a trapezoid (a four-sided polygon with two parallel sides) in which one of the angles formed by the non-parallel sides is a right angle (90 degrees).
The parallel sides of a right trapezoid are called the bases of the trapezoid, and the other two sides are called the legs. The perpendicular distance between the bases of a right trapezoid is called the height of the trapezoid.
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Select the correct texts.
A survey was conducted regarding level of education and income. The results of the survey are shown in the table below. Tiffany is a career
counselor. Using the data in the table, she makes conclusions by calculating probabilities related to a randomly selected person from the survey.
Education Level
High School Diploma
Bachelor's Degree
Master's Degree
<$40,000
51
24
3
Total
78
What can Tiffany conclude from the data?
Income
$40,000-$60,000
19
40
22
81
$60,000 Total
76
81
73
230
6
17
48
71
Given a person has only a high school diploma, they are most likely to have an income less than $40,000.
Given a person has only a high school diploma, they are most likely to have an income greater than $60,000.
Given a person has an income greater than $60,000, it is most likely that their highest level of education is a high school diploma
Given a person has an income greater than $60,000, it is most likely that their highest level of education is either a Bachelor's or Master's degree.
The correct answer is that if someone simply gets a high school certificate, their salary is most likely to make less than $40,000.
What exactly is a source of income?In general, the phrase "income" refers to the sum of money, assets, and other transfers that are worth something obtained over a predetermined period period of time as an exchange for goods or services.
Only having completed high school:
51>24>3
Therefore, it is highly likely that they make less than $40,000.
Has a salary of at least 60,000.
6<17<48
Therefore, a Master's degree is most likely their greatest level of education.
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in a mall parking lot, 60% of the cars are compacts. If there are 240 compact cars in the parking lot, how many cars are not compact
Answer: 144
Step-by-step explanation:
60/100 times x/240
Cross multiply!!!
I hope this helps, have a nice day!!
I have tried for days on this its due sunday I really need the answer pls
Answer:
Space explorer A traveled about 77,000 miles in roughly 10 hours.
Step-by-step explanation:
space traveler b travels about 155 miles faster per hour than space traveler A
Suppose in an orchard the number of apples
in a tree is normally distributed with a mean
of 300 and a standard deviation of 30 apples.
Find the probability that a given tree has
between 270 and 330 apples.
210 240 270 300 330 360 390
P = [?]%
Hint: use the 68-95 99.7 rule.
Enter
To find the probability that a given tree has between 270 and 330 apples, we need to calculate the area under the normal curve between the z-scores corresponding to 270 and 330.
How is probability of an event determined?First, we need to convert the values of 270 and 330 to z-scores using the formula:
z = (x - μ) / σ
where x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation.
For x = 270, we get:
z = (270 - 300) / 30 = -1
For x = 330, we get:
z = (330 - 300) / 30 = 1
Using the 68-95-99.7 rule, we know that approximately 68% of the area under the normal curve is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations.
Since the z-scores for 270 and 330 are within one standard deviation of the mean (i.e., they are both less than 1 standard deviation away from the mean of 300), we can use the 68% rule to estimate the probability that a given tree has between 270 and 330 apples.
According to the 68% rule, approximately 68% of the trees will have between 270 and 330 apples.
Therefore, P = 68%.
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Please help me find the arc!
Step-by-step explanation:
pi * d = total 360° circumference....you want 210/360 ths of this total
pi * 10 * 210 / 360 = calculate this.....
(x-2)(x+1)
(x-3)(x-1)²
3. Determine the asymptotes for y=
Answer: To find the vertical asymptotes of the given function, we need to find the values of x that make the denominator equal to zero. So, we set each denominator equal to zero and solve for x:
(x-3)(x-1)² = 0
x = 3 or x = 1
Therefore, the vertical asymptotes of the function occur at x = 3 and x = 1.
To find the horizontal asymptotes, we need to look at the degree of the numerator and denominator. Since both the numerator and denominator are degree 2, we can find the horizontal asymptote by dividing the leading coefficient of the numerator by the leading coefficient of the denominator. In this case, the leading coefficient of both the numerator and denominator is 1, so the horizontal asymptote is y = 1/1 = 1.
Therefore, the vertical asymptotes are x = 3 and x = 1, and the horizontal asymptote is y = 1.
Step-by-step explanation:
A student started a project using a pencil with a length of 7 1/2 inches. After the student completed the project, the pencil had a length of 5 7/8 inches. How much shorter, in inches, was the pencil after the student completed the project than when the student started the project? 4 A 1 4/8 B 1 5/8 C 2 3/8 D 2 6/8. also subscribe to my friends channel it's called your local kirby guy.
Answer:
Step-by-step explanation:
To find out how much shorter the pencil was after the student completed the project, we need to subtract the final length from the initial length:
7 1/2 - 5 7/8
To subtract these two mixed numbers, we need to convert them to a common denominator. The smallest common multiple of 2 and 8 (the denominators of the fractions) is 8, so we can rewrite the numbers as:
15/2 - 47/8
Now we can find a common denominator of 8:
(15/2) * (4/4) - (47/8) = 30/8 - 47/8
Subtracting the numerators, we get:
-17/8
Therefore, the pencil was 17/8 inches shorter after the student completed the project than when the student started the project. We can simplify this fraction to a mixed number:
-2 1/8
So the answer is C) 2 3/8 inches.
The picture below is being enlarged by a scale factor of 2.5 how many inches of framing will the picture require
Answer:
Multiply the given numbers by a factor of 2.5, then find the perimeter by adding up all 4 of the sides.
Step-by-step explanation:
While there isn't a picture given, it can be assumed that the shape given is a rectangle.
Then, simply multiply all 4 sides by a factor of 2.5, since that's the number it is being enlarged by.
Then to find the "framing" of said rectangle, add up all 4 of the sides that you just calculated to find the perimeter.
help please i need the answers in order please
A car was valued at $42,000 in the year 1994. The value depreciated to $11,000 by the year 2006.
A) What was the annual rate of change between 1994 and 2006?
r=------------ Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2010 ?
value=$---------------- Round to the nearest 50 dollars.
A) To find the annual rate of change, we can use the formula:
r = (V2/V1)^(1/n) - 1
where:
V1 = initial value ($42,000)
V2 = final value ($11,000)
n = number of years (2006 - 1994 = 12)
Plugging in the values, we get:
r = (11000/42000)^(1/12) - 1 ≈ -0.1135
Therefore, the annual rate of change between 1994 and 2006 is approximately -0.1135.
B) To convert the rate of change to a percentage, we can multiply by 100 and add a percent sign:
r = -0.1135 × 100% ≈ -11.35%
Therefore, the correct answer to part A written in percentage form is approximately -11.35%.
C) Assuming the car value continues to drop by the same percentage, we can use the formula for exponential decay:
V = V0 * (1 - r)^t
where:
V0 = initial value ($11,000 in 2006)
r = annual rate of change (-0.1135)
t = number of years (2010 - 2006 = 4)
Plugging in the values, we get:
V = 11000 * (1 - (-0.1135))^4 ≈ $6,250
Therefore, the value of the car in the year 2010 would be approximately $6,250, rounded to the nearest 50 dollars.
the cost to run the gym each month is 5,000. Find Eds total monthly expenses for each loan option.
Ed's total monthly expenses for each loan option includes:
First bank = $6,792City bank = $6,803Star bank = $6,817 How do we calculate the monthly expenses for each loan option?The lists of banks and their annual interest rates are as follows:
Because the interest rate at the first bank is 7.5%, the total interest:
= 7.5% of $20000
= 0.075 * $20000
= $1500.
Since the interest rate at City Bank is 8.2%, the total interest:
= 8.2% of $20000
= 0.082 * $20000
= $1640.
Because the interest rate at Star Bank is 9%, the total interest:
= 9% of $20000
= 0.09 * $20000
= $1800.
The annual loan plus interest for banks is:
First bank:
= $20,000 + $1500
= $21,500
City bank:
= $20000 + $1640
= $21640
Star Bank:
= $20000 + $1900
= $21900
The banks' monthly payments are as follows:
First bank = $21500 / 12 months = $1,792.
City bank = $21640 / 12 months = $1,803
Star bank = $21800 / 12 months = $1,817
Now, since monthly cost of running the gym is $5,000. Ed's total monthly expenses for each loan option are equal to the monthly payments plus the cost for each month. It is calculated as follows:
First bank = $5000 + $1792 = $6792.
City bank = $5000 + $1803 = $6803
Star bank = $5000 + $1817 = $6817
Full question "Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best loan option, Ed wants to know the percent profit he will make each month. Part A The cost to run the gym each month is $5,000. Find Ed's total monthly expenses for each loan option.
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Simplify
5(x+1)-7(x-1)
Answer:
- 2x + 6
Step-by-step explanation:
Expand
5(x+1)-7(x-1) = 5x + 5 - 7x + 1 and upon adding, = - 2x +6
- 2x + 6 can also be written as 6 - 2x
Identify a pair of segments that are marked perpendicular to each other on the
diagram below. (Diagram is not to scale.)
T
U
R
S
A bag of marbles contains 5 red, 7 purple, and 3 blue marbles. If one marble is
chosen at random, what is the probability that the marble is NOT blue?
Answer: 4/5
Step-by-step explanation:
Total marbles = 5 + 7 + 3
P(Red) = 5/15
P(Purple) = 7/15
P(Not Blue) = P(Red) + P(Purple)
= 5/15 + 7/15
= 12/15 or 4/5
A clinic has recorded the age, x, versus weight, y, of many babies for their first 12 months of life, and claim the line of best fit is ŷ = 0.60x + 3.3, where y is in kg, and x is in months.
A new baby, who is 10 months and weighs 10 kg, is added to the clinic records.
What is the residual of the data for this new baby?
The residual of the data for this new baby is 0.7
What is a linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Here, we have
Given: A clinic has recorded the age, x, versus weight, y, of many babies for their first 12 months of life, and claims the line of best fit is ŷ = 0.60x + 3.3, where y is in kg, and x is in months.
ŷ = 0.60x + 3.3
Substitute, x=10
ŷ = 0.60(10) + 3.3 = 9.3
Residual = y - ŷ = 10 – 9.3 = 0.7
Hence, the residual of the data for this new baby is 0.7
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Find the length of major arc PQ
The length of major arc PQ is 35π units.
What is major arc?
In geometry, an arc is a portion of the circumference of a circle. A major arc is an arc that spans more than 180 degrees of the circle. In other words, a major arc is an arc that is greater than a semicircle (which spans exactly 180 degrees).
we know that,
length of arc = s = 2 π r (θ/360°)
where, r is the radius and θ is the angle of arc.
we have, r = 30
θ = 210
so, length of major arc PQ :
= 2 π r (θ/360°)
= 2 π × 30 × (210/360)
= 60 π × 7/12
= 35π units.
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