Answer:
Sure, I can help you with that!
To start, let's look at the ingredient list and see what information we have:
- 8 cups water
- ½ cup garlic
- ½ cup onion
- 1 ½ cups chopped carrots
- ½ cup tomato paste
- 2 cups sliced potatoes
- 1 cup olive oil
To make the calculations, we can set up ratios that relate the amount of each ingredient to the number of servings of soup. For example, if we want to know how much garlic we need for 40 servings of soup, we can set up the following ratio:
½ cup garlic / 10 servings = x cups garlic / 40 servings
To solve for x, we can cross-multiply and simplify:
(½ cup garlic) * 40 servings = (10 servings) * x cups garlic
20 cups = 10x
x = 2 cups
So we would need 2 cups of garlic to make 40 servings of soup.
Similarly, we can set up ratios for the other questions:
Question 2:
½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings
(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste
30 cups = 10x
x = 3 cups
So we would need 3 cups of tomato paste to make 60 servings of soup.
Question 3:
1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings
(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots
45 cups = 10x
x = 4.5 cups
So we would need 4.5 cups of chopped carrots to make 30 servings of soup.
here I simplified and checked the cross products of the ratios.
Question 1:
½ cup garlic / 10 servings = x cups garlic / 40 servings
Cross-multiplying, we get:
(½ cup garlic) * 40 servings = (10 servings) * x cups garlic
20 cups = 10x
Dividing both sides by 10, we get:
x = 2 cups garlic
Therefore, we need 2 cups of garlic to make 40 servings of soup.
Checking the cross products:
(½ cup garlic) * 40 servings = (10 servings) * 2 cups garlic
20 cups = 20 cups
The cross products are equal, so my answer is correct.
Question 2:
½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings
Cross-multiplying, we get:
(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste
30 cups = 10x
Dividing both sides by 10, we get:
x = 3 cups tomato paste
Therefore, we need 3 cups of tomato paste to make 60 servings of soup.
Checking the cross products:
(½ cup tomato paste) * 60 servings = (10 servings) * 3 cups tomato paste
30 cups = 30 cups
The cross products are equal, so my answer is correct.
Question 3:
1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings
Cross-multiplying, we get:
(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots
45 cups = 10x
Dividing both sides by 10, we get:
x = 4.5 cups chopped carrots
Therefore, we need 4.5 cups of chopped carrots to make 30 servings of soup.
Checking the cross products:
(1 ½ cups chopped carrots) * 30 servings = (10 servings) * 4.5 cups chopped carrots
45 cups = 45 cups
The cross products are equal, so my answer is correct.
What is 2097 plus 3284
Answer:
What is 2097 plus 3284
2097 + 3284
= 5381Step-by-step explanation:
You're welcome.
Write a simplified expression for the area of the figure below ⬇️
Step-by-step explanation:
Area of a rectangle = Height * width
area = 5y * ( 7y-4)
= 35 y^2 - 20y ( or y ( 35y-20) )
You borrowed $150 from your friend and she's created 2 plans to help you decide how you want to pay it back. Her plans are below.
a- How much money did you borrow initially?
b- How much does each plan have you paying each week?
c- which plan would you choose and why?
Answer:
its prob a
Step-by-step explanation:
I think for sure its A
Use the image to answer the question help Danny and Sarah interpret this insurance quote for the 2015 sports car and 2018 minivan what deductible amount does the policy show 
A. 85.60
B. 114.40
C. 210
D. 250
In linear equation, 85.60 deductible amount does the policy show.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
As you can see in the above table
Insurance for A = Bodily injury + Property damage + Medical payments + Comprehensive + Collision + Additional Coverages + Towing and labor + loss of use
= 115+49.5+18.2+38.9+250+250+2+20
= 743.6
Calculation for B :
As you can see in the above table
Insurance for B = Bodily injury + Property damage + Medical payments + Comprehensive + Collision + Additional Coverages + Towing and labor + loss of use
= 118.2 + 45.9+ 18.2 +42.3 + 250+250+ 2 +20
= 746.6
Calculations for C :
Total each vehicle:2015 sports = A + extra passangers * Uninsurared motorised bodily injury
= 743.6 + 1*0 = 743.6
Calculations for D :
Total each vehicle:2018 minivan = B + extra passengers * Uninsured motorized bodily injury
= 746.6 + 1*76.1 = 822.7
Calculations for E:
= C + D
= 743.6 + 822.7
= 1566.3
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Mrs. Dugan plans to serve
100 barbecue sandwiches at the
company picnic. How many packages
of barbecue buns will she need if buns
come in packages of 83 Packages of 12?
Answer:
For packages of 8: She will need 13 packages
For packages of 12: She will need 9 packages
Step-by-step explanation:
Number of barbecues sandwiches = 100 (given)
For packages of 8 we have, (100/8) = 12 (without the remainder)
We then add one extra package so that the 100 barbecue sandwiches are served.
So, for packages of 8, packages of barbecue buns = 12 + 1 = 13
For packages of 12 we have, (100/12) = 8 (without the remainder)
We then add one extra package so that the 100 barbecue sandwiches are served.
So, for packages of 12, packages of barbecue buns = 8 + 1 = 9
Describe the association for this scatterplot.
no association
negative association
positive association
Answer: A scatter plot shows the association between two variables. A scatter plot matrix shows all pairwise scatter plots for many variables. If the variables tend to increase and decrease together, the association is positive. If one variable tends to increase as the other decreases, the association is negative.
Step-by-step explanation:
A survey of American households asked 1000 Americans and found that 20% of them own 2 pets. Identify the sample.
Therefore, the sample size was approximately 1360 Americans.
What is sample?In statistics, a sample is a subset of a larger population. It is a representative selection of individuals or objects taken from the population of interest to be studied. Samples are often used in statistical analysis because it is usually impractical or impossible to collect data from the entire population.
Here,
The survey states that 20% of American households own 2 pets, and the survey was conducted on 1000 Americans. Since we are trying to identify the sample size, we can use the formula:
sample proportion = x / n
where x is the number of households that own 2 pets, and n is the sample size.
We are given that 20% of the sample own 2 pets, so we can write:
0.20 = x / n
Multiplying both sides by n, we get:
n * 0.20 = x
Simplifying, we get:
n = x / 0.20
We don't know the value of x, but we can estimate it using the proportion of households that own 2 pets in the entire population. According to a study by the American Pet Products Association, about 68% of American households own at least one pet, and about 40% of pet-owning households own two or more pets. Assuming that these percentages hold true for the survey sample as well, we can estimate that:
x = 0.40 * 0.68 * 1000
= 272
Substituting this value into the equation above, we get:
n = 272 / 0.20
= 1360
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The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
Let x= the number of busses and y= the number of vans
Create an equation representing the number of vehicles needed.
Preview Change entry mode
Create an equation representing the total number of seats in vehicles for the orchestra members.
Create an equation representing the total number of seats in vehicles for the orchestra members.x*25 + y*12 = 111 Create an equation representing the total number of licensed drivers.x + y = 6
The local orchestra has been invited to play at a festival, and they need to figure out how to transport the 111 members. We can create a system of equations to find the smallest number of busses the orchestra can rent. We need to create an equation representing the number of vehicles needed and one representing the total number of seats in vehicles for the orchestra members. We also need an equation representing the total number of licensed drivers. The equation for the number of vehicles needed is x + y = 6, where x is the number of busses and y is the number of vans. The equation for the total number of seats in vehicles is x*25 + y*12 = 111. Solving these equations will give us the smallest number of busses the orchestra can rent.
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PLEASE HELP ME WITH THE MATH QUESTIONS!!! BRAINLIEST + 25 POINTSS (tysmm)
What is the solution to this inequality?
4m - 9 > 19
(A) m > 7
(B) m > 4
(C) m > 6
(D) m > 5
_____
What is the solution to this inequality?
- 3p - 12 < 3
(A) p < 5
(B) p < - 5
(C) p > 5
(D) p > -5
____
What is the solution to the inequality?
S/4 + 6 > 9
(A) s > 16
(B) s > 12
(C) s > 8
(D) s > 4
____
please try to answer all! thanks <3
Answer:
1) A
2) D
3) B
Step-by-step explanation:
Math
:)
Drag the tiles to the correct boxes to complete the reasoning of the proof. Not all tiles will be used. Given: The lines shown in the diagram are parallel. Prove: The sum of the interior angles of the triangle is . Diagram shows 2 parallel lines with a vertical segment between them. A segment extends from the intersection point on top line to below line to the right, forming a right triangle. At top, angles are 1, 2, 3. At below, angles are 4 and 5. Since the given lines are parallel, then by the alternate interior angle theorem, , , and .
The reasοns for angles fοr each οf the given statements are respectively;
1) Substitutiοn
2) Definitiοn οf a Straight angle because a straight angle is 180°.
3) Cοngruent Angles have equal measures
Hοw tο prοve angles in a triangle?We are given that;
m∠1 = 90°
m∠1 + m∠2 = m∠5
∠3 ≅ ∠4
Statement 1; 90° + m∠2 + m∠4 = 180°
Reasοn 1; Substitutiοn
Statement 2; m∠1 + m∠2 + m∠3 = 180°
Reasοn 2; Definitiοn οf a Straight angle because a straight angle is 180°.
Statement 3; m∠3 = m∠
Reasοn 3; Cοngruent Angles have equal measures
Thus, the missing reasοns fοr each οf the given statements are respectively;
1) Substitutiοn
2) Definitiοn οf a Straight angle because a straight angle is 180°.
3) Cοngruent Angles have equal measures
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Complete question:
1237568×646773÷5373737
Answer:
14,896.1456Step-by-step explanation:
please make me brainalist and keep smiling dude I hope you will be satisfied with my answer is updated upStep-by-step explanation:
[tex] \frac{1237568 \times 646773}{5373737} = \frac{800425568064}{5373737} = 148951 \frac{2068177}{5373737} [/tex]
First, multiply the numbers that are in numerator
Then divide the product of the numerator by the denominator
And lastly take out the whole part of the fraction and write what remains
It think that's it
A rectangular garden is 25 feet long and 13 feet wide. A brick walk way with uniform width is going to be constructed around the garden. The brick walk way will have an area of 287 square feet. What should be the width of the brick walk way? Type in your answer to the nearest thousandth. The width of the walk way should be
feet wide.
The width of the walkway around the rectangular garden should be approximately 2.061 feet wide.
What is rectangle?
A rectangle is a type of quadrilateral with four sides and four right angles (90-degree angles). It is characterized by two pairs of parallel sides of equal length.
Let's represent the width of the brick walkway by "x" feet.
Then the dimensions of the entire rectangle including the brick walkway will be [tex]$(25+2x)$[/tex] feet by [tex]$(13+2x)$[/tex] feet.
The area of the rectangle with the walkway will be:
[tex]$$(25+2x)(13+2x)$$[/tex]
We know that the area of the walkway itself is 287 square feet. So we can set up the following equation:
[tex]$$(25+2x)(13+2x) - 25\cdot 13 = 287$$[/tex]
Simplifying and solving for x, we get:
[tex]$$4x^2 + 86x - 216 = 0$$[/tex]
Using the quadratic formula, we get:
[tex]$x = \frac{(-86 \pm \sqrt{86^2 - 4(4)(-216)})}{2(4)}$$[/tex]
[tex]$$x \approx 2.061 \text{ or } x \approx -26.311$$[/tex]
Since the width of the walkway cannot be negative, we reject the negative solution. Therefore, the width of the walkway should be approximately 2.061 feet wide (rounded to the nearest thousandth).
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Answer please I need helppp
0.33 is the approximate experimental probability of landing on B or C.
What is Experimental Probability?The actual outcome of an experiment, which may differ from the theoretical probability, is known as experimental probability.
Consider an experiment where 100 coin flips are performed. Theoretically, the odds are 50% heads and 50% tails. Your experiment's true results might be 47 heads and 53 tails.
We have this table
outcome A B C D
frequency 20 11 14 30
The values in the bottom row add to 20+11+14+30 = 75, so that matches up with the fact that the spinner was spun 75 times. Of those 75 spins, 11+14 = 25 landed on either B or C.
So 25/75 = 0.33 is the approximate experimental probability of landing on B or C.
Answer: Choice A) 0.33
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ABC Company has outstanding 6% cumulative preferred stock. Two years ago, ABC paid a 6% preferred dividend. Last year, ABC paid a 4% preferred stock dividend. This year, ABC wishes to pay a common dividend. The preferred shareholders must receive_____________
In circulation is 6% cumulative preferred stock for ABC Corporation. ABC distributed a 6% preferred dividend two years ago. ABC distributed a 4% preferred stock dividend last year. The minimum payout to preferred stockholders is 8%.
As per the given information, ABC Company has outstanding 6% cumulative preferred stock. This means that the preferred shareholders are entitled to receive a dividend at a fixed rate of 6% every year before any dividend is paid to the common shareholders.
The term "cumulative" implies that any unpaid dividends from previous years must be paid before any dividends can be paid to the common shareholders.
Now, we are given that two years ago, ABC paid a 6% preferred dividend. This means that the preferred shareholders received their full dividend payment for that year.
ABC distributed a 4% preferred stock dividend last year. This means that the preferred shareholders did not receive their full dividend payment for that year, and there is an unpaid amount of 2% (6% - 4%) from the previous year.
Since the preferred stock is cumulative, the unpaid dividends from the previous year must be paid before any dividend is paid to the common shareholders. Therefore, this year, ABC must pay the preferred shareholders their full dividend of 6% for the current year, as well as the unpaid amount of 2% from the previous year, totalling 8%.
To summarize, this year, ABC must pay the preferred shareholders a dividend of 8% before any dividend is paid to the common shareholders.
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simplify 2×5(16÷2-2×3)-2
A 0
B10
C18
D72
Answer:
C ) 18
Step-by-step explanation:
2×5(16÷2-2×3)-2
= 2×5(8-2×3)-2 (16 ÷ 2 = 8)
= 2×5(8-6)-2 (2×3 = 6)
= 2×5(2)-2
= 10(2)-2
= 20-2
= 18
Whats the answer for 500-25a>200
Answer:
a < 12
Step-by-step explanation:
500 - 25a > 200
500 - 200 > 25a
300 > 25a
divide both sides by 25
300/25 > 25a/25
12 > a
therefore, a < 12
I think of a number, double it, and add eleven. I get twenty five.
a)
Using the statement above, form an equation.
Use the letter 'x for the unknown number.
x*2+11 = 25
25 - 11 / 2 = x
14/2 = x
7 = x
x = 7
The equation representing the above statement is 2x + 11 = 25 and the value of the unknown number, x is 7.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Let x be the unknown number.
The unknown number is first doubled, which is represented as 2x.
Then the doubled number is added to 11, which is represented as 2x + 11.
The resulting number is 25.
So, the equation representing the situation can be represented as,
2x + 11 = 25
Subtracting both sides by 11,
2x = 14
Dividing both sides by 2,
x = 7
Hence the value of the unknown number, x is 7.
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An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model is $10,000. The probability of being awarded the bid is 0.15. If the architect is awarded the bid, she will make $55,000 minus the $10,000 cost for plans and a model. The probability of not being awarded the bid is 0.85. What is the expected value in this situation?
As a result, the anticipated value in this circumstance is -$1,750, which probability suggests that if the architect decides to bid on the design of the new museum, she can expect to lose $1,750 on average.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
0.15 x $45,000 = $6,750.
Consider the following scenario in which the architect is not granted the contract:
The likelihood of not winning the bid is 0.85.
In this case, the payback is -$10,000 (a negative value since the architect would lose the $10,000 cost of creating blueprints and presenting a model).
In this case, the anticipated value is:
0.85 x (-$10,000) = -$8,500.
We sum the anticipated values of both situations to determine the overall expected value:
$6,750 + (-$8,500) = -$1,750.
As a result, the anticipated value in this circumstance is -$1,750, which suggests that if the architect decides to bid on the design of the new museum, she can expect to lose $1,750 on average.
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Determine whether the statement is always true, sometimes true, or never true.
The difference of a negative value and a positive value is 0.
a. always true
b. sometimes true
c. never true
Using expressions -3 - 5 = -8 and -3 - 3=0, we can say that the statement The difference of a negative value and a positive value is 0 is never true i.e. C.
What exactly are expressions?
In computer programming, an expression is a combination of one or more constants, variables, operators, and functions that are interpreted and evaluated by the computer to produce a value.
Expressions can be simple, such as a single variable or constant, or they can be more complex, involving multiple operators and functions.
For example, in the expression "2 + 3 * 4", the operators "+" and "*" are used to perform arithmetic operations, and the constants "2", "3", and "4" are operands that are used in those operations.
Now,
Example: -3 - 5 = -8, which is not equal to 0.
Example: 5 - 3 = 2, which is also not equal to 0.
However, even if the negative and positive values have the same absolute value, then their difference will not be 0. For example: -3 and 3 have a difference of -6.
Hence,
the statement The difference of a negative value and a positive value is 0 is never true.
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What is the solution to the equation m+44-m m²-16
4
m²
?
m = -4
m = -2
m = 2
m = 4
Answer:
m = -2
Step-by-step explanation:
-m^3 + 17m + 44 = -(m + 2)(m^2 - 2m - 22)
m + 2 = 0 or m^2 - 2m - 22 = 0
m = -2 or m = 1 ± √23
Sam buys a new tent for $866. He knows that the value of the tent will depreciate 12% each year. How much will it be worth in 3 years? Give your answer to two decimal places.
Answer:
Step-by-step explanation:
If the value of the tent depreciates by 12% each year, then its value at the end of each year is 100% - 12% = 88% of its value at the beginning of the year.
So after the first year, the value of the tent will be:
$866 x 0.88 = $761.28
After the second year, the value of the tent will be:
$761.28 x 0.88 = $670.58
After the third year, the value of the tent will be:
$670.58 x 0.88 = $590.99
Therefore, the tent will be worth $590.99 in 3 years, to two decimal places.
Answer:
After one year, the value of the tent will be worth 100% - 12% = 88% of its original value.
After two years, the value of the tent will be worth 88% - 12% = 77.44% of its original value.
After three years, the value of the tent will be worth 77.44% - 12% = 68.1472% of its original value.
To find out how much the tent will be worth in 3 years, we can use the following formula:
Value after 3 years = original value x (1 - depreciation rate)^number of years
Value after 3 years = $866 x (1 - 0.12)^3 = $518.98
Therefore, the tent will be worth $518.98 in 3 years.
A company determines that monthly sales S(t), in thousands of dollars, after t months of marketing a product is given
by S(t)=31³-501² +220t+150.
a) Find S'(2), S'(3), and S'(4).
b) Find S(2), S'(3), and S''(4).
c) Interpret the meaning of your answers to parts (a) and (b).
gfo
Part (a) replies provide us with the instantaneous rates of change in sales derivatives at t=2, t=3, and t=4 months, respectively. These are 372, 327, and 252 in tens of thousands of dollars each month, respectively.
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
a) find the derivatives,
[tex]S(t) = 31t^3 - 501t^2 + 220t + 150\\S'(t) = 3(31t^2) - 2(501t) + 220\\S'(2) = 3(31(2)^2) - 2(501(2)) + 220 = 372\\S'(3) = 3(31(3)^2) - 2(501(3)) + 220 = 327\\S'(4) = 3(31(4)^2) - 2(501(4)) + 220 = 252\\[/tex]
b) To find S(2), S(3), and S''(4), we use the original expression for S(t):
[tex]S(2) = 31(2)^3 - 501(2)^2 + 220(2) + 150 = 662\\S(3) = 31(3)^3 - 501(3)^2 + 220(3) + 150 = 669\\S''(t) = (S'(t))' = 6(31t) - 2(501)\\S''(4) = 6(31(4)) - 2(501) = 264\\[/tex]
c) Part (a) replies provide us with the instantaneous rates of change in sales at t=2, t=3, and t=4 months, respectively. These are 372, 327, and 252 in tens of thousands of dollars each month, respectively.
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Simplify: 516−−√ + 1254−−√ − 38√
ANS : 2√(3 × 43) + √(1254) - √(38)
Let's break down the expression step by step:
Expression: √(516) + √(1254) - √(38)
Step 1: Identify prime factors of each number in the Square roots.
- Prime factors of 516: 2^2 × 3 × 43
- Prime factors of 1254: 2 × 3^1 × 11 × 19
- Prime factors of 38: 2 × 19
Step 2: Simplify the square roots using prime factors.
- √(516) = √(2^2 × 3 × 43) = 2√(3 × 43)
- √(1254) = √(2 × 3 × 11 × 19) (This square root cannot be simplified further.)
- √(38) = √(2 × 19) (This square root cannot be simplified further.)
Step 3: Substitute simplified square roots back into the expression.
- 2√(3 × 43) + √(1254) - √(38)
Since we cannot simplify the square roots of 1254 and 38 further, and there are no common terms to combine, the given expression is already in its simplest form:
Answer: 2√(3 × 43) + √(1254) - √(38)
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I need help with this please
Answer:
80 minutes
Step-by-step explanation:
80x3 is 240
240 mins=4 hrs
(i promise its right this time- i bet)
Answer:
c. 80 minutes
Step-by-step explanation:
Some problems give you too much information, and you need to choose only the information you need. The number of pages is not important. Here you only need the time, 4 hours, and the number of assignments, 3.
4 hours × 60 minutes / hour = 240 minutes
240 minutes / 3 assignments = 80 minutes/assignment
Answer: c. 80 minutes
A real estate broker decides to lease a car for 36 months. Suppose the anual interest rate is 7.8%, the negotiated price is $49,000, there is no trade-in, and the down payment is $4,000. Find the monthly lease payment (in dollars). Assume that the residual value is 49% of the MSRP of $51,500. (Round your answer to the nearest cent.)
To calculate the monthly lease payment, we need to use the formula:
Monthly Payment = Depreciation + Finance Charge
The depreciation represents the portion of the car's value that is lost during the lease period, while the finance charge is the interest charged on the lease.
First, let's calculate the depreciation:
MSRP = $51,500
Residual Value = 49% of MSRP = 0.49 x $51,500 = $25,235
Depreciation = (Negotiated Price - Residual Value - Down Payment) / Lease Term
Depreciation = ($49,000 - $25,235 - $4,000) / 36 = $541.53
Next, let's calculate the finance charge:
Lease Balance = (Negotiated Price - Down Payment) - Residual Value
Lease Balance = ($49,000 - $4,000) - $25,235 = $19,765
Money Factor = Annual Interest Rate / 2400
Money Factor = 7.8% / 2400 = 0.00325
Finance Charge = Lease Balance x Money Factor
Finance Charge = $19,765 x 0.00325 = $64.26
Finally, we can calculate the monthly payment:
Monthly Payment = Depreciation + Finance Charge
Monthly Payment = $541.53 + $64.26 = $605.79
Therefore, the monthly lease payment is $605.79.
(2, 7) reflected across the x-axis?
A.(2,7)
B.(-2,7)
C.(2,-7)
D(-2,-7)
Answer:
C
Step-by-step explanation
The Y axis becomes the opposite when being reflected across the X axis
In this scenario, Y becomes -7
The same thing with X when something is reflected across the Y axis
For any number n > 1, |(1/2 + 2/3)n| a. Greater than 1? b. Less than 1? c. Equal to 1?
For any number n > 1, the given complex equation will always be less than 1.
What is a complex equation?
Complex numbers are described as equations of the type z= a+ib, where a and b are real numbers. Re z = a and Im z = ib are used to signify the real and imaginary parts, respectively.
We are given an expression as [tex]|(\frac{1}{2} +\frac{2}{3} i)^{n}|[/tex].
On taking the LCM, we get
⇒ [tex]|(\frac{3 +4i}{6})^{n}|[/tex]
Now, using the exponent rule, we get
⇒ [tex]|(\frac{(3 +4i)^{n} }{6^{n} }|[/tex]
Now, let us assume n = 2.
By substituting this, we get
⇒ [tex]|(\frac{(3 +4i)^{2} }{6^{2} }|[/tex] < 1
Hence, for any number n > 1, the given complex equation will always be less than 1.
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The complete question has been attached below.
In the diagram below, ABC~ DBE. If AD = 24, DB = 12, and DE = 4, what is the length of
AC?
The length of AC is 32.
Describe Triangle?A triangle is a geometric shape that consists of three straight sides and three angles. The three angles of a triangle always add up to 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.
Since the triangles ABC and DBE are similar, we have:
AB/DB = BC/BE
Substituting the given values, we get:
AB/12 = BC/(BE + 4)
We also have another similar ratio:
AD/DB = AC/BE
Substituting the given values, we get:
24/12 = AC/(BE + 4)
Simplifying this equation, we get:
AC = 2(BE + 4)
Substituting this expression for AC into the first equation, we get:
AB/12 = BC/(BE + 4)
AB/(2(BE + 4)) = BC/(BE + 4)
Simplifying this equation, we get:
AB/2 = BC
Now we have two equations:
AB/2 = BC
AC = 2(BE + 4)
Substituting these expressions into the ratio AD/DB = AC/BE, we get:
24/12 = 2(BE + 4)/(AB/2)
Simplifying this equation, we get:
AB = 48/(BE + 4) * (BE/2 + 2)
Substituting the given value DE = 4, we get:
AB = 48/(BE + 4) * (BE/2 + DE/2)
AB = 24 * BE/(BE + 4)
Now we can substitute this expression for AB into the equation AB/2 = BC to get:
24 * BE/(BE + 4) / 2 = BC
12 * BE/(BE + 4) = BC
Substituting this expression for BC into the equation AC = 2(BE + 4), we get:
AC = 2(BE + 4) = 2 * 16 * (BE + 4)/(BE + 4) = 32
Therefore, the length of AC is 32.
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Which expression is in simplest form
The expression that is in simplest form is:
[tex]$1/3 + x^7$[/tex], [tex]$x^{-5} - y^{-4}$[/tex], [tex]$x^{-9} - y^{-1}$[/tex]
What is expression?
In mathematics, an expression is a combination of numbers, symbols, and/or variables that are grouped together in a meaningful way.
The expression that is in simplest form is:
[tex]$1/3 + x^7$[/tex], [tex]$x^{-5} - y^{-4}$[/tex], [tex]$x^{-9} - y^{-1}$[/tex]
This is because there are no common factors that can be factored out of either term. All the other expressions have terms that can be simplified or combined. For example:
[tex]$1/3 + x^7$[/tex] cannot be simplified any further.
[tex]$x^{-9} - 1/y$[/tex] can be written as [tex]$x^{-9} - y^{-1}$[/tex], but it is not simpler than the original expression.
[tex]$1/(x^3) - 1/(y^4)$[/tex] can be combined into a single fraction with a common denominator: [tex]$(y^4 - x^3)/(x^3y^4)$[/tex].
[tex]$x^3 + 1/y - t^6$[/tex] can be simplified to [tex]$x^3 + 1/y - 1$[/tex].
[tex]$x^{-5} - y^{-4}$[/tex] cannot be simplified any further, as noted earlier.
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The difference of x and 3 is?
Answer:
Step-by-step explanation:
3 3 more than x x " can be written as the algebraic expression x+ 3 x +3. But why? Why use math if we can describe things in words? One of the many reasons is that math is more precise and easier to work with than words are. This is a question you should keep thinking about as we dig deeper into algebra.