a) The required down payment = $4,700
b) The amount of the auto loan is = $42,300
c) The monthly payment is $864.97
Given data ,
Maria plans to purchase a new work truck. The dealer requires a 10% down payment on the $47,000 vehicle
Maria will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years
(a)
The required down payment is 10% of $47,000, which is:
Down payment = 0.1 x $47,000 = $4,700
(b)
The amount of the auto loan is the total cost of the truck minus the down payment, which is:
Auto loan = $47,000 - $4,700 = $42,300
(c)
To find the monthly payment, we can use the formula for a fixed-rate amortized loan:
PMT = r(PV) / [1 - (1 + r)^(-n)]
where PMT is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), PV is the present value of the loan (which is the auto loan amount), and n is the total number of payments (which is the number of years multiplied by 12).
Substituting the given values, we get:
r = 0.085 / 12 = 0.00708333 (monthly interest rate)
PV = $42,300
n = 5 x 12 = 60 (total number of payments)
PMT = 0.00708333($42,300) / [1 - (1 + 0.00708333)^(-60)] = $864.97
Hence , the monthly payment is $864.97
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Help plssssssss tyyyyyyyy
The solution of measure of angle e is,
⇒ e = 58 degree
We have to given that,
Two lines are intersect each other.
Hence, By definition of linear pair angle, we get;
⇒ e + 122 = 180
Subtract 122 from both sides to isolate e.
This gives us,
⇒ e = 180 - 122
⇒ e = 58
Therefore, The solution of measure of angle e is,
⇒ e = 58 degree
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The water usage at a car wash is modeled by the equation W(x) = 3x^3 + 4x^2 − 18x + 4, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x^3 + 2x^2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day.
Answer:
C(x) = 2x^3 + 2x^2 - 18x - 11
Step-by-step explanation:
Step 1: To model the water used by the car wash on a shorter day, we can subtract the amount of water saved from the original water usage function.
Step 2: Therefore, we can define the new function C(x) as: C(x) = W(x) - D(x)
Step 3: Substituting the given functions for W(x) and D(x), we get: C(x) = (3x^3 + 4x^2 - 18x + 4) - (x^3 + 2x^2 + 15)
3x^3 + 4x^2 - 18x + 4 -x^3 - 2x^3 - 15
Step 4: Simplifying by combining like terms, we get:
C(x) = 2x^3 + 2x^2 - 18x - 11
Step 5: Therefore, the function C(x) that models the water used by the car wash on a shorter day is: C(x) = 2x^3 + 2x^2 - 18x - 11
Calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents
If there are 220 pieces of 20 cents, then there are 380 pieces of 50 cents in the container.
Thabang conserves money by depositing coins in a money box. There are 600 coins in the money box, including 20- and 50-cent pieces.
We proceed as follows to determine how many 50 cent pieces are in the container if there are 220 pieces of 20 cent.
Assume that,
x = number of 20 cents
y = number of 50 cents
So, the total number of cents in the container is 600,so
x + y = 600
Making y the formula's subject, we therefore get that
y = 600 - x
Since x = 220
y = 600 - 220
y= 380
So, there are 380 fifty cents.
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The correct Question is
Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents
An experiment involves 32 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible?
PLEASE ANSWER QUICKLY
What is the correct definition for sec 0? A. sec 0 = cos-1 0 B. sec 0 = sin-1 0 C. sec 0 = 1/sin 0 D. sec 0 = 1/cos 0 E. sec 0 = 1/tan 0
sec(theta) = 1/cos(theta)
I believe that is your option D
25° с Solve for c. 14 60° Length of c c = [?] C Round your final answer to the nearest tenth. Enter D O O
The measure of length c using the law of cosines is 11.79 units
Calculating the measure of length C using the law of cosinesfrom the question, we have the following parameters that can be used in our computation:
The triangle (see attachment)
The measure of length c is calculated using the following law of cosines
c² = a² + b² - 2ab * cos(C)
So, we have
c² = 10² + 3² - 2 * 10 * 3 * cos(120)
Evaluate
c² = 139
Take the square root of both sides
This gives
c = 11.79
Hence, the value of c is 11.79
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Monique and two friends want to zip line through the mountains in the national park. Each person must rent zip gear which includes a harness, gloves and a helmet. They must also pay one experienced trainer to zip with them. If the total bill is for $70.25, how many hours did they zip line for? About how much did each person pay?
To find out how many hours they zip lined for, we need to subtract the cost of the gear and trainer from the total bill and then divide the remaining amount by the hourly rate.
Cost of gear per person:
Shoes: $10
Helmet: $3
Gloves: $2.50
Harness: $5.00
Total gear cost per person: $10 + $3 + $2.50 + $5.00 = $20.50
Total cost of gear for 3 people: $20.50 x 3 = $61.50
Cost of trainer: $15.00
Total bill (including gear and trainer): $70.25
Remaining amount for zip lining:
= $70.25 - $61.50 - $15.00
= $-6.25
Since the remaining amount is negative, it seems there might be an error in the calculation or information provided. The total bill should not be lower than the cost of gear and trainer.
However, if we assume the total bill is correct and there was an error in the calculation, we can proceed with finding out how many hours they zip lined for and how much each person paid.
Approximate number of hours:
Number of hours = Remaining amount / Hourly rate = $6.25 / $4.75 ≈ 1.32 hours
Approximate amount each person paid:
Amount each person paid
= Total bill / 3
= $70.25 / 3
≈ $23.42
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1+3z-2x+4z=7z+__x + __
Answer:
5 and 6
Step-by-step explanation:
cause
Use the information above to answer the questions that follow. Show that the total floor area to be tiled is 32 m². You may use this formula: Area of a rectangle = length x width Determine how many boxes of tiles Tshego will need if an extra 10% of the number of tiles must be added for cutting and breakages. S 2.1 2 Show by means of calculations if Ishego's budget is enough to finish the tiling project. (9)
Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his Budget is less than R7200, then it would not be enough.
We are not provided with any information in the question, so we cannot answer it as is. However, we can use the formula provided to calculate the total floor area to be tiled:
Area of a rectangle = length x width
Let's say the length is L and the width is W. Then, the total floor area to be tiled is:
Total floor area = L x W
We are not given the values of L and W, so we cannot calculate the exact total floor area. However, we can assume that Tshego has already calculated the total floor area to be 32 m².
To determine how many boxes of tiles Tshego will need, we need to know the size of each box of tiles and the total area that one box can cover. Let's assume that each box of tiles covers an area of 1 m².
If the total floor area to be tiled is 32 m², and an extra 10% of the number of tiles must be added for cutting and breakages, then the total area to be covered with tiles would be:
Total area to be covered = 32 m² x 1.1 = 35.2 m²
Therefore, Tshego would need 36 boxes of tiles to cover the entire floor area.
To determine if Tshego's budget is enough to finish the tiling project, we need to know the cost of each box of tiles and the total cost of the project. Let's assume that each box of tiles costs R200.
The total cost of the project would be:
Total cost = Number of boxes x Cost per box
Total cost = 36 x R200 = R7200
If Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his budget is less than R7200, then it would not be enough.
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find the 5th term of the sequence: 2,5,10,17....... pls I need workings
Answer:
37
Step-by-step explanation:
The pattern is
2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37
So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers
Answer:
5th term is 26.
Step-by-step explanation:
5-2 =3. 10 - 5 = 5. 17 - 10 = 7.
notice how the differences are 3, 5, 7?
there's a gap of 2 between each difference.
so, let's call our next term in the sequence a.
a - 17 = (7+2).
a - 17 =9.
a = 26.
so, 5th term is 26.
what is the mean of this data set 3,5,15
Answer:
7.6
Step-by-step explanation:
when trying to find the mean of a data set
you begin by finding the sum of all the numbers.
3+5+15=23. Then because there are only three
numbers in the data set you'll need to divide
23 by 3. 23 / 3 = 7.6.
compare a and 0 if -12a<-2a
The variable a can take infinite many values (including 0)
Comparing the variable a and the number 0From the question, we have the following parameters that can be used in our computation:
-12a < -2a
This expression can be expressed as
-2a > -12a
Divide both sides by -2a
So, we have
1 < 6
The above expression is true
This means that the variable a can take infinite many values (including 0) i.e. 0 is a subset of a
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what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ?
Note that he probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long is 0.6%
How did we arrive at this?The percent of eggs total 100.
Based on the frequency, we now that the eggs that are at least 19.75 mm include:
18.75 - 19.75 = 0.8
those that are less than 22.75mm long are:
19.75-20.75 = 4.0
20.75 - 21.75 = 17.3
21.75 - 22.75 = 37.9
Thus, the total of their frequencies are:
0.8 + 4.0 + 17.3 + 37.9 = those that are less than 22.75mm long but at least 19.75 long.
= 60
Thus, the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long is 0.6%
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Full Question:
A biologist measured the lengths of hundreds of cuckoo bird eggs. Use the relative frequency distribution below to answer the questions that follow.
what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ? See attached image.
Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average length of time, in months, patients live once starting the treatment. Two researchers each follow a different set of 50 AIDS patients from the start of treatment until their deaths.
a. What is the population of this study?
b. List two reasons why the data may differ.
c. Can you tell if one researcher is correct and the other one is incorrect? Why?
d. Would you expect the data to be identical? Why or why not?
e. If the first researcher collected her data by randomly selecting 40 states, then selecting 1 person from each of those states. What sampling method is that?
f. If the second researcher collected his data by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method?
The correct answers are:
a. The population of this study is all AIDS patients with revealed symptoms receiving the new AIDS antibody drug.b. Two reasons for potential data differences are variability in patients' health and treatment initiation times.c. Determining correctness between researchers is not possible based solely on data as multiple factors can influence outcomes.d. The data may not be identical due to variations in patients, treatment responses, and data collection methods.e. The first researcher used stratified and simple random sampling by selecting 40 states and one person from each state.f. The second researcher used convenience sampling, which may introduce bias and limit the representativeness of the data set.The explanation for each response can be given as:
a. The population of this study would be all AIDS patients who have revealed symptoms and are receiving the new AIDS antibody drug.
b. Two reasons why the data may differ are:
1. Variability in the patient's overall health and response to the treatment.
2. Differences in the time of diagnosis and initiation of treatment among the patients.
c. It is not possible to determine if one researcher is correct and the other is incorrect solely based on the collected data. Multiple factors, such as the patient's individual characteristics and treatment protocols, could influence the outcomes.
d. The data may not be identical because each researcher is following a different set of patients, and individual patient experiences and outcomes can vary. Additionally, differences in data collection methods or other external factors could contribute to variations.
e. The sampling method used by the first researcher, randomly selecting [tex]40[/tex] states and then selecting one person from each state, is a combination of stratified sampling (based on states) and simple random sampling (within each state).
f. The second researcher used a non-random sampling method by choosing [tex]40[/tex] patients they knew. This method is known as convenience sampling. Concerns regarding this data set include potential bias in patient selection, as the researcher's personal knowledge could introduce subjectivity and may not represent a diverse range of patients receiving the treatment.
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Divide: 5m³n-25m²n²
5m²n
Om³n² - 5m²n³
Om-25m²n²
Om-20n
Om-5n
Answer:m-5n
Step-by-step explanation:
HELP PLS WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the surface area of the composite figure.
The surface area of the composite figure is 2,283 m².
option A.
What is the surface area of the composite figure?
The surface area of the composite figure is calculated as follows;
The composite figure is composed of a cube and a cuboid and their total surface area is calculated as follows;
Surface area of the cuboid = 2 (35 m x 9 m + 35 m x 16 m + 16 m x 9 m)
Surface area of the cuboid = 2038 m²
Surface area of a cube = 6L²
There is a surface of the cube on the cuboid, which is include in the surface area of the cuboid, so we will subtract that one surface.
Surface area of the cube = 6L² - L² = 5L²
= 5 x (7 m)²
= 245 m²
Total surface area = 2038 m² + 245 m²
Total surface area = 2,283 m²
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how many points of inflection will f(x) = 3x^4+2x^3-5x-12 have?
5
4
3
2
It is found that x = -1/3 is the point of inflection again for function f(x) = 3x⁴ + 2x³ - 5x - 12.
Since the second variation of the function f(x) = 3x⁴ + 2x³ - 5x - 12 and then solving for the values of x where the second derivative equals zero
f'(x) = 12x³ + 6x² - 5
f''(x) = 36x² + 12x
We should discover the solutions to the equation f"(x) = 0 for x to determine the locations of inflection:
36x² + 12x = 0
12x(3x + 1) = 0
If x = 0 or x = -1/3, the equation is true.
Here F"(x) > 0 demonstrates that the graph of f(x) is concave if x 1/3.
Concavity in the curve of f(x) at -1/3 x 0 shows that f"(x) 0.
When x is greater than zero, then f"(x) is greater than zero, showing that f(x graph) is concave up.
When x = 0, the graph's concavity does not change, making x = 0 not an inflection point =only x = -1/3
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twice the sum of a number and 2 is equal to three times the difference of the number and 2
Answer:
10---------------
Let the number be n.
Set up an equation per the problem:
2(n + 2) = 3(n - 2)Distribute and solve for n:
2n + 4 = 3n - 63n - 2n = 4 + 6n = 10The number is 10.
Intelligence Iq scores are often reported to be normally distributed with u=100.0 and o=15.0. A random sample of 47 people is taken. What is the probability of a random person on the street having an IQ score of less than 96?
Find the range and the interquartile range of the data. Determine if there are outliers. 8, 9, 1, 5, 5, 7, 9, 12, 15
Answer: Range: 14 Interquartile: 5.5
Step-by-step explanation:
SOMEONE PLEASE HELP ME ASAP!!!!!!! it will mean a lot
The surface area of the composite solid would be about 576. 05 square feet .
How to find the surface area ?The composite shape is made up of two shapes which are a a cylinder and a pentagonal prism. To find the surface area, you need to find the surface area of these two shapes and then sum these areas.
Area of pentagonal prism :
= 5 a h + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) a ²
a = 4 ft
h = 7 ft
Area of the pentagonal prism is:
= 5 x 4 x 7 + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) 4 ²
= 195.05528 square feet
Area of cylinder:
= 2 π r h + 2 π r ²
= 2 π x 6 x 4 + 2 π x 6 ²
= 376.99112 square feet
The surface area is therefore :
= 195.05528 + 376.99112
= 576. 05 square feet
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Tianna recently ran a marathon. It took her 4.9 hours to run the 26.2 miles required to complete a marathon.
Find her average speed in miles per hour. Then convert her speed to feet per second. (Hint: 1 mile = 5,280 feet).
(Round your answers to two decimal places)
Number
miles per hour
Number
feet per second
Answer:
8.01 ft/sec
Step-by-step explanation:
Distance = 26.2 miles
Time is taken to run the distance = 4.8hrs
Average speed = ??
Average speed = distance/time
= 26.2miles /4.8hr
= 5.46 miles/hr
Convert 5.46 miles/hr to ft/sec
1 mile = 5280 ft
We have 5.46*5280 = 28828.8 ft/hr
28828.8/3600 = 8.01 ft/sec
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Suppose a jar contains 15 red marbles and 32 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
The probability of drawing 2 red marbles is 0.081 or 8.1%.
There are 15 red marbles and 32 blue marbles, so there are 15+32=47 marbles total.
The probability of pulling a red marble on the first draw is 15/47.
If the first marble drawn is red, then there are 14 red marbles and 32 blue marbles remaining.
So, the probability of pulling a second red marble is 14/46.
To find the probability of both events happening, we multiply the probabilities:
P(both red) = P(first red) × P(second red | first red)
P(both red) = (15/47) × (14/46)
P(both red) = 0.081 (rounded to 3 decimal places)
Therefore, the probability of drawing 2 red marbles is approximately 0.081 or 8.1%.
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The first rule is add 10, then divide by 2 starting from 2. The second rule is multiply by 3, then subtract 2 starting from 2. What are the first four ordered pairs using the two sequences? (4 points)
(2, 0), (6, 4), (8, 12), (9, 32)
(2, 2), (6, 4), (8, 10), (9, 28)
(6, 4), (8, 10), (9, 28)
(2, 2), (10, 8), (16, 20), (18, 56)
The ordered pair of the two sequences are (6, 4), (8, 10), (9, 28)
Given data ,
The first sequence is add 10, then divide by 2 starting from 2
The second sequence is multiply by 3, then subtract 2 starting from 2
On simplifying , we get
Let the first number be 2
So , ( 2 + 10 )/2 = 6
Now , ( 2 x 3 ) - 2 = 4
And , the first ordered pair is ( 6 , 4 )
Now , ( 6 + 10 ) / 2 = 8
And , ( 4 x 3 ) - 2 = 10
So , the second ordered pair is ( 8 , 10 )
Now , ( 8 + 10 ) / 2 = 9
And , ( 10 x 3 ) - 2 = 28
So , the third ordered pair is ( 9 , 28 )
Hence , the sequence is solved and (6, 4), (8, 10), (9, 28)
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3x + y = 11
X + 3y = 1
How many solution does it have
If you roll a 6-sided die 6 times, what is the best prediction possible for the number of times you will roll a six?
How many times?
The best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.
The best prediction possible for the number of times you will roll a six in a six-sided die depends on the probability of getting a six in each roll. The probability of getting a six in a single roll of a six-sided die is 1/6 or 16.67%.
Since the rolls are independent events, the probability of rolling a six in any one of the six rolls is still 1/6 or 16.67%. Therefore, the best prediction possible for the number of times you will roll a six is one.
However, it is important to note that probability is not a guarantee, and it is possible to roll a six more than once or not at all. But based on the laws of probability, one is the most likely outcome for the number of times you will roll a six in six rolls of a six-sided die.
In summary, the best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.
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Alonzo's gas tank is 1/3 full. After he buys 3 gallons of gas, it is 1/2 full. How many gallons can Alonzo's tank hold?
Answer:
18 gallons
Step-by-step explanation:
18 gallons because 1/3 equals 2/6 and 3/6 equals 1/2 so 3 gallons is 1/6. then just 6×3
Hope this helped
a box is 12cm long and 12cm wide and its 15cm tall what is the surface area of 4 boxes
The surface area of four boxes is 4032cm².
To calculate the surface area of one box, we need to find the area of each of its six faces and then add them up.
The top and bottom faces are both squares with sides of 12cm, so each has an area of 12cm x 12cm = 144cm².
The front and back faces are both rectangles with dimensions of 12cm x 15cm,
So each has an area of 12cm x 15cm = 180cm².
The two side faces are also rectangles with dimensions of 12cm x 15cm, so each has an area of 12cm x 15cm = 180cm².
Adding up the areas of all six faces, we get:
144cm² + 144cm² + 180cm² + 180cm² + 180cm² + 180cm² = 1008cm²
Therefore, the surface area of one box is 1008cm².
To find the surface area of four boxes, we just need to multiply the surface area of one box by 4:
The surface areas of all the faces together:
(144 x 2) + (180 x 2) + (180 x 2) = 504 sq.cm
The surface area of one box is 504 square centimeters.
Since you want the surface area of four boxes, simply multiply this number by 4:
504 sq.cm x 4 = 2016 sq.cm
1008cm² x 4 = 4032cm²
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May you please help me
Answer:
scienific scienific
Step-by-step explanation:
The circle below has a radius of 8 inches, find it's approximate area and circumference. Use the fact that π ≈ 3.14.
.
The approximate area and circumference of the circle is given as 201 inch² and 20 inch respectively
What is the area of a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant
The area and perimeter of a circle can be calculated using the formula
πr = πd, where r is the radius and d is the diameter of the circle
Area = πr² and
the perimeter is 2πr
r= 8 inch, π = 3.14
Area = 3.14 * 8 * 8
Area = 200.96 square inches
Area = 201 inch²
the perimeter is = 2*3.14*8
The perimeter is = 50.24 square inches
Perimeter = 50 inch
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The area and circumference of the circle with a radius of 8 inches are 200.96 square inches and 50.24 inches respectively.
What is the area and circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed as:
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 )
Given that the radius of the circle is 8 inches.
Substituting this value into the formula, we get:
A = πr²
A = 3.14 × ( 8 in )²
A = 3.14 × 64 in²
A = 200.96 in²
Next, we calculate the circumference:
C = 2πr
C = 2 × 3.14 × 8 in
C = 50.24 in
Therefore, the value of the circumference is 50.24 in.
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