Percentage of lifetime cost that was interest = $407.
Let's begin by finding the monthly payment that Hillary made to pay off her laptop over two and a half years.
If she paid off the $804 balance with identical monthly payments, then the total amount she paid is equal to the balance plus the interest:
Total amount paid = balance + interest
We can use the formula for the present value of an annuity to solve for the monthly payment, where PV is the present value (in this case, $804), r is the monthly interest rate (which we can find from the APR), n is the total number of payments (30 months), and PMT is the monthly payment:
PV = PMT * (1 - (1 + r)^(-n)) / r
We can solve this equation for PMT:
PMT = PV * r / (1 - (1 + r)^(-n))
The monthly interest rate is the annual percentage rate divided by 12, and the number of payments is the number of years times 12:
r = 0.1127 / 12 = 0.009391667
n = 2.5 * 12 = 30
Using these values, we get:
PMT = 804 * 0.009391667 / (1 - (1 + 0.009391667)^(-30)) = $33.00
So Hillary made 30 monthly payments of $33.00 to pay off her laptop.
Next, we can calculate the cost of electricity over six years. There are 365 days in a year, and 2 leap years in the six-year period, for a total of 6*365+2 = 2192 days.
At $0.27 per day, the total cost of electricity is:
2192 * $0.27 = $592.64
Now we can calculate the total cost of the laptop over six years.
Hillary paid $33.00 per month for 30 months, or a total of 30 * $33.00 = $990.00. She also paid $592.64 for electricity. Therefore, the total cost of the laptop is:
$990.00 + $592.64 = $1582.64
The interest she paid on her credit card is the difference between the total amount she paid and the cost of the laptop:
Interest = Total amount paid - Cost of laptop
Interest = $990.00 + interest on $804 balance - $804 - $592.64
Simplifying this expression, we get:
Interest = $185.36 + interest on $804 balance
To find the interest on the $804 balance, we can use the formula for compound interest, where P is the principal (in this case, $804), r is the annual interest rate (11.27%), and t is the time in years (2.5 years):
A = P*(1 + r/n)^(n*t)
Here, we can set the number of compounding periods per year, n, to 12 since the interest is compounded monthly. Substituting the given values, we get:
A = $804*(1 + 0.1127/12)^(12*2.5) = $1026.12
So the interest on the $804 balance is:
Interest on $804 balance = $1026.12 - $804 = $222.12
Plugging this value into our expression for Interest, we get:
Interest = $185.36 + $222.12 = $407.48
Finally, we can find the percentage of the lifetime cost of the laptop that was interest:
Percentage of lifetime cost that was interest = Interest / Total cost of laptop * 100%
Percentage of lifetime cost that was interest = $407.
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Instructors led an exercise class from a raised rectangular platform at the front of the room. The width of the platform is (x+4) meters long and the area of the rectangular platform is 3x^2+10x−8. Find the length of the platform
The length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.
Let's start by using the formula for the area of a rectangle, which is:
Area = length x width
We are given that the width of the platform is (x+4) meters, so we can write:
Area = length x (x+4)
We are also given that the area of the platform is 3x^2+10x−8, so we can set these two expressions equal to each other and solve for the length:
3x^2+10x−8 = length x (x+4)
Expanding the right side, we get:
3x^2+10x−8 = length x^2 + 4length
Subtracting 4length from both sides, we get:
3x^2+10x−8−4length = length x^2
Rearranging, we get a quadratic equation:
length x^2 + 4length − 3x^2 − 10x + 8 = 0
To solve for length, we can use the quadratic formula:
length = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 4, and c = -3x^2 - 10x + 8. Plugging in these values, we get:
length = (-4 ± sqrt(4^2 - 4(1)(-3x^2 - 10x + 8))) / 2(1)
Simplifying under the square root:
length = (-4 ± sqrt(16 + 12x^2 + 40x - 32)) / 2
length = (-4 ± sqrt(12x^2 + 40x)) / 2
length = (-4 ± 2sqrt(3x^2 + 10x)) / 2
length = -2 ± sqrt(3x^2 + 10x)
Since the length must be positive, we take the positive square root:
length = -2 + sqrt(3x^2 + 10x)
Therefore, the length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.
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Please help ASAP!! It's due VERY SOON!!!
Answer:
The answer is A. 135 cm2.
Area of a parallelogram is base * height. In this case, the base is 24 cm and the height is 9 cm. Therefore, the area is 24 * 9 = 135 cm2.
Answer: the answer would be 360
Step-by-step explanation:
the equation for area of a parallelogram is base x height.
The base is 24 as it is at the top of the shape.
The height is 15 as well since a parallelogram is congruent.
multiply the two and it gives you 360
What is the approximate area of the triangle?
A. 12. 5 square units
B. 18 square units
C. 21. 5 square units
D. 31 square units
The approximate area of the triangle is 21. 5 square units (option c).
Triangles are three-sided polygons that can have different shapes and sizes. Now, let's focus on your question about finding the area of a triangle.
To begin with, the area of a triangle is given by the formula:
Area = (base × height) ÷ 2
where the base is the length of the side that is perpendicular to the height. The height, on the other hand, is the distance between the base and the opposite vertex.
In your problem, the base of the triangle is given as 7 units, and the height is given as 6.1 units. So, we can substitute these values into the formula to get:
Area = (7 × 6.1) ÷ 2
Area = 21.35 square units
Therefore, the approximate area of the triangle is 21.35 square units. In the answer choices provided, the closest option is C, which is 21.5 square units.
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Complete Question:
What is the approximate area of the triangle when base = 7 and height = 6.1?
A. 12. 5 square units
B. 18 square units
C. 21. 5 square units
D. 31 square units
A salesperson's commission rate is 6%. What is the commission from the sale of $37,000 worth of furnaces? Use pencil and paper. Suppose sales would double. What would be true about the commission? Explain without using any calculations.
The sale's person commission from the sale of $37,000 worth of furnaces is $2,220. If this is doubled, he would have $4,440.
What would the commission be?If the salesperson's commission from the sale of $37,000 is at the rate of 6%, then we will do the following:
6/100 × $37,000 = $2,220
If sales, double, we will now record the amount, 74,000. Now 6% of 74,000 will be $4,440. So, the resultant amount, if the salesperson was to increase his sales to double the original, will be $4,440.
This follows a simple logic. When you have a number and are told to double it, you simply multiply by 2. In the same manner, we multiply the salesperson's commission by 2.
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Triangles UVW and WXY are similar right triangles. Which proportion can be used to show that the slope of uw is equal to the slope of wy ?
a: 1-2 -3 - ( -1 )
9-8 1-2
b: 2-8 -1-2
1-9 -3-1
c: 1-9 -3-1
2-8 -1-2
d: 2 - ( -1 ) -1 - ( -3 )
9 -8 2 -1
The proportion that can be used to show that the slope of uw is equal to the slope of wy is B) 2-8 -1-2.
Let the angles opposite to sides UV, VW, and WU be denoted by theta1, theta2, and theta3, respectively, in triangle UVW. Similarly, let the angles opposite to sides WY, YX, and XW be denoted by theta4, theta5, and theta6, respectively, in triangle WXY. Since triangles UVW and WXY are similar right triangles, we have:
theta1 = theta4 = 90 degrees (both triangles are right triangles)
theta2 = theta5 (corresponding angles in similar triangles are equal)
theta3 = theta6 (corresponding angles in similar triangles are equal)
UW/VW = WY/YX (sides in similar triangles are proportional)
The slope of uw is given by the rise over run or (VU - UW)/(WV), and the slope of wy is given by the rise over run or (XY - WY)/(YW). Using the similar triangles proportion, we can substitute UW/VW = WY/YX and simplify to get (VU - UW)/(WV) = (XY - WY)/(YW). This equation shows that the slope of uw is equal to the slope of wy.
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In a recent study on worldâ happiness, participants were asked to evaluate their current lives on a scale from 0 toâ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5. 7 with a standard deviation of 2. 3.
â(a) What response represents the 90th âpercentile?
â(b) What response represents the 62nd âpercentile?
â(c) What response represents the first âquartile?
The z-score for the 90th percentile is approximately 1.28, for the 62nd percentile is approximately 0.31, and for the first quartile (25th percentile) is approximately -0.67.
To calculate the percentiles for this dataset, we need to use the z-score formula. Unfortunately, I cannot directly provide you the responses for the 90th, 62nd, and first quartile percentiles without more information.
However, I can help you understand the process of finding these percentiles:
1. Determine the z-score corresponding to the desired percentile using a z-score table or calculator. For example, the z-score for the 90th percentile is approximately 1.28, for the 62nd percentile is approximately 0.31, and for the first quartile (25th percentile) is approximately -0.67.
2. Use the following formula to find the response corresponding to the z-score:
Response = Mean + (Z-score × Standard Deviation)
For example, to find the 90th percentile:
Response = 5.7 + (1.28 × 2.3)
Calculate this for each percentile using their respective z-scores, and you will find the responses you are looking for.
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For what values of a and b will this equation have infinitely many solutions?
5(x + 3) = a(x + 4) + 3x + b
Answer: To have infinitely many solutions, the equation must be true for all values of x. In other words, the left side and right side of the equation must be equivalent, meaning that the coefficients of x on both sides of the equation must be equal, and the constant terms on both sides must be equal.
We can simplify the given equation as follows:
5(x + 3) = a(x + 4) + 3x + b
5x + 15 = ax + 4a + 3x + b
Simplifying further, we get:
8x + 4a + b = 5x + 15
Rearranging terms, we get:
3x + 4a + b - 15 = 0
For this equation to have infinitely many solutions, the coefficients of x on both sides must be equal to zero, meaning that:
3 = 0
This is not possible, so the equation cannot have infinitely many solutions for any values of a and b.
Therefore, there are no values of a and b for which the given equation will have infinitely many solutions.
PLEASE I NEED HELP ASAP
8.4, 42, 210,....
In the sequence above, each term after the first is equal to the previous term times n. What is
the value of the next term in the sequence?
(A) 650
(B) 825
(C) 1,050
(D) 3,050
(E) 5,250
Answer:
C) 1,050
Step-by-step explanation:
We can see that to get from 8.4 to 42 and to get from 42 to 210, we have to multiply by 5.
To complete the sequence, multiply 210 by 5
210·5
=1,050
Hope this helps!
Use the variable x to write the phrase in symbols. the sum of 148 and the product of a number raised to the third power and 19
The expression 148 + 19x³ represents the sum of 148 and the product of a number raised to the third power and 19.
To write the phrase "the sum of 148 and the product of a number raised to the third power and 19" in symbols using the variable x, we can write it as:
148 + 19x³
Here, we are adding 148 to the product of 19 and x raised to the third power. This expression represents the sum of 148 and the product of a number raised to the third power and 19. We can substitute any value for x to get the result of the expression. For example, if x is 2, then the expression becomes:
148 + 19(2³) = 148 + 19(8) = 300
Therefore, the sum of 148 and the product of a number raised to the third power and 19 is represented by the expression 148 + 19x³.
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Tayshia mailed two birthday presents in a box weighing 14 pound. One present weighed 15 pound. The other present weighed 12 pound. What was the total weight of the box and the presents.
Group of answer choices
311 lb
1911 lb
1140lb
320lb
None of the provided answer choices are correct, as the correct answer should be 41 lb.
To find the total weight of the box and the presents, you simply add the weights together:
Box weight: 14 lb
Present 1 weight: 15 lb
Present 2 weight: 12 lb
Total weight = 14 lb + 15 lb + 12 lb = 41 lb
None of the provided answer choices are correct, as the correct answer should be 41 lb.
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The quantity of a substance can be modeled by the function R(t) that satisfies the differential equation dR/dt= -1/5(R – 20). One point on this function is R(2) = 35. Based on this model, use a linear approximation to the graph of Rat t = 2 to estimate the quantity of the substance at t 1.9. \
The estimated quantity of the substance at t = 1.9 is approximately 35.3 units.
To estimate the quantity of the substance at t = 1.9 using linear approximation, we can use the formula:
ΔR ≈ dR/dt * Δt
Given the point R(2) = 35 and the differential equation dR/dt = -1/5(R – 20), we can first find the value of dR/dt at t = 2.
dR/dt(2) = -1/5(R(2) – 20) = -1/5(35 – 20) = -1/5(15) = -3
Now, we can calculate Δt, which is the difference between the given t-value (2) and the desired t-value (1.9):
Δt = 1.9 - 2 = -0.1
Next, we can calculate ΔR using the linear approximation formula:
ΔR ≈ dR/dt * Δt ≈ -3 * (-0.1) = 0.3
Finally, we can estimate the quantity of the substance at t = 1.9 by adding ΔR to the given value of R(2):
R(1.9) ≈ R(2) + ΔR ≈ 35 + 0.3 = 35.3
Therefore, the estimated quantity of the substance at t = 1.9 is approximately 35.3 units.
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Amelia read 5 books in 3 months. what was her rate of reading in books per month?
also where should i resize the right columns represent the unit rate?
Amelia's rate of reading was approximately 1.67 books per month (calculated by dividing the total number of books, 5, by the number of months, 3).
How many books did Amelia read per month, and where should I resize the columns to represent the unit rate?To calculate Amelia's rate of reading in books per month, we divide the total number of books she read (5) by the number of months (3). Therefore, her rate of reading is 5/3 books per month.
To resize the right columns to represent the unit rate, you would need to scale them down. If the left column represents the number of months and the right column represents the number of books read, you could adjust the scale so that each unit on the right column represents 1 book per month.
For example, if each square unit on the left column represents 1 month and each square unit on the right column represents 0.5 books, you could resize the right column so that each square unit represents 1 book. This would ensure that the visual representation accurately reflects the unit rate of books per month.
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Algebra please help
Your school newspaper has an editor-in-chief and an assistant editor-in-chief. The newspaper staff
has 5 students. How many different ways can students be chosen for these positions?
There are 20 different ways the students can be chosen for the positions of editor-in-chief and assistant editor-in-chief.
There are 5 students in the newspaper staff, and two positions to fill i.e. editor-in-chief and assistant editor-in-chief. We need to find the number of different ways the students can be chosen for these positions.
To solve this problem, we can use the formula for permutation
We know the formula for Permutation is
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]
Here, n=5 and r=2
So, P(5,2) = 5!/(5-2)!
= 5!/3!
= 120/6
= 20
Therefore, there are 20 different ways the students can be chosen for the positions of editor-in-chief and assistant editor-in-chief.
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There are (2a+b) books in a pile. The thickness of each book is 2cm. Find the height of the pile of books in terms of a and b, expressing the answer in the expanded form
The height of the pile of books in terms of a and b is 4a cm + 2b cm.
To find the height of the pile of books in terms of a and b, we need to multiply the number of books by the thickness of each book. Since there are (2a+b) books in the pile and the thickness of each book is 2cm, the height of the pile can be expressed as:
(2a+b) x 2cm
Expanding this expression, we get:
4a cm + 2b cm
Therefore, the height of the pile of books in terms of a and b is 4a cm + 2b cm. This means that for every additional 'a' book, the height of the pile will increase by 4cm and for every additional 'b' book, the height of the pile will increase by 2cm.
It's important to note that this formula assumes that all the books are the same size and have the same thickness. If there are any variations in size or thickness, the formula may not accurately represent the height of the pile. Additionally, it's important to ensure that all units of measurement are consistent (in this case, cm for both the thickness of the book and the height of the pile).
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Find AB if AC = 21 and BC =9.
Answer:
12
Step-by-step explanation:
Length AC is the total length between ABC
If we already know BC=9, and we're solving for AB, then we just subtract the total amount (AC) from BC
21-9
We get 12
Suppose that someone is offering to sell you raffle tickets. there are blue, green, yellow, and red tickets available.
each ticket costs the same to purchase regardless of color. the person selling the tickets tells you that 369 blue tickets,
488 green tickets, 523 yellow tickets, and 331 red tickets have been sold. at the drawing, one ticket of each color will
be drawn, and four identical prizes will be awarded. which color ticket would you buy? explain your answer.
Buy yellow or green ticket for best chance of winning.
Which color ticket to buy?To determine which color ticket to buy, we need to calculate the probability of winning with each color.
First, we need to determine the total number of possible combinations of one ticket of each color. This can be calculated by multiplying the number of tickets of each color together:
Total number of possible combinations = 369 x 488 x 523 x 331 = 39,123,833,144
Next, we need to determine the probability of winning with each color. Since there are four identical prizes, the probability of winning with any one color is the same. We can calculate the probability of winning with a specific color by dividing the number of tickets of that color by the total number of possible combinations:
Probability of winning with blue ticket = 369 / 39,123,833,144 ≈ 0.00000943
Probability of winning with green ticket = 488 / 39,123,833,144 ≈ 0.00001248
Probability of winning with yellow ticket = 523 / 39,123,833,144 ≈ 0.00001337
Probability of winning with red ticket = 331 / 39,123,833,144 ≈ 0.00000846
From the calculations above, we can see that the highest probability of winning is with the yellow ticket, followed closely by the green ticket. Therefore, if we want to maximize our chances of winning one of the prizes, we should buy the yellow or green ticket.
It's important to note that the difference in probabilities between the yellow and green tickets is very small, so the decision of which color to choose ultimately depends on personal preference.
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How would the variation that exists between the distance that a man walks in one hour and the rate at which the man is walking be described? f inversely g directly h both inversely and directly j irregular
The relationship between these two variables can be described as inversely proportional.
The variation between the distance that a man walks in one hour and the rate at which the man is walking can be described as inversely proportional.
This means that as the rate at which the man is walking increases, the distance that he walks in one hour decreases. Similarly, as the rate at which he is walking decreases, the distance that he walks in one hour increases.
Therefore, the relationship between these two variables can be described as inversely proportional.
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3 3/4 converted from feet to yards
Answer: 1 1/4 yards
Step-by-step explanation: To convert from feet to yards, divide the value in feet by 3. So, 3 3/4 ft = (3 3/4)/3 = 1.25 yd (exactly).
Answer:
5/4 yards
Step-by-step explanation:
Convert feet to fraction.
[tex]3+\frac{3}{4} =\frac{(3)(4)+3}{4} =\frac{15}{4}[/tex] ft.
If we know that each yard equals 3 feet, divide by 3:
[tex]\frac{\frac{15}{4} }{3} =\frac{15}{(4)(3)} =\frac{15}{12}[/tex]
Simplified:
[tex]\frac{5}{4}[/tex] yards
Hope this helps.
Find the surface area of the prism.
the surface area of the prism is _ in2
To find the surface area of a prism, you need to add up the area of all of its faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Make sure that all of these measurements are in the same units, such as inches or centimeters.
Once you have calculated each of the areas, add them together to get the total surface area of the prism. Make sure to include the units in your answer, which will be in square inches or in2.
You will need to know its dimensions and follow these steps:
1. Determine the shape and dimensions of the base and top faces.
2. Calculate the area of the base and top faces.
3. Determine the shape and dimensions of the lateral faces.
4. Calculate the area of the lateral faces.
5. Add the areas of all the faces to find the total surface area.
Without specific dimensions, I cannot provide a numerical answer. However, once you have the dimensions, follow the steps above to find the surface area of the prism in square inches (in²).
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_A student wanted to assess the average time spent studying for his most recent exam taken in class. He asked the first 45 students who came to class how much time they spent and recorded the values. He then used this information to calculate a 95% confidence interval for the mean time spent by all students. Was this an appropriate use of the t procedure for a confidence interval
The student's use of the t procedure for a confidence interval was appropriate because the sample size was greater than 30 and the population standard deviation was unknown. A 95% confidence interval was calculated using the t-distribution.
It was an appropriate use of the t procedure for a confidence interval. The student wanted to assess the average time spent studying for his most recent exam taken in class, and he used a sample of 45 students to estimate the population mean with a 95% confidence interval.
Since the population standard deviation is not known, the student used the t-distribution to calculate the confidence interval. The t-distribution is used when the sample size is small, and the population standard deviation is unknown.
The student assumed that the sample was randomly selected, and the data was approximately normally distributed. By using the t procedure, the student was able to estimate the population mean with a margin of error and a level of confidence of 95%.
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What can be the universal sets from which the following substes can be formed? a) set of cricket players of class 9.
b)set of cricket players of the school.
c)The set of odd numbers less than 10.
The only option that represents the universal set from the subsets is:
B: A set of cricket players of the school.
How to identify the universal set?The universal set is defined as a set that is said to consist of all the elements or objects, which includes its own elements. This universal set is represented by just a symbol 'U'
Now, a subset is also defined as a part of the universal set which is basically a group under the universal set.
Now, from the given options, the only one that could possible represent a universal set of all the options given is "a set of cricket players of the school."
Therefore we conclude that Option B provides the correct answer to the universal set definition.
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Guadalupe drove 45 miles in 1 1/3 hours. on average how fast did she drive per hour
Guadalupe drove at an average speed of 33.75 miles per hour.
To find the average speed, we need to divide the total distance by the total time:
Average speed = t d/t t
Guadalupe drove 45 miles in 1 1/3 hours, which is the same as 4/3 hours.
So, average speed = 45 miles / (4/3) hours
= 45 x 3/4
= 33.75 miles per hour (rounded to two decimal places)
Therefore, Guadalupe drove at an average speed of 33.75 miles per hour.
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Javier and ellema both get there cars wash and filled there gas tanks at the same gas station javier pays 26. 96 for a car wash and 5. 6 gallon of gas. Ellema pays 48. 62 for a car wash and 13. 2 gallons of gas
We can start by finding the cost per gallon of gas for each person:
Javier: 5.6 gallons of gas for $26.96, so cost per gallon = 26.96/5.6 = $4.79/gallon
Ellema: 13.2 gallons of gas for $48.62, so cost per gallon = 48.62/13.2 = $3.68/gallon
Now we can find the cost of just the car wash for each person:
Javier: $26.96 - (5.6 gallons * $4.79/gallon) = $-1.344, which doesn't make sense. It's possible there was a mistake in the numbers given.
Ellema: $48.62 - (13.2 gallons * $3.68/gallon) = $1.958, which also doesn't make sense. There may be an error in the given information.
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Desmond kept track of his results for all 72 rolls. The table at right shows some of his results. Based on his partial results, how many times did he roll a 5 or a 6?
The number of times of rolling a 5 or a 6 in the fair die is 24
What is a reasonable prediction for the number of times of rolling a 5 or a 6?From the question, we have the following parameters that can be used in our computation:
Fair 6-sided die = 72 times
In a 6-sided die, we have
P(5 or 6) = 2/6
When evaluated, we have
P(5 or 6) = 1/3
So, when the die is rolled 72 times, we have
Expected value = 1/3 * 72
Evaluate
Expected value = 24
Hence, the number of times is 24
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what’s is the distance between (-2,7) and (-5,9)
We can use the distance formula to find the distance between two points in a coordinate plane:
d = √[(x2 - x1)² + (y2 - y1)²]
where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
Using the given coordinates of the two points, we have:
x1 = -2, y1 = 7
x2 = -5, y2 = 9
Substituting these values into the distance formula, we get:
d = √[(-5 - (-2))² + (9 - 7)²]
d = √[(-3)² + 2²]
d = √(9 + 4)
d = √13
Therefore, the distance between the points (-2, 7) and (-5, 9) is approximately √13 units. We can also approximate this value as 3.61 units (rounded to two decimal places).
Jamie McAllister is a wonderful rebounder for her high school basketball team. Of
her final 10 games, here are her rebound totals for each game:
8 12 8 11 15 6 9 8 10 13
1.
2.
From the collected data, what
is the mean number of
rebounds Jamie had per
game?
From the collected data, what
is the median number of
rebounds Jamie had for her
final 10 games?
Step-by-step explanation:
1. To find the mean number of rebounds Jamie had per game, we need to add up all the rebounds she had and then divide by the total number of games played:
Mean = (8 + 12 + 8 + 11 + 15 + 6 + 9 + 8 + 10 + 13) / 10
Mean = 100 / 10
Mean = 10
Therefore, the mean number of rebounds Jamie had per game was 10.
2. To find the median number of rebounds Jamie had for her final 10 games, we need to first arrange the data in order from least to greatest:
6, 8, 8, 8, 9, 10, 11, 12, 13, 15
Since there are an even number of data points, the median will be the average of the two middle values, which are 9 and 10:
Median = (9 + 10) / 2
Median = 9.5
Therefore, the median number of rebounds Jamie had for her final 10 games was 9.5.
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PLEASE HELP ME ASSAP!!!!!!!!!
The slope of UF is 1/6
What is a slope of a line?The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The slope is given = change in point on y axis/ change in point on x axis
slope = y2-y1/x2-x1
The cordinate of F = (-2,-3) and U ( 4, -2)
y1 = -3 and y2 = -2
x1 = -2 and x2 = 4
slope = -2-(-3)/4-(-2)
= -2+3/(4+2)
= 1/6
therefore the slope of UF is 1/6
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$3,900 at 1% compounded annually for 6 years
Answer:
$4139.93
Step-by-step explanation:
Formula for amount accrued at compound interest annually is given by
A = P( 1+ r)ⁿ
where
P = principal
r = interest rate expressed as a decimal
n = number of years
Given P = 3900, r = 1/100 = 0.01, n = 6 we get
A = 3900(1 + 0.01)⁶ = 3900(1.01)⁶ = 4139.93
So the amount accrued after 6 years = $4139.93
Determine whether each situation can have only one value for the variable or more than one value for the variable.
select only one or more than one for each situation.
the total cost to buy t movie tickets for $8.50 each
o only one
more than one
the number of ounces of tomato juice, j, in 2 quarts
o only one
o more than one
the number of pizzas to order, p, if each person eats 2 slices
only one
more than one
the greatest number of $6 notebooks, n, ed can buy with $36
only one
0. more than one
the area, a, of a wall with a length of 5 meters and a height of 3 meters
o only one
o more than one
The total cost to buy t movie tickets for $8.50 each is o only one, the number of ounces of tomato juice, j, in 2 quarts o only one, the number of pizzas to order, p, if each person eats 2 slices more than one, the greatest number of $6 notebooks, n, ed can buy with $36 only one, and the area, a, of a wall with a length of 5 meters and a height of 3 meters o only one.
1. The total cost to buy t movie tickets for $8.50 each:
- Only one value for the variable
The cost to buy a specific number of movie tickets at a fixed price will have only one total cost value.
2. The number of ounces of tomato juice, j, in 2 quarts:
- Only one value for the variable
There are 32 ounces in a quart, so 2 quarts will always have 64 ounces.
3. The number of pizzas to order, p, if each person eats 2 slices:
- More than one value for the variable
The number of pizzas needed depends on the number of people attending, which can vary, leading to different values for p.
4. The greatest number of $6 notebooks, n, Ed can buy with $36:
- Only one value for the variable
Since each notebook costs $6, Ed can buy exactly 6 notebooks with $36 (36/6 = 6).
5. The area, a, of a wall with a length of 5 meters and a height of 3 meters:
- Only one value for the variable
The area of a rectangle is calculated by multiplying its length and height. In this case, the area will always be 15 square meters (5m x 3m = 15m²).
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What’s the answer? I need help asap help me
The matrix that represents a dilation by a factor of 3 followed by a reflection over the horizontal axis is given as follows:
[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The scale factor for this problem is given as follows:
k = 3.
Hence the matrix is:
[tex]\left[\begin{array}{cc}3&0\\0&3\end{array}\right][/tex]
For the reflection over the horizontal axis, we have that the y-coordinate is multiplied by -1, hence the matrix rule is:
[tex]\left[\begin{array}{cc}3&0\\0&-3\end{array}\right][/tex]
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