The length of the hypotenuse of the right triangle is 15 cm.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Using this formula, we can calculate the length of the hypotenuse of a right triangle.
Given that the longer sides of the right triangle are 9 cm and 12 cm long, we can assume that one of these sides is the shorter side and the other is the longer side. Let's assume that the shorter side is 9 cm long and the longer side is 12 cm long.
Using the Pythagorean Theorem, we can calculate the length of the hypotenuse as follows:
Hypotenuse² = Shorter side² + Longer side²
Hypotenuse² = 9² + 12²
Hypotenuse² = 81 + 144
Hypotenuse² = 225
Taking the square root of both sides, we get:
Hypotenuse = √225
Hypotenuse = 15
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(c) Katrina recorded the average rainfall amount, in inches, for two cities over the course of 6 months. City A: {5, 2. 5, 6, 2008. 5, 5, 3} City B: {7, 6, 5. 5, 6. 5, 5, 6} (a) What is the mean monthly rainfall amount for each city? (b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth. (c) What is the median for each city?
The mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.
The mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.
The median for City A is 5.5 inches, and for City B, it is 6 inches.
(a) To find the mean monthly rainfall amount for each city, we sum up the rainfall amounts for each city and divide by the number of months.
For City A:
Mean = (5 + 2.5 + 6 + 2008.5 + 5 + 3) / 6 = 2030 / 6 ≈ 338.3 inches per month
For City B:
Mean = (7 + 6 + 5.5 + 6.5 + 5 + 6) / 6 = 36 / 6 = 6 inches per month
So, the mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.
(b) The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean. To calculate the MAD, we first find the absolute difference between each data point and the mean, sum them up, and then divide by the number of data points.
For City A:
Absolute differences from the mean: |5 - 338.3|, |2.5 - 338.3|, |6 - 338.3|, |2008.5 - 338.3|, |5 - 338.3|, |3 - 338.3|
MAD = (333.3 + 335.8 + 332.3 + 1670.2 + 333.3 + 335.3) / 6 ≈ 557.0 / 6 ≈ 92.8
For City B:
Absolute differences from the mean: |7 - 6|, |6 - 6|, |5.5 - 6|, |6.5 - 6|, |5 - 6|, |6 - 6|
MAD = (1 + 0 + 0.5 + 0.5 + 1 + 0) / 6 ≈ 3 / 6 = 0.5
So, the mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.
(c) To find the median, we arrange the rainfall amounts in ascending order and find the middle value. If there are an even number of data points, we take the average of the two middle values.
For City A: {2.5, 3, 5, 5, 6, 2008.5}
Median = (5 + 6) / 2 = 11 / 2 = 5.5 inches
For City B: {5, 5.5, 6, 6, 6.5, 7}
Median = 6 inches
So, the median for City A is 5.5 inches, and for City B, it is 6 inches.
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Which angle in AXYZ has the largest measure? 4 Y A. LX B. LY C.
(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."
Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.
The angle in degrees separates these lines or planes.
So, we know that:
The side opposite to the largest angle is also the largest side of the triangle and vica-versa.
Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.
Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
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Correct question:
Which angle in AXYZ has the largest measure?
A. ∠X
B. ∠Y
C. ∠Z
D. Cannot be determined
Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project.
"(help me with this pls asap)"
Eric has completed 37.5% (or 0.375) of the project, while Victoria has completed 33.3% (or 0.333) of the project. Together, they have completed approximately 70.8% (or 0.708) of the project.
If Eric and Victoria are working on a project and Eric has completed 3/8 of the project, and Victoria has completed 1/3 of the project, then to find the total portion of the project completed, you can add their individual contributions: (3/8) + (1/3).
To add these fractions, you need a common denominator, which is 24 in this case. So, you can rewrite the fractions as (9/24) + (8/24). Adding them together gives you a total of 17/24 of the project completed by both Eric and Victoria, which is equal to 70.8% (or 0.708).
*complete question: Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project. Calculate the total work they have completed together.
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A random sample of 318 students from a large college were asked if they are planning to visit family during Thanksgiving break. Based on this random sample, a 95% confidence interval for the proportion of all students at this college who plan to visit family during Thanksgiving break is 0. 78 to 0. 98. Which of the following is the correct interpretation of the confidence interval?
Group of answer choices
1)We are 95% confident that the interval from 0. 78 to 0. 98 captures the true proportion of all students at this college who plan to visit family during Thanksgiving break.
2)We are 95% confident that the interval from 0. 78 to 0. 98 captures the true mean of all students at this college who plan to visit family during Thanksgiving break.
3)95% of students at this college are going home during Thanksgiving Break.
4)None of these are correct
The correct interpretation of the given confidence interval is 95% confidence that the true proportion of all students at this college who plan to visit family during Thanksgiving break is between 0.83 and 0.93 .
Then the required answer to the given question is Option D.
Let us consider a random sample of 318 students from a large college that were asked if they are planning to visit family during Thanksgiving break. Now placing the given random sample, the proportion of 95% confidence interval of all students at this college that planned to visit family during Thanksgiving break is 0.78 to 0.98 .
The formula for evaluating the confidence interval is
CI = p ± z × √((p × (1 - p)) / n)
Here,
CI = confidence interval,
p = sample proportion,
z = z-score corresponding to the desired level of confidence (in this case, 95%)
n is the sample size .
Applying the values
CI = 0.88 ± 1.96 × √((0.88 × (1 - 0.88)) / 318)
CI = 0.88 ± 0.05
CI = (0.83, 0.93)
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Arturo has $480 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $201. 87.
• He buys 3 bicycle reflectors for $9. 82 each and a pair of bike gloves for $15. 79.
• He plans to spend some or all of the money he has left to buy new biking outfits
for $32. 80 each.
Write and solve an inequality which can be used to determine o, the number of outfits
Arturo can purchase while staying within his budget.
Inequality: 1
Submit Answer
attempt 1 out of 2
Answer:
Step-by-step explanation:
201.87 + 3(9.82) + 15.79 + 32.80(o) < 480
247.12 + 32.80(o) < 480
32.80(o) < 480 - 247.12
32.80(o) < 232.88
o < 232.88/32.8
o < 7.1
He can purchase 7 outfits and stay within the $480 budget
how do i change a mixed number to a improper fraction and simplify
Answer:
To change a mixed number to an improper fraction quickly we can multiply the whole number by the denominator, add the numerator and then write that over the original denominator.
The music industry has steadily moved from selling music in a physical format such as records, eight tracks, cassettes, and CDs telling music in digital formats. In 2001, the music industry sold $26.5
billion of music in the physical format. Each year after 2001, the amount of sales of music constantly decreased by 10%.
Select the function P(t), where P represents the sales, in billions of dollars, of music in the physical format and t represents the number of years since 2001.
P(0) 26 5/0 1
Answer:
P(t)=26.5 (0.1)^t
Step-by-step explanation:
Given n with chord AB, which point lies on the perpendicular bisector of AB?
The Midpoint of AB ((x1 + x2)/2, (y1 + y2)/2) lies on the perpendicular bisector of AB.
Which point lies on the perpendicular bisector of AB?Assuming that chord AB is a straight line segment, the point that lies on the perpendicular bisector of AB is the midpoint of AB. This is because the perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to it.
Therefore, to find the point that lies on the perpendicular bisector of chord AB, we need to find the midpoint of AB. This can be done by finding the average of the x-coordinates and the average of the y-coordinates of points A and B, respectively.
Let (x1, y1) and (x2, y2) be the coordinates of points A and B, respectively. Then the midpoint of AB is:
((x1 + x2)/2, (y1 + y2)/2)
This point lies on the perpendicular bisector of AB.
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Two vans leave a campground at the same time. One is traveling north at a speed that is 10 miles per hour faster than the other, which is traveling south. After 2. 5 hoursthe vans are 255 miles apart. What is the speed in miles per hour of the van traveling south?
The speed of the van traveling south is 46 miles per hour.
Let the speed of the van traveling south be x miles per hour. Then, the speed of the van traveling north is (x + 10) miles per hour.
Since both vans are moving apart, we add their speeds: x + (x + 10) = 2x + 10 miles per hour.
In 2.5 hours, they are 255 miles apart. So, (2x + 10) * 2.5 = 255.
Now, we solve for x:
5x + 25 = 255
5x = 230
x = 46
The speed of the van traveling south is 46 miles per hour.
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The function f(x) = 1. 25x2 models the packaging costs, in cents, for a box shaped like a rectangular prism. The side lengths are 2x in. , 2x in. , and 0. 5x in. What are reasonable domain and range values for this function, if the longest side length of the box can be no greater than 20 in. ? Write the answers in interval notation
The range of the function f(x) is Range: [0, 125] In interval notation, this can be written as [0, 125] if the longest side length of the box can be no greater than 20 in.
The function f(x) = 1.25x^2 models the packaging costs, in cents, for a rectangular prism-shaped box with side lengths of 2x in., 2x in., and 0.5x in.
We need to determine the reasonable domain and range values for this function, given that the longest side length of the box can be no greater than 20 in.
Since the longest side length is 20 in., we know that:
2x ≤ 20
x ≤ 10
Therefore, the domain of the function f(x) is all real numbers less than or equal to 10, or: Domain: [-∞, 10]
To find the range of the function, we need to examine the behavior of the function as x varies. Since the coefficient of x^2 is positive, the function is quadratic with a minimum value at x = 0. Therefore, we know that the range of the function must start at its minimum value, which is f(0) = 0, and increase as x increases.
To determine the upper limit of the range, we can evaluate f(x) when x = 10 (the maximum value of x allowed):
f(10) = 1.25(10)^2 = 125
Therefore, the range of the function f(x) is:
Range: [0, 125]
In interval notation, this can be written as [0, 125].
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!!I NEEEDD HELPPP!! Please helppp :(
The customer would save $492 in the first year by switching to Intellivision.
The customer would save $207 in the second year by switching to Intellivision.
For the third year, it would be cheaper to stick with ElectroniSource.
How to find the savings ?To calculate the savings for the first year, we need to find the total cost for ElectroniSource and compare it to the flat fee from Intellivision for all three services.
The savings for the first year by switching to Intellivision would be:
$1,632 - $1,140 = $492
Therefore, the customer would save $492 in the first year by switching to Intellivision.
After the first year, Intellivision raises the rates by 25%. So the new flat fee for the second year would be:
$95 + ($95 x 25%) = $118.75
The savings for the second year by switching to Intellivision would be:
$1,632 - $1,425 = $207
Therefore, the customer would save $207 in the second year by switching to Intellivision.
For the third year, Intellivision raises the rates by 16% compared to the second year. So the new flat fee for the third year would be:
$118.75 + ($118.75 x 16%) = $137.78
Therefore, for the third year, it would be cheaper to stick with ElectroniSource, which costs $1,632 for the year, compared to Intellivision, which costs $1,653.36 for the year.
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A doctor saw 8 patients a day for 7 days. How many patiencents did he see altogether
The doctor saw 56 patients altogether during the 7 days.
To find out how many patients the doctor saw altogether, we need to use multiplication.
Identify the number of patients seen per day (8 patients).
Identify the number of days the doctor worked (7 days).
Multiply the number of patients per day by the number of days worked.
8 patients/day × 7 days = 56 patients.
The doctor saw 8 patients per day for 7 days, so the total number of patients he saw in a week is
Therefore, the doctor saw a total of 56 patients in 1 week.
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Jayden just accepted a job at a new company where he will make an annual
salary of $41000. Jayden was told that for each year he stays with the
company, he will be given a salary raise of $2500. How much would Jayden make as a salary after 4 years working for the company? What would be his salary after t years?
Jayden's starting salary is $41000 per year. If he stays with the company for one year, he will receive a raise of $2500, bringing his new salary to $43500. If he stays for two years, he will receive another raise of $2500, bringing his salary to $46000.
If he stays for three years, he will receive a third raise of $2500, bringing his salary to $48500. And finally, if he stays for four years, he will receive a fourth raise of $2500, bringing his salary to $51000.
Therefore, after four years working for the company, Jayden's salary would be $51000 per year.
After t years, Jayden's salary would be calculated as follows:
- After one year: $41000 + $2500 = $43500
- After two years: $41000 + ($2500 x 2) = $46000
- After three years: $41000 + ($2500 x 3) = $48500
- After four years: $41000 + ($2500 x 4) = $51000
- After t years: $41000 + ($2500 x t).
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how many different triangles can be formed by side lengths 2 cm, 7cm, and 70 degrees angle formed by these given sides?
Lines AC and BD intersect at point O. Lines AC and BD intersect at point O. If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?
A. 6°
B. 53°
C. 89°
D. 106°
Answer: the answer is B. 53°
Step-by-step explanation:
(10x-7) = (7x+11)
10x-7-7x =7x+11-7x
3x-7=11
3x-7+7=11+7
3x=18
x=6
Plug 6 into angle ∠BOC
7x+11
7(6)+11
42+11
53°
Given that lines AC and BD intersect at point O, we know that ∠AOD and ∠BOC form a linear pair. It means that the sum of those angles should be 180° since the straight line's sum is 180°.
Therefore, we can create the equation (10x - 7)° + (7x + 11)° = 180°, where x is the variable we need to find.
By combining like terms, we simplify this equation to 17x + 4 = 180.
To isolate x, we have to subtract 4 from both sides of the equation, resulting in 17x = 176.
Now, dividing both sides by 17, we find that x equals approximately 10.35.
Finally, to find measure of ∠BOC, we just need to substitute the value of x we found into the expression of m∠BOC: m∠BOC = 7*10.35 + 11, which is approximately 83.47°.
Based on the choices given, C. 89° is the closest to our calculated value. Therefore, the answer is C. 89°.
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A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 8% vinegar. The chef wants to make 300 milliliters of a dressing that is 7% vinegar. How much of each brand should she use?
First Brand: ?
Second Brand: ?
The chef should use 100 milliliters of the first brand and 200 milliliters of the second brand.
To create a 300 milliliters dressing with 7% vinegar using two brands of Italian dressing, we can use a system of equations to find the quantities of each brand needed.
Let x be the amount of the first brand (5% vinegar) and y be the amount of the second brand (8% vinegar).
First equation (total volume):
x + y = 300
Second equation (vinegar percentage):
0.05x + 0.08y = 0.07 * 300
Now, solve the system of equations:
From the first equation, y = 300 - x
Substitute this into the second equation:
0.05x + 0.08(300 - x) = 21
Expand and simplify:
0.05x + 24 - 0.08x = 21
0.03x = -3
Now, divide by 0.03:
x = 100
Now, find the value of y:
y = 300 - x = 300 - 100 = 200
So, the chef should use 100 milliliters of the first brand and 200 milliliters of the second brand.
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A dealer paid $10,000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction price. The salesperson received a commission of 25% of the difference between the auction price and the dealership price. What was the salesperson’s commission?
The commission of the salesperson is $750 if he received a commission of 25% of the difference between the auction price and the dealership price.
The salesperson's commission can be calculated by first finding the dealership price, which is 30% more than the auction price of $10,000.
30% of $10,000 = $3,000
Dealership price = $10,000 + $3,000 = $13,000
Next, we need to find the difference between the dealership price and the auction price
$13,000 - $10,000 = $3,000
The salesperson's commission is 25% of this difference
25% of $3,000 = $750
Therefore, the salesperson's commission is $750.
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1. What are the current health issues and concerns in your community?
2. If you are a health worker in your community,what health issues and concerns do you think should be addressed immediately?why?
3. What will the world be like if health issues and concerns are not properly addressed by people around the world?
HELPPPPP PO
Infectious diseases, chronic conditions, mental health, healthcare access, health disparities. Vaccination campaigns, disease prevention, healthcare access, mental health support, social determinants. Increased disease burden, higher costs, reduced quality of life, higher mortality, strained healthcare systems, hindered socio-economic development.
What are the current health issues and concerns in your community? The current health issues and concerns in the community include a range of factors such as infectious diseases, chronic conditions, mental health challenges, healthcare access and affordability, health disparities, and the impact of lifestyle choices on overall well-being. As a health worker in the community, immediate attention should be given to addressing issues such as promoting vaccination campaigns, disease prevention and control measures, improving healthcare access and affordability, advocating for mental health support and awareness, and addressing social determinants of health. If health issues and concerns are not properly addressed globally, the consequences could be severe. There would likely be increased prevalence of diseases, higher healthcare costs, reduced quality of life, higher mortality rates, and widening health inequalities.Learn more about mental health support
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A father and his three children decide on all matters with a vote. Each member of the family gets as many votes as their age. Right now, the family members are 36, 13, 6, and 4 years old, so the father always wins. How many years will it take for the three children to win a vote if they all agree? Show your work.
Answer:
Step-by-step explanation:
Answer:
13 years
Step-by-step explanation:
Intuition for how sons can collectively win after a certain period of time:- After a certain period of time the father's age will increase by that certain period of time (say 5 years) but for the sons (since there are 3 of them) their collective age will increase by three times that of their father (5 for each 1 one them). Therefore there exist a time after which collective increase in sons' age can cover the current gap of 13 years.
Hudson Marine provides boats sales, service, and maintenance. Boat trailers are one of its top sales items. Suppose the quarterly sales values for the seven years of historical data are as follows. Do not round intermediate calculations. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 7 17 9 2 35 2 9 19 17 8 53 3 13 28 23 12 76 4 18 27 23 17 85 5 23 32 30 20 105 6 23 38 31 19 111 7 26 41 33 28 128
a. Compute the centered moving average values (first find Four-Quarter Moving Average) for this time series (to 3 decimals). Centered Moving Sales Average 1 6 t N 16 3 11 4 3 5 10 6 6 16 7 17 8 6 9 12 10 28 11 21 12 12 13 20 14 28 15 23 16 16 17 20 18 35 19 30 20 19 21 25 22 37 23 30 24 20 25 30 26 41 27 34 28 27
b. Compute the seasonal indexes for the four quarters (to 3 decimals). Quarter Adjusted Seasonal Index 1 2 3 4
c. When does Hudson Marine experience the largest seasonal effect? Hudson Marine experiences the largest seasonal increase in quarter The largest seasonal effect is the seasonal decrease in quarter
Hudson Marine experiences the largest seasonal effect in quarter 4.
How to calculate the four-quarter moving average values, the seasonal indexes, and the largest seasonal effect of Hudson Marine?a. The four-quarter moving average values can be calculated as follows:
Quarter 1: (7 + 9 + 13 + 18) / 4 = 11.75
Quarter 2: (17 + 19 + 28 + 27) / 4 = 22.75
Quarter 3: (9 + 17 + 23 + 23) / 4 = 18
Quarter 4: (2 + 8 + 12 + 17) / 4 = 9.75
Quarter 5: (17 + 8 + 12 + 20) / 4 = 14.25
Quarter 6: (53 + 23 + 17 + 19) / 4 = 28
Quarter 7: (76 + 85 + 105 + 111) / 4 = 94.25
The centered moving average values can be calculated by averaging the adjacent four-quarter moving averages:
Quarter 3: (11.75 + 22.75 + 18 + 9.75) / 4 = 15.06
Quarter 4: (22.75 + 18 + 9.75 + 14.25) / 4 = 16.19
Quarter 5: (18 + 9.75 + 14.25 + 28) / 4 = 17.75
Quarter 6: (9.75 + 14.25 + 28 + 94.25) / 4 = 36.31
Quarter 7: (14.25 + 28 + 94.25 + 28) / 4 = 41.38
Therefore, the centered moving average values are:
Quarter 3: 15.06
Quarter 4: 16.19
Quarter 5: 17.75
Quarter 6: 36.31
Quarter 7: 41.38
b. The seasonal indexes for the four quarters can be calculated by dividing the centered moving average values by the average of all the centered moving average values and then multiplying by 100:
Quarter 1: (15.06 / 20.31) x 100 = 74.18
Quarter 2: (16.19 / 20.31) x 100 = 79.79
Quarter 3: (17.75 / 20.31) x 100 = 87.40
Quarter 4: (36.31 / 20.31) x 100 = 178.63
Therefore, the seasonal indexes for the four quarters are:
Quarter 1: 74.18
Quarter 2: 79.79
Quarter 3: 87.40
Quarter 4: 178.63
c. Hudson Marine experiences the largest seasonal effect in quarter 4, with a seasonal index of 178.63. This means that the sales in quarter 4 are, on average, 178.63% higher than the average sales for all quarters.
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trapezoid ABCD is similar to trapezoid EFGH what is the value of M
The value of M is 4.
The value of M represents the length of the segment that connects the midpoints of the non-parallel sides of trapezoid ABCD. To find the value of M, we can use the fact that the trapezoids are similar.
Now, let's label the points where MN intersects sides BC and FG as P and Q, respectively. We can use the fact that MN is parallel to sides BC and FG to show that triangles BMP and FQN are similar to trapezoids ABCD and EFGH, respectively.
Therefore, we can write:
BM/AB = MP/CD = k
and
FQ/EF = QN/GH = k
Since we know that AB/EF = k, we can substitute this into the first equation to get:
BM/EF = MP/GH
Similarly, we can substitute FQ/EF = k into the second equation to get:
FQ/EF = QN/GH
Now, let's combine these two equations to get:
(BM + FQ)/EF = (MP + QN)/GH
But we know that BM + FQ = EF, and MP + QN = GH. Therefore, we can simplify the equation to get:
EF/EF = GH/GH
Or simply:
1 = 1
This means that our calculations are correct, and that we can use the ratio k to find the value of M. Specifically, since MN is parallel to AB and CD, we know that the length of MN is equal to half the difference between the lengths of AB and CD. Therefore, we can write:
M = (1/2)(AB - CD)/k
When we apply the values on it, then we get,
M = (1/2) (56 - 48) / 1
M = (1/2) x 8 = 4
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8: Hector’s Math test grades for the final
quarter are 89, 93, 100, 98, and 95. He has one
more test to take this quarter. All tests count
equally. What is the minimum grade Hector must
make on the last test in order to obtain an
average of at least 93?
Hector needs to score at least a 97 on his last test to obtain an average of at least 93 for the final quarter.
The average grade for the final quarter can be calculated by summing up all the grades and dividing by the total number of tests. In this case, Hector has taken 5 tests, and his grades are 89, 93, 100, 98, and 95. Therefore, his current total score is 89+93+100+98+95 = 475.
To obtain an average of at least 93, Hector's total score for all 6 tests should be at least 93*6 = 558.
So, Hector needs to score a minimum of 558 - 475 = 83 on his last test. Since all tests count equally, Hector needs to score at least 83% on his last test. Therefore, the minimum grade Hector must make on the last test in order to obtain an average of at least 93 is 97 (rounded up from 96.6).
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3. Find a quadratic polynomial whose one zero is 5 + √3 and sum of the zeroes is 10.
Answer:
f(x) = x² - 10x + 22
Step-by-step explanation:
Let's assume the quadratic polynomial as:
f(x) = ax² + bx + c
Now we know that if one of the zeroes is 5 + √3, then the other zero must be 5 - √3 (because complex roots always come in conjugate pairs).
So the sum of the zeroes will be:
(5 + √3) + (5 - √3) = 10
10 = 2 * 5
The product of the zeroes will be:
(5 + √3) * (5 - √3) = 25 - 3 = 22
Now, using the sum and product of zeroes, we can write:
b/a = 10
c/a = 22
Solving for b and c, we get:
b = -10a
c = 22a
Substituting these values in f(x), we get:
f(x) = a(x - 5 - √3)(x - 5 + √3)
Expanding the right-hand side:
f(x) = a[(x - 5)² - (√3)²]
f(x) = a(x² - 10x + 22)
Comparing the coefficients of f(x) with ax² + bx + c, we get:
a = 1, b = -10, c = 22
Therefore, the quadratic polynomial is:
f(x) = x² - 10x + 22
F(x)= x⁴ +14x²+45 (100 points)
for this function: state the number of complex zeros, the possible number of imaginary zeros, the possible number of positive and negative zeros, and the possible rational zeros
then factor to linear factors and find all zeros
-number of complex zeros: ___________________
-possible # of imaginary zeros: ______________________
-possible # of positive real zeros: _____________________
-possible # negative real zeros: __________________
-possible rational zeros: ___________________
-factors to: _________________________
-zeros: ______________________
For the function,
-number of complex zeros: four
-possible # of imaginary zeros: two pairs
-possible # of positive real zeros: zero
-possible # negative real zeros: 0 or 2
-possible rational zeros: ±1, ±3, ±5, ±9, ±15, ±45
-factors to: (x + 3i)(x - 3i)(x + √5i)(x - √5i)
-zeros: x = ±3i, x = ±√5i.
The function is: F(x) = x⁴ +14x²+45.
Number of complex zeros: By the Fundamental Theorem of Algebra, the function has at most four complex zeros.
Possible number of imaginary zeros: If the complex zeros are not real, then there are at most two pairs of imaginary zeros.
Possible number of positive real zeros: The function has no positive real zeros since F(x) is always positive for x>0.
Possible number of negative real zeros: By Descartes' Rule of Signs, the function has either 0 or 2 negative real zeros.
Possible rational zeros: The rational zeros can be found using the Rational Root Theorem. They are of the form ±(a factor of 45) / (a factor of 1), which gives the following possible rational zeros: ±1, ±3, ±5, ±9, ±15, ±45.
To factor the polynomial:
F(x) = x⁴ +14x²+45
= (x² + 9)(x² + 5)
So the factors to linear factors are: (x + 3i)(x - 3i)(x + √5i)(x - √5i), where i is the imaginary unit.
Therefore, the zeros are: x = ±3i, x = ±√5i.
Note that all zeros are complex since there are no real roots.
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1. consider the pyramid.
(a) draw and label a net for the pyramid.
(b) determine the surface area of the pyramid. show your work.
(pyramid is listed in the pdf)
2. the back of nico’s truck is 9.5 feet long, 6 feet wide, and 8 feet tall. he has several boxes of important papers
that he needs to move. each box of papers is shaped like a cube, measuring 1.5 feet on each side.
how many boxes of papers can nico pack into the back of his truck? show your work.
please help!
A net for the pyramid is drawn and labeled. The surface area of the pyramid is found using the formula and the given measurements is 96 square units. The number of boxes of papers Nico can pack into the back of his truck is 135 boxes.
The labeled pyramid is shown in image.
To find the surface area of the pyramid, we need to find the area of each face and add them together. The area of the base is a square with side length 6, so its area is
6² = 36 square units.
The area of each triangular face can be found by using the formula for the area of a triangle, which is 1/2 times base times height.
The height of each face is the slant height of the pyramid, which we can find using the Pythagorean Theorem.
The base of each face is one of the sides of the base of the pyramid, which has length 6.
The slant height of the pyramid can be found by drawing the height from the apex to the center of the base and then using the Pythagorean Theorem to find the length of the hypotenuse of the right triangle formed by the height, half the base (3), and the slant height. We get
slant height = √(4² + 3²) = 5
So the area of each triangular face is 1/2 times base times height = 1/2 times 6 times 5 = 15 square units. Since there are four triangular faces, the total surface area of the pyramid is
4(15) + 36 = 96 square units.
Therefore, the surface area of the pyramid is 96 square units.
The volume of one box of papers is 1.5 x 1.5 x 1.5 = 3.375 cubic feet. The volume of the truck is 9.5 x 6 x 8 = 456 cubic feet. The number of boxes Nico can pack into the truck is therefore
456 / 3.375 = 135.11
Since Nico cannot pack a fraction of a box, he can fit a maximum of 135 boxes of papers in his truck.
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Mia is participating in a kite-flying competition. She wanted to find out how long is the string needed for fly her kite 33 meters from the ground if she is 56 meters away from the kite.
how do i do this assignment while showing the work?
The length of the string needed is 65 meters
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Pythagoras theorem shows the relationship between the sides of a right angle triangle.
To find the length of string, Mia needs. A triangle is formed with hypotenuse (l) represent the length of string. The height of the kite (h) = 33 m which is the triangle height; while the 56 m is the base of the triangle (b). Hence:
l² = b² + h²
l² = 33² + 56²
l = 65 meters
The length of the string needed is 65 meters
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URGENTEEEE!! REPONDER RAPIDO POR FAVOR!!!
Which of the following could be the graph of f(x)=(2/5)^x?
Answer:
The third graph from the top could be the graph of f(x) = (2/5)^x. As x approaches infinity, f(x) approaches 0.
Question content area top Part 1 Point B has coordinates (3,2). The x-coordinate of point A is −9. The distance between point A and point B is 15 units. What are the possible coordinates of point A
The possible coordinates of point A are (-9, -7) and (-9, 11).
What are coordinates?Coordinates refers to a set of numbers that are used to identify the position of a point in a space, usually defined by an x-axis, y-axis, and in sometimes a z-axis.
Let the y-coordinate of point A be y. Then the coordinates of point A are (-9, y).
Using the distance formula, we have:
√[(3 - (-9))² + (2 - y)²] = 15
Simplify the equation:
√[(12)² + (2 - y)² = 15
Square both sides of the equation, we get:
(12)² + (2 - y)² = 15²
144 + (2 - y)² = 225
(2 - y)² = 225 - 144
(2 - y)² = 81
We now take the square root of both sides:
2 - y = ±9
Solve for y in each case, we get:
y = 2 - 9 = -7 or y = 2 + 9 = 11
Therefore, the possible coordinates of point A are (-9, -7) and (-9, 11).
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What is the volume of the regular pyramid to the nearest whole number?
Regular pyramid
1452 cm
594 cm
1188 cm
1029 cm
The volume of the regular pyramid is 1188 cm³.
What is a regular pyramid?A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length.
To calculate the volume of the regular pyramid, we use the formula below
Formula:
V = bhH/6....................... Equation 1Where:
V = Volume of the pyramidb = Base of of the triangleh = Height of the triangleH = Height of the pyramidFrom the question,
Given:
H = 22 cmb = 18 cmh = 18 cmSubstitute these values into equation 1
V = 18×18×22/6V = 1188 cm³Hence, the right option is C. 1188 cm³
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Solve the quadratic function by factoring x^2 +10x+9-0
The solution for the quadratic function by factoring x^2 +10x+9-0 is x = -1 and x = -9.
Given that the equation is x^2 +10x+9-0.
To solve the quadratic equation x^2 + 10x + 9 = 0 by factoring, follow the steps given below:
First we need to find two numbers that multiply to 9 and add to 10. These numbers are 1 and 9:
x^2 + 10x + 9 = (x + 1)(x + 9)
So the solutions to the equation are the values of x that make each factor equal to zero:
x + 1 = 0 or x + 9 = 0
Solving for x in each case, we get:
x = -1 or x = -9
Therefore, the solutions to the quadratic equation x^2 + 10x + 9 = 0 are x = -1 and x = -9.
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