a. Dan's z-score is 1.5.
b. Dan scored better than approximately 6.68% of his classmates.
To find Dan's z-score, we'll use the formula:
z = (x - μ) / σ
Where:
x = Dan's score (83)
μ = mean (65)
σ = standard deviation (12)
a. To find Dan's z-score:
z = (83 - 65) / 12
z = 1.5
Therefore, Dan's z-score is 1.5.
b. To find the percentage of students Dan scored better than, we need to find the area under the normal curve to the left of Dan's z-score.
From the z-score table, we can see that the area to the left of z = 1.5 is approximately 0.9332.
To find the percentage of students Dan scored better than, we subtract this value from 1 and multiply by 100:
Percentage = (1 - 0.9332) * 100
Percentage = 6.68
Therefore, Dan scored better than approximately 6.68% of his classmates.
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If Lucy instead invested her $20,000 in an account with 5% simple interest,
how much would she end up with after 10 years?
Answer:
The 2009 Nobel Peace Prize was awarded to United States President Barack Obama for his "extraordinary efforts to strengthen international diplomacy and cooperation between people".
Step-by-step explanation:
The 2009 Nobel Peace Prize was awarded to United States President Barack Obama for his "extraordinary efforts to strengthen international diplomacy and cooperation between people".
Find the curvature k(t) of the curve r(t) = (-2 sin t)i + (-2 sin t)j + (-1 cost)k = 2sqrt2/(sqrt(8cost^2t+sin^2t)^(3/2))
The curvature k(t) of the Eequation r(t) = (-2sint) i + (-2sint) j + (-cost) k will be [tex]\frac{2\sqrt{2} }{(8cos^2t + sin^2t)^{3/2}}[/tex]
Given r(t) = (-2sint) i + (-2sint) j + (-cost) k
We can clearly see that r(t) is a vector equation of t.
If r(t): R→R³ is a vector-valued function of a real variable with independent scalar output variables x, y & z
where, r(t) = {x, y, z}
Where x = (-2sint) , y = -2sint and z = -cost
We know that the curvature to be
|| r'(t) X r"(t) || / ||r'(t)||³
This implies we need to find the determinant of the cross product of the derivative and double derivative of the equation r(t) for the numerator
r'(t) = (-2cost) i + (-2cost) j + (sint) k
r"(t) = (2sint) i + (2sint) j + (cost) k
hence we get || r'(t) X r"(t) || to be
[tex]\left|\begin{array}{ccc}i&j&k\\-2cost&-2cost&sint\\2sint&2sint&cost\end{array}\right|[/tex]
[tex]= \left|\begin{array}{ccc}-2cost&sint\\2sint&cost\end{array}\right| i - \left|\begin{array}{ccc}-2cost&sint\\2sint&cost\end{array}\right|j + \left|\begin{array}{ccc}-2cost&-2cost\\2sint&2sint\end{array}\right|k[/tex]
= -2i + 2j
Hence the magnitude will be
√(2² + 2²)
= 2√2 units
magnitude of r'(t) is
[tex]\sqrt{(2sint)^2 + (2sint)^2 + (cost)^2}[/tex]
= [tex]\sqrt{8cos^2t + sin^2t}[/tex]
Hence we get the curvature to be
[tex]\frac{2\sqrt{2} }{(\sqrt{8cos^2t + sin^2t})^3}[/tex]
simplifying this will give us
[tex]\frac{2\sqrt{2} }{(8cos^2t + sin^2t)^{3/2}}[/tex]
Hence the curvature k(t) will be [tex]\frac{2\sqrt{2} }{(8cos^2t + sin^2t)^{3/2}}[/tex]
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Correct Question
Find the curvature k(t) of the curve r(t) = (-2 sin t)i + (-2 sin t)j + (-1 cost)k
Actual sales for January through April are shown below.
Month Actual Sales (Yt)
January 18
February 25
March 34
April 40
May -
Use exponential smoothing with α = .3 to calculate smoothed values and forecast sales for May from the above data. Assume the forecast for the initial period (January) is 18. Show all the forecasts from February through April along with the answer.
The forecasted sales for February through April are as follows:
February: 19.5, March: 25.65, April: 30.755. The forecasted sales for May is approximately 35.928.
Exponential smoothing is a time series forecasting method that assigns weights to past observations, with the weights decreasing exponentially as the observations get older. The smoothed value for a particular period is a weighted average of the previous smoothed value and the actual value for that period.
To calculate the smoothed values and forecast sales using exponential smoothing with α = 0.3, we start with the initial forecast for January, which is given as 18. Then, for February, we use the formula:
Smoothed value (February) = α * Actual sales (February) + (1 - α) * Smoothed value (January)
= 0.3 * 25 + 0.7 * 18 = 19.5
Similarly, for March:
Smoothed value (March) = α * Actual sales (March) + (1 - α) * Smoothed value (February)
= 0.3 * 34 + 0.7 * 19.5 = 25.65
And for April:
Smoothed value (April) = α * Actual sales (April) + (1 - α) * Smoothed value (March)
= 0.3 * 40 + 0.7 * 25.65 = 30.755
Finally, for the forecasted sales in May:
Forecasted sales (May) = Smoothed value (April) = 30.755
Therefore, the forecasted sales for May, using exponential smoothing with α = 0.3, is approximately 35.928.
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Which of the following polynomials is reducible over Q 4x3³ + x - 2 5x³ + 9x² - 3 This option 3x³ - 6x² + x - 2 This option 08 O This option None of choices This option Activ 74°F Sun
None of the options are reducible polynomial
How to determine the reducible polynomialFrom the question, we have the following parameters that can be used in our computation:
The list of options
The variable Q means rational numbers
So, we can use the rational root theorem to test the options
So, we have
(a) 4x³ + x - 2
Roots = ±(1, 2/1, 2, 4)
Roots = ±(1, 1/4, 2, 1, 1/2)
(b) 3x³ - 6x² + x - 2
Roots = ±(1, 2/1 ,3)
Roots = ±(1, 1/3, 2, 2/3)
(c) 5x³ + 9x² - 3
Roots = ±(1, 3/1 ,5)
Roots = ±(1, 1/5, 3, 3/5)
See that all the roots have rational numbers
And we cannot determine the actual roots of the polynomial.
Hence, none of the options are reducible polynomial
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please help, i will give brainilest.
Answer:
-36
Step-by-step explanation:
Answer:
i think x = 21
Step-by-step explanation:
interference is a property of a. light waves. b. sound waves. c. water waves. d. all of these e. none of these
Interference is a property of ALL the given wave options, which are light waves, sound waves, and water waves.
Interference is the phenomenon of two or more waves combining to form a resultant wave of greater, lower, or the same amplitude.
When two waves meet at the same point at the same time, they either combine constructively (resulting in the formation of a wave of greater amplitude) or destructively (resulting in the formation of a wave of lower amplitude).
For instance, when two sound waves or light waves meet, they create a resultant wave whose amplitude is equal to the sum of the two original waves.
This is known as constructive interference.
On the other hand, when two waves meet and their amplitudes are in opposite directions, they produce a resultant wave whose amplitude is equal to the difference between the two waves.
This is known as destructive interference.
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How do you do these? I'm not sure on how to solve these and what to do to solve them.
Answer:
c) 59.6516 miles
d) 158.503 quarts, 64.3738 km
2 The table below shows the cost, s, to purchase p pounds of steak at a
local grocery store.
Cost of Steak
Number of
Pounds (p)
2.5
3.0
$23.98
$28.77
$33.57
$38.36
3.5
4.0
Which statement is true about the relationship shown in the table?
A The relationship is proportional, and the equation that represents this
relationship is s = 9.59 + p.
B. The relationship is proportional, and the equation that represents this
relationship is s = 9.59 + P.
The relationship is proportional, and the equation that represents this
relationship is s = 9.59p.
The relationship is not proportional.
Answer:
OMg whats there ikdd im tring
Step-by-step explanation: Im starting to solve it
two positive numbers x and y with maximum value 4 add up to 5. what is the difference between the maximum and minimum value of the product x^2y^3
The difference between the maximum and minimum value of x^2y^3 is determined by finding the product at the extreme values.
Given that two positive numbers x and y with a maximum value of 4 add up to 5, we can solve for the minimum value of x and y. Since the maximum value for x and y is 4, we assume that one number is 4 and the other number is 1, as they add up to 5.
Calculating the product x^2y^3 for these values, we have (4^2)(1^3) = 16. To find the maximum value of x and y, we need to distribute the sum of 5 unevenly between them. By assigning x = 1 and y = 4, we get (1^2)(4^3) = 64.
Therefore, the difference between the maximum and minimum value of x^2y^3 is 64 - 16 = 48.
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Adan took a test at school and completed it in an hour and a half. The test had two sections. If he took 45 minutes to complete the first Section, how much time did he use to finish the second section?
Answer:
45 minutes
Step-by-step explanation:
1 1/2 hours = 90 minutes
90 - 45 = 45
!PLEASE ANSWER ASAP! VERY IMPORTANT! THANK YOU!!
An experiment compares weight of fish for two different brands fish food. Nacho Average Minos
fish food has a mean fish weight 10 lbs. and a standard deviation of 1.5 lbs. Impossible Minos fish
food has a mean fish weight of 12 lbs. and a standard deviation of 1 lb. A fish is measured to be
11.25 lbs. Which brand of fish food, Nacho Average Minos or Impossible Minos, is more likely to have
been used to feed this fish?
Answer:
Nacho Average Minos
Step-by-step explanation:
z=11.25-10/1.5 = 1.25/1.5 = 0.834
z=11.25-12/1 = -0.75/1 = -0.75
i'm really stuck on this part. once i figure out how i'll mark brainliest (however you spell it).
just the first one 11 ........
The graph shows the height(t) of a model rocket t seconds after it is launched from the ground at 48 feet per second. Where is the height of the rocket increasing? Where is it decreasing?
A. The height of the rocket is always decreasing
B. The height of the rocket is always increasing
C. The height of the rocket is increasing when 0< t < 3 and decreasing when 3 < t < 6.
D. The height of the rocket is increasing when 3 < t< 6 and decreasing when 0 < t < 3
The height of the rocket is increasing when 0< t < 3 and decreasing when 3 < t < 6.
Option C is correct.
Increasing function:From the graph,
It is observed that , In interval 0< t < 3 , slope of graph is positive. Therefore, the height of the rocket is increasing
It is observed that , In interval 3 < t< 6 , slope of graph is negative. Therefore, the height of the rocket is decreasing.
Therefore, option C is correct.
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The odds against drawing a face card out of a deck are 9:4. What is the probability of drawing a face card?
The probability of drawing a face card from a deck is 3/13 or approximately 0.23.
The odds against an event is defined as the ratio of the number of ways the event doesn't occur to the number of ways it occurs. In this case, the odds against drawing a face card from a deck are 9:4. So, there are 9 ways to not draw a face card and 4 ways to draw a face card.
The total number of cards in a deck is 52, and there are 12 face cards (4 jacks, 4 queens, and 4 kings). Therefore, the probability of drawing a face card is:
P(face card) = number of face cards/total number of cards = 12/52 = 3/13
We can check that this probability satisfies the given odds against:
9/4 = 9/(9+4) = 9/13
1 - P(face card) = 1 - 3/13 = 10/13
The odds against drawing a face card is the same as the probability of not drawing a face card, which is 10/13. Therefore, the odds in favour of drawing a face card can be calculated as:
odds in favour= (3/13)/(10/13) = 3/10
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What is the numerical coefficient in y=−6x−3
A catering business purchased a light truck on April 5, 2019 to deliver breakfast
restaurants. The business paid $27,000 for the truck
Determine the total depreciation amount for 2020 assuming the taxpayer opted out of Sec. 179 and bos (if alable) in the your of pe In addition, assume all taxpayers use a calendar year tax period and that the property memmoned was the only property purchased a bey of acquisition. Use the appropriate depreciation table from your note sheet textbook where nocevary
OL None of the answers given here.
O $5,400
$8,640
OV $6,612
OV. $8,100
Using the appropriate depreciation table, MACRS 5 years, the total depreciation amount for 2020, assuming the taxpayer opted out of Sec. 179 in the year of purchase and other assumption, is B) $8,640.
What is depreciation?Depreciation refers to the gradual expensing of a long-term asset.
Under the MACRS 5 years for a light equipment, the depreciation rate applicable to the second year is 32%.
The cost of the truck = $27,000
Purchase date = April 5, 2019
Depreciation rate = MACRS 5 years
Depreciation rate for the second year under the MACRS 5 years table = 32%
Depreciation amount for 2020 = $8,640 ($27,000 x 32%)
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please help me with this one!!
Answer:
V = 960 cm^3
Step-by-step explanation:
Volume of a rectangular prism = L * W * H
V = 12 * 8 * 10
V = 960 cm^3
Answer:
d. 960 cm^3
Step-by-step explanation:
The formula for volume is length x width x height. To solve you have to multiply 12 by 8 by 10 to get 960
Measure of the triangle
Answer: 30
Step-by-step explanation: Both of them are thirty because total angle adds up to 180 on a triangle
decrease 1800 by 2 percent
Answer:
1764
Step-by-step explanation:
2% of 1800 = 0.02 * 1800 = 36
1800 - 36 = 1764
Answer: 1764
does anyone here know how to write negative 1 on there
Answer:
you fo to the fourth box on there and put - then go to the box after that and put 1
Step-by-step explanation:
sorry if im wrong
What is the product of (3y^-4)(2y^-4)?
Answer:
6/ y^8
Step-by-step explanation:
Calculate each unit price. Determine which is the best buy.
$1.25 for 6 oz.
$1.33 for 8 oz.
$1.50 for 12 oz.
$2.05 for 16 oz.
Answer:
1.50 for 12 ounces would be the best buy.
Step-by-step explanation:
We can calculate the unit price by dividing the price the the amount. In this case, we use ounces as our amount. Based on the calculations below, the best buy would be the 1.50 for 12 ounces as it has the lowest unit price.
1.25/6 = 0.208
1.33/8 = 0.166
1.50/12 = 0.125
2.05/16 = 0.128
if u know what to do pls help
Answer:
6.2 miles
Step-by-step explanation:
10 kilometers=.62 miles
.62*10= 6.2 miles
please helpppp to find the answer would really appreciate it !
Answer:
the answer is in the attachment
If the point (x,y) is in Quadrant IV, which of the following must be true?
x<0 and y>0
x>0 and y<0
The statement x > 0 and y < 0 must be true for any point (x, y) located in Quadrant IV.
If the point (x, y) is in Quadrant IV, it means that the x-coordinate is positive and the y-coordinate is negative. In Quadrant IV, the x-values are positive, as they are to the right of the y-axis, and the y-values are negative, as they are below the x-axis.
Therefore, the correct statement is:
x > 0 and y < 0.
In Quadrant IV, the x-values are greater than 0, indicating a positive x-coordinate, and the y-values are less than 0, indicating a negative y-coordinate. This is because in Quadrant IV, the x-axis is to the right of the y-axis, and the y-axis is below the x-axis.
Hence, the statement x > 0 and y < 0 must be true for any point (x, y) located in Quadrant IV.
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anybody know how to do this or what to do
Answer:
we know that 25% of something is = to 1/4 of something and we know 1/4 of that number is 8 so we have to do 8 plus 8 plus 8 plus 8 to get the answer or 8 times 4 which = 32
Step-by-step explanation:
(- x * y) ^ 2 - 8x ^ - 7 * y ^ - 2
I need help fast!!!
What is the answer??
Answer:
answer is \/
Step-by-step explanation:
Vincent paints 75% of his statues. He paints 60 statues. How many statues does Vincent have in total?
Answer:
80
Step-by-step explanation:
Let the total number of statues be s. Then 0.75s = 60, and s = (4/3)(60 statues) = 80
He has 80 statues total.
Sam is practising free-throws in basketball. She has a 4/5 chance of scoring each time she shoots from the free-throw line. (You should assume that the probability of scoring for each shot is independent of the result of other attempts.) What is the expected value of the number of free-throws that Sam will score before her first miss? 4/25 What is the variance of the number of free-throws that Sam will score before her first miss?
Sam has a 4/5 expected value of scoring each time she shoots from the free-throw line.
How is this so?
This means that the probability of her missing her first shot is 1/5. The expected value of the number of free-throws that Sam will score before her first miss is therefore 1/(1/5) = 5.
The variance of the number of free-throws that Sam will score before her first miss is (1−p)/p²
, where p is the probability of success.
In this case, p=4/5, so the variance is (1−4/5)/(4/5)²
=16/25.
= 4/5
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Five countries enter a race. The first three racers in order, Jamaica finished before Barbados, but behind Trinidad. Haiti finished before Guyana, but behind Barbados. Who won the Bronze (finished in 3rd place)?
Answer:
Barbados won the Bronze.
Step-by-step explanation:
The information indicates that Jamaica finished before Barbados, but behind Trinidad which means that Trinidad was the first one, then Jamaica and the third one was Barbados:
1. Trinidad
2. Jamaica
3. Barbados
Then, it indicates that Haiti finished before Guyana, but behind Barbados which indicates that Haiti was in 4th place after Barbados and the last one was Guyana:
1. Trinidad
2. Jamaica
3. Barbados
4. Haiti
5.Guyana
According to this, the answer is that Barbados won the Bronze.