a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).
The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:
Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5
Next, we can calculate SSTr using the formula:
SSTr = n * (sample mean - overall mean)^2
where n is the number of observations in each sample. In this case, n = 5 for each sample.
So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5
For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5
For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5
For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5
Therefore, the total SSTr is:
SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750
b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.
df(SSTr) = k - 1 = 5 - 1 = 4
df(SSE) = N - k = 20 - 5 = 15
The mean square for treatments (MSTr) is calculated as:
MSTr = SSTr / df(SSTr) = 12 / 4 = 3
The mean square for error (MSE) is calculated as:
MSE = SSE / df(SSE) = (20 - 5) / 15 = 1
Finally, we can calculate the F-test statistic as:
F = MSTr / MSE = 3 / 1 = 3
Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.
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he data collected on the number of points scored in a basketball season are represented in the box plot. A box plot uses a number line from 13 to 33 with tick marks every one-half unit. The box extends from 16 to 31 on the number line. A line in the box is at 24. The lines outside the box end at 14 and 32. The graph is titled Number of Points, and the line is labeled Points Scored in Basketball. What value does 25% of the data lie above? Find the value. Lower quartile (Q1) = 14 Lower quartile (Q1) = 16 Upper quartile (Q3) = 24 Upper quartile (Q3) = 31
The value that lie above 25% of the data of the box plot is 31 and the lower quartile (Q1) = 14 upper quartile (Q3) = 31
Given data ,
The minimum value, which is 14
Now , the lower quartile, which is 16 (25% of the data is below this value)
And , the median, which is 24 (50% of the data is below this value)
Now , the upper Quartile, which is 31 (75% of the data is below this value)
And , the maximum value is 32.
The upper and lower quartiles of a box plot, also known as the 75th percentile (Q3) and 25th percentile (Q1) respectively, represent the range within which the middle 50% of the data falls.
Lower quartile (Q1) = 14
Upper quartile (Q3) = 31
Hence , 25% of the data lie above 31, which is the upper quartile.
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A human heart pumps about 7 × 10-2 liter of blood pe-
heartbeat. The average human heart beats about 72 times per minute.
How many liters of blood does a heart pump in 1 year? 70 years?
The heart will pumps 31,536 litres in 1 year and pumps 2,207,520 liters in 70 years.
Simple solution to how blood is pumpedThere are 72 heartbeats in a minute.
If heart pumps 7 × 10⁻² litre per heartbeat,
then in 1 min,
7 × 10⁻² x 72 = 5.04 litres/minute
In one year (365 days), the heart pumps:
5.04 x 60 x 24 x 365 = 31,536 litres/year
Hence in 1 year, heart pumps 31,536 litres
In 70 years, the heart would pump:
31,536 x 70 years = 2,207,520 litres
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A 1300-seat theater sells two types of tickets for a concert. Premium seats sell for $30 each and regular seats sell for $20 each. At one event $32,240 was collected in ticket sales with 10 seats left unsold. How many of each type of ticket was sold
The required, there were 644 premium seats and 646 regular seats sold.
Let x be the number of premium seats sold and y be the number of regular seats sold. Then we have two equations:
x + y = 1290 (total seats sold)
30x + 20y = 32240 (total revenue)
We can use the first equation to solve for y in terms of x:
y = 1290 - x
Substituting this into the second equation, we get:
30x + 20(1290 - x) = 32240
Simplifying and solving for x, we get:
x=644
So 644 premium seats were sold. Substituting this into the first equation, we get:
644+ y = 1290
y = 646
So 646 regular seats were sold.
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Add 2x+ 3 y + 7 and 4x-7y-8 PLLSSS QUICKKK
Answer:
3
Step-by-step explanation:
A bag of marbles has 4 red, 3 blue, 2 green, and 1 yellow marbles. If Aisha reaches into the bag, what is the probability she picks a red marble?
There are a total of 4 + 3 + 2 + 1 = 10 marbles in the bag. The probability of picking a red marble is the number of red marbles divided by the total number of marbles:
Probability of picking a red marble = 4/10 = 2/5
Therefore, the probability Aisha picks a red marble is 2/5 or 0.4 when written as a decimal.
Alan owes the bank $11750. To repay his debt, he paid a fixed amount back to the bank each month. After 0.5 year(s), Alan's remaining debt was $6650. How much did Alan pay each month?
Alan paid an amount $850 to the bank each month to repay his debt.
The total amount that Alan paid back to the bank is equal to the initial amount that he owed minus the remaining amount after 0.5 year(s):
Total amount paid = Initial amount - Remaining amount
= $11750 - $6650
= $5100
We know that Alan paid this amount back over a period of 0.5 year(s), which is equivalent to 6 months.
Let x be the fixed amount that Alan paid back to the bank each month. Therefore, we can set up the following equation:
Total amount paid = Monthly payment × Number of months
$5100 = x × 6
x = $5100 / 6
= $850
Therefore, Alan paid an amount $850 to the bank each month to repay his debt.
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Pls help
Cole is building a model rocket in science class. He selects the rocket parts from a set of solid cylinders and cones made from metal. Cole wants to build a rocket with the dimensions shown. For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. Will Cole's rocket meet the requirement for launch?
Part A
What will be the total length of the assembled rocket? Explain how you found your answer.
Part B
What is the approximate volume of the rocket.
Use 3.14 for r. Explain.
Part C
If Cole's rocket parts are made of aluminum weighing 0.006 pound per cubic centimeter, will Cole be able to launch his rocket? Explain.
For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.
How to solveThe volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi* r^2 *h[/tex]
Part A
The total length of the assembled rocket will be the length of the cone and the cylinder.
The total length of the assembled rocket = 25 + 3 = 28cm
Part B
The volume of the rocket is the combined volume of the cone and cylinder.
= 4/3 × 3.14 × 16 × 28
= 1875.62 cubic cm
To convert cm into pounds
1875.62 cubic cm = 4.135 pound
Part C
If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.
Then 1875.62 cubic cm × 0.006
= 11.253
For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.
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Use the game board to answer
each question.
7. What fraction of the game board is orange?Write the fraction using three different forms.
The fraction of the game board that is orange is 1/6
What fraction of the game board is orangeFrom the question, we have the following parameters that can be used in our computation:
Sections = 6
Orange = 1
using the above as a guide, we have the following:
Fraction = Orange /Total Number of sections
So, we have
Fraction = 1/6
Other forms of the fraction are
Fraction = 2/12 and 3/18
Hence, the fraction is 2/6
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Grayson can text 70 words in 4 minutes. At this rate, how many minutes would it take him to text 140 words?
5m) Change to metres. a) 1.241 km D) 3.4 km (b) 6.002 km (e) 21.32 km (c) 5.168 km (f) 0.895 km
The distances in meters are:
a) 1241 m
b) 6002 m
c) 5168 m
d) 3400 m
e) 21320 m
f) 895 m
We have,
To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.
a) 1.241 km = 1.241 × 1000 m = 1241 m
b) 6.002 km = 6.002 × 1000 m = 6002 m
c) 5.168 km = 5.168 × 1000 m = 5168 m
d) 3.4 km = 3.4 × 1000 m = 3400 m
e) 21.32 km = 21.32 × 1000 m = 21320 m
f) 0.895 km = 0.895 × 1000 m = 895 m
Therefore,
The distances in meters are:
a) 1241 m
b) 6002 m
c) 5168 m
d) 3400 m
e) 21320 m
f) 895 m
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Let f (x) = log2(x) + 2 and g(x) = log2(x3) – 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)
The simplified expression for h(x) is h(x) = 4 log₂(x) - 4.
Given information:
f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)
h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)
Using the rules of logarithms, we can simplify g(x) as follows:
g(x) = log₂(x³) - 6
= 3 log₂(x) - 6.
Now we can substitute this into the expression for h(x):
h(x) = (log₂(x) + 2) + 3 log₂(x) - 6
= 4 log₂(x) - 4
Therefore, the simplified expression for h(x) is h(x) = 4 log₂(x) - 4.
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Help as soon as possible!
Find the height of each figure.
(Triangle)
The area of the triangle is 6,460 inches squared.
The base is 136 inches and 196 inches. Find the missing height of the figure which is X inches.
The missing height of the triangle is h = 66 inches
Given data ,
Let's denote the missing height of the triangle as "h" inches.
The formula for the area of a triangle is given by:
Area = (1/2) * base * height
Given that the area of the triangle is 6,460 inches squared and the base is either 136 inches or 196 inches, we can set up two equations to solve for "h".
For the base of 136 inches:
Area = (1/2) * 136 * h
6460 = 68h
h = 6460 / 68
h ≈ 95 inches
For the base of 196 inches:
Area = (1/2) * 196 * h
6460 = 98h
h = 6460 / 98
h ≈ 66 inches
Hence , the height of the triangle is h = 66 inches or 95 inches
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Select all the conditions for which it is possible to construct a triangle
A triangle with angle measures 50, 40, and 10°
A triangle with angle measures 80, 40, and 60
A triangle with angle measures 60, 80, and 80
A triangle with angle measures 100°, 30°, and 50
A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The correct equation is 45(x+3)=60x. Option A
How do you form an equation?We are told in the word problem that the contractor got 45 expensive wood and 60 cheap wood for the same total price and that the 45 expensive wood cost $3.00 more than the 60 cheap wood.
If x =price of the 60 cheap wood then we have that 45(x + 3) + 60x = total cost of the wood.
45x + 135 + 60x = total cost of the wood
105x + 135 = total cost of the wood
45(x + 3) + 60x = 105x + 135
Simplifying;
45(x + 3) = 60x
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Can someone please solve this y = 5x² + 2x + 7
The roots of the quadratic equation y = 5 · x² + 2 · x + 7 are contained by x = - 1 / 5 ± i √34 / 5.
How to solve a quadratic equation
In this problem we must solve a quadratic equation, whose roots must be found. This can be done by using algebra properties, by completing the square. First, write the entire quadratic equation:
y = 5 · x² + 2 · x + 7
Second, use algebra properties to find all roots:
y = 5 · [x² + (2 / 5) · x + 7 / 5]
y = 5 · [x² + (2 / 5) · x + 1 / 25] + 5 · (34 / 25)
y = 5 · (x + 1 / 5)² + 34 / 5
Third, use y = 0:
5 · (x + 1 / 5)² + 34 / 5 = 0
5 · (x + 1 / 5)² = - 34 / 5
(x + 1 / 5)² = - 34 / 25
x + 1 / 5 = ± √(- 34) / 5
x = - 1 / 5 ± √(- 34) / 5
x = - 1 / 5 ± i √34 / 5
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Pick the linear model for this equation: y=-2x-3
Answer:
y=2x3 - 3
Step-by-step explanation:
Here's the photo for the solution if needed.
The linear model for the given equation would be the model that has the points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).
How to find the linear model ?To find the linear model that has the given equation, come up with values of x and then use the equation to solve for y. The linear model that has the points that you solve for, would be the right one.
Assuming values of x of -1, 0, 1, 2, 3
The y values would be:
x = - 1 :
y = - 2 x ( - 1 ) - 3
y = - 1
x = 0
y = - 3
x = 1
y = - 5
x = 2
y = - 7
x = 3
y = - 9
The linear model has points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).
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What’s -35.7 as a mixed number
Answer:
-35.7 as a mixed number is -35 and 7/10.
Answer:
Your answer should be [tex]-35 \frac{7}{10}[/tex]
Step-by-step explanation:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.
39 and (2x + 1) as a two step equation
The solution of the equation 39=2x+1 is 19
The given equation is 39=2x+1
We have to find the solution of the equation
2x+1=39
Let us find the value of x
Subtract 1 from both sides
2x=38
Divide both sides by 2
x=19
Hence, the solution of the equation 39=2x+1 is 19
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Can someone graph this? It is for a project about the tides. Thank you!
Just want to check my own answer.
The graph of the table is attached accordingly. It examines the relationship betwen Hours and Height of the tides.
What does the graph show?The graph shows that there is very wide variations between the height of the tides.
The relationship cannot said to be inverse or positive
Note, the following are three advantages of graphs: It makes data more attractive and understandable. It aids in the concise summarization of facts. It allows for more accurate data comparison.
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Which is a function and what is not a function?
Find the measure of ∠GJK. (I need the answer as fast as possible)
Answer:
∠ GJK = 102°
Step-by-step explanation:
(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so
2x + 92 + 3x + 63 = 180
5x + 155 = 180 ( subtract 155 from both sides )
5x = 25 ( divide both sides by 5 )
x = 5
Then
∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°
I need help with this, thx! (Pls show working and steps so I would know how to do other questions!)
Answer:
t = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
calculate the gradient (slope) of AB using the slope formula and equate to the slope of the perpendicular line.
given line with slope 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex]
calculate [tex]m_{AB}[/tex] using slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (2, - 3 ) and (x₂, y₂ ) = B (- 2, t )
[tex]m_{AB}[/tex] = [tex]\frac{t-(-3)}{-2-2}[/tex] = [tex]\frac{t+3}{-4}[/tex]
equating corresponding slopes
[tex]\frac{t+3}{-4}[/tex] = - [tex]\frac{4}{5}[/tex] ( multiply both sides by - 4 to clear the fraction )
t + 3 = - [tex]\frac{4}{5}[/tex] × - 4 = [tex]\frac{16}{5}[/tex] ( subtract 3 from both sides )
t = [tex]\frac{16}{5}[/tex] - 3 = [tex]\frac{16}{5}[/tex] - [tex]\frac{15}{5}[/tex] = [tex]\frac{1}{5}[/tex]
the ferris wheel in Adventure Land has a diaeter of 30 meters the ferris wheel in kiddie land has a diameter of 10 meters how much farther does the person travel in one revolution of the adventure land ferris wheel than in one reveloution of the kiddie land ferris wheel
The person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.
The above problem is asking how much farther a person will travel in one revolution of the Adventure Land ferris wheel compared to one revolution of the Kiddie Land ferris wheel.
The Adventure Land ferris wheel has a diameter of 30 meters, and the Kiddie Land ferris wheel has a diameter of 10 meters.
This means that the circumference of the Adventure Land ferris wheel (the distance traveled in one revolution) is
3.14×30= 94.2 meters
The circumference of the Kiddie Land ferris wheel is
3.14 ×10= 31.4 meters
Here, 94.2-31.4 =62.8 meters
Therefore, the person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.
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Michel-Eugène Chevreul found that the greatest intensity came from placing ______ colors next to each other.
tertirary
analogous
complementary
arbitrary
Answer:
your answer
Step-by-step explanation:
analogous colors
Johnson cut a round pizza into 12 equal pieces. He ate 4 adjacent pieces. What is the measure of the angle of the pizza that Johnson ate?
A) 48 deegrees
B) 90 deegrees
C)120 deegrees
D) 160 deegrees
Please help fast!
Johnson's pizza had a 120-degree angle when he ate it. The solution is choice C.
When a pizza is cut into 12 equal pieces, each piece has a central angle of:
360 degrees / 12 pieces = 30 degrees/piece
If Johnson ate 4 adjacent pieces, then he ate a total central angle of:
4 pieces * 30 degrees/piece = 120 degrees
Therefore, the measure of the angle of the pizza that Johnson ate is 120 degrees. The answer is option C).
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6ft=____yd
Remember to convert to a larger unit divide
Answer:
2 yards
Step-by-step explanation:
2 yards equals 6 feet because 2x3=6 or 72 inches because 6x12 equals 72. 1 yard is equal to 3 feet.
Find two numbers with a sum of 3 and product of -40.
Answer:
8 and -5
Step-by-step explanation:
8 - 5 = 3
(-5) (8)=-40
Answer:
-8,+5
Step-by-step explanation:
-8+5 = 3
-8×+5 = -40
It takes 4 minutes to complete an administrative task. There are 60 seconds in 1 minute. How many seconds does it take to complete the same task?
There are 60 seconds in 1 minute, so 4 minutes would be:
4 minutes * 60 seconds/minute = 240 seconds
Therefore, it takes 240 seconds to complete the administrative task.
if it takes three people 4 hours to clean a warehouse how long will it take 4 people to clean the warehouse
The solution is ,if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.
Here, we have,
given that.
if it takes three people 4 hours to clean a warehouse
now, we have to find that how long will it take 4 people to clean the warehouse.
i.e. we have,
3 people take to clean = 4 hours
let, 4 people will take to do it x hours.
now, we have,
3 people take to clean = 4 hours
so, 1 people take to clean = 4*3 hours
so, 4 people take to clean = 4*3 / 4 hours
i.e. we get,
x = 4*3 / 4 hours
or, x = 12/4 hours
= 3 hours
Hence, if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.
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I don’t get this can someone help me please?
Answer:
x=144
Step-by-step explanation:
since they are similar their sides have a common ratio
24/x=42/7
7x=42*24
7x=1008
x=144