Assuming the population of times is normally distributed, and using the 0. 01 level of significance, we can conclude that the new booklet is effective.
To determine if the new instructional booklet is effective in reducing the assembly time for novices, we will perform a one-sample t-test using the given information.
1. State the null hypothesis (H0) and the alternative hypothesis (H1):
H0: There is no difference in the mean assembly time with the new booklet (µ = 3.15 hours).
H1: The mean assembly time with the new booklet is less than 3.15 hours (µ < 3.15 hours).
2. Identify the level of significance, sample size, sample mean, and sample standard deviation:
α = 0.01
n = 25
x = 2.98 hours
s = 0.23 hours
3. Calculate the test statistic:
t = (x - µ) / (s / √n) = (2.98 - 3.15) / (0.23 / √25) = -0.17 / 0.046 = -3.70
4. Find the p-value for the test:
Using a t-distribution table or calculator, the p-value for a one-tailed test with t = -3.70 and degrees of freedom (df) = 24 is approximately 0.0005.
5. Compare the p-value with the level of significance:
Since the p-value (0.0005) is less than α (0.01), we reject the null hypothesis.
Based on the p-value, we have enough evidence to conclude that the new instructional booklet is effective in reducing the assembly time for novices at the 0.01 level of significance.
Learn more about Level of significance:
https://brainly.com/question/30542688
#SPJ11
find the line parallel to y=4x+1 that includes the point (-2, -5)
y=4x+3
Parallel lines have the same gradient - 4x
substitute the x and y values from the coordinates into y=mx+c
so
-5=(4×-2)+c
-5=-8+c
c=3
therefore, the answer is y=4x+3
The table shows the amount of rainfall, in cm, that fell each day for 30 days.
Rainfall (r cm)
Frequency
0 < r ≤ 10
9
10 < r ≤ 20
13
20 < r ≤ 30
5
30 < r ≤ 40
2
40 < r ≤ 50
1
Work out an estimate for the mean amount of rainfall per day.
Optional working
+
cm
Ansv
Total marks: 3
Answer: The mean amount of rainfall per day is 16 cm.
Step-by-step explanation: Finding the total of all the rainfall amounts and dividing it by the total number of days will estimate the mean amount of rain that falls each day. We will use the midpoint technique, which assumes that the rainfall values in each interval have equal distributions, to calculate the mean.
Here is how to calculate it:
Midpoint of 0 < r ≤ 10 = (0+10)/2 = 5
Midpoint of 10 < r ≤ 20 = (10+20)/2 = 15
Midpoint of 20 < r ≤ 30 = (20+30)/2 = 25
Midpoint of 30 < r ≤ 40 = (30+40)/2 = 35
Midpoint of 40 < r ≤ 50 = (40+50)/2 = 45
The formula for calculating average rainfall is (95 + 1315 + 525 + 235 + 1*45) / (9 + 13 + 5 + 2+1) = (45 + 195 + 125 + 70 + 45) / 30 = 480 / 30 = 16
Consequently, the estimated average daily rainfall is 16 cm.
To know what is mean:
https://brainly.in/textbook-solutions/q-define-arithmetic-mean?source=quick-results
WILL MARK BRAINLIEST QUESTION IN PHOTO
Step-by-step explanation:
See image....check my math ! ( I didn't)
Find the arc length of CD
Answer: 15 feet
Step-by-step explanation:
There are 5 children running in a relay race. in a relay race, each person runs part of the race. the next runner starts where the previous runner stops. each runner runs the same distance. in this relay race, each child runs of a mile, then stops so the next , a runner can continue. plot the point on the number line that represents the location where the fourth child will stop running.
The location where the fourth child will stop running in the relay race is 4/5 of the way.
To determine the location where the fourth child will stop running in the relay race, we need to find out the total distance covered by the first four children.
Since each child runs 1/5 of a mile, we can find the total distance for the first four children by multiplying their individual distances.
Total distance = (Number of children) * (Distance run by each child)
Total distance = 4 * (1/5)
Now, let's multiply:
Total distance = 4/5
So, the fourth child will stop running at a location 4/5 of a mile from the starting point. To plot this point on a number line, locate the point between 0 and 1 that is 4/5 of the way. This point represents the location where the fourth child will stop running in the relay race.
To learn more about relay race problems go to :
https://brainly.com/question/1658477?referrer=searchResults
#SPJ11
Suppose z = x+ sin(y) , x = 2t = - 482, y = 6st. - 1 A. Use the chain rule to find дz as and Oz as functions of дz Ət X, Y, s and t. - az მs/Əz as/Əz B. Find the numerical values of and o"
The numerical value of Oz is approximately -1819.86.
Using the chain rule, we have:
[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt\\dz/ds = dz/dy * dy/ds[/tex]
We can calculate each term using the given equations:
dz/dx = 1
dx/dt = 2
dy/dt = 0
dz/dy = cos(y)
dy/ds = 6t
Substituting these values, we get:
[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt = 1 * 2 + cos(y) * 0 = 2\\dz/ds = dz/dy * dy/ds = cos(y) * 6t = 6t * cos(6st)[/tex]
To find дz as/Əz, we need to solve for as in terms of z and s:
z = x + sin(y) = 2t + sin(6st)
x = 2t
y = 6st - 1
Solving for s in terms of t, we get:
s = (y + 1)/(6t)
Substituting this into the equation for z, we get:
z = 2t + [tex]sin(6t(y+1)/(6t)) = 2t + sin(y+1)[/tex]
Taking the partial derivative of z with respect to as, we get:
[tex]дz/Əz = 1[/tex]
B. To find the numerical values of дz and Oz, we need to plug in the given values of x, y, s, and t into our equations. Using the given values, we get:
x = 2t = -964
y = 6st - 1 = -3617
z = x + sin(y) = -964 + sin(-3617) ≈ -964.73
Using the values of s and t, we can find:
s = (y + 1)/(6t) ≈ -0.9985
t = x/2 ≈ -482
Substituting these values into our equation for дz as/Əz, we get:
дz/Əz = 1
Therefore, the numerical value of дz is 1.
Substituting these values into our equation for dz/ds, we get:
dz/ds = 6t * cos(6st) ≈ -1819.86
Therefore, the numerical value of Oz is approximately -1819.86.
To know more about chain rule here
https://brainly.com/question/30895266
#SPJ4
please help.
1. Complete the Pythagorean triple. (24,143, ___)
2. Given the Pythagorean triple (5,12,13) find x and y
3. Given x=10 and y=6 find associated Pythagorean triple
4. Is the following a possible Pythagorean triple? (17,23,35)
The value that will complete Pythagorean triple would be = 24,143, 145 )
How to calculate the missing value of a triangle using the Pythagorean formula?To calculate the missing value of a triangle that completes a Pythagorean triple that formula that should be used is given as follows.
That is;
C ² = a² + b²
C = Missing value of the Pythagorean triple
a = 24
b.= 143
C² = 24²+143²
= 576+20,449
C =√21,025
= 125
Learn more about Pythagorean theorem here:
https://brainly.com/question/28981380
#SPJ1
Segment cd is the mid segment of trapezoid wxyz what is the value of xy?
Since segment CD is the mid-segment of trapezoid WXYZ, it means that segment CD is parallel to both bases WX and YZ and it is also half the length of their sum. Therefore, we can use the mid-segment formula which states that the length of segment CD is equal to the average of the lengths of the bases WX and YZ.
So, we can write:
CD = (WX + YZ)/2
Since we want to find the value of XY, we need to know its length in terms of WX and YZ.
If we draw a diagonal of the trapezoid, say diagonal WZ, it will divide the trapezoid into two triangles, namely triangle WXY and triangle ZYX.
We know that the mid-segment CD is also the median of triangle WZY, so it divides it into two equal areas.
Therefore, the area of triangle WXY is equal to the area of triangle ZYX.
We can write:
1/2 * WX * CD = 1/2 * YZ * CD
Simplifying this equation by dividing both sides by CD, we get:
1/2 * WX = 1/2 * YZ
Multiplying both sides by 2, we get:
WX = YZ
Therefore, the trapezoid WXYZ is actually an isosceles trapezoid with equal bases WX and YZ.
So, we can substitute WX for YZ in the formula for CD:
CD = (WX + WX)/2
Simplifying this equation, we get:
CD = WX
Therefore, the length of segment XY is equal to the length of the shorter base of the trapezoid, which is WX.
So, the value of XY is equal to the value of WX, and we can conclude that XY = WX.
Learn more about trapezoid at https://brainly.com/question/31371933
#SPJ11
A searchlight is shaped like a paraboloid of revolution. if the light source is located 1 feet from the base along the axis of symmetry and the opening is 6 feet across, how deep should the searchlight be?
The searchlight should be 1/3 feet deep at the edge of the opening. Since the paraboloid is a continuous surface, the depth will increase gradually from the edge of the opening to the vertex at (0,0,1).
Determine the depth of the searchlight shaped like a paraboloid of revolution, we need to use the equation for the standard form of a paraboloid of revolution:
z = (x^2 + y^2) / (4f)
where z is the depth, x and y are the horizontal and vertical coordinates, and f is the focal length of the paraboloid.
We know that the light source is located 1 feet from the base along the axis of symmetry, which means that the vertex of the paraboloid is at (0,0,1).
We also know that the opening is 6 feet across, which means that the horizontal distance from one side of the opening to the other is 3 feet.
Using this information, we can find the value of f:
f = (d/2)^2 / 2r
where d is the diameter of the opening (6 feet), and r is the radius of curvature at the vertex (1 foot).
f = (6/2)^2 / 2(1) = 4.5 feet
Now we can plug in the values for x, y, and f to solve for z:
z = (x^2 + y^2) / (4f)
z = (x^2 + y^2) / (4(4.5))
z = (x^2 + y^2) / 18
Since the opening is 6 feet across, we know that the maximum value of x is 3 feet. Therefore, we can use the maximum value of y (also 3 feet) to find the depth at the edge of the opening:
z = (3^2 + 3^2) / 18
z = 6/18
z = 1/3 feet
So the searchlight should be 1/3 feet deep at the edge of the opening. However, since the paraboloid is a continuous surface, the depth will increase gradually from the edge of ×the opening to the vertex at (0,0,1).
Read more about paraboloid.
https://brainly.com/question/18850313
#SPJ11
purab bought twice the number of rose plants that he had in his lawn. however, he threw 3 plants as they turned bad. after he planted new plants, there were total 48 plants in the garden. how many plants he had in his lawn earlier?
Purab initially had 17 rose plants in his lawn before buying the new ones.
Purab initially had a certain number of rose plants in his lawn. He bought twice that number, but had to discard 3 plants as they turned bad
After planting the new ones, there were a total of 48 plants in the garden.
To determine how many plants he had earlier, let's use a variable x to represent the initial number of plants.
Purab bought 2x plants, and after removing the 3 bad plants, he had (2x - 3) good plants.
Adding these to the initial number of plants, the equation becomes:
x + (2x - 3) = 48
Combining like terms, we get:
3x - 3 = 48
Next, we add 3 to both sides:
3x = 51
Finally, we divide by 3: x = 17
Learn more about equation at
https://brainly.com/question/2081704
#SPJ11
Show that p(0,7), q(6,5), r(5,2) and s(-1,4) are the vertices of rectangular
Answer:
Step-by-step explanation:
P(0,7), Q(6,5), R(5,2), and S(-1,4) form the vertices of a rectangle. To prove this, we need to show that the opposite sides of the quadrilateral are parallel and that the diagonals are equal in length and bisect each other.
To explain this solution in more detail, we can start by finding the slopes of the line segments connecting each pair of points. The slope of a line segment can be calculated using the formula:
slope = (change in y) / (change in x)
For example, the slope of the line segment connecting P and Q is:
slope PQ = (5 - 7) / (6 - 0) = -2/6 = -1/3
We can calculate the slopes of the other line segments in a similar way. If the opposite sides of the quadrilateral are parallel, then their slopes must be equal. We can check that this is true for all pairs of opposite sides:
slope PQ = -1/3, slope SR = -1/3
slope QR = (2 - 5) / (5 - 6) = -3/-1 = 3, slope PS = (4 - 7) / (-1 - 0) = -3/-1 = 3
Next, we can calculate the lengths of the diagonals using the distance formula:
distance PR = sqrt[(5 - 0)^2 + (2 - 7)^2] = sqrt(5^2 + (-5)^2) = sqrt(50)
distance QS = sqrt[(6 - (-1))^2 + (5 - 4)^2] = sqrt(7^2 + 1^2) = sqrt(50)
If the diagonals are equal in length, then we should have distance PR = distance QS, which is indeed the case.
Finally, we need to show that the diagonals bisect each other. This means that the midpoint of PR should be the same as the midpoint of QS. We can calculate the midpoint of each diagonal using the midpoint formula:
midpoint of PR = [(0 + 5)/2, (7 + 2)/2] = (2.5, 4.5)
midpoint of QS = [(6 + (-1))/2, (5 + 4)/2] = (2.5, 4.5)
Since the midpoints are the same, we have shown that the diagonals bisect each other.
Therefore, we have shown that the points P(0,7), Q(6,5), R(5,2), and S(-1,4) form the vertices of a rectangle.
To know more about vertices of a rectangle refer here:
https://brainly.com/question/16071215#
#SPJ11
7. The table shows the linear relationship between the total amount Mrs. Jacobs will be
charged for a skating party and the number of children attending.
Which equation best represents y, the total amount in dollars Mrs. Jacobs will be
charged for
x number of children attending the skating party?
The equation that best represents the linear relationship between the total amount Mrs. Jacobs will be charged and the number of children attending the skating party is y = mx + b.
In this case, y represents the total amount in dollars that Mrs. Jacobs will be charged, x represents the number of children attending the party, m represents the slope of the line, and b represents the y-intercept.
To find the equation, we need to determine the slope and y-intercept from the table given. From the table, we can see that for every additional child attending the party, the total amount charged increases by $10. This means that the slope (m) of the line is 10.
To find the y-intercept (b), we can look at the table and see that when there are zero children attending the party, the total amount charged is $50. This means that the y-intercept is 50.
Putting it all together, the equation that best represents the linear relationship is y = 10x + 50.
To know more about linear relationship refer here:
https://brainly.com/question/29066440#
#SPJ11
What is the value of the expression below? (3 1/2 - 9 3/4) entre (-2.5)
PLEASE HELP
Answer:
Let's solve this in steps:
1. Convert mixed numbers to fractions:
```
3 1/2 = 7/2
9 3/4 = 39/4
```
2. Perform the subtraction:
```
7/2 - 39/4 = -11/4
```
3. Divide by -2.5:
```
-11/4 / -2.5 = 4.4
```
Therefore, the value of the expression is **4.4**.
You decide to work fewer hours per week, which results in an 8% decrease in your pay. what percentage increase in pay would you have to receive in order to gain your original salary again?
You would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.
To find the percentage increase in pay needed to regain your original salary after an 8% decrease, follow these steps:
1. Assume your original salary is 100%. After an 8% decrease, your salary becomes 100% - 8% = 92%.
2. Calculate the difference between your original salary (100%) and your current salary (92%). The difference is 100% - 92% = 8%.
3. To find the percentage increase needed to regain your original salary, divide the difference (8%) by your current salary (92%): 8% / 92% = 0.08696.
4. Multiply the result by 100 to convert it to a percentage: 0.08696 (100) = 8.696%.
So, you would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.
To know more about "Percentage" refer here:
https://brainly.com/question/10893287#
#SPJ11
Each side y of a square is increased by 5 units. Which expression represents the number of square units in the area of the new square?
O 2y + 10
O y^2 + 10y + 25
O y^2 + 25
O y^2 + 10y + 10
The expression for the area of the new square is y² + 10y + 25.
How to find area?To find the expression that represents the area of the new square, we need to consider that when each side of a square is increased by 5 units, the new side length becomes y + 5. The area of the new square is then given by:
(New side length)² = (y + 5)²
Expanding the square, we get:
(y + 5)² = y² + 10y + 25
Therefore, the expression that represents the area of the new square is y² + 10y + 25.
So, the correct option is:
O y² + 10y + 25
Learn more about area
brainly.com/question/27683633
#SPJ11
A gym offers a trial membership for 2 months. It discounts the regular monthly fee, f, by $15. Logan would like to sign up if the total price of the trial membership is less than $60. Which inequality could help Logan determine if he would like to sign up?
If he would like to sign up, then the inequlity could help Logan is defined as 2x ≤ 30, where, x --> monthly fee.
Inequality is defined as the 'not equal'. An inequality is a statement that shows a non-equal comparison between two numbers or mathematical expressions and expresses relationship between them. The symbols used for showing inequality are <, > , ≤, ≥. We have a gym offers a 2 months trials membership. The discounts the regular monthly fee, f
= $ 15
Now, Logan interested to sign up. Total price trial membership is less than $60. Let the total price of trial membership and regular monthly fee be P dollars and x dollars respectively. So, P ≤ $60 and P
= 2x - 2×15 = 2x - 30
If he would like to sign up, then the inequlity could help Logan is defined as below, 2x - 30 ≤ 60. Hence, required inequlity is 2x ≤ 30.
For more information about inequality, visit:
https://brainly.com/question/28230245
#SPJ4
What is the volume of a right rectangular prism with a length of 4. 8 meters, a width of 2. 3 meters, and a height
of 0. 9 meters?
O4. 968 m3
O9. 936 m3
O 11. 94 m3
O 34. 86 m3
PLS ANSWER FAST I WILL GIVE BRAINIEST!!!!!
Answer:
Step-by-step explanation:
The volume of the given prism is 9.936 cubic meters, To calculate the volume of a right rectangular prism, we need to multiply its length, width, and height together.
Given that the length of the prism is 4.8 meters, the width is 2.3 meters, and the height is 0.9 meters, we can calculate the volume using the formula:
Volume = length x width x height
Volume = 4.8 m x 2.3 m x 0.9 m
Volume = 9.936 m^3
Therefore, the volume of the right rectangular prism is 9.936 cubic meters.
It is important to note that when we calculate volume, we are dealing with a three-dimensional space, and the units we use must be cubed (m^3 in this case). This is because we are measuring the amount of space occupied by the object in all three dimensions.
In summary, to find the volume of a right rectangular prism, we simply multiply its length, width, and height together. In this case, the volume of the given prism is 9.936 cubic meters.
To know more about volume of a right rectangular prism refer here:
https://brainly.com/question/3248292#
#SPJ11
I need helpp
5x+3=2x-15
Answer:
x = -6
Step-by-step explanation:
5x + 3 = 2x - 15
3x + 3 = -15
3x = -18
x = -6
Let's Check
5(-6) + 3 = 2(-6) - 15
-30 + 3 = -12 - 15
-27 = -27
So, x = -6 is the correct answer.
Answer:
x = -6
Step-by-step explanation:
Equation is 5x + 3 = 2x - 15
First, we can subtract the constants
5x = 2x - 18
Then, we can subtract 2x on both sides
3x = -18
Divide both sides by 3 to isolate x
x = -6
A leaf blower was marked up 150% from an original cost of $80. Last Friday, Lee bought the leaf blower and paid an additional 7. 75% in sales tax. What was his total cost?
$
Lee's total cost for the leaf blower was $215.50.
First, let's find the selling price of the leaf blower before sales tax was added:
The leaf blower was marked up by 150%, so the selling price is:
= [tex]80 + (\frac{150}{100}) 80[/tex]
= 80 + 120
= 200
So the selling price of the leaf blower before sales tax was $200.
Next, we need to find the amount of sales tax that Lee paid. To do this, we need to multiply the selling price by the sales tax rate:
Sales tax = 7.75% ($200)
= 0.0775 ($200)
= $15.50
Finally, we can find Lee's total cost by adding the selling price and the sales tax:
Total cost = Selling price + Sales tax
= $200 + $15.50
= $215.50
Therefore, Lee's total cost for the leaf blower was $215.50.
To know more about "Selling price" refer here:
https://brainly.com/question/3798799#
#SPJ11
1) What do you think this graph is suggesting regarding skill levels for future employment, give two suggestions..
2) What occupational group will people with a skill level 5 be able to join?
Answer:
1) I think the graph is suggesting that a higher level of skill, or degree, will ultimately help you get a better job easier and faster.
2) With a skill level of five, you can become a sales worker or labourer. It is a low percentage of people with a skill level five to become community and personal service workers.
Thanks for reading! Always work toward your dreams! :)
What is the exact solution to the system of equations?
Answer:
Step-by-step explanation:
the point at which the lines representing the linear equations intersect
Need help please show work
Answer:
Add the lengths:
5x - 16 + 2x - 4 = 7x - 20
An aquarium manager drena
blueprint for a cylindrical fish tanka
the tank has a vertical tube in the
middle in which visitors can stand
and view the fish
the best average density for the species of fish that will go in the
tankis 16 fish per 100 gallons of water. this provides enough
room for the fish to swim while making sure that there are
plenty of fish for people to see
the aquarium has 275 fish available to put in the tank, s bis he
right number of fish for the tank. if not, how many fich should
be added or removed? explain your reasoning
To determine if the 275 fish are the right number for the cylindrical fish tank, we need to calculate the tank's capacity and compare it to the recommended average density of 16 fish per 100 gallons of water.
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder.
Assuming the tank has a height of h and a radius of r, we can calculate its volume as follows:
[tex]V = πr^2h[/tex]
Since the tank has a vertical tube in the middle, we need to subtract the volume of the tube from the total volume of the tank. Let's assume the tube has a radius of 2 feet and a height of 8 feet. Then the volume of the tube is:
Vtube = π(2)^2(8) = 100.53 cubic feet
Thus, the volume of the tank without the tube is:
Vtank = πr^2h - Vtube
To find the value of r, we need to know the diameter of the tank. Let's assume the tank has a diameter of 10 feet, which means the radius is 5 feet.
Then the volume of the tank without the tube is:
Vtank = π(5)^2h - 100.53
We need to convert the volume of the tank from cubic feet to gallons, so we multiply by 7.48 (1 cubic foot = 7.48 gallons):
Vtank(gallons) = 7.48[π(5)^2h - 100.53]
Now we can calculate the recommended number of fish for the tank:
Recommended number of fish = 16 fish/100 gallons x Vtank(gallons)
Recommended number of fish = 16 fish/100 gallons x 7.48[π(5)^2h - 100.53]
Recommended number of fish = 1.175[π(5)^2h - 100.53]
So, if the number of fish available is 275, we can set up the following equation:
275 = 1.175[π(5)^2h - 100.53]
Solving for h, we get:
h = (275/1.175π(5)^2) + (100.53/π(5)^2)
h ≈ 8.3 feet
Therefore, the cylindrical fish tank with a height of 8.3 feet and a radius of 5 feet can hold 275 fish with an average density of 16 fish per 100 gallons of water. If the aquarium manager wants to add more fish, they should recalculate the volume of the tank and adjust the height accordingly to maintain the recommended density of 16 fish per 100 gallons of water. Conversely, if they want to remove fish, they can do so without changing the height of the tank.
To know more about volume refer here
https://brainly.com/question/25282116#
#SPJ11
Danielle's basic cell phone rate each month is $29.95. add to that $5.95 for voice mail and $2.95 for text messaging. this past month danielle spent an additional c dollars on long distance. her total bill was $62.35how much did danielle spend on long distance?
Danielle spent $23.50 on long distance charges this past month.
To determine how much Danielle spent on long distance, we need to consider her basic cell phone rate, voice mail, and text messaging charges. Here is a step-by-step explanation:
1. Danielle's basic cell phone rate each month is $29.95.
2. She pays an additional $5.95 for voice mail.
3. She also pays $2.95 for text messaging.
4. Her total bill for the month was $62.35.
Now, let's calculate her total expenses without the long distance charges (c dollars):
$29.95 (basic cell phone rate) + $5.95 (voice mail) + $2.95 (text messaging) = $38.85
Since Danielle's total bill was $62.35, we can find out how much she spent on long distance by subtracting her total expenses without long distance charges from her total bill:
$62.35 (total bill) - $38.85 (total expenses without long distance) = $23.50
So, Danielle spent $23.50 on long distance charges this past month.
To know more about charges, visit:
https://brainly.com/question/22313086#
#SPJ11
3. Peter throws a dice and spins a coin 150 times as part of an experiment. He records 71 heads, and a six 21 total times. On 68 occasions, he gets neither a head nor a six. Complete the table. Roll a b Not a six Total Head Tail Totals
After evaluating the given question the number of rolls that were both heads and sixes is 142, under the condition that Peter throws a dice and spins a coin 150 times.
Here we have to depend on the principle of probability,
Its given that he recorded 71 heads, and a six 21 total times.
Then,
| Roll | A (dice) | B (coin) | Not a six | Total |
|------|----------|----------|-----------|-------|
| Head | | | | |
| Tail | | | | |
| Total| | | | |
To find the number of rolls that were tails, we can subtract the number of heads from the total number of rolls:
150 - 71 = 79
So we can put in the Tail row with 79.
Now to find the number of roll s that were both heads and sixes, we can add up the number of heads and sixes and then subtract the number of rolls that were both heads and sixes
21 + 71 - x = y
Here
x = number of rolls that were both heads and sixes
y = total number of rolls that were either heads or sixes .
We know that there were 71 heads and 21 sixes, so
y = 71 + 21 = 92.
There were 68 rolls that were neither heads nor sixes,
so
x + y = 150 - 68 = 82.
Solving for x, we get:
x = y - 21 + 71
x = 92 - 21 + 71
x = 142
Lets fill the table
| Roll | A (dice) | B (coin) | Not a six | Total |
|------|-------|-------|-----------|-------|
| Head | - | 71 | - | 71 |
| Tail | - | 79 | - | 79 |
| Total| - | 150 | 68 | - |
To learn more about probability
https://brainly.com/question/13604758
#SPJ4
The quantity of a product manufactured by a company is given by Q = aK^{0.6}L^{0.4}
where a is a positive constant, Kis the quantity of capital and Listhe quantity of labor used. Capital costs are $44 per unit, labor costs are $11 per unit, and the company wants costs for capital and labor combined to be no higher than $330. Suppose you are asked to consult for the company, and learn that 6 units each of capital and labor are being used, (a) What do you advise? Should the company use more or less labor? More or less capital? If so, by how much?
The company should increase the quantity of capital used from 6 units to 3 units, an increase of 3 units.
The cost of capital and labor can be expressed as:
C = 44K + 11L
The company wants to limit the cost of capital and labor to $330:
44K + 11L ≤ 330
Substituting Q = aK^{0.6}L^{0.4} into the inequality, we get:
44K + 11L ≤ 330
44K + 11(Q/aK^{0.6})^{0.4} ≤ 330
44K^{1.6} + 11(Q/a)^{0.4}K ≤ 330
Solving for K, we get:
K ≤ (330 - 11(Q/a)^{0.4}) / 44K^{1.6}
Substituting K = 6, Q = aK^{0.6}L^{0.4}, and solving for L, we get:
Q = aK^{0.6}L^{0.4}
Q/K^{0.6} = aL^{0.4}
L = (Q/K^{0.6})^{2.5}/a
Substituting Q = a(6)^{0.6}(6)^{0.4} = 6a into the equation, we get:
L = (6/a)^{0.4}(6)^{2.5} = 9.585a^{0.6}
Therefore, the company is currently using 6 units each of capital and labor, and the total cost of capital and labor is:
C = 44(6) + 11(6) = 330
This means that the company is already using the maximum allowable cost. To reduce the cost, the company should use less labor or less capital.
To determine whether to use more or less labor, we can take the derivative of Q with respect to L:
∂Q/∂L = 0.4aK^{0.6}L^{-0.6}
This is a decreasing function of L, so as L increases, the quantity of product Q produced will decrease. Therefore, the company should use less labor.
To determine how much less labor to use, we can find the value of L that would reduce the cost to the maximum allowable level of $330:
44K + 11L = 330
44(6) + 11L = 330
L = 18
Therefore, the company should reduce the quantity of labor used from 6 units to 18 units, a decrease of 12 units.
To determine whether to use more or less capital, we can take the derivative of Q with respect to K:
∂Q/∂K = 0.6aK^{-0.4}L^{0.4}
This is an increasing function of K, so as K increases, the quantity of product Q produced will increase. Therefore, the company should use more capital.
To determine how much more capital to use, we can find the value of K that would reduce the cost to the maximum allowable level of $330:
44K + 11L = 330
44K + 11(18) = 330
K = 3
Therefore, the company should increase the quantity of capital used from 6 units to 3 units, an increase of 3 units.
To learn more about quantity of capital visit: https://brainly.com/question/24183446
#SPJ11
What is a sine wave in Trigonometry
Answer:
Read Below
Step-by-step explanation:
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the sine trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in mathematics, as well as in physics, engineering, signal processing and many other fields
Answer:
It is a type of wave. There are also cosine waves and tangent waves.
Step-by-step explanation:
help me with this please!!! i need the answer rn
: (
Answer:
Its B because you find the number in the middle, if theres two numbers in the middle, you add them up and divide by 2
the answer is B
the answer is B because 21 and 23 both seem to be in the middle. when two numbers are in the middle, you add them, then divide by two as a result, you would get 22.
Volume of a sphere with a radius of 41
Answer:
Volume = 288695.6 in³
Step-by-step explanation:
Volume of a sphere is given by
v=4/3πr^3
Where r is the radius of the sphere
From the question
radius = 41 in
Substitute the value into the above formula
We have
v=4/3 x 41^3π
=275684/3 π
= 288695.6097
We have the final answer as
Volume = 288695.6 in³ to the nearest tenth
Volume = 288695.6 in³ to the nearest tenth
Hope this helps you
PLS MARK BRAINLIEST
A speaker is in the shape of a cube with an edge length of 3. 5 inches. The speaker is sold in a package in the shape of a square prism with a base area of 16 square inches and a height of 4. 25 inches. How much empty space, in cubic inches, remains in the package after the speaker is placed in the package?
The volume of the cube-shaped speaker is 42.875 cubic inches. The volume of the package is 68 cubic inches. Subtracting the volume of the speaker from the volume of the package gives the empty space remaining, which is 25.125 cubic inches.
The volume of the cube-shaped speaker is given by V₁ = (edge length)³ = 3.5³ = 42.875 cubic inches.
The volume of the square prism-shaped package is given by V₂ = (base area) x (height) = 16 x 4.25 = 68 cubic inches.
Therefore, the empty space remaining in the package after the speaker is placed in it is V₂ - V₁ = 68 - 42.875 = 25.125 cubic inches.
So, the empty space remaining in the package is 25.125 cubic inches.
To know more about volume:
https://brainly.com/question/11168779
#SPJ4
