Answers
The child can make 120 different bracelets using one of each charm. To solve this problem, we need to use a combinatorial approach.
The number of different bracelets that the child can make depends on the number of charms that can be used for each bracelet & the order in which they are arranged. Since each charm can be used only once, we have to choose five charms out of the total of five available charms, which can be done in 5C5 ways.
We can think of this problem as a permutation problem. There are five distinct charms, and we need to choose five of them to make a bracelet. The order in which we choose the charms matters, as each order gives us a different bracelet. Therefore, we need to use the formula for permutations.
The formula for permutations is given by:
nPr = n! / (n-r)!
where n is the total number of objects, and r is the number of objects we want to choose.
For this problem, n = 5 (since there are five distinct charms), and r = 5 (since we want to choose all five charms).
Plugging these values into the formula, we get:
5P5 = 5! / (5-5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 / 1 = 120
Therefore, the child can make 120 different bracelets.
Alternatively, we can also think of this problem as a multiplication principle problem. There are five distinct charms, & we need to choose one charm out of five for the first position, one charm out of four for the second position, one charm out of three for the third position, one charm out of two for the fourth position, & one charm out of one for the fifth position.
Using the multiplication principle, we can multiply these numbers together to get the total number of different bracelets:
5 x 4 x 3 x 2 x 1 = 120
Therefore, the child can make 120 different bracelets using one of each charm.
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Related Questions
The National Vital Statistics Reports for November 2011 states that U. S. Cesarean delivery rate for 2010 was about 32. 8%. Cesarean delivery is also called a "C-section. " It means the baby is not delivered in the normal way. The baby is surgically removed through an incision in the mother’s abdomen and uterus. Suppose this year a random sample of 100 births has 41 that are C-sections. Use the estimate from the NVS Report for 2011 as the population proportion, p, and the result from this year’s random sample to estimate the U. S. Cesarean delivery rate for this year with 95% confidence. (Be sure to check that a normal model is appropriate. )
Answers
The 95% confidence interval for the U.S. Cesarean delivery rate for this year is approximately (0.3314, 0.4886) or 33.14% to 48.86%.
How to find the delivery rate for a particular year using a sample and a population proportion estimate from a previous report?To estimate the U.S. Cesarean delivery rate for this year with 95% confidence using the provided information, we can construct a confidence interval for the population proportion.
Given:
Population proportion estimates from the NVS Report for 2011: p = 0.328 (32.8%)
Sample size: n = 100
Number of C-sections in the sample: x = 41
First, we need to check if a normal model is appropriate for the sample proportion. For this, we can verify if the sample size is sufficiently large and if both np and n(1-p) are greater than 10.
np = 100 * 0.328 = 32.8
n(1-p) = 100 * (1 - 0.328) ≈ 67.2
Since both np and n(1-p) are greater than 10, we can assume that the conditions for a normal model are met.
Now, we can calculate the confidence interval using the sample proportion and the critical value corresponding to a 95% confidence level.
Sample proportion (p-hat) = [tex]\frac{x }{ n}[/tex] =[tex]\frac{ 41 }{ 100 }[/tex]= 0.41
The critical value for a 95% confidence level can be obtained from a standard normal distribution or a Z-table. In this case, the critical value is approximately 1.96.
The margin of error (E) can be calculated as:
E = Z * [tex]\sqrt((\frac{p-hat * (1 - p-hat))} { n})[/tex]
E = 1.96 * [tex]\sqrt((\frac{0.41 * (1 - 0.41))}{ 100)}[/tex]
E ≈ 0.0786
Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion.
Confidence interval = p-hat ± E
Confidence interval = 0.41 ± 0.0786
Therefore, the 95% confidence interval for the U.S. Cesarean delivery rate for this year is approximately (0.3314, 0.4886) or 33.14% to 48.86%.
Note: It's important to consider that this calculation assumes the sample is representative of the U.S. population and that the conditions for a normal model are satisfied. Additionally, the estimate from the NVS Report for 2011 is used as the population proportion.
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"first one could you use the product rule or the quotient rule
whichever applies and simplify within reason please, for last two
take the deratives usinh tbe chain rule, product rule or quotient
rule o
2 (+ }+) 2x+ + 3 (5x + 2) k(x) = ) 6x = 7 (8) The profit (in hundreds of dollars) from selling * units of a product is given by -2 the profit function P(x) =- Find the marginal profit when 4 units a" are produced
and sold and interpret your answer using words, numbers and units. Be very specific.
(Round the number part of your answer to the nearest cent.)
Answers
For the first equation, we can use the product rule. Let f(x) = 2x+ and g(x) = 5x+2. Then, f'(x) = 2 and g'(x) = 5. Using the product rule formula, we get:
k'(x) = f(x)g'(x) + g(x)f'(x)
k'(x) = (2x+)(5) + (5x+2)(2)
k'(x) = 10x+ + 4x+10
For the profit function, P(x) = -2x^2 + 6x + 7, we can use the derivative to find the marginal profit. The derivative of P(x) is:
P'(x) = -4x + 6
To find the marginal profit when 4 units are produced and sold, we plug in x = 4 into P'(x):
P'(4) = -4(4) + 6
P'(4) = -10
Therefore, the marginal profit when 4 units are produced and sold is -10 hundred dollars or -$1,000. This means that for each additional unit produced and sold beyond the initial 4 units, the profit will decrease by $1,000.
Hi! It seems that your question has some missing information and typos, but I'll try my best to help you with the given data. The main task here is to find the marginal profit when 4 units are produced and sold, and interpret the answer.
The profit function P(x) appears to be incomplete. However, since we're asked to find the marginal profit, we need to take the derivative of the profit function with respect to x. Marginal profit is the derivative of the profit function with respect to the number of units sold (x). We can use the chain rule, product rule, or quotient rule to find the derivative, depending on the given profit function.
Once we have the derivative, we can evaluate it at x = 4 to find the marginal profit when 4 units are produced and sold. The result will indicate how much additional profit (in hundreds of dollars) the company will gain for producing and selling one more unit.
Please provide the complete profit function P(x), and I will be glad to help you find the marginal profit and interpret the answer.
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In 2015, there were roughly 1 X 10^6 high school football players and 2 X 10^3 professional football players in the United States. About how many times more high school football players are there? Explain how you know
Answers
There are approximately 500 times more high school football players than professional football players in the United States.
How to determine ratio of football players?To determine how many times more high school football players there are than professional football players in the United States, we need to divide the number of high school players by the number of professional players:
1 x 10⁶ / 2 x 10³ = 500
Therefore, there are approximately 500 times more high school football players than professional football players in the United States.
We can determine this by dividing the two numbers and finding the ratio of high school players to professional players. The result tells us how many times greater the number of high school players is than the number of professional players. In this case, the ratio is 500:1, which means that for every professional football player, there are 500 high school football players.
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Gina made a
playlist of children's songs. In 1 hour,
how many more times could she play
"Row, Row, Row Your Boat" than "Twinkle,
Twinkle, Little Star"?
Answers
The number of times more that Gina can play the playlist of children's songs in an hour would be 94. 7 times.
How to find the number of times ?The playlist that Gina made of children's songs. In an hour, the number of seconds we have is :
= 60 secs x 60 mins
= 3, 600 seconds
The number of times that "Row, Row, Row Your Boat" can be played is:
= 3, 600 / 8
= 450 times
The number of times that Gina can play "Twinkle, Twinkle, Little Star" is :
= 3, 600 / 20
= 180 times
The number of times more :
= 450 - 180
= 270 times
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3 15, 18, 16, 18, 19, 22
Mean = 1
Median = 18
Mode = 14
Answers
Answer:
Mean=15.86
Median=18
Mode=18
Find the volume of the solid generated by revolving the region bounded by the curve y=7secx and the line y=72 over the interval − π 4≤x≤ π 4 about the x-axis.
Answers
To find the volume of the solid generated by revolving the region bounded by the curve y=7secx and the line y=72 over the interval − π/4≤x≤π/4 about the x-axis, we can use the method of cylindrical shells.
First, we need to find the equation of the curve of the region being revolved. We have y=7secx and y=72, so at the intersection point, we have 7secx=72, which gives us secx=10.285. Taking the inverse secant function of both sides, we get x=1.37 (approximately).
Now, we can set up the integral for the volume using cylindrical shells. The radius of each shell is y-72, and the height of each shell is 2π times the distance from x to the intersection point, which is x-1.37. The integral is:
V = ∫(2π)(y-72)(x-1.37) dx, from -π/4 to π/4
We can substitute y=7secx into the integral:
V = ∫(2π)(7secx-72)(x-1.37) dx, from -π/4 to π/4
Using integration by parts, we can evaluate the integral:
V = (2π)[(7/2)ln|secx+tanx| - 72x + (1.37)(7/2)ln|secx+tanx| + 46.8] from -π/4 to π/4
V = (2π)(7/2)(ln|11+6√3| + ln|11-6√3| + 1.37ln|11+6√3| + 1.37ln|11-6√3| - 144)
V ≈ 305.64 cubic units.
Therefore, the volume of the solid generated by revolving the region bounded by the curve y=7secx and the line y=72 over the interval − π/4≤x≤ π/4 about the x-axis is approximately 305.64 cubic units.
To find the volume of the solid generated by revolving the region bounded by the curve y=7sec(x) and the line y=72 over the interval -π/4≤x≤π/4 about the x-axis, you can use the disk method. The formula for the disk method is:
Volume = π * ∫[R(x)² - r(x)²] dx from a to b
In this case, R(x) represents the outer radius, which is given by y=72, and r(x) represents the inner radius, which is given by y=7sec(x). The limits of integration are a=-π/4 and b=π/4. Therefore, the volume can be calculated as:
Volume = π * ∫[72² - (7sec(x))²] dx from -π/4 to π/4
Now, evaluate the integral and multiply by π to find the volume of the solid.
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The expected increase (I) of a population of organisms is directly proportional to the current population (n). If a sample of 240 organisms increases by 20, by how many will a population of 600 increase?
Answers
A population of 600 organisms is expected to increase by 50.
To solve this problem
We can use the equation I = k * n to determine whether the anticipated growth (I) of an organism population is directly related to the size of the current population (n).
Where k is a proportionality constant that connects the anticipated growth to the current population.
We can use the details provided in the problem to determine the value of k. We can write: 20 = k * 240 to represent an increase of 20 in a sample of 240 organisms.
We can calculate k as follows: k = 20 / 240 = 1 / 12.
Now that we know the value of k, we can use it to calculate the predicted growth for a population of 600:
I = (1 / 12) * 600 = 50
Therefore, a population of 600 organisms is expected to increase by 50.
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In a circle, the acr length of an intercepted arc is ten inches. The radius of the circle measures 2 inches. What is the measure of the central angle that intercepts that acr?
Answers
The measure of the central angle that intercepts the arc of the circle is approximately 286.48 degrees.
A circle's circumference is comprised of arcs. In other words, if you draw any two locations on a circle's circumference, the curved line that joins them around the border of the circle is referred to as an arc.
The formula for the relationship between arc length and central angle is:
arc length = radius x central angle
We are given the arc length and radius, so we can solve for the central angle:
10 = 2 x central angle
Dividing both sides by 2, we get:
central angle = 10/2
= 5 radians
To convert from radians to degrees, we multiply by 180/π:
central angle = 5 x 180/π
≈ 286.48 degrees.
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one year ago, jay was 140 cm tall. He is 5% taller now than he was then. How tall is Jay now?
Answers
Answer:
Recall 5%=.05 as a decimal. Then multiply 140(.05)=7 to get how many centimeters he grew. Add 140+7=147 to get his current height.
My sister is 16 years old. My brother says that his age minus nighteen is equal to my sister's age. How old is my brother? Write a equation with b as variable
Answers
The brother is 35 years old.
How to use the variable "b" to represent the brother's age?Let's use the variable "b" to represent your brother's age.
According to the problem, your brother's age minus nineteen (b - 19) is equal to your sister's age, which is 16. So we can write an equation:
b - 19 = 16
To solve for b, we can add 19 to both sides of the equation:
b - 19 + 19 = 16 + 19
Simplifying, we get:
b = 35
Therefore, your brother is 35 years old.
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Joey needs to buy chocolate milk they only sell it in pint containers how many pint containers of chocolate milk should he buy
Answers
To determin how many pint containers of chocolate milk Joey should buy, we need to know how much chocolate milk he wants in total.
Let's assume Joey wants to buy "x" pints of chocolate milk. Then, the total amount of chocolate milk he will get in quarts can be calculated as:
Total amount of chocolate milk = x pints/2 pints per quart = x/2 quarts
If Joey has a specific total amount of chocolate milk he wants to buy, we can solve for "x". For example, if Joey wants to buy 3 quarts of chocolate milk, we can set up the following equation:
x/2 = 3
Multiplying both sides by 2, we get:
x = 6
So, Joey needs to buy 6 pint containers of chocolate milk to get 3 quarts in total.
If Joey has a different desired amount of chocolate milk, we can adjust the equation accordingly to find the number of pint containers he needs to buy
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If the area of the top of a cylinder is 16 square cm and the height is 8 cm, what is the volume of the cylinder?
Answers:
A. 128 cm cubed
B. 512 cm cubed
C. 256 cm cubed
D. 64 cm cubed
Answers
A. 128CM CUBED
Step-by-step explanation:
THE FORMULLA : it's v(volume) =AB (BAZE AREA OR TOP AREA ) × HEIGHT SO
16 SQUARE CM ×8CM
=128CM CUBEDAn a frame house has a front facade measuring 30' across and 20' in height what is the area of the facade
Answers
The area of the facade measuring 30' across and 20' in height is 300 square feet.
The front facade of an A-frame house is a triangular shape, with a base of 30 feet and a height of 20 feet. To calculate the area of the facade, we need to use the formula for the area of a triangle, which is 1/2 times the base times the height = 1/2 * b * h, where b is the base and h is the height.
In this case, the base is 30 feet and the height is 20 feet, so we can plug those values into the formula:
Area = 1/2 x 30 x 20
Simplifying the multiplication, we get:
Area = 300 square feet
Therefore, the area of the front facade of the A-frame house is 300 square feet.
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Answer each one please 20 points! :3 and (brainly)
caden exercises daily by walking on a treadmill. he sets the machine so that he will walk at a steady rate of 3.6 miles per hour.
a. if t represents time in hours and d represents distance in miles, write an equation that models the relationship between these variables.-
b. use your equation to calculate the distance caden will walk in 3/4 of an hour.--
c. use your equation to calculate how long it will take for caden to walk 4.32 miles.--
answer each one please 20 points! :3 and (brainly)
Answers
a. If t represents time in hours and d represents distance in miles, and Caden walks at a steady rate of 3.6 miles per hour, the equation that models the relationship between these variables is:
d = 3.6t
b. To calculate the distance Caden will walk in 3/4 of an hour, plug 3/4 into the equation for t:
d = 3.6(3/4) = 2.7 miles
Caden will walk 2.7 miles in 3/4 of an hour.
c. To calculate how long it will take for Caden to walk 4.32 miles, plug 4.32 into the equation for d and solve for t:
4.32 = 3.6t
t = 4.32/3.6 ≈ 1.2 hours
It will take Caden approximately 1.2 hours to walk 4.32 miles.
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let f be the function defined above. what is the integral of f(x) from -1 to 1
Answers
The value of given function [tex]\int\limits^1_{-1}[/tex]f(x)dx is equal is 5/6. So, correct option is A.
To find the integral of f(x) from -1 to 1, we need to split the interval [-1,1] into three parts, where f(x) is defined differently.
For x < 0, f(x) = x², so the integral of f(x) from -1 to 0 is:
[tex]\int\limits^0_{-1}[/tex](x²)dx = (-1/3)x³ evaluated at x=0 and x=-1 = (-1/3)(0 - (-1)) = 1/3
For x = 0, f(x) = -1, so the integral of f(x) at x=0 is simply -1.
For x > 0, f(x) = x, so the integral of f(x) from 0 to 1 is:
[tex]\int\limits^1_{0}[/tex](x)dx = (1/2)x² evaluated at x=1 and x=0 = (1/2)(1 - 0)² = 1/2
Therefore, the integral of f(x) from -1 to 1 is:
[tex]\int\limits^1_{-1}[/tex]f(x)dx = [tex]\int\limits^0_{-1}[/tex](x²)dx + [tex]\int\limits^0_{0}[/tex](-1)dx + [tex]\int\limits^1_{0}[/tex](x)dx
= 1/3 + (-1) + 1/2
= 5/6
Thus, the correct answer is (a) 5/6.
So, correct option is A.
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PLEASE HELP 30 POINTS
Answers
The volume of the oblique cylinder whose base and height is given would be = 9,646.08 m³. That is option B.
How to calculate the volume of a cylinder?To calculate the volume of a cylinder, the formula that should be used is given as follows:
Volume of a cylinder = πr²h
π = 3.14
R = diameter/2 = 16/2 = 8m
Height = 8²+48² (using the Pythagorean formula)
= 64+2304
=√ 2368
= 48.66cm³
The volume of the cylinder = 3.14 × 8×8×48.66
= 9,646.08 m³
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Daria performed an experiment in which she randomly pulled a marble from a bag, recorded its color, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.
Color of Marble Frequency
Yellow 26
Green 34
Purple 18
Red 22
If Daria repeats the experiment 50
more times, how many of those times should she expect to pull a yellow marble?
Answers
The number of times she should expect to pull a yellow marble is 13
How many of those times should she expect to pull a yellow marble?From the question, we have the following parameters that can be used in our computation:
Color of Marble Frequency
Yellow 26
Green 34
Purple 18
Red 22
This means that
Times she should expect to pull a yellow marble is
Yellow = P(Yellow) * 50
So, we have
Yellow = 26/(26 + 34 + 18 + 22) * 50
Evaluate
Yellow = 13
Hence, the number of times she should expect to pull a yellow marble is 13
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A pathway made of slate tiles measures 5 1/3 yards long. A tile measuring 2 feet is added to the end of the pathway.
What is the total length of the pathway now?
1. 5 1/3 ft
2. 10 2/3 ft
3. 18 ft
4. 22 ft
Answers
Answer:
18 feet
Step-by-step explanation:
multiply 5 1/3 yards by 3 to find the measurement in feet.
16/3 x 3 = 16
16 + 2 = 18
Helping in the name of Jesus.
A hummingbird flaps its wings 80 times in one second. A bumblebee flutters its wings 7,800 times in 1 minute. Which animal flutters its wings more times in 1 minute?
Answers
Answer:
Step-by-step explanation:
The bumblebee flutters its wings more times in 1 minute, as it flutters its wings 7,800 times in one minute, whereas the hummingbird flaps its wings 80 times in one second, which translates to 4,800 times in one minute.
To understand this calculation in more detail, we can use unit conversions and multiplication. Since the hummingbird's wing flaps are given in seconds and the bumblebee's wing flutters are given in minutes,
we convert the hummingbird's wing flaps from seconds to minutes by multiplying by 60. We then compare the total number of wing flaps for each animal and find that the bumblebee flutters its wings more times in one minute than the hummingbird flaps its wings.
This is due to the bumblebee's higher frequency of wing movement, which enables it to achieve more wing flutters in a given amount of time.
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Quadrilateral ABCD is a square with diagonals AC and BD. If A(4, 9) and C(3, 2), find the slope of BD.
Answers
7 is the slope of BD in Quadrilateral.
What in arithmetic is a quadrilateral?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. Additionally, there are several subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.
There are four closed sides to a quadrilateral. Quadrilaterals are the following figures: produced by Raphael. a quadrilateral form. The form features a single pair of parallel sides and no right angles.
points A(4, 9) and C(3, 2)
slope = y₂ - y₁/x₂ - x₁
= 2 - 9/3 - 4
= - 7/-1
= 7
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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?
Answers
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.
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Does anyone know how to help
Answers
The volume of the cylinder after the rotation of rectangle is V = 12π units³ = 37.68 units³
Given data ,
Let the width of the rectangle be w = 2 units
Let the length of the rectangle be l = 3 units
Now , on rotating a rectangle , we get a cylinder
And , the radius of the cylinder = 2 units
And , the height of the cylinder = 3 units
Now , Volume of Cylinder = πr²h
On simplifying , we get
V = π ( 2 )² ( 3 )
V = 12π units³
V = 37.68 units³
Hence , the volume of cylinder is V = 37.68 units³
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Use the aleks calculator to evaluate each expression.
round your answers to the nearest hundredth.
tan 33°
cos 42°
sin 70°
Answers
When rounded to the nearest hundredth, the result of the expression tan 33° × cos 42° × sin 70° is approximately 0.4511 .
To evaluate the given expression using the terms tan 33°, cos 42°, and sin 70°, you can use a scientific calculator or an online tool like the ALEKS calculator.
After evaluating each term, you would multiply the values together and round the result to the nearest hundredth. Here's the breakdown:
tan 33° ≈ 0.6494
cos 42° ≈ 0.7431
sin 70° ≈ 0.9397
Now multiply the values:
0.6494 × 0.7431 × 0.9397 ≈ 0.4511
So, the result of the expression tan 33° × cos 42° × sin 70° is approximately 0.4511 when rounded to the nearest hundredth.
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You bike 2 miles the first day of your training, 2.3 miles the second day, 2.9 miles the third day, and 4.1 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day? Use a recursive formula.
Answers
Answer:
5.6 miles
Step-by-step explanation:
the patteren in 0.3 0.6 0.3 0.6
A company manufactures computers. Function N represents the number of components that a new employee can assemble per day. Function E
represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours
worked in one day.
50€
1+4
N (t) =
E (t)
Which function describes the difference of the number of components assembled per day by the experienced and new employees?
=
O A D (t):
=
OB.
D (t)
O C.
OD.
D (t)
D (t)
=
=
10(2-13)
10(2-13)
(+3)(+4)
100 (21+13)
1+3
10e(2+13)
(+3)(+4)
Answers
lmno is a parallelogram. if nm = x + 27 and ol = 3x + 9 find the value of x and then find nm and ol.
Answers
The length of NM and OL in the parallelogram LMNO are both 36 units.
How we find the value of x?Since LMNO is a parallelogram, we know that opposite sides are equal in length. Therefore, we can set NM and OL equal to each other:
NM = OL
We also know that NM = x + 27 and OL = 3x + 9, so we can substitute these expressions into the equation:
x + 27 = 3x + 9
Solving for x:
2x = 18
x = 9
Now that we know x, we can substitute it back into the expressions for NM and OL:
NM = x + 27 = 9 + 27 = 36
OL = 3x + 9 = 3(9) + 9 = 36
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HURRY WHO IS RIGHT!!!
Answers
Answer:
Step-by-step explanation:
cat
A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. List the sample space when choosing one marble.
S = {1, 2, 3, 4, 5}
S = {red, blue, green, yellow}
S = {g, r, b, y, o}
S = {green, blue, yellow, orange}
Answers
The sample space for choosing one marble from the given marbles which are red, green, blue, yellow, and orange is s = {red, green, blue, yellow, orange}
Given color of the marbles which are present in the paper bag are,
red greenblueyelloworangeThe five color marbles are present in the paper bag so, the sample space also contains all five marbles without repeating any color again.
Sample space: sample space is nothing but listing all the outcomes of the event. In the above event, we have to list the all outcomes when choosing one marble from the paper bag which containing five different marbles.
So, the sample space S = {red, green, blue, yellow, orange}
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Find the volume and surface area of the composite figure. Give four answer in terms of π.
The figure shows a compound solid that consists of a right cylinder with a hemisphere on top of it. The height of the right cylinder is equal to 12 inches. The diameters of both the right cylinder and the hemisphere are equal to 4 inches.
PLEASE ANSWER I WILL GIVE BRAINLIST
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To find the volume and surface area of the composite figure, we need to find the volume and surface area of the right cylinder and the hemisphere separately, and then add them together.
First, let's find the volume of the right cylinder.
The formula for the volume of a right cylinder is V = πr^2h, where r is the radius and h is the height. In this case, the radius is half of the diameter, which is 4/2 = 2 inches. So, the volume of the right cylinder is:
V1 = π(2)^2(12) = 96π cubic inches
Next, let's find the volume of the hemisphere. The formula for the volume of a hemisphere is V = (2/3)πr^3, where r is the radius. In this case, the radius is also 2 inches. So, the volume of the hemisphere is:
V2 = (2/3)π(2)^3 = 16/3π cubic inches
To find the total volume of the composite figure, we just need to add V1 and V2:
Vtotal = V1 + V2 = 96π + 16/3π = 320/3π cubic inches
Now, let's find the surface area of the composite figure.
To do this, we need to find the surface area of the curved surface of the cylinder, the top of the cylinder, and the curved surface of the hemisphere separately, and then add them together.
The formula for the surface area of the curved surface of a cylinder is A = 2πrh, where r is the radius and h is the height. In this case, the radius is still 2 inches, and the height is 12 inches. So, the surface area of the curved surface of the cylinder is:
A1 = 2π(2)(12) = 48π square inches
The formula for the surface area of the top of a cylinder is A = πr^2, where r is the radius. In this case, the radius is still 2 inches. So, the surface area of the top of the cylinder is:
A2 = π(2)^2 = 4π square inches
Finally, the formula for the surface area of the curved surface of a hemisphere is A = 2πr^2, where r is the radius. In this case, the radius is still 2 inches. So, the surface area of the curved surface of the hemisphere is:
A3 = 2π(2)^2 = 8π square inches
To find the total surface area of the composite figure, we just need to add A1, A2, and A3:
Atotal = A1 + A2 + A3 = 48π + 4π + 8π = 60π square inches
So, the volume of the composite figure is 320/3π cubic inches, and the surface area of the composite figure is 60π
square inches.
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Question 1 4 pts 1 Details Suppose that the position of a particle is given by 8 = f(t) = 56° +61 +9. (a) Find the velocity at time t. m2 v(t) = 8 (b) Find the velocity at time t = 3 seconds. m (c) Find the acceleration at time t. a(t) = m 32 (d) Find the acceleration at time t = 3 seconds. m/s^2
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The velocity at time t is 56 + 6 m/s, the velocity at time t = 3 seconds is 62 m/s, the acceleration at time t is 0 m/s², and the acceleration at time t = 3 seconds is 0 m/s².
Hi, I can help you with your question involving acceleration, time, and a particle.
(a) To find the velocity at time t (v(t)), take the first derivative of the position function f(t) = 56t + 6t + 9.
v(t) = d(56t + 6t + 9)/dt = 56 + 6
(b) To find the velocity at time t = 3 seconds, plug in t = 3 into the velocity function:
v(3) = 56 + 6 = 62 m/s
(c) To find the acceleration at time t (a(t)), take the first derivative of the velocity function v(t) = 56 + 6:
a(t) = d(56 + 6)/dt = 0
(d) To find the acceleration at time t = 3 seconds, since the acceleration is constant (a(t) = 0), it remains the same for all time:
a(3) = 0 m/s²
So, the velocity at time t is 56 + 6 m/s, the velocity at time t = 3 seconds is 62 m/s, the acceleration at time t is 0 m/s², and the acceleration at time t = 3 seconds is 0 m/s².
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