There are 70 ways to split 8 people into two teams of 4. There are 1680 ways to split 9 people into 3 teams of 3. There are 945 ways to choose 2 teams of 4 from 10 prospects.
To find the number of ways to split 8 people into two teams of 4, we can first choose the first team in $\binom{8}{4} = 70$ ways, and the second team will be the remaining 4 people.
To split 9 people into 3 teams of 3, we can first choose the first team in $\binom{9}{3} = 84$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{3} = 20$ ways. The final team will be the remaining 3 people.
To choose 2 teams of 4 from 10 prospects, we can first choose the first team in $\binom{10}{4} = 210$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{4} = 15$ ways. However, since the order in which we choose the two teams does not matter, we must divide by 2 to get the final answer of $\frac{210 \cdot 15}{2} = 945$.
Learn more about Binom here: brainly.com/question/28384466
#SPJ11
you are selling oranges for $3 per pound. in a given day, you sell 100 pounds of oranges. what was your total revenue for that day?
Answer: $300
Step-by-step explanation:
To calculate the total revenue from selling oranges, we need to multiply the amount of oranges sold by the price per pound.
In this case, we sold 100 pounds of oranges at $3 per pound. So, the total revenue for that day is:
Total revenue = Amount of oranges sold × Price per pound
Total revenue = 100 pounds × $3
Total revenue = $300
Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities: a. P(X < 4) b. P(X > 3.5) c. P(4 < X < 5) d. P(X < 4.5) e. P(X < 3.5 or X > 4.5)
The value of the probabilities are
a. P(X < 4) = 0
b. P(X > 3.5) ≈ 0.796875
c. P(4 < X < 5) ≈ 0.5625
d. P(X < 4.5) ≈ 0.703125
e. P(X < 3.5 or X > 4.5) = 0
a. P(X < 4):
To calculate P(X < 4), we need to find the area under the curve of the function f(x) = x/8 for values of x less than 4. However, the given function is only defined for the range 3 < x < 5. Therefore, we cannot directly calculate P(X < 4) using this function. The probability of X being less than 4 is zero since the function does not cover that range.
b. P(X > 3.5):
To calculate P(X > 3.5), we need to find the area under the curve of the function f(x) = x/8 for values of x greater than 3.5. Since the function is defined for 3 < x < 5, we can calculate this probability by integrating the function over the range 3.5 to 5.
Integrating f(x) from 3.5 to 5:
∫[3.5, 5] (x/8) dx = [x²/16] evaluated from 3.5 to 5
= [(5²/16) - (3.5²/16)]
= (25/16) - (12.25/16)
= 12.75/16
= 0.796875
Therefore, P(X > 3.5) ≈ 0.796875.
c. P(4 < X < 5):
To calculate P(4 < X < 5), we need to find the area under the curve of the function f(x) = x/8 for values of x between 4 and 5. We can calculate this probability by integrating the function over the range 4 to 5.
Integrating f(x) from 4 to 5:
∫[4, 5] (x/8) dx = [x²/16] evaluated from 4 to 5
= [(5²/16) - (4²/16)]
= (25/16) - (16/16)
= 9/16
= 0.5625
Therefore, P(4 < X < 5) ≈ 0.5625.
d. P(X < 4.5):
To calculate P(X < 4.5), we need to find the area under the curve of the function f(x) = x/8 for values of x less than 4.5. We can calculate this probability by integrating the function over the range 3 to 4.5.
Integrating f(x) from 3 to 4.5:
∫[3, 4.5] (x/8) dx = [x²/16] evaluated from 3 to 4.5
= [(4.5²/16) - (3²/16)]
= (20.25/16) - (9/16)
= 11.25/16
= 0.703125
Therefore, P(X < 4.5) ≈ 0.703125.
e. P(X < 3.5 or X > 4.5):
To calculate P(X < 3.5 or X > 4.5), we can calculate the sum of probabilities P(X < 3.5) and P(X > 4.5). However, as mentioned earlier, the function f(x) = x/8 is not defined for values less than 3 or greater than 5. Therefore, the probability of X being less than 3.5 or greater than 4.5 is zero.
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
if the first and last terms of an arithmetic series are 5 and 27, respectively, and the series has a sum 192, then the number of terms in the series is
If the first and last terms of an arithmetic series are 5 and 27, respectively, and the sum of the series is 192, then the number of terms in the series can be calculated as 12.
To find the number of terms in the arithmetic series, we can use the formula for the sum of an arithmetic series:
Sum = (n/2)(first term + last term)
We are given the first term (5), the last term (27), and the sum (192). Plugging these values into the formula, we have:
192 = (n/2)(5 + 27)
Simplifying the equation:
192 = (n/2)(32)
192 = 16n
Dividing both sides of the equation by 16:
n = 192/16
n = 12
Therefore, the number of terms in the arithmetic series is 12.
Learn more about Arithmetic Series here: brainly.com/question/30214265
#SPJ11
What is the equation of a line that passes through the points (0,4) and (3,8)?
Answer:
y = 4/3x + 4
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (0,4) and (3,8)
We see the y increase by 4 and the x increase by 3, so the slope is
m = 4/3
Y-intercept is located at (0,4)
So, the equation is y = 4/3x + 4
The slope of the line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0, 4) and (x2, y2) = (3, 8)
slope = (8 - 4) / (3 - 0) = 4/3
Now we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is one of the given points. Choosing (0, 4) as the point, we get:
y - 4 = (4/3)(x - 0)
Simplifying:
y - 4 = (4/3)x
y = 4/3 x + 4
Therefore, the equation of the line is y = 4/3 x + 4.
Clara+usually+walks+briskly+to+the+farmers+market,+and+it+takes+her+22+minutes+.+Today+she+walked++leisurely,+and+it+toke+her+61/2+minutes+.+How+much+more+time+than+usual+did+her+take+to+reach the market
The Clara took 15.5 minutes more than usual to reach the farmers' market today, given that she walked leisurely.
Clara usually takes 22 minutes to walk briskly to the farmers' market. However, today she walked leisurely and it took her 6.5 minutes to reach the market. We need to find how much more time she took than usual to reach the market.
To find the difference in time, we need to subtract the usual time from the time she took today:
Time taken today - Usual time = Difference in time
Substituting the given values:
6.5 minutes - 22 minutes = Difference in time
Simplifying the expression:
-15.5 minutes = Difference in time.
For such more questions on Farmers' market:
https://brainly.com/question/23823330
#SPJ11
How long would it take to pay off a $1000 balance with an interest rate of 14% APR when you only make the minimum payments of $20 each month?
It's important to note that this calculation assumes that the interest rate remains constant and that no additional charges are added to the balance. In reality, the time it takes to pay off the balance could be longer due to these factors.
Assuming the minimum payment is calculated as a percentage of the balance, we can use the following formula to determine the time it would take to pay off the balance:
t = (-1/12) * log(1 - (r/12) * b/p) / log(1 + r/12)
where t is the time in years, r is the annual percentage rate (APR), b is the balance, and p is the minimum payment.
Substituting the given values, we get:
t = (-1/12) * log(1 - (0.14/12) * 1000/20) / log(1 + 0.14/12) = 94.5 months
It would take approximately 94.5 months or 7.9 years to pay off the balance with only minimum payments.
For such more questions on Balance:
https://brainly.com/question/31667715
#SPJ11
You move up 4 units. You end at (-3, -1). Where did you start?
Answer: (-3,-5)
Step-by-step explanation: -1-4=-5
if the functional form of a curve is known, differentiation can be used to determine all of the following except the: o a. concavity of the curve o b. location of inflection points on the curve o c. number of inflection points on the curve o d. area under the curve between certain bounds
The process of differentiation is used to determine the rate at which one quantity changes with respect to another.
If the functional form of a curve is known, differentiation can be used to determine various characteristics of the curve. However, there are some features that cannot be determined through differentiation alone.
Firstly, differentiation can be used to find the slope of the curve at any point. This slope represents the rate at which the dependent variable changes with respect to the independent variable. It can also be used to determine whether the curve is increasing or decreasing at a given point. Additionally, differentiation can be used to find the local maxima and minima of the curve, which correspond to the points where the slope is zero.
However, differentiation cannot be used to determine the concavity of the curve. Concavity refers to the shape of the curve and describes whether the curve is bending upwards or downwards. This characteristic can be determined using the second derivative of the function. If the second derivative is positive, then the curve is concave up, while if it is negative, then the curve is concave down.
Similarly, differentiation cannot be used to determine the location or number of inflection points on the curve. Inflection points are the points on the curve where the concavity changes from concave up to concave down or vice versa. To find the location and number of inflection points, the second derivative must be set equal to zero and solved for the independent variable.
Lastly, differentiation cannot be used to determine the area under the curve between certain bounds. This requires integration, which is the inverse operation of differentiation. Integration can be used to find the area between the curve and the x-axis, and can be approximated using numerical methods.
In summary, differentiation can be used to determine various characteristics of a curve, including its slope and local maxima and minima. However, it cannot be used to determine the concavity, location or number of inflection points, or the area under the curve between certain bounds. These features require additional calculations using the second derivative or integration.
To know more about Functional form visit:
https://brainly.com/question/32053723
#SPJ11
Direction: Look at the examples of pictures, after that, answer the “Let's Try”. (Show me the solutions)
For the lengths of the triangle, what is true and false is;
1. YES 2. NO 3. YES 4. YES 5. NO 6. NO 7. NO 8. YES 9. YES
10. YES (if x, y > 0 and the sum of any two sides is greater than the third side)
How do you identify the lengths of the correct lengths of the triangle?To determine if a set of three side lengths can form a triangle, they have to fulfil the Triangle Inequality Theorem.
The theorem says that the sum of the lengths of any two sides must be greater than the length of the remaining side.
a. 12, 11, 10
11+10 > 12, 12+10 > 11, and 12+11 > 10
b. 3, 7, 10
3+7 > 10, but 3+10 < 7 and 7+10 < 3.
c. 2+3 > 4, 2+4 > 3, and 3+4 > 2.
d. 4, 6, 7
4+6 > 7, 4+7 > 6, and 6+7 > 4
e. 3, 2, 1
3+2 > 1, but 3+1 < 2 and 2+1 < 3
Find more exercises on lengths of triangle;
https://brainly.com/question/29609563
#SPJ1
a publisher used standard boxes for shipping books. the mean weight of books packed per box is 25 pounds, with a standard deviation of two pounds. the mean weight of the boxes is one pound, with a standard deviation of 0.15 pounds. the mean weight of the packing material used per box is two pounds, with a standard deviation of 0.25 pounds. what is the standard deviation of the weights of the packed boxes?
The standard deviation of the weights of the packed boxes is 2.02 pounds.
To find the standard deviation of the weights of the packed boxes, we need to use the formula for the standard deviation of a sum of random variables.
We know that the mean weight of books packed per box is 25 pounds, and the mean weight of the boxes is one pound.
Therefore, the mean weight of the packed boxes is 26 pounds. The standard deviation of the weights of the books is two pounds, and the standard deviation of the weights of the boxes is 0.15 pounds.
Using the formula for the standard deviation of a sum of random variables, we can calculate the standard deviation of the weights of the packed boxes to be 2.02 pounds.
We also know that the mean weight of the packing material used per box is two pounds, with a standard deviation of 0.25 pounds.
However, since this is a constant weight and not a random variable, it does not affect the standard deviation of the weights of the packed boxes.
Learn more about Standard Deviation here: brainly.com/question/29115611
#SPJ11
Will give brainlest and 100 points!!!!
Answer:
a) 35 degrees
b) 170 degrees
Step-by-step explanation:
In A the angles are complementary meaning they add up to 90 degrees. so that means that angle 1 + angle 2 = 90. We know angle 1 is 55 so
55+ angle 2 = 90
subtract 55 on both sides
angle 2 = 35 degrees
B is the same as A but the angles are supplementary so they add up to 180 degrees
10 + angle 2 = 180 degrees
subtract 10 from both sides
angle 2 = 170 degrees
Answer:
A) 35°; B) 170°---------------------------
Part AIf the two angles are complementary and one of them is 55°, then the second one is:
m∠2 = 90° - 55° = 35°Part BIf the two angles are supplementary and one of them is 10°, then the second one is:
m∠2 = 180° - 10° = 170°A woodcarver draws cut lines on the top of a wooden disc. She uses the drawing of her design, as shown. In chords BFand CE are perpendicular to diameter AD. Which of the following relationships is true?
A AG = OH
B CH = HE
C FG = HD
~ BG = HE
The option that shows the relationship that is true is B CH = HE.
How to explain the informationIn tho case, Chord BF is perpendicular to diameter AD, so it bisects the diameter and creates two congruent semicircles.
Chord CE is also perpendicular to diameter AD, so it bisects the diameter and creates two congruent semicircles.
Chord BF is perpendicular to diameter AD, so it bisects the diameter and creates two congruent semicircles.
Chord CE is also perpendicular to diameter AD, so it bisects the diameter and creates two congruent semicircles. In this case, CH is equal to HE as they have same length.
Learn more about perpendicular on
https://brainly.com/question/1202004
#SPJ1
jacob payed $120 for a portable e-book reader that was 80% of the original price. what was the original price?
To answer this question, we need to use a little bit of algebra. Let's call the original price of the e-book reader "x." We know that Jacob paid 80% of this price, or 0.8x. We also know that this price was $120. So we can set up an equation:
0.8x = 120. So, the original price of the portable e-book reader was $150.
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.8:
x = 150
So the original price of the e-book reader was $150.
In terms of length, this answer is more than 100 words. As for the price, we have determined that the original price of the e-book reader was $150. Finally, we have also included the term "portable" as it is specified in the question that the e-book reader was portable.
To solve this problem, we'll use the concept of percentages. Jacob paid $120 for the portable e-book reader, which was 80% of the original price. Let's represent the original price as "x." We can set up the equation:
80% of x = $120
0.8x = $120
Now, we'll solve for "x" by dividing both sides of the equation by 0.8:
x = $120 / 0.8
x = $150
So, the original price of the portable e-book reader was $150.
To know more about Price visit:
https://brainly.com/question/14871199
#SPJ11
The length of a rectangle is twice its width. If the diagonal measures 10, then find the dimensions of the rectangle.
The dimensions of the rectangle, obtained using Pythagorean Theorem are;
The length of the rectangle = 4·√5 units
The width of the rectangle = 2·√5 units
What is the Pythagorean Theorem?Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equivalent to the square of the length of the hypotenuse side.
Let x represent the width of the rectangle, we get;
The length = 2·x
Therefore, according to Pythagorean Theorem, we get;
√((x² + (2·x)²) = 10
((x² + (2·x)²) = 10² = 100
5·x² = 100
x² = 100 ÷ 5 = 20
x = √(20) = ±2·√5
Whereby the dimensions of a rectangle are natural numbers, we get;
The width of the rectangle, x = 2·√5The length of the rectangle = 2·x = 2 × 2·√5 = 4·√5Learn more on Pythagorean Theorem here: https://brainly.com/question/343682
#SPJ1
find the product of mode and median of the set:8,3,1,7,3,4,8,3,4,9,5
To find the product of the mode and median of the set 8,3,1,7,3,4,8,3,4,9,5, we first need to find the mode and median of the set.
The mode is the number that appears most frequently in a data set. In this case, the number 3 appears three times in the set, which is more than any other number. So the mode of this set is 3.
The median is the middle value when a data set is ordered from least to greatest. To find the median, we first need to put the numbers in order: 1,3,3,3,4,4,5,7,8,8,9. Since there are an odd number of numbers in the set (11), the median is the middle number. In this case, the median is 4.
So the product of the mode and median of this set is 3 * 4 = 12.
Answer:
med = 3
mode = 4
product of mode and median = 12
Step-by-step explanation:
1) Rearrange terms 1,3,3,3,4,4,5,7,8,9
2) Multiply terms 4 x 3 = 12
muriel ran from her house to the corner store and back to her house, a total distance of 600 meters, in 200 seconds. what was muriel's average speed in meters per second?
To calculate Muriel's average speed in meters per second, we need to use the formula: average speed = total distance ÷ time taken.
In this case, Muriel ran a total distance of 600 meters in 200 seconds. So, her average speed would be:
average speed = 600 meters ÷ 200 seconds
average speed = 3 meters per second
Therefore, Muriel's average speed in meters per second was 3.
Now, let's apply the formula: average speed = 600 meters / 200 seconds. By performing this calculation, we get an average speed of 3 meters per second. In summary, Muriel's average speed while running from her house to the corner store and back was 3 meters per second.
To know more about average speed visit:-
https://brainly.com/question/2346024
#SPJ11
For what value of n does
(1/36)n =216?
Answer:
The second option is the correct answer.
30 points!!
question is in picture
pls
[tex]\cos A=\dfrac{AB}{26}\\\\(AB)^2+10^2=26^2\\(AB)^2+100=676\\(AB)^2=576\\AB=24\\\\\cos A=\dfrac{24}{26}=\dfrac{12}{13}[/tex]
HALP FAST FOR BRAINIEST
Answer:
24
Step-by-step explanation:
Another way to say median is middle value.
Since the five numbers are already arranged from least
to greatest you pick the number in the middle, which is 24.
Answer:
Mark me brainliest Answer D. 24
Step-by-step explanation:
A tortise, or land turtle, might move 150m in half an hour. what is this speed in meters per minute
Answer:
5 m/ min
Step-by-step explanation:
speed = [tex]\frac{distance}{time}[/tex]
half an hour = 30 minutes, then
speed = [tex]\frac{150}{30}[/tex] = 5 m/ minute
I need help for this question
Answer: 8
Step-by-step explanation:
Use the formulas to find the volume of the figure. Show your work.
Answer: 7238.23 ft
Step-by-step explanation:
Formula for volume of a sphere V = (4/3)*(π)*(r^3)
π = 3.141
r = 12
V = (4/3)*(3.141)*(12^3)
V = (4/3)*(3.141)*(1728)
V = 7238.23 ft
Or if you want you answer in terms of π:
V = (4/3)*(1728)*(π)
V = 2304π ft
farmers Market has 472 crates of apples. Each crate holds 28 bags of apples with 6 apples in each bag How many apples are there?
Answer:
79,296
Step-by-step explanation:
472x28x6=79,296
7. A car lot owner pays his salespeople
a commission of 10% on total sales.
The owner wants to make a profit of
1 Lakh on each car. The cost price of a
car is Nu 90,000. What must the selling
price of the car be for the owner to
make a profit and pay commission?
Answer: 2,11,111
Step-by-step explanation:
The cost price is: 90000
The profit needed is 100000
Profit + commission = Selling price - cost price
Selling Price - 90,000 = 1,00,000 + 10%Selling Price
SP - 90,000 = 1,00,000 + 0.1 * SP
0.9 * SP = 1,00,000 + 90,000
0.9 * SP = 1,90,000
Selling Price = 1,90,000 / 0.9
SP= 2,11,111.11
A shop owner offered a 20% discount off the regular price of a mirror. The amount of the discount is $3. What is the regular price of the mirror?
Answer:$15
Step-by-step explanation: Okay if the discount is of 3$ and a 20% is 100% if multiplied by 5 then you multiply 3 times 5 there EZ
Which of the following accurately summarizes a test variable
(independent variable) in an experiment?
Aconstant variable that is not changed
by the experimenter.
O Avariable that is measured in the
experiment.
Avariable that is changed in the
experiment on purpose by the
experimenter.
A statement that gives you information
about the control variable.
A variable that is changed in the experiment on purpose by the experimenter accurately summarizes a test variable (independent variable) in an experiment.
In an experiment, there are different types of variables that are used to measure the effect of the experiment on the outcome.
The independent variable, also known as the test variable, is the variable that is intentionally changed by the experimenter to measure its effect on the dependent variable, which is the variable that is being measured in the experiment.
Therefore, a variable that is changed in the experiment on purpose by the experimenter accurately summarizes a test variable (independent variable) in an experiment.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ1
the mean systolic blood pressure for a sample of 500 individuals is 110 with a standard deviation of 16. a patient's systolic blood pressure is measured at 84. what is the z-score for this measurement?
The z-score for of a patient's systolic blood pressure measured at 84 is -1
How to determine the z-score for this measurement?From the question, we have the following parameters that can be used in our computation:
Sample = 500 individuals
Standard deviation = 16
Mean = 110
Measurement = 84
The z-score for this measurement is calculated as
z = (Measurement -Mean)/Standard deviation
substitute the known values in the above equation, so, we have the following representation
z = (84 -110)/16
Evaluate
z = -1
Hence, the z-score for this measurement is -1
Read more about z-score at
https://brainly.com/question/25638875
#SPJ1
Ethan has a hot dog cart. His hot dogs sell for $3.50 each. He has sold $28 worth of hot dogs so far today. Ethan wants his hot dog sales to be more than $70 today. Write and solve an inequality to represent the number of hot dogs Ethan still needs to sell. Show your work. Then describe the solution set in terms of the whole number of hot dogs Ethan needs to sell.
a construction worker tosses a scrap piece of lumber from the roof of a building. how long does it take the piece of lumber to reach the ground 121 feet below? use the formula d
It would take the scrap piece of lumber approximately 2.75 seconds to reach the ground 121 feet below.
To determine how long it would take for a scrap piece of lumber tossed from the roof of a building to reach the ground 121 feet below, we would use the following formula:
d = 16t²,
where d is the distance in feet and t is the time in seconds.
To use the formula, we would first need to determine the value of d, which is 121 feet. We can then plug this value into the formula to get:
121 = 16t²
To solve for t, we need to isolate the variable t by dividing both sides of the equation by 16:
121/16 = t²
7.56 = t²
We can then take the square root of both sides of the equation to find the value of t:
t = √7.56t ≈ 2.75
You can learn more about variables at: brainly.com/question/15078630
#SPJ11
write the (Tn) for 1;4;7;10
The nth term of the arithmetic progression is Tₙ = 3n - 2
Given data ,
Let the arithmetic progression be represented as A
Now , the value of A is
A = 1 , 4 , 7 , 10 ..
Now , the first term a = 1
The common difference d = second term - first term
d = 4 - 1 = 3
And , the nth term is Tₙ
where Tₙ = a + ( n - 1 )d
On simplifying , we get
Tₙ = 1 + ( n - 1 )3
Tₙ = 3n - 2
Hence , the nth term is Tₙ = 3n - 2
To learn more about arithmetic progression click :
https://brainly.com/question/1522572
#SPJ1
