The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.
What is permutation and combination?By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Here, the differences between permutation and combination are described in detail.
The number of ways in which we can select a committee of 4 democrats from ten democrats is:
P = 10C 4 = 10! / (4)! (10 - 4)!
P = 210
The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:
P = 11C 3 = 11! / 3! (11 - 3)!
P = 165
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:
P = (210) (165) = 34650
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.
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I need help with this. Please explain
I=PRT
P=5,600
R=0.2
T=4
Step-by-step explanation:
The formula "I=PRT" is the simple interest formula, where:
I = interest
P = principle (the initial amount of money)
R = interest rate (as a decimal)
T = time (in years)
Given the values of P, R, and T:
P = 5,600
R = 0.2
T = 4
We can plug these values into the formula to find the interest:
I = P * R * T = 5,600 * 0.2 * 4 = 4,480
So, the interest earned on a principle of $5,600 at an interest rate of 0.2 (or 20%) for 4 years would be $4,480.
Solve for 4|u-2| +6 < 42
You have decided to build your shelter close enough to the coastline to be able to fish but far enough away to not bear the brunt of the bitter cold winds. After watching previous seasons of the show, you decide that 50 meters is a good distance away from the coastline. To estimate, you will convert meters to feet (you do not have a tape measure). How many feet is this?
50 meters in feet is 164.042 feet
How to convert from meters to feetIn order to convert meters to feet we would have to cross multiply
That is. one meter is given as 3.28084 feet
We are to convert 50 meters to feet, hence we would have:
If 1 meter = 3.28084
50 meters = ?
When we cross multiply, we would have
? = 3.28084 * 50 meters
? = 164.042
Hence the amount of 50 meters in feet is given as 164.042 feet
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Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265. 1a. Explain what it would mean for the null hypothesis to be true in this setting. 1b . Interpret the p-value. 1c. What conclusion would you make at the alpha = 0.05 signifigance level?
Answer:
1a. The null hypothesis in this setting would mean that the proportion of students who completed their math homework is equal to or greater than 75%.
1b. The p-value represents the probability of observing a sample proportion as extreme as or more extreme than the sample proportion observed (68%), given that the null hypothesis is true. In this case, the p-value of 0.1265 indicates that there is a 12.65% chance of observing a sample proportion as extreme or more extreme than 68%, assuming the true proportion is equal to or greater than 75%.
1c. At the alpha = 0.05 significance level, we reject the null hypothesis if the p-value is less than 0.05. In this case, the p-value of 0.1265 is greater than 0.05, meaning we fail to reject the null hypothesis. Therefore, at the alpha = 0.05 significance level, we cannot conclude that less than 75% of students completed their math homework.
The following frequency distribution presents the batting averages Major League Baseball players who had 300 or more plate appearances during recent season; Batting Average Frequency 0.180-0.199 0.200-0.219 0.220-0.239 0.240-0.259 0.260-0.279 0.280-0.299 0.00-0.319 0.320-0,339 0.340-0.359
The construction of the graph is shown here.
Also cumulative frequency in the table form mentioned here. This can be solved using the concept of frequency distribution.
What is frequency distribution?Tables or charts of frequency distributions are used to represent them. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.
Relative frequency distributions and cumulative frequency distributions are the two primary forms of frequency distributions utilised in data analysis. Both depend on frequency, which is the amount of times something happens inside a specific data set in descriptive statistics.
Class Frequency Cumulative frequency
0.180-0.199 2 2
0.200-0.219 10 12
0.220-0.239 39 51
0.240-0.259 56 107
0.260-0.279 60 167
0.280-0.299 49 216
0.300-0.319 27 243
0.320-0.339 12 255
0.340-0.359 1 256
The construction of the graph is shown below:
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The complete question is as follows:
An item is regularly priced at $47. Joe bought it at a discount of 65% off the regular price. Use the ALEKS calculator to find how much Joe paid.
Winston installs a fence post every eight yards after the first post he installs 25 more how long is the fence that he builds
The length of the fence that Winston installs is 200 yards
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Winston installs a fence post every eight yards after the first post he installs 25 more, therefore:
The length of the fence = 8 yards * 25 post = 200 yards
The length of the fence is 200 yards
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HELP ASAP.Next time, the rabbit from the previous problem started at 10 where on the number line can he be after the same three jumps?
This is the previous problem: A rabbit started at point 0 and made 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit we do not know the direction of either jump where on the line could the rabbit be.
Since the rabbit from the previous problem started at 10, it would be at 17 units on the number line after the same three jumps.
What is a number line?In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.
From the previous problem, the total distance covered by the rabbit is given by:
Total distance = 4 units + 2 units + 1 unit
Total distance = 7 units.
Since the second point is at 10 units and the open circle arrow points to the right of the number line, the rabbit would cover 7 more distance from this point:
Total distance = 10 units + 7 units
Total distance = 17 units.
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Using Pythagorean Theorem, Find the area of the right triangle.
Be sure to include the correct unit in your answer.
20 m
25 m
Answer:
Step-by-step explanation:
Five rectangular picture frames are shown below.
Which 2 of the picture frames are similar shapes?
Answer:
A and E
Step-by-step explanation:
Ratio of A=20/30=2/3
Ratio of B=28/50=14/25
Ratio of C=35/50=7/10
Ratio of D=14/26=7/13
Ratio of E=32/48=2/3
therefore A and E are similar shapes
How can I find the perimeter of rectangle
Answer:
19
Step-by-step explanation:
top = bottom so 4x-4y = 3x+5y so x = 9y
left = right so 2-2y = x-3y so x= y+2
so 9y = y+2
8y = 2
y= 0.25
x=2.25
so just add them all up
2*(4x-4y) + 2*(2-2y )
= 8*(x-y)+4*(1-y)
=16+4*0.75
=19
Sheridan Industries had sales in 2021 of $7,752,000 and gross profit of $1,254,000. Management is considering two alternative budget plans to increase its gross profit in 2022.
The cost of sales for Sheridan Industries, given the gross profit and the sales, is $ 6, 498, 000
How to find the cost of sales ?The cost of sales refers to the amount that the company invested to be able to make the sales they did. This includes the cost of purchases of goods which were then sold ( or their cost of manufacturing ).
The cost of sales to Sheridan Industries can be found by the formula :
= Sales - Gross profit
The cost of sales is therefore :
= 7, 752, 000 - 1, 254, 000
= $ 6, 498, 000
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The full question is:
Sheridan Industries had sales in 2021 of $7,752,000 and gross profit of $1,254,000. Management is considering two alternative budget plans to increase its gross profit in 2022. To do this this, management first needs to determine its cost of sales. Find the cost of sales for 2021.
Miko packed 40 bottles of perfume in a box. She sold each bottle of perfume for $30. How much money did she receive from sale of 15 boxes of perfume in all?
Answer: $18 000
Step-by-step explanation:
40 bottles per box
40*15 = 600 bottles total
600 * $30 = $18 000
She made $18 000 in total.
Amount of money she receives from sale of 15 boxes of perfume in all is $18,000.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Given that,
Number of bottles of perfume packed in a box = 40
Cost for each perfume = $30
Cost for 40 perfumes = 40 × $30 = $1200
So cost for a box of perfume = $1200
Cost for 15 boxes of perfume = 15 × $1200
= $18,000
Hence the amount for 15 boxes of perfume is $18,000.
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Translate this sentence into an equation. 171 is the product of 9 and Rhonda’s height. Use the variable R to represent Rhonda’s height
Answer:
171=9R
Hope this helped! :)
Answer:Rx9=171
Step-by-step explanation:
Find the volume of each solid. Round to the nearest tenth if necessary. There’s to questions so there is two answers. 1=? 2=?
The volume of the sphere with radius 5 yd rounded to the nearest tenth is 523.3 yd³.
What is the volume of the sphere?The volume of a sphere is expressed as;
V = 4/3 × π × r³
Where r is radius and constant pi π = 3.14.
Given the data in the question;
Radius r = 5 ydVolume V = ?To find the volume of the sphere, plug the given value into the above formula and simplify.
V = 4/3 × π × r³
V = 4/3 × 3.14 × ( 5 yd )³
V = 4/3 × 3.14 × 125 yd³
V = 523.3 yd³
Therefore, the volume of the sphere is 523.3 yd³.
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The subtotal for Abdiel's takeout order is $21.50. What will Abdiel's total be if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount? (2 points)
$22.15
$27.95
$23.22
$23.65
Answer:
Abdiel's total would be $23.22, which is the answer choice C.
Step-by-step explanation:
The total cost of Abdiel's order would be calculated as follows:
Calculate the tip before the discount: $21.50 x 20% = $4.30
Add the tip to the subtotal: $21.50 + $4.30 = $25.80
Calculate the discount: $25.80 x 10% = $2.58
Subtract the discount from the total cost: $25.80 - $2.58 = $23.22
So, Abdiel's total would be $23.22, which is the answer choice C.
The perimeter of a rectangle is 60 cm. Its width measures
16 cm. What is its length?
Let x= the length of the rectangle. Choose the equation that represents this
problem.
O A. 2x-32=60
O B. 2x+16=60
O C. 2x+32=60
O D. x+16=60
Find the measurement of the following angels and please show work, Im doing corrections aa due at the end of today I will give crown if you try ur best and giving 15 points please please help
Answer:
x=90° (given)
54°+90°+z=180°
144°+z=180°
z=180°-144°
z=30°
What percentage of the budgeted food is the actual food?
Budgeted: 200
Actual: 230
The actual food is 115% of the budgeted food.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The data is given in the question, as follows:
Budgeted: 200
Actual: 230
To determine the percentage of the budgeted food that is the actual food, we can divide the actual amount by the budgeted amount and multiply by 100.
Percentage = (Actual / Budgeted) * 100
Percentage = (230 / 200) x 100
Percentage = 1.15 x 100
Apply the multiplication operation, and we get
Percentage = 115%
So, the actual food is 115% of the budgeted food.
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F(x)=[[x]]. What is f(10)
If a 123 pound man can have 1213 mg of a medicine in a day, how much can a 102 pound woman have?
(round answer to one decimal place)
The woman weighing 123 pound can take 1005.9 mg of medicine
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
If a 123 pound man can have 1213 mg of a medicine in a day. Hence:
Unit rate = 1213 mg / 123 pound = (1213/123) mg per pound
For a 102 pound:
Amount of medicine = (1213/123) mg per pound * 102 pound = 1005.9 mg
The woman can take 1005.9 mg of medicine
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How many solutions does this system have
X+3y=0
Y=-8+2
Answer: x=18 and y=-6
Step-by-step explanation:
y=-6; x+3y=0
A bean plant measures 1.5 cm and grows 0.1 cm per day. A tomato plant of 0.85 cm grows steadily too. How much can it grow each day knowing that it will have the same height as the bean plant in no more than 10 days?
Answer:
Let's call the growth rate of the tomato plant "g". We know that the height difference between the tomato plant and the bean plant decreases by 0.1 cm per day, so we can write the following equation:
1.5 - 0.85 - (10 * g) = 0
Solving for g:
g = (1.5 - 0.85) / 10 = 0.065 cm/day
So the tomato plant grows at a rate of 0.065 cm per day, and will reach the height of the bean plant in no more than 10 days.
The tomato plant will grow 0.165 cm per day.
Solution:
Given,
Height of bean plant = 1.5 cm
Height of tomato plant = 0.85 cm
The growth rate of bean plant = 0.1 cm/ day
The bean plant will grow 1.5 + (0.1* 10) in 10 days = 2.5 cm
So, the tomato plant will have to grow (2.5 - 0.85) cm in 10 days = 1.65 cm
Since, the tomato plant will grow steadily,
Hence, 1.65/ 10 = 0.165
Therefore, the tomato plant will grow at a rate of 0.165 cm per day
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Cual es el producto de x(x+1)?
Answer:
x² + x
Step-by-step explanation:
x(x+1) →
[a(b + c) = ab + ac]
x (x) + x (1) →
[x • x = x²] + [x • 1 = x] →
x² + x
Edudig Digger
£35950
Samir buys this digger and expects to use it for 1250 hours each year.
The digger will decrease in value at a yearly rate of 18% of its value at the end of the previous
year.
Use this information to calculate the decrease in value of Samir's digger when it has been
used for 10000 hours.
Answer: To calculate the decrease in value of Samir's digger after 10000 hours, we need to determine its value at the end of each year, taking into account the yearly depreciation of 18%.
Here's the calculation for the first year:
Value at the end of Year 1 = £35950 - (£35950 * 18%) = £29576
And for the second year:
Value at the end of Year 2 = £29576 - (£29576 * 18%) = £24480.48
And so on, until we reach 10000 hours. To determine the exact value after 10000 hours, we would need to perform the calculation for each year until we reach the total number of hours used. However, this calculation would involve multiple steps and can become quite complex. A simpler way to estimate the decrease in value would be to use the concept of present value.
What is the slope of the line passing through the points (2, 5) and (-1,-4)?
Answer:
m=3
Step-by-step explanation:
slope of the line is 3
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A total of $25,000 is going to be split between adam and krissy with adam receiving $3000 less than krissy. how much will each get?
Answer:
Adam=$11000, Krissy=$14000
Step-by-step explanation:
Adam gets 3000 less
Adam=(25000-3000)÷2=11000
Krissy=11000+3000=14000
What is the Cartesian form of (5i-3)?
Answer: The Cartesian form of a complex number is the expression of the number in the form of x + yi, where x and y are real numbers and i is the imaginary unit.
The Cartesian form of (5i - 3) is 0 + (5i - 3).
Step-by-step explanation:
The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random variable ranging from 5 to 15. Find the mean and standard deviation of this random variable. (Round your answers to 2 decimal places.)
Stefany's salary at her company, Horizon Logistics starts at a base salary of $60,000. The table below shows her salary g(x) after x years. Write an explicit rule for the g(x).
help lssssa
The explicit rule for the g(x) is g(x) = 54000 + 6000x
How to determine the explicit ruleThe definition of the function is given as
Initial = 60000
And the table of values
The definitions from the table imply that we simply add 6000 to the previous term to get the current term
This means that
Common difference, d = 6000
The sequence is then represented as
f(x) = a + (x - 1)d
So, we have
f(x) = 60000 + (x - 1) * 6000
Evaluate
f(x) = 54000 + 6000x
Hence, the equation is f(x) = 54000 + 6000x
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