Answer:
Number of committees that are possible =210
Step-by-step explanation:
Total names in ballot = 10
Total members to be elected for the committee = 4
So, we need the number of different ways in which 4 names out of 10 can be elected for the committee.
To find the number of ways in which the committee can be elected, we use the combinations which is given as
[tex]aCb=\frac{a!}{(a-b)!b!}[/tex]
where [tex]a[/tex] represents total number of members and [tex]b[/tex] represents total number of members to be elected.
So, [tex]10C4=\frac{10!}{(10-4)!4!}[/tex]
[tex]10C4=\frac{10!}{6!4!}[/tex]
[tex]10C4=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{6\times5\times4\times3\times2\times1\times4\times3\times2\times1}[/tex]
[tex]10C4=\frac{10\times9\times8\times7}{4\times3\times2\times1}[/tex] [Canceling the common numbers]
[tex]10C4=210[/tex]
∴ Number of committees that are possible =210
Using the combinations formula, we will see that 210 different committees are possible.
How many different committees are possible?
Here we need to use the combinations function. It says that for a set of N elements, the number of different subsets of K elements (such that K is equal or smaller than N) that we can make is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have N = 10 and K = 4, replacing that we will get:
[tex]N(10, 4) = \frac{10!}{(10 - 4)!*4!} = \frac{10!}{6!*4!} = \frac{10*9*8*7}{4*3*2} = 210[/tex]
This means that from 10 names, there are 210 different committees of 4 members that can be made.
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×/76 = 4/12
Solving proportions
Answer:
x = 25.33333333
Step-by-step explanation:
x = 4
76 12
Cross multiply:
x * 12 = 76 * 4
Simplifying
x * 12 = 76 * 4
Reorder the terms for easier multiplication:
12x = 76 * 4
Multiply 76 * 4
12x = 304
Solving
12x = 304
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '12'.
x = 25.33333333
Simplifying
x = 25.33333333
One third of a store’s inventory is children’s clothing. Two fifths of its inventory is women’s clothing. What fraction of the total inventory is children’s or women’s clothing?
Answer:
11/15
Step-by-step explanation:
To answer this, add (combine) 1/3 and 2/5.
First we must rewrite these fractions with the same denominator, the LCD.
The LCD here is obtained by multiplying the denominators 3 and 5 together, obtaining 15.
Thus, 1/3 + 2/5 becomes 5/15 + 6/15, which, in turn, is 11/15.
The fraction of the total inventory that is children’s or women’s clothing
is 11/15.
To the nearest hundredth, what is the value of x?
Answer:
60.42
Step-by-step explanation:
tan40 = opposite/adjascent
tan40 =x/72
x=72tan40
x = 72 * 0.8391
x = 60.42
PLEASE HELP QUICKLY 25 POINTS
What is the common difference,d,of the sequence ?
-92,-74,-54,-38,-20
Enter your answer in the box
D = [ ]
Answer:
+18
Step-by-step explanation:
Solve the system of linear equations. 2x + 5y = 12 4x − y = 2
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
2x+5y=12
4x-y=2
--------------
y=4x-2
2x+5(4x-2)=12
2x+20x-10=12
22x-10=12
22x=12+10
22x=22
x=22/22
x=1
4(1)-y=2
4-y=2
y=4-2=2
y=2
Answer:
x = 1, y = 2 → (1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+5y=12\\4x-y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+5y=12\\20x-5y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad22x=22\qquad\text{divide both sides by 22}\\.\qquad x=1\\\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\4(1)-y=2\\4-y=2\qquad\text{subtract 4 from both sides}\\-y=-2\qquad\text{change the signs}\\y=2[/tex]
Marcela estimates the distance between the library and town hall is 735 ft. The actual distance is 612 ft.
What is the percent error in Marcela's estimate?
Round your answer to the nearest tenth of a percent.
Enter your answer in the box.
Answer:
20.1%.
Step-by-step explanation:
(735 - 612 = 123 ft.
% error = (123/612) * 100
= 20.1%.
please solve the equation (15m + 3)/2 = -6
Answer:
m = - 1
Step-by-step explanation:
Given
[tex]\frac{15m+3}{2}[/tex] = - 6
Multiply both sides by 2 to clear the fraction
15m + 3 = - 12 ( subtract 3 from both sides )
15m = - 15 ( divide both sides by 15 )
m = - 1
[tex]\text{Solve:}\\\\\frac{15m+3}{2}=-6\\\\\text{Multiply both sides by 2}\\\\15m+3=-12\\\\\text{Subtract 3 from both sides}\\\\15m=-15\\\\\text{Divide both sides by 15}\\\\\boxed{m=-1}[/tex]
what are associative on rational numbers
Answer:yo7 can add or multiply numbers regardless how they are grouped
Step-by-step explanation:
in the picture below x=
Answer:
[tex]\displaystyle 79°[/tex]
Step-by-step explanation:
The m∠x is 79°, according to the Alternate Exterior Angles Theorem.
I am joyous to assist you anytime.
* That does NOT look like an acute angle because 79° is considered an acute angle, since it is less than 90°.
Find the common factors and the GCF of 8 and 24
Answer:
8
Step-by-step explanation:
A garden patio is covered with grey slabs and yellow slabs
1/5 of the slabs are grey
The ratio of grey to yellow slabs are 1:4
There are 55 slabs in total
Work out number of yellow slabs
Answer:
There are 44 yellow slabs.
Step-by-step explanation:
Multiply 1/5 x 55. This gives you 11. 55 - 11 = 44.
The number of yellow slabs in a garden patio is 44.
Given that, a garden patio is covered with grey slabs and yellow slabs 1/5 of the slabs are grey.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The ratio of grey to yellow slabs are 1:4.
There are 55 slabs in total.
Number of grey slabs =1/5 ×55
= 11
So, the number of yellow slabs
= 55-11
= 44
Therefore, the number of yellow slabs in a garden patio is 44.
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Year 11 Maths:
500ml of water is used to make 80g of pasta. How many grams of pasta could be made with 2.5 litres of water?
With 2.5 litres of water, it can be estimated that you can make 400 grams of pasta.
Explanation:The question is asking how many grams of pasta could be made with 2.5 litres (or 2500 ml) of water. According to the initial ratio, 500 ml of water is used to make 80 grams of pasta.
To find out how many grams of pasta can be made with 2.5 liters of water, you first need to find the pasta-to-water ratio which is 80 grams pasta to 500 ml water, or 0.16 grams/ml. You then multiply this ratio by the total amount of water you have:
0.16 grams/ml * 2500 ml = 400 grams of pasta.
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Admission to a baseball game is $2.50 for general admission and $5.50 for reserved seats. The receipts were $3702.00 for 1140 paid admissions. How many ticket were sold?
1140
Step-by-step explanation:
A student number system for a county requires that the student number be 5 characters.
The first 4 characters are any single digit number, but no character can repeat and the last
character must be a letter. How many unique student numbers are possible?
30,240
131,040
260,000
315,160
Answer:
131040
Step-by-step explanation:
10*9*8*7*26
=131040
Final answer:
To calculate the unique student numbers possible, multiply the number of options for each character position: 10 x 9 x 8 x 7 for the digits and multiply by 26 for the final letter, yielding 131,040 unique numbers.
Explanation:
The question asks us to calculate how many unique student numbers are possible with a specific format: the first four characters must be single-digit numbers with no repeat, and the last character must be a letter.
To find the total number of unique student numbers, we multiply the possibilities for each position. For the first position, we have 10 choices (0-9), for the second position 9 choices (excluding the first digit chosen), for the third position 8 choices, and for the fourth position 7 choices. This can be calculated using factorial notation as 10 x 9 x 8 x 7. The last character is a letter and since there are 26 letters in the English alphabet, we have 26 choices for the last character. The total number of combinations is hence 10 x 9 x 8 x 7 x 26, which equals 131,040.
Find three consecutive even integers whose sum is -132
Answer:
The consecutive even numbers are -42, -44, -46
Step-by-step explanation:
As the numbers are consecutive even integers,
Let,
The first number is "x"
The second number is "x+2"
The third number is "x+4"
According to the equation,
x + (x+2) + (x+4) = -132
As the sum is -132. Now we break the parenthesis by using the addition rule.
or, x + x + 2 + x + 4 = -132
or, 3x + 6 = -132
or, 3x = -132 - 6 (side change)
or, 3x = -138
or, x = -138/3 (interchange)
or, x = -46
Therefore, the first number is -46
The second number is -46+2 = -44
And the third number is -46+4 = -42
The consecutive even numbers are -42, -44, -46
The ballpark made a total of $15,000 from ticket sales at Wednesday's game. The ballpark
charges $20 for each adult ticket and $10 for each child's ticket. They sold 3 times as many
children's tickets as adult tickets.
Write a system of equations that can be used to determine the number of adult ar
child tickets sold.
Answer:
The number of adult tickets sold was 300 and that of child's ticket sold is 900.
Step-by-step explanation:
Let us assume that the ticket sales at Wednesday's game are x number adult and y number child's tickets.
Therefore, as per given conditions, we can write, y = 3x .......... (1)
Again, each adult ticket cost $20 and each child's ticket costs $10 and there was a $15000 ticket sale.
So, 20x + 10y = 15000
⇒ 2x + y = 1500 ......... (2)
Now, solving equations (1) and (2) we get,
2x + 3x = 1500
⇒ 5x = 1500
⇒ x = 300 and y = 3x = 900
Therefore, the number of adult tickets sold was 300 and that of child's ticket sold is 900. (Answer)
Plz solve all:
4x+3−9x=
5+3.2n−6−4.8n=
2y−5(y−3)
−1/2(8b+3)+3b=
Answer:
4x+3−9x= 3-5x
5+3.2n−6−4.8n= -1.6n-1
2y−5(y−3)= -3y-15
−1/2(8b+3)+3b= -1b-1.5
Step-by-step explanation:
Add the numbers with the variables.
4x-9x= -5x
Then add the rest of the equation to it.
3-5x
Again, add the numbers with the variables and simplify the others.
3.2n- 4.8n= -1.6n
5-6= -1
That leads to....
-1.6n-1
Distribute the 5 into the parenthesis.
2y-5y- 15
Now, subtract the variables.
-3y-15
Distribute into the parenthesis.
-4b+(-1.5)+ 3b
Add the variables together.
-1b-1.5
If the price of a stock goes from $4.25 per share to $6.50 per share, by what percent has the
value of the stock increased? Round to the nearest whole percent.
Answer:
53%
Step-by-step explanation:
subtract 6.5 - 4.25 = 2.25
then divide 2.25/4.25 = .529
times answer by 100 = 53% rounded
Answer: 53% increase
=============================================
Work Shown:
A = old value = 4.25
B = new value = 6.50
C = percent change
C = 100*(B-A)/A
C = 100*(6.50 - 4.25)/4.25
C = 52.94%
C = 53%
------------
notes:
The positive C value indicates we have a percent increase. If C was negative, then we'd have a percent decrease.
The formula shown above for C is basically having us compute the difference in price (B-A) and then we divide that difference over the original price A. This computes the decimal form of the answer. The "100*" tacked out front will convert from decimal to percent form.
If you took 52.94% of the original price 4.25, then you would get 0.5294*4.25 = 2.24995 which rounds to 2.25; this is the amount the price increases so we add this to 4.25 and we get 4.25+2.25 = 6.50 which is the new share price.
Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56
miles per hour. Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour.
Solve the system
Answer:
2.5
Step-by-step explanation:
56(t+1/2)=70 t
56T + 28= 70T
28=70T-56T
28=14
2=T
s=T+ 1/2
S=2+ 1/2
S=2.5 hours
Tina traveled for 2 hours at a speed of 70 miles per hour, covering a distance of 140 miles.
Stephanie traveled for 2.5 hours at a speed of 56 miles per hour, also covering a distance of 140 miles.
What's the expression about?The distance traveled by a vehicle is given by the formula: distance = speed × time.
For Stephanie:
Distance_stephanie = Speed_stephanie × Time_stephanie
Distance_stephanie = 56 × (t + 0.5)
For Tina:
Distance_tina = Speed_tina × Time_tina
Distance_tina = 70 × t
Since both Stephanie and Tina are traveling the same route, the distances they travel should be equal:
Distance_stephanie = Distance_tina
Substitute the expressions for distances:
56 × (t + 0.5) = 70 × t
Now solve for "t":
56t + 28 = 70t
28 = 14t
t = 28 / 14
t = 2
So, Tina traveled for 2 hours.
Now we can find the distance traveled by both Stephanie and Tina:
Distance_tina = 70 × t
Distance_tina = 70 × 2
Distance_tina = 140 miles
Distance_stephanie = 56 × (t + 0.5)
Distance_stephanie = 56 × (2 + 0.5)
Distance_stephanie = 56 × 2.5
Distance_stephanie = 140 miles
Both Stephanie and Tina traveled a distance of 140 miles.
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Uncle drew scored 28 points in 5 5/6 minutes. How many points did he average per minute
Answer:4.6
Step-by-step explanation:
28/6
Answer:
168/35 points per minute
Step-by-step explanation:
5 5/6=35/6
28/(35/6)=(28/1)(6/35)=168/35
PLEASE HELP ASAP!!! heres the screenshot... please answer with two senteces! srry it is sideways :(
Answer:
jo mamma
Step-by-step explanation:
What is the following product square root 10* square root 10
Answer: 10
Step-by-step explanation:
Answer:
The answer would be ten.
Step-by-step explanation:
I plugged it into my TI-84 plus calculator.
A gardener is planting two types of trees:
Type A is 6 feet tall and grows at a rate of 12 inches per year.
Type B is 2 feet tall and grows at a rate of 24 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
It will take 4 years for these trees to be the same height
Step-by-step explanation:
A gardener is planting two types of trees:
Type A is 6 feet tall and grows at a rate of 12 inches per year
Type B is 2 feet tall and grows at a rate of 24 inches per year
We need to find exactly how many years it will take for these trees to be the same height
Assume that it will take x years for these trees to be the same height
Type A:
∵ The initial height of the tree is 6 feet
∵ 1 foot = 12 inches
∴ 6 feet = 6 × 12 = 72 inches
∴ The initial height of the tree is 72 inches
∵ It grows at a rate of 12 inches per year
∵ The number of years is x
∴ The height of the tree in x years = 72 + 12 x
Type B:
∵ The initial height of the tree is 2 feet
∴ 2 feet = 2 × 12 = 24 inches
∴ The initial height of the tree is 24 inches
∵ It grows at a rate of 24 inches per year
∵ The number of years is x
∴ The height of the tree in x years = 24 + 24 x
Equate The heights of the two types
∴ 72 + 12 x = 24 + 24 x
- Subtract 2 from both sides
∴ 48 + 12 x = 24 x
- Subtract 12 x from both sides
∴ 48 = 12 x
- Divide both sides by 12
∴ x = 4
It will take 4 years for these trees to be the same height
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solve the systems of equations using elimination
3x-5y=-2
4x-7y=-3
a.(-1,-1)
b.( -7/3, -1)
c. (-7/3, 1)
d.(1, 1)
Answer:
x=1, y=1. (1, 1). The answer is D).
Step-by-step explanation:
3x-5y=-2
4x-7y=-3
--------------
4(3x-5y)=4(-2)
-3(4x-7y)=-3(-3)
------------------------
12x-20y=-8
-12x+21y=9
--------------------
y=1
3x-5(1)=-2
3x-5=-2
3x=-2+5
3x=3
x=3/3
x=1
Direct variation or not a direct variation
y=5/x
Answer:
not direct variation
Step-by-step explanation:
The equation for x and y in direct variation is
y = kx ← k is the constant of variation
y = [tex]\frac{5}{x}[/tex] is not in this form, thus not direct variation.
The equation for x and y varying inversely is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
y = [tex]\frac{5}{x}[/tex] is in this form and represents inverse variation
The circumference of a pizza is about 38 inches. What is the diameter of the pizza? Round to the nearest tenth if necessary
Choices
6 in.
12.1 in.
12.7 in.
24.2 in.
Answer:
The diameter of the pizza is 12 inches
Step-by-step explanation:
Given:
Circumference of a pizza = 38 inches
To Find:
The Diameter of the pizza =?
Solution:
Circumference:
The distance around the edge of a circle (or any curvy shape). It is a type of perimeter.
We know that the shape of the pizza is circle.
So the given circumference is circumference of a circle.
Now,
Circumference of the circle(pizza)=[tex]2\pi r[/tex]
where r is the radius of the circle
circumference of the pizza =38
Thus
[tex]2\pi r= 38[/tex]
[tex]\pi r=\frac{38}{2}[/tex]
[tex]\pi r=19[/tex]
[tex]r=\frac{19}{3.14}[/tex]
r=6.050 inches
Now,
Diameter = [tex]2\times r[/tex]
Diameter = [tex]2\times 6.05[/tex]
Diameter=12.1 inches
Rounding to the nearest tenth
Diameter=12 inches
Final answer:
To find the diameter of a pizza with a circumference of about 38 inches, we apply the formula C = πD, leading to a calculation of 38 / 3.14, which results in approximately 12.1 inches.
Explanation:
The question is about finding the diameter of a pizza given its circumference, which is approximately 38 inches. To calculate the diameter from the circumference, we use the formula C = πD, where C is the circumference and D is the diameter. Since π (Pi) is approximately 3.14, we rearrange the formula to find the diameter: D = C / π. Thus, substituting the given value of C = 38 inches, we get D = 38 / 3.14, which is approximately 12.1 inches.
Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles) 1 1.5 3 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.23 1.8 2.4 3
Which statement best compares the mean distances for the two groups?
tie anual for Group A and Group B.
Answer:
(b) The statement : It is greater for Group B than Group A is correct.
Step-by-step explanation:
Here, the given question is INCOMPLETE.
Two groups of students were asked how far they lived from their school. The table below shows the distances in miles
Group A (distance in miles) 1 1.5 3.03 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.23 1.3 1.8 2.4 3 1.5 1.8
Which statement best compares the mean distances for the two groups?
It is equal for Group A and Group B.
It is greater for Group B than Group A.
Its value for Group A is double the value for Group B.
Its value for Group B is double the value for Group A.
Answer:
Now,here the calculating the mean as calculated by the group A.
[tex]\textrm{Mean} = \frac{\textrm{Sum of Obseravtion}}{\textrm{ Number of Observation}}[/tex]
Mean as calculated by Group A = [tex]\frac{\textrm{1 + 1.5 +3 +3.2+ 2.8+ 1.5 +1.8+ 2.5 +2.2}}{\textrm{ Number of Observation}} = \frac{19.5}{9} =2.16[/tex]
So, mean by Group A = 2.16
Now, calculating the mean as calculated by the group B.
[tex]\textrm{Mean} = \frac{\textrm{Sum of Obseravtion}}{\textrm{ Number of Observation}}[/tex]
Mean as calculated by Group B = [tex]\frac{\textrm{2 + 2.5 +3.23 +1.3 + 1.8+ 2.4 +3 +1.5 +1.8}}{\textrm{ Number of Observation}} = \frac{14.93}{9} =2.48[/tex]
So, mean by Group B = 2.17
Hence, the statement : It is greater for Group B than Group A is correct.
Answer:
The correct answer is B. It is greater for Group B than Group A.
Step-by-step explanation:
The values are not equal and the difference just isn't enough for it to be any of the other answers making B the right option.
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The temperature is -2∘C. If the temperature rises by 15∘C, what is the new temperature?
13 Degrees Celsius, or 55.4 degrees Fahrenheit.
-2 + 15 = 13. To find your answer in Fahrenheit, just do (Celsius here) x 9/5 + 32.
The new temperature value if an initial temperature value of - 2°C rises by 15°C will be 13°C
Using the addition operation :
Initial temperature = - 2°Temperature increase = 15°Final temperature = Initial temperature + Final temperature
Final temperature = (-2°C + 15°C) = 13°C
Therefore, the final temperature is 13°C
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The total cost of a jacket and a pair of shoes was $52.95. If the price of the jacket was $3.87 less than the pair of shoes, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.
The price of jacket was $24.54
Step-by-step explanation:
Let,
Cost of jacket = x
Cost of pair of shoes = y
According to given statement;
x+y=52.95 Eqn 1
x = y-3.87 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](y-3.87)+y=52.95\\y-3.87+y=52.95\\2y=52.95+3.87\\2y=56.82\\[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{56.82}{2}\\y=28.41[/tex]
Putting y=28.41 in Eqn 2,
[tex]x=28.41-3.87\\x=24.54[/tex]
The price of jacket was $24.54
Keywords: linear equation, division
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Final answer:
The price of the jacket is $24.54, calculated by first finding the price of the shoes from the total cost and the price difference between the jacket and shoes, and then subtracting the difference from the price of the shoes.
Explanation:
The question at hand involves finding the price of a jacket given the total cost of the jacket and a pair of shoes and the relationship between their prices. Let's denote the price of the jacket as J and the price of the shoes as S. According to the information provided, we have the following two equations:
J + S = $52.95 (The total cost of both items)
J = S - $3.87 (The jacket costs $3.87 less than the shoes)
We can substitute the second equation into the first to find the price of the shoes:
(S - $3.87) + S = $52.95
2S - $3.87 = $52.95
2S = $52.95 + $3.87
2S = $56.82
S = $56.82 / 2
S = $28.41
Now we can find the price of the jacket by substituting the price of the shoes back into the second equation:
J = $28.41 - $3.87
J = $24.54
Therefore, the price of the jacket is $24.54.
in a sale normal prices are reduced by 10% nathelie bought a pair of shoes in the sale for £54 what was the original price of the shoes
Answer:
Step-by-step explanation:
10% of £54=£5.4 (price reduced by 10%)
Normal price should be £5.4 +£54= £59.4
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