Answer:
a lot
960
Step-by-step explanation:
Since there are 4 woman in total, there are 14-4=10 men.
Part 1
They can choose either 2 women, 3 women, or 4 woman.
If they choose 2 out of the 4 woman, they can have 6 different combinations.
4!/(2!(4-2)!)
=24/(2(2!))
=24/4=6
There are 8 remaining men to be chosen on the committee (because 10-2=8).
There are 10 total men and 8 men need to be chosen out of them, so the number of combinations for men is given below.
10!/(8!(10-8)!)
=10!/(8!(2!))
Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 8! from both the numerator and denominator to simplify it. This leaves the numerator with 9x10, which is 90, and the denominator with 2!, which is just 2.
90/2=45
Now we need to multiply 45 (number of combinations to choose 8 men from 10 men) and 6 (number of combinations to choose 2 women from 4 woman).
45x6=270 combinations if 2 woman are chosen
Part 2
Next we need to find out how many combinations there are if they choose 3 women for the committee.
If they choose 3 out of the 4 woman, they can have 4 different combinations.
4!/(3!(4-3)!)
=24/(6(1!))
=24/6=4
There are 7 remaining men to be chosen on the committee (because 10-3=7).
There are 10 total men and 7 men need to be chosen out of them, so the number of combinations for men is given below.
10!/(7!(10-7)!)
=10!/(7!(3!))
Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 7! from both the numerator and denominator to simplify it. This leaves the numerator with 8x9x10, which is 720, and the denominator with 3!, which is 6.
720/6=120
Now we need to multiply 120 (number of combinations to choose 7 men from 10 men) and 4 (number of combinations to choose 3 women from 4 woman).
120x4=480 total combinations if 3 women are chosen
Part 3
If 4 women out of 4 women are chosen for the committee, then obviously, there will only be 1 combination for that, since all the women will be chosen.
This leaves us with 10-4=6 spots for men in the committee.
There are 10 total men and 6 men need to be chosen out of them, so the number of combinations for men is given below.
10!/(6!(10-6)!)
=10!/(6!(4!))
Instead of multiplying out 1x2x3x4x5x6x7x8x9x10 to find 10!, we can divide 6! from both the numerator and denominator to simplify it. This leaves the numerator with 7x8x9x10, which is 5040, and the denominator with 4!, which is 24.
5040/24=210
Now we need to multiply 210 (number of combinations to choose 6 men from 10 men) and 1 (number of combinations to choose 4 women from 4 woman).
210x1=210 total combinations if 3 women are chosen
Part 4
Finally, we need to add all the final answers from the previous parts.
270+480+210=960 total combinations if at least 2 women were chosen for the committee
Please let me know if you find any errors
Find the measure of angle 1
Answer: 58 degrees
Step-by-step explanation: add the 2 angles that you know together, then subtract that number from 180. This is using the triangle sum theorem.
Answer:
b is the correct answer
Step-by-step explanation:
92 degree +30 degree +angle 1 = 180 (Since, Sum of angles of triangle is 180 degree)
Therefore, angle 1 is 58 degree .
A farmer wants to make a rectangular field with a total area of. It is surrounded by a fence. It is divided into equal areas by fences. What is the shortest total length of fence with which this can be done?.
The shortest total length of the fence is 808 m.
What is a rectangle?
A rectangle is a quadrilateral with all four interior angles 90°.
Given that the area of the rectangular field is 800 m².
Let the length and the width of the rectangle be x and y.
Then, the area of the rectangle is:
A= xy
Or, xy = 800
x = 800/y (1)
The perimeter of the triangle is:
2x +2y
Since the triangle is divided into three equal parts by fence, the total length of the fence is equal to the sum of the perimeter of the triangle and two times the length or width of the triangle.
Therefore, the total length of the fence is:
L = 2x + 2y + 2x
L = 4x +2y
Substitute x = 800/y into the above equation:
L = 4(800/y) + 2y
L = 3200/y +2y (2)
Differentiate the equation with respect to y:
L' = -3200/y² +2
Substitute L'= 0 into the above equation:
0 = -3200/y² + 2
y² = 3200/2
y² = 1600
y = 400
Substitute y = 400 into equation (2):
L = 3200/400 + 2(400)
L = 8 + 800
L = 808
Hence, the shortest total length of the fence is 808 m.
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How do I find the slope between (8,12) (10,20)
Answer: m = 4
hope thats right .
Step-by-step explanation:
Answer:
Let
Step-by-step explanation:
Let, (8,12) be (x1 and y1)
(10,20) be (x2 and y2)
We know that,
Slope = y2-y1
-----------.
x2-x1
= 20-12
-----------
10-8
= 8
-------
2
= 4 ans
so, the slope between twoo points is 4
Use elimination to solve the system of equations. −3x−8y=−24 3x−5y=4.5
We can eliminate a variable by adding the two equations, doing that we will find the solution (4, 1.5)
How to solve a system of equations by elimination?Here we have the following system of equations:
-3x - 8y = -24
3x - 5y = 4.5
To eliminate a variable, we can simply add the two equations and the variable x will be eliminated, let's do that:
(-3x - 8y) + (3x - 5y) = -24 + 4.5
Grouping like terms we get:
(-3x + 3x) + (-8y - 5y) = -19.5
0 - 13y = -19.5
Now we can solve this for y:
y = -19.5/-13 = 19.5/13 = 1.5
To get the value of x, we need to replace the value of y in one of the equations:
-3x - 8*(1.5) = -24
-3x = -24 + 8*1.5
-3x = -12
x = -12/-3 = 4
The solution is (4, 1.5)
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please anyone help me with this question i need it ASAP!! all it’s asking if the following lines parallel or perpendicular or neither. please anyone help meee
Answer: Neither.
Step-by-step explanation: I believe it's neither because I plotted the given points below and it gave me this for the result:
Hope this helps! :)
question 161 pts suppose a 95% confidence interval for obtained from a random sample of size 13 is (3.5990, 19.0736). find the upper bound of a 90% confidence interval for (round off to the nearest integer).
Following the route shown, what is the total distance traveled by the architectural tour if it ends where it started? What properties and theorems did you use to find the distance?
Using, -------------------- it can be shown that the two triangles formed are congruent. Then using ,---------------------------- the length of the road from the intersection to the first turn can be found to be ---------------------- feet. Thus, the total length of the tour is --------------- feet.
Answer's first blank:
Side-Angle Side
CPCTC
Side- Side - Side
Answer's second blank:
Side- Side - Side
CPCTC
Side-Angle Side
The theorems used are:
First blank: side-angle-side theorem
Second blank: CPCTC
Third blank: 200 feet
Fourth blank: 1,700 feet.
What is the Side-angle-side Congruence Theorem (SAS):Wen two triangles have a pair of included congruent angles and two pairs of corresponding congruent sides, then both triangles are congruent to each other by the side-angle-side theorem.
Furthermore, if two triangles are known to be congruent to each other, the CPCTC states that "corresponding parts of corresponding triangles are congruent". This means all angles and all sides that corresponds to each other are congruent.
Therefore:
Using the side-angle-side theorem it can be shown that the two triangles are congruent to each other.
Then using CPCTC , the length of the road from the intersection to the first turn would be 200 feet.
The total length of the tour would be = 2(200 + 300 + 350)
= 1,700 feet.
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Using, SAS it can be shown that the two triangles formed are congruent. Then using ,-CPCTC the length of the road from the intersection to the first turn can be found to be 200 feet. Thus, the total length of the tour is 1,700 feet.
What is SAS?The SAS Triangle Theorem indicates that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
By the use of the corresponding parts of congruent triangles are congruent (CPCTC) rule, we can state that the missing side is 200 feet. If that is the case, then the total distance traveled can be obtained by adding all the lengths of triangles:
=200 + 200 + 300 + 350 + 350 + 300
= 1,700 feet.
Hence, te total length of the tour is 1,700 feet.
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A rectangle has a length of 24 inches and a width of 13 inches. If 1 inch = 2.54 centimeters, find the area of the rectangle in centimeters. Round the answer to the nearest tenth.
A. 48.4 cm2
B. 480.4 cm2
C. 792.5 cm2
D. 2,012.9 cm2
The area of the rectangle in centimeter square is 2013 cm².
How to find the area of a rectangle?The area of a rectangle is the product of its length and width.
If the values of area and one of the sides of a rectangle is given the other one can be found by forming a suitable equation.
The length and width of the given rectangle can be written in cm as follows,
The length is given as 24 × 2.54 = 60.96 cm
And, the width is 13 × 2.54 = 33.02 cm
Now, the area of the rectangle can be obtained by taking the product of length and width as follows,
Area = 60.96 × 33.02
= 2012.89
Which can be approximated as 2013 cm².
Hence, the area of the rectangle is obtained as 2013 cm².
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Write the equation of the line that passes through the points (−1,−9) and (−9,−9). pls
Answer:
y= -9
Step-by-step explanation:
slope intercept form is y=mx+b
m is slope
b is y intercept
slope formula is y2-y1/x2-x1
-9-(-9)/-9-(1)
0/-10
0 is the slope
y=0x+b
-9=0(-9)+b
-9=b
hopes this helps
solve the problem and you get 30 coins
x3+y3+z3=k
Answer: 42
Step-by-step explanation:
I need somebody to help me on this. 20 points. Please
Answer:
I have no idea sorry
Step-by-step explanation:
i'm in middle school
8. Two triangles have the same perimeter. One of
the triangles is an equilateral triangle with all of the
side lengths equaling x + 1. The other triangle has
side lengths of 2x, x, and 4x - 7. Find the perimeteter
of the equilateral triangle.
Answer:
he perimeter of the equilateral triangle is $3(x + 1) = 3x + 3$.
Step-by-step explanation:
The perimeter of the equilateral triangle is $3(x + 1)$ since the sides are all equal and there are three sides. The perimeter of the other triangle is $2x + x + 4x - 7$, which is also equal to $3(x + 1)$
The collection of ordered pairs below represents a function: {(4, 19), (-2, 77), (0, 10), (), (1, 10). (-3,0), (100, 100)} a. State the domain of the function. b. State the range of the function.
Answer:
Domain: [-3,100] if continuous. {x|x=-3,-2,0,1,4,100} if discrete.
Range: [0,100] if continuous. {y|y=0,10,19,77,100} if discrete.
Step-by-step explanation:
Which reason justifies step 6 below?
Use the diagram.
The congruence theorem that justifies the similar triangles of triangles EFH and GFH is given as follows:
D. AAS.
Why the two triangles are similar?For the triangles EFH and GFH in this problem, we have that:
The angles E and G have the same measure.The right angles have the same measure.The side lengths HF is the same, by the reflective property of congruence.These three features are used to identify the congruence theorem as follows.
Then the congruence theorem that justifies the similar triangles of triangles EFH and GFH is the Angle-Angle-Side theorem, given by option D, as:
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the expected frequencies in a chi-square test . a. are always whole numbers b. can contain fractions or decimal values c. can contain both positive and negative values d. can contain fractions and negative numbers
The expected frequencies in a chi-square test is can contain fractions or decimal values
What is Chi-Square Test?
When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine if two categorical factors have independent effects on the test statistic.
What is Expected Frequencies?
A theoretical frequency that we anticipate to show up in an experiment is known as an expected frequency.
Expected frequency = Expected percentage * Total count
The expected frequencies in a chi-square test is can contain fractions or decimal values
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Answer question with steps asap I’ll give brainliest! Use photo above
This is a table of values of three functions at selected values of x.
It is asking for h(f(-2))
Its saying, take f(-2), and take whatever you get from that and put it into h(x)
So, find f(-2).
Find x = -2, then see what f is there.
f(-2) = -1
So, find h(-1)
h(-1) = 0
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 20 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 22 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Using the equation we know that the flowerbed is 2250 feet away from the hive.
What are equations?A mathematical assertion that has an "equal to" symbol between two expressions with equal values is known as an equation.
As in 3x + 5 Equals 15, for instance.
So, let's say the flowerbed is feet away from the hive.
The bee travels directly from its hive at a speed of 20 feet per second to a flowerbed before returning at a speed of 12 feet per second.
Time = distance/speed
Therefore, the bee needed x/20 seconds to get to the flowerbed and x/12 seconds to fly back to the hive.
The bee spends a total of 20 minutes, or 2060 seconds, or 1200 seconds away from the hive. I
t spends 15 minutes, or 1560 seconds, at the flowerbed.
Consequently, the equation will be:
x/20 + x/12 + 900 = 1200
3x + 5x/60 = 300
8x = 60 * 300
8x = 18000
x = 18000/8
x = 22550
Therefore, using the equation we know that the flowerbed is 2250 feet away from the hive.
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Complete question:
A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 20 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 22 minutes.
What equation can you use to find the distance of the flowerbed from the hive?
The sum of 3 consecutive odd numbers is 51.
What is the second number in this sequence?
Answer:
17
Step-by-step explanation:
15 + 17 + 19= 51
48 ÷ ((2 + 6) × 2) − 1
Answer:
Step-by-step explanation:
pemdas - parenthesis , exponet, multiply, divide, add, subtract. your answer is 3.5
Given the geometric sequence 512 over 243 comma negative 128 over 81 comma 32 comma 27 comma and continuing comma what is a6?.
The 6th term of the geometric sequence is -1/2.
Here we have to find the a6the term of the geometric sequence.
Data given:
The series = 512/243, -128/81, 32/27.....
The formula to find the nth term of the geometric sequence:
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where [tex]a_{n}[/tex] = nth term of the sequence
a = first term of the sequence
r = common ratio
common ratio(r) = -128/ 81 ÷ 512/ 243
= -128/81 × 243/512
= -3/4
Now we have to find the 6th term of the series.
[tex]a_{6}[/tex] = 512/ 243 (-3/4[tex])^{6-1}[/tex]
= 512/243 (-3/4[tex])^{5}[/tex]
= 512/243 × 243/1024
= -512/1024
= -1/2
Therefore the 6th term is -1/2.
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When trevor and brian play ping pong, the probability that trevor will win is 0. 6. If trevor and brian play two games of ping pong, what is the probability that they each win one of the games? assume games are independent.
The probability that they will each win a game = 0.24
Given,
The probability that Trevor will win the game p = is 0.6
The formula we will use for calculating Trevor losing the game
⇒ q = 1 - p
Now the probability of Trevor losing the game ⇒ q = 1 - 0.6
= 0.4
Now the probability that Brian wins = 0.4 when Trevor loses and the probability that Trevor wins = 0.6 when Brian loses the game.
Now the four possibilities that will decide the outcome for 2 ping pong games-
Trevor wins both games = 0.6 x 0.6 ⇒ 0.36Trevor wins the first and Brian wins the second ⇒ 0.6 x 0.4 = 0.24Brian wins the first and Trevor wins the second ⇒ 0.4 x 0.6 = 0.24Brian wins both games ⇒ 0.4 x 0.4 = 0.16Total probability = 0.36 + 0.24 + 0.24 + 0.16
= 1
Therefore, the probability that they each win one of the games = is 0.24
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the family fine arts center charges $24 per adult and $12 per senior citizen for its performances. on a recent weekend evening when 483 people paid admission, the total receipts were $7548. how many who paid were senior citizens?
337 were senior citizens.
What is the system of equations?
A system of equations, also known as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.
Here, we
Let
x = the number of adult tickets sold
y = the number of senior tickets sold
483 people paid admission => a total of 483 tickets were sold and
x + y = 483
the total receipts were $7548
24x + 12y = 7548
by solving the system of equations
x + y = 483....(1)
24x + 12y = 7548....(2)
From equation (1), we get
x = 483-y....(3)
Now, we put the value of x in equation (2) and we get
24(483 - y) +12y = 7548
11592 - 24y + 12y = 7548
12y = 4044
y = 337
Now, we put the value of y in equation (1) and we get
x = 483 - 337
x = 146
Hence, 337 were senior citizens.
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answers only help pls
Answer:
[tex]f(x) = 32(3x-1)[/tex]
Step-by-step explanation:
I just plugged in values of x into the different functions provided this function check out. Also charge your computer
The length of a rectangle is 3 inches longer than half of its width. The area of the rectangle is 416 square inches. How many inches in width is the rectangle?
A. 16 inches
B. 19 inches
C. 26 inches
D. 32 inches
Answer:
C
Step-by-step explanation:
Approximate the area under the curve y = x 3 from x = 3 to x = 5 using a right endpoint approximation with 4 subdivisions.
The approximation of the area of the region R is 182.8125
Given:
y = x^3
from [2,5] using 6 subdivisions
deltax = (5 - 2)/6 = 3/6 = 0.5
hence the subdivisions are:
[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]
hence the right endpoints are:
x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5
now the area is given by:
A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]
A = 0.5*365.625
A = 182.8125
The area using the Right Endpoint approximation is 182.8125.
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The area of the base of the oblique pentagonal pyramid is 50 cm2 and the distance from the apex to the center of the pentagon is 6startroot 2 endroot cm. the measure of ∠acb is 45°. the height, ab, is cm. the volume of the pyramid is cm3.
The height, ab, is 6 cm
The volume of the pyramid is 100 cm3.
we know that
ABC is a right triangle and we know that
∠ACB=45°
AC=hypotenuse------ 6√2 cm
sin 45=AB/AC----- AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm
AB=6 cm
we already know that the formula for getting the volume of a pyramid
volume of the pyramid=(1/3)*Area of the base*height
We will now Substitute all the values in the formula;
area of the base=50 cm²
height=6 cm
so
volume of the pyramid=(1/3)*50*6---->
1/3*300
300/3
1=00 cm³
volume=100 cm³
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Answer:
6, 100
Step-by-step explanation:
right on edge
what does a z-score tell us? question 14 options: 1) how many standard deviations an observation is from the mean. 2) the middle value if the data is in ascending order. 3) the average of a data set. 4) how many standard deviations an observation is from the median.
If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is: z = x−μ/ σ
The z-score indicates the number of standard deviations that the value x is above (right) or below (left) the mean μ. Values of x greater than the mean have positive z values, and values of x less than the mean have negative z values. The z-score of x is zero if x is equal to the mean.
The standard normal distribution is the normal distribution of standardized values called z-scores. Z-scores are measured in units of standard deviation. For example, if the normal distribution has a mean of 5 and a standard deviation of 2, then the value 11 is 3 standard deviations above (or to the right of) the mean. Here's the calculation:
x = μ + (z)(σ)
= 5 + (3)(2)
= 11
The standard normal distribution has zero mean and one standard deviation. The transformation
z= x − μ/σ
gives the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.
The next two videos explain what it means to have a "normal" distributed data set.
If X is a random variable and follows a normal distribution with mean µ and standard deviation σ, the rule of thumb states within 1 standard deviation of the mean.
About 95% of the x-values lie between –2σ and +2σ of the mean µ (within two standard deviations of the mean).
About 99.7% of the x-values lie between –3σ and +3σ of the mean μ (within 3 standard deviations of the mean) .
Almost all x-values are within 3 standard deviations of the mean.
1) +1σ and -1σ have z-scores of +1 and -1 respectively.
2) +2σ and -2σ have Z-scores of +2 and -2 respectively.
3) +3σ and -3σ have Z-scores of +3 and -3 respectively.
The rule of thumb is also known as the 68-95-99.7 rule.
The exact value used to calculate the median; further decreasing the minimum value or increasing the maximum value will not change the median value. Therefore, the median does not use all the information in the data and is therefore shown to be less efficient than the mean or average, which uses all the values in the data. To calculate the average, add the observations and divide by that number.
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Please help. I’m struggling so bad. It’s ASAP :((
The interquartile range of the given data set is 2.16.
The given data is 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22 and 3.26.
What is the interquartile range?The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.
Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1
The order of the given data is 1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02.
Here,
Q1= 1/4 (n+1) = 11/4= 2.75
= 2.22
Q3 = 3/4 (n+1) = 8.25
= 4.38
Q2 =4.38-2.22
= 2.16
Therefore, the interquartile range of the given data set is 2.16.
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three and fifty-four thousandths written in number form
Answer:
3.054
i think
Please help!!!! 2
Josh is inviting his friends to a party. He has 42 granola bars and 56 fruit drinks, and he wants to give the same number of each item to each friend. He also wants to give all of them to his friends, having nothing left over.
Fill in the blanks to describe how many friends Josh can invite.
At most, Josh can invite
friends to the party. If he invites that many friends, each will receive
granola bars and
fruit drinks.
At most Josh can invite 14 friends to the party. If he invited that many friends, each will receive 3 granola bars and 4 fruit drinks.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of granola = 42
Number of fruit drinks = 56
The highest common multiples of 42 and 56.
14 x 3 = 42
14 x 4 = 56
Now,
The number of friends that can be invited is 14.
Where each friend gets an equal number of each item.
Thus,
At most Josh can invite 14 friends to the party.
The number of items each friend received is 3 granola bars and 4 fruit drinks.
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