There are 8855 ways in which a 4-member committee be formed from 23 members
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The number of ways that a 4-member committee be formed from 23 members is:
Number of ways = 23! / [(23 - 4)!4!] = 8855 ways
There are 8855 ways in which a 4-member committee be formed from 23 members
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Answer:
The answer is 212,520.
Step-by-step explanation:
This is a permutation, not a combination. So, we need to follow the formula
[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]
Plug in the numbers and solve:
[tex]nP_{r}= \frac{23!}{(23-4)!}[/tex]
[tex]nP_{r}= \frac{23!}{19!}\\[/tex]
[tex]nP_{r}= \frac{25,852,016,738,884,976,640,000}{121,645,100,408,832,000}[/tex]
[tex]nP_{r}= 212,520[/tex]
Because 212,520 is an answer choice, this is the correct answer.
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 5x2 x 3
The solutions to the system of equations involving quadratic function f(x) and linear function g(x) are (-1,5) and (4/3,29/3), respectively.
What is a polynomial function?A polynomial function is a relationship in which a dependent variable equals a polynomial expression. A polynomial expression is one that has numbers and variables that are raised to non-negative powers.To find the solution to the given system of equations:
A polynomial expression has the following generic form:a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.The degree of the polynomial expression has the greatest power on a variable.When degree = 2, the function is quadratic.When degree = one, the function is linear.Given quadratic equation: f(x) = 3x^2 + x + 3
We must solve the linear equation g(x). Because it is a linear equation, we utilize the two-point approach to solve it.The two point formula is: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(2) = 11, g(1) = 9
g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)
or, g(x) - 9 = ((11-9)/(2-1))*(x-1)
or, g(x) - 9 = 2(x-1)
or, g(x) = 2x - 2 + 9 = 2x + 7
g(x) = 2x +7, is the linear function g(x)
We are asked to solve the system of equations f(x) and g(x).
To get the solution, we must first determine what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).
3x² + x + 3 = 2x + 7
or, 3x² - x - 4 = 0
or, 3x² + 3x - 4x - 4 = 0
or, 3x(x+1) -4(x+1) = 0
or, (3x-4)(x+1) = 0
∴ Either 3x-4=0 ⇒ x = 4/3
or, x+1=0 ⇒ x = -1.
g(-1) = 5 (from the table)
f(-1) = 3(-1)² + (-1) + 3 = 3 - 1 + 3 = 5
g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3
f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3
∴ f(-1) = g(-1) and f(4/3) = g(4/3).
Therefore, the solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).
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The correct question is given below:
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
f(x) = 3x^2 + x + 3
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
Town B
10 15 20
H
5
ㅏ
20
30
30
40
55
55
05 10 15 20 25 30 35 40 45 50 55 60
Degrees (F)
The correct option regarding the data-sets represented by the box and whisker plots is:
B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.For data-set A, we have that:
The 25th percentile is of 15.The median is of 20.The 75th percentile is of 30.Since 30 - 20 > 20 - 15, the distribution is positively skewed.
For data-set B, we have that:
The 25th percentile is of 20.The median is of 30.The 75th percentile is of 40.Since 40 - 30 = 30 - 20, the distribution is symmetric.
Hence the correct option is:
B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
I need help locating , x=,y=,z= please. Thanks
Select the order in which the operations should be performed
12-4/4
Divide 12 by 4, then subtract 4 from that number.
Divide 4 by 4, then subtract that number from 12.
Subtract 4 from 12, then divide that number by 4.
Subtract 4 from 12, then multiply that number by 4.
None of the above
Answer: Divide the 4/4 then subtract that from 12.
Step-by-step explanation:
Use PEMDAS. The Division comes first, then the subtraction.
In 1993, the moose population in a park was measured to be 4760. By 1999, the population was measured again to be 5960. If the population continues to change linearly:
The formula for moose population is P = 4760 + (number of years x 200).
The moose population in 2003 would be 6760.
What would be the moose population in 2003?When a population increases linearly, it means that it increases by the same amount each year.
Rate of linear increase: (population in 1999 - population in 1993) / difference in years
(5960 - 4760) / (1999 - 1993)
1200 / 6 = 200
Linear function : initial population + (rate of increase x number of years)
Population in 2003: 4760 + (200 x 10)
4760 + 2000 = 6760
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What is the multiplicity of f(x) = -2x3(x + 2)2?
PLS HELP!!!!
The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 27% of Carbon-14 as compared to a living sample. How old is the fossil?
Answer: 1547.10
Step-by-step explanation: Since you are not in a physics class, in which case requires the usage of the radioactive decay formula, definite integrals, and natural logarithms) but an Algebra class which deploys the usage of percentages, this should be rather simple.
I believe they want you to find 27% of the half life of Carbon-14 since it is below 50%. To find the percent of a number (in this case 27%), you multiply the number by 0.27.
5730 * 0.27 = 1547.10
Hope this helped! And if I'm wrong, please don't hesitate to correct me.
Let R(x)=3x3+2x2+x and S(x)=4x2+1. Find R(x)+S(x).
The function R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].
What is a function?An expression, rule, or law that describes a relationship between one variable (independent variable) and another variable (dependent variable) exists named a function.
Let the functions be [tex]R(x)=3x^3+2x^2+x[/tex] and [tex]S(x)=4x^2+1.[/tex]
Adding both of the equations, we get
[tex]$R(x)+S(x)=(3x^3+2x^2+x) +(4x^2+1)[/tex]
simplifying both of the equations we get
[tex]$R(x)+S(x)=3x^3+2x^2+x+4x^2+1[/tex]
[tex]=3x^3+6x^2+x+1[/tex]
Therefore, the function R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].
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In a hypothesis test, what should we conclude if the data would be very unusual if the original assumption about our parameter were correct?
We conclude the hypothesis test as Alternative Hypothesis if the data would be very unusual if the original assumption about our parameter were correct.
A hypothesis in statistics is a claim or supposition on the properties of one or more variables in one or more populations. There are two hypothesis to choose between because a statement might either be true or wrong.The null hypothesis is the assertion that we (or someone else) consider to be true. Our hypothesis test will come to one of two conclusions: "reject H0" or "do not reject H0." Remember that until data provide evidence to the contrary, we always proceed under the null hypothesis.If the null hypothesis is incorrect, the alternative hypothesis must be true. The hypothesis test can be different in one of three ways: greater than, smaller than, or just different (not equal). As a result, there will always be an inequality requirement in the notation for H.Learn more about Alternative hypothesis here: https://brainly.com/question/17173491
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A regular-size box of crackers measures 214 inches by 912 inches by 14 inches. The manufacturer also sells a snack-size box that has a volume that is 15 of the volume of the regular-size box. What is the volume of the snack-size box of crackers
Answer:
182,156.8
Step-by-step explanation:
214 x 912 x 14 = 2,732,352
1/15 of that Volume is 182,156.8
P.S. I'm assuming you meant 1/15, when you said the volume was 15 of
Follow my gram it's Greyhasnoshame
A softball pitcher has a 0. 431 probability of throwing a strike for each pitch. if the softball pitcher throws 22 pitches, what is the probability that exactly 12 of them are strikes?
The probability that exactly 12 of them are strikes is 0.09.
In this question,
Number of pitches, n = 22
Probability of throwing a strike for each pitch, p = 0.431
Then, q = 1 - p
⇒ q = 1 - 0.431
⇒ q = 0.569
Number of strikes, x = 12
The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,
[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]
⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]
⇒ P(X=12) = (646646)(0.000041)(0.00355)
⇒ P(X=12) = 0.09431 ≈ 0.09
Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.
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Can you please help me with this question
When you have negative exponents, you flip it around. Let me give you two examples below.
[tex]x^{-5} = \frac{1}{x^{5} }[/tex]
[tex]10^{-2} = \frac{1}{10^{2} }[/tex]
Therefore you will be doing: [tex]\frac{4}{1} * \frac{1}{10^{2} } = \frac{4}{1} * \frac{1}{100} } = \frac{4}{100} = \frac{1}{25}[/tex]
Your final answer is 1/25.
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Translate the triangle by
(-2
-4)
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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Instructions: Find the surface area of
each figure. Round your answers to the
nearest tenth, if necessary.
Surface Area:
5.2 cm.
cm²
Answer:
Given is radius of circle that is 5.2, you just need to find the area of the circle.
To find the are of circle is A=πr2
π value is 3.14 and radius value is 5.2 you just need to square the 5.2, answer will come 27.04
now multiply the πr and 27.04.
the answer will come 84.9 and question says to round to the nearest tenth, that will be 85.
Rounding to the nearest tenth, the surface area of the circle with a 5.2 cm radius is approximately 84.8 cm².
The surface area of a circle can be calculated using the formula:
Surface Area = π * radius²
where π (pi) is a mathematical constant approximately equal to 3.14159, and the radius is the distance from the center of the circle to any point on its edge.
Given the radius is 5.2 cm, we can now calculate the surface area:
Surface Area = 3.14159 * (5.2 cm)²
Surface Area = 3.14159 * 27.04 cm²
Surface Area ≈ 84.823 cm²
The surface area represents the total area of the circle's two-dimensional space. In this case, it gives us the total area of the circular region with a 5.2 cm radius.
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A diver is standing on a spring board 48 feet above the pool. She jumps from the platform with an
initial upward velocity of 8 feet /second. Use the formula d(t)= -16(2t - 3)(t+1), where d is the
height of the diver above the water and t is the time in seconds. How long will it take for her to hit
the water?
It will take the diver 1.5seconds for her to hit the water
Linear equationsLinear equations are equation that has a leading degree of 2. Given the expression that expresses the distance covered by the diver as a function of time as shown;
d(t)= -16(2t - 3)(t+1)
where;
d is the height of the diver above the water and;
t is the time in seconds.
Given the following
d = 0 (the distance on the ground)
Substitute into the formula below;
-16(2t - 3)(t+1)= 0
Divide through by -16
(2t - 3)(t+1) = 0
Determine the time
2t - 3 = 0
t = 3/2
Similarly;
t +1 = 0
t = -1
Hence it will take the diver 1.5seconds for her to hit the water
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The box plot shows the heights of grade 7 students in two random samples from two different schools. The sample from each school is 30% of the student population. Based on the box plot, which comparison is true?
image
A.
Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in the interquartile ranges of grade 7 student heights at the schools
B.
Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools.
C.
Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the interquartile ranges of grade 7 student heights at the schools.
D.
Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools.
The true statement is Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools. (option D)
What is the true statement?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.
The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Median for School A = 57
Median for School B = 61
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A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 record??
Answer: 5 games
Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.
Given sin theta=5/13 and cos theta=12/13, which of the following can be proven using a Pythagorean identity?
Answer:
4th option
Step-by-step explanation:
given
sinΘ = [tex]\frac{5}{13}[/tex] and cosΘ = [tex]\frac{12}{13}[/tex] , then
( [tex]\frac{5}{13}[/tex] )² + ( [tex]\frac{12}{13}[/tex] )²
= [tex]\frac{25}{169}[/tex] + [tex]\frac{144}{169}[/tex]
= [tex]\frac{25+144}{169}[/tex]
= [tex]\frac{169}{169}[/tex]
= 1
showing sin²Θ + cos²Θ = 1
Elena reflects the word 'MOM' over the x-axis and finds that it makes a new word. What is the new word?
If two solids are similar and have a linear ratio of 2:5, what is the ratio of the areas?
Answer:
4 : 25
Step-by-step explanation:
given 2 similar figures with linear ratio a : b , then
ratio of areas = a² : b²
here the linear ratio = 2 : 5 , then
area ratio = 2² : 5² = 4 : 25
Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle
[tex]5th \: row = 1 \: \: \: 5 \: \: \: 10 \: \: \: 10 \: \: \: 5 \: \: \: 1[/tex]
[tex](x - 4) {}^{5} = x {}^{5} + 5x {}^{4} ( - 4) {}^{1} + 10x {}^{3} ( - 4) {}^{2} + 10x {}^{2} ( - 4) {}^{3} + 5x( - 4) {}^{4} + ( - 4) {}^{5} [/tex]
[tex](x - 4) {}^{5} = x {}^{5} - 20x {}^{4} + 160x {}^{3} - 640x {}^{2} + 1280x - 1024[/tex]
How many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11?
Answer:
130
Step-by-step explanation:
The number of integers meeting the criteria can be found by counting them using a counting formula.
Divisible by 7Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...
7n ≤ 1000
n ≤ 142.857
There are 142 integers less than 1000 that are divisible by 7.
Divisible by 7 and 11Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.
77n ≤ 1000
n ≤ 12.987
There are 12 integers less than 1000 that are divisible by both 11 and 7.
Divisible by 7, not 11The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.
142 -12 = 130 integers divisible by 7, but not 11.
Simplify the expression. x≠0. (4x^2)^0
1
Step-by-step explanation:Anything raised to the power of zero is 1, other than zero itself.
However, as it is given that x is not equal to zero, the answer must be 1.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{(4x^2)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(4x^2)^0}\\\\\mathsf{= (4 \timesx^2)^0}\\\\\mathsf{= 4(x \times x)^0}\\\\\mathsf{= (4x^2)^0}\\\\\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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Which measurements of triangle BAC are correct
The measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
Trigonometrical ratiosFrom the question, we are to determine which of the given trigonometrical ratios for the given triangle are correct
The given triangle is a right angle triangle
Using SOH CAH TOA
sin C = 9/15
∴ The option sin C = 9/15 is correct
Also,
Using SOH CAH CAH
tan B = 12/9
∴ The option tan B = 9/12 is NOT correct
To determine the measure of angle B (m ∠B)
From tan B = 12/9
Then,
tan B = 1.33333
B = tan⁻¹(1.33333)
∴ B ≈ 53.13°
Thus, the option B ≈ 53.13° is correct
Hence, the measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
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G= -x^2 - 2xy - y^2
K= x^2 + 4y^2 + 4xy
H= 4x^2 - 12xy + 9y^2
L= 25 - 10 + y^2
M= 10y^4 + 25x^6 +y^8
Answer:
Step-by-step explanation:
I am assuming you want to factor these functions
G= -x^2 - 2xy - y^2
= -(x^2 + 2xy + y^2)
We need 2 terms whose product is y^2 and whose sum is +2xy
- they are + x and + y
= - (x + y)(x + y)
= -(x + y)^2
The other functions are worked out in the same way:
K = x^2 + 4y^2 + 4xy
= (x + 2y)(x + 2y)
= (x + 2y)^2
H = 4x^2 - 12xy + 9y^2
= (2x - 3y)^2
L= 25 - 10 + y^2
= (5 - y)^2
M = 10y^4 + 25x^6 +y^8
- this is prime (no factors)
Find the slope of the line.
Simplify completely.
1 2 3 4
-4 -3 -4 -1
-1
Slope = [?]
Hint: The slope of a line is the rise
run
The slope of a line is -2.
How to find the slope a line?The slope of a line can be described as follows:
The slope of a line is a measure of its steepness
Slope = rise / run
slope = y₂ - y₁ / x₂ - x₁
using (0, -4)(-1, -2)
x₁ = 0
x₂ = -1
y₁ = -4
y₂ = -2
Therefore,
slope = -2 - (-4) / -1 - 0
slope = -2 + 4 / -1
slope = 2 / -1
slope = -2
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how would i solve this?
Answer:
66.0 (nearest tenth)
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the poor drawing)
This is a pure trigonometry question.
Based on the question, we can use the TOA CAH SOH method.
[tex] \cos(x) = \frac{adj}{hypo} \\ \cos(32) = \frac{56}{x} \\ x \cos(32) = 56 \\ x = \frac{56}{ \cos(32) } \\ = 66.0 \: (nearest \: tenth)[/tex]
Please help..this is due tomorrow morning.