The number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is; 705 ways
How to solve permutation and combination?The formula for probability combination is;
nCr = n!/(r! * (n – r)!)
where;
n is the total number of items.
r is the number of things that may be selected at one time.
The number of ways that 2 students can be selected from the senior class is;
N(2 students from the SR class) = 3C2 * 10C2 = 135 ways
Similarly;
N(1 student from the SR class) = 3C1 * 10C3 = 360
N(0 students from the SR class) = 3C0 * 10C4 = 210
Thus, number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is;
135 + 360 + 210 = 705 ways
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Q4.
The 5th term of an arithmetic series is 4k, where k is a constant.
The sum of the first 8 terms of this series is 20k + 16
(a) (i) Find, in terms of k, an expression for the common difference of the series.
(ii) Show that the first term of the series is 16 - 8k
Given that the 9th term of the series is 24, find
(b) the value of k,
(c) the sum of the first 20 terms.
Answer:
check the attached file
Step-by-step explanation:
identifying values in the domain f(x)=x-3/x+2
The rational function f(x) = (x - 3) / (x + 2) have a domain corresponding to any real number except x = - 2.
What is the domain of a rational equation?
In this problem we find a defined rational functions whose numerator and denominator are both linear equation. The domain of a function is the set of all values of x such that f(x) exists.
By function theory, the domain of all linear equations is the set of all real numbers and the domain of rational equations is the domain of the numerator except the values of x such that the denominator becomes zero.
Then, we need to determine the values of x such that:
x + 2 = 0
x = - 2
The domain of the rational function f(x) = (x - 3) / (x + 2) is all the real numbers except x = - 2.
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The exponential model A = 796.2e0.006t describes the population, A, of a country in millions, t years after
2003. Use the model to determine the population of the country in 2003.
Answer:
796.2 million
(796,200,000)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=ae^{kx}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\\end{minipage}}[/tex]
Given exponential function:
[tex]A=796.2e^{0.006t}[/tex]
where:
A is the population of the country in millions.t is the number of years after 2003.The initial value is 796.2, which means the population of the country in 2003 was 796.2 million.
Which graph represents the function f(x)=4x?
Responses
Answer:
slope = 4
points on graph = (0,0), (1,4)
Step-by-step explanation:
line going through quadrants 1 and 3. Straight line.
I need to show work
#1. (-2/7) + (-4/7)
#2. 5.4+ (-8.6)
Answer:
#1. -6/7
#2. -3.2
Step-by-step explanation:
#1. (-2/7) + (-4/7)
You are adding two negative numbers.
When you add two positive numbers or two negative numbers, just ignore the signs and add the numbers as positive numbers. Then the answer has the same sign as the original numbers.
Step 1. Ignore the signs and make both numbers positive.
Add 2/7 and 4/7.
2/7 + 4/7 = 6/7
Step 2. Since the two numbers are originally negative, the answer is negative.
(-2/7) + (-4/7) = -6/7
#2. 5.4 + (-8.6)
When you add a positive number and a negative number, first make both numbers positive. Then, subtract the smaller positive number from the larger positive number. Finally, the answer has the same sign as the original number that corresponds to the larger positive number.
Here we do it step by step.
5.4 + (-8.6)
Step 1. Make both numbers positive. The numbers now are:
5.4 and 8.6
Step 2. Subtract the smaller positive number from the larger positive number.
8.6 - 5.4 = 3.2
Now look at the two positive numbers. 5.4 and 8.6. The larger number is 8.6. The original number that 8.6 came from is -8.6, a negative number, so the answer is negative.
5.4 + (-8.6) = -3.2
SOLVE FOR P!
2p − 10 = –2
P=
the larger number is 18 more than twice the smaller . if the sun of the numbers is 93 find both numbers
Answer: The numbers are 25 and 68.
Step-by-step explanation:
Answer:
x = 68
y = 25
Step-by-step explanation:
Let the larger number be x and smaller number be y.
Condition 1:x = 18 + 2y ----------------(1)
Condition 2:x + y = 93 -----------------(2)
Put Eq. (1) in Eq. (2)
18 + 2y + y = 93
18 + 3y = 93
Subtract 18 to both sides
3y = 93 - 18
3y = 75
Divide 3 to both sides
y = 72/3
y = 25Put y = 24 in Eq. (1)
x = 18 + 2(25)
x = 18 + 50
x = 68[tex]\rule[225]{225}{2}[/tex]
Let a,b,c be positive real numbers. Prove the inequality
[tex]\dfrac{(a+b)^2}{c} +\dfrac{c^2}{a} \geq 4b.[/tex]
If a,b,c are positive real numbers, the inequality [tex]\frac{(a+b)^{2} }{c} +\frac{c^{2} }a[/tex] [tex]\geq 4b[/tex] is not correct because it gives the value a³+2a²b+ab²≥4abc
How to find the solution set of an inequality?
Inequality is a mathematical statement showing that two quantities are not equal.
The given inequality is [tex]\frac{(a+b)^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex][tex]\geq[/tex]4abc
Simplifying the inequality we have [tex]\frac{(a+b)(a+b)}{c}[/tex] +[tex]\frac{c^{2} }{a }[/tex] [tex]\geq[/tex]4b
This implies that: [tex]\frac{a^{2}+ab+ab+b^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex] [tex]\geq[/tex] 4b
Taking the LCM,
[tex]\frac{a^{2}+2ab+b^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex] [tex]\geq[/tex]4b
Simplifying further
[tex]\frac{a^{3}+2a^{2}b+ab^{2}+c^{3} }{ac}[/tex] [tex]\geq[/tex]4b
The expression gives that: a³+2a²b+ab²≥4abc
Comparing the values of a,b,c on both sides of the inequality, the inequality is wrong.
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Find the midpoint of the line segment from (1,-3) to(-5,2)
Midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).
What is straight line?A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.
The midpoint of a line segment is a point that lies exactly halfway between two points
The formula for midpoint (x,y)=(x₁+x₂/2,y₁+y₂/2)
We need to find midpoint of the line segment from (1,-3) to(-5,2)
Midpoint=(1-5/2,-3+2/2)
=(-4/2, -1/2)
=(-2,-1/2)
Hence, midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).
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Consider the following data of mathematics students.
60 study French, 30 study French and German
55 study German, 25 study French and Russian
75 study Russian, 35 study German and Russian
12 students study all the three languages.
Let F, G, R denote the set of students studying French, German and Russian respectively. Then find the number of students studying at least one of the three languages i.e, n(FUGUR)
The value of n (FUGUR) will be;
⇒ n (FUGUR) = 112
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The data of mathematics students is,
60 study French, 30 study French and German
55 study German, 25 study French and Russian
75 study Russian, 35 study German and Russian
12 students study all the three languages.
Now,
Let F, G, R denote the set of students studying French, German and Russian respectively.
And, The data of mathematics students is,
n (F) = 60, n (F ∩ G) = 30
n (G) = 55, n (F ∩ R) = 25
n (R) = 75 , n (G ∩ R) = 35
n (F ∩ G ∩ R) = 12
Since, We know that;
⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)
+ n (F ∩ G ∩ R)
Substitute all the values, we get;
⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)
+ n (F ∩ G ∩ R)
⇒ n (FUGUR) = 60 + 55 + 75 - 30 - 25 - 35 + 12
⇒ n (FUGUR) = 112
Thus, The value of n (FUGUR) will be;
⇒ n (FUGUR) = 112
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The ratio of a to b is constant, and a = 9 when b = 6. What is the value when a = 2? Round your answer to the nearest hundredths, if necessary
If ratio of a to b is constant, and a = 9 when b = 6 then value of b is 4/3 when a is 2.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
The ratio of a to b is constant,
a = 9 when b = 6.
We need to find value of b when a=2.
Let us consider the value be x.
Let us form an equation
9/6=2/x
Apply cross multiplication
9x=12
Divide both sides by 9
x=12/9=4/3
Hence, if ratio of a to b is constant, and a = 9 when b = 6 then value of b is 4/3 when a is 2.
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Evaluate the expression: −(8 − 12) + 60 + (−4)2.
Answer: 80
Step-by-step explanation:
⇒ −(8 − 12) + 60 + (−4)²
⇒ -(-4) + 60 + 16
⇒ 4 + 60 + 16
⇒ 80
Graph the following equation using a table of values,
y=x+10
Answer:
The table in the attached figure N 1
The graph in the attached figure n 2
Step-by-step explanation:
we have
x+2=y
we know that
To graph a linear equation the best way is plot the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
0+2=y
y=2
The y-intercept is the point (0,2)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For y=0
x+2=0
x=-2
The x-intercept is the point (-2,0)
Find additional points to create a table (is not necessary for plot the line)
For x=1
1+2=y
y=3
For x=2
2+2=y
y=4
The table in the attached figure N 1
Graph the linear equation ------> plot the intercepts a joined the points
see the attached figure N 2
Which equation models the line on the graph?
Answer:
C) y - 2 = 2 ( x - 3 )
Step-by-step explanation:
This is point-slope form btw. Hope it helps!
which property justifies the step?
2x +3 = -5x -1
7x + 3 = -1
A. distrubutive property
B. addition property of equality
c. commutative property
D. subtraction property of equality
The required property justifies the step is an addition property of equality.
What is mathematical property?
The rules governing how numbers relate to and interact with one another are known as mathematical properties. There are four fundamental properties. i.e. distributive, addition, commutative and subtraction.
Given, 2x +3 = -5x -1
Applying addition property of equality,
Adding 5x to both sides, we get
7x + 3 = -1
Hence, the required property justifies the step is an addition property of equality.
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Car makers (Toyota, Ford, Honda, Hyundai, etc.) often provide low-interest financing to attract people to buy: 3%, 2%, 1%, and even 0%. A 1% loan for 4 years ends up costing about 2% of the original loan. How much total interest is paid for a $20,000 loan?
Using the formula of simple interest, the total interest paid on a $20000 loan at rate of 2% over 4 years is $1600
Simple InterestSimple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.The formula is given S.I = P(1 + RT)
Data;
P = 20000r = 2%t = 4 yearsS.I = 20000(1 + 0.02 * 4)
S.I = 21600
The total interest paid is 21600 - 20000 = 1600
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Simplify the Expressions Drag and drop the matching
The simple form of all the expressions are:
-3 + 4m + (-7) - 6m = -2m -10
6x + (-1) - 3x + 12 = 3x + 11
3xy +2z - 16 + 6xy = 9xy +2z - 16
-4x - 8 + 2x + (-3) - 5x = -7x - 11
3m² - m + 7 + 3m² + 1 = 6m² - m + 8.
What is the simple form of the polynomial?
f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.
We have,
-3 + 4m + (-7) - 6m
6x + (-1) - 3x + 12
3xy +2z - 16 + 6xy
-4x - 8 + 2x + (-3) - 5x
3m² - m + 7 + 3m² + 1
The simple form of the expressions:
-3 + 4m + (-7) - 6m
= -2m -10
6x + (-1) - 3x + 12
= 3x + 11
3xy +2z - 16 + 6xy
= 9xy +2z - 16
-4x - 8 + 2x + (-3) - 5x
= -7x - 11
3m² - m + 7 + 3m² + 1
= 6m² - m + 8
Hence, the simple form of all the expressions are:
-3 + 4m + (-7) - 6m = -2m -10
6x + (-1) - 3x + 12 = 3x + 11
3xy +2z - 16 + 6xy = 9xy +2z - 16
-4x - 8 + 2x + (-3) - 5x = -7x - 11
3m² - m + 7 + 3m² + 1 = 6m² - m + 8
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WILL GIVE BRAINLIEST Suppose that the functions q and r are defined as follows.
q (x) = x^2 + 7
r (x) = [tex]\sqrt{x+4}[/tex]
Find the following:
(r *q) (5) =
(q *r) (5) =
The values of the composite functions are
(r * q)(5) = 96
(q * r)(5) = 96
How to evaluate the composite functions?From the question, we have the following functions that can be used in our computation:
q(x) = x² + 7
r(x) = √(x + 4)
The composite functions are given as
(r * q)(5) and (q * r)(5)
The base functions of the above composite functions are
(r * q)(x) and (q * r)(x)
And they are calculated using
(r * q)(x) = r(x) * q(x)
(q * r)(x) = q(x) * r(x)
Substitute the known values in the above equations
So, we have the following equations
(r * q)(x) = (x² + 7) * (√(x + 4))
(q * r)(x) = (√(x + 4)) * (x² + 7)
Substitute 5 for x
(r * q)(5) = (5² + 7) * (√(5 + 4))
(q * r)(5) = (√(5 + 4)) * (5² + 7)
Evaluate the equations
(r * q)(5) = 96
(q * r)(5) = 96
Hence, the solution of the composite functions is 96
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Solve the system of equations.
2/3 x - y/2 = 17/6
x/4 - 5/8 y = 5/8
Answer:
x = 3y/4 + 17/4 and
x = 5y/2 + 5/2
Step-by-step explanation:
hope this help
at the zoo 1/3 of the animals are mammals. 1/4 of the mammals are elephants. what fractuon of the animals at the zoo are elephants
Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].
What is the fraction?
A fraction defined as the part of the whole thing.
Fractions help to distribute and judge the numbers easily and make the calculation faster.
Here given that,
At the zoo [tex]\frac{1}{3}[/tex] of the animals are mammals [tex]\frac{1}4}[/tex] of the mammals are elephants.
So, the fraction of the animals at the zoo are elephants is
[tex]\frac{1}3}+\frac{1}{4}=\frac{4+3}{12}\\\\=\frac{7}{12}[/tex]
Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].
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The cleaning service charges $15 per hour. Mr. Henrickson is hiring the cleaning service but does not want to spend more that $75. What is the maximum number of hours that he can hire the cleaning service? Write an inequality and solve.
The maximum number of hours that he can hire the cleaning service is 5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us consider the number of hours for which the total cost would be the same be x
The first equation would be
$15x > $75
Now equate these equations
$15x - $75 = 0
15x = 75
x = 5
Hence, the maximum number of hours that he can hire the cleaning service is 5.
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2x - 7 + 3x + 10 > x - 6 + 8x - 11
The answer would be (5,0)
You have $20 to spend and apples cost $1 per apple. The independent variable is apples. What is the Range and Domain?
The Range and Domain for the apples as per the given information is (1, 20) and (1, 20).
What is meant by range?The difference between the greatest and lowest values of a set of integers is defined as its range. To find it, subtract the distribution's lowest number from its highest.
Because the term "range" can have multiple meanings, it is recommended that it be defined the first time it is used in a textbook or article. When older books use the term "range," they usually indicate what is currently known as the codomain. More recent works, if they use the phrase "range," usually use it to refer to what is now known as the picture. A number of current books avoid using the word "range" entirely to avoid confusion.
Given,
We need to spend $20 for each apple
And also given that,
The cost of each apple is $1
Here the independent variables are apples
Range=(1, 20)
Domain=(1, 20)
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16.5 + 2.75h = 9h + 7.5 − 4.25h for h. please show how you got
Answer:
h = 4.5
Step-by-step explanation:
16.5 + 2.75h = 9h + 7.5 − 4.25h
Combine like terms on the right side.
16.5 + 2.75h = 4.75h + 7.5
Subtract 4.75 h from both sides.
16.5 - 2h = 7.5
Subtract 16.5 from both sides.
-2h = -9
Divide both sides by -2.
h = 4.5
Answer:
h = 1.2
Step-by-step explanation:
1.) Isolate the variable H. To isolate the variable H, you have to move numbers onto one side and variable onto another. I will show this process in the next steps:
2.) First, move the numbers onto one side. You will subtract 7.5 on both sides, ending up with 16.5 - 7.5 + 2.75h = 9h - 4.25h.
3.) Now, move the variable to one side. You will subtract 2.75h on both sides, and get 16.5 - 7.5 = 9h - 4.25h + 2.75h.
4.) Finally, Simplify. 16.5 - 7.5 = 9. 9h - 4.25h + 2.75h = 7.5h. Therefore, 7.5h = 9.
5.) If we divide both sides by 7.5, we get h = 9/7.5, which is 1.2. By this, h = 1.2
y = 5x + 4
y = 5x - 2
One solution
No solution
Infinite solution
Answer: No solution
Step-by-step explanation:
Since both equations are equal to y you can set them equal to each other
5x+4=5x-2
0=-6
zero does not equal -6 which is that there is no solution.
Answer:
Step-by-step explanation:
the answer is 2 1/2 miles
Find the value of c guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].
The value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].
What is Mean Value Theorem?Mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
Given.
Function is 2x+1 on the interval [3,6]
f(x)=2x+1
f(x) continuous on [3, 6] and differentiable on (3, 6) so the MVT applies here.
f(3)=7
f(6)=13
Average rate of change of f on [3,6]
= (13-7) / (6-3) = 6/3=2
To find the c-value guaranteed by the MVT, such that the instantaneous rate of change when x = c is 2, we differentiate, set f'(x) = 2, and solve:
f'(x) = 2 and x = 1.
c = 0 is the only c-value in the interval at which the instantaneous rate of change = the average rate of change.
Hence, the value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].
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Graph
50 points
Marking brainliest
Answer:
[tex]\textsf{Vertex form}: \quad f(x)=(x-4)^2+2[/tex]
[tex]\textsf{Standard form}: \quad f(x)=x^2-8x+18[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
From inspection of the given graph:
vertex = (4, 2)y-intercept = (0, 18)Substitute the vertex and point (0, 18) into the vertex formula and solve for a:
[tex]\begin{aligned}y&=a(x-h)^2+k\\\implies 18&=a(0-4)^2+2\\18&=a(-4)^2+2\\18&=16a+2\\16a&=16\\a&=1\end{aligned}[/tex]
Substitute the found value of a and the vertex into the formula:
[tex]\implies y=1(x-4)^2+2[/tex]
[tex]\implies f(x)=(x-4)^2+2[/tex]
To write the equation in standard form, expand the brackets:
[tex]\implies f(x)=(x-4)^2+2[/tex]
[tex]\implies f(x)=(x-4)(x-4)+2[/tex]
[tex]\implies f(x)=x^2-8x+16+2[/tex]
[tex]\implies f(x)=x^2-8x+18[/tex]
Describe and correct the error in writing an equation of the line that passes through (1, 3) and is parallel to the line y=1/2x+2
The equation of the line that is parallel to the line y = 1/2x + 2 is: y = 1/2x + 5/2.
How to Write the Equation of Parallel Lines?Recall that if two lines are parallel, they will have the same slope (m).
Slope of a line (m) = change in y / change in x.
The slope (m) of the equation, y = 1/2x + 2, that represents a line is 1/2.
This means that the line that is parallel to it will also have a slope (m) that is equal to 1/2.
Find the y-intercept by substituting m = 1/2 and (x, y) = (1, 3) into y = mx + b:
3 = 1/2(1) + b
3 = 1/2 + b
3 - 1/2 = b
5/2 = b
b = 5/2
To write the equation of the parallel line, substitute m = 1/2 and b = 5/2 into y = mx + b:
y = 1/2x + 5/2.
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Find an equation of the line that goes through the points (7,20) and (2,10). Write your answer in the slope-intercept form, y = mx + b.
Answer: y =
The linear equation of the line that goes through points (7,20) and (2,10) is y = 2x + 6.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
Now,
At x = 0 ⇒ y = b so it will be a y-intercept.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (10 - 20)/(2 - 7) = 2
Substitute,(2,10) and m = 2
10 = 2(2) + b
b = 6
Thus, the equation will be y = 2x + 6
Hence "The linear equation of the line that goes through points (7,20) and (2,10) is y = 2x + 6".
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Select a newspaper or magazine article that involves a statistical study and write a paper answering these questions. 1.Is this study descriptive or inferential? Explain your answer. 2.What are the variables used in the study? In your opinion, what level of measurement was used to obtain the data from the variables? 3.Does this article define the population? If so, how is it defined? If not, how could it be defined? 4.Does the article state the sample size and how the sample was obtained? If so, determine the size of the sample and explain how it was selected. If not, suggest a way it could have been obtained. 5.Explain in your own words what procedure (survey, comparison of groups, etc.) might have been used to determine the studys conclusions. 6.Do you agree or disagree with the conclusions? State your reason.
There are 300 students at Josefa Espinoza School.
reported viral illnesses very ... so the
in charge of the health of the Wisconsin area health department,
The study was in total in a sample of 60
According to the question. A journal article that involves a statistical study.
find:
a) The study descriptive or inferential
Yes, know the study is infrential according to the obtained from
Data
find :-) The Variable used in study. low,
과 a continuous variable. is size and weight
Know The sample is varied and representative