The number of groups, using the combination formula, for each case, is given as follows:
a) Same number of students from each grade: 1,245,816,000
b) At least two grade nine students: 31,650,886,995.
c) James and Lucy are in it: 2,481,256,778.
How to obtain the number of groups?The number of groups is obtained for the three cases using the combination formula, as the order in which the students are chosen is not important.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For item a, the same number of students is taken from each class, hence 3 students are taken from each class, as 12 students are taken from 4 classes, hence 12/4 = 3.
Hence the number of groups, considering the number of students in each class, is of:
[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]
For item b, we use complementary events, first obtaining the total number of students that can be taken, and then removing the combinations that do not have at least two grade nine students.
The total number of groups is obtained as follows:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
(as there are 10 + 11 + 12 + 13 = 46 students, and 12 are taken).
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
(removing the 10 students from grade 9).
The number of groups with one student from grade 9 is:
[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]
(one from grade 10 and the remaining from the other classes).
This the number of groups with at least two grade 9 students is calculated as follows:
38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.
For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set containing the 44 remaining students, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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Martina is taxed at a rate of 25% for her federal taxes. Last year, she reduced her taxable income by contributing to a flexible savings plan in the amount of $2,700. If her
wages before the deduction were $68,000, how much did she save in federal taxes by using the FSA?
▸
Answer:
14300
Step-by-step explanation:
this is the answer that I got I hope it works
Saving of Martina in taxes = $675
What is FSA?A flexible spending account (FSA) is a type of savings account, usually for healthcare expenses, that sets aside funds for later use. It is also known as a flexible spending arrangement, is one of a number of tax-advantaged financial accounts, resulting in payroll tax savings.
Given,
Wages of Martina = $68000
Tax rate = 25%
Amount to flexible savings = $2700
Then saving in taxes = $2700 × 25/100
= $675
Hence, Martina saved $675 in taxes using FSA.
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Consider the polynomial function []
p
given by p(x)=5x3+8x2−3x+1
A(x)
. Evaluate the function at x=−2
x
.
Tough question help asap
The function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Given,
The function; f(x) = 9 × 4ˣ
The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. coordinate's
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
We have to find the following function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Learn more about functions here;
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A taxi ride cost a customer a total of \$13.73$13.73dollar sign, 13, point, 73, which included 4\%4%4, percent sales tax and then a \$1$1dollar sign, 1 surcharge. What was the subtotal before the surcharge and sales tax?
The subtotal before the surcharge and sales tax is $12.2
How to determine the subtotal amount?In this question, we have the following parameters
Total = $13.73
Sales tax = 4%
Surcharge = $1
The above parameters imply that:
Total = Subtotal * (1 + sales tax) + Surcharge
Substitute the known values in the above equation, so, we have the following representation
13.73 = Subtotal * (1 + 4%) + 1
This gives
Subtotal * (1 + 4%) = 12.73
Divide both sides by 1.04
Subtotal = 12.2
Hence, the subtotal is $12.2
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Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students? 50 students 200 students 124 students 250 students
The number of students that chose band as an elective is 50
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic
let the total number of seats for choir be x and that for band be y
if there are 4 times as many seats as there in band then mathematically,
x = 4y.--------------------1
If there are 250 students, then, there would be 250 seats for the combined class.
so,
x + y = 250--------------2
substitute x = 4y in equation 2
4y + y = 250
5y = 250
y = 250/5
y = 50
In conclusion, 50 students can choose band.
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Bob invested his savings in two investment funds. The amount he invested in Fund A was 3 times as much as the amount he invested in Fund B. Fund A returned a 5% profit and Fund B returned a 7% profit. How much did he invest in Fund B, if the total profit from the two funds together was $2200?
The amount that he invested in Fund B if the total profit from the two funds together was $2200 is $8,800.
How to find the amount invested?Let x represent the amount invested in Fund B
Let 3x represent the amount invested in Fund A
Hence,
.07x + .05(3x) = 2200
.07x + .15x = 2200
.25x = 2200
Divide both side by .25x
x = 2200/.25
x = $8,800 (invested in Fund B)
Fund A:
3x = 3(8,800)
3x = $26,400 (Invested in Fund A)
Therefore $8800 was invested in Fund B.
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You have a 64-ounce pitcher of tea.
After you pour as many 7-ounce cups of tea as possible, how much tea will be left
over?
Answer:
You can pour nine 7-ounce cups of tea (63 ounces) and be left with one ounce of tea.
Step-by-step explanation:
Dividing 64 by 7 and finding the remainder.
two groups of hikers left camp at the same time. each traveled at a constant rate
group A covered 3/4 mile in 1/2 hour
It took Group B 3/4 hour to travel 1/3 mile
The group that travels faster when groups of hikers left camp at the same time and each traveled at a constant rate is group B.
How to calculate the rate?From the information, two groups of hikers left camp at the same time. each traveled at a constant rate.
Since group A covered 3/4 mile in 1/2 hour, the speed will be:
= Distance / Time
= 3/4 ÷ 1/2
= 1.5 miles per hour.
It took Group B 3/4 hour to travel 1/3 mile. The speed will be:
= Distance / Time
= 3/4 ÷ 1/3
= 2.25 miles per hour.
Group B had a faster speed.
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Complete question
Two groups of hikers left camp at the same time. each traveled at a constant rate
group A covered 3/4 mile in 1/2 hour
It took Group B 3/4 hour to travel 1/3 mile
Which group so travelling at a faster rate?
Which is bigger 21.17 or 2.117
Answer:
21.17
Step-by-step explanation:
If you were to round each number to the nearest whole number you would get :
21.17 ⇒ 21
2.117 ⇒ 2
Now the question is , which is bigger 21 or 2?
Now that is a very straightforward answer (21 in case your still lost)
Hope this helped and have a good day
find the difference in centimetres between 5m and 465cm
Answer:
35 cm
Step-by-step explanation:
pls help I don't get the problem
Simplified form is the -(1+sinα).
Given in question,
[tex]cos^{2}[/tex]α/sinα-1
[tex]sin^{2}[/tex]α + [tex]cos^{2}[/tex]α = 1
[tex]cos^{2}[/tex]α = 1 - [tex]sin^{2}[/tex]α
[tex]cos^{2}[/tex]α/sinα-1 = (1 - [tex]sin^{2}[/tex]α ) / (sinα-1)
= (1-sinα)(1+sinα)/(sinα-1)
= (1-sinα)(1+sinα)/-(1-sinα)
= (1+sinα)/-1
= -(1+sinα)
Hence, in simplified form [tex]cos^{2}[/tex]α/sinα-1 = -(1+sinα)
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K
Assume that females have pulse rates that are normally distributed with a mean of μ-750 beats per minute and a standard deviation of e=125 beats per minute. Complete parts (a) through (c) below
B. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 69 beats per minute and 81 bears per minute
The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute, using the normal distribution and the central limit theorem, is of:
0.663 = 66.3%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for the problem are given as follows:
[tex]\mu = 75, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]
The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute is the p-value of Z when X = 81 subtracted by the p-value of Z when X = 69, hence:
X = 81:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (81 - 75)/6.25
Z = 0.96
Z = 0.96 has a p-value of 0.8315.
X = 69:
Z = (69 - 75)/6.25
Z = -0.96
Z = -0.96 has a p-value of 0.1685.
0.8315 - 0.1685 = 0.663 = 66.3%.
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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Apply the properties of operations to multiply the expression
The properties of operations to multiply the expression are commutative property, associative property, and distributive property.
Let us understand the properties of operations to multiplication:
The foundation of arithmetic is the Properties of Operations; we use them when performing computations and recalling basic facts.
There are basically three properties of operations to multiplication which are:
Commutative Property: The commutative property of multiplication states that the order in which values are multiplied does not matter and will result in the same answer. That is to say: a * b = b * aAssociative Property: The associative property of multiplication states that when three or more numbers are multiplied, the order in which the multiplication occurs has no effect on the answer. That is to say: (a * b) * c = a * (b * c)Distributive Property: Students are asked to create two groups of six (2 x 6) using connecting cubes and to locate two hidden facts inside the 2 x 6 such as 2 x 3 and 2 x 3. That is: 2 x 6 = 2 x 3 + 2 x 3.Thus, the properties of operations to multiply the expression are commutative property, associative property, and distributive property.
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Can you solve please
Answer:
I'm assuming that you want to find x and y.
x = 18
y = 42
Step-by-step explanation:
Angle ACD = 138°
(5x + 2) + (2x + 10) = 138
7x + 12 = 138
7x = 126
x = 18
y + (5x + 2) + (2x + 10) = 180 (sum of adjacent angles on a straight line)
Substitute x = 18 into the equation.
y + 5(18) + 2 + 2(18) + 10 = 180
y + 90 + 2 + 36 + 10 = 180
y = 42
The point N lies on the segment MP
Find the coordinates of N so that MN is 3/7
of MP.
M(-4,6)
N (?,?
P (17,-22)
The coordinates of N are (5,-6) so that segment MN is 3/7 of MP.
Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).
now we have to find the coordinates of N such that the MN : NP is 3:4 .
We will use the section formula:
The section formula states that:
[tex]{\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}[/tex]
Where the coordinates of the points are given and the ratio in which the points are divided is given.
Now we will substitute the values:
[tex]{\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}[/tex]
Solving we get:
N=(5,-6)
The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.
Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.
Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.
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How does the graph of g(x) = (x − 4)3 + 5 compare to the parent function f(x) = x3?
The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.
What is transformation of function?
Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f (x) = x 2 + 3 is obtained by just moving the graph of g (x) = x 2 by 3 units up.
Given,
function g(x) = (x − 4)3 + 5 and compares to function f(x) = x3,
The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.
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Solve the inequality.
Question 1
3y≤−9
The solution is
The solution of the given inequality is y ≤ -3.
The given inequality is -
3y ≤ −9
We have to solve this given inequality.
Now, we have the inequality as -
3y ≤ −9
=> y ≤ -3
Thus, the solution of the given inequality is y ≤ -3.
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50 points to whoever answers!!
Answer:
create a line between (0,0) and (1,3)
the unit rate is 3/2 or 1.5
Step-by-step explanation:
pls mark
**BRAINLIEST** TO WHOEVER ANSWERS CORRECTLY! PLEASE HELP ME!
- During a certain time of year, the daily temperature in a certain city, in degrees Celsius follows a periodic pattern. The graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day.
- Write an equation for the graph below in terms of Y (temperature in degrees Celsius) and T (time in hours) to represent the given context.
ANSWER SHOULD BE IN THIS FORM
y = ( a ) sin ( b ) (t - h) + k
GRAPH IS GIVEN BELOW PLEASE HELP ME OUT!
Answer:
y = A cos B(x - C) + D
Step-by-step explanation:
The equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -
y = √180 sin (π/12.5)(t - 25) + 12
What is the general equation of a sinusoidal wave?The sinusoidal wave is of the form -
y{x} = A sin (ωt - kx + Ф)
Given is that during a certain time of year, the daily temperature in a certain city (in degrees Celsius) follows a periodic pattern.
We can write the amplitude as -
A = √(18 - 12)² + (13 - 1)²
A = √(36 + 144)
A = √180 ... { 1 }
{K} = 12 ... { 2 }
The time taken to complete one complete wave is 25 hours. So, we can write -
{T} = 25 ... { 3 }
ω = 2π/T = 2π/25 = π/12.5
{ω} = π/12.5 ... { 4 }
So, we can write the equation as -
y = √180 sin (π/12.5)(t - 25) + 12
Therefore, the equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -
y = √180 sin (π/12.5)(t - 25) + 12
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A pendant of gold alloy weighs 15/32 troy ounces. How many pendants can a jeweler make
from 5 5/8 troy ounces of gold alloy?
Solve the problem mathematically by finding the quotient.
The Jeweler makes the number of Pendants from the total weight of gold alloy = 12
The Jeweler has the total weight of gold alloy = 5 [tex]\frac{5}{8}[/tex] = 45/8 troy ounces.
Weight of a single gold alloy pendant = 15/32 troy ounces.
Jeweler makes the number of Pendants from the total weight of gold alloy = 45/8 ÷ 15/32.
Dividing Fractions by Fractions
We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,
x/y ÷ a/b
⇒ x/y × b/a (reciprocal of a/b is b/a)
⇒ xb/ya
Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.
45/8 ÷ 15/32 = 45/8 × 32/15 = 12
∴ The value of 45/8 ÷ 15/32 = 12.
Hence the Jeweler makes the number of Pendants from the total weight of gold alloy = 12
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I'm taking the math pert tomorrow I've failed it 2 times already I've been studying nonstop for the past two weeks and still feel like I'm going to fail any tips on how to pass ?
Help. I'll mark as brainlist. I am always giving brainlist points.
Answer: 18 square unit
Step-by-step explanation:
We can divide the shape into two pieces.
a triangle and a square.
The square is 2*6=12 square unit
and the triangle is 1/2*6*2=6 square unit
So if we sum this up we get the answer
answer = 6+12 = 18 square unit
Is this column graph skewed or symmetrical?? and if skewed what way?
Answer:
skewed to the right
Step-by-step explanation:
look at the graph
divide it in half
if both the sides are not equal then it is skewed
then to find out which way it is skewed look which side has more.
party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $25. The total cost to rent 6 chairs and 5 tables is $49. What is the cost to rent each chair and each table?
The cost to rent each chair and each table is $2.75 and $6.50 respectively.
How to calculate the cost?The total cost to rent 2 chairs and 3 tables is $25. This will be:
2c + 3t = 25
The total cost to rent 6 chairs and 5 tables is $49. This will be:
6c + 5t = 49
2c + 3t = 25
6c + 5t = 49
6 × (2c + 3t = 25)
2 × (6c + 5t = 49)
12c + 18t = 150
12c + 10t = 98
Subtract
8t = 52
Divide
t = 52/8
t = 6.5
Cost to rent table = $6.50
Since 2c + 3t = 25
2c + 3(6.5) = 25
2c + 19.5 = 25
Collect like terms
2c = 25 - 19.5
2c = 5.5
c = 5.5/2
c = 2.75
Cost to rent chair = $2.75.
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what do they mean, (Grade 10 real numbers)
X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.
So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.
So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.
help pleaseeeeee !!!
Answer:
[tex]\sqrt{6}, -\sqrt{6}[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+3x^2-6x-18 \\ \\ =x^2(x+3)-6(x+3) \\ \\ =(x^2-6)(x+3) \\ \\ \implies (x^2-6)(x+3)=0 \\ \\ x=\pm \sqrt{6}, -3[/tex]
Evaluate the expression.
−5 × (−8 − 6 ÷ −3)
Answer:
=30
Step-by-step explanation:
-5×(-8-6÷-3)-5×(-8+2)........as -6÷-3=2-5×-630A continuous random variable is normally distributed. The probability that a value in the distribution is greater than 23 is 0.6784. Find the probability that a value in the distribution is less than 23.
The probability that are a normally distributed variable is less than 23 is 0.3216
What is normal distribution?The most significant probability distribution in statistics for independent, random variables is the normal distribution, sometimes referred to as the Gaussian distribution.
In statistical reports, its well-known bell-shaped curve is generally recognized.
While calculating for probability for normally distributed variables the relationship the relationship is written in the form
P > 23 = 1 - P < 23
0.6784 = 1 - P < 23
P < 23 = 1 - 0.6784
P < 23 = 0.3216
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Angles X and Y are supplementary. Angle X measures 127.42°, and angle Y measures (m − 12)°. Find m∠Y. anwsers 115.42° 74.84° 64.58° 52.58°
The measure of angle Y, m ∠Y, is 52.58°. The correct option is the last option 52.58°
Calculating the measure of an angleFrom the question, we are to determine the measure of angle Y.
From the given information,
Angles X and Y are supplementary angles.
NOTE: Supplementary angles are angles that sum up to 180°
Thus,
m ∠X + m ∠Y = 180°
Also,
From the given information,
Angle X measures 127.42°
That is,
m ∠X = 127.42°
Therefore,
127.42° + m ∠Y = 180°
m ∠Y = 180° - 127.42°
m ∠Y = 52.58°
Hence, the measure of the angle is 52.58°
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