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.
What is the combination formula?[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 groups are taken as follows:
3 students from grade 9, from a set of 10.3 students from grade 10, from a set of 11.3 students from grade 11, from a set of 12.3 students from grade 12, from a set of 13.Hence the number of groups is:
[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, the total number of groups, without considering the restriction, is:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
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]
Using complementary events, the number of groups with at least two grade 9 students is:
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 of 44, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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What is the simplified value of the exponential expression 27
1/3
Answer:
3
Step-by-step explanation:
[tex]27^{\frac{1}{3}}[/tex]
1 ) Factor the number [tex]27=3^{3}[/tex]
[tex]=\left(3^3\right)^{\frac{1}{3}}[/tex]
2 ) Simplify...
3
Hope this helps! :)
Function or not
x y
-10 5
4 -4
-8 6
7 5
-10 5
Answer: function
Step-by-step explanation: for ever input the is one output, even though -10,5 showed up multiple times it had the same input and output. So it’s a function …if I remember correctly.
If the 5 is negative on just one, it’s not a function.
so sorry if it’s wrong, best of luck :)
Show how to add the following by adding the opposite: 8-(-3)
Can someone please find the area of the shaded area? Thanks! :) I’ll give brainly
Answer:
87 [tex]ft^{2}[/tex]
Step-by-step explanation:
11x9=99
99 ft is the area of the rectangle
Now we need the area of the triangle
4x6=24
24/2=12
12 ft is the area of the triangle so we subtract this from the area of the rectangle
99-12=87
Hopes this helps please mark brainliest
Describe the function‘s end behavior. f(x)=−10+6x^5+4x^3
as x→ ∞, f(x)→
as x→ −∞, f(x)→
Possible answers for both are:
-∞
∞
0
an asymptote
We have an odd degree polynomial wit a positive leading coefficient, then the end behavior is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
What is the end behavior of the function?Here we have the function:
f(x) = -10 + 6x^5 + 4x^3
Notice that this is a polynomial of degree 5 (odd degree).
When we have a odd degree polynomial, we know that:
If the leading coefficient is positive, then the end behavior is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
If instead, the leading coefficient is negative, then:
as x → -∞, f(x) → ∞
as x → ∞, f(x) → -∞
For the case of:
f(x) = −10+6x^5+4x^3
The leading coefficient is 6, so it is positive, then the end behavior of our function is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
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The population of a city has increased by 15% since it was last measured. If the current population is 27,600, what was the previous population?
The previous population for the city is 23460.
How to calculate the previous population?Given that the population of a city has increased by 15% since it was last measured, the previous population will be:
= 1 - 15%
= 85%
Therefore, the previous population will be:
= Percentage × New population
= 85% × 27600
= 0.85 × 27600
= 23460
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What is the slope of a line perpendicular to the line whose equation is 2x+3y=24 Fully simplify your answer.
Answer:
y = -2/3 x + 8
Step-by-step explanation:
here is the answer in the image above
what is the answer for this question I am stuck
The area of triangle XYZ in the given graph with points X(-6,-5), Z(-4,-2) and Y(-2,-6) is 4 units square.
If the triangle's three vertices are specified on the coordinate plane, the area of a triangle in coordinate geometry may be determined. In coordinate geometry, a triangle's area is the area or space it occupies in the 2-D coordinate plane. The formula for finding the area of a triangle with three coordinates [tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex] is as follows:
Area of triangle [tex]=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Now, finding the area of trianlge with points X(-6,-5), Z(-4,-2) and Y(-2,-6).
Area of triangle [tex]=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
[tex]=\frac{1}{2}|-6(-2+5)-4(-6+5)+-2(-5+2)|\\=\frac{1}{2}\times|-18+4+6|\\ =4[/tex]
Therefore, the area of triangle XYZ in the given graph is 4 units square.
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If 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. Find the probability of more than 5 people use the emergency room.
The probability of more than 5 people is 0.4729
Find the probability of more than 5 people use the emergency room?Since 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. To find the probability of more than 5 people use the emergency room, we use binomial probability.
What is binomial probability?The binomial probability of x is given by P(X = x) = ⁿCₓpˣ(1 - p)ⁿ⁻ˣ
where
n = number of total trialsp = probability of event andx = number of required trialsSince
n = 11, p = 49% = 0.49 and x = 5,We determine the probability of x ≤ 5.
So, P(X ≤ 5) = ¹¹C₀p⁰(1 - p)¹¹⁻⁰ + ¹¹C₁p¹(1 - p)¹¹⁻¹ + ¹¹C₂p²(1 - p)¹¹⁻² + ¹¹C₃p³(1 - p)¹¹⁻³
+ + ¹¹C₄p²(1 - p)¹¹⁻⁴ + ¹¹C₅p⁵(1 - p)¹¹⁻⁵
= ¹¹C₀(0.49)⁰(1 - 0.49)¹¹ + ¹¹C₁(0.49)¹(1 - 0.49)¹⁰ + ¹¹C₂(0.49)²(1 - 0.49)⁹ + ¹¹C₃(0.49)³(1 - 0.49)⁸
+ ¹¹C₄(0.49)⁴(1 - p)⁷ + ¹¹C₅(0.49)⁵(1 - 0.49)⁶
= (1)(1)(0.51)¹¹ + (11)(0.49)(0.51)¹⁰ + (55)(0.49)²(0.51)⁹ + (165)(0.49)³(0.51)⁸
+ (330)(0.49)⁴(0.51)⁷ + (462)(0.49)⁵(0.51)⁶
= 0.0006071 + (11)(0.49)(0.0011904) + (55)(0.2401)(0.0023341) + (165)(0.117649)(0.0045768)
+ (330)(0.0576480)(0.0089741) + (462)(0.0282475)(0.0175963)
= 0.0006071 + 0.0064163 + 0.0308230 + 0.0888452
+ 0.1707218 + 0.2296378
= 0.5270512
≅ 0.5271
So, P(X ≤ 5) = 0.5271, the probability of more than 5 people is P(X ≥ 5) = 1 - P(X ≤ 5)
= 1 - 0.5271
= 0.4729
The probability is 0.4729
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Find the distance from point A to XZ . Round your answer to the nearest tenth.
The distance is about (Blank)
units.
Using the distance formula, the distance between A to point Z to the nearest tenth is 4.1 .
How to find the distance using the coordinates?The 2D distance formula gives the shortest distance between two points in a two-dimensional plane.
Using the distance formula,
d = √(y₂ - y₁) + (x₂ - x₁)²
let's use the distance formula, to find the distance between point A and XZ.
Using the coordinates,
A(3, 3) and XZ(4, -1)
Therefore,
x₁ = 3
x₂ = 4
y₁ = 3
y₂ = -1
d = √(4 - 3)² + (-1 - 3)²
d = √1² + (-4)²
d = √1 + 16
d = √17
Therefore,
d = 4.12310562562
d = 4.1
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Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.)
x = -8,0, 1; n = 3
Answer: f(x) = x³ + 7x² -8x
Step-by-step explanation:
Zeros means that at that x-value, the graph crosses the x-axis and y = 0. Hence, to meet those criteria, the function would be:
[tex]f(x)=x(x+8)(x-1)[/tex]
At those three x-values, the corresponding y-values would equal 0.
Multiply them out to find the polynomial function:
[tex]f(x)=x(x+8)(x-1)=x(x^{2} -x+8x-8)=x^{3} +7x^{2} -8x[/tex]
How many tons are in 12,000 pound
Answer: 12,000pd=6 tons
Step-by-step explanation:
suppose that $36,000 is deposited in an account and the balance increases to $39,786.15 after 2.5 years. how long will it take for the account to grow to $51,806.67? Assume continous compounding
It will take about _ years for $36,000 to grow to $51,806.67
Answer:
About 9 years===================================
Continuous compounding equation:
[tex]P(t) = P_0e^{rt}[/tex]Given[tex]P_0=36000[/tex][tex]P(t)=39.876.15[/tex][tex]t=2.5[/tex]Find the value of r[tex]39786.15= 36000*e^{r*2.5}[/tex][tex]e^{2.5r}=39786.15/36000[/tex][tex]ln \ e^{2.5r}= ln \ 1.10517[/tex][tex]2.5r=0.099[/tex][tex]r=0.099/2.5[/tex][tex]r=0.04[/tex]Now find the time t for the balance to grow to $51806.67:
[tex]51806.67= 36000*e^{0.04t}[/tex][tex]51806.67/36000=e^{0.04t}[/tex][tex]e^{0.04t}= 1.439[/tex][tex]ln \ e^{0.04t}= ln \ 1.439[/tex][tex]0.04t=0.3639[/tex][tex]t=0.3639/0.04[/tex][tex]t=9.0975[/tex]The time required is about 9 years.
Answer:
9 years
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).Given values:
P = $36,000A = $39,786.15t = 2.5 yearsSubstitute the given values into the formula and solve for r to find the annual interest rate:
[tex]\implies \sf 39786.15=36000 \cdot e^{2.5r}[/tex]
[tex]\implies \sf \dfrac{39786.15}{36000}= e^{2.5r}[/tex]
[tex]\implies \sf \ln \left(\dfrac{39786.15}{36000}\right)=\ln e^{2.5r}[/tex]
[tex]\implies \sf \ln \left(\dfrac{39786.15}{36000}\right)=2.5r[/tex]
[tex]\implies \sf \dfrac{1}{2.5}\ln \left(\dfrac{39786.15}{36000}\right)=r[/tex]
[tex]\implies \sf r=\dfrac{2}{5}\ln \left(\dfrac{39786.15}{36000}\right)[/tex]
[tex]\implies \sf r=0.03999996933...[/tex]
[tex]\implies \sf r=0.04\;(2\;d.p.)[/tex]
Therefore, the annual interest rate is 0.04 = 4%.
To calculate how many years it will take for $36,000 to grow to $51,806.67, substitute the values into the formula and solve for t:
[tex]\implies \sf 51806.67=36000 \cdot e^{0.04t}[/tex]
[tex]\implies \sf \dfrac{51806.67}{36000}= e^{0.04t}[/tex]
[tex]\implies \sf \ln\left(\dfrac{51806.67}{36000}\right)= \ln e^{0.04t}[/tex]
[tex]\implies \sf \ln\left(\dfrac{51806.67}{36000}\right)= 0.04t[/tex]
[tex]\implies \sf \dfrac{\ln\left(\dfrac{51806.67}{36000}\right)}{0.04}=t[/tex]
[tex]\implies \sf t=9.10 \; (2\;d.p.)[/tex]
Therefore, it will take about 9 years for $36,000 to grow to $51,806,67.
358.584 divided by 9.92
Answer:
36.147580645161
Step-by-step explanation:
Hope it helps you
4+3 × (2 − 1) + 8 + (9-7)
Answer:
1
Step-by-step explanation:
Answer:17
Step-by-step explanation:
its just the order of operations aka PEMDAS If you want to know more about the order of operations just look it up. :)
NO LINKS!! Use the diagram below to answer the following questions. Part 3
Answer:
a) Line r
b) Line q
c) Line s
d) Line q
e) Line p
Step-by-step explanation:
A transversal is a line that crosses two other lines in the same plane at two distinct points.
a) The transversal connecting ∠1 and ∠5 is line r.
Line r is the transversal of lines p and q. ∠1 and ∠5 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal r.b) The transversal connecting ∠7 and ∠14 is line q.
Line q is the transversal of lines r and s.∠7 and ∠14 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.c) The transversal connecting ∠8 and ∠11 is line s.
Line s is the transversal of lines p and q. ∠8 and ∠11 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal s.d) The transversal connecting ∠6 and ∠15 is line q.
Line q is the transversal of lines r and s. ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.e) The transversal connecting ∠3 and ∠9 is line p.
Line p is the transversal of lines r and s. ∠3 and ∠9 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal p.How do I write this out?
The magnitude of the second earthquake, using an logarithmic function, is of:
5.77.
How to obtain the magnitude of the earthquakes?The magnitude of an earthquake is given by the logarithmic rule presented as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
The first earthquake had a magnitude of 3.9, hence it's energy is obtained as follows:
[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]
The logarithm and the base 10 are inverse functions, hence the base 10 is applied to both sides to isolate the energy variable as vollows:
[tex]\frac{E}{E_0} = 10^{5.85}[/tex]
[tex]E = 707945.784E_0[/tex]
For the second earthquake, it's energy was 650 times greater, hence:
[tex]E = 707945.784 \times 650E_0 = 460164760E_0[/tex]
Hence it's magnitude is obtained as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{460164760E_0}{E_0}\right)}[/tex]
M = 5.77.
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Juan scored a total of 37 points in the basketball game, and he scored p points in the second half of the game. Write an expression to determine the number of points he scored in the first half of the game. Then, find the number of points he scored in the first half of the game if he scored 11 points in the second half of the game.
Rewrite, using the distributive property. -3(-4x+5)=
By applying the distributive property of multiplication, this mathematical expression can be rewritten as -3(-4x + 5) = 12x - 15.
What is the distributive property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
Mathematically, the distributive property of multiplication can be represented by this mathematical expression:
a(b + c) = ab + ac.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
-3(-4x + 5) = -3(-4x) + [-3(5)]
-3(-4x + 5) = 12x - 15.
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The equation of the line that goes
through the point (3, 1) and is
perpendicular to the line
2x + 4y = 5 can be written in the
form y
y = mx + b where m= and b=
The equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.
According to the question,
We have the following information:
Points = (3,1)
Equation of the line: 2x+4y = 5
Now, converting this line into y = mx+b form:
4y = -2x+5
y = -2y/4+5/4
y = -y/2+5/4
Now, the slope of this line is -1/2.
Slope of the line perpendicular to this line will be 2 (-1/m).
Now, the equation of the line will be:
(y-y') = m(x-x')
x' = 3 and y' = 1
y-1 = 2(x-3)
y-1 = 2x-6
y = 2x-6+1
y = 2x-5
The value of m is 2 and b is -5.
Hence, the equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.
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Solve the compound inequality 3x+1>2x-3>x-11 enter the exact answer in interval notation
The exact interval notation of given equation is x > - 8.
What is interval notation for compound inequalities?
The numbers that bound a continuous set of real numbers can be used to express the continuous set in interval notation. Intervals have many characteristics in common with ordered pairs when written.
We have,
3x+1 > 2x-3 > x-11
Apply the rule that if m > v > n, then m > v and v > n to the given compound inequality to find the solution.
∴ m = 3x + 1,
v = 2x - 3,
n = x - 11.
Hence, by applying the rule of compound inequality we get,
3x + 1 > 2x - 3 and 2x - 3 > x - 11
3x + 1 > 2x - 3
3x + 1 - 1 > 2x - 3 -1
3x > 2x - 4
3x - 2x > 2x - 4 - 2x
x > - 4
2x - 3 > x - 11
2x - 3 + 3 > x - 11 + 3
2x > x - 8
2x - x > x - 8 - x
x > - 8
The two computations above indicate that the acquired intervals, x > - 4 and x > - 8, will be combined to yield the answer to the given inequality.
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will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest
Area of the given figure is 27.852 in².
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
In the given figure there is a square.
First let us find the area of square, which has length of side 3 in
Area of square=3²=9
Now there are two semicircles with diameter 3 in.
Radius of semicircle = 3/2=1.5 in
Area of semicircle=2πr
=2×3.142×1.5
=9.426
As there are two semicircles
2×9.426
18.852
Area of figure is 9+18.852
27.852 in²
Hence, area of the given figure is 27.852 in².
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Function or not
x y
6 4
-8 2
9 -4
-3 8
6 -4
-6 4
Answer: not a function
Step-by-step explanation: one input has more than one output and to be a function it must have one output for every input.
I hope it’s right, best of luck :)
Ava went shopping for a new pair of pants the listed price of the pair of pants was $21 but the price with tax came out to $21.63 find the percent sales tax
The sales tax percent when Ava went shopping for a new pair of pants is 3%.
How to calculate the sales tax?From the information, Ava went shopping for a new pair of pants the listed price of the pair of pants was $21 but the price with tax came out to $21.63.
The sales tax will be:
= $21.63 - $21
= $0.63
The percentage of sales tax will be:
= Sales tax / Original price × 100
= 0.63 / 21 × 100
= 3%
The sales tax is 3%.
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Multiple-Choice Exam A student takes a 20-question, multiple-choice exam with two choices for each question and guesses on
each question. Assume the variable is binomial.
Find the probability of guessing at least 10 out of 20 correctly. Round the answer to at least four decimal places.
P(guessing at least 10 out of 20 correctly)
27
0
E
The probability is 0.5881.
From the question, we have
n = 20
P(X[tex]\geq[/tex]10) = 1-P(X<10)
P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)
P(X[tex]\leq[/tex]9) = P(X=0)+P(X=1)+..................+P(X=9)
=0.4119
P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)
=1-0.4119
=0.5881
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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Tim has 53 boxcars. His grandfather gave him his entire collection from when he was a child. Use the following equation to find out how many cars Tim’s grandfather gave him: 1.6 x 102. How many cars does Tim have in all?
The number of cars that Tim has in all is 215.
How many cars does Tim have?The boxcars that Tim has is written in standard form. While the boxcars that Tim's grandfather gave him is written in scientific form. The first step is to convert the scientific form to standard form.
Number of boxcars that Tim's grandfather gave him: 1.62 x 10²
= 1.62 x 100
= 162
The next step is to add the boxcars that Tim's grandfather gave him to the number of boxcars that Tim has.
Total boxcars that Tim has = 162 + 53 = 215 box cars
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Una bolsa de palomitas contiene 438 calorias y sirve a 3.5 personas cuantas calorias hay en cada porcion?
The number of calories in each serving is 125.14 calories.
How to calculate the number of calories?The bad of popcorn has 438 calories. Also, it was stated that it can serve 3.5 people.
The number of calories for each serving will be the division of the calories given.
This will be:
Number of calories = Total calories / Number of people
= 438 / 3.5
= 125.14 calories
Each serving has 125.14 calories.
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Find the perimeter of the rectangle. The drawing is not to scale.
Answer: 190
Step-by-step explanation:
first you add 29 + 29 and you get 58. Next, you add 66 + 66 which is 132 then you add the 2 sums together and get 190. :)
Graph the equation y= - 7/2 x + 2 on the coordinate plane.
Step-by-step explanation:
your intercepts are:
y-intercept:
y = - 7/2x + 2
y = - 7/20 + 2
y = 2
( 0 , 2 )
x-intercept:
y = - 7/2x + 2
0 = - 7/2x + 2
-2 = - 7/2x
-7/2x = -2
2x = 2/7
x = 4/7
( 4/7 , 0 )
Please help!!
Will give 5 points asap
The probabilities are given as follows:
a) P(both marbles are red) = 0.167 = 16.7%.
b) P(red then green) = 0.111 = 11.1%.
c) P(green then blue) = 0.083 = 8.3%.
d) P(blue and red, any order) = 0.333 = 33.3%.
How to obtain a probability?The probability of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
In this problem, the are nine marbles, of which four are red, hence the probability of both red is:
p = 4/9 x 3/8 = 0.167 = 16.7%.
(the marble is not replaced, hence for the second marble there will be eight possible marbles, of which 3 are red).
For red then green, the probability is:
p = 4/9 x 2/8 = 0.111 = 11.1%.
For green then blue, the probability is:
p = 2/9 x 3/8 = 0.083 = 8.3%.
For blue or red, there are two possible outcomes, blue then red or red then blue, hence:
p = 3/9 x 4/8 + 4/9 x 3/8 = 0.333 = 33.3%.
More can be learned about probabilities at https://brainly.com/question/14398287
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