Using the Fundamental Counting Theorem, it is found that 60 different possible student council teams could be elected from these students.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for president, vice president, treasurer and secretary the parameters are:
n1 = 5, n2 = 2, n3 = 2, n4 = 3.
Hence the number of different teams is:
N = 5 x 2 x 2 x 3 = 60.
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Verify whether the given differential equation is exact or not. if exact, solve. cosx y/x dx dy
The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
For given question,
we have been given a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]
We have to determine given differential equation is exact or not.
Compare it with M dx + N dy = 0
⇒ M = cos(x) and N = y/x
Find the derivative of M with respect to y.
[tex]\Rightarrow M_y=-sin(x)[/tex]
Now, find the derivative of N with respect to x.
[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]
Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.
Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
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The volume of a cone is 1,782 cubic centimeters. a cylinder has the same radius and height as the cone. what is the volume of the cylinder?
The volume of the cylinder that has same height and radius with the given cone is 5,346 cm³
What are the 3-D figure?Pyramids and prisms are examples of three-dimensional shapes, as are shapes with curved surfaces. The three-dimensional prism shape has two bases that are parallel and congruent. Any polygon is acceptable for the bases, which are two of the faces. Rectangles make up the remaining faces.
What is the Volume of a Cylinder?Given that the cylinder and the cone have the same radius and height, the volume of a cylinder equals 3 times the volume of a cone.
According to the given figure:
Given, a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder,
therefore,
Volume of the cylinder = 3 x (1,782)
Volume of the cylinder = 5,346 cubic centimeters
Hence, the volume of the cylinder is 5,346 cubic centimeter.
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You randomly choose a block from each
set in the diagram. What is the probability
that you will choose a block labeled with a
Tor a block labeled with a 6?
Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:
There are 8 outcomes with a T and a block from the second square.Removing the 2 outcomes below with a 6 and a T, as they are already counted, there are 7 outcomes with a six.Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:
p = 15/64 = 0.2344.
0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
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Troy travels 100 miles in 2 hours. Find the unit rate of speed by filling in the missing number.
100 miles/ 2hours = ? miles/ 1 hour = ? miles/hour
Answer:
50 miles/1 hour = 50 miles/hour
Step-by-step explanation:
The fraction is reduced by dividing numerator and denominator by their common factor of 2.
100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour
PLEASE HELP IM STUCK
Answer:
y = -3x + 1
Step-by-step explanation:
First, we can find the slope of the line.
The slope is (change in y)/(change in x).
We can use the points that are marked in orange: (0,1) and (1,-2)
The change in y is 1 to -2, which is -3.
The change in x is 0 to 2, which is 1.
The slope will be -3/1, which is also: -3.
We have y = -3x + b currently.
The b is the y-intercept, meaning (the point that touches the y axis, the vertical line).
The point (0,1) touches the y-intercept, so b will be 1.
We can finish our equation as: y = -3x + 1
If amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.
C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
What is linear regression?
Linear regression analysis is used to predict the value of a variable based on the value of another variable.
The variable you want to predict is called the dependent variable.
The variable you are using to predict the other variable's value is called the independent variable.
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Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.
What is a linear model?The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models. However, the phrase is also used with a different connotation in time series analysis.Linear regression analysis predicts the value of one variable depending on the value of another.The variable you wish to forecast is referred to as the dependent variable.The variable you are using to forecast the value of the other variable is known as the independent variable.Therefore, Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.
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The complete question is given below:
If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.
A) Company A: Using linear regression models from both data sets, she determines that it pays about $14 more.
B) Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more.
C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
D) Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.
Lines b and c are parallel.
Which is the measure of 6
Answer:
m∠6 = 54°
Step-by-step explanation:
Given the diagram, we know that line b is a straight line and angles 1 (the angle measuring 13x + 9°) and 2 are supplementary angles and thus add up to 180.
We also know angles 2 and 7 (the angles measuring 5x + 9°) are alternate exterior angles and are therefore congruent.
So since angle 2 = 5x + 9, we can do:
13x + 9 + 5x + 9 = 180
18x + 18 = 180
18x = 162
x = 9
Angles 7 and 6 are also congruent plugging x into angle 7 also gives us the measure of angle 6:
5(9) + 9 = 45 + 9 = 54°
Sierra found that 15 meters is equivalent to 49.2 feet. Which of the following is an equivalent ratio?
3 to 8.84
5 to 18.22
7 to 22.96
9 to 25.32
Answer:
7 to 22.96
Step-by-step explanation:
Hello!
We can represent each ratio as a fraction:
Original: 15 to 49.2 = [tex]\frac{15}{49.2}[/tex]3 to 8.84 = [tex]\frac{3}{8.84}[/tex]5 to 18.22 = [tex]\frac{5}{18.22}[/tex]7 to 22.96 = [tex]\frac{7}{22.96}[/tex]9 to 25.32 = [tex]\frac{9}{25.32}[/tex]To find equivalent values, we can convert each fraction into a decimal by dividing them.
ConvertOriginal: [tex]\frac{15}{49.2} = 0.304878048780488[/tex][tex]\frac{3}{8.84} = 0.339366515837104[/tex][tex]\frac{5}{18.22} = 0.274423710208562[/tex][tex]\frac{7}{22.96} = 0.304878048780488[/tex][tex]\frac{9}{25.32} = 0.355450236966825[/tex]The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.
(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.
Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm
Perimeter of a polygonPerimeter = 150 cmPerimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)
150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4
150 = 6x + 24
150 - 24 = 6x
126 = 6x
x = 126/6
x = 21
The longest side of the polygon is (x + 8)
= 21 + 8
= 29 cm
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Use the elimination method to slice the system of equations Choose the correct ordered pair 6x+2y=8 12x+y=22
Answer:
x=2 and y=-2
Step-by-step explanation:
Solution Given:
6x+2y=8....................................................[1]
12x+y=22....................................................[2]
Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get
equation 1 becomes 12x+4y=16
and subtracting by equation 2 we get
12x+4y=16
-12x-y=-22[Note: while subtracting we must change sigh)
__________________
0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]
3y=-6
dividing both side by 3, we get
3y/3=-6/3
we get y=-2
Again similarly
Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get
equation 2 becomes 24x+2y=44
and subtracting by equation 1 we get
24x+2y=44
-6x-2y=-8
_____________________
18x-0y=36
18x=36
dividing both side by 18, we get
18x/18=36/18
x=2
solve this if u can pls!
using the numbers 5, 7, and 8 only once each, fill in the boxes to make the statement true.
Answer:
its log 5 7/8
Step-by-step explanation:
The function f(x) = x2 is graphed above. which of the graphs below represents the function g(x) = (x 1)2?
The graph (C) Y represents the function g(x) = (x 1`)2.
What is a graph of a function?The graph of a function f is the set of ordered pairings where display style f(x) = y in mathematics. When x and f(x) are both real values, these pairings represent Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane.To find which of the graphs below represents the function g(x) = (x 1)2:
Parabola: It's a conic section formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements.
The equation of parabola: [tex]y =x^{2}[/tex]The graph of [tex]y=x^{2}[/tex] is given.To draw the graph of [tex]y=(x+1)^{2}[/tex], shift the graph of [tex]y=x^{2}[/tex] one unit left.The graph of [tex]y=(x+1)^{2}[/tex] is attached below.Therefore, the graph (C) Y represents the function g(x) = (x 1)2.
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tan 45- cos ~ 60° = x. Sin 45. ta
The trigonometric values we require :
[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]
Now, let's solve for x.
tan 45° - cos 60° = x (sin 45°)
[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]
[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]
[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]
[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]
The value of x is 1/√2.
I hope it helped you solve the problem
Good luck on your studies!
please help
the line ABC is tangent to a circle at B centre O with diameter EB the angle DAB = 28
(a) ABE=
(b) EDB=
(c) AOB=
(d) BOD=
(e) OBD=
(f)DBC=
Answer:
A 90°
B 90°
C 62°
D 118°
Hopefully this helps u
What is the classification of AABC with vertices A(0, 0), B(4, 3), and C(4, -3) by
its sides?
(A) equilateral
(B) isosceles
(C) scalene
(D) right
Check the picture below.
well, let's take a peek at the distances of each side.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{[ 4- 0]^2 + [ 3- 0]^2} \\\\\\ ~\hfill AB=\sqrt{25}\implies \boxed{AB=5} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-3}) ~\hfill BC=\sqrt{[ 4- 4]^2 + [ -3- 3]^2} \\\\\\ ~\hfill BC=\sqrt{36}\implies \boxed{BC=6}[/tex]
[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) ~\hfill CA=\sqrt{[ 0- 4]^2 + [ 0- (-3)]^2} \\\\\\ ~\hfill CA=\sqrt{25}\implies \boxed{CA=5} \\\\\\ \textit{so it's an \underline{isosceles triangle}}[/tex]
16. The average age of a group of 8 people is 22. After the oldest person leaves the room the average age decreases to 20. How old was the person who left the room? (A) 15 (B) 16 (C) 24 (D) 36
The age of the oldest person that leaves the room is 36 years
How to calculate the average of a data?The average of a data is defined as the ratio of the sum of the data to the sample size. Mathematically;
Average = sum/sample size
If the average age of a group of 8 people is 22. then;
22 = Xn/8
Xn = 22 * 8
Xn = 176
If after the oldest person leaves the room the average age decreases to 20, hence;
20 = H/7
H = 140
Xn = H + x
176 = 140 + x
x = 176 - 140
x = 36
Hence the age of the oldest person that leaves the room is 36 years
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Simplify 7 + (−3)
A: -10
B: -4
C: 4
D: 10
Answer: 4
Step-by-step explanation:
[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]
help me please 20 points
Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:
3.4 pounds 3.4 pounds 3.6 pounds3.8 poundsThe range of the sample means is 0.4 pounds.
The true statements on the mean weights to be used by the scientists are:
A single sample mean will tend to be a worse estimate than the mean of the sample means. The closer the range of the sample mean is to 0, the more confident they can be in their estimate. What does the means show?First, find the sample means of each sample.
Sample 1:
= (3 + 2 + 6 + 4 + 2) / 5
= 3.4 pounds
Sample 2:
= (2 + 2 + 3 + 7 + 3) / 5
= 3.4 pounds
Sample 3:
= (6 + 4 + 2 + 2 + 4) / 5
= 3.6 pounds
Sample 4:
= (5 + 3 + 2 + 5 + 4) / 5
= 3.8 pounds
The range is;
= 3.8 - 3.4
= 0.4
The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.
Using all the sample means as an average captures the data better than if a single sample mean is used.
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b)Find z
: (√z+√22)(√z-√22) = 35
Answer: [tex]\Large\boxed{z=57}[/tex]
Concept:
Here, we need to know how to expand expressions like (a - b)(a + b).
For expressions like (a - b)(a + b), the expanded form must be:
a² - b²
For checking whether it is true:
(a - b)(a + b)
= a² - ab + ba - b²
= a² - b²
Solve:
Given equation
[tex](\sqrt{z}+\sqrt{22})(\sqrt{z}-\sqrt22)}=35[/tex]
Expand the parenthesis by the concept
[tex](\sqrt{z})^2-\sqrt{22}^2=35[/tex]
Simplify the exponents
[tex]z-22=35[/tex]
Add 22 on both sides
[tex]z-22+22=35+22[/tex]
[tex]\Large\boxed{z=57}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
From the figure below, identify all pairs of alternate interior and alternate exterior angles
A.
alternate exterior
exterior means outside
like a front entrance to a home
1. o & t
2. n & u
B.
alternate interior
interior means inside
like as if its inside a house
1. p & s
2. q & r
( p & s ) AND ( q & r ) both look like the letter Z
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Are the two triangles similar?
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
Evaluate the following fractions giving your awnser in its simplist form. 50 POINTS!
a) 2/5 divided by 6
b) 3 and 1/3 times 5 and 2/5
c) 1/4 + 1/3 -1/2
a. 1/ 15
b. 76/ 15
c. 1/12
How to determine the valuea. 2/5 divided by 6
= 2/ 5 ÷ 6
= 2/ 5 ÷ 6/ 1
Take the inverse of the dividing fraction, we have
= 2/ 5 × 1/ 6
Multiply through
= 2/30
= 1/ 15
b. 3 and 1/3 times 5 and 2/5
= 3 + 1/ 3 × 5 + 2/ 5
From the knowledge of BODMAS, we multiply first
= 3 + 5/3 + 2/ 5
Find the LCM
= 45 + 25 + 6/ 15
= 76/15
c. 1/4 + 1/3 -1/2
Let's find the LCM
= 3 + 4 - 6 / 12
Add first
= 7 - 6/ 12
= 1/ 12
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Build Your Math Skills 2C, Round decimals to the nearest hundredth (0.01): 2.364
Answer:2.36
Step-by-step explanation:
Choose the equation that satisfies the data in the table.
-1 0 1
0
3
6
X
Y
OA. y = 3x +3
B.y = -x +9
Oc.y=x+9
OD. y=-3x +3
Answer: A: y= 3x + 3
Step-by-step explanation:
The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.
If a diameter intersects a chord of a circle at a perpendicular, what conclusion can be made?
If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.
What is the relation between the chord and diameter of a circle?The segments of a circle whose endpoints are on its perimeter are called chords.A circle's diameter is the chord that passes across its center.The circle's longest chord equals its diameter.Any line that is perpendicular to a chord on the circle cuts it in half and goes through the center.The solution to the problem:
A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.
Therefore, the chord is bisected.
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Select the correct answer. the diameter of a sphere measures 10.4 inches. what is the surface area of the sphere? a. b. c. d.
The surface area of the sphere is 108.16π in². So, option b is correct.
What is the surface area of a sphere?The surface area of the sphere is calculated by the formula,
A = 4πr²
In terms of diameter - d;
A = 4π × (d/2)²
= 4π × d²/4
= πd² sq. inches
Calculation:The given sphere has a diameter d = 10.4 inches
So, the surface area of the sphere is calculated by
A = πd²
= π × (10.4)²
= 108.16 π sq. inches
So, option b is correct.
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Disclaimer: The given question on the portal is incomplete. Here is the complete question.
Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
a. 432.64π in²
b. 108.16π in²
c. 54.08π in²
d. 216.32π in²
Answer:
Step-by-step explanation:
The surface area of the sphere is 108.16π in². So, option b is correct.
What is the surface area of a sphere?
The surface area of the sphere is calculated by the formula,
A = 4πr²
In terms of diameter - d;
A = 4π × (d/2)²
= 4π × d²/4
= πd² sq. inches
Calculation:
The given sphere has a diameter d = 10.4 inches
So, the surface area of the sphere is calculated by
A = πd²
= π × (10.4)²
= 108.16 π sq. inches
So, option b is correct.
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Disclaimer: The given question on the portal is incomplete. Here is the complete question.
Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
a. 432.64π in²
b. 108.16π in²
c. 54.08π in²
d. 216.32π in²
**The equation y = 15x + 100 can be used to model the amount of money, y, that has
been saved by Jared for his bike based on the number of months that have passed. What
does the coordinate (0, 100) mean in the context of the problem?
If the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.
Given an equation y=15x+100 that shows the amount of money saved by Jared for his bike based on the number of months that have passed.
We are required to find what the coordinate (0,100) mean in the context of the equation.
Equation is like relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation, cubic equation or many more dependng on the power of variable present in that equation.
When we put x=0 in the equation we get the following:
y=15*0+100
y=100
It means that he had $100 in the beginning when he just started doing his savings.
Hence if the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.
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what value ofx is in the solution set of 3(x-4)>5x +2?
[tex]\boldsymbol{\sf{3(x-4) > 5x +2 }}[/tex]
Use the distributive property to multiply 3 by x−4.
[tex]\boldsymbol{\sf{3x-12 > 5x+2 }}[/tex]
Subtract 5x on both sides.
[tex]\boldsymbol{\sf{3x-12-5x > 2 } }[/tex]
Combine 3x and −5x to get −2x.
[tex]\boldsymbol{\sf{-2x-12 > 2 }}[/tex]
Add 12 to both sides.
[tex]\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}[/tex]
[tex]\boldsymbol{\sf{-2x > 14}}[/tex]
Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.
[tex]\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}[/tex]
[tex]\boxed{\boldsymbol{\sf{x < -7 }}}[/tex]
So in the inequality 3(x-4)>5x +2, the value of x is -7.
ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:
https://brainly.com/question/17070130Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).
Which statement is true for the functions?It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².
On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.
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Annel sells a phone which costs $180 and earns $9 commission. If he sells $640
worth of phones the following day, how much will he earn on commission?
Answer:
he will earn 32$ worth of commision
Step-by-step explanation:
so if the commission is 9$ and 9 is 5% of 180$ then commission percentage is 5% so to find how much commission he got selling 640$ worth of phones we just have to find 5% of 640$ which is 32$