The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.
How to explain permutations and combination?Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the amount of potential combinations of unrelated objects.
Fir example, if we want to select 2 players from 6. This will be:
= 6! / 2! (6 - 2)!
= 15 ways
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ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
The inequality that is represented by the given graph is; y ≤ (3/4)x - 2
How to Interpret Inequality Graphs?
From the given inequality graph, we see that;
Slope; m = 3/4
x-intercept = -2.5
y-intercept = -2
Now, the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, our graph is ordinarily;
y = (3/4)x + (-2)
y = (3/4)x - 2
However, it is an inequality that is shaded at the bottom with a thick line and so the inequality becomes;
y ≤ (3/4)x - 2
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1.) Which one of these shapes is not like the others? Explain what makes it different b
representing each width and height pair with a ratio.
Shape C is different from shape A and B.
Here, we are given 3 shapes as shown in the image below.
Let us look at each of the shapes one by one.
Shape A-
The height of shape A is 4
The width of shape A is 5
The ratio of width and height = 5/4
Shape B-
The height of shape B is 10
The width of shape B is 8
The ratio of width and height = 8/10 or 4/5
Shape C-
The height of shape C is 10
The width of shape C is 6
The ratio of width and height = 6/10 or 3/5
Thus, we can see that the ratio of width and height is equal for shape A and B. Thus, C is different.
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Your question was incomplete. Check for the missing image below.
Show where the balance point is for the two sides .
Tell weather the graph shows a reflection across the y -axis or neither
Step-by-step explanation:
yes, this is a reflection across the y-axis.
the points near to the mirror appear also near in the reflection. and the points far from the mirror appear also far in the reflection.
Help me pls- maths
Division
Based on the information given, the values are:
1. 80 rides
2. 53. 3%
3. 56. 6%
4. 30 students
What is percentage?
Percentage can be defined as the ratio of a number to 100.
It is denoted with the symbol, '%'
How to determine the values;
1.. 24 rides = thirty percent of the total rides
Total rides = 24 rides/ 30%
Total rides = 24/ 30/ 100 = 24/ 0. 3 = 80 rides
2. There are 14 Apple computers
16 PC computers
% of PC computers = 16/ 16 + 14 × 100/ 1
% of PC computers = 16/ 30 × 100
% of PC computers = 0. 53 × 100 = 53. 3
3. 3 out of 30 are not working
% of the working computers = 30- 3/ 30 × 100
% of the working computers = 17/ 30 × 100
% of the working computers = 56. 6
4.
If 12 students = 0. 4
Then x students = 1 - 0. 4 = 0. 6
cross multiply
x = 18 students
Total number of students = 40% + 60% of students = 18 + 12 = 30
Thus, the values are 80 rides, 53. 3%, 56. 6% , 30 students respectively.
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help me with all of them
Answer:
1) 34
2) 282.4
3) $183.70
4) 0.324
HELP PLS I DONT WANT TO FAIL
Answer:
11.9a − 3
Step-by-step explanation:
Charles can run at a speed of 8.6 meters per second. If he runs for 65 seconds, how far does he run?
A. 559 meters
B. 755 meters
C. 86 meters
D. 16 meters
A. 559 meters Is the answer
your teacher was driving on a toll road which has a speed limit of 60 mph (miles per hour). two weeks later they receive a ticket for speeding for going at least 25 mph over. your teacher is outraged and doesn’t believe that they have any way of proving they went 85 mph since there weren’t any radar guns on the road. because you are good at math the teacher turns to you and asks you to help them make a case against the toll road company. here is the information that the toll company provided your teacher as proof of their speeding. toll booth a – entrance on toll road time: 6:00 mile marker: 15 toll booth b – exit on toll road time: 7:00 mile marker: 100 is the toll road company correct to give your teacher a ticket? come up with some arguments one way or the other. include the mean value theorem where appropriate.
Yes , the toll company is correct to give the teacher a ticket.
Mean Value Theorem for a function f(x): [a,b]→ R such that f(x) is continuous and differentiable over the interval.
(i) f(x) is continuous on [a,b].
(ii) f(x) is differentiable on (a,b).
(iii) There exist a point c in (a,b) such that f'(c)=f(b)-f(a)/(b-a).
In the given question
Speed Limit = 60 mph
Time of entrance on toll road = 6:00
Time of exit from toll road = 7:00
Total time on toll road = 1 hr
Mile marker on entry in toll road = 15 mile
Mile marker on exit from toll road = 100 mile
Total distance travelled on toll road = 100-15= 85 miles
[tex]Average.Speed=\frac{total . distance}{total.time}[/tex]
Substituting the values we get .
Avg Speed = 85/1 = 85 mph
Overspeed = Avg Speed - Speed Limit
=85-60
=25 mph
The teacher over speed by 25 mph.
Since 85 mph is the average speed , it means that for some instance he was travelling below the average speed and for some instance he was travelling above the average speed.
By Mean value Theorem , it is clear that there have been at least one point where the teacher was travelling above 85 mph , which means he was over speeding .
Therefore , Yes , the toll company is correct to give the teacher a ticket.
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Does the following set of ordered pairs of ( 0 , -4 ) , ( 3 , 2 ) , ( -3 , -1 ) , ( 2 , 0 ) represent a function?
Answer:
yes, each input (x) has only one output (y)
Step-by-step explanation:
- 58 + (-62)
please solve this
Answer:
-120
Step-by-step explanation:
(3/x+3 - 4/x+4) divided by (2x/x+3 - x/x+4)
The answer is
7x-1/8x
-6x+4y=24
3 plot points for a graph
Answer:
(1, 7.5)
(2, 9)
(3, 10.5)
Step-by-step explanation:
-6x+4y=24
first we want to put the equation in slope intercept form which is y=mx+b
-6x+4y=24
first we add 6x to both sides
4y=24+6x
now we divide everything by 4
y=6+6/4x
simplified
y=3/2x+6
now we input our x values to find the y values (x,y)
y=3/2(1)+6
y=15/2 or 7.5
y=3(2)+6
y=9
y=3/2(3)+6
y=21/2 or 10.5
with this information, our points to plot on the graph are
(1, 7.5)
(2, 9)
(3, 10.5)
i hope this helped! if you have any questions just ask!
• x represents the weight of each triangle.
• y represents the weight of each square.
Jamir changed the number of shapes on each side of Hanger A to make Hanger B.
Write an EQUATION that could represent a balanced Hanger B.
Press "Try It" to see if Hanger B is balanced.
The equation that could represent a balanced hanger B, which is equivalent to hanger A, is: 6x + 3y = 3(3y + x).
How to Model a Situation Using Equations?Variables, which are alphabets represents unknown values and can be used in creating equations that model a scenario.
For example, in the model shown in the image, x represents the weight of each triangle while y = the weight of each square.
From the first balance, we can rearrange the squares and triangles to create hanger B.
The first equation is: 3(2x + y) = 9y + 3x
The second equation that can be created using the set of shapes would be:
6x + 3y = 3(3y + x)
Therefore, the equation that could represent a balanced hanger B, which is equivalent to hanger A, is: 6x + 3y = 3(3y + x).
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Answer: 2x+y=3y+x
Step-by-step explanation:
Devise a plan to find the value of x .
x= √2 + √2+ √2+.
x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2
We have to find the value of x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]
First take squares on both sides, then,
⇒ x² = 2 + [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]
As the terms inside the square roots are non terminating, we can substitute x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] into the above equation.
i.e., x² = 2 + x
⇒ x² - x -2 = 0
This is a quadratic equation which can be solved using factorization.
⇒ x²+(-2+1)x +(-2.1) = 0
⇒ (x-2)(x+1) = 0
So x = 2 or -1
But here the value of √2 is positive and square root of sum of positive numbers will always be positive.
So we can conclude that
x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2
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X+2/y-1=2 solve for x
What is the slope of the line that passes through the points (2, 8) and
(12, 20)? Write your answer in simplest form
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{2}}} \implies \cfrac{12}{10}\implies {\LARGE \begin{array}{llll} \cfrac{6}{5} \end{array}}[/tex]
State which property or properties need to be used to write each expression as a single logarithm.
b. log₅4 - log₅6
To write the expression log₅4 - log₅6 in a single logarithm, we have to use division property of logarithm.
Given that expression is log₅4 - log₅6.
We have to tell the name of the property of logarithm which will help us to express the expression in a single logarithm.
The quotient rule for logarithms tells us that the logarithm of a quotient is equal to a difference of logarithms. Just as with the product rule we use the inverse property to derive the quotient rule.
Division of logarithm says that log(m/n)=log m-log n.
The expression is log₅4 - log₅6.
log₅4 - log₅6=[tex]log_{5}[/tex](4/6)
=[tex]log_{5}[/tex] 0.67
Hence to write the expression log₅4 - log₅6 in a single logarithm, we have to use division property of logarithm.
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answer the question attached
The answer is cone -7 7=9÷7
Pre-Calc: Consider the following function.
(answer (a), (b), and (c))
Using the Factor Theorem, we have that:
a) The zeros of the function are x = 3i, x = -3i, x = 4.5.
b) The factored function is: F(x) = (x² + 9)(x - 4.5).
c) From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).
For this problem, the function is defined by the following rule:
F(x) = 2x³ - 9x² + 18x - 81.
Using a calculator, the zeros of the function are given as follows:
x = 3i, x = -3i, x = 4.5.
In factored form, the function is given by:
F(x) = (x - 3i)(x + 3i)(x - 4.5)
Considering that i² = -1, we have that:
The factored function is: F(x) = (x² + 9)(x - 4.5).
From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.
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Evaluate each logarithm. log₅ 1/ 125
The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3
How do you look for log properties?The similarity between the characteristics of exponents linear logarithms can be used to find the property for a quotient's logarithm. To create multiple numbers with the same base using exponents, add the exponents. Subtraction of exponents is used to split two numbers having the same base.
The Four Basic Properties of Logs:logb(xy) = logbx + logby.
logb(x/y) = logbx - logby.
logb(xn) = n logbx.
logbx = logax / logab.
According to the equation:log₅ 1/ 125 given
log₅ 1/ 125 applying the log property (log[tex]_a[/tex]ᵇ = log b/log a)
(log 1 - log 125)/ log 5
(log 1 - log 5³)/ log 5
(log 1 - 3log 5)/ log 5
((log1)/log 5 )) - 3
log₅¹ - 3
The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3
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Given m \| nm∥n, find the value of x.
m
n
t
(7x-1)°
(8x-14)°
The value of x is 13.
What are corresponding angles?Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.
We have,
Two lines m and n are parallel.
Two angles (7x -1)° and (8x - 14)° are corresponding angles.
We know that corresponding angles are equal.
We can write as:
7x - 1 = 8x - 14
We will find the value of x.
We will keep the like terms on one side.
14 - 1 = 8x - 7x
13 = x
x = 13
Therefore the value of x is 13.
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The Diaz family spent $85.97 on Martin's birthday dinner at
a pizza place. Tax on the meal was 7.5%, and they wanted
to leave a 20% tip because the service was excellent! How
much was the meal, including TAX and TIP?
O $110.90
O $92.42
O $109.60
O $113.47
Charlie and Kathy want to borrow $20,000 to make some home improvements. Their bank will lend them the money for 10 years at an interest rate of 5.75 %. How much will they pay in interest? (Round monthly payment calculations to 2 decimal places.)
The amount Charlie and Kathy would pay interest on the loan of $20,000 is $6,344.80.
What is an ordinary annuity?An ordinary annuity is payment of level cash flows for a defined period of time, in this case, a fixed monthly payment would be made for 10 years, hence, using the present value formula of an ordinary annuity we can determine the monthly payment:
[tex]PV=PMT*(1-(1+r)^{-N/r}[/tex]
Where:
PV=loan amount=$20,000PMT=monthly payment =5.75%/12number of monthly payments in 10 years=120[tex]PMT*(1+1+0.00479166666666667)^-120/0.00479166666666667\\PMT=$219.54[/tex]
total payment=$219.54*120total payment=$26,344.80 interest=$26,344.80 -$20,000interest=$6,344.80Find out more about present value on: brainly.com/question/17322936
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help me with 43 pls 1.29 & 1.3 midpoint I'll mark brainliest
The midpoint of the given numbers (1.29 and 1.3) is 1.295
Calculating MidpointFrom the question, we are to calculate the midpoint of the given numbers
The given numbers are 1.29 and 1.3
To determine the midpoint of two numbers on a number line, we will add the two numbers together, and then divide value of their sum by 2
Adding up the numbers
1.29 + 1.3
= 2.59
Now, divide the result by 2
Dividing
2.59/2
= 1.295
∴ On the number line, the midpoint of the given numbers is 1.295
Hence, the midpoint of the given numbers (1.29 and 1.3) is 1.295
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Graph the points (–4,–4.5), (1,2.5), and (–2,–0.5) on the coordinate plane.
Answer:
Step-by-step explanation:
To graph any point (±x, ±y) we must follow the steps as illustrated below.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, The points (- 4,- 4.5), (1, 2.5), and (- 2, - 0.5).
Now, To graph the point (-4, - 4.5) we should move 4 units left along the x-axis and down 4.5 units along the y-axis.
Similarly, for points (1, 2.5) and (- 2, - 0.5) we must follow the exact steps.
The graph of the points is shown in the attached image.
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how do you solve 2x²+4x=3+3x²
Elina has a total of $2.60. All of her change are in nickels, quarters, and dimes. She has twice as many dimes as quarters and two less quarters than nickels. Is it possible that Elina has eight dimes, four quarters, and six nickels?
Answer:
10 Dimes, 5 quarters, and 7 Nickels
Step-by-step explanation:
10 Dimes - 1 dollars
5 Quarters - 1.25 dollars
7 Nickels - 35 cents
1 + 1.25 = 2.25
2.25 + 35 = 2.60
An environmental equipment supplier sells hemispherical holding ponds for treatment of chemical waste. The volume of a pond is V₁=1/2(4/3 π r₁³) , where r₁ is the radius in feet. The supplier also sells cylindrical collecting tanks. A collecting tank fills completely and then drains completely to fill the empty pond. The volume of the tank is V₂=12 π r₂², where r₂ is the radius of the tank.
a. Since V₁=V₂ , write an equation that shows r₁ as a function of r₂ . Write an equation that shows r₂ as a function of r₁.
The equation for r₁ as a function of r₂ is r₁ = ∛ 18 ₂² and the equation for r₂ as a function of r₁ is r₂ = r₁ / 3 √r₁ / 2.
We are given that:
To fill a pond whose volume is given as V₁ = 1 / 2 (4 / 3 π r₁³), we need a cylindrical tank whose volume is given by V₂ = 12 π r₂².
Also, V₁=V₂
So, we get that:
1 / 2 (4 / 3 π r₁³) = 12 π r₂².
4 / 3 π r₁³ = 24 π r₂²
r₁³ = 18 r₂²
r₂ = √ ( r₁³ / 18)
r₂ = r₁ / 3 √r₁ / 2
Now, r₁³ = 18 r₂²
r₁ = ∛ 18 ₂²
Therefore, the equation for r₁ as a function of r₂ is r₁ = ∛ 18 ₂² and the equation for r₂ as a function of r₁ is r₂ = r₁ / 3 √r₁ / 2.
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find
by using implicit differentiation:
e^x/y = 3x - y
Can someone help me solve this problem !
now, the assumption is that, "x" is a simple variable whilst "y" is a function in x-terms, so
[tex]e^{\frac{x}{y}}=3x-y\implies \stackrel{\textit{\LARGE chain~rule}}{e^{\frac{x}{y}}\stackrel{quotient~rule}{\left( \cfrac{1\cdot y-x\cdot \frac{dy}{dx}}{y^2} \right)}} =3-\cfrac{dy}{dx} \\\\\\ \cfrac{ e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \frac{dy}{dx}}{y^2}=3-\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}=3y^2-y^2\cfrac{dy}{dx}[/tex]
[tex]e^{\frac{x}{y}}y-3y^2=e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}-y^2\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-3y^2= \cfrac{dy}{dx}\left( e^{\frac{x}{y}}x-y^2 \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \cfrac{e^{\frac{x}{y}}y-3y^2}{e^{\frac{x}{y}}x-y^2}=\cfrac{dy}{dx} \end{array}}~\hfill[/tex]