Answer:
The theoretical probability of rolling a two with one standard die is 1/6. This can be written as a decimal by dividing 1 by 6, which is approximately 0.167. As a percentage, this is approximately 16.7%. Here are all three forms:As a fraction: 1/6As a decimal: 0.167As a percentage: 16.7%
Step-by-step explanation:
Find the probability of royal flush poker hand when 5 cards are dealt from an ordinary deck. Enter your answer as a fraction. P(royal flush) - )
Probability p(Royal flush)= 4/2598960 = 1/649740
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
A royal rush in Poker Card is five of each of the following: ace, king, queen, jack, and ten.
The ten, Jack, Queen, King, and Ace of a single suit make up a royal flush. These hands come in fours.
Total no. of ways = selecting 5 cards out of 52 cards = 52 C5 = 2598960
So, P(royal flush)= 4/2598960 = 1/649740
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Use the "at least once" rule to find the probabilities of the following events.
Getting at least one tail when tossing seven
fair coins
The required probability will be 127/128 that getting at least one tail when tossing seven.
We know that the total number of sides on a coin [Tail, Heads] =2
The probability of getting a tail = 1/2
The probability of getting no tail = 1 -1/2 = 1/2
According to the "at least once" rule, when a coin is tossed n times, the chance of obtaining at least one tail is given by:-
P(at least one tail) = 1 - [P(no tail)]ⁿ
In this case, n=7
Then, the probability of getting at least one tail is given by:-
P(at least one tail) = 1 - (1/2)⁷
P(at least one tail) = 1 - (1/128)
P(at least one tail) = 127/128
Thus, the required probability will be 127/128 that getting at least one tail when tossing seven.
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What equation represents this function?
What is the domain and range of this function?
The equation is [tex]36x-y=145[/tex].
The domain is (∞,-∞), {x,x∈R}.
What is the domain of a function?
The domain of a function is the set of all conceivable values that are acceptable as inputs, or alternatively, it can be interpreted as the full set of potential values for independent variables. The denominator of the fraction is not equal to zero, and the digit under the square root bracket is positive, which is an indicator of the domain.
Let us first take any 2 coordinates of the function, say (-143,-2) and (0,-71).
let us take the slope of these 2 points,
[tex]m=\frac{x_{2}-x_{1} }{y_{2}- y_{1} } \\m=\frac{-71+143}{0+2} \\m=\frac{72}{2} \\m=36[/tex]
Now, using the slope, we can find the required equation:
[tex]y-y_{1} =m (x-x_{1} )\\y+143=36(x+2)\\36x-y=145\\[/tex]
The domain for the function is (∞,-∞), {x,x∈R}.
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3. Pedro can pay 3 dollars for one T-shirt, or he can get 2 T-shirts for 5 dollars. Which is a better
deal? Why?
Answer:
Buying two T-shirts for 5 dollars is a better deal.
Step-by-step explanation:
If you bought one T-shirt for 3 dollars, that would be more than half of the money than two T-shirts. Therefore, it's a better deal to get 2 T-shirts for 5 dollars.
[tex]3x^{2} +x -5=0[/tex]
The two solutions of the quadratic equation are:
x = 1.135
x= -1.468
How to solve the quadratic equation?
A general quadratic equation:
a*x^2 + b*x + c = 0
Has solutions of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here the quadratic equation is:
3*x^2 + x - 5 = 0
So the values are:
a = 3
b = 1
c = -5
Replacing that in the quadratic formula for the solutions we will get:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*3*(-5)} }{2*3}\\\\x = \frac{-1 \pm 7.81 }{6}[/tex]
Thus, the two solutions are:
x = (-1 + 7.81)/6 = 1.135
x = (-1 - 7.81)/6 = -1.468
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R(x) = -40x^2 + 5000x
Determine the prices where the revenue is zero?
For each price where the revenue is zero, explain why the revenue is zero.
Answer:
The prices where the revenue is zero are $x = 0 and $x = 125.
When x = 0, the revenue is 0 since the function is equal to zero (R(0) = -40(0)^2 + 5000(0) = 0).
When x = 125, the revenue is 0 since the coefficient of the x^2 term is negative and the coefficient of the x term is positive. Since the equation is equal to zero, the two terms must cancel each other out, resulting in zero revenue (R(125) = -40(125)^2 + 5000(125) = 0).
Step-by-step explanation:
PLEASE HELP ME SLOVE FOR X
Answer:
x = 5
Step-by-step explanation:
Since the lines with red arrows are parallel, we can use the ratios
(28 - 12)/28 = 4x/35
35(16) = 28(4x)
560 = 112x
x = 560/112
x = 5
Determine which set of side measurements could be used to form a right triangle.
04, 11, 20
16, 21, 25
5, 13, 25
3, 4, 5
Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )
What is the Pythagoras Theorem ?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
For a triangle to be Right Angled , It should obey the Pythagoras Theorem
[tex]c^{2} = a^{2}+b^{2}[/tex]
c = hypotenuse
a = perpendicular side
b = base
Hence
if c = 5 , a = 3 and b = 4
Then
[tex]c^{2} = a^{2}+b^{2}[/tex]
[tex]5^{2}= 3^{2}+4^{2}[/tex]
25 = 3 + 16
25 = 25
So
It obeys the Pythagoras Theorem
Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )
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I need help asap
If anyone can help bro
The minimum length of the slanted poles needed to support the fly is 20 feet.
What is a Pythagoras theorem?
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
To find the minimum length of the slanted poles, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the slanted pole) is equal to the sum of the squares of the other two sides (the heights of the tent and fly).
We are given that the height of the tent is 12 feet and the height of the fly is 16 feet. The Pythagorean theorem can be written as follows:
c² = a² + b²
where c is the length of the slanted pole, a is the height of the tent, and b is the height of the fly.
Substituting in the given values, we get:
c² = 12² + 16²
= 144 + 256
= 400
Taking the square root of both sides gives:
c = √400
= 20
Therefore, the minimum length of the slanted poles needed to support the fly is 20 feet.
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You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
(a) Loan you can afford is $143097.67. (b) Total money will you pay the loan company is $378000. (c) Interest amount is $234902.33.
What is Loan interest ?Loan interest is the additional cost that a borrower must pay on top of the principal amount of a loan. Interest is typically expressed as a percentage of the principal and is charged over a specific period of time. The rate of interest charged on a loan is determined by a variety of factors, including the borrower's creditworthiness and the type of loan. The purpose of interest is to compensate the lender for the risk and cost of providing the loan.
Given data:
Principal = $1050 per month
Time = 30 year
= 30 × 12
= 360 months
Interest rate = 8%
= 0.08/12
= 0.006667 monthly
(a) We get here first maximum amount of loan by present value of annuity as
Present value of annuity = principal × [tex]\frac{1-(1+rate)^{-t} }{rate}[/tex] .........(1)
Put here value we get
value of annuity = 1050 × [tex]\frac{1-(1+0.006667)^{-360} }{0.006667}[/tex]
value of annuity = $143097.67
(b) Total amount = principal × time period
= $1050 × 360
= $378000
(c) Total amount of interest paid will be
interest amount = total amount paid - loan amount
interest amount = $378000 - $143097.67
interest amount = $234902.33
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[tex]4c^2+10c+4[/tex]
Answer:
Factor for this problem is
2(2c+1)(c+2)
Answer:(c+2)(4c+2)
Step-by-step explanation:
Factor by grouping
(c+2)(4c+2)
What is the domain of the inverse of the function graphed below?
Write your answer as a compound inequality.
The domain of an inverse function, f1, is the domain of a function, f(x) (x). The range of f1 is the scope of f(x) (x).
What's the inverse equation?The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) (= g(f(x)) = x. The initial value is fetched via a function that is its inverse.
What does the math sentence inverse mean?The opposite is called inverse. In mathematics, an inverse operation is one that reverses the effects of a preceding operation. Inverse operations refers to the set of two opposing operations.
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read the whole question and then answer it!!
1a. No, the value of 60% of 400 is 240.
1b. No, the value of 60% of 200 is 120.
1c. No, the value of 60% of 120 is 72.
2. The equation the express the relation 60%, x, and 87 is 0.6x = 87. The value of x is 145.
3a.The equation is0.6c = 43.2. The value of c is 72.
3b. The equation is0.38e = 190. The value of e is 500.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
1.a
Compute the vale of 60% of 400.
Using the formula a% = a/100
60% of 400 = 60/100 of 400
Replace of by multiplication:
60% of 400 = (60/100) × 400
60% of 400 = 240.
1b.
Compute the vale of 60% of 200.
Using the formula a% = a/100
60% of 200 = 60/100 of 200
Replace of by multiplication:
60% of 200 = (60/100) ×2 00
60% of 400 = 120.
1c.
Compute the vale of 60% of 120.
Using the formula a% = a/100
60% of 120 = 60/100 of 120
Replace of by multiplication:
60% of 120 = (60/100) × 120
60% of 400 = 72.
2.
Given that 60% of x is 87.
Compute the vale of 60% of x.
Using the formula a% = a/100
60% of x = 60/100 of x
Replace of by multiplication:
60% of x = (60/100) × x
60% of x = 0.6x
Therefore the relationship is 0.6x = 87
Now divide both sides by 0.6:
x = 87/0.6
x = 145.
3a.
Given that 60% of c is 43.2.
Compute the vale of 60% of c.
Using the formula a% = a/100
60% of c = 60/100 of c
Replace of by multiplication:
60% of c = (60/100) × c
60% of c = 0.6c
Therefore the relationship is 0.6c = 43.2
Now divide both sides by 0.6:
c = 43.2/0.6
c =72.
3b.
Given that 38% of e is 190.
Compute the vale of 38% of e.
Using the formula a% = a/100
38% of e = 38/100 of e
Replace of by multiplication:
38% of e = (38/100) × e
38% of e = 0.38e
Therefore the relationship is 0.38e = 190
Now divide both sides by 0.38:
e = 190/0.38
e = 500.
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Suppose you have a group of 20 people, 7
are women and the remaining people are
men. What is the probability you select 4
women from the group?
The probability of select 4 women from the group is, P = 35.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: You have a group of 20 people, 7 are women and the remaining people are men.
7 are women then 13 are men.
No. of ways in which 4 women can be chosen from 7 women are 7C4.
So, the probability of select 4 women from the group is,
[tex]P = {7_C_4} \\P = \frac{7!}{4!*(7-4)!} \\P=\frac{7!}{4!*3!} \\P = 35[/tex]
Hence, the probability of select 4 women from the group is, P = 35.
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Solve for a.
a+(−7)=−17
Answer: a= (-10)
Step-by-step explanation:
step 1- move the -7 to the other side of the equal sign to combine with -17.
step 2- to do this we need to make -7 positive so instead of (-17) -7, it would be (-17) +7.
step 3- leaving you with
a= (-10) hope this helped :)
A new gaming chair costs $239.87. You have already saved $106.37 and earn $44.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
44.5w + 106.37 = 239.87; w = 3
44.5w − 106.37 = 239.87; w = 9
44.5w − 239.87 = 106.37; w = 9
44.5 + 106.37w = 239.87; w = 3
The equation will be 44.50 w + 106.37 = 239.87, and it will take 3 weeks to collect money for gaming chair.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the data provided in the question,
Cost of new gaming chair = $239
Savings for gaming chair = $106.37
Each week earning = $44.50
Then the expression will be,
44.50 w + 106.37 = 239.87
44.50 w = 239.87 - 106.37
w = 133.5/44.50
w = 3
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What is the value of 5(y+3)-3 x² when x=4 and y=2 ?
A) -23
B) -10
C) 10
D) 23
Step-by-step explanation:
5(2+3)-3*4²
=5*5-3*16
=25-48
=-23(A)
I need help for a grade
Answer:
36
Step-by-step explanation:
[tex]\frac{1}{4}(12^2)=\frac{1}{4}(144)=36[/tex]
The graph below shows a transformation of y=2^x .
Write an equation of the form y=A . 2^x+k for the graph above.
y=
The graph showing the transformation of the function y = 2ˣ, with points (0, -1), and (1, -4), as well as an horizontal asymptote of y = 2, indicates that the equation of the graph in the form y = A·2ˣ + k is; y = -3·2ˣ + 2
What is an asymptote of a graph?The asymptote is a line that can be drawn on the graph such that the curve of the graph approaches the line without touching it as the values of the variables increase.
The required form of the exponential equation is; y = A·2ˣ + k
Where;
k = The horizontal asymptote
The graph included in the question indicates that an horizontal asymptote is indicated by the line y = 2
= 2
Points on the graph of the transformed function are (1, -4), (0, -1)
When x = 0, y = -1, therefore;
-1 = A·2⁰ + 2
A·2⁰ + 2 = -1 - 2 = -3
A = -3
The equation for the graph is therefore;
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Stem and leaf plots
And box
Pls help I have no idea what this is
Answer:
61 is the mode.
Step-by-step explanation:
Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).
Answer:
61 is the correct answer
A thermometer shows the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F). One day, it shows 87°F and 31°C. The next day, it shows 94°F and 34°C. Determine if there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.
No, there is not a proportional relationship because 87 over 31 does not equal 94 over 34.
Yes, there is a proportional relationship because 87 over 31 equals 94 over 34.
No, there is not a proportional relationship because degrees Celsius and degrees Fahrenheit are not the same measurement.
Yes, there is a proportional relationship because degrees Celsius and degrees Fahrenheit are the same measurement.
The values shown by the thermometer of 87 °F and 94 °F which in degrees Celsius are 31 °C and 34 °C indicates that the relationship is not a proportional relationship. The correct option is therefore;
No, there is not a proportional relationship because 87 over 31 does not equal 94 over 34.What is a proportional relationship?A proportional relationship is one in which one variable is a constant multiple of the other, such that the ratio of each data pair is a constant.
The temperature it shows on the first day = 87 °F and 31°CThe temperature it shows on the next day = 94 °F and 34 °CThe ratio of the two temperatures are therefore;
[tex]\dfrac{87}{31}[/tex] and [tex]\dfrac{94}{34}[/tex]
31 is a prime number, therefore'
[tex]\dfrac{87}{31} \neq \dfrac{94}{34}[/tex]
The ratio of the ordered pair of a proportional relationship is constant, the ratio of the specified values is not constant, therefore, the relationship is not a proportional relationship.
The correct option is therefore;
No there is not a proportional relationship because 87 over 31 does not equal 94 over 34
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Jenna had fifty pieces of laundry to wash. First, she removed her ten favorite shirts, which she will wash by hand. Then she divided the rest into piles of 8 to wash in the machine. How many piles does she have for the machine? Show all work.
Using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, we know that:
Jenna has 50 pieces of laundry.
She removed her 10 favorite shirts.
50 - 10 = 40
She divided the rest into 8 piles.
40/8 = 5
Therefore, using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.
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Tolu, Abram, and Nevis are partners in a
new business. The bank account for the
business currently shows a balance of
-$123, so the partners agree to pay
equal amounts to bring the balance to
$0. Write and solve an equation using
negative numbers to find each partner's
share of the balance.
Please help
Each partner needs to pay $41 to bring the balance to $0.
What is the linear equation in one variable?
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
Let x be the amount each partner pays.
We can set up the equation as follows:
(-123) + 3x = 0
To solve for x, we can add 123 to both sides of the equation:
(-123) + 123 + 3x = 0 + 123
This simplifies to:
3x = 123
To solve for x, we can divide both sides of the equation by 3:
(3x)/3 = 123/3
This simplifies to:
x = 41
Therefore, each partner needs to pay $41 to bring the balance to $0.
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I NEED HELP ASAP PLEASE
v/b - c = d/e make e the subject of the formula
Answer:
[tex]e = \frac{bd}{v - bc} [/tex]
Step-by-step explanation:
[tex] \frac{v}{b } - c = \frac{d}{e } [/tex]
[tex] = > multiply \: bothsides \: by \: e[/tex]
[tex] = > \frac{v}{b} \times e - c \times e = \frac{d}{e} \times e[/tex]
[tex] \frac{ve}{b} - ce = d[/tex]
[tex] = > multiply \: both \: sides \: by \: b[/tex]
[tex] \frac{ve}{b} \times b - ce \times b = bd[/tex]
[tex] = > ve - bce = bd[/tex]
[tex] = > e(v - bc) = bd[/tex]
[tex] = > divide \: both \: sides \: by \: (v - bc)[/tex]
[tex] = > e = \frac{bd}{v - bc } [/tex]
A sample of 200g of an isotope decays to another isotope according to the function A(t)= 200е⁻⁰⁰⁵⁴⁺ ,where t is the time in years
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about __g of the sample will be left.
(Round to the nearest hundredth as needed.)
The amount of initial sample will be left in the sample after 25 years is $771.49.
What is isotope decay?
An unstable atomic nucleus loses energy via radiation during the process of radioactive decay. A substance is regarded as radioactive if it has unstable nuclei. The three most frequent types of decay are alpha decay, beta decay, and gamma decay, all of which involve the emission of one or more particles.
Given:
A sample of 200g of an isotope decays to another isotope according to the function [tex]A(t) = 200e^-^0^.^0^5^4^t[/tex],where t is the time in years.
We have to find the amount of initial sample will be left in the sample after 25 years.
Plug t = 25 in the given equation.
[tex]A(25) = 200e^-^0^.^0^5^4^(^2^5^)\\A(25) = 771.4851\\A(25) = 771.49[/tex]
Hence, the amount of initial sample will be left in the sample after 25 years is $771.49.
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how many ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
10ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find how many ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
Let x = number of ml of 20% acid
x mL of 20% acid plus (20 - x )mL of 100% acid = 20 mL of 60% acid
0.20x+1.00(20-x)=0.6(20)
0.20x+20-x=12
20-0.8x=12
Subtract 20 on both sides
-0.8x=12-20
-0.8x=-8
Divide both sides by -0.8
x=10
Hence, 10ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
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What is the slope of the line that contains these points? xxx 151515 171717 191919 212121 yyy -10−10minus, 10 222 141414 262626
According to the given information the slope of the linear function containing these points is of 1.
A linear function is what?The graph of a linear function is a horizontal line. The following is the form of a linear transformation. a + bx = y = f(x). One regression coefficient or one predictor variables make up a linear function.
Briefing:A linear function is modeled by:
y=mx+b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the value of y when x = 0.In this problem, the points given are: (-10, 22) and (14, 26), hence, the slope is given by:
[tex]y_2=26 ,y_1=22 ,x_2=14 , x_1=10\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\text { m }=\frac{26-22}{14-10}\\\\\m=1[/tex]
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The volume of a room is 80 m³. The area of the floor is 20 m². The height of the room is:
Answer:
4
Step-by-step explanation:
Let's think of this as a cube with layers.
(Layer = height)
If the first layer has 20, and the cube has a total of 80, we can use this equation:
80 = 20 × number of layers
Let's figure out how many times we need to multiply 20 to get 80.
20 × 4 = 80
The cubes height is 4.
Answer:
4m
Step-by-step explanation:
The volume of a room is 80 m³. The area of the floor is 20 m². The height of the room is:
Volume = l x w x h (base area times height)
we use the inverse formula
Height = 80 : 20 =
4
The sum of 5 consecutive odd numbers
is 145.
What is the third number in this sequence?
Hello,
I hope you and your family are doing well!
The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. Since the sum of 5 consecutive odd numbers is 145, we can set up the equation:
(a + (a + 4)) / 2 * 5 = 145
where a is the first term in the sequence.
Solving this equation gives us:
a = -23
The third number in the sequence is the third odd number after a, which is a + 4. Substituting -23 for a gives us:
(-23) + 4 = -19
Therefore, the third number in the sequence is -19.
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Happy Holidays & New Year!
Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?
The number of handshakes that occur in Tom's workshop is 105
Given: Number of people in the workshop is 15 and Every person shakes hands once with every other person
To find: Number of handshakes
Since every person has to meet the other person only once and shake hands only once. So every handshake has only one possible combination.
Total number of combinations (handshakes) that can be possible with 15 people = [tex]15C_2[/tex]
The formula for a combination is
[tex]nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n is the number of items and r is the unique arrangements.
Plugging in our numbers of n = 15 and r = 2, we get
[tex]15C_2= \frac{15!}{2!(15-2)!}\\= \frac{15!}{2! \times 13!} \\=\frac{15 \times 14 \times 13!}{2! \times 13!}\\[/tex]
On cancelling out 13! from numerator and denominator , we get
[tex]15C_2=\frac{15 \times 14}{2 \times 1}= 15 \times 7=105[/tex]
What is combination?A combination is a method of picking things from a collection in which the order of selection is irrelevant. Assume we have three numbers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.
It is feasible to count the number of combinations in smaller collections, but the possibilities of a set of combination increases with the number of groups of elements or sets. As a result, a formula has been developed to determine the number of things that can be selected.
The formula is
[tex]nC_r = \frac{n!}{r!(n-r)!} \, when \, n > r\\nC_r = 0 \, when \, n < r[/tex]
Where n = number of distinct objects to choose from
C = Combination
r = spaces to fill
The number of handshakes that occur in Tom's workshop is 105
To know more about combinations, check out https://brainly.com/question/26852614
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