The explanatory variable in this scenario is B. the concession advertisements.
What is an explanatory variable?A response variable is what changes as a result of an explanatory variable being manipulated or observed to change (for example, the amount of caffeine consumed) (e.g., reaction times). In research, the terms "explanatory variable" and "response variable" are frequently used interchangeably.
Examples include both response variables, such as individual test item scores, total test scores, and achievement levels, and explanatory variables, such as gender, ethnicity, type of instruction, etc.
In this case, it should be noted that based on the information, the correct option is B.
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Conrad Savings Bank has a $50 overdraft fee. On Friday, Mr. McQuire deposited his paycheck of $332 for a total
account balance of $750. The next morning, his wife wrote a check for $1,183.15 for a new refrigerator and stove.
The check cleared the bank by the end of the day. What is the current balance in the McQuire's account?
Answer: -433.15
Step-by-step explanation:
he's id debt and has to pay off the 433.15 later on.
Answer:
The McQuires' account is currently overdrawn by $483.15.
Step-by-step explanation:
If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.
How do I solve this problem. Please explain step by step if u could
0.25 + (-3) =
Answer:
0.25 − 3
=0.25 + −3
= −2.75
( a number line to help to)
Step-by-step explanation:
Write a quadratic function in standard form whose graph has a vertex of (2, 6) and passes through the point (4, 10) .
Let the discrete random variable X have the geometric distribution with parameter p. (a) Give a real-life example in which the geometric distribution can be applied. (b) Use the definition of the expected value to show that: E[X] = 1/p. (c) Explain why it makes sense that the expected value of X is inversely proportional to p.
a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.
b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.
c) E(x) = 1/p
Discrete Random Variable:
A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.
Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...
Geometric Distribution :
The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.
The Geometric Random Variable can be written as X ~ G(p).
The probability mass function is P(X = x) = (1 - p)ˣ⁻¹ p
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Problems 14 and 15 pertain to the following situation: a woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%.
14. The probability that in any one month at least three of the tickets that the woman buys are winning tickets is about?
15. The average number of winning tickets that the woman buys each month is about?
The required probability is P(X≥3) =0.3234
The average number of winning tickets that the woman buys each month is 2.
The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.
The probability mass function of the binomial distribution is defined as:
[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]
Given that,
n = 20
p = 0.10
The required probability is P(X≥3)
P(X≥3) = 1-P(X<3)
P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)
P(X≥3)= 1- 0.1216- 0.270- 0.285
P(X≥3) = 0.3234
The mean of the distribution is defined as μ=n*p= 20*0.10= 2
The average number of winning tickets that the woman buys each month is 2.
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which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
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, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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1. Which property justifies the second line in the following solution?
(1) Multiplicative Property of Equality
(3) Distributive
(2) Associative
(4) Additive Property of Equality
3x+2=8
3x+2-2=8-2
Additive Property of Equality justifies the second line in the 3x + 2 = 8
3x+ 2 - 2 = 8 - 2 solution.
What is Multiplicative Property of Equality?
When we multiply on both sides of an equation then the equation is remain same.
Distributive property: a(b + c) = ab + ac in other words the product of a number with sum of two numbers is equal to the sum of product first two numbers and "first and third" numbers.
Associative property: (a + b) + c = a + (b + c): If we shift the parenthesis then the result will remain the same.
Given equation is
3x+2=8
The second step is 3x + 2 - 2 = 8 - 2.
The additive inverse of 2 is -2.
-2 is added in second step. Thus Additive Property of Equality is used.
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Cassie wants to purchase a pair of binoculars that is on sale for $155.75.
The sales tax rate in her county is 7%. How much will Cassie pay in all for
the pair of binoculars after sales tax is included? Round to the nearest cent
if necessary.
$10.12 will Cassie pay in all for the pair of binoculars after sales tax is included.
What is sales tax?
A sales tax is a fee that is paid to the government when specified products and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are often used to describe taxes on goods and services that consumers pay directly to a governing authority.
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
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Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.
The given triangles are congruent to each other by the rule of (AAS) Angle Angle side.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given figure in the question,
There are two given triangles in the question,
Δ ABC and Δ MNO
As we can see that,
∠ C = ∠ M
∠ B = ∠ N and,
The side, AC = OM
So, Δ ABC ≅ Δ MNO
So, by using AAS (Angle Angle Side) rule, triangle ABC and triangle MNO are congruent to each other.
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what is equivalent to (32−−√5)13
Answer:
Your answer is 416 + 13 [tex]\sqrt{5}[/tex].
Step-by-step explanation:
A survey shows that the probability that an employee gets placed in a suitable job is 0.65. A psychometric test consultant claims that he could help place any employee in a suitable job based on the result of a psychometric test. The test has an accuracy rate of 70%. An employee working in a particular company takes the test. The probability that the employee is in the right job and the test predicts that he is in the wrong job is . The probability that the employee is in the wrong job and the test predicts that he is in the right job is
The probability that someone is in the right job and the test is then wrong is 0.195.
The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In
The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3. Thus, the probability that someone is in the right job and the test is then wrong is:
= 0.65*0.3
= 0.195
The probability that someone is in the wrong job and the test is right is:
= 0.35 × 0.3
= 0.105.
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David says that a triangle with side measures 9 cm, 12 cm, and 17 cm is a right triangle. Susie says it is not. Who is correct? Explain
your reasoning.
12 cm
17 cm
9 cm
Answer: Susie is correct.
Step-by-step explanation:
Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.
a²+b² = c²
a = 9
b = 12
c = 17
9² + 12² = 17²
==> 81 + 144 = 289
==> 225 = 289, This is not true
Therefore this triangle is not a right triangle.
which properties of equality do you use to solve the
equation 15 =x/3 + 18?
The adding property of equality should be used to satisfy the given equation.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-15 + x/3 = 18
Add 15 on both sides of the equation
So, we have
45 + x = 18 × 3
x = 54 + 45
x = 99
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What is 0.6 divided by 10
Answer: 0.06
Step-by-step explanation:
the number of violent crimes committed in a city on a given day in a random sample of 90 days is a random variable.
The number of violent crimes committed in a city on a given day in a random sample of 90 days is a discrete random variable.
A random variable refers to a numerical quantity that is obtained by a random experiment. A random variable is known as discrete if it has either a finite or a countable number of possible values while it is called continuous if its possible values contain a whole interval of numbers. Hence, a discrete random variable refers to a variable that can take any whole number values as outcomes of a random experiment. It is a variable whose value is obtained by counting. Probability distributions are used to illustrate the values of discrete random variables. A discrete random variable is also known as a stochastic variable. Examples of a discrete random variable are a binomial random variable and a Poisson random variable. As the number of crimes committed in a city can only take discrete values such as 40 crimes, 50 crimes and cannot be 40.5 crimes, it is a discrete random variable.
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What is the approximate perimeter of this triangle?
Answer:
163.6 in---------------------------
Given:
a = 56 in,m∠A = 55°.Find the missing sides:
56/b = tan 55° ⇒ b = 56 / tan 55° = 39.21 in,56/c = sin 55° ⇒ c = 56 / sin 55° = 68.36 in.Perimeter is:
56 + 68.36 + 39.21 = 163.57 ≈ 163.6 inAfter a snowstorm in the town of Golden Glen, the morning temperature was
–
10°F. But by the afternoon, the temperature had risen by 17°F.
The change in temperature based on the information is 27°F.
How to illustrate the relationship?It should be noted that temperature simply means the degree of coldness and hotness in a body. In this case, after a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F.
Let the change in temperature be represented by x.
Therefore, -10 + x = -17
x = 17 + 10
x = 27
The Temperature is 27°F.
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After a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F. What was the change in temperature?
Answers fast please I need them fast
The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
What are similar triangles?When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.
Given are the similar triangles,
1) Δ HJG ~ Δ CAB
Scale factor = 3:1
2) Δ NPM ~ Δ ABC
Scale factor = 1:2
3) KJML ~ CDAB
Scale factor = 1:2
4) 40/x = 20/5
x = 10
5) 18/x = 21/7
x = 6
6) 6/3 = x/15
x = 30
Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
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Your class council determined that its profit from the upcoming homecoming dance is directly
related to the ticket price for the dance. Looking at past dances, the council determined that the
profit p can be modeled by the function p(t) = -1212 + 480t + 30, where t represents the price of
each ticket. What should be the price of a ticket to the homecoming dance to maximize the
council's profit?
The price of a ticket to the homecoming dance to maximize the council's profit is 4830.
Define vertex?A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.The vertex of an angle is the point around which it is measured, and the vertex angle is the angle that corresponds to a particular vertex.A face is a flat surface, an edge is a straight line connecting two faces, and a vertex is the corner of the shape.Given: a= -12, b = 480Vertex t= -b/2at= -480/2(-12) = 20Therefore, $20 per ticket.p(20) = -12(20) pow 2 + 480(20) + 30= 4830To learn more about vertex refer to:
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Answer:
$2 each ticket
Step-by-step explanation:
I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.
an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
A bag contains 3 red, 6 blue, and 7 yellow marbles. What is
the probability of drawing 2 marbles of different colors out of
the bag?
The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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sketch the region enclosed by the given curves (within the given bounds, if provided) and find its area.
The area enclosed by the curves f(x) and g(x) is 1/12
Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.
When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.
Let our given curves be :
f(x) = x² and g(x) = x³ within the interval [0,1]
Formula to calculate area under these curves is
=> A = [tex]\int\limits^{c}_{a} {|f(x) - g(x)| \, dx[/tex]
Interval is given from 0 to 1
Therefore ,
=> A = [tex]\int\limits^{1}_{0} {[x^2 - x^3]} \, dx[/tex]
Integrating,
=> [tex][\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}[/tex]
=> 1/3 - 1/4
=> 1/12 is required area
The given question is incomplete So, I've answered the question in general
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What is the range of f(x) = |x| − 5?
−∞ < y ≤ −5
−5 ≤ y < ∞
0 ≤ y < ∞
5 ≤ y < ∞
Answer:
-5 ≤ y < ∞.
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = |x| − 5, we can first consider what happens when x is positive. In this case, the absolute value of x is just x, so the function becomes f(x) = x − 5. For example, if x = 6, then f(x) = 6 - 5 = 1. We can do this for any positive value of x to find the y-values that the function produces when x is positive.
Next, we can consider what happens when x is negative. In this case, the absolute value of x is -x, so the function becomes f(x) = -x - 5. For example, if x = -6, then f(x) = -6 - 5 = -11. We can do this for any negative value of x to find the y-values that the function produces when x is negative.
We can then combine the y-values that the function produces when x is positive and negative to find the range of the function. Since the function produces all y-values greater than or equal to -5 when x is positive and all y-values less than or equal to -5 when x is negative, the range of the function is -5 ≤ y ≤ ∞.
Therefore, the correct answer is -5 ≤ y < ∞.
Say that we have three voters deciding among seven candidates, a, b, c, d, e, f, g. Their preference orderings are as follows.
1 2 3
(Best) c f g
a b b
e c c
g g d
b a e
d d f
(W orst) f e a
a. Find the top cycle.
b. For each candidate in the top cycle, write down an agenda (a sequence of majority rule
votes) that makes that candidate win (you can write the agenda as a tree).
c. Say that the voters use the Borda count system (each voter gives 6 points to their first
choice, 5 points to their second choice, and so on) to decide among the candidates. Which
candidate wins?
d. Is the Borda count winner also the Condorcet winner?
e. Which candidate does the worst in the Borda count?
f. Say that the person who does worst in the Borda count (your answer in part e. above) is
embarrassed about their poor performance, and tries to convince another candidate to drop
out so that they are no longer the worst person. If a candidate drops out, there would be
six candidates, and hence in the Borda count system, each voter gives 5 points to their first
choice, 4 to their second choice, and so forth. If a candidate drops out, is it possible for the
person who was originally the worst to no longer be the worst? If so, which candidate should
drop out? If not, please explain why not.
A. The top cycle in this case is a -> b -> c -> a.
B. The agenda that wins the candidate is:
First vote:
a vs b -> a wins
Second voice:
versus. c -> a wins
The agenda that Candidate B wins is:
First vote:
b vs c -> b wins
Second Voice:
b vs a -> b wins
The agenda that Candidate C wins is:
First vote:
c vs a -> c wins
Second Voice:
c vs b -> c wins
C. Using the Borda count system, the candidates' scores are as follows:
a:
18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)
b:
18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)
c:
18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)
d:
12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)
e:
12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)
f:
12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)
g:
6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)
Therefore, candidates a, b, and c tie for first place with 18 points each.
D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.
E. The candidate with the worst score in the Borda count is g of 6 points.
F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:
a:
15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)
b:
15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)
c:
15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)
Day:
10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)
e:
10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)
f:
10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)
In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.
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The mass of a cube,
M
(kg), is proportional to the cube of the length of its edge,
L
(m).
The mass of the cube is 90 kg when the length of its edge is 20 cm.
Work out
L
(to 2 DP) when
M
=
1700
kg
Answer:
Below
Step-by-step explanation:
m = k l^3 <=======given
when m = 90 kg and l = 20 cm
90 = k (20^3) shows k = .01125 kg/cm^3
sooooo : m = .01125 l^3
when m = 1700:
1700 = .01125 l^3
l = cubrt ( 1700/.01125) = 53.26 cm
Bag A contains 2 black marbles and 3 white marbles. Bag B contains 5 black marbles and 8 white marbles. Sarah adds some marbles to bag B, the probability of picking a black marble at random from either bag is now the same. Work out the smallest number of black marbles and white marbles he adds to bag B
Answer:
add one black and one white marble
Step-by-step explanation:
you have to make bag b equivalent to a 2:3 ratio.
add 1 to 5 to make it divisible by 2
divide 6 by 2
=3
multiply 3 by 3 to get a 2:3 ratio
=9
subtract initial marbles
9-8=1
A building has a height of 125 meters and a length of 80 meters. On a scale drawing of the building, the height is 25 centimeters. What is the length of the building on the scale drawing in centimeters?
The length of the building on the scale drawing is found as 16 centimeters.
Describe the term scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a specific widths is known as a scale factor (bigger or smaller).Scale factor ratios can be written as a colon, 1:2, or as a fraction, 12. A ratio calculates the difference between two values.However, that ratio isn't a scale factor, thus you could not build a ratio for left-handed pupils to all students.For the given data in the question-
Dimensions of the building;
Height of 125 meter length of 80 meters.Dimensions of the drawing of the building;
height is 25 centimetersLet the length be 'x'.Thus, taking ratios of Height to length
125/80 = 25/x
On simplification;
x = 80 x 25 / 125
x = 16
Thus, the length of building on the scale drawing is found as 16 centimeters.
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Consider the sample space given below. A die is a cube with six sides and each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray.S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66)a) Let E be the event that the sum of the numbers showing face up is equal to 6. Write E as a set. (Write your answer in set-roster notation.) b) What is the probability of e? c) Let F be the event that the sum of the numbers showing face up is at most 4. Write Fas a set. (Write your answer in set-roster notation. ) d) What is the probability of F? Show all work in either the answer box shown or upload your answer with a file - can be PDF or jpeg only.
a) The event E, that the sum of the numbers showing face up is equal to 6, can be written as the set:
E = {11, 15, 24, 33, 42, 51}
b) The probability of E is 6/36 = 1/6.
c) The event F, that the sum of the numbers showing face up is at most 4, can be written as the set:
F = {11, 15, 22, 31, 33, 42, 44, 51}
d) The probability of F is 2/9.
Probability is a measure of the likelihood of an event occurring in a statistical experiment. It is a number between 0 and 1, where 0 indicates that the event will never happen and 1 indicates that the event will always happen. Probability can be used to make predictions about the outcome of statistical experiments, and it is a useful tool in many fields, including economics, finance, and science. It is also used in gambling and games of chance to determine the odds of winning.
The probability of event E is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 6 outcomes in the event E and 36 outcomes in the sample space.
So, the probability of E is 6/36 = 1/6.
The probability of event F is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 8 outcomes in the event F and 36 outcomes in the sample space.
So, the probability of F is 8/36 = 2/9.
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If 1+3+5+7+…+49 =625, what is 2+4+6+8+…+50?
If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.
What is arithmetic series?
A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Here, we have
Given: 1+3+5+7+…+49 =625
We have to find the value of 2+4+6+8+…+50.
Here, we calculate the sum of all even numbers and we get
2+4+6+8+…+50 = 650
Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.
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Find the measure of the exterior angle:_______
The measure of the exterior angle is 60°.
What is the Exterior Angle Theorem?
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
We have,
interior angles:
∠ABC = z + 10
∠BAC = 4z
Exterior angle:
∠ACB = z + 50
Exterior Angle Theorem:
The measure of exterior angle = Sum of two opposite interior angles’ measure.
According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠ABC and ∠BAC would be equal to the exterior angle ∠ACB.
∴ ∠ABC + ∠BAC = ∠ACB
z + 10 + 4z = z + 50
5z = z + 40
z = 40/4
∴ z = 10
so, the value of the z is 10.
exterior angle:
∠ACB = 10 + 50 =60
Hence, the measure of the exterior angle is 60°.
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