We will observe that the anticipated value is $0, indicating that Laura should anticipate neither winning nor losing any money after a significant number of games.
What is the expected value?The predicted result of an experiment with N outcomes, each with a probability of p1, p2,..., pn, is:
EV = x₁*p₁ + ... + xₙ*pₙ
The results in this situation are:
x₁ = drawing an unlucky card = -$6
If there are five odd cards in a deck of ten cards, the probability is:
p₁ = 5/10 = 1/2.
x₂ = drawing a 2 = $2
There is only one 2 card on the deck, so the probability of drawing it is: p₂ = 1/10
x₃ = drawing a 4 = $4
p₃ = 1/10
x₄ = drawing a 6 = $6
p₄ = 1/10
x₅ = drawing a 8 = $8
p₅ = 1/10
x₆ = drawing a 10 = $10
p₆ = 1/10
So the expected value will be:
EV = (-$6)*(0.5) + ($2 + $4 + $6 + $8 + $10)*(1/10)
EV = 0
Thus, we will observe that the anticipated value is $0, indicating that Laura should anticipate neither winning nor losing any money after a significant number of games.
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Look at the pattern.
72, 67, 62, 57
Which of these is the rule for the pattern?
a
b
d
subtract 5
add 5
subtract 9
add 9
Answer:
Subtract 5
Step-by-step explanation:
72 , 67, 62, 57,..
Each term is obtained by subtracting 5 from the previous term.
72 - 5 = 67
67 - 5 = 62
62 - 5 = 57
What does it mean when the discriminant is greater than 0?
We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.
An discriminant value definition ?
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
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Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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Can the two triangles be proven congruent by SAS explain?
Yes, two triangles can be proven congruent by SAS(Side angle side) congruence.
What is SAS Congruence?If any pair of comparable sides and their included angles are the same in both triangles, then the triangles are said to be congruent.
There are five ways to determine whether two triangles are congruent. It's one of them (SAS). Congruent Triangles provides a list. If any two comparable sides and their included angle in both triangles are same, then the triangles are congruent.
Why does this matter?
Due to the congruence of the triangles:
Third sides also have identical angles.
the other two complementary angles are equal
Two triangles, congruent since all three sides are the same length, but one flipped and rotatedCongruent triangles can be turned and/or mirror images of each other (reflected).
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5 2/3 divided by 2 1/8 Perform the indicated operation.
Answer: 2 and 2/3
Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.
You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.
So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.
This gives us 17/3 ÷ 17/8.
When we divide fractions, we just change the division sign
to multiplication and take the reciprocal (flip) the second fraction.
So we have 17/3 · 8/17.
before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.
So we have 1/3 · 8/1 which is 8/3.
Now since 3 goes into 8 twice, our we have 2 as our whole fraction.
Since there is 2/3 left over, we have a fraction of 2/3.
So our final answer is 2 and 2/3.
What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 80 less than the sum of the measures of the base angles?
Answer: 65 °
Step-by-step explanation:
Let x = measure of a base angle
Base angles of an isosceles triangle are equal
Sum of interior angles of a triangle is always 180:
x + x + (2x - 80) = 180
4x - 80 = 180
4x = 260
x = 65
The questions are in the picture
The linear function is of:
P(t) = 3265t + 34687.
Using the linear function, the estimate for 2016 is of:
54,277.
The exponential function is of:
P(t) = 34687(1.0941)^t.
Using the exponential function, the estimate for 2016 is of:
59,499.
What is the linear function?The linear function is defined as follows:
P(t) = mt + b.
The coefficients of the function are given as follows:
m is the slope, representing the yearly change in the population.b is the intercept, representing the population in 2010.In the context of this problem, these parameters are given as follows:
m = 37,952 - 34,687 = 3265.b = 34,687.Hence the function is:
P(t) = 3265t + 34687.
2016 is 6 years after 2010, hence the estimate is given as follows:
P(6) = 3265(6) + 34687 = 54,277.
What is the exponential function?The exponential function is defined as follows:
P(t) = ab^t.
In which the coefficients are given as follows:
a is the population in 2010.b is the rate of change.Hence the parameters are given as follows:
a = 34687.b = 37952/34687 = 1.0941.Hence the function is of:
P(t) = 34687(1.0941)^t.
Then the estimate for the year of 2016 is of:
P(6) = 34687(1.0941)^6 = 59,499.
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which number line represents the solution set for the inequality 4x 3 2 2x
The solution to the inequality expression is x ≥ - 5
what is inequality expressions ?
Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.
solution:
The given expression - 4(x + 3) ≤ –2 – 2x
- 4x - 12 ≤ -2 - 2x
-4x + 2x ≤ -2 + 12
-2x ≤ 10
-x ≤ 5
Multiply both sides by - 1
Then x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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Raul hit a golf ball 26.4 yards. A.J. can hit a golf ball 10 times as far. How far can A,J, hit the ball?
Answer:
264
Step-by-step explanation:
26.4 * 10 = 264
May I please have a brainliest? Thank you!
Answer:
264 yards
Step-by-step explanation:
When we multiply a decimal number by ten, we can just move the decimal point to the right by one!
So, 26.4 becomes 264
So, A.J. can hit a golf ball 264 yards
Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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This exercise uses, the population growth model
A culture starts with 8300 bacteria, After 1 hour the count is 10,000 .
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t)=8300(1)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
17485.75 x bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
50times
P is equal to 8700% for population x time in hours.
What is population growth model?P is equal to 8700% for population x time in hours. 2Ae%5E%28kx%29
K's model must be solved. ln%28p%29=ln%288700%29%
2Bkx%2Aln%28e%
29\skx%
2A1=ln%28p%29-ln%288700%
29\sk=%281%
2Fx%29%
28ln%28p%29-ln%288700%29%29
Replace the point (1,10000).
k=%281%
2F1%29%
28ln%2810000%
29-ln%288700%
29%
29\sk=ln%2810000%
29-ln%288700%
29 k=0.13926, which you might only desire to three or maybe even two significant figures.
You may just enter 10000% if you want p after two hours.
And it SHOULD be the same as 8700% (2810000%2F8700%).
Just give it a shot and see, 2Ae%5E%280.139%2A2%29. More particular, the model is highlighted by p=8700%. 2Ae%5E%280.139% 2Ax%29% 29.
Determine how long to double x.
Take the logs on both sides, then find x.
To put it more simply, start with this form: 2=1%2Ae%5E%280.13926%2Ax%29
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How do you know if a graph has two solutions?
If the line intersects the parabola in two places, then two solutions are true for both equations.
We graph both equations in the same coordinate system to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.
There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel). There are an infinite number of solutions that hold for both equations if the equations' graphs are identical.
Two solutions hold for both equations if the line crosses the parabola twice.
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If the boundary line is dashed and the graph is shaded below the line what inequality do we use and why?
Answer: <
Step-by-step explanation:
If the boundary line is dashed, it means we will use < or > because it is not equal to, so that rules out ≤ or ≥.
Next, if the graph is shaded below the line we will use < because the graph is less than.
if somthing costid 64 dolers and thay sold it for 90% of the originol price how much wold it be
?
Answer:
6.40
Step-by-step explanation:
For this we will divide,
look below for a explanation
Purchase Price:
$64
Discount:
(64 x 90)/100 = $57.60
Final Price:
64 - 57.60 = $6.40
A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
what is the range of the function on the graph all real numbers
The required range is [0,∞]
All values, or inputs, constitute a function's domain, while all values, or outputs, constitute its range.
When examining a graph, the range of the function is from up to down, and the domain refers to all of the values on the graph from right to left.
Therefore , the range of the function on the graph of all real numbers extends from zero to positive infinity.
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convert 1/2 into a decimal
Answer:0.5
Step-by-step explanation:
here you go
TO furnish a cafeteria, a school can spend $5200 on tables and chairs. Tables cost 200$ and chairs cost 40$. Each table will have 8 chairs around it. Write and solve a system of equations for x$ and y$. How many tables and chairs will the school purchase?
The school will purchase 10 tables and 80 chairs.
With the aid of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems. We employ definite or fixed-value numbers in algebra, such as -1, 5, 0, 06, etc. In addition to using numbers, algebra also makes use of variables like x, y, and z.
Given that a school can spend $5200 on tables and chairs. The tables cost 200$ and the chairs cost 40$. There will be 8 chairs around each table.
We have to determine the number of tables and chairs will the school purchase.
Let us consider x represents the tables and y represents the chairs.
Tables cost = 200x chairs cost= 40y
200x + 40y = 5200 ----(1)
There will be 8 chairs around each table.
1 table = 8 chairs
t = 1/8c
x = (1/8)y (t means x and c means y)
substitute x value in equation(1)
200(1/8)y + 40y = 5200
(200/8)y + 40y = 5200
25y + 40y = 5200
65y = 5200
y = 5200/65
y = 80
Substitute y value in equation (1)
200x + 40(80) = 5200
200x + 3200 = 5200
200x = 5200 – 3200
200x = 2000
X = 2000/200
X = 10
Therefore the school will purchase 10 tables and 80 chairs.
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Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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Solve for x xx. Enter the solutions from least to greatest. Round to two decimal places. ( x + 3 ) 2 − 3 = 0 (x+3) 2 −3=0
The solution of the equation (x + 3)² − 3 = 0 least to greatest will be negative 4.73 and negative 1.27.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
(x + 3)² − 3 = 0
Simplify the equation, then the value of the variable 'x' is given as,
(x + 3)² − 3 = 0
(x + 3)² = 3
x + 3 = ± √3
x = - 3 ± √3
x = - 3 ± 1.73
x = -4.73, -1.27
The solution of the equation (x + 3)² − 3 = 0 least to greatest will be negative 4.73 and negative 1.27.
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How do you know if AB and CD are congruent?
If the length of two segments is equal then the two segments are congruent.
If l(AB) = l(CD) then seg AB ≅ seg CD.
Two line segments to be congruent if and only if they have the same length.
Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.
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Please I need help on both part A and B
Answer:
Step-by-step explanation:
I hope anyone answers
Help
Please
What is the rule of proof?
The rules of proof is that every statement should be justified and never assume things when proofing in contradiction
The basic rules of proofs are as followings:
Each assertion should be legitimate.A support can allude to earlier lines of the verification, the speculation as well as recently demonstrated explanations from the book.Cases are frequently expected to finish a proof which has proclamations with an "or" in them.A logical inconsistency is reached when an assertion goes against any of the speculations, an earlier line of the confirmation, or any well established truth .A proof by logical inconsistency is possibly finished when a logical inconsistency has been arrived at for each situation.On the off chance that you can't find a defense and you are certain it is valid, you might wish to compose a separate verification as an after thought to demonstrate that support and afterward apply it to your unique circumstanceDuring a proof you might present new factors by saying "Let x be..."To know more about Proof here
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please help!
Jocelyn has a points card for a movie theater.
She receives 25 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Jocelyn can make to earn her first free movie ticket.
Answer:
25 + 12.5v ≤ 170
Step-by-step explanation:
Match each equation with a graph above:
log (x) a. red R
10× b. black K
e× c. green G
ln (x) d. blue B
The equations are matched as below and the graph is plotted and attached
log (x) b. black K 10× d. blue Be× c. green Gln (x) a. red RWhat is logarithm graph?A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.
The exponential graph is the opposite of logarithmic graph
In the given functions
log (x) is logarithmic function
10× is exponential function
Similarly, the natural exponent graph is the opposite of natural logarithm graph
in the given functions
e× is the natural exponential
ln (x) is the natural logarithm
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Why is it important to make ten?
It is important to make a ten in lower grades to make students understand the subtraction.
According to the question,
We have the following information:
Making a ten
Now, we know that in making a ten method we take 1 from the next left digit of the number from which we are subtracting any other number. Now, this number 1 is treated as 10 instead of 1 and then 10 is added to the digit to ease subtraction in lower grades.
Now, the subtraction can be easily performed by subtracting the smaller number from the larger number.
Hence, it is important to make tens in lower grades to make students understand the subtraction.
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EVALUATE ₈C₇ and ₁₁P₅
₈C₇=
₁₁P₅=
The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440
How to determine the permutation and combination expressions?From the question, we have
⁸C₇ and ¹¹P₅
The combination expression: ⁸C₇
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 8 and r = 7
Substitute the known values in the above equation
Total = ⁸C₇
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
⁸C₇ = 8!/7!1!
Evaluate
⁸C₇ = 8
(b) The permutation expression: ¹¹P₅
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 11 and r = 5
Substitute the known values in the above equation
Total = ¹¹P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)
So, we have
¹¹P₅ = 11!/6!
Evaluate
¹¹P₅ = 55440
Hence, the values are 8 and 55440
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Look at the transformation of a 2-dimensional shape on the coordinate plane.
(x, y)→(−y,−x)
Which statement is true?
In the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x), the statement which is true is that: d. Transformation preserves distance and angle measure both.
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
Based on the transformation rule (x, y) → (-y, -x), we can reasonably infer and logically deduce that it represents or models a rotation of the geometric shape, followed by a reflection, which both preserves distance and angle measure based on these transformation rules:
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Complete Question:
Look at the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x). Which statement is true?
a. Transformation preserves only distance.
b. Transformation preserves only angle measures.
c. Transformation preserves neither distance nor angle.
d. Transformation preserves distance and angle measure both.
if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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