Answer: Choice B
Game A is not fair, and game B is fair.
==============================================================
We'll start with game A.
The sides of the dice are {1,2,3,4,5,6}
There are 6*6 = 36 ways to roll two dice.
If we roll two odd numbers, say 3 and 5, the product is odd because 3*5 = 15.
If any of the numbers are even, then the product is even. Eg: 4*5 = 20 or 2*6 = 12.
To be an even number, 2 must be a factor.
So you can probably see that it's more likely to get an even number product considering that in order to get an odd product, both values must be odd (which narrows the selection pool). We can say that game A is not fair. It favors player 1 more. If you're sure about this, then I recommend looking at a multiplication table but only focus on the first 6 rows and 6 columns. Ignore the row and column that has 0s in it.
------------------------------
Now onto game B
The rules are nearly the same, except now instead of multiplying the dice values, we add them up.
We still have 6*6 = 36 outcomes.
Here are some handy rules we'll take into account
even+even = eveneven+odd = oddodd+odd = evenIf the first dice rolls to '1', then there are 3 ways to get an even number (rolling either 1,3,or 5 on the second dice) and there are 3 ways to get an odd number (rolling either 2,4,or 6 on the second dice). We can see that there are the same number of ways to get an even sum or an odd sum. Apply this in general to any result that the first dice shows, and this basically leads to the conclusion that half of the 36 sums are even, and the other half are odd. We have a fair game now. Refer to a sum of dice chart if you need more convincing.
Answer:
Game A is not fair, and game B is fair.
Step-by-step explanation:
test on iready
giải phương trình vi phân: y" - 5y' + 6y = 6x + 7
Неоднородное ДУ второго порядка. Детали в аттаче.
PLEASE HELP ME WILL GIVE BRAINLIEST
Answer:
Reason 5
Step-by-step explanation:
Reason 1 and 2 are Given
Reason 3 is Reflexive
Reason 4 is Side-Side-Side congruency
Answer:
Reason 5
Step-by-step explanation:
It helps to know what CPCTC means and how it's used.
CPCTC means "corresponding parts of congruent triangles are congruent."
To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.
Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.
In step 4, the triangles are proven congruent by SSS.
Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.
i need help pls it’s timedd!!!!
Answer:
5.
Step-by-step explanation:
If you were to rotate the triangle, you can apply Pythagoras Theorem.
Therefore,
a^2 = 12^2 - 13^2 (Note: a^2 = a squared)
a^2 = 144 - 169
a^2 = -25.
a = 5.
Not sure why its negative though im pretty sure its the right answer.
in BCD triangle :
DC^2 = BC^2 + BD^2
13^2 = 12^2 + BD^2
169 = 144 + BD^2
BD^2 = 169 - 144
BD^2 = 25
BD = 5
_______________________
In the other hand we have :
BD^2 = AB × BC
5^2 = AB × 12
AB = 25/12
________________________
Also we have :
AD^2 = AB × AC
AD^2 = 25/12 × ( 25/12 + 12 )
AD^2 = 25/12 × ( 25/12 + 144/12 )
AD^2 = 25/12 × 169/12
AD^2 = 25 × 169 / 12 × 12
AD^2 = 5 × 5 × 13 × 13 / 12 × 12
AD = 5 × 13 / 12
AD = 65 / 12
AD = 5.42
Thus the correct answer is option C
Can I get some help with this question? I have attempted several times and failed.
9514 1404 393
Answer:
B. relative maximum of 8.25 at x=2.5
Step-by-step explanation:
A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...
x = -5/(2(-1)) = 5/2
The value of the extreme is ...
f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25
The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.
The function has a relative maximum of 8.25 at x = 2.5.
__
A graphing calculator can show this easily.
CAN SOMEONE PLEASE HELP ME GOOD, I need this to graduate ): 5. Given that AABC - ADEC, find the
value of x.
Answer:
ans: 4
Step-by-step explanation:
corresponding sides are proportional since given triangle are similar triangle, I.e
(4/5.5) = { (2x+8)/(6x-2)}
8/11 = ( x+ 4 ) / ( 3x - 1 )
8( 3x - 1 )= 11( x + 4 )
24x - 8 = 11x + 44
13x = 52
x = 4
At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is
Answer:
The appropriate answer is "$12".
Step-by-step explanation:
As per the question,
Price per ticket,
= [tex]4+k[/tex]
Number of people,
= [tex]1800-90k[/tex]
Now,
The revenue (R) will be:
= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]
By putting the values, we get
= [tex](4+k) (1800-9k)[/tex]
= [tex]-90k^2+1440k+7200[/tex]
or,
⇒ [tex]R'=1440-180k=0[/tex]
⇒ [tex]180k=1440[/tex]
⇒ [tex]k=\frac{1440}{180}[/tex]
[tex]=8[/tex]
hence,
The ticket price will be:
= [tex]4+k[/tex]
= [tex]4+8[/tex]
= [tex]12[/tex] ($)
anyone help me, let's prove
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
Find x. Round to the nearest tenth: 29° 500ft
X=[?]ft
9514 1404 393
Answer:
437.3 ft
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(29°) = x/(500 ft)
x = (500 ft)cos(29°)
x ≈ 437.3 ft
what are functions in math
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.
Required:
Is it likely that his team's scores is different than the national average?
Answer:
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Step-by-step explanation:
The National average number of runs scored by a LL team is
μ = 5.7
Sample Information:
size sample n = 5
sample average x = 7.4
sample standard deviation s = 2.88
Is required to investigate if that sample average is statistically different from the National average
We will do a test with 95 % of confidence Interval that means
significance level α = 5 % or α = 0.05.
The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.
Then α = 0.05 α/2 = 0.025
df = n - 1 df = 5 - 1 df = 4
Then from t-student table we get t(c) = 2.132
Hypothesis test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate t (s)
t(s) = ( x - μ ) / s/√n
t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88
t(s) = 1.7* 2.24 / 2.88
t(s) = 1.32
Comparing t(s) and t(c)
1.32 < 2.132
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Nếu cắt mặt cầu bởi một mặt phẳng chiếu đứng thì hình chiếu bằng của giao tuyến là:
Answer:
Im sorry I can't understand you
Helppppo plsssssssssss I need helppp with thissss
Answer:
82 is what r equals
Step-by-step explanation:
So, lets go over what we know:
D equals rt, or r * t:
D=r*t
The table shows:
t=2 - d=164
t=3 - d=246
These are the only 2 values we need to look at.
We know that D= r*t, and we can just plug in the values found in the table for t and d to solve for r. So:
164= r * 2
Divide both sides by 2 to iscolate r:
82=r
So it seems like r is equal to 82, however this might be exponential or inaccurate, so lets double check witht the nexty values on the table:
246=r*3
Divide by 3 to iscolate the r:
82=r
So we know that r must equal 82.
Hope this helps!
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%:
There are 750 identical plastic chips numbered 1 through 750 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Answer:
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box
This means that [tex]a = 1, b = 750[/tex]
What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?
[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
what percentage of the appies are yellow?
Answer:
20%
Step-by-step explanation:
6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Learn more about triangle congruency here:
https://brainly.com/question/12413243
#SPJ7
Choose the correct vertex of the function f(x) = x2 - X + 2.
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
f(x) = x² - X + 2.
Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]
[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
A box with a square base and open top must have a volume of 256000 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base.
Answer:
Follows are the response to the given question:
Step-by-step explanation:
The volume of the box:
[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]
The surface area of the open box is:
[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]
Use above formula
[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]
[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]
Now
[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]
therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.
[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]
I need help please I dont understand
I don’t get this at all
Answer:
0.21
Step-by-step explanation:
There's 21 kids with a cell phone and no tablet
so 21/100 = 0.21
HELP PLEASE IM STUCK!
1. Which of these describes the relation for this set of coordinate pairs?
{(-1, 5), (12, 18), (0, 6), (-3, 3), (4, ?), (?, 11)}
a. x - y = 6 b. f(x) = x +6 c. f(x) = 6 d. y = 6x e. None of these
Answer:
b) f(x) = x + 6
Step-by-step explanation:
The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.
How do you solve x[tex]x^{2} +4x+3=0[/tex]?
Answer:
[tex]{ \tt{ {x}^{2} + 4x + 3 = 0}} \\ { \tt{(x + 1)(x + 3) = 0}} \\ \\ { \tt{x = - 1 \: \: and \: \: - 3}}[/tex]
Find the value of y and show work
Answer:
75
Step-by-step explanation:
∠K and ∠ R are congruent (equal)
Triangle Sum Theory - angles of all triangles add to 180
180 - 79 - 26 = 75
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
Find the length of side x
Answer:
Step-by-step explanation:
tan(30) = x/1
sqrt(3) / 3 = x/1
x= sqrt(3) / 2
Which expression are greater than 1/2? Choose all the apply
Answer:
25/30
5/8
Step-by-step explanation:
Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?
to determine which fractions are greater than 1/2, convert the fractions to decimals
to convert to decimals, divide the numerator by the denominator
1/2 = 0.5 less than half
6/14 = 0.43 less than half
5/8 = 0.625 greater than half
25 / 30 = 0.83 greater than half
3 / 6 = 0.5 equal to half
When comparing two box-plots that show the same type of information, what determines agreement within the data?
A.the range of the quartiles in each data set
B.the median of each data set
C.the mean of each data set
D.the number of values in each data set
Answer:
c.the mean of each data set
Answer:
A
Step-by-step explanation:
Segment [tex]$s_1$[/tex] has endpoints at [tex]$(3+\sqrt{2},5)$[/tex] and[tex]$(4,7)$[/tex]. Segment [tex]$s_2$[/tex] has endpoints at [tex]$(6-\sqrt{2},3)$[/tex] and[tex]$(3,5)$[/tex]. Find the midpoint of the segment with endpoints at the midpoints of [tex]$s_1$[/tex] and [tex]$s_2$[/tex]. Express your answer as [tex]$(a,b)$[/tex].
Answer:
The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).
Step-by-step explanation:
Midpoint of a segment:
The coordinates of the midpoint of a segment are the mean of the coordinates of the endpoints of the segment.
Midpoint of s1:
Using the endpoints given in the exercise.
[tex]x = \frac{3 + \sqrt{2} + 4}{2} = \frac{7 + \sqrt{2}}{2}[/tex]
[tex]y = \frac{5 + 7}{2} = \frac{12}{2} = 6[/tex]
Thus:
[tex]M_{s1} = (\frac{7 + \sqrt{2}}{2},6)[/tex]
Midpoint of s2:
[tex]x = \frac{6 - \sqrt{2} + 3}{2} = \frac{9 - \sqrt{2}}{2}[/tex]
[tex]y = \frac{3 + 5}{2} = \frac{8}{2} = 4[/tex]
Thus:
[tex]M_{s2} = (\frac{9 - \sqrt{2}}{2}, 4)[/tex]
Find the midpoint of the segment with endpoints at the midpoints of s1 and s2.
Now the midpoint of the segment with endpoints [tex]M_{s1}[/tex] and [tex]M_{s2}[/tex]. So
[tex]x = \frac{\frac{7 + \sqrt{2}}{2} + \frac{9 - \sqrt{2}}{2}}{2} = \frac{16}{4} = 4[/tex]
[tex]y = \frac{6 + 4}{2} = \frac{10}{2} = 5[/tex]
The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).
