Given:
Initial number of participants = 128
During each round, half of the players are eliminated.
To find:
The number of players remain after 5 rounds.
Solution:
It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.
If half of the players are eliminated, then half of the players are remained.
So, the initial value is 128 and the decay factor is [tex]\dfrac{1}{2}[/tex].
The general exponential decay model is:
[tex]y=a(b)^x[/tex]
Where, a is the initial value and b is the decay factor.
Putting [tex]a=128[/tex] and [tex]b=\dfrac{1}{2}[/tex] in the above model, we get
[tex]y=128\left(\dfrac{1}{2}\right)^x[/tex]
Here, y is the number of remaining players after x rounds.
Substituting [tex]x=5[/tex], we get
[tex]y=128\left(\dfrac{1}{2}\right)^5[/tex]
[tex]y=128\left(\dfrac{1}{32}\right)[/tex]
[tex]y=4[/tex]
Therefore, the required model is [tex]y=128\left(\dfrac{1}{2}\right)^x[/tex] and the number of players remain after 5 rounds is 4.
The class average on a math test was an 82 with a standard deviation of 5. If the
data is normally distributed, which statements are true?
1. A student scoring a 74 would have a z -score of -1.6.
2. About 68% of the students scored below an 87.
3. A z-score of 2.6 would be a test
score of 95.
4. About 16% of the class scored a 77 or below.
45. About 25% of the class scored above a 92.
Answer:
Option 3 and 4.
Step-by-step explanation:
The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation[/tex]
Given that mean (μ) = 82, standard deviation (σ) = 5
1) For x = 74:
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{74-82}{5} =-1.6[/tex]
Option 1 is incorrect
2) For x < 87
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{87-82}{5} =1[/tex]
From the normal distribution table, P(x < 87) = P(z < 1) = 0.8413 = 84.13%
Option 2 is incorrect
3) For x = 95:
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{95-82}{5} =2.6[/tex]
Option 3 is correct
4) For x < 77
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{77-82}{5} =-1[/tex]
From the normal distribution table, P(x < 77) = P(z < -1) = 0.16 = 16%
Option 4 is correct
5) For x > 92
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{92-82}{5} =2[/tex]
From the normal distribution table, P(x > 92) = P(z > 2) = 1 - P(z < -2) = 1 - 0.9772 = 0.0228 = 2.28%
Option 5 is incorrect
please answer and explain the link below
Answer:
See explanation.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FunctionsFunction NotationCalculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Left-Side Limit: [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.[/tex]
Step 2: Find Right Limit
Substitute in variables [Right-Side Limit]: [tex]\displaystyle \lim_{x \to 3^+} 5 - x[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 3^+} 5 - x = 5 - 3[/tex]Subtract: [tex]\displaystyle \lim_{x \to 3^+} 5 - x = 2[/tex]∴ the right-side limit equals 2.
Step 3: Find Left Limit
Substitute in variables [Left-Side Limit]: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1}[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}[/tex][√Radical] Add: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}[/tex][√Radical] Evaluate: [tex]\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = 2[/tex]∴ the left-side limit equals 2.
Step 4: Find Limit
The right and left-side limits are equal.
∴ [tex]\displaystyle \lim_{x \to 3} f(x) = 2[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Help please, I swear I can't even try on this. I'm just gonna die if I try.
Answer:
1) word form
three million,two hundred and ninety eight thousand and seventy six
expanded form
5000000+3000+87
2)5,003,087
3)64,000,239
Which number on the number line should be plotted?
A grocery store owner budgets $5,000 to buy and maintain a booth for 300 days to give out samples of food. If she bought the booth for $1,400, how much money, in dollars, can she spend on food each day for samples and stay within budget? Write an inequality that represents this situation and indicate what the solution to the inequality will look like.
Answer:
x ≤ $12 a day
Step-by-step explanation:
5000-1400=3600
3600/300=12
sometimes we can determine the number of solutions that a system of equations has by simply observing and drawing conclusions from the equations. this is called
Answer:
observations and quadratic formula
what does the challenges do?
Answer:
question that must be answered in a given time for a lot of points
Answer:
so if you do them the percentages will increase and you will get points so gou can ask questions i did one and spent all 100 just for someone to translate im s-t-u-p-i-d and then i commented no youre not
may I please have help from anyone thank you so much !
Please help, giving Brainliest and 50 points!
Answer:
5^8
Step-by-step explanation:
Hey,
Know out exponent division propety knowledge. We can solve.
5^12/5^4 = 5^12-4=5^8
Hope this helped,
Joe Louis2
Answer:
5^8
Step-by-step explanation:
We know that a^b ÷ a^ c = a^ ( b-c)
5^12 ÷ 5^4 = 5^ (12-4) = 5^8
12% of 4 meters ( in cm)
Answer:
48 cm
Step-by-step explanation:
percent x meters x centimeters in meters
.12 x 4 x 100
Answer:
48 cm
Step-by-step explanation:
12/100 * 4 = 48 meters
1 meter = 100 cm
0.48 m = x Cross Multiply
1*x = 0.48 * 100
x = 48 cm
find the area of a circle if x=12 and y=3
Answer:
12.3693169
Step-by-step explanation:
x^2+y^2=r^2
(12)^2=(3)^2=sqroot(153)
=12.3693169
8.
Find the slope of the in line containing the ordered pairs. (7 marks)
a. A(2,-5), B(-2,6)
Answer:
= -11/4
Step-by-step explanation:
To find the slope given two points
m = ( y2-y1)/(x2-x1)
= (6 - -5)/(-2 -2)
= (6+5)/(-2-2)
= 11/-4
= -11/4
Answer:
-2.75 (-2 3/4)
Step-by-step explanation:
you can do rise of a run whenever you have two points so you have 6-(-5)/-2-2 and solve so -11/4 and that equals -2.75.
What is the solution to the system of equation?
Answer:
x = 0
y = 3
Step-by-step explanation:
-x - 2y = - 6
0 - 2(3) = -6
6 = 6
-3x + 2y = 6
-3(0) + 2(3) = 6
0 + 6 = 6
which number is represented by the number line
Answer: B
Step-by-step explanation: The number line has tally marks up to 3, so 3 has to be divided by something, meaning A and C do not work. There are 9 total tally marks circled, so the equation equals 9, leaving B as the only possible answer. Also, there are three tally marks per whole number, so each tally is 1/3, which is equal to 2/6, further proving it is B.
Solving right triangles
Answer:
i can see the actual question, what is it?
In right triangles one of the angles will always be 90 degrees.
So if you had a right triangle with one right angle, a number, and a number, they always have to add up to 90 degrees as well, because a triangle is always 180 degrees
so
side a = 90side b = xside c = yx + y = 90x + y + 90 = 180What is the nth term rule of the linear sequence below?
22,18,14,10,6.....
Answer:
it goes down by 4 every time
What is the product of (3a)(-6b)(-4)?
Carly is buying deli meat for her lunches this week. Turkey is on sale for $5.80 per pound. If Carly buys 1.25 pounds of turkey, how much money does she spend?
Answer:
Carly will have to spend $7.25
Step-by-step explanation:
We know that:
1 pound of turkey = $5.80
To find how much 1.25 pounds of turkey will cost, multiply:
5.80 x 1.25 = 7.25
Therefore, 1.25 pounds of turkey will cost $7.25
I really hope this helps!
-SpaceMarsh
Joe has eaten 2/5 of a pizza. Jane has eaten 1/9 of a pizza.
How many times more pizza has Joe eaten than Jane?
Two circles have a scale factor of 3:2. What is the ratio of the circumferences of these circles?
A. 12:26
B. 13:12
C. 9:4
D. 3:2
Answer:
3:2
Step-by-step explanation:
The circumference is a distance. The ratio of the distance is the same as the scale factor. The ratio of the areas is the ratio of the scale factor squared and the volume is the scale factor cubed.
Layla and Bobby are making potholders with their grandmother. They have a total of 1.5 yards of fabric they can use, and it takes one-eighth of a yard to make each potholder. What is the maximum number of potholders they can make?
3
A rectangle is 20 cm long and 8 cm wide find the perimeter
(1 Point)
56 cm
28 cm
110 cm
52 cm
help jekrjrifirnrifjrnrifn
Answer:
c
I hope it's the right answer
Guys I need your help , what is - 16t2 + 64+ + 3?
Answer:
the answer is -32t + 67
Step-by-step explanation:
-16t2 +64 + 3
= -16t x 2 +64 +3
= -32t +67
Answer:
−16[tex]t^{2}[/tex]+67Step-by-step explanation:
HURRYYYY. which linear inequality is represented by the graph?
Answer:
C
Step-by-step explanation:
i did this in 6th grade too man i gotchu
Please help!! I will brainlest your right answer please!!! I am stuck very badly!! Please
Answer:
See below.
Step-by-step explanation:
2a. E = 8.25h + 1.2n
2b. E = 8.25 * 3.5 + 1.2 * 10 = $40.88
2c. 8.25 * 8 + 1.2n = 91.2
66 + 1.2n = 91.2
1.2n = 25.2
n = 21 magazines.
Answer:
In picture
Step-by-step explanation:
Please give brainliest if it helped, thanks!
Review this code snippet: var time = 15; var greeting; if ( time < 12 ) { greeting = “good morning”; } else if ( time < 18 ) { greeting = “good afternoon”; } else { greeting = “good evening”; } console.log(greeting); What is the message that gets printed to the console?
Explanation:
We're given that time = 15
From this, we see that time < 12 evaluates to false, because 15 is not smaller than 12. Put another way, 15 < 12 is false.
But time < 18 is true since 15 < 18 is true. So we execute the second block of code and have the greeting variable be set to the string "good afternoon". This is what's displayed to the console without any quotes of course.
Customers can pick their own cherries at cherry hill. they pay $4 to enter the farm and $3.50 per pound for the cherries they pick. write an equation to model the total cost, y, for x pounds of cherries
Answer:
The Equation would be $4 + $3.50x = y
Step-by-step explanation:
HELP ASAP PLEASEE
I WILL MARK BRAINLIST
A die has 6 faces numbered 1 to 6.On a single roll of die,find the probability of not getting the number 6
Step-by-step explanation:
probability of not getting six=5/6
is your answer
