Answer:
[tex]h \circ m \circ n \text{ where } h(x)=\sqrt{x} \text{ and } m(x)=1+\frac{15}{n} \text{ and } n(x)=x^3-9[/tex]
Step-by-step explanation:
Ok so I see a square root is on the whole thing.
I'm going to let the very outside function by [tex]h(x)=sqrt(x)[/tex].
Now I'm can't just let the inside function by one function [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] because we need three functions.
So I'm going to play with [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] a little to simplify it.
You could do long division. I'm just going to rewrite the top as
[tex]x^3+6=x^3-9+15[/tex].
[tex]g(x)=\frac{x^3-9+15}{x^3-9}=1+\frac{15}{x^3-9}[/tex].
So I'm going to let the next inside function after h be [tex]m(x)=1 + \frac{15}{x}[/tex].
Now my last function will be [tex]n(x)=x^3-9[/tex].
So my order is h(m(n(x))).
Let's check it:
[tex]h(m(x^3-9))[/tex]
[tex]h(1+\frac{15}{x^3-9})[/tex]
[tex]h(\frac{x^3-9+15}{x^3-9})[/tex]
[tex]h(\frac{x^3+6}{x^3-9})[/tex]
[tex]\sqrt{ \frac{x^3+6}{x^3-9}}[/tex]
To express the function √(x^3+6)/√(x^3-9) as a composition of non-identity functions, we can rewrite it in terms of exponential and logarithmic functions.
Explanation:To express the function √(x^3+6)/√(x^3-9) as a composition of three or more non-identity functions, we can start by rewriting √(x^3+6) and √(x^3-9) as powers:
√(x^3+6) = (x^3+6)^(1/2)
√(x^3-9) = (x^3-9)^(1/2)
Next, we can express (x^3+6)^(1/2) and (x^3-9)^(1/2) in terms of powers of its components. Let's denote a = x^3+6 and b = x^3-9:
(x^3+6)^(1/2) = (a)^(1/2)
(x^3-9)^(1/2) = (b)^(1/2)
Finally, we can express these in terms of exponential and logarithmic functions:
(a)^(1/2) = e^(0.5ln(a))
(b)^(1/2) = e^(0.5ln(b))
Therefore, the function √(x^3+6)/√(x^3-9) can be expressed as a composition of three non-identity functions:
√(x^3+6)/√(x^3-9) = e^(0.5ln(a))/e^(0.5ln(b))
19.) Here's the data (sorted) of the ages of 91 women who won the Oscar for Best Actress in a Leading Role:
21, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 37, 37, 37, 37, 38, 38, 38, 39, 39, 39, 41, 41, 41, 41, 42, 42, 44, 45, 45, 45, 47, 49, 49, 54, 60, 60, 61, 61, 61, 62, 62, 74, 81
Give the five number summary.
Final answer:
The five number summary for the ages of best actress Oscar winners is composed of the minimum (21), first quartile (Q1 - 30), median (Q2 - 33), third quartile (Q3 - 41), and maximum (81) values.
Explanation:
The first step to finding the five number summary is to identify the minimum, first quartile (Q1), median (second quartile Q2), third quartile (Q3), and the maximum from the sorted dataset of best actress Oscar winners.
Minimum: The smallest number in the dataset is 21.
Q1: The first quartile is the median of the first half of the data. Since we have an odd number of data points (91), we split the data into two parts of 45 values each. The first quartile is the median of the first 45 ages, which is the 23rd data point in the sorted list when counting from the smallest age. In our case, Q1 is 30.
Median (Q2): The median is the middle value, which is the 46th data point for our 91 data points. The median is also the age of 33.
Q3: The third quartile is the median of the second half of the data. The third quartile is the 68th data point, which is the age of 41.
Maximum: The largest age in the dataset is 81.
Therefore, the five number summary of the ages of best actress Oscar winners is 21, 30, 33, 41, and 81.
Need to find A, B, and C!
Answer:
Mean: 4.44 add up every number and divide it by how many there is.
Median: 3 put from least to greatest and count till the middle.
Mode: 3 because it appears the most
Answer:
A. Mean = $41900
B. Median = $37000
C. Mode = $37000
Step-by-step explanation:
A. Mean
Here
n=40
Mean = Sum of values/n
[tex]Mean = \frac{(3)(18000)+(3)(22000)+(3)(25000)+(5)(34000)+(17)(37000)+(2)(45000)+52000+(5)(80000)+140000}{40}\\=\frac{54000+66000+75000+170000+629000+90000+52000+400000+140000}{40} \\=\frac{1676000}{40}\\=41900[/tex]
Mean = $41900
B. Median:
As the number of salaries is even,
the median will be mean of middle two terms
[tex]Median= \frac{1}{2}(\frac{n}{2}th\ term+ \frac{n+2}{2}th\ term)\\= \frac{1}{2}(\frac{40}{2}th\ term+ \frac{40+2}{2}th\ term)\\=\frac{1}{2} (20th + 21st)}\\[/tex]
The 20th and 21st term will be 37000
So their mean will be same
So,
Median = $37000
C. Mode
Mode is the value which occurs most of the time in data.
the occurrence of 37000 is highest in the given data.
So,
Mode = $37000 ..
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, what is the total weight in tons of all the wheat that will be placed on the first 51 squares? (Assume that each grain of wheat weighs 1/7000 pound. Remember that 1 ton equals 2000 lbs.)
Answer:
Step-by-step explanation:
The number of grains of wheat on the n(th) square is 2^(n-1), or 2 to
the power of n-1. This is because the first square has 2^0 = 1 grain,
the second has 2^1 = 2, and the n(th) square has twice as many as the
previous. Thus the total number of grains of wheat is
S = 1 + 2 + 4 + 8 + ... + 2^63.
Since this is a geometric sequence with common ratio 2, the sum is
2^64 - 1
S = -------- = 2^64 - 1 = 18446744073709551615.
2 - 1
can someone help me solve this step by step? tyyyy
Answer:
x=4/7
Step-by-step explanation:
6 - 2/3(x+5) = 4x
First I want to clear the fraction so I will multiply everything by 3
3*6 -3* 2/3(x+5) = 3*4x
18 - 2(x+5) =12x
Distribute
18 - 2x-10 =12x
Combine like terms
8 -2x = 12x
Add 2x to each side
8 -2x+2x =12x+2x
8 = 14x
Divide each side by 14
8/14 =14x/14
8/14=x
Divide top and bottom by 2
4/7=x
Which set of ratios could be used to determine if one triangle is a dilation of the other
Final answer:
To determine if one triangle is a dilation of another, ratios of corresponding sides must be compared and set up as proportions to see if they are equivalent. When the proportions are equivalent, it indicates a consistent scale factor, confirming a dilation.
Explanation:
To determine if one triangle is a dilation of the other, we compare the ratios of corresponding sides from each triangle. A dilation occurs when all sides of one triangle are in proportion with the sides of a second triangle by the same scale factor. For example, if one triangle has sides of length 3, 4, and 5, and the second triangle has sides of length 6, 8, and 10, then the ratios of the corresponding sides (3/6, 4/8, 5/10) all simplify to 1/2, indicating that the second triangle is a dilation of the first.
To use ratios to determine if one triangle is a dilation of another, you need to set up proportions. For instance, we can express the ratios of corresponding lengths as fractions, and then set each of these ratios equal to the unit scale to form proportions. If the lengths of the triangles are given as 1 inch to 50 inches and 0.5 inches to 5 inches, we can set up the proportion 1/50 = 0.5/5 to show that they are equivalent.
In problems like this, proper notation and maintaining consistency across corresponding dimensions (e.g., width to width and length to length) is essential for accurate comparison.
The net of a square pyramid is shown:
Answer:
The surface area of the pyramid is 0.6625 inches²
Step-by-step explanation:
* Lets explain how to find the surface area of the square pyramid
- The square pyramid has 5 faces
- A square base
- Four triangular faces
- Its surface area is the sum of the areas of the five faces
- Area of the square = L × L , where L is the length of its sides
- Area of the triangle = 1/2 × b × h , where b is the length of its base
and h is the length of its height
∵ The length of the side of the square is 0.25 inches
∴ Area of the base = 0.25 × 0.25 = 0.0625 inches²
∵ The length of the base of the triangle is 0.25 inches and the length
of its height is 1.2 inches
∴ The area of its triangular face = 1/2 × 0.25 × 1.2 = 0.15 inches²
∵ The surface area of the pyramid = the sum of the areas of the 5 faces
∵ The area of the four triangular faces are equal
∴ The surface area = 0.0625 + (4 × 0.15) = 0.0625 + 0.6
∴ The surface area = 0.6625 inches²
* The surface area of the pyramid is 0.6625 inches²
the values in the table represent a linear function. what is the common difference of the associated arithmetic sequence?
x: 1, 2, ,3 ,4 ,5
y: 6, 22, 38, 54, 70.
A) 1
B) 20
C) 16
D) 5
Answer:
c
Step-by-step explanation:
You can find that 22-6=38-22=54-38=70-54=16
so the answer is c 16
Answer: The correct opion is
(C) 16.
Step-by-step explanation: Given that the values in the following table represent a linear function.
x: 1, 2, 3, 4, 5
y: 6, 22, 38, 54, 70.
We are to find the common difference of the associated arithmetic sequence.
If y = f(x) is the given function, then we see that
f(1) = 6, f(2) = 22, f(3) = 38, f(4) = 54 and f(5) = 70.
So, the common difference of the associated arithmetic sequence is given by
[tex]f(2)-f(1)=22-6=16,\\\\f(3)-f(2)=38-22=16,\\\\f(4)-f(3)=54-38=16,\\\\f(5)-f(4)=70-54=16,~~~\cdots.[/tex]
Thus, the required common difference of the associated arithmetic sequence is 16.
Option (C) is CORRECT.
What is the range of the function f(x) = -|X - 4| + 5?
19 A. (-0,5)
B. (-09. 5)
C. (-5. infinity)
D. (5 .infinity)
Answer:
Range = (-∞, 5)
Step-by-step explanation:
This is the absolute value function with transformation.
The parent function is f(x) = |x|
This function has a "negative" in front, so it makes it reflect about x axis
The -4 after x makes horizontal translation of 4 units right
the +5 at the end makes the function translate 5 units UP
The graph is shown in the attached picture.
Looking at the graph, we can clearly see the range. The range is the allowed y-values. Hence, we can see that the range is -infinity to 5
answer is not properly given, so i can't choose from the options, but the answer is -∞, 5 to 5
Does the equation represent a direct variation? If so, find the constant variation. 3y=5x+4
Answer:
No.
Step-by-step explanation:
Direction variation is of the form y = kx.
This is not direct variation.
The equation 3y = 5x + 4 does not represent a direct variation because it includes a constant term '+4'. A direct variation would only have the form y = kx without any added or subtracted constants.
The equation 3y=5x+4 represents a direct variation, and if so, to find the constant of variation. A direct variation is when one variable is a constant multiple of another, expressed in the form y = kx, where k is the constant of variation. In this case, the equation 3y = 5x + 4 is not a direct variation because of the additional constant term '+4'. For it to be a direct variation, y must be alone on one side of the equation, and there should be no constant term added or subtracted with the term that is a multiple of x.
To be a direct variation, the equation needs to have the form y = kx. In the practice equation y + 7 = 3x, if we solve for y, we get y = 3x - 7 which still would not be a direct variation because of the -7. The other example equation 4y = 8 is not in the form of direct variation either since it has no variable x in it; it represents a horizontal line where y is a constant.
What is the area of the trapezoid
O 120in
O 140in
O 91in
O 182in
Answer:
A = 91 in²Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]
b₁, b₂ - bases
h - height
We have b₁ = 20in, b₂ = 6in and h = 7in.
Substitute:
[tex]A=\dfrac{20+6}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)=91\ in^2[/tex]
What is the coefficient of x3y2 in the expansion of (2x + y)5?
Step-by-step answer:
The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n. Pascal's triangle will start with (1,1) = coefficients of (p,q)^n =1. For n=2, we add successive terms of the previous value of n. Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:
(1,1)
(1,2,1)
(1,3,3,1)
(1,4,6,4,1)
(1,5,10,10,5,1)
meaning for n=5, the binomial expansion for (P+Q)^5 is
P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5
Setting P=2x, Q=y in the term 10P^3Q^2, we get a term
10(2x)^3(y)^2
=10(8x^3)(y^2)
=80x^3y^2
So the required coefficient is K=80.
We can also find the coefficient 10 by binomial expansion of
n=5, x=3 in
C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10
Then again substituting 10(2x)^3(y)^2 = 80x^3y^2
to get the coefficient K=80.
Answer: 80
Step-by-step explanation: cuz
X^-2+4x^-1+3=0 solve by making appropriate substitution
ANSWER
[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]
EXPLANATION
The given equation is:
[tex] {x}^{ - 2} + 4 {x}^{ - 1} + 3 = 0[/tex]
Recall that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
[tex] \frac{1}{ {x}^{2} } + \frac{4}{x} + 3 = 0[/tex]
Or
[tex] {( \frac{1}{x} )}^{2} + 4( \frac{1}{x} ) + 3 = 0[/tex]
Let
[tex]u = \frac{1}{x} [/tex]
Our equation then becomes:
[tex] {u}^{2} + 4u + 3 = 0[/tex]
The factors of 3 that add up to 4 are:
[tex] {u}^{2} + 3u + u + 3[/tex]
[tex]u(u + 3) + 1(u + 3) = 0[/tex]
[tex](u + 1)(u + 3) = 0[/tex]
[tex]u + 1 = 0 \: or \: u + 3 = 0[/tex]
[tex]u = - 1 \: or \: u = - 3[/tex]
This implies that:
[tex] \frac{1}{x} = - 1 \: or \: \frac{1}{x} = - 3[/tex]
[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]
How do u get straight A’s?
YOU
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Study hard and don't let any thing distract you from your goal
What is the average rate of change for this function for the interval from x = 2
to x = 4?
Answer:
D
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 2, 4 ]
From the table
f(b) = f(4) = 16
f(a) = f(2) = 4, hence
average rate of change = [tex]\frac{16-4}{4-2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
The average rate of change for a function is calculated using the change in y-values divided by the change in x-values.
Explanation:The average rate of change for a function is the change in the y-values (output) divided by the change in the x-values (input) over a given interval. To calculate the average rate of change for the function from x = 2 to x = 4, we need to find the change in y-values and the change in x-values for this interval.
Let's assume the function is f(x). We can calculate the average rate of change using the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
Replace f(4) and f(2) with the corresponding y-values for x = 4 and x = 2, respectively, to get the final result.
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Given f (x). find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely x.
f(x)=
[tex] \sqrt{ - 2 {x}^{2} + 3 } - 5[/tex]
find g(x) and h(x)
[tex]g(x)=\sqrt x-5\\h(x)=-2x^2+3[/tex]
5/6 n=10 what is n in this equation
Y intercept 3 and a slope of -6
Answer:
y=-6x+3
Step-by-step explanation:
Answer:
y=-6x+3
Step-by-step explanation:
because the slope will always have the X and in the middle you can put them together to get your answer
If i^2 = −1 and a = (i + 7), which is the result of squaring a?
Answer:
48+14i
Step-by-step explanation:
So squaring (i+7) looks like this
(i+7)^2
(i+7)(i+7)
Use foil.
First: i(i)=i^2=-1
Outer: i(7)=7i
Inner: 7(i)=7i
Last: 7(7)=49
____________Add the terms.
48+14i
After solving the expression, the result of squaring value of a will be equal to 14i + 48.
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 by the question,
i² = -1
a = (i + 7)
Squaring the value of a,
a = (i + 7)(i + 7)
a = i² + 7i + 7i +49
a = -1 + 14i + 49
a = 14i +48
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define the radius of a circle
Answer: The radius is the distance between the center and the circumference of a circle and is half of the diameter of the circle .
Hopefully, this helps!
A line segment that joins the center of a circle to any point on the circle is called the radius of the circle. Whichever point on the circle we choose, the distance to the center of the circle will always be the same.
help with 1-10 , please!!!!!!
Step-by-step explanation:
hi I have answered ur question
Answers:
1. 75/w=5/6
5*w=75*6
5w=450
Divide by 5 for 5w and 450
5w/5=450/5
w=90
2. 1/5=11/p
1*p=5*11
p=55
3. 9/z=3/13
3z=13*9
3z=117
Divide by 3 for 3z and 117
3z/3=117/3
z=39
4. 210=15m
Divide by 15 for 210 and 15m
210/15=15/15m
m=14
5. 22n=11*19
22n=209
22/22n=209/22
n=9.5
6. 9p=180
9p/9=180/9
p=20
7. 100=5x
100/5=5x/5
x=20
8. 4*x=3*24
4x=72
x=18
9. 10*y=14*7
10y=68
10y/10=68/10
y= 68/10
10. 16x=8*15
16x=120
16x/16=120/16
x=7.5
What is the least common multiple of 4 and 6?
Answer:
12
Step-by-step explanation:
Consider the list of multiples
multiples of 4 are 4, 8, 12, 16, 20, ....
multiples of 6 are 6, 12, 18, 24, ....
The least common multiple is 12
HELP me please !! I really need it
Answer:
D
Step-by-step explanation:
To find the critical values , that is the zeros
Solve the quadratic
x² - x - 20 = 0 ← in standard form
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
(x - 5)(x + 4) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 4 = 0 ⇒ x = - 4
Thus the critical values are - 4, 5 → D
Answer:
D. -4, 5
Step-by-step explanation:
x² - x - 20 factorised = (x - 5) (x + 4)
In order to get the answers, you have to make each bracket equal zero.
(x - 5) = x = 5
(x + 4) = x = -4
The crucial numbers are -4 and 5.
Hope this helps!
NEED HELP with this word problem ASAP!
Answer:
[tex]t=280\ minutes[/tex]
Step-by-step explanation:
Let's call "v" the speed of the commercial airplane and call "t" at the travel time of the commercial plane
The distance in kilometers of the trip is: 1730 km
Then we know that:
[tex]vt=1730[/tex]
Then for the jet we have that the speed is:
[tex]2v[/tex]
The flight time for the jet is:
[tex]t-140[/tex]
Therefore:
[tex](2v)(t-140) = 1730[/tex]
Substituting the first equation in the second we have to:
[tex](2*\frac{1730}{t})(t-140) = 1730[/tex]
[tex](\frac{3460}{t})(t-140) = 1730[/tex]
[tex]3460-\frac{484400}{t} = 1730[/tex]
Now solve for t
[tex]\frac{484400}{t} = 3460 - 1730[/tex]
[tex]\frac{484400}{t} =1730[/tex]
[tex]\frac{t}{484400} =\frac{1}{1730}[/tex]
[tex]t=\frac{484400}{1730}[/tex]
[tex]t=280\ minutes[/tex]
find the area of the parallelogram answer option 15 25 30 44
There is no picture of the parallelogram needed to answer this question.
Find angle measures and use angles to classify triangles.
Answer:
1) 55 degrees
2) 90 degrees
3) 105 degrees
Step-by-step explanation:
All triangles equal to 180 degrees. So to find the missing angle measure you have to subtract the two given measures by 180.
First triangle:
180 - 50 - 75 = 55 degrees
Second triangle:
180 - 60 - 30 = 90 degrees
Third triangle:
180 - 45 - 30 = 105 degrees
Jagdish is 3 years younger than Resham and Rajesh is 5 years older than Jagdish. If the product of present age of Resham and Rajesh is 960.How old is Jagdish?
Answer:
Jagdish is 27 years old
Step-by-step explanation:
Jagdish=x
Resham=x+3
Rajesh=x+5
(x+3)(x+5) = 960
x²+8x+15=960
x²+8x=945
x²+8x-945=0
now factor this to solve
(x-27)=0 (x+35)=0
which means
x=27 and x=-35
obviously, we cannot have negative ages so we use x=27
so, Jagdish=27
Resham=30
Rajesh=32
and we can check this by doing 30x32 which does equal 960 so it is correct
The age of Jagdish for the condition is 27 years.
What are quadratic equations?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
Given Jagdish is 3 years younger than Resham
and Rajesh is 5 years older than Jagdish
let age of Jagdish be x
Resham = x + 3
Rajesh = x + 5
according to conditions,
(x + 3)(x + 5) = 960
x² + 8x + 15 = 960
x² + 8x = 945
x² + 8x- 945=0
now factor this to solve
(x - 27)(x + 35) = 0
(x - 27) = 0, (x + 35) = 0
which means
x=27 and x=-35
obviously, we cannot have negative ages so we use x = 27
Therefore, the age of Jagdish is 27 years.
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What type of number can be written as a fraction plq, where p and q are integers
and q is not equal to zero?
A. 7
B. All numbers can written in this way
C. A rational number is
D. An irrational number
Answer:
rational number
Step-by-step explanation:
written as a fraction p/q, where p and q are integers and q is not equal to zero, is called as rational numbers. Example - 4/5, 2, 100, 1/7 etc all are rational numbers.
Two similar triangles are shown.
Triangle MNO was dilated, then _______ to create Triangle YHO.
rotated
reflected
translated
dilated
Answer:
rotated
Step-by-step explanation:
The triangle MNO has already been dilated and therefore, the answers were left to 3: rotated, reflected and translated. Triangle YHQ is not an image of triangle MNO. Thus, leaving only 2 choices: rotated and translated. If triangle MNO was translated, triangle YHQ was supposed to be in the same position as triangle MNO is and leaving only 1 option which is rotated.
Answer:
rotated
Step-by-step explanation:
the correct answer is rotated
when triangle Δ M N O was dilated to create Triangle Δ Y H Q
we can clearly see that the length of the sides of the triangle is increased and from the figure we can clearly see that the largest side is rotated.
marked angle is also rotated.
so, we can clearly say that to make Triangle Δ Y H Q triangle Δ M N O is dilated and rotated.
Kayla rolls a die 84 times. How many times can she expect to roll a 3?
Answer:
14
Step-by-step explanation:
Assuming the die is 6 sided, there are only 6 possible rolls she can get. And assuming that this is a perfect world where probability is perfect, she will roll each number 14 times, because 84/6 is 14.
Final answer:
Kayla can expect to roll a number 3 approximately 14 times out of 84 rolls of a fair six-sided die, since each roll has a 1 in 6 chance of landing on any given number.
Explanation:
When Kayla rolls a die 84 times, she can expect to roll a 3 in a proportion equal to the probability of rolling a 3 on a single die. A fair six-sided die has a 1 in 6 chance of landing on any given number, including the number 3. Since each roll of the die is independent, we can calculate the expected frequency of rolling a 3 by multiplying the total number of rolls by the probability of rolling a 3.
The calculation is straightforward:
Probability of rolling a 3 = 1/6.Expected frequency of rolling a 3 = Total number of rolls × Probability of rolling a 3.Expected frequency of rolling a 3 = 84 × (1/6) = 14.Therefore, Kayla can expect to roll a 3 approximately 14 times in 84 rolls.
can u help me wit A, B, C, and D
And can you explain which statement would have the largest answer on the four choices
Answer:
D is 36080
Step-by-step explanation:
D is the largest since A is 3.608, B is 360.8, C is 36.08
When dividing, the smaller decimal points will be larger, but if you multiple, the numbers shrink.