For a fair die has four faces numbered one to four, the probability of rolling a two exactly three times in ten rolls of the die is 25.02% determined using binomial distribution.
Binomial distribution is used to determine the probability of observing a specified number of successful outcomes in a specified number of trials and is given by:
P(x:n,p) = nCx px (1-p)n-x
Where n is the number of experiments, x is a random variable, and p is the probability of success in a single experiment.
The probability of rolling a two in one trail = ¼ = 0.25
In the give case,
n = 10
x =3
p = 0.25
Therefore,
P(3) = 10C3 0.25^3 (1-0.25)^(10 – 3)
Solving 10C3 = 10!/3!(10-3)! = 120
P(3) = 120. 0.25^3 (1-0.25)^(10 – 3) = 0.2502
Hence, the probability of rolling exactly 2 three times in a ten trails is 25.02%
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Translate the sentence into an inequality.
The product of y and 5 is greater than or equal to - 20.
The product of y and 5 is greater than or equal to - 20 is 5y ≥ -20
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the product of y and 5 is greater than or equal to - 20 will be:
(5 × y) ≥ -20
5y ≥ -20
This is the inequality.
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Justin ran 15 miles at a constant rate in 2.5 hours. The next day, he ran at a rate that was 1 mph slower. What was Justin’s rate the second day?
A. 2.5 mph
B. 4 mph
C. 5 mph
D. 6.5 mph
Answer:
5mph
Step-by-step explanation:
Find the perimeter of ALMN. Round your answer to the nearest tenth if necessary.
Answer:
148
Step-by-step explanation:
The triangle are similar because the angle measurements are the same.
180-51-34 = 95
180-95-51 = 34
If we match up the corresponding sides we see that the side with 45 corresponds to the side with 36. Now we need to find the scale factor.
Let s = the scale factor
45s = 36 Divide both sides by 45
s = .8
This means that the corresponding length of the triangle on the right is .8 of the triangle on the left.
The corresponding side to x is 79, so 79 x .8 = 63.2. Now that we know the three sides we can add them together to find the perimeter.
63.2 + 36 + 48.8 = 148
Answer:
Perimeter = 147.9
hope this helps!
What are the zeros of the polynomial function f(x)=x^4-3x^3-2x^2+6x
The zeros of the polynomial function are x = 0, x = 3 and x = ±√2
How to determine the zeros?The equation of the function is given as
f(x) = x⁴ - 3x³ - 2x² + 6x
Factor out x from the equation of the function
So, we have
f(x) = x(x³ - 3x² - 2x + 6)
Factorize the expression in the bracket
So, we have
f(x) = x(x²(x - 3) - 2(x - 3))
Factor out x - 3
So, we have
f(x) = x(x - 3)(x² - 2)
Set the factors to 0
x(x - 3)(x² - 2) = 0
Expand
x = 0, x = 3 and x² = 2
Take the square roots
x = 0, x = 3 and x = ±√2
Hence, the zeros are 0, 3 and ±√2
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Determine the measure
Answer:
∠ D ≈ 31.0°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan D = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{EF}{DE}[/tex] = [tex]\frac{9}{15}[/tex] , then
∠ D = [tex]tan^{-1}[/tex] ( [tex]\frac{9}{15}[/tex] ) ≈ 31.0° ( to the nearest tenth )
aisha had 4 yards of fabric she used 3/5 of the fabric to make a backpack.Which fraction shows how many yards of fabric aisha used
Answer:
[tex] = \frac{3}{5} \\ [/tex]
What is the reciprocal number of 1 1 9?
Answer:
1/119
Step-by-step explanation:
119 is a whole number which you convert into 119/1 then the reciprical would be 1/119
What is the equation of the line that passes through the point (−3,−6) and has a slope of -2/3
Answer:
y = -2/3(x) - 8
Step-by-step explanation:
y = mx + b
y = -2/3(x) + b
given: (-3, -6) x=-3 y=-6
-6 = -2/3(-3) + b
-6 = 2 + b
b= -8
so..
y = -2/3(x) - 8
4. pls help will mark brainliest
Answer:
y = -16 + 4x
Step-by-step explanation:
The standard slope equation is y=mx+b. M is the slope and also the y intercept so if you look at the graph you can see that -16 is the y intercept, next you have to find the x intercept, why? I don't remember but then you do that in the equation, as you can also see on the graph, 4 is the x intercept so its 4x. put that into y intersect form at it's y = -16 + 4x
Solve the inequality |x+4|-6<9
The solution to the inequality |x+4| - 6 < 9 is -19 < x < 11.
How to solve inequality?The inequality can be solved as follows;
|x+4| - 6 < 9
add 6 to both sides of the inequality
|x+4| - 6 < 9
|x+4| - 6 + 6< 9 + 6
|x+4| < 15
applying absolute rule,
- 15 < x + 4 < 15
Therefore,
x + 4 > -15 and x + 4 < 15
x > -15 - 4 and x < 15 - 4
x > - 19 and x < 11
Therefore, the final inequality is -19 < x < 11
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Solve for a10a7a =✓ [?]Pythagorean Theorem: a b = c2
In order to calculate the value of 'a', we can use the Pythagorean theorem, where the hypotenuse squared is equal the sum of each leg squared:
[tex]h^2=l^2_1+l^2_2[/tex]In this case, the hypotenuse is 10 and the legs are 'a' and 7, so we have:
[tex]\begin{gathered} 10^2=a^2+7^2 \\ 100=a^2+49 \\ a^2=100-49 \\ a^2=51 \\ a=\sqrt[]{51} \end{gathered}[/tex]So the value of 'a' is √51.
Tamia has owned a pet-sitting business for several years. The majority of clients hire her to take care of either cats or fish while they travel.
Define the random variables C = the number of cats Tamia takes care of in a typical week and
F = the number of fish Tamia feeds in a typical week. Their probability distributions and parameters can be found here.
Let T = the total number of cats and fish that Tamia takes care of in a typical week.
1. Find Mu Subscript T
Mu Subscript T =
pets
2. Calculate Sigma Subscript T
Sigma Subscript T =
pets
Answer: C
Step-by-step explanation:
answer for the first one is 3.55 pets
second one is 1.4790 pets
i hope this helped! :)
How many times larger than 6 x 10-2 is 24 x 1062
Need 5 or more pairs pretty sure have to be different and i belive you need to use 3 rigid motion steps which are rotate clockwise 90 degrees, flip or reflect accrss line,axis,point and translate or shift up,down left, right blob:chrome-untrusted://media-app/3a17e069-2696-48ff-84dd-bd2e0126810c
Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.
Rigid Motion:Any way of moving all the points in the plane such that
a) the relative distance between points stays the same and
b) the relative position of the points stays the same.
There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.
Translation:In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance. See Image-1.
Rotation:A rotation fixes one point (the roto center) and everything rotates by the same amount around that point. Every rotation has a roto center and an angle. See Image-2.
Reflection:A reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every reflection has a mirror line. See Image-3.
Glide Reflection:A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every glide reflection has a mirror line and translation distance. See Image-4.
Therefore,
Simply put, rigid motions are transformations that preserve the side lengths and angles in a shape. You can see any of these transformations by moving an object you may have around you right now. Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.
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I have a review work sheet that’s not Homework and I don’t get it
1)
white (w) marble
yellow (y) marble
green (g) marble
red (r) marble
Pw+Pw+Pg+Pr=1 (Eq. 1 )
w+y+g+r=12 (Eq. 2)
Answer: There are 12 marbles in the bag. SInce the question says the bag contains 12 marbles.
2)
a) Pw+Py = Pg
w + y = g (Eq. 3)
b) Pw = 10/40 = 1/4
If P = 1/4, if we have 12 marbles, P=3/12
Then, we know that we have 3 white marbles
Answer: There are 3 white marbles in the bag.
3) Pr = 1/5. Considering that 2 marbles were removed, we have 10 markles. The Pr=2/10.
Answer: Thus, we have 2 balls red.
4) From 12 marbles, we already know that 3 are white and 2 are red.
Then: 12-3-2= 7
Answer: 7 marbles are green or yellow.
5)
From question 4 , we know that;
y + g = 7
y = 7 - g (Eq. 4)
And from Eq. 3
w + y = g
3 + y = g
Substituing Eq. 4 in Eq. 3:
3 + 7 - g = g
10 = 2g
10/2 = g
g = 5
And:
y = 7 - g
y = 7-5
y = 2
The numeratiors are:
3 (Pw), 2 (Py), 5 (Pg)
5) 2 = yellow marbles
5 = green marbles
An airplane takes 4.5 hours to travel 913.5 miles while flying against the wind. If the speed of the airplane on awindless day is 237 miles per hour, what is the speed of the wind?The wind ismiles ? per hour.
Let's call the speed of the wind as w, and the speed of the plane when its windless as p.
Since an airplane takes 4.5 hours to travel 913.5 miles while flying against the wind, to find its speed we just need to divide the distance travelled by the time
[tex]p_{aw}=\frac{913.5}{4.5}=203[/tex]When the plane is flying against the wind, its speed is equal to the speed of the plane when its windless minus the speed of the wind.
[tex]p_{aw}=p-w[/tex]Since we already know the speed of the plane on both situations, we can substitute those values on the expression above and solve for w.
[tex]203=237-w\Rightarrow w=34[/tex]The speed of the wind is 34 miles/h.
Solve for X -5x>2(x-14)
Hey there!
[tex]-5x > 2(x-14)[/tex]
Our first step is to simplify both sides of the inequality:
[tex]-5x > 2x-28[/tex]
Now, we need to subtract 2x from both sides:
[tex]-5x-2x > 2x-28-2x\\-7x < -28[/tex]
Our final step is to divide both sides by -7:
[tex]\frac{-7x}{-7} > \frac{-28}{-7}[/tex]
[tex]x < 4[/tex]
Hope this helps!
is 0.4141... a rational number or an irrational number?
Rational number
Step-by-step explanation:it repeats - { 4 1 4 1 }it is both non-terminating and repeating.Answer:
It is rational, as it is both non-terminating and repeating.
hope it helps :D
what is the slope when the pairs are (-1, -7) And (3, 9)
Answer:
Please see photo for explanation and answer.
The different between the upper class limit and lower class limit is called width of the class intervals true or false
The given statement "The different between the upper class limit and lower class limit is called width of the class intervals" is True
In the frequency distribution, define the class limits.Frequency distributions should normally contain 5 to 20 equal-width classes, be continuous, exhaustive, and mutually exclusive.
Clarification of the quoted phrase,
The breadth or size of the class interval in a frequency distribution table is the distance between the upper and lower class limits.
A class interval, for instance, is any of the groups 20–25, 25–30, 30-35, etc. There is a five-point spread between the upper and lower limits. the class width is therefore 5.
As a result, the assertion is true.
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I am thinking of a number between one and one thousand if you get it right I will give you a hundred points.
also if you can solve this problem,
3+2(3x-1)=100/3(2-3)
Answer:
x= -103/18
Step-by-step explanation:
1.distribute, 3+2(3x-1)=100/3(2-3)
3+6x-2=100/3 (2-3)
2
Subtract the numbers
3
Rearrange terms
4
Subtract the numbers
5
Multiply the numbers
6
Subtract
1
from both sides
7
Simplify
8
Divide both sides by the same factor
9
Simplify
Determine the parent function.
Answer:
Determine the Parent Function: y=√x
I verified with a graphing calculator: Demsos. y=x^3 will cross intercepts (x) which is not the parent function and y=1/x is a rational function that is not the parent function that is being asked for.
Can someone help me with this?
m is perpendicular to l, s is perpendicular to t, and t is perpendicular to u. Based on the angle shown, these lines are parallel.
What is parallel?Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees). If two lines in two-dimensional Euclidean space do not intersect, they are said to be parallel. Parallel lines in three-dimensional Euclidean space not only do not intersect, but also maintain a constant separation between points closest to each other on the two lines. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never meet. They can be both horizontal and vertical in orientation.To learn more about parallel, refer to:
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Mr jones wants to fence in a rectangular field for his horse using the 600 feet of fence he has stored in his barn. He wants to maximize the area of the field in order to give his horse the most pasture possible. Help mr jones design his field to achieve the maximum area.
Step-by-step explanation:
l = length
w = width
we know, the perimeter of our rectangle is
2×l + 2×w = 600
and that tells us
l + w = 300
l = 300 - w
the area of the rectangle is
A = l × w
so, we use the previous equation in this one :
A = (300 - w) × w = -w² + 300w
this is a quadratic equation that is opening down (negative initial factor).
so the vertex of this parabola is the maximum.
the x (or in our case w) coordinate of the vertex is
-b / 2a
a = -1
b = 300
so,
w = -300 / (2×-1) = -300/-2 = 150 ft
and l × w = 300
l = 300 - w = 300 - 150 = 150 ft.
the maximum area for 600 ft fence is a square with 150 ft side length.
Which types of dilation are the given scale factors? select expansion or contraction to correctly describe the type of dilation for each given scale factor.
This question is based on dilation. Therefore, the scale factor [tex]$-\mathbf{4}$[/tex] and [tex]$\mathbf{2 . 5}$[/tex] are for expansion of flgure. And, 2/3 and -3/4 are for the contraction of flgure.
We must choose the scale factor of dilation for contraction and expansion in this question.
As we know that,
In a dilation, a scale factor is greater than 1 or less than -1 cause an expansion. It will make the figure larger.
That means, -4 is an expansion, since it is less than -1,
And 2.5 is an expansion, since it is greater than 1.
A scale factor that is greater than -1 but less than 1 cause contraction of figure. It will make the figure smaller.
This means that,
2/3 Is an expansion, slnce It is less than 1 , and -3/4 Is a contraction, slnce It is greater than -1.
Therefore, the scale factor [tex]$-\mathbf{4}$[/tex] and [tex]$\mathbf{2 . 5}$[/tex] are for expansion of flgure. And, 2/3 and -3/4 are for the contraction of flgure.
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20 rabbits are captured and marked. two weeks later, 12 rabbits are recaptured. of these 12 only 5 are marked. what is the estimated population? show all work for credit.
The estimated population is found to be 48 rabbits
The estimated population, P is determined by using the following formula:
[tex]P=T_{F} *T_{L} /M[/tex]
P=estimated population
[tex]T_{F}[/tex]=total animals captured in first trapping
M=recaptured animals that are marked
[tex]T_{L}[/tex]=total animals captured in a later trapping
From the question, [tex]T_{F}[/tex]=20 rabbits, M=5 rabbits, [tex]T_{L}[/tex]=12
P=20*12/5
P=240/5
P=48 rabbits
Hence, the estimated population is 48 rabbits
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. Constructed Response. Be sure to answer all parts of the constructed response.
Miles, Hayden, and Dubem are going to have a paint battle. Miles fills his wall at a rate of
12 wall in 9 minutes, Hayden can fill his wall at 15 wall in 313 minutes, and Dubem can cover 49 wall in 638 minutes.
Part A Place the students in order from fastest to slowest, in terms of who has the fastest water filling rate.
1.
2.
3.
Part B Explain how you determined the fastest rate.
Placing the students in order from fastest to slowest, in terms of who has the fastest water filling rate is;
1. Miles
2. Dubem
3. Hayden
The way the fastest rate is determined is by finding the unit rates
What is the unit rate of work done?A unit rate (or unit ratio) is a ratio that describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
Now, from the question, the rate would clearly be number of walls filled per minute.
1) Mills fills his wall at a rate of 12 wall in 9 minutes. Thus;
Mills unit rate = 12/9 = 4/3 walls filled per minute = 1.333 walls filled per minute
2) Hayden can fill his wall at 15 wall in 313 minutes. Thus;
Hayden's unit rate = 15/313 walls filled per minute = 0.0479 walls filled per minute
3) Dubem can cover 49 wall in 638 minutes. Thus;
Dubem's unit rate = 49/638 walls filled per minute = 0.0768 walls filled per minute
Looking at the decimal unit rates, we can see that fastest to slowest in order are;
1. Miles
2. Dubem
3. Hayden
The way I knew who was faster was to look at the decimal values of their unit rates and it is seen that Miles covered the most part of wall in one minute
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PLEASE HELP
Susan is mixing 4% butterfat milk with 1% butterfat milk to create 6 quarts of 2% butterfat milk. How many quarts of each will
she need?
O 1 of 4% and 5 of 1%
O 2 of 4% and 4 of 1%
Answer:
the first one took it on egde
Step-by-step explanation:
03 Fill in the Blank Text
Simplify the following expression:
14a + 3(a + 4b) - 2b
Answer:
17a+10b
Step-by-step explanation:
hope this work have a nice day
Matilda leaves work at 18:00. She drives 42 kilometres from
work to home at an average speed of 56 km/h.
What time does Matilda arrive home?
Give your answer using the 24 hour clock
Matilda arrives home at 18.45 after driving 42 kilometers from her workplace at an average speed of 56 km/h.
How is the time determined?The time Matilda uses to drive home from her workplace is a function of the distance she travels and the average speed she goes.
Using the above formula gives us the time in hours/minutes that she took for the home drive.
This derived time is then added to the time she leaves her workplace to get the time she arrives home using the 24-hour clocking system.
The time Matilda leaves her workplace = 18:00
The total distance Matilda travels from work to her home = 42 km
The average driving speed that Matilda traveled with = 56 km/h
Time used for driving home (in hours) = Distance/Speed
= 42/56
= 0.75 hours
= 45 minutes (0.75 x 60)
Arrival Time = 18:45 (18:00 + 45)
Thus, using the 24-hour clocking system, the time Matilda is expected to reach her home is 18:45.
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