Answer:
i) [tex]P(X=12)=0.0355[/tex]
ii) [tex]P(X<10)=0.7553[/tex]
iii) [tex]P(X\geq 5)=0.9490[/tex]
Step-by-step explanation:
Let's start by defining the random variable ⇒
[tex]X:[/tex] '' Number of students that will get 7 marks out of 10 in first attempt of a certain Quiz while attempting Quiz on BlackBoard LMS ''
[tex]X[/tex] is a discrete random variable.
The probability of a randomly selected student getting 7 marks out of 10 is 0.4
(This is a data from the question).
Now, if we assume independence between the students while they are doing the Quiz and also we assume that this probability remains constant , we can modelate [tex]X[/tex] as a binomial random variable ⇒
[tex]X[/tex] ~ Bi (n,p)
Where ''n'' and ''p'' are the parameters of the variable.
''n'' is the number of students attempting the Quiz and ''p'' is the probability that a student will get 7 marks out of 10 which is 0.4 ⇒
[tex]X[/tex] ~ Bi (20, 0.4) in the question.
The probability function for [tex]X[/tex] is
[tex]p_{X}(x)=P(X=x)=\left(\begin{array}{c}n&x\end{array}\right)p^{x}(1-p)^{n-x}[/tex] (I)
Where [tex]\left(\begin{array}{c}n&x\end{array}\right)[/tex] is the combinatorial number define as
[tex]\left(\begin{array}{c}n&x\end{array}\right)=\frac{n!}{x!(n-x)!}[/tex]
Replacing the parameters in the equation (I) ⇒
[tex]P(X=x)=\left(\begin{array}{c}20&x\end{array}\right)(0.4)^{x}(0.6)^{20-x}[/tex] (II)
For i) we need to find [tex]P(X=12)[/tex]
Then, we only need to replace by [tex]x=12[/tex] in equation (II) ⇒
[tex]P(X=12)=\left(\begin{array}{c}20&12\end{array}\right)(0.4)^{12}(0.6)^{8}=0.0355[/tex]
For ii) we need to calculate [tex]P(X<10)[/tex]
This probability is equal to ⇒ [tex]P(X<10)=P(X\leq 9)[/tex] and to calculate it we need to sum [tex]P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)[/tex]
[tex]+P(X=6)+P(X=7)+P(X=8)+P(X=9)[/tex]
We can do it summing each term or either using any program.
The result is [tex]P(X<10)=P(X\leq 9)=0.7553[/tex]
Finally for iii) we need to find ⇒ [tex]P(X\geq 5)[/tex]
This probability is equal to ⇒ [tex]P(X\geq 5)=1-P(X\leq 4)[/tex] ⇒
[tex]1-P(X\leq 4)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)][/tex]
Again we can find each term by using the equation (II) or either using a program. The result is [tex]P(X\geq 5)=0.9490[/tex]
The point 3/4 of the way from A(-4,- 7) to B(12, 5)
Answer:
The coordinates of C are (8,2)
Step-by-step explanation:
We are given the segment from A(-4,-7) to B(12,5) and it's required to find a point C(x,y) that is located at 3/4 of the distance from A to B.
This means that:
[tex]d_{AC}=3/4\cdot d_{AB}[/tex]
where dAC is the distance from A to C and dAB is the distance from A to B.
The same proportion of the distances is satisfied by the coordinates of the point C, that is:
[tex]\displaystyle x-x_A=\frac{3}{4}(x_B-x_A)[/tex]
Adding xA:
[tex]\displaystyle x=\frac{3}{4}(x_B-x_A)+x_A[/tex]
[tex]\displaystyle x=\frac{3x_B+x_A}{4}[/tex]
Similarily:
[tex]\displaystyle y=\frac{3y_B+y_A}{4}[/tex]
Calculating:
[tex]\displaystyle x=\frac{3(12)-4}{4}[/tex]
x = 8
[tex]\displaystyle y=\frac{3(5)-7}{4}[/tex]
y = 2
The coordinates of C are (8,2)
What is the value of x
Answer:
x=39
Step-by-step explanation:
First I try to find the angle measurements for the rest of the angles inside the triangle. I saw that the 68 degrees and I notice that it was vertical angles, meaning that the inside is also 68. I then notice that the 107 and the other unknown angle besides x must be 180 when adding up, so I can do 180-107=73. Now I know that that angle is 73 degrees I can find x by solving this equation 180=73+68+x, which the answer comes out to be 39. so x=39.
Hope this helps you
It takes Taylor hour to make of a batch of cookies. About how long will it take him to make 8 batches?
B.
3.6 hours
C.
5.4 hours
D.
7.2 hours
Answer:
it would be 8 hours.....
Step-by-step explanation:
im am a bit confused, why is that not an answer choice
At a plant nursery, 5/8 of the planets for sale are flowers and another 1/3 of the plants are shrubs. What amount of the plants for sale are either flowers or shrubs?
Answer: 23 / 24
Step-by-step explanation:
Given that:
Fraction of flowers for sale = 5/8
Fraction of shrubs for sales = 1/3
Amount of flowers that are either flowers or shrubs :
(Fraction of flowers +. Fraction of shrubs)
(5/ 8 + 1 /3)
L.C.M of 8 and 3 = 24
= (15 + 8) / 24
= 23 / 24
a lawnmower that regularly sells for %150 was discounted by 25% off.
Questions:
Markup?
Sale price?
300x7065
A tough one can you solve it without looking the answer up or not cheating in any way
in the expression shown below, the number 2 and 5 that are place in front of the variables are called
2x^2+5x-3
A. Degrees
B. Polynomials
C. Coefficient
D. Radicals
PLEASE HELP
At a family reunion, 6 families share 500 photos equally. How many photos does 13 each family get and how many photos are left over?
Answer:
83 photos each
2 photos left over
Answer:
Each Family gets 83 photos each and 2 photos are left over
Step-by-step explanation:
Hope this helps and have a great day :)PLSS HELPPP HELP ASP
Karen has 560 friends and family on social media of the friends, 50% are from high school, and 30% are from her after school job. The rest are family
members
How many family members does Karen know on social media?
Answer: 112
Step-by-step explanation:
560/5
Which expression is equivalent to 6(4v)?
Answer:
24v
Step-by-step explanation:
simply multiply perform the distributive property. so multiply 6 and 4 and you should get 24. after just add in the v.
pls mark brainlest
What is the measure of angle y?
Answer:
y =50°
Step-by-step explanation:
40°+90°+y = 180° {the sum of angle of triangle is 180°}
or, 130°+ y = 180°
or, y = 180°-130°
or, y =50°
The value of the measure of an angle y in a triangle would be 50 degrees.
Used the concept of angle in a triangle that states,
The sum of all three interior angles in a triangle gives 180 degrees.
Given that,
A triangle is shown in the attached figure.
Here, the triangle shown in the image is a right-angle triangle.
Hence, a measure of an angle = 90 degree
And, the second measure of an angle = 40 degree
So, the sum of interior angles in a triangle gives 180 degrees.
Hence,
40° + 90° + y = 180°
Solve for y,
130° + y = 180°
y = 180° - 130°
Therefore, the value of y is,
y = 50 degree
To learn more about the triangle visit;
brainly.com/question/1058720
#SPJ6
17) When filled to maximum capacity, a silo can hold about 4,000 cubic meters of corn. The radius of the silo is 8 meters. To the nearest meter, what is the approximate height (h) of the silo?
Answer: ion know i'm guessing 4
Step-by-step explanation: because it shows 8 at the top, so since it's full and it's 4,000 then that'll basically make 8 the 4000, so since 4 is half of 8 then we prolly have our answer right there
Answer: It would be 20
Step-by-step explanation: The formula for height would be h= v/pi r squared, just plug in the numbers
What is the range of the function on the graph?
LO
4
all the real numbers
O all the real numbers greater than or equal to 0
O all the real numbers greater than or equal to 2
O all the real numbers greater than or equal to -3
21
2 1
2 3 4 5 x
-5 -4 -3 -2 -11
-2
-3
-4
-5
the answer is all real numbers
The range of the function on the graph are all the real number greater than or equal to -3.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given the graph of a function.
A function f(x) has the domain equal to the all values of x that the function is defined for.
Range of the function is the set of all the values of the function for the x in the domain.
Here, the function values are from infinity to -3 and then again mover from -3 to infinity.
So the range consists of all the real numbers from -3.
Hence the range of the function is the set of all real numbers from -3.
Learn more about Range here :
https://brainly.com/question/21027387
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6 gallons to 42 gallons
Express each ratio as a fraction in the simplest form
6x(2x+y-5) rewrite as a sum
Answer: 12x^2+6xy−30x
^=power sighn
Step-by-step explanation:
6x(2x+y−5)=(6x)(2x+y+−5)=(6x)(2x)+(6x)(y)+(6x)(−5)=12x^2+6xy−30x
Please help need this before 4:15pm
In which part of the periodic table (top-left, top-middle, top-right, bottom-left, bottom-middle, bottom-right, middle-left, middle-center, middle-right) do we find most of the atoms that make up life?
Answer:
Top right i believe
Step-by-step explanation: the elements that make up life are carbon, hydrogen, oxygen, nitrogen, phosphorus, and sulfur.
A survey was conducted to see how many people ride a bus to school everyday 160 people reported that they ride the bus school everyday this number represents 80%of the people surveyed how many were surveyed
Answer:
200 people
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Answer:
x is also 63 degrees this is because vertical angles are congruent or like equal in measure
Step-by-step explanation:
HOPE THIS HELPEDDDD
Answer:
63 degrees
Step-by-step explanation:
Since m is parallel to n, the angle that is marked 63 degrees and x are alternate interior angles. The alternate interior angle theorem states that alternate interior angles are congruent when a line cuts through two parallel lines. So, since m and n are parallel, these are congruent angles, making x also 63 degrees.
What is the solution to the equation?
3 + 3x – 5 = r
A.
-2 and -7
B.
2 and 7
O c.
-2
D. 7
Solve equation Y=9x-70 and y=2x-32
Step-by-step explanation:
y = 9x - 70 ...1
y = 2x - 32 ...2
...1 - ...2
0 = 7x -38 ...3
7x - 38 = 0
7x = 38
x = 38/7
PLEASE HELP! THANK YOU!!!
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]3(x - 2) = 12[/tex]
[tex]x = 6[/tex]
_________________________________
[tex]6(x + 5) = 54[/tex]
[tex]x = 4[/tex]
_________________________________
[tex]3x + 5 = 32[/tex]
[tex]x = 9[/tex]
_________________________________
[tex]5(x + 7) = 45[/tex]
[tex]x = 2[/tex]
_________________________________
[tex]7x + 6 = 41[/tex]
[tex]x = 5[/tex]
_________________________________
[tex]2(x + 7) = 29[/tex]
[tex]x = 7.5[/tex]
_________________________________
[tex]4(x + 3) = 30[/tex]
[tex]x = 4.5[/tex]
_________________________________
[tex]5(x - 4) = 20[/tex]
[tex]x = 8[/tex]
_________________________________
[tex]3x - 10 = 23[/tex]
[tex]x = 11[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Card A: x = 6
Card B: x = 4
Card C: x = 9
Card D: x = 2
Card E: x = 5
Card F: x = [tex]\frac{15}{2}[/tex]
Card G: x = [tex]\frac{9}{2}[/tex]
Card H: x = 8
Card I: x = 11
There you go bud. :')
You owe me for this lol.
5. Find the difference of 785 and 543
785+543
Step-by-step explanation:
785-543=242
difference means subtract
A teacher weighed 145 lbs in 1986 and weighs 190 lbs in 2007. What is the rate of change in weight? HELP
Answer:
c
Step-by-step explanation:
she gained 45 pounds which is 15/7 of 145
Help pls<---
ASAP DUE TODAY BY 9:05
Answer:covert - 2/3 to -4/6. Then after you do the math...you get -9/6....simplify that to -3/2e=-27. You then multiply -27 by the reciprocal -2/3 and the answer is 18.
Step-by-step explanation:
Solve the equation 4x - 6 = 34. Write a justification for each step.
47-6= 34
Given equation
+6 +6
4x
Simplify.
= 40
4x 40
44
[2]
X= 10
Simplify
[1] Addition Property of Equality,
[2] Reflexive Property of Equality
[1] Substitution Property of Equality,
[2] Division Property of Equality
[1] Division Property of Equality,
[2] Subtraction Property of Equality
[1] Addition Property of Equality:
[2] Division Property of Equality
8
Answer:
[1] Addition property of equality
[2] Division property of equality
Step-by-step explanation:
Given the equation, [tex] 4x - 6 = 34 [/tex], the following are steps and justification for each step taken:
[tex] 4x - 6 = 34 [/tex] => Given equation
Add 6 to both sides
[tex] 4x - 6 + 6 = 34 + 6 [/tex] => addition property of equality [1]
[tex] 4x = 40 [/tex] => simplify
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{40}{4} [/tex] => Division property of equality [2]
[tex] x = 10 [/tex] => simplify
The justification for the steps taken are:
[1] Addition property of equality
[2] Division property of equality
Rounding decimals. 0.01426; thousandths
Answer:
0.014
Step-by-step explanation:
the square root of 84 is it closer to 9 or 10
Answer: It is closer to 9
Step-by-step explanation: The square root of 84 is 9.16515139
Answer:
9
Step-by-step explanation:
The square root of 84 rounded the hundredth is 9.17, making it closer to 9 than 10.
Your friend has $100 when he goes to the fair.he spends $10 to enter the fair and $20 on food.rides at the fair cost $2 per ride.which function can be used to determine how much money he has left over after x rides
Answer:
The answer is A f(x)=-2x + 70
Step-by-step explanation:
Triangles ABC and DEF are similar. Find e.
A.) 11
B.) 12
C.) 10
D.) 9