Answer:
the probability of getting exactly 2 fours is 0.16
Step-by-step explanation:
The probability of obtaining a number that is four = ¹/₆
The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆
The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways
If the die is tossed five times, the probability of the events is calculated as;
P = 10 x (¹/₆)² x (⁵/₆)³
P = 10 x (¹/₃₆) x (¹²⁵/₂₁₆)
P = 10 x 0.02778 x 0.5787
P = 0.16
Therefore, the probability of getting exactly 2 fours is 0.16
The probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is [tex]0.1608[/tex].
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]X[/tex] be the number of fours in [tex]5[/tex] coin tosses.
We have no. of tosses [tex]n=5[/tex].
Probability of a success i.e., getting four [tex](p)=\frac{1}{6}[/tex] and probability of not getting a four [tex](q)=\frac{5}{6}[/tex].
[tex]X[/tex] follows a binomial distribution. So,
[tex]P(X=x)=\binom{n}{x}p^{x}q^{n-x}[/tex]
[tex]\therefore[/tex] the probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is given by,
[tex]P(X=2)=\binom{5}{2}\left ( \frac{1}{6}^{2} \right )\left ( \frac{5}{6} \right )^{3}[/tex]
[tex]=0.1608[/tex]
Learn more about the topic of Probability: https://brainly.com/question/26959834
Plz check theses aswell
Answer:dont worry :) its right! hit enter!
Step-by-step explanation:
Answer:
Step-by-step explanation:
w' = (1, - 1 ) check
C' = ( 4, 2 ) check
A person purchased a used Chevrolet
Cavalier for $4500. The car is expected to
decrease in value by 22% each year over
the next several years.
What would be the decay factor of a model
that would represent the value of the car?
1.22
0.78
-1.22
0.22
Answer:
B. 0.78Step-by-step explanation:
With 22% decrease the value after the year is:
100% - 22% = 78% of the current valueTo find 78% we need to multiply the current value by 0.78.
The same number is multiplied each year to find the decreased value.
The formula for the car would be:
P = 4500*0.78ˣThe decay factor is 0.78
Correct choice is B
Answer:
m. m, .;.
Step-by-step explanation:
Anita collects shells and stones in a ratio of 1:2.
If she has a total of 8 shells how many stones does she have
Answer:
The answer is 16 stones
Step-by-step explanation:
It's 8:16 because
8/1 = 8
and
2 x 8 = 16
To check your answer to see if its correct :
1/2 = 2
16/2=8
Hope this helps!! ;)
A penguin walks 10 feet in 6 seconds. At this speed how far does the penguin walk in 45 seconds?
Answer:
The penguin will walk 75.15 feet in 45 seconds. It will take the penguin 26.95 seconds to walk 45 feet
Step-by-step explanation:
hope it helps !
Answer: 75 feet
Step-by-step explanation:
A sector of a circle of diameter 11 cm is formed from an angle of size 51. Find the length of the arc rounded to two decimal places
Answer:
4.90m
Step-by-step explanation:
A sector of a circle of diameter 11 cm is formed from an angle of size 51. Find the length of the arc rounded to two decimal places
Length of an arc = 2πr(θ/360)
(θ) = 51°
r = Diameter/2 = 11/2
= 5.5
Length of an arc = 2 × π × 5.5(51/360)
= 4.89565m
Approximately = 4.90m
How many different committees can be formed from 12 teachers Abs 43 students of the committee consists of 4 teachers and 3 students ? In how many ways can the committee of 7 members be selected ?
Answer:
6108795
Step-by-step explanation:
To obtain the number of ways the committee can be selected :
4 teachers from the 12 teachers available and 3 students from the 43 students available
Using combinatorics :
12C4 * 43C3
recall :
nCr = n! ÷ (n - r)!r!
Using calculator :
12C4 = 495
43C3 = 12341
12C4 * 43C3
495 * 12341
= 6108795
The computer lab at school has $110 to spend on blank compact disks for their CD ROMS. If 2 packages of disks cost $10 how many packages can the computer lab buy?
Answer:
22
Step-by-step explanation:
10/2 $5 per pack
110/5= 22 packs
how to calculate the Triangle Proportionality Theorem
Step-by-step explanation:
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
I need this ASAP:
Find the volume
Please help with any of this Im stuck and having trouble with pre calc is it basic triogmetric identities using quotient and reciprocal identities
How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.
#3
Let's start with sin here. [tex]\frac{2\sqrt{5}}{5} = \frac{2}{\sqrt{5}}[/tex] Therefore, because sin is y/r, r = [tex]\sqrt{5}[/tex] and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.
cos = [tex]\frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}[/tex]
#4
Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = [tex]4\sqrt{2}[/tex]. Now, to find csc, we have to do r/y.
csc = [tex]\frac{9}{4\sqrt{2}} = \frac{9\sqrt{2}}{8}[/tex]
The pythagorean identities are
sin^2 + cos^2 = 1,
1 + cot^2 = csc^2,
tan^2 + 1 = sec^2.
#5
Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.
sin^2 + (-3/4)^2 = 1
sin^2 + 9/16 = 1
sin^2 = 7/16
sin = [tex]\sqrt{7/16}[/tex] = [tex]\frac{\sqrt{7}}{4}[/tex]
Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.
tan^2 + 1 = (-4/3)^2
tan^2 + 1 = 16/9
tan^2 = 7/9
tan = -[tex]\sqrt{7/9} = \frac{-\sqrt{7}}{3}[/tex]
#6
Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.
1 + cot^2 = [tex](\frac{-\sqrt{6}}{2})^{2}[/tex]
1 + cot^2 = 6/4
cot^2 = 2/4
cot = [tex]\frac{\sqrt{2}}{2}[/tex]
tan = [tex]\sqrt{2}[/tex]
Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.
[tex](\frac{2}{\sqrt{2}})^2[/tex] + 1 = sec^2
4/2 + 1 = sec^2
2 + 1 = sec^2
sec^2 = 3
sec = -[tex]\sqrt{3}[/tex]
cos = [tex]\frac{-\sqrt{3}}{3}[/tex]
Hope this helps!! :)
Answer:
sin(θ)=√7/4
tan(θ)= - √7/3
Step-by-step explanation:
c^2= √(4^2-(-3^2))
c^2= √(16-9)
c^2= √7
sin(θ)= opp/hyp=√7/4
tan(θ)= (opp )/adj= - √7/3
Help pls!!! question in the picture!!!
Answer:
The Y intercept is two
Step-by-step explanation:
The y intercept is the point on a graph where the graph crosses the y axis.
Basically, it is the value of y when x is 0 is (x,y)
Looking at the attached graph, our y intercept is (0,2), meaning that the y-intercept is 2.
The answer is: the Y-INTERCEPT is 2
If you take of a number and add 4, you get 16. The equation represents this situation. If x represents the original number, what does x equal?
Answer:
x = 12
Step-by-step explanation:
equation:
x + 4 = 16
to solve for x, subttract 4 on each side:
x + 4 - 4 = 16 - 4
x = 12
PLEASEEEE SOMEONE HELP ME WITH THIS ITS DUE IN A COUPLE HOURS!!!!!
Answer:
27°
Step-by-step explanation:
I'm assuming you have learned basic trigonometry: SOH CAH TOA. In this diagram to find the angle x we are given the opposite side and the hypotenuse, therefore we will use SOH. sinθ = opp/hyp. Plugging in those values we get sinθ = 5/11 -> θ = sin⁻¹ (5/11) = 27.03569179° = 27°
Jake's parents want $100,000 at the end of 40 years. They put their money in an account that yields 4% per year compounded continuously. How much money should jakes parents deposit?
Answer:
$ 20,189.65
Step-by-step explanation:
Jake's parents want $100,000 at the end of 40 years. They put their money in an account that yields 4% per year compounded continuously. How much money should jakes parents deposit?
From the above question, we are to find the Principal. The formula for Principal compounded continuously =
P = A / e^rt
Where:
A = Amount after time t = $100,000
r = Interest rate = 4%
t = Time in years = 40 years
First, convert R percent to r a decimal
r = R/100
r = 4%/100
r = 0.04 per year,
Then, solve our equation for P
P = A / e^rt
P = 100,000.00 / e ^(0.04×40)
P = $ 20,189.65
Therefore, the amount Jake's parents should invest = $ 20,189.65
1 Katie is raising money to buy
a dog. She starts a
neighborhood babysitting service.
She paid $40 for a CPR class and
charges $5 per kid. Write an
equation she could use to calculate
her profit, p, if she has k kids.
O p = 5k - 40
P = 5k + 40
O p = 40k + 5
k = 40p - 5
Answer:
p = 5k - 40
Step-by-step explanation:
Since we're finding the profit (p), it's not the last answer choice because it's finding kids (k).
Because we have to take out from her profit whatever Katie spent, we would have -40.
Because she'd charging $5 per kid, or $5 per k, we would have 5k.
So now we know the profit is whatever she makes, then minus whatever she spent. So:
p = 5k (what she makes) - 40 (what she spent)
p = 5k - 40
Answer:
O p = 40k + 5
Step-by-step explanation:
Katie is raising money to buy a dog. She starts a neighborhood babysitting service.
asap please help i really need it
Answer:
x ≈ 261 ft
Step-by-step explanation:
Using the sine ratio in the right triangle
sin50° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{200}{x}[/tex] ( multiply both sides by x )
x × sin50° = 200 ( divide both sides by sin50° )
x = [tex]\frac{200}{sin50}[/tex] ≈ 261 ft ( to the nearest foot )
x ≈ 261 ft
that is the answer
If you solve the equation for ax+by/c=d for x, what would you get?
Answer:
x=d/a - by/ac
Steps:
ax+by/c=d
(cax+by)/c=d
cax+by=cd
cax=cd-by
x=(cd-by)/ca
x=cd/ca - by/ca
x=d/a - by/ac
help me please help me
Answer:
3.95
Step-by-step explanation:
R = 7.9/2 = 3.95
Answer:
Step-by-step explanation:
rate of change is the slope of the line
plot the data and calculate the slope or simple find the delta cost divided by the delta people
(cost x - cost y) / (people x - people y) = rate of change
you can pick any cost as long as you use the coresponding people
(19.75 - 7.90) / (5 - 2) = rate of change
( 11 .85) / (3) = rate
3.95 = rate
try it for different cost and people and see if you get the same rate, it looks linear to me
It costs $32 per day to rent a medium-sized car, plus $0.25 for each mile driven over 150 miles. The equation that represents this situation is y = 0.25x + 32, where y represents the total cost of renting a car, and x represents the number of miles driven over 150 miles.
a.) What is the slope and what does it represent in the context of this problem?
b.) What is the y- intercept and what does it represent in the context of this problem?
Answer:
Read explanation
Step-by-step explanation:
A)The slope is the number before the X so 0.25, this represents the amount of money people have to pay for each mile driven over 150 miles.
B) The y-intercept is the number after the X so 32, this number represents the amount people have to pay rent the car before actually using it.
Find the value of x.
Answer:
im 95% sure the answer is 6
Step-by-step explanation:
when i wrote it down it just never came out to one of thoes answers, but 6 was the closest
solve this equation graphically using table 5m-2n=4,m-4n=-1
Answer:
m = 1; n = 0.5
Step-by-step explanation:
5m - 2n = 4; m - 4n = - 1
differentiate x+sinx/x+cosx with respect to x
Step-by-step explanation:
content://com.cryptotab.android.FileProvider/images/screenshot/1615820475640483392397139554304.jp
inverse function. sketch the graph of each function.
Answer:
I cant see picture
Step-by-step explanation:
In a class, there are twice more boys than girls. Six boys leave the class and six girls arrive ;
therefore, there are twice more girls than boys .
How many boys and girls were there at first ?
please show calculations steps plus this should be solved as a system
Answer:
Boys= 12
Girls= 6
Step-by-step explanation:
Let no: of girls be 'x'
No: of boys= 2x
boys after= 2x-6
girls after = x+6
according to the question,
2(2x-6)=x+6
4x-12=x+6
3x=18
x=6
No: of girls at first= 6
No: of boys at first=2*6=12
solve for h in the literal equation g(h+3/2)=5
Answer: h= 5/g−3/2
Step-by-step explanation:
h= 5 over g minus 3 over 2
Answer:
[tex]h\neq -3/2[/tex]
Step-by-step explanation:
Divide both sides by h+3/2;
g(h+3/2)/h+3/2=5/h+3/2
simplify
g=10/2h+3; h[tex]\neq[/tex]-3/2
Last year, the Humane Society found 96 homes for its stray kittens.
If each home adopted 3 kittens, how many kittens found homes
last year? write the operation and the answer
Solve 8 = 2^x + 4
x=-4
x=-1
x=0
x=7
Answer:
x=-1
Step-by-step explanation:
because 2^3 is 8
and when you do -1+4 you get left with 3
so x=-1
Answer:
x = -1
Step-by-step explanation:
can someone help me solve this please
Answer:
The answer is C.
Step-by-step explanation:
A square pyramid was sliced perpendicular to its base but not through its vertex. What is the shape of the cross section shown in the figure?
A rectangular pyramid. The cross section is a trapezoid.
a parallelogram that is not a rectangle or square
a rectangle that is not a square
a square
a trapezoid
Answer:
a trapezoid
Step-by-step explanation:
Answer:
D: Trapezoid.
Step-by-step explanation:
Because you can see that the shape has only one set of parralel sides it is a trepezoid.
AB is a diameter of the
circle. Find the angle
BCO.
A 70°
B 20°
C 60°
D50°
Answer:
70°, ,have a nice day
Answer:
∠BCO = 70°
Step-by-step explanation:
AO = CO = BO because all radii of the same circle are equal.
∠ACO = 20° because it is an isosceles triangle.
∠BCA = 90° because a triangle with it's hypotenuse being the diameter of a circle is a right triangle.
∠BCA - ∠ACO = ∠BCO
90° - 20° = 70°
∠BCO = 70°
