Answer:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]p = 60\%[/tex]
[tex]n = 4[/tex]
Required
The distribution of x
The above is an illustration of binomial theorem where:
[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]
This gives:
[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]
Express percentage as decimal
[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]
[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]
When x = 0, we have:
[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]
[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]
[tex]P(x=0) = 0.0256[/tex]
When x = 1
[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]
[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]
[tex]P(x=1) = 0.1536[/tex]
When x = 2
[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]
[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]
[tex]P(x=2) = 0.3456[/tex]
When x = 3
[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]
[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]
[tex]P(x=3) = 0.3456[/tex]
When x = 4
[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]
[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]
[tex]P(x=4) = 0.1296[/tex]
So, the probability distribution is:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
4.
A turtle crawls 567 mm in 27 minutes. How far (measured in cm) can the turtle
crawl in a minute?
Answer: 2.1 cm per minute
Step-by-step explanation:
567/27 =21 mm
convert mm to cm (1mm = 0.1c,)
21mm = 2.1cm
Answer:
2.1 cm or 21 mm
Step-by-step explanation:
567 ÷ 27 = 21
Therefore the turtle can crawl 21 mm in a minute.
To covert mm to cm, we simply divide by 10.
21 ÷ 10 = 2.1
Assuming you are creating a book with 549 pages with a size of 8.5in x 11in. how many words will the story be?
A student was conducting a study to determine how many pages he would need for the book he is writing. So, he found that the following number of words fit on each type of the following papers using an 11 point font:
Answer:
439,200 words
Step-by-step explanation:
800 words per 8.5 inches by 11 inches piece of paper
800 times 549 = 439,200 words
Find the indicated side of the right triangle
Answer:
Step-by-step explanation:
tan30°=3/x
xtan30°=3
x=3/tan30°
x= 5.2
The greatest number which on dividing 1657 and 2037 leaves nemainder 6 ands respectively is?
Answer:
It would be 127
Step-by-step explanation:
We see that they only have 127 common in their prime factorization. Hence, HCF(1651, 2032) = 127. Hence, the greatest number which divides 1657 and 2037 leaves a remainder of 6 and 5 respectively is 127.
Plzzz help 10 points and will mark brainiest
hint: answer is a fraction
Answer:
1/3
Step-by-step explanation:
The left side of FA is 6 units.
The left side of FB is 2 units.
From 6 to 2, you divide by 3.
Same for the top,
FA is 9 units, while FB is 3 units.
I hope this helps!
pls ❤ and mark brainliest pls!
Carrie rolls two 1-6 number cubes. How many outcomes are possible?
Answer:
36
Step-by-step explanation:
The first dies has 6 possible outcomes
1,2,3,4,5,6
The second die has 6 possible outcomes
1,2,3,4,5,6
6*6 = 36
There are 36 outcomes
First Sample space
[tex]\\ \sf\longmapsto S=\left\{1,2,3,4,5,6\right\}[/tex]
[tex]\\ \sf\longmapsto |S|=6[/tex]
Now There are two cubes mean n=2
[tex]\\ \sf\longmapsto |S|^n[/tex]
[tex]\\ \sf\longmapsto 6^2[/tex]
[tex]\\ \sf\longmapsto 36[/tex]
i need B.
EMERGENCY THANK YOU VERY MUCH!!!
Answer:
A. Mean = 9.7 (take all the numbers and divide by 10)
Mode = 12
Range = 5
B. Unsure. Would suggest either Mean - average and can tell when bus is running late or early or Mode - highest and lowest time combined
Problem 2 Find the mBC.
Answer:
38º
Step-by-step explanation:
<BAC is a central angle. The corresponding arc, BC will be equal to the measure of the central angle.
So mBC = 38º
There are 7 blue counters, 3 green counters and 1 red counter in a bag.
There are no other counters in the bag.
Hubert takes at random 2 counters from the bag.
Work out the probability that both counters are blue.
Answer:
21/55
Step-by-step explanation:
7 blue counters, 3 green counters and 1 red counter = 11 counters
1st counter
P(blue)= blue / total = 7/11
Now there are only 10 counters
6 blue counters, 3 green counters and 1 red counter = 10 counters
2nd counter
P(blue)= blue / total = 6/10 = 3/5
P(blue blue) = 7/11 * 3/5 = 21/55
Please help asap!!!!
Answer:
1. B,D
2. D
3. C
4. J
Step-by-step explanation:
Triple a number is 18.
hi
so 3X = 18
X = 18/3 = 6
The product of 2 and a number x is 34.
What is the value of x?
x=54
x=38
x=114
x=32
Pls help me with this guyssss plssss ( I will give brainliest too!) :)
Answer:
x=17
Step-by-step explanation:
Product means multiply is means equals
2x = 34
Divide each side by2
2x/2 = 34/2
x = 17
Translate this sentence into a equation. The sum of 22 and chau’s are is 54. Use the variable c to represent chums age
Answer:
22+c=54
Step-by-step explanation:
22 + his age =54
HELP PLZ!! Convert 80 mph (miles per hour) to feet per second.
Answer:
117.33333 feet per second
Step-by-step explanation:
1. Eddie ordered customized cups. He was
charged a $30 design fee plus $8 per cup. His
total order was $334. How many cups did Eddie
order?
Answer:
38 cups
Step-by-step explanation:
8c + 30 = 334
8c = 334 - 30
8c = 304
c = 304 ÷ 8
c = 38 cups
The total number of cups ordered by Eddie is 8
Design fee = $30
Cost per cup = $8
Total cost of order = $334
Let the number of cups ordered = p
The total cost of order can be represented by the equation :
Design cost + (cost per order × Number of orders)
$30 + (8p) = $334
8p = 334 - 30
8p = 304
p = 303 / 8
p = 38
Hence, the number of cups ordered is 8
Learn more : https://brainly.com/question/18109354
If the density of the wood is 3 pounds per cubic foot and if the weight of the solid is
360 pounds, what is the width, w, in feet, of the solid?
(A) 5.0
(B) 2.5
(C) 2.4
(D) 1.5
The area of the triangular face of the solid is 48 if that helps
The width in feet of the given solid is 1.136
Density is defined as the ratio of the mass per unit volume
Density = Mass/Volume
Given
Weight = 360 pounds
Density = 3 pounds per cubic foot
Get the mass;
Since W = mg
m = W/g
m = 360/2.2
m =163.64 lbm/kg
Get the volume
From the formula;
Volume = Mass/Density
Volume = 163.64 /3
Volume = 54.55 ft³
Next is to get the width
Volume of the triangular prism = Base Area * Width
Base Area = 48ft²
54.55 = 48w
w = 54.55/48
w = 1.136
Hence the width of the solid in feet is 1.136ft
Learn more on how to calculate density here https://brainly.com/question/17887628
Isabella saved $13,000 and bought a car that cost $11,675. The insurance for the car will cost $650 per year.
How many full years will Isabella be able to pay for car insurance with her remaining savings?
Answer:
isabella will be able to pay 2 full years of insurance with her remaining savings
Step-by-step explanation:
as we know isabella saved $13,000
the car cost $11,675 - so subtracting that from her total we will know that she has: $1,325 remaining
insurance for a year costs $650,
so we will divide her remaining sum by the yearly cost giving us -
1,325/650
= 2.0.3....
this means that she will be able to pay for 2 full years of insurance with her remaining savings
hope this helped:)
========================================================
Explanation:
x = number of years
Since it costs $650 a year for insurance, she will pay 650x dollars of insurance in total over those x years.
For example, if x = 4, then 650*x = 650*4 = 2600 dollars is paid in insurance.
The expression 650x is added onto the 11675 which is the cost of the car.
Overall, Isabella pays 650x+11675 dollars as the combined cost of the car itself and the insurance over those x years.
Set this equal to 13000 and solve for x
650x+11675 = 13000
650x = 13000 - 11675
650x = 1325
x = 1325/650
x = 2.03846 which is approximate
Rounding down to the nearest whole number gets us to x = 2
She will be able to afford 2 full years of insurance
Note that if x = 3, then,
650x+11675
650*3+11675
13625
Which is 625 dollars over her budget. This shows that she cannot have x = 3 or larger.
What is five ones and eight tenths greater than or less than or equal to fifty eight tenths
Answer:
definetely 2
Step-by-step explanation:
Answer:
Less than
Step-by-step explanation:
Five ones and eight tenths simplifies to 85 and fifty eight tenths simplifies to 580. So, here you can clearly see 85 < 580.
Hope this helps! :)
order the following expressions by their values from least to greatest
Can the quotient of two irrational numbers ever be a rational number?
Answer: Yes, it can.
Step-by-step explanation:
3π / 2π = 1.5
√20 / √5 = 2
I guess it can.
Sally collected 22 pounds of cans to recycle
and plans to collect 1.8 more pounds each
week. In this situation, what is the value of
the y-intercept?
Step-by-step explanation:
this is an example u can see and write it yourself...
Element X is a radioactive isotope such that every 42 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 50 grams, how long
would it be until the mass of the sample reached 45 grams, to the nearest tenth of a
year?
Answer:
6.38548 years
Step-by-step explanation:
1 = 2 [tex]e^{42k}[/tex]
1/2 = [tex]e^{42k}[/tex]
ln(1/2) = 42k ln(e)
ln(1/2)/42 = k
k = -0.01650
~~~~~~~~~~~~~~
45 = 50 [tex]e^{-0.01650t}[/tex]
45/50 = [tex]e^{-0.01650t}[/tex]
ln(45/50) = -0.01650 t ln(e)
ln(45/50)/ -0.01650 = t
t = 6.38548 years
The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years
What is half-life of an element?The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the number of years be t
Let the initial mass of the element be a = 50 grams
The final mass of the element be ( a - x ) = 45 grams
Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half
And , half life t½ = 42 years
So , the decay constant k = 0.693/t½
k = 0.693 / ( 42 )
k = 0.0165
And , k= 2.303/t {log (a/a-x)}
So , t = 2.303 / ( 0.0165 ) log ( 50/45 )
On simplifying , we get
t = 6.384129 years
Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years
To learn more about half-life of an element click :
https://brainly.com/question/16387602
#SPJ2
The lines below are perpendicular. If the slope of the green line is ž, what is
the slope of the red line?
-5
5
m =
Answer:
B or (-2/3)
Step-by-step explanation:
Perpendicuar lines have negative inverse slopes SO
3/2 ---> -2/3
I'm stuck on here, please, someone help me.
Answer:
Answer B
Step-by-step explanation:
therw is one full one and one with five
irrational numbers on a number line pls help!!
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART
Answer:
a7 = 55 + (7-1) 10
Step-by-step explanation:
See,
It's given that it will take 7 hours for Jiya to move.
$55 are charged for 1 (first) hour. Now, 6 hours are left (unpaid). $10 per every hour after that.
Among the total 7 hours, the payment for first hour is done ($55) so we are left with the other 6 hours multiplied by 10.
Therefore, the correct option is:
a7 = 55 + (7-1) 10
The function m is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
m(x) = 2(x +4)^2 – 8
m(x)= 2x^2 + 16x + 24
m(x)=2(x+6)(x+2)
Write one of the zeros
Evaluate 10 + 8 ÷ 2 − 4
Step-by-step explanation:
we will solve this question according to BODMAS rule...
B for bracket
O for of
D for division
M for multiplication
A for addition
S for Subtraction
10+4-4
14-4
10 Answer..
Answer:
10
Step-by-step explanation:
Using order of operations as stated in PEMDAS , that is
division is performed before addition/ subtraction , then
10 + 8 ÷ 2 - 4
= 10 + 4 - 4
= 14 - 4
= 10
the set is points indicated by 12.is the ___ of the angle
Answer:
Vertex
Step-by-step explanation:
The vertex is the point were two rays meet to form an angle.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. This process continues through 3 more generations.
4x4=16 16x3=48 so I think the answer is 48
