Answer:
7/8
Step-by-step explanation:
Using the binomial distribution, it is found that there is a [tex]\frac{7}{8}[/tex] probability that at least one of the coins comes up heads.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
A coin is fair, hence p = 1/2.Three coins are thrown, hence n = 3.The probability that at least one of the coins comes up heads is given by:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.\left(\frac{1}{2}\right)^{0}.\left(\frac{1}{2}\right)^{3} = \frac{1}{8}[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = \frac{8}{8} - \frac{1}{8} = \frac{7}{8}[/tex]
[tex]\frac{7}{8}[/tex] probability that at least one of the coins comes up heads.
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A virus takes 13 days to double its original population (A=2A_0). How long will it take to triple its population? Round to the nearest tenth.
Answer:
20.6
Step-by-step explanation:
A virus takes approximately 20.6 days to triple its original population.
What is the formula of exponential growth?"[tex]f(x)=ab^x[/tex],
where a is the initial value
b is the growth rate
x is time. "
For given question,
Suppose the function for the population growth is,
[tex]A(t)=A_0\times b^t[/tex] .........(1)
For t = 13, the population growth of virus would be,
[tex]\Rightarrow A(13)=A_0\times b^{13}[/tex] ..........(2)
But we have been given that a virus takes 13 days to double its original population.
[tex]\Rightarrow A(13)=2\times A_0[/tex] .........(3)
From (2) and (3),
[tex]\Rightarrow A_0\times b^{13}=2\times A_0\\\\\Rightarrow b^{13}=2\\\\\Rightarrow b=1.0548[/tex]
We need to find the number of days to triple its original population
[tex]\Rightarrow A(t)=3\times A_0[/tex] ...........(4)
From (1) and (4),
[tex]\Rightarrow A_0\times b^t=A_0 \times 3\\\\\Rightarrow (1.0548)^t=3\\\\\Rightarrow t=20.6[/tex]
Therefore, a virus takes approximately 20.6 days to triple its original population
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Write (p^2)^3 without exponents
Using the power of power property, it is found that [tex](p^2)^3 = p^6[/tex].
What is the power of a power property?To find the power of a power, keep the base and multiply the exponents.
In this problem, the term is:
[tex](p^2)^3[/tex]
The exponents are 2 and 3, hence:
[tex](p^2)^3 = p^{2 \times 3} = p^6[/tex]
Hence, with a single exponent, [tex](p^2)^3 = p^6[/tex].
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If the mole fraction of NaCl in an
aqueous solution is 0.0927, what is
the weightweight % (percent by
mass) of NaCl.
Molar Mass
NaCl: 58.44 g/mol
H0: 18.016 g/mol
Answer: Y=2x-13 Y=2x-13
Step-by-step explanation:
You purchase a new sweater for $35. The original
price was $50. What was the percent change of the
price of the sweater
Refer to the graph to estimate x when f(x)= 7/2
Answer:
x = 4
Step-by-step explanation:
We are asked to find the value of x when [tex] \frac{7}{2} [/tex].
Note that [tex] f(x) [/tex] is also y.
What this means is, what is the value of x when y = 7/2 = 3.5.
On the graph given, trace where y = 3.5. check the x-value that corresponds with it on the point on the line.
Thus, at y = 3.5, x = 4.
Therefore,
x = 4, when [tex] \frac{7}{2} [/tex].
Find the value of x.
5X°
(7X+9)
27°
Answer:
If f(x) = x2 – 5 for all values x and f(a) = 4, what is one possible value of a? Possible Answers: ... If f(x) = x2 + 5x and g(x) = 2, what is f(g(4))?. Possible ... (1/3) * (27 + 15 – 15). (1/3) * (27)
Sasha deposited $600 in a simple-interest savings account.In one year the value of the account increased to $621.By what percentage did the value increase?
Answer:
103.5%
Step-by-step explanation:
To find the percent change you will need to divide 621 by 600.
621/600 = 1.035
Multiply 1.035 by 100 to find the percent
(1.035)(100) = 103.5
Therefore, the value increased by 103.5%.
I hope this helps!!
- Kay :)
Answer:
103.5
Step-by-step explanation:
If 140 bricks are used to build a wall 20 feet high, how many bricks will you use to build a wall 30 feet high?
Answer:
210
Step-by-step explanation:
Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?
Answer:
It would take 6 years for the value of the account to reach $5,920
Step-by-step explanation:
Principal Amount = $4900
Interest rate r = 3% = 0.03
Compounded monthly = n=12
Time t =?
Future Value = $5920
We can find time using formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and solving:
[tex]A=P(1+\frac{r}{n})^{nt}\\5920=4900(1+\frac{0.03}{12})^{12t} \\5920=4900(1+0.0025)^{12t}\\5920=4900(1.0025)^{12t}\\\frac{5920}{4900}= (1.0025)^{12t}\\1.21=(1.0025)^{12t}[/tex]
Applying exponent rule; [tex]a=b^c\\c\:ln(b)=ln(a)[/tex]
[tex]12t\:ln(1.0025)=ln(1.21)\\12t\:(0.00249)=0.19062\\t=\frac{0.19062}{12*0.00249}\\t=6.3\approx6[/tex]
So, It would take 6 years for the value of the account to reach $5,920
There were 239 people at a Travis Scott concert. Admission to the drive-in concert was $15 for adults and $5.50 for children. The total cost was $2758.50.
Answer:
{x + y= 239
{15x + 5.50y = 2758.50
Step-by-step explanation:
x = adults y = children and the total amount of people is 239.
$15 for adults and $5.50 for children and the total cost equals $2758.50.
y[tex]x^{2}[/tex]=8y
I just need helping solving this please
The value of x from the equation is 2√2
What are linear equations?
Linear equations are equations with one or two variables.
It is also important to note that the highest power of variable is 1
Given the equation;
yx² = 8y
Let's make 'x' the subject of the equation
Divide both sides by y, we have;
yx²/y = 8y/ y
x² = 8
Take the square root of both sides
(√x²) = √8
The square root takes the square, we have
x = √8
x = √4 × 2
x = 2√2
Thus, the value of x from the equation is 2√2
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If I have 150 late assignments and there is 3 assignments a day, how many days are there?
Answer:
50
Step-by-step explanation:
150 divided by 3 =50
because 50 ×3 =150
Help plz and tanks............
Answer:
1 I 3
8 I 24
6 I 18
3 I 9
Step-by-step explanation:
Step-by-step explanation:
the first one is 1 apple , 3 strawberries
the second is 8 apples, 24 strawberries
the third one is 5 apples, 15 strawberries
and the last one is 3 apples, and 9 strawberries
I'm sorry if I'm wrong I'm not good at math :( but i hope it helps :D
The graph of y=f(x) is shown below.According to the graph what is f(0)
The elves were busy
planting Christmas trees.
If they planted 51 rows with
14 trees in a row, how many
trees did they plant?
Can anyone please answer?
How many years will it take an initial investment of $25,000 to triple to $75,000 at an annual rate of 7% compounded continuously
Answer:
[tex]t = 15.7[/tex]
Step-by-step explanation:
Given
[tex]Principal = 25000[/tex] --- P
[tex]Amount = 75000[/tex] --- A
[tex]Rate = 7\%[/tex] --- R
Required
Determine the time (t)
Using continuous growth formula:
We have
[tex]A = Pe^{rt}[/tex]
Convert rate to decimal
[tex]Rate = 7\%[/tex]
[tex]r = 0.07[/tex]
Substitute values for A, P and r
[tex]75000 = 25000 * e^{0.07t}[/tex]
Divide both sides by 25000
[tex]3 = e^{0.07t}[/tex]
Rewrite the exponential function as logarithmic, we have:
[tex]ln3 = 0.07t[/tex]
Reorder
[tex]0.07t = ln3[/tex]
Divide both sides by 0.07
[tex]t = \frac{ln3}{0.07}[/tex]
[tex]t = \frac{1.09861228867}{0.07}[/tex]
[tex]t = 15.69[/tex]
[tex]t = 15.7[/tex]
Hence, the time is approximately 15.7 years
¿Qué parentesco tiene conmigo un joven que es el hijo de la esposa del único hijo de mi abuela?
Answer:
I would love to help but I cant speak spanish.
Maybe try posting this again just in english then I will answer!
Answer:
Because He is your grandmothers only child
Step-by-step explanation:
which makes him your Cousin I think.
Solve for y.
8
= -7
y +7
Simplify your answer as much as possible.
y = 0
No
solution
3
X Х
?
Answer:
y=−1/7
for the picture is y=-57/7
Step-by-step explanation:
1. 8= -7y +7Switch:sides
-7y+7=8
subtract 7 from both sides
-7y=1
divide both sides by -7
y=−1/7
2.so for 8/y+7=-7multiply both sides by (y+7)
8/y+7(y+7)=-7(y+7)
simplify 8=-7(y+7)
flip
-7(y+7)=8
divide both sides by -7
y+7=-8/7
subtract 7 from both sides
and simplify
y=-57/7
look at attached pictures it is from khan academy
Answer:
n=7m
Step-by-step explanation:
n=7m
21=7(3)
35=7(5)
56=7(8)
Answer:
m=1 , n=8
i think this is the answer
f(x)=5x-3
f(5)=????
Please give me the answer
Answer:
f(5) = 22
Step-by-step explanation:
Plug in 5 as x into the function:
f(x) = 5x - 3
f(5) = 5(5) - 3
f(5) = 25 - 3
f(5) = 22
7th- Grade question is super easy trust me
8. A bottle contained 3 7/12 cups of juice. Then Mark drank 1 1/6 cups of the
juice. How much juice was left in the bottle?
A. 2 1/12 cups
B. 2 1/6 cups
C. 2 5/12 cups
D. 2 5/6 cups
Answer:
C
Step-by-step explanation:
3 7/12 - 1 1/6
1. Change 1 1/6 into the same denominator as 3 7/12.
3 7/12 - 1 2/12
2. Subtract whole numbers.
3 - 1 = 2
3. Subtract the fractions.
7/12 - 2/12 = 5/12
4. Answer is 2 5/12 (C).
hope this helps :)
How do you this? Whoever shows full work, I’ll mark brainlist
Answer:
hese angles are supplementary, and x=19 degrees
These two angles are a linear pair, meaning that they are supplementary.
This means that their angles measures must add up to 180 degrees.
65+6x+1=180
6x=114
x=19
Hope this helps!
Step-by-step explanation:
USING ALL MY POINTS! PLEASE HELP, AND SHOW/EXPLAIN UR WORK!
A city has a record low temperature of -27 degrees Fahrenheit and a record high temperature of 12 degrees
Fahrenheit for the month of January. Write an inequality to correctly compare the high and low January temperatures for this city.
Answer:
-27 minus 12 = -39 if that's what you're asking.
Step-by-step explanation:
0=x^2+4x+1 Rewrite the equation by completing the square
Step-by-step explanation:−
x
2
−
4
x
−
1
=
0
What is the area of the kite?
Answer:
90 ft
Step-by-step explanation:
first you find the area of the 10 by 3 triangle, since on the other side it,s the same, all we need to do is find one of each triangle then mulitply it by 2 to get the area. then find the area of the 20 by 3 triangle. once you do that you will get 45, then you multiply it by 2 because it is the exact same on the other sides. then when you do that you get 90 ft. I hope this helps you! peace out.
The high school choir hosts a concert for the community. The members of the choir sell
tickets for the concert. Each member of the choir sells 3 tickets. Tickets are also sold at thedoor before the concert. A total of 125 tickets are sold at the door. How many total tickets are sold if there are 18 members of the choir?
The total number of tickets sold for the concert is 179.
What is unitary method ?Unitary method is a mathematical way of obtaining a single unit then deriving the required units by multiplying it with the single unit.
According to the given question The high school choir hosts a concert for the community.
Tickets are sold for this concert by members of the choir and at the door before concert.
Also given that 125 tickets are sold at the door and each member of the choir sell 3 tickets each and they were 18.
∴ The no. of tickets members of the choir sold is
= (18×3) = 54 tickets.
So, the total number of tickets sold for the concert is (125+54) = 179.
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What are two ways that you can earn income without working?
Answer:
How to Make Money Without a Job:
Get paid to test websites.Become a crowdworker.Design and sell t-shirts.Work as a transcriber.Shop for others.Sell crafts online.Get paid to pet sit.Sell your photos online.How do I solve 24=14-x/10
Answer:
I answer got was x= - 100
rearrange 24 and x/10 so it is x/10 = 14-24
then you have x/10 = -10
multiply 10 and -10 to get -100
Find the volume of the sphere pictured below. Give your answer in terms of
[tex]\pi[/tex]
Answer:
98 784[tex]\pi[/tex] cm³
Step-by-step explanation:
Formula for volume of sphere: [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × r³
Volume of sphere = [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × 42³
= [tex]\frac{4}{3}[/tex] × 74 088 × [tex]\pi[/tex]
= 98 784[tex]\pi[/tex] cm³
Step-by-step explanation:
4/3 × pi × 42³= 98784pi
[tex]\frac{4}{3} \pi \: r {}^{3}
[/tex]
In an aquarium,
the number of minnows and the number of clown fish are in the ratio 8:3
the number of clown fish and the number of gold fish are in the ratio 6: 11
There are 33 gold fish in the aquarium.
How many minnows are there in the aquarium?
There are 48 minnows in the aquarium and there are 18 clownfish in aquarium
Given that in an aquarium ratio of minnows and clown fish is 8:3 and the ratio of clownfish and goldfish are in ratio 6:11 and there are 33 gold fishes in the aquarium.
⇒[tex]\frac{6}{11} =\frac{x}{33}[/tex] ( Here x is the number of clownfish)
⇒x=6×3
⇒x=18
Therefore, The number of clownfish in the aquarium is 18
Now,[tex]\frac{8}{3} =\frac{y}{18}[/tex](Here, y is the number of minnows in an aquarium)
⇒y=8×6
⇒y=48
Therefore, The number of minnows in the aquarium is 48
Therefore,The number of minnows in the aquarium is 48 and The number of clownfish in the aquarium is 18
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