Grade 12 data!!
18% of a population eats yogurt daily. What is the probability that, in a group of 10 people, 4 of them eat yogurt daily?
0.0032 0.072 0.067 0.00032
Answer:
The probability that, in a group of 10 people, 4 of them eat yogurt daily is 0.067
Step-by-step explanation:
In this case we can apply a Binomial distribution in which there are n events and every event have a probability p to get a success. Then, the probability of x is:
[tex]P(x)=nCx*p^{x}*(1-p)^{n-x}[/tex]
Where x is the number of people who eat yogurt daily, n is the total number of people and p is the probability of eats yogurt daily.
Additionally nCx is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, for the question we know that:
n=10
p=0.18
x=4
Replacing this values on the equation, we get:
[tex]P(4)=10C4*0.18^{4}*(1-0.18)^{10-4}[/tex]
P(4)=0.067
Finally, the probability that, in a group of 10 people, 4 of them eat yogurt daily is 0.067
(20 points) You are writing a research paper on plant cells. You got 48,600,000 results on the online search. How do you write 48,600,000 in scientific notation?
Alicia drove 265 miles in 5 hours What is the average rate that she traveled 49 miles per hour 51 miles per hour 53 miles per hour 55 miles per hour
Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half hour. how many bacteria will the colony contain at the end of 24
A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.
Explanation:The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.
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A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?
The function f(x) is represented by this table of values .Match average rate of change of f(x) with corresponding intervals
THIS IS TIMED AND I NEED HELP!!!
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)
Simplify.
6m+7n+5m−3n
15mn
11m + 10n
m + 10n
11m + 4n
to simplify combine all like terms
6m +5m = 11m
7n-3n = 4n
so it would be 11m+4n
If you have a $1 bill a 5 bill a 10 bill and a 20 bill how many different sums of money
Which expression is equivalent to 34 ⋅ 3−9?
1 over 3 to the 13th power
1 over 3 to the 5th power
35
313
Answer:
b.1 over 3 to the 5th power.
Step-by-step explanation:
We are given that an expression
[tex]3^4\cdot 3^{-9}[/tex]
We have to find that which expression is equivalent to given expression
[tex]3^4\cdot 3^{-9}[/tex]
We know that [tex]a^b+a^c=a^{b+c}[/tex]
Using this identity
Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]
[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]
Using [tex]a^{-b}=\frac{1}{a^b}[/tex]
Hence, option b is true.
Answer:b.1 over 3 to the 5th power.
The table below shows the surface area y, in square feet, of a shrinking lake in x days:
Time (x)
(days) 5 10 15 20
Surface area (y)
(square feet) 90 85 70 61
Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points)
Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points)
Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
Confused. Please help thank you!
#6 is using using ratios:
7/2x+4 = 4/x+3 =
8x+16 =7x+21 =
8x=7x+5 =
x=5
AC = 2(5)+4= 14 + 5+3=8, 14+8 =22
#7
ratio of known sides 9/4 =2.25 now multiply other 2 sides by 2.25
7*2.25 = 15.75
9*2.25=20.25
perimeter = 9 +15.75+20.25 = 45
If a triangle has legs measuring 8 inches and 15 inches and has a hypotenuse measuring 17 inches, what is the ratio, in simplest form, of the shorter leg to the hypotenuse?
Melanie is flying from washington,
d.c., to seattle. her flight leaves at 10
a.m. when her plane lands, the pilot announces that it is 2 p.m. in seattle. how long did her flight take
How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.
Answer:
40,320.
Step-by-step explanation:
We are asked to find the number of ways in which 8 books could be arranged on a shelf.
The 1st could be arranged in 8 ways. Since one place is filled, so 2nd book could be arranged in 7 ways.
Similarly, the 3rd book could be arranged in 6 ways as first two places are already taken. This process will go on.
So the 8 books can be arranged in [tex]8\times 7 \times 6\times5\times4\times3\times2\times1=8![/tex]
[tex]8!=40,320[/tex]
Therefore, 8 books could be arranged in 40,320 ways.
The number of ways to arrange 8 books on a shelf is 40,320.
We have to determineHow many ways can 8 books be arranged on a shelf?
According to the questionThere is total number of books is 8.
Then,
The arranging the way of 8 books also be 8.
If one of the 8 books is placed in the first place, only 7 of them can be placed in 2nd place. In 3rd place, only 6 of them can be placed.
This continues all the way to 1.
A permutation is an arrangement of objects in a particular way.Then,
The number of ways to arrange 8 books on a shelf is,
[tex]= 8!\\ \\ = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\\ \\ =40,320 [/tex]
Hence, The number of ways to arrange 8 books on a shelf is 40,320.
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How do I find the terms?
Cannon took out a mortgage for $85,290 on his new house. If the interest rate is 8.5 percent and the loan is for 25 years, how much will he pay monthly if he must pay $8.05 per $1,000?
Answer:
The answer is $686.584
Step-by-step explanation:
Given is, Cannon pays $8.05 per month for every $1,000, so we have a ratio: 8.05 / 1000
Now, we will find the second ratio which is an unknown payment per month over the price: x / 85290
Equaling them to solve for x :
[tex]\frac{8.05}{1000}=\frac{x}{85290}[/tex]
[tex]1000x=8.05*85290[/tex]
[tex]1000x = 686584.50[/tex]
So, x = 686.584
Hence, the answer is $686.584
Perform the following food service calculation. Size of juice can = 54 oz. Portions of juice served = 6 oz. Number of cases used = 2 Number of cans per case = 12 How many guests can be served? 54 216 1,944 7,776
Answer: 216 guests.
Step-by-step explanation: We are given total number of cases = 2 Number of cans.
Number of cans per case = 12 cans.
Total number of cans in 2 cases = 2 cases × 12 cans = 24 cans
Each can contain = 54 oz of juice.
24 cans would contain total = 24 cans × 54 oz per can = 1296 oz juice.
Number of oz per serving = 6 oz.
Total number of guests can be served = 1296 oz / 6 oz per serving = 216 guests.
f(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i
Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.
The zeros are:
x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*iFirst, for a given function f(x), we define the zeros as the values of x such that:
f(x) = 0.
Then we must solve:
f(x) = 16*x^4 - 81 = 0
Solving this for x leads to:
16*x^4 = 81
x^4 = 81/16
x^2 = ±√(81/16) = 9/4
x = ±√±(9/4) = ±3/2 and ±(3/2)*i
So there are 4 zeros, and these are:
x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*iWhere the two complex zeros come from evaluating the second square root on -9/4.
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To which part of the prism are the arrows pointing
The measure of ______________ in a circle is half the measure of the intercepted arc.
A. a central angle
B. an interior angle
C. an inscribed angle
YES slay5 is correct the answer is : C. an inscribed angle
Answer: C. An inscribed angle
Step-by-step explanation:
Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.
Interior angle is an angle between two sides inside a polygon or a shape.
Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.
Express -2 in triganomic form
Final answer:
To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.
Explanation:
The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.
In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.
For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.
Are the traingles congruent? Why or why not?
Yes, A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
No, C is not congruent to any angle in DEF.
No, the congruent sides do not correspond.
Yes , A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
• Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
• Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
• A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
From the given data ,
AB ≅ DE
and , ∠BAC = 33°
∠EDF = 33°
Therefore by rules of congruent triangles
The two angles are the same and the corresponding sides are same
Hence , The two triangles ΔABC and ΔDEF are congruent
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If you put down 20% on a $7000 car and pay monthly payments of $109.40 for 60 months, what is the total price of the car?
Answer:
7964
Step-by-step explanation:
How old am i if i was born in 05/22/1965?
Answer:
In 2021 you would be 56 or 55 years old
Step-by-step explanation:
2021-1965=56 or the other way you could do it 52+4 because the other person said you would be 52 in 2017 so 4 years after you would be 55 or 56
Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property
1 acre = 43560 square feet
43560 = 484 * X
X=43560/484 = 90
the width = 90 feet
Answer:
90 feet
Step-by-step explanation:
Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?
A.The horse hair is 2 times as thick as the human hair.
B.The horse hair is 5 times as thick as the human hair
C.The human hair is 2 times as thick as the horse hair
D.The human hair is 5 times as thick as the horse hair
Answer:
A.The horse hair is 2 times as thick as the human hair.
Step-by-step explanation:
We have been given that Mateo is studying a human hair with a diameter of [tex]6.5\times 10^{-4}[/tex] inches and a horse hair with a diameter of [tex]1.3\times 10^{-3}[/tex] inches.
Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.
[tex]\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}[/tex]
Now we will quotient rule of exponents to simplify our given problem.
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=2\times \text{Diameter of human hair}[/tex]
We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.
ms johnson and ms smith were folding report cards to send home to parents. the ratio of the number of report cards ms johnson folded to the number of report cards ms smith folded is 2:3. At the end of the day , ms Johnson and ms smith folded at total of 300 report cards. How many did each person fold?
You give your friend a head start of 20 feet in a race. A linear equation representing your friend’s progress (in feet) after x seconds is y = 9x + 20. A linear equation representing your progress (in feet) after x seconds is y = 9x. Will you catch up to your friend? Explain.
To catch up to your friend or not in a race explained with equations and steps.
The question is: Will you catch up to your friend? Explain.
Step-by-step explanation:
Friend's progress equation: y = 9x + 20
Your progress equation: y = 9x
To catch up, set the equations equal: 9x + 20 = 9x
Solve for x: 20 = 0 (This equation has no solution)
You will not catch up to your friend.
Assume that all chickens have 4725 feathers. if it takes you 5.6 seconds to pluck 24.8 feathers, how many hours would it take you to defeather 7728 chickens? answer in units of hours.
It would take approximately 2284.722 hours to defeather 7728 chickens.
Explanation:To find out how many hours it would take to defeather 7728 chickens, we need to consider the time it takes to pluck a certain number of feathers. We are given that it takes 5.6 seconds to pluck 24.8 feathers. First, we find the time it takes to pluck one feather by dividing the time by the number of feathers: 5.6 seconds ÷ 24.8 feathers = 0.2258 seconds per feather.
Next, we find the total number of feathers on 7728 chickens by multiplying the feather count per chicken by the total number of chickens: 4725 feathers/chicken × 7728 chickens = 36,396,000 feathers.
Finally, we find the total time it would take to defeather all the chickens by multiplying the time per feather by the total number of feathers: 0.2258 seconds/feather × 36,396,000 feathers = 8,224,996.8 seconds. Converting this to hours, we divide by the number of seconds in an hour: 8,224,996.8 seconds ÷ 3600 seconds/hour ≈ 2284.722 hours.
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