As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
The value of p=0.8 and n=20
The probability that exactly 12 flights are on time = 0.1772
The probability that exactly fewer than 12 flights are on time = 0.1049
The probability that at least 12 flights are on time = 0.8951
The probability that between 10 and 12 flights, are on time = 0.1795
(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,
p = 80% = 0.8
As, we made 20 trials and n is the total number of trials then,
the value of n be,
n = 20
(c) Now, if the probability of success on an individual trial is p ,
Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)
The probability that exactly 12 flights are on time, be
P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)
P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)
P(X=12) = 10,07,760×0.0687×0.00000256
P(X=12) = 0.1772
(d) Now, the probability that exactly fewer than 12 flights are on time, be
P(X<12) = 1 - P(X>12)
So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)
So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115
P(X>12) = 0.8951
P(X<12) = 1 - 0.8951
P(X<12) = 0.1049
(e) Now, the probability that at least 12 flights are on time, be
P(X>12)=0.8951
(f) The probability that between 10 and 12 flights, are on time, be
P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772
P(X=10)+P(X=11)+P(X=12) = 0.1795
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83.978, 78.934, 84.765 Underline the thousandths digit in each number
help meee pleaseeee
Answer:
83.978 the thousandth digit is 3, 78.934 the thousandth digit is 8,84.765 the thousandth digit is 4
Answer:
Step-by-step explanation:
Ok:
1. Identify the thousandths digit
The numbers to the left of the decimal point are the ones and hundreds digits
The first number to the right of the point is the tenths digits
The second to the right of point i s the Hundreths
The third number to the right of point is the thounsandths which is what we are looking for!
2. Apply to problem!
1. 83.978 : Thousandths digit is 8
2. 78.934 : Thousandths digit is 4
3. 84.765 : Thousandths digit it 5
Extra tips and tricks writing as fractions!Ps: Some are not simplified!
1. 83.978= 83 978/1000 as fraction
2. 78.932= 78 932/1000 as fraction
3. 84.765= 84 765/1000 as fraction
Use the formula for the area of a circle (A-ar) to find the area of the bull's-
eye.
12
20
100 mm 12 mm
180 mm
A. 101,736 mm2
B. 452.39 mm2
C. 22,686 mm2
D. 31,400 mm²
13
The area of a bull's eye is equal to: B. 452.39 mm².
What is the area of a circle?The area of a circle simply refers to the region enclosed or space occupied by a circle within its boundary, and in a two-dimensional plane.
How to calculate the area of a circle?Mathematically, the area of a bull's eye can be calculated by using this formula:
Area of bull's eye = πr²
Where:
r is the radius of a circle.
Note: The radius of the bull's eye is equal to 12 mm and π = 3.14159.
Substituting the given parameters into the formula, we have;
Area of bull's eye = π × (12)²
Area of bull's eye = 3.14159 × 144
Area of bull's eye = 452.39 mm².
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Is -97 prime or composite?
Answer:
Prime
Step-by-step explanation:
Because this number is only divisible by itself and no other number.
Sasha is studying a type of coral that grows at a constant rate. Every month, she visits two pieces of the coral and measures their heights. She made this table:
Month 1 2 3
Piece A's height (cm) 24 26 28
Piece B's height (cm) 27 29 31
When Piece A's height is 49cm, what will Piece B's height be?
Answer:
Step-by-step explanation: The constant growth for Plant A is two cm a month and the growth of Plant B is also two cm a month.
In relation, Plant B will also be 3cm taller than Plant A on any month so when Plant A is 49cm, Plant B is 52.
When Piece A's height is 49 cm then the Piece B's height will be 52 cm.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can see that Piece A's height increases by 2 cm each month and Piece B's height increases by 2 cm each month as well.
To find out what Piece B's height will be when Piece A's height is 49 cm, we need to find how many months it will take for Piece A to reach 49 cm.
From Month 1 to Month 2, Piece A's height increased by 2 cm, and from Month 2 to Month 3, Piece A's height increased by another 2 cm. Therefore, Piece A's height increases by 2 cm per month.
To go from 28 cm (Piece A's height in Month 3) to 49 cm, it takes 21 cm ÷ 2 cm/month = 10.5 months.
So 10.5 months after Month 3 is Month 13.5.
In Month 13.5, Piece A's height will be 49 cm and Piece B's height will be:
Piece B's height in Month 3 + 2 cm/month × (13.5 - 3 months)
= 31 cm + 2 cm/month × 10.5 months
= 52 cm
Therefore, when Piece A's height is 49 cm, Piece B's height will be 52 cm.
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neeed helppp pleaseeeeee
The attendant at a parking lot compared the number of hybrid vehicles to the total
number of vehicles in the lot over a weekend. The ratios for the three days were
equivalent. Complete the table.
Day Hybrids Total
Fri.
5
9
Sat.
63
Sun. 40
Enter your answer in each of the answer boxes.
Day
Fri.
Sat.
Sun.
Hybrids
40
Total
63
The attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend.
Day hybrids total
Fri 5 9
sat 63
sun 40
we need to find number of hybrids in sat and total in sun.
Number of hybrids in sat = 5*7 = 35(ratios are equal)
Total in sum = 9*8 = 72.
Day hybrids total
Fri 5 9
sat 35 63
sun 40 72
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Determine whether each statement is always, sometimes, or never true.
13. For a 0, the value of a¹ is positive. ●
14. If n is an integer, then 3" 3" equals 1.
15. If 6P 0, then p > 0. 16. 4* equals 1. 4*
17. If m is an integer, then the value of 2m is negative
Problem 13
Answer: Sometimes trueReason:
If a > 0, then the statement would always be true. However, if 'a' was negative, then the statement is false.
For example, if a = -2 then:
[tex]a^{-1} = (-2)^{-1} = \frac{1}{(-2)^1} = -\frac{1}{2} = -0.5[/tex]
In short,
[tex]a^{-1} = -0.5 \ \ \text{ when } a = -2[/tex]
This is one of infinitely many counter-examples to prove the original statement isn't always true.
===================================================
Problem 14
Answer: Always trueReason:
The rule to use here is [tex]a^b*a^c = a^{b+c}[/tex]
We add exponents b and c, while the base 'a' stays the same the whole time.
In this problem we have: [tex]3^n*3^{-n} = 3^{n+(-n)} = 3^{n-n} = 3^0 = 1[/tex]
Therefore [tex]3^n*3^{-n} = 1[/tex] is always true regardless of what you replace n with. The variable n doesn't have to be an integer.
===================================================
Problem 15
Answer: Sometimes trueReason:
Let's say p = -1 is plugged into the expression
[tex]6^p = 6^{-1} = \frac{1}{6^1} = \frac{1}{6} \approx 0.1667[/tex]
which is a positive outcome showing that [tex]6^p > 0[/tex] doesn't automatically guarantee that p > 0. Feel free to try other negative values as counter-examples. Also p = 0 works as well. It turns out that [tex]6^p[/tex] is always positive regardless of what real number you use for p.
===================================================
Problem 16
Answer: Always trueReason:
The rule used here is [tex]a^{-b} = \frac{1}{a^b}[/tex]
An equivalent rule is [tex]\left(\frac{a}{b}\right)^{-c} = \left(\frac{b}{a}\right)^c[/tex]
The idea is to flip the fraction to turn the exponent positive.
Examples: [tex]2^{-5} = \frac{1}{2^5} \ \ \text{ and } \ \ \left(\frac{7}{9}\right)^{-3} = \left(\frac{9}{7}\right)^{3}[/tex]
===================================================
Problem 17
Answer: Never trueReason:
This is similar to problem 15 in that [tex]2^m[/tex] is always positive regardless if m is negative, zero, or positive. It might help to graph out [tex]y = 2^x[/tex] and see that the curve never dips below the x axis.
the time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 15 minutes. the average time necessary for 100 randomly selected students is computed. the probability the sample mean time necessary to complete the examination is less than 47.5 minutes equals approximately:
The likelihood that the sample mean time required to finish the exam will be less than 47.5 minutes is 0.566.
Given;
The average amount of time needed to finish an exam is 45 minutes, with a standard deviation of 15 minutes. The average amount of time required for 100 randomly chosen pupils is calculated.
Mean (μ) = 45
Standard deviation (σ) = 15
Here, σ/√n = 15/√100
= 1.5
To get the probability the sample mean time necessary to complete the examination is less than 47.5 minutes, we need;
P (x < 47.5) = P(z < (x-μ /σ/√n ) )
= P(z < 47.5 - 45/1.5)
= P(z < 17.5)
= 0.566
The probability the sample mean time necessary to complete the examination is less than 47.5 minutes is 0.566
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Write this ratio another way.
120/150
The ratio 120/150 represented in the simplest form is 4 : 5 .
The given ratio is 120 /150 .
Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.
The HCF of the number is 30. Hence the ratio in simplest form will be
120÷30 : 150÷30 = 4 : 5 .
By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.
Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.
Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.
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fast pls!!!!!!!!!!!!!!!!!!! What is the product?
67 times 48 = blank
2,966
3,016
3,116
3,216
Answer:
D, 3216
Step-by-step explanation:
Calculators are great. I love calculators.
Can somone help me with this will mark u brainliest
The simplest radical form of √(11/(x + 4)) when x is 16 is; ¹/₁₀√55
How to simplify surds in radical form?Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.
We are given the expression of the surd as;
√(11/(x + 4))
We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;
√(11/(16 + 4))
= √(11/20)
Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;
√(55/100)
Square root of 100 is 10 and as such we now have;
√(55/100) = ¹/₁₀√55
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For a ride on a rental scooter, Tom paid a 5 fee to start the scooter plus 9 cents per minute of the ride. The total bill for Tom's ride was 21.38 . For how many minutes did Tom ride the scooter?
Answer:
182 minutes
Step-by-step explanation:
0.09x+5=21.38
-5. -5
0.09x=16.38
/0.09. /0.09
X=182
182 minutes
Hopes this helps please mark brainliest
evaluate (-3)^3 x (-5/3)^-4
Answer:
answer. {-2187x}/{625}
40 points bc im ducking struggling!!!! 5. Why is -x/y equivalent to x/-y? Explain..
-x/y is equivalent to x/-y according to the division rule a/b*d/c=a/b*c/d.
Describe division.In division, a number is divided, which is an easy operation. In mathematics, division is the division of a sum into equal parts. A group of 20 people, for instance, could be divided into four groups of 5, five groups of 4, and so on. Division's opposite is multiplication. If 3 groups of 4 add up to 12, then 4 are in each group when 12 is divided into 3 equal groups.
According to the division rule a/b/c/d=a/b*d/c,
=1/(y/-x)
=1*-x/y
=-x/y
-x/y is equivalent to x/-y according to the division rule a/b÷c/d=a/b*d/c.
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suppose i randomly assign one group of angelenos to read a book about the history of the seattle supersonics, and the other to read a book about cheese. i then give them a quiz about basketball history (including recent events such as the los angeles lakers' twelfth championship). what is the independent variable in this experiment?
Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.
The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.
Hence, when i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then the independent variable in this experiment is the book given by me.
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Find the domain and range of the functions represented by the graph
The domain and range of the functions represented by the graph is equal to [-2, 2]. Also, the range of the functions represented by the graph is equal to [-2, 2].
How to identify the domain and range of this graph?The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Note: Each interval on this graph represent -1 unit.
By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:
Domain = [-2, 2].
Range = (-2, 2).
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simplify 1/x^-5 HELP ME PLEASE FIRST ANSWER GETS BRAINLIEST
Answer:
x^5
Step-by-step explanation:
15 ten büyük 25 den küçük tek sayılar
Answer:
Step-by-step explanation:
15 ile 25 arasında toplam 10 tam sayı var,
buna 25-15=10 şeklinde ulaşabiliriz. Ardından tek sayılar sorulduğu için ve bu 10 tam sayı içerisinde hem tek hemde çift olduğu için sayıyı ikiye böleriz
10/2=5 ve ardından en sonda bulunan 25 sayısını çıkarırız yani, 5-1=4
cevaplar: 17, 19,21,23
How can I evaluate P = 3n+2r+t -1 when n=3, r=2, and t=5?
Answer:
p=17
Step-by-step explanation:
P = 3n+2r+t -1
when n=3, r=2, and t=5?
we will just substitute for the values
p=3(3)+2(2)+5-1
p=9+4+4
p=9+8
p=17
;- The value for p is 17
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true or false? finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely.
It is false that " finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely".
What is standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, however, is obviously more dispersed.
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A line passes through the points (–4, –1) and (8, 2). What is its equation in slope-intercept form?
I always get it wrong when I write it out
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{2 +1}{8 +4} \implies \cfrac{ 3 }{ 12 } \implies \cfrac{1 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y +1 = \cfrac{1 }{ 4 } ( x +4) \\\\\\ y+1=\cfrac{1 }{ 4 }x+1\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 4 }x \end{array}}[/tex]
Mia’s family drinks a total of 10 gallons of milk every 6 weeks. How many gallons of milk do they drink per week
Whats the answer to question 10?
Answer:
[tex]y = |x - 3|+ 5[/tex]
y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.
Reid's Hardware discounts all riding lawnmowers 9% to customers paying in cash. If Trey paid $1,517.74 in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower?
(Let x represent the original price of the lawnmower and y represent the discounted price.)
A.
y = 1.09x
B.
y = 0.91x
C.
y = 1.9x
D.
y = x - 9x
An equation to determine the original price of the lawnmower discounted at 9% to $1,517.74 is B. y = 0.91x.
What is an equation?An equation summarizes a mathematical statement that equates two or more mathematical expressions.
Equations operate with values, numbers, and variables, using the equation symbol (=) and mathematical operands to establish the equality of values.
Discount offered = 9%
Amount paid for a lawnmower = $1,517.74
Original price = x
Discounted price, y = 0.91x
Y = 0.91x
1,517.74 = 0.91x
x = 1,667.85
Thus, the original price of the lawnmower is determined by Equation B.
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Place a. Point on the number line to show the value that is 1/10 of 0.5
The value of 1/10 of 0.5 lies between 0.1 and 0.2
What is Number line?A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
Given:
Point on the number line to show the value that is 1/10 of 0.5
So, 1/10 of 0.5
= 1/10 x 0.5
= 0.05
Hence, the value of 1/10 of 0.5 lies between 0.1 and 0.2
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Finding the derivatives using The Chain Rule
a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².
b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².
How to determine the derivative of a function by chain rule
Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:
df / dx = (df / du) · (du / dx)
a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:
F'(x) = [2 · g(x) + 6] · g'(x)
F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²
b) Now we proceed to expand the polynomial in its standard form:
F'(x) = [(2 / 3) · x³ + 7] · x²
F'(x) = (2 / 3) · x⁵ + 7 · x²
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help
Simplify the ratio of 0,5 kg: 250 g
Answer:
2:1
Step-by-step explanation:
.5 kg : 250g
the units must be same at both sides
500g : 250g
{as 1 kg = 1000g}
by simplifying both sides
10g : 5g
2g : 1g
2:1
Can someone pls help me it’s do in 10 mins
The value of x is 22.5528.
Let ABC be the triangle , <A = 70, <B = 30 ,<C = 80.
Sum of angles in a triangle is 180.
70 + 30 + <C = 180
<C = 180 - 100
<C = 80.
Let sides be a = x , b = 12 and c = ?
According to sines law,
a/sin A = b/sin B = c/sin C
substitute a ,b,A,B values
a/sin A = b/sin B
x/sin 70 = 12/sin 30
x = 0.9397*12/1/2
= 11.2764*2/1
x = 22.5528.
Therefore the value of x is 22.5528.
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Explain how the function y=-1/3|x+2|+5 is transformed from the original function of y=-1/3|x|.
The original function of y = -1/3|x| was translated 2 units to the right and 5 units up.
The types of transformation.In Mathematics, there are four (4) main types of transformation and these include the following:
DilationRotationReflectionTranslationWhat is a translation?In Mathematics, the translation of a geometric figure (shape) to the right simply means adding a digit to the numerical value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure (shape) that is translated up simply means adding a digit to the numerical value on the y-coordinate (y-axis) of the pre-image.
In this scenario, the original function was shifted 2 units to the right and then shifted 5 units up to produce the new function as follows:
Original function (x, y) → New function (x + 2, y + 5)
y = -1/3|x| → y = -1/3|x + 2| + 5
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can you guys help me with these?
