Using the binomial distribution, the mean and the standard deviation of the amounts are given as follows:
Mean: 1.37.Standard deviation: 1.16.What are the mean and the standard deviation of the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The mean is given by the following rule:
E(x) = np.
The standard deviation is given by the following rule:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the context of this problem, the parameters are found as follows:
p = 0.01, as about 1% of the population has a particular genetic mutation.n = 137, as 137 people are randomly selected.Hence the mean and the standard deviation are, respectively, given by:
E(x) = np = 137 x 0.01 = 1.37.[tex]\sqrt{V(X)} = \sqrt{137(0.01)(0.99)} = 1.16[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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If 13 is subtracted from a number, the result is -4. Find the number.
A flag measures 475 feet by 220 feet. Find its area answer
Answer:104,500
Step-by-step explanation:
Area = l × w= 475 × 220= 104500 feet2
compute the indicated derivative U(t) = 5.1t^2 − 1.7t; U'(6)
Answer: 59.5
Step-by-step explanation:
U(t) = 5.1t^2 − 1.7t
U'(t)=2*5.1t-1.7
U'(t)=10.2t-1.7
U'(6)=10.2(6)-1.7
U'(6)=61.2-1.7
U'(6)=59.5
HELP! I need this done now!
John ran 3 miles in 25.5 minutes. The equation y = 8.5x can be used to represent this situation.
What is the constant of proportionality? Express your answer as a decimal.
Answer:
.................................................................................................................................
Rosita paid $32.08, including tax, for her family to eat dinner at a restaurant. She wants to tip a whole dollar amount that is close to 20%. What is a reasonable tip that Rosita should leave?
Answer:
$6
Step-by-step explanation
$32 is the total(100%)
in order to find what she needs to tip, you have to divide by 5 because 100% / 5=20%
now, to find 20% of 32, you divide 32 by 5.
32 you can just round to 30, so that you can divide it by 5.
30/5=$6
you could've rounded the total up to 35, but 30 was closer, therefore $6 was the closest whole number tip rosita could've left.
hope this helps
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Natalie works as a playground supervisor for 8 weeks during the summer at a rate of
$15.27/h. She works a 40-hour week but averages 3 hours of overtime each week,
paid at time and a half. How much will she earn each week, and for the whole
summer?
Natalie will be paid $656.61 every week in addition to $10505.76 for the summer.
What is an expression?The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Natalie works as a playground supervisor for 8 weeks over the summer and makes $15.27 per hour. She works a 40-hour work week, although she usually works 3 hours of overtime.
For a week = ( 40 + 3 ) x 15.27 = $656.61
For a summer = 4 x 4 = 16 weeks
For a summer = 16 x $656.61 = $10505.76
Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.
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Please help me i need help with this i dont understand it see photo whats the name of the equations
Answer:
commutative property of multiplicationassociative property of additionadditive inverse propertymultiplication property of zeroStep-by-step explanation:
You are asked to identify the real number properties that justify various changes in the way an expression is written.
Properties of numbersIn general, there are associative, commutative, identity, and inverse properties of addition and multiplication. You can use these properties to simplify and rewrite expressions, and to help perform arithmetic.
This is basically a vocabulary question, to see if you know the names associated with the behaviors these properties describe.
Commutative propertiesWhen an operation (such as addition or multiplication) has the commutative property, it means the order of its operands does not matter
addition: a + b = b + a
multiplication: a × b = b × a
Associative propertiesWhen an operation has the associative property, it means that grouping of operands does not matter.
addition: (a + b) + c = a + (b + c)
multiplication: (ab)c = a(bc)
Identity propertiesWhen an operation is performed using its identity element, the value of the other operand is not changed:
addition: a + 0 = a
multiplication: a × 1 = a
Inverse propertiesWhen an operation has an inverse, performing the operation with the inverse produces the identity element.
addition: a + (-a) = 0
multiplication: a × (1/a) = 1
Note: these last two properties are used to simplify and solve algebraic expressions. They let you "undo" operations done to variables or expressions.
Questions at handYou can match the given expressions to the example expressions shown above. The "multiplication property of zero" is also known as the "zero product rule": a product is zero if and only if a factor is zero.
[tex]\begin{aligned}d\cdot4=4\cdot d\quad&\text{commutative property, multiplication}\\(2+a)+8=2+(a+8)\quad&\text{associative property, addition}\\m+(-m)=0\quad&\text{additive inverse property}\\0\cdot b=0\quad&\text{multiplication property of 0}\end{aligned}[/tex]
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From the given table, the relationship that is an inverse variation is the fourth relationship with (1, -2) and (3, -6).
What is an inverse variation?An inverse variation refers to when the values of x and y move in opposite directions.
For instance, when x increases, y decreases. The decrease will have to be constant however which is why the fourth relationship is an inverse variation.
When x increases by 1, the value of y decreases by 2.
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E
3
A. bd
If a, b, c, and d are four different numbers and the proportion
a C
B. a b
C
I
C. b
a
11
IL
D. a+b
b
d
C
HE
3
c+d
d
E
a
11
U
bd
40:09
is true, which of the following is false?
If a, b, c, and d are four different numbers and the proportion. The given statement is true.
We take one example,
When you split them, they will all equal the same thing.
A = 5 ,B = 20 20 divided by 5 equals 4
C = 28 ,D = 7 28 divided by 7 equals 4
The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.
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leg 1: is 5 and leg 2: is 12 what is the hypotenuse
Answer:
13
Step-by-step explanation:
Hypotenuse is c
so c^2 = a^2 + b^2
c^2 = 5^2 + 12^2
c^2 = 25 + 144 = 169
c^2 = 13^2
c = 13
Eric walks around a man made circular lake three times how far in km has he walked ?
Considering the circumference of a circle, it is found that Eric has walked 151.68 km.
What is the missing information?The missing information is that the lake is a circle of radius 5 miles.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by:
C = 2πr.
Hence the circumference in miles of the circle is:
C = 2π x 5 = 10π miles.
This is the length of one lap, hence the length of 3 laps is:
3 x 10π = 30π miles.
In kilometers, the distance is:
30π x 1.60934 = 151.68 km.
Hence Eric has walked 151.68 km.
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John sold 36 cookbooks at 27 dollars each. How much did he make?
Answer:
$972
36 × 27 = 972
Find the length of the missing side. Leave your answer in the simplest radical form.
Length of the missing side. Leave your answer in the simplest radical form b= root of 69 feet
Pythagorean theorem:
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2
The Pythagorean Theorem is tremendously useful. In many realistic scenarios it is possible to measure a and b with ease, but it is often difficult to measure c. For instance, c might pass through a lake or private property or might be up in the air! We'll do a few example puzzles in class together to show you how this works.
Nonetheless, the Pythagorean Theorem still presents a substantial limitation to utility. Specifically, it requires that the angle between a and b is 90 degrees. If the angle is not 90 degrees, the Pythagorean Theorem doesn't help.
This is where the Law of Cosines comes in. The Law of Cosines allows us to find c even when the angle between a and b is not 90 degrees. Check out this applet which illustrates the relationship between a2 and b2 and c2 that also takes into account the angle C (note the angle is capital C to distinguish it from lower case c, the side opposite angle C) between the legs a and b.
Adjust the blue dots in the triangle on the right right side of the screen to see the relationship. At the outset, when angle C is 90 degrees, a2+b2 is exactly equal to c2. However, when you move any of the three vertices of the triangle, note that the equality is not maintained. The problem is that angle C becomes not 90 degrees.
Now ,
a= 10
c= 13
b=?
a2 + b2 = c2
[tex]10^{2} +b^{2} = 13^{2} \\\\100+ b^{2} = 169\\\\b^{2} = 169-100\\\\b=\sqrt{69}[/tex]
Length of the missing side. Leave your answer in the simplest radical form
b= root of 69 feet
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Mayerlin needs to order some new supplies for the restaurant where she works. The restaurant needs at least 623 forks. There are currently 223 forks. If each set on sale contains 8 forks, write and solve an inequality which can be used to determine , the number of sets of forks Mayerlin could buy for the restaurant to have enough forks.
Answer:
≥ 50 sets
Step-by-step explanation:
Mayerlin wants to know how many sets of 8 forks she needs to buy to increase her supply of forks from 223 to at least 623.
SetupThe number of additional forks will be the number of sets (s) times 8 forks each. Mayerlin wants at least 623.
223 +8s ≥ 623 . . . . . . the inequality
SolutionSubtract 223:
8s ≥ 400
s ≥ 50 . . . . . . divide by 8
Mayerlin could by at least 50 sets of forks to have enough.
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Find the LCM of 32, 40, 36?
Answer:
The least common multiple of 40, 36 and 32 is 1440.
Step-by-step explanation:
Greetings !
Definition :-The LCM of a, b
Is the smallest positive number that is divisible by both a and b.
prime factorization of 32:
[tex]2.2.2.2.2[/tex]
prime factorization of 40:
[tex]2.2.2.5[/tex]
prime factorization of 36:
[tex]2.2.3.3[/tex]
Compute a number comprised of factors that appear in at least one of the following
32,40,36
[tex] = 2.2.2.2.2.5.3.3[/tex]
Multiply the numbers 2.2.2.2.2.5.3.3 = 1440
[tex] = 1440[/tex]
Hope it helps !!!
Triangle ABC is an equilateral triangle. Use the figure to find the value of x
The value of x in the equilateral triangle is 10
The equilateral triangle's three characteristics are: Equal on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure. Additionally, each inside angle is identical (60 degrees).
A unique isosceles triangle with three equal sides is called an equilateral triangle. The formulas that we take into account most frequently for a triangle are: Dimensions of an equilateral triangle , the equilateral triangle's circumference, Equilateral triangle's height
An equiangular triangle's area can be calculated using the following formula:
If A=√3a2/4, then ABC's perimeter 3a
where a is the triangle's side length.
In equilateral triangle, the sum of the 3 angles are 180°.then the angle of each side is 60°
From the given data,
(7x-10)°=60°
7x=60+10
7x=70, x=10
Hence the value of x is 10
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find the value of px5 when p=4.
Which expression is equivalent to the image below.
Answer:
t - s
------------
t + s
Step-by-step explanation:
To solve a problem like this you need to flip the denominator and multiply
Step 1: Write the equation
s
1 - ------
t
--------------
s
1 + -------
t
Step 2: Flip it and multiply
s t
1 - ------ × 1 + -------
t s
Step 3: Multiply Across
s t -s + t t - s
1 - ------ × 1 + ------- = -------------- or ---------------
t s t + s t + s
I hope this helps!
Select the correct answer.
Which function defines (g. f)(z)?
f(z)
g(z)
log(5z)
5z + 4
OA
(9. f)(z)
OB.
(g-f)(z): = 5x + 4+ log(5z)
OC (g. f)(z) = 5z log(5z) +4
OD. (g. f)(z) = 5z - 4-log(5z)
5z log(52) + 4log(5z)
Answer: A. (g•f)(x)= log(5x) ( 5x + 4)=5x log(5x) + 4log(5x)
Step-by-step explanation:
Hope this helps :)
If f(x) = 4x-2, what does f(-2) equal?
What is the 7 1/2 divided by 1 9/10 in the simplest form
Answer:
3 18/19
Step-by-step explanation:
7 1/2 ÷ 1 9/10 =
= 15/2 × 10/19
= 150/38
= 75/19
= 3 18/19
Grayson's retirement party will cost $60 if he invites 10 guests. If there are 86 guests, how much will Grayson's retirement party cost? Solve using unit rates.
Answer:
Grayson's party will cost $516.
Step-by-step explanation:
Start with putting a unit rate for money per person
60/10
Divide by 10
6/1 (6$ per person)
Then multiply by 86 (# of guests attending)
86 x 6 = 516
Write a slope-intercept equation for a line that passes through (7,0) and (-5,3).
Answer:
y = -1/4x + 7/4
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
m = (3 - 0)/(-5 - 7) = 3/(-12) = -1/4
using m = -1/4, y = 0 , x = 7
y = mx + b
0 = -1/4(7) + b
0 = -7/4 + b
b = 7/4
y = -1/4x + 7/4
Find the area of a quadrilateral formed by the points of intersection of the graphs f(x) = (x − 3)(x + 1) and g(x) = 4x − 2x^2 + 6 and the points of extrema of f(x) and g(x).
Answer:
24
Step-by-step explanation:
The extrema is halfway between the roots, so for f(x), it has coordinates (1, f(1)) = (1, -4).
For g(x), we can rewrite it as -2(x²-2x-3) = -2(x-3)(x+1). We can see that the extrema has coordinates (1, 8).
Finding the intersection,
[tex](x-3)(x+1)=-2(x-3)(x+1) \\ \\ 3(x-3)(x+1)=0 \\ \\ x=-1, 3 \\ \\ x=-1 \implies f(x)=g(x)=0 \\ \\ x=3 \implies f(x)=g(x)=0[/tex]
So, we need to find the quadrilateral with vertices (1,-4), (1,8), (-1,0), and (3,0).
We observe this is a kite with diagonals of lengths 4 and 12. So, using the formula for the area of a kite, the area is 24.
Evaluate the function /(x) = 5x²+2x for the given value of x. Simplify your answer.
h(-4)
Answer:
h(-4) = 72
Step-by-step explanation:
Given:
h(x) = 5x² +2x
Evaluate the function h(x) = 5x²+2x for x=-4 means to
find h(-4) by substituting x with -4:
h(-4) = 5·(-4)² +2·(-4)
h(-4) = 5·16 -2·4
h(-4) = 5·16 -2·4
h(-4) = 80 -8
h(-4) = 72
47=
\,\,-\frac{x}{11}+43
−
11
x
+43
Answer:
x=−44
Step-by-step explanation:
Rewrite the equation as
−x11+43=47.−x11+43=47
Move all terms not containing
x
to the right side of the equation.
−x11=4
Multiply both sides of the equation by
−11.−11(−x11)=−11⋅4
Simplify the following (1/7x+3/8) + (2x - 1/8)
the length of a rectangle is 5 feet longer than the width if the perimeter is 94 feet find the length and width of the rectangle
The length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.
What is the length and width of the rectangle?The perimeter of rectangle is expressed as;
P = 2( l + w )
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width w = xLength = x+5Perimeter = 94ftPlug these values into the equation above.
P = 2( l + w )
94 = 2( (x+5) + x )
94 = 2x + 10 + 2x
94 = 4x + 10
4x = 94 - 10
4x = 84
x = 84/4
x = 21
Hence;
Width of the rectangle = x = 21ft
Length of the rectangle = x+5 = 21+5 = 26ft
Therefore the length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.
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