The lower bound on the probability that the plant will fill between 9,000 and 11,000 cans on a particular day is at least 1 - 1/10 = 9/10.
What is probability ?
A probability is a number that reflects the chance or likelihood that a particular event will occur.
(a) P(X > 11,000) ≤ E[X] / 11,000
Where X is the random variable representing the number of cans filled in a day, and E[X] = 1,000 is the expected value.
So, P(X > 11,000) ≤ 1,000 / 11,000 = 1/11
(b) P(|X - E[X]| ≥ kσ) ≤ 1/k^2
Where X is the random variable representing the number of cans filled in a day, E[X] = 1,000 is the expected value, and σ is the standard
As we know that for any random variable X, E[X^2] >= (E[X])^2
therefore Var(X) = E[X^2] - (E[X])^2 >= 0.
so the standard deviation of X is
σ = √(Var(X)) = √(1000) = 31.62
We can choose k = (11000-9000)/(2*31.62) = 3.16
so P(|X - E[X]| ≥ 3.16σ) = P(|X - 1000| ≥ 10000) ≤ 1/3.16^2= 1/10
Therefore, the lower bound on the probability that the plant will fill between 9,000 and 11,000 cans on a particular day is at least 1 - 1/10 = 9/10.
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If $4,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is: (a) 7% simple interest: $ (b) 7% compounded annually: $ (c) 7% compounded quarterly: $ (d) 7% compounded monthly: $ Round your answers to the nearest cent.
The interest is a) $7000
b) $17709.73
c) $18672.62
d) $18901.67
What is the formula for simple and compound interest?
Simple interest = (P× r× t)
Compound interest = P(1+r/n)^nt - P
We will find the interest as shown below:
P=$4,000
t=25 years
a) r=7%=0.07
Simple interest = (P× r× t)
= (4000×0.07×25)
= $7000
b) r=7%=0.07
Compound interest = P(1+r)^t - P
= 4000(1+0.07)^25-4000
= $17709.73056
rounding to nearest cents
= $17709.73
c) r=7%=0.07
n=4
Compound interest = P(1+r/n)^nt - P
= 4000(1+0.07/4)^(25*4)-4000
= $18672.62375
rounding to nearest cent
= $18672.62
d) r=7%=0.07
n=12
Compound interest = P(1+r/n)^nt - P
= 4000(1+0.07/12)^(25*12)-4000
= $18901.6728
rounding to nearest cent
= $18901.67
Hence, the interest is a) $7000
b) $17709.73
c) $18672.62
d) $18901.67
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If x is a real number, what is the smallest possible value of x^2+8 ?
hi,
smallest value is 8.
x^2 will always be a positive number regardless of the value of x.
the smallest value for a positive number is 0, therefore x^2 +8 will never be smaller than 8
An American roulette wheel contains 38 slots. Eighteen of the slots are colored red and eighteen are colored
black. The remaining two slots are colored green. A ball is spun on the wheel and comes to rest in one of the
38 slots. If you bet $1 on the the number 32 and win, the house pays you $36.
What is the expected value of betting on 32?
$1
O-$1
4
O-$5.30
O-$0.053
The expected value of betting 32 is -$0.053, making the 4th option the right choice.
In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.
The probability distribution can be shown as:
x $35 -$1
p(x) 1/38 37/38
as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.
Thus, the expected value can be calculated as E(x) = ∑x.p(x).
Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.
Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.
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Which equation is an integer?
5-3 =
6-10 =
11.6 - 3 =
63 - 4 x 5 =
[tex]5-3=2\\\\6-10=-4\\\\11.6-3=8.6\\\\63-4\times 5=63-20=43[/tex]
So, the first, second, and fourth equations are integers.
The first and last are positive integer and second is negative integer.
What are integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
a) 5-3 =2
b) 6-10 = -4
c) 11.6 - 3 =8.6
d) 63 - 4 x 5 =63- 20 = 43
So, among the above first and last are positive integer and second is negative integer.
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what is the inverse of the following function? 50 points
The inverse of the given function [tex]f(x)=\sqrt[5]{x^3}[/tex] is [tex]f^{-1}(x)=x^{\frac{5}{3}}[/tex]
Inverse of a functionThe given function is:
[tex]f(x)=\sqrt[5]{x^3}[/tex]
This function can be written in exponent form as:
[tex]f(x)=x^\frac{3}{5}[/tex]
Make x the subject of the formula:
[tex]x=[f(x)]^\frac{5}{3}[/tex]
Let x be replaced by [tex]f^{-1}(x)[/tex] and f(x) be replaced by x
The inverse function therefore becomes:
[tex]f^{-1}(x)=x^{\frac{5}{3}}\\\\ f^{-1}(x)=\sqrt[3]{5}[/tex]
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A pendant is formed using a cylinder and cone. Once assembled, as shown below, the pendant is painted.
How many square millimeters are covered with paint? Express the answer in terms of π.
336π square millimeters
400π square millimeters
416π square millimeters
464π square millimeters
336π square millimeter answer
Step-by-step explanation:
Answer:
336pi square millimeters
Step-by-step explanation:
E2020 Geometry B :3 !!
Which of the following estimates at 895% confidence level most likely comes from a small sample?
A. 67% (+-7%)
B. 59 % (+-21%)
C. 53 % (+-3%)
D. 48 % (+-5%)
Option B. The estimate that would most likey come from the small sample is going to be B. 59 % (+-21%).
How to find the sample
The sample space can be gotten rom the margin of error. A smaller sample space would be gotten by dividing with a larger number.
This would give a margin of error that is large. In the second option, we can see that the largest margin of error is ± 21%.
Hence this is the answer to the question.
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The transformation from parallelogram LMNO to parallelogram L'M'N'O' was carried out as shown in the coordinate plane below.
The transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis
How to determine the transformation?The complete question is added as an attachment
From the graph, we have the following highlights:
Parallelogram LMNO and parallelogram L'M'N'O' are on either sides of the x-axisThey are equidistant from the x and y axesThey have equal dimensionsThis means that parallelogram LMNO is reflected across the x-axis to get parallelogram L'M'N'O'
Hence, the transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis
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Question 22: 4 pts
Nine cards are numbered from 1 to 9 and placed in a box. One card is selected at random and not replaced.
Another card is randomly selected. What is the probability of selecting two prime numbers?
2/9
O1/12
1/9
1/6
The probability of selecting two prime numbers is 1/6.
What is the probability?Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.
The probability of selecting two prime numbers = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]
Prime numbers between 1 and 9 = 2, 3, 5, 7
4/9 x 3/8 = 1/6
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Give the name (monomial, binomial,
trinomial, etc.) and the degree of the
polynomial.
2x - 4
Name? [?]
Degree? [ ]
Binomial
First Degree
Step-by-step explanation:Naming and giving the degree of a polynomial can help people understand the different properties of an expression.
Naming Polynomials
Polynomials are named based on the number of terms in the expression.
Terms are the different coefficients and variables that are added or subtracted together.For example, the expression above has 2 terms. The first being 2x and the second being 4. There are 2 separate terms being subtracted.
There are 3 main types of polynomials
Monomials have 1 termBinomials have 2 termsTrinomials have 3 termsMost polynomials above that are just called polynomials.This specific expression is a binomial.
Degree
The degree of a polynomial is the highest exponent in the expression. For example, if the largest exponent is a 6, then the degree is also 6.
In the binomial above, there is no written exponent; however, it can be assumed that the variable "x" has an exponent of 1. Thus, this binomial is of the first degree.
Additionally, when writing a polynomial in standard form, the terms should be written in descending order of exponents.
decreased by 0% is 800 what number?
Answer:
800
Step-by-step explanation:
zero percent is just no percent...
800 - (0% × 800) =
800 - (0 ÷ 100 × 800) =
800 - (0 × 800) =
800 - 0 =
800
lol
The 0% of 800 is 800
What is percentage?Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Calculation of PercentageCalculating percentage means to find the share of a whole, in terms of 100. There are two ways to find a percentage:
By using the unitary method.By changing the denominator of the fraction to 100.Given:
800 - (0% × 800)
=800 - (0 ÷ 100 × 800)
=800 - (0 × 800)
=800 - 0 =800
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Find the missing length indicated. need help
The missing length of given right triangle is equal to 25.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²=(leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ leg}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ leg}{hypotenuse} \\ \\ tan(x)=\frac{opposite\ leg}{adjacent\ leg}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
From Pythagorean Theorem you can find h (heigth). Thus,
15²=9²+h²
h²=225-81
h²=144
h=12
If h=12 and m=9, from h²=m*n you can find n.
h²=m*n
12²=9*n
144=9n
n=144/9
n=16
Therefore, x= m+ n= 9+16=25.
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Complete the statements. If both expressions have the same value after substituting and simplifying two different values for the variable, then they are . The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are .
When both expressions have the same value, then they are equal to each other.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
Consider the expressions 5 + 8k and 8k + 5.
Using k = 3
5 + 8k = 8k + 5
5 + 8(3) = 8(3) + 5
5 + 24 = 24 + 5
29 = 29
Using k = 5
5 + 8k = 8k + 5
5 + 8(5)= 8(5) + 5
5 + 40 = 40 + 5
45 = 45
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Complete question:
Consider the expressions 5 + 8k and 8k + 5. Determine why the expressions are equivalent.
Using k = 3 5 + 8k 8k + 5 5 + 8(3) 8(3) + 5 5 + 24 = 29 24 + 5 = 29
Using k = 5 5 + 8k 8k + 5 5 + 8(5) 8(5) + 5 5 + 40 = 45 40 + 5 = 45
Complete the statements.
If both expressions have the same value after substituting and simplifying two different values for the variable, then they are.
The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are.
Write -3/12 as a mixed number in reduced form.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-\dfrac{3}{12}}[/tex]
[tex]\huge\textbf{Simplify:}[/tex]
[tex]\mathsf{-\dfrac{3}{12}}[/tex]
[tex]\mathsf{= \dfrac{-3\div 3}{-12\div3}}[/tex]
[tex]\mathsf{= -\dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{- \dfrac{1}{4}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
which of the following regression equation best fits the data graphed below?
Answer:
D
Step-by-step explanation:
Suppose a line has a slope of −5.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
The slope of a line parallel to this line is -5 and the slope of a line perpendicular to this line is 1/5
How to determine the slopes?The slope is given as:
m = -5
Parallel line have the same slope.
So, the slope of a line parallel to this line is -5
However, perpendicular lines have their slopes to be opposite reciprocal
This means that:
Perpendicular slope = -1/-5Perpendicular slope = 1/5The slope of a line perpendicular to this line is 1/5
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how do I find the value of x?
Answer: x = 15
Step-by-step explanation:
The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.
sum of angles = (n - 2) × 180
sum of angles = (7 - 2) × 180
sum of angles = 5 × 180
sum of angles = 900°
Now to find the value of x, we have to set each of the interior angles, added up, equal to 900°:
7x + 1 + 10x + 6x + 7 + 10x - 9 + 9x + 4 + 8x + 10 + 9x + 2 = 900
Combine like terms:
(7x + 10x + 6x + 10x + 9x + 8x + 9x) + (1 + 7 - 9 + 4 + 10 + 2) = 900
59x + 15 = 900
59x + 15 - 15 = 900 - 15 subtract 15 from both sides
59x = 885
59x/59 = 885/59 divide by 59 on both sides
x = 15
Select the correct answer. Which chart best represents the following information about student results from a class assignment? Frequency 10 Score Frequency Chart 1 23 2 Frequency 10 24 8 25 4 Chart 2 26 3 27 5 28 4 29 5
The chart that best represents the student results from a class assignment is B. Histogram or bar graph.
What is a histogram or bar graph?Both histograms and bar charts are graphic vertical and horizontal bars that visually display frequencies with columns plotted on a graph.
The frequencies are depicted on the Y-axis (vertical axis).
The X-axis (horizontal axis) represents the measured variable.
Question Completion with Answer Options:A. Frequency table
B. Histogram or bar graph
C. Pareto chart
D. Pictogram
E. Pie chart
Thus, the best chart to represent the student results from a class assignment is B. Histogram or bar graph.
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The base of the right pyramid is a rectangle with an area of 1326 square cm. If the volume of the pyramid is 21,452 cubic cm, find its approximate height.
The height of the right pyramid is 48.53 cm.
What is the height of the pyramid?A rectangle pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces.
Height = ( 3 x Volume of a pyramid) /( area)
Height = (3 x 21452) / 1326 = 48.53 cm
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For a function f(x), the difference quotient is x + one-half h + 15. Which statement explains how to determine the average rate of change of f(x) from x = 5 to x = 8? Substitute 5 for x and 3 for h in the expression x + one-half h + 15. Substitute 5 for x and 8 for h in the expression x + one-half h + 15. Substitute 8 for x and 5 for h in the expression x + one-half h + 15. Substitute 8 for x and 3 for h in the expression x + one-half h + 15.
The average rate of change of f(x) from x = 5 to x = 8 would be gotten by; B: Substituting 5 for x and 8 for h in the expression x + one-half h + 15
How to used difference quotient to find average rate of change?The difference quotient is defined as a measure of the average rate of change of a function over an interval.
The limit of the difference quotient which is the derivative is the instantaneous rate of change.
This differential quotient in calculus is usually expressed as;
[f(x + h) - f(x)]/h
We are given the differential quotient as;
f(x) = x + ¹/₂h + 15
Thus, the average rate of change of f(x) from x = 5 to x = 8 would be gotten by;
Substituting 5 for x and 8 for h in the expression x + one-half h + 15
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. Trevor mows 5 times as
many lawns in the
summer as he does in
the fall. If he mows 20
lawns in the summer,
how many does he mow
in the fall?
Answer:
4 lawns
Step-by-step explanation:
20/5
What is the area of this parallelogram?
h = 2 in.
A
b= 10 in.
in.
in²
The area of a parallelogram is 20 inches square
What is the area of a parallelogram?
The area of a parallelogram is the base of the shape multiplied by the height
Area of parallelogram = b × h
Where h = height = 2 In
base = 10 in
Area = 2 × 10
Area = 20 Inches square
Thus, the area of a parallelogram is 20 inches square
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ayuda, no le entiendo :)
Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.
¿Cuántos dias tardarán en fabricar 3000 ruedas si trabajan 10 horas diarias?Sabemos que trabajando 8 horas, en 5 dias producen 2000 ruedas.
El número total de horas que trabajan en esos 5 dias es:
(8 horas)*5 = 40 horas
Entonces se producen 2000 ruedas en 40 horas, es decir, la razon de trabajo es:
(2000 ruedas)/(40 horas) = 50 ruedas por hora.
Ahora, sí en la fabrica trabajan 10 horas al día, entonces van a producir:
10h*(50 ruedas por hora) = 500 ruedas por día.
El número x de días que deben trabajar para producir 3000 ruedas es:
x*(500 ruedas por dia) = 3000 ruedas
x = (3000 ruedas)/(500 ruedas por dia) = 6 dias.
Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.
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Please help me with this, going to take an exam on these tomorrow, wish me luck.
The Cartesian equation of the parametric formulae is x² - y² = 1. Please see the image attached below for further details of the behavior of the function.
How to analyze and to graph a hyperbolic parametric function
In this question we have an hyperbolic function, a kind of transcendent function based on exponential functions. The parametric equations can be rewritten in rectangular coordinates by the using the following property:
sinh² t - cosh² t = 1 (1)
x² - y² = 1
The graph of the Cartesian equation is present in the figure attached below, in which the directions are shown in detail.
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sin0=7/25 and cos0=-24/25. find tan0.
A. -7/24
B. 24/7
C. -24/7
D. 7/24
The answer is A
sin0 = p/h = 7/25
cos0 = b/h = -24/25
Therefore , p = 7 , b = -24
tan0 = p/b = 7 / -24 = -7/24
Question 4 of 10
What should you substitute for y in the second equation (bottom equation) in
order to solve the system by the substitution method?
5x+y=10
3x-2y =6
A. -0.2y+2
B. -5x+10
C. 5x-10
D. 1.5x+3
Answer:
B
Step-by-step explanation:
5x+y=10
-5x -5x
y= -5x+10
Find function then simplify tje answer
Answer:
a)(x+h+2)²=x²+2xh+h²+4x+4h+2
b)(x+h+2)²–(x+2)²=2xh+h²+4h
c)2x+4+h
Step-by-step explanation:
f(x)=x²+4x+2
Aight so for part a you have to replace x with x+h
a)f(x+h)=(x+h)²+4(x+h)+2=x²+2xh+h²+4x+4h+2
and then for part b you need to subtract f(x) from part a:
b)f(x+h)–f(x)=x²+2xh+h²+4x+4h+2–x²–4x–2===>
2xh+h²+4h
and for part c divide the answer by h:
c)
[tex] \frac{f(x + h) - f(x)}{h} = = = > \\ \frac{2xh + 4h + {h}^{2} }{h} = = = > \\ 2x + 4 + h[/tex]
and if you limit h by 0 you'll get the derivative of f(x)
Consider the probability that fewer than 26 out of 107 cell phone calls will not be disconnected. Assume the probability that a given cell phone call will not be disconnected is 25%.
Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Yes or no
please explain in detail how to do these
Since both np > 5 and n(1 - p) > 5, the normal curve can be used as an approximation to the binomial distribution.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The normal approximation can be used if:
np > 5.n(1 - p) > 5.In this problem, the parameters are:
n = 107, p = 0.25.
Hence:
np = 107 x 0.25 = 26.75.n(1 - p) = 107 x 0.75 = 80.25.More can be learned about the binomial distribution at https://brainly.com/question/24863377
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convert this into a standard number
[tex]10^{6}[/tex]
Answer:
1,000,000
Step-by-step explanation:
The attached place value chart shows the power of ten associated with each number place in a decimal number.
ApplicationYou have ...
1 × 10⁶ = 1,000,000
(Put the multiplier digit in the appropriate number place, and fill the remaining spaces with zeros. The digits 32,465 on the chart can be ignored.)
__
Additional comment
For powers of 10, the exponent (6 in this case) tells you the number of zeros to the right of the digit 1. That is, 10^6 is 1 followed by 6 zeros:
1,000,000
find the slope of this line