Answer:
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2
Three weeks, so [tex]\mu = 2*3 = 6[/tex]
Calculate the probability that fewer than four tornadoes occur in a three-week period.
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025[/tex]
[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149[/tex]
[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446[/tex]
[tex]P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512[/tex]
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
In a certain region, the probability of a baby being born a is instead of 0.5. Let A denote the event of getting a when a baby is born. What is the value of ?
Answer:
[tex]P(\bar A) = 0.5[/tex]
Step-by-step explanation:
Given
[tex]P(A) = 0.5[/tex]
Required
[tex]P(\bar A)[/tex]
To do this, we make use of complement rule:
[tex]P(\bar A) = 1 - P(A)[/tex]
So, we have:
[tex]P(\bar A) = 1 - 0.5[/tex]
[tex]P(\bar A) = 0.5[/tex]
Heeeeeeelp please ;-;
t value lies between (2,3) so, answer is option d
HELP PLEASE!!!!!!!!!!
Answer:
12
Step-by-step explanation:
Mai drives a truck for a soft drink company. Her truck is filled with 15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the
truck is carrying, and let b be the number of 70-ounce bottles.
The truck must be carrying less than 4000 pounds (64,000 ounces). Using the values and variables given, write an inequality describing this.
Answer:
15c + 70b < 64,000
Step-by-step explanation:
15c will represent the amount of ounces in the truck from the 15 ounce cans.
70b will represent the amount of ounces in the truck from the 70 ounce bottles.
These need to be added together in the inequality to represent the total weight in the truck.
Then, a less than inequality sign needs to be used, since the truck has to be carrying less than 64,000 ounces.
Put this all together:
15c + 70b < 64,000
So, the inequality is 15c + 70b < 64,000
Which System of inequalities has this graph as its solution?
A. y<2x-3
y<1/3x+4
B. y>2x-3
y>1/3x+4
C. y>2x-3
y<1/3x+4
D. y<2x-3
y>1/3x+4
Answer: B
Step-by-step explanation:
The line [tex]y=2x+3[/tex] is dotted and shaded above.
Eliminate A and D.Similarly, the line [tex]y=\frac{1}{3}x+4[/tex] is also shaded above.
Eliminate C.This leaves B as the correct answer.
2+8+5+9+90=
3+45+111=
Answer:
1) 114
2) 159
Step-by-step explanation:
2+8+5+9+90 = 114
3+45+111 = 159
Hope this helps.
Answer:
1)144
2)159
..........
BAC can be proved congruent to DEF by
Answer:
ASA
Step-by-step explanation:
∠ABC ≅ ∠EDF Angle
BC ≅ DF Side
∠C ≅ ∠F Angle
If a:b = 1:2 then find the value of (3a + b): (4a + 2b).
Answer:
5:8
Step-by-step explanation:
By question it's given that ,
[tex]\implies a:b = 1:2 [/tex]
Let us suppose that the common ratio is x , therefore the Numbers ,
[tex]\implies a = 1x [/tex]
[tex]\implies b = 2x [/tex]
And we need to find the value of ,
[tex]\implies (3a + b): (4a + 2b ) \\\\\implies (3 * x + 2x ) : (4*x + 2*2x ) \\\\\implies (3x + 2x):(4x+4x)\\\\\implies 5x : 8x \\\\\implies 5:8 [/tex]
Hence the required answer is 5:8 .
Someone pls help me due in 30 min. Given that x and y show inverse variation, complete the table.
Answer:
1st blank=[tex]y_{1}[/tex]
2nd blank=[tex]x_{1}[/tex]
3rd blank= [tex]y_{2}[/tex]
3*27=81
so 1*[tex]y_{1}[/tex]=81
hence [tex]y_{1}[/tex]=81
9* [tex]x_{1}[/tex]= 81
[tex]x_{1}[/tex]=9
27*[tex]y_{2}[/tex]=81
[tex]y_{2}[/tex]=3
Thus solved.
Hope this helps.
Please mark me as brainliest.
Please help asap!!! :(
Answer:
Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3
Step-by-step explanation:
First, we can graph these inequalities out. As you can see in the picture, the three vertices where the inequalities all connect form a triangle. We can check each of these vertices to find our minimum and maximum.
First, we have (3,7). 4y-3x = 4(7)-3(3)=28-9=19
Next, for (3, -3), we have 4y-3x = 4(-3)-3(3) = -12-9=-21
Finally, for (0.5, 2), we have 4y-3x=4(2)-3(0.5)=8-1.5 = 6.5
Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3
What is the surface area of this rectangular prism
Answer:
3*7 = 21*2=42
13*3=39*2=78
7*13=91*2=182
42+78+182=302
So the answer is D
Hope This Helps!!!
Answer:
D. 302
Step-by-step explanation:
This is how I did it:
First multiply 7 by 3, 21
Multiply that by 2 because there are 2 of those faces. 42.
Then multiply 3 by 13, and again by 2. 78.
And 13 by 7 by 2. 182.
Add. 302.
Or do an equation and use a calculator: 7(3)(2)+3(13)(2)+13(7)(2)=302
Express 20% as a decimal number
Answer:
.20
Step-by-step explanation:
take the two digit % and move the decimal two places to the left
Answer: 0.2
Step-by-step explanation: 20/100 is 1/5 and 1/5 means 1 divided by 5 so the answer is 0.2
If a silver alloy that costs $6.75 an ounce is
going to be mixed with 55 ounces of a silver
alloy that costs $10 an ounce to make a
mixture that costs $8 an ounce, how many
ounces of the $6.75 an ounce alloy must be
used?
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Answer:
88 ounces
Step-by-step explanation:
Let x represent the number of ounces of the less expensive alloy in the mix. Then the cost of the mix will be ...
6.75x +10(55) = 8(55+x)
110 = 1.25x . . . . . . subtract 440+6.75x
88 = x . . . . . . . . divide by 1.25
88 ounces of $6.75/oz silver must be used.
Which of the following functions shows the reciprocal parent function, F(x) = 1, shifted left?
Answer:
G(x)=1/x+15
Step-by-step explanation:
.
find the slope of the line graphed above
Answer:
The slope of the line is -6.
find the equation of the line shown
Answer:
y=1/2x+1/2
Step-by-step explanation:
In order to find the slope, you can use rise/run, in this case, the slope is 1/2 and the y-intercept is at (0, 0.5)
can you help please I have no clue
Answer:
6, 15, 24, 33
Step-by-step explanation:
Basically, the number on top of the sigma represents the number of terms total in that sequence, and on the right you have the equation in which you can plug in whichever value that falls into what the top number says to find the output. In other words, just plug in 1 for k to find a1, 2 for k to find a2, etc.
Hope that helps!
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on an even number and a number greater than 17? (A number is even if it is divisible by 2. 0 and 00 are considered even as well.)
Answer:
the wording (punctuation) of the question can lead to different interpretations....
I assume that the question was >17 & even which is "5/19",
BUT... it can also be read as two questions
first >17 which is "10/19"
and second an even number which is "9/19"
BUT !!! I think that the question answer is 5/19
Step-by-step explanation:
Even Number = 18/38 = 9/19
greater 17 = 20/38 = 10/19
Even & greater 17 = 10/38 = 5/19
For any number n>1, is
|(.5 +.2i)^n|
A. greater than 1?
B. less than 1?
C. equal to 1?
PLZ HELP
Answer:
B. Less than 1
Step-by-step explanation:
You could plug in values of n greater than 1 and see what happens....
Example n=2 gives |(.5+.2i)^2|
Simplifying inside gives |(.5)^2+2(.5)(.2i)+(.2i)^2|
=|.25+.2i+.04i^2|=|.25+.2i-.04|=|.21+.2i|.
Applying the absolute value part gives sqrt(.21^2+.2^2)=sqrt(.0441+.04)=sqrt(.0841)=.29
This value is less than 1.
We should also be able to do the absolute value first then the power.
|.5+.2i|=sqrt(.25+.04)=sqrt(.29)
So |.5+.2i|^2=.29 which is what we got long way around.
Anyways (sqrt(.29))^n where n is greater than 1 will result in a number greater than 0 but less than 1.
Consider the set S of primes less than 15. List the set S . (Input this as a list with no spaces, use commas.) How many subsets does the set have
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Answer:
S = {2, 3, 5, 7, 11, 13}
2^6 = 64 subsets
Step-by-step explanation:
The list of primes less than 15 is ...
S = {2, 3, 5, 7, 11, 13}
__
A set with n unique elements has 2^n unique subsets, including the empty set and the full set. This set of 6 elements has 2^6 = 64 subsets.
Square Footage Frequency
0-499 5
500-999 17
1000-1499 36
1500-1999 115
2000-2499 125
2500-2999 81
3000-3499 47
3500-3999 45
4000-4499 22
4500-4999 7
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
Answer:
2424.5
904.16
Step-by-step explanation:
the mean = ∑frequency /n
∑f = 5+17+36+115+125+81+47+45+22+7 = 500
∑xf = 1212250
∑x²f = 3347037625
sample mean = 1212250/500
= 2424.5
variance = 1/500-1[3347037625 - 1212250²]
= 815710.02
standard deviation is = √variance
standard deviation = √815710.02
= 904.16
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 39 beats per minute, the mean of the listed pulse rates is x=76.0 beats per minute, and their standard deviation is s=13.8 beats per minute. a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 39 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 39 beats per minute significant
Answer:
a) The difference is of -37, that is, this pulse rate is 37 beats per minute below the mean.
b) 2.68 standard deviations below the mean.
c) Z = -2.68.
d) Z-score below -2, so a pulse rate of 39 beats per minute is significantly low.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the females?
Difference between 39 and 76, so 39 - 76 = -37.
The difference is of -37, that is, this pulse rate is 37 beats per minute below the mean.
b. How many standard deviations is that [the difference found in part (a)]
Standard deviation of 13.8, so:
-37/13.8 = -2.68
So 2.68 standard deviations below the mean.
c. Convert the pulse rate of 39 beats per minutes to a z score.
2.68 standard deviations below the mean, so Z = -2.68.
d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 39 beats per minute significant?
Z-score below -2, so a pulse rate of 39 beats per minute is significantly low.
The following data were collected from a simple random sample from an infinite population.
13 15 14 16 12
The point estimate of the population standard deviation is _____.
Answer:
15
Step-by-step explanation:
Find dy/dx of the function y = √x sec*-1 (√x)
Hi there!
[tex]\large\boxed{\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}}[/tex]
[tex]y = \sqrt{x} * sec^{-1}(-\sqrt{x}})[/tex]
Use the chain rule and multiplication rules to solve:
g(x) * f(x) = f'(x)g(x) + g'(x)f(x)
g(f(x)) = g'(f(x)) * 'f(x))
Thus:
f(x) = √x
g(x) = sec⁻¹ (√x)
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{\sqrt{x}\sqrt{\sqrt{x}^{2} - 1}} * \frac{1}{2\sqrt{x}}[/tex]
Simplify:
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{2|x|\sqrt{{x} - 1}}[/tex]
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}[/tex]
Answer:
[tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Arctrig Derivative: [tex]\displaystyle \frac{d}{dx}[arcsec(u)] = \frac{u'}{|u|\sqrt{u^2 - 1}}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{x}sec^{-1}(\sqrt{x})[/tex]
Step 2: Differentiate
Rewrite: [tex]\displaystyle y = \sqrt{x}arcsec(\sqrt{x})[/tex]Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[\sqrt{x}]arcsec(\sqrt{x}) + \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})][/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[\sqrt{x}]arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{d}{dx}[\sqrt{x}] \bigg][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{d}{dx}[x^\bigg{\frac{1}{2}}]arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{d}{dx}[x^\bigg{\frac{1}{2}}] \bigg][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}x^\bigg{\frac{1}{2} - 1}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2}x^\bigg{\frac{1}{2} - 1} \bigg][/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}x^\bigg{\frac{-1}{2}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2}x^\bigg{\frac{-1}{2}} \bigg][/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2x^\bigg{\frac{1}{2}}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2x^\bigg{\frac{1}{2}}} \bigg][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2\sqrt{x}} \bigg][/tex]Arctrig Derivative: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{1}{|\sqrt{x}|\sqrt{(\sqrt{x})^2 - 1}} \cdot \frac{1}{2\sqrt{x}} \bigg][/tex]Simplify: [tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Find the value of x in each case
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
Given: triangle ABC with side lengths a, b, and c, and height h
Prove: Area = 1/2absin C
Answer:
Step-by-step explanation:
Statements Reasons
1). ΔABC with side lengths a, b, c, and h 1). Given
2). Area = [tex]\frac{1}{2}bh[/tex] 2). Triangle area formula
3). [tex]\text{sin}C=\frac{h}{a}[/tex] 3). Definition of sine
4). asin(C) = h 4). Multiplication property of
equality.
5). Area = [tex]\frac{1}{2}ba\text{sin}C[/tex] 5). Substitution property
6). Area = [tex]\frac{1}{2}ab\text{sin}C[/tex] 6). Commutative property of
multiplication.
Hence, proved.
answer it correctly:)
can anyone help me?:)
Answer:
JAR WITH MARBLES.
There's
5 Blue Marbles
3 Red Marbles
2 Yellow Marbles
Pr = No of desired outcome/No of Possible Outcomes
No of Possible Outcomes = 10.
1. Pr(yellow) = 2/10 = 1/5.
2. Pr(Red) = 3/10
3. Pr(Blue) = 5/10 = 1/2
4. Pr(Yellow and Red) = 2/10 x 3/10 = 6/100 = 3/50.
5.Pr(Blue and Red)= 5/10 x 3/10 = 15/100 = 3/20.
6.Pr( Yellow and Blue) = 2/10 x 5/10 = 10/100 = 1/10.
THE CHIPS ARE PLACED IN A JAR AND MIXED.
No of Possible Outcomes = 8.
The Numbers are 1,2,3,4,5,6,7,8.
There's
4 Even Numbers
4 Odd Numbers
1. Pr(Even) = 4/8 = 1/2
2. Pr(Odd) = 4/8 = 1/2
3. Pr(Chip with Biggest No) = 1/8.
Reason. There can only be one Number which Is the biggest amongst all. So the Probability of picking it is 1.
4.Pr(Smallest Number) = 1/8 (Same concept).
5.Pr(Prime Number)
The prime Numbers above are 2,3,5,7
Pr(Prime) = 4/8 = 1/2.
Hope this helps!.
A 3 phase traffic signal is designed with 2 seconds of all red per phase and phase lengths of 25 seconds, 30 seconds, and 15 seconds. The cycle length is ____ seconds.
Answer:
[tex]CL=76secs[/tex]
Step-by-step explanation:
From the question we are told that:
Traffic Phases p=3
Phase time Lengths
25 seconds, 30 seconds, and 15 seconds
Red Per Phase [tex]T=2sec[/tex]
Generally the equation for Cycle Length is mathematically given by
[tex]CL=Phase\ Length+Red\ Per\ Phase[/tex]
[tex]CL=(25+2)+(30+2)+(15+2)[/tex]
[tex]CL=76secs[/tex]
X S2.0.2
A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic function S(t) = -52 + 80t can be used to find
the heights of the rocket, in meters, at any time t in seconds. Find the height of the rocket 8 seconds after it takes off. During the
course of its flight, after how many seconds will the rocket be at a height of 290 meters?
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Answer:
320 m after 8 seconds5.6 seconds, 10.4 seconds to height of 290 mStep-by-step explanation:
To find the height at 8 seconds, evaluate the formula for t=8.
S(t) = -5t^2 +80t
S(8) = -5(8^2) +80(8) = -320 +640 = 320
The height of the rocket is 320 meters 8 seconds after takeoff.
__
To find the time to 290 meters height, solve ...
S(t) = 290
290 = -5t^2 +80t
-58 = t^2 -16t . . . . . . . divide by -5
6 = t^2 -16t +64 . . . . . complete the square by adding 64
±√6 = t -8 . . . . . . . . . take the square root
t = 8 ±√6 ≈ {5.551, 10.449}
The rocket is at 290 meters height after 5.6 seconds and again after 10.4 seconds.
Suppose U1 and U2 are i.i.d. Unif(0,1) withU1=0.1 and U2=0.8. Use the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees.
a. 0.326
b. 0.326
c. 0.663
d. 1.96
Answer:
0.663 ( c )
Step-by-step explanation:
U1 = 0.1 , U2 = 0.8
using the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variable
first step : generate single obsⁿ from N ( -1,4 )
attached below is the detailed solution
