Answer:
0.7125
Step-by-step explanation:
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes (with probability p) in a sequence of n independent events.
The probability of getting exactly x successes in n independent Bernoulli trials = [tex]n_{C_{x}}(p)^x(1-p)^{n-x}[/tex]
Total number of watches in the shipment = 50
Number of defective watches = 6
Number of selected watches = 10
Let X denotes the number of defective digital watches such that the random variable X follows a binomial distribution with parameters n and p.
So,
Probability of defective watches = [tex]\frac{X}{n}=\frac{6}{50}=0.12[/tex]
Take n = 10 and p = 0.12
Probability that the shipment will be rejected = [tex]P(X\geq 1)=1-P(X=0)[/tex]
[tex]=1-n_{C_{x}}(p)^x(1-p)^{n-x}\\=1-10_{C_{0}}(0.12)^0(1-0.12)^{10-0}[/tex]
Use [tex]n_{C_{x}}=\frac{n!}{x!(n-x)!}[/tex]
So,
Probability that the shipment will be rejected = [tex]=1-\left ( \frac{10!}{0!(10-0)!} \right )(0.88)^{10}[/tex]
[tex]=1-(0.88)^{10}\\=1-0.2785\\=0.7125[/tex]
Which of the following is the slope of the line that passes through the points (-3,5) and (-3,-2)
Answer:
undefined.
Step-by-step explanation:
-2-5/-3-(-3)
-7/0
Undefined
The probability of obtaining a defective 10-year old widget is 66.6%. For our purposes, the random variable will be the number of items that must be tested before finding the first defective 10-year old widget. Thus, this procedure yields a geometric distribution. Use some form of technology like Excel or StatDisk to find the probability distribution. (Report answers accurate to 4 decimal places.) k P(X = k) 1 .666 Correct 2 3 4 5 6 or greater
Answer:
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
Step-by-step explanation:
The probability of obtaining a defective 10-year old widget is 66.6%
p = 66.6% = 0.666
The probability of obtaining a non-defective 10-year old widget is
q = 1 - 0.666 = 0.334
The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.
The geometric distribution is given by
[tex]$P(X = k) = p \times q^{k - 1}$[/tex]
Solving manually:
For k = 1:
[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]
For k = 2:
[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]
For k = 3:
[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]
For k = 4:
[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]
For k = 5:
[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]
For k = 6:
[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]
Using Excel function:
NEGBINOMDIST(number_f, number_s, probability_s)
Where
number_f = k - 1 failures
number_s = no. of successes
probability_s = the probability of success
For the geometric distribution, let number_s = 1
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
As you can notice solving manually and using Excel yields the same results.
Identify the domain of a radical function with an odd index.
Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.
Can someone please help me I’m stuck I don’t know
Answer:
140
Step-by-step explanation:
Because the lines are parallel:
[tex]\dfrac{DE}{35}=\dfrac{60}{15} \\\\DE=4\cdot 35=140[/tex]
Hope this helps!
Please help! Correct answer only, please! Consider the matrix shown below: Using your calculator find the inverse of the matrix Q (i.e. Find Q^-1).
Answer: C
Step-by-step explanation:
In order to find the inverse, transpose the matrix then find the determinant of each 2 x 2 matrix within it.
[tex]Q=\left[\begin{array}{ccc}2&2&3\\1&1&1\\3&2&1\end{array}\right] \qquad \rightarrow \qquad Q^T=\left[\begin{array}{ccc}2&1&3\\2&1&2\\3&1&1\end{array}\right][/tex]
[tex]det\left[\begin{array}{cc}1&2\\1&1\end{array}\right] =\bold{-1}\qquad det\left[\begin{array}{cc}2&2\\3&1\end{array}\right]=\bold{-4}\qquad det\left[\begin{array}{cc}2&1\\3&1\end{array}\right] =\bold{-1}\\\\\\\\det\left[\begin{array}{cc}1&3\\1&1\end{array}\right] =\bold{-2}\qquad det\left[\begin{array}{cc}2&3\\3&1\end{array}\right]=\bold{-7}\qquad det\left[\begin{array}{cc}2&1\\3&1\end{array}\right] =\bold{-1}\\[/tex]
[tex]det\left[\begin{array}{cc}1&3\\1&2 \end{array}\right] =\bold{-1}\qquad det\left[\begin{array}{cc}2&3\\2&2\end{array}\right]=\bold{-2}\qquad det\left[\begin{array}{cc}2&1\\2&1\end{array}\right] =\bold{0}[/tex]
[tex]Q^{-1}=\large\left[\begin{array}{ccc}1&-4&1\\-2&7&-1\\-1&-2&0\end{array}\right][/tex]
Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?
Answer:
[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]
[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
2. The width of a rectangle is 12 inches less than its length. The perimeter of the rect-
angle is 56 inches. Find the length and width of the rectangle.
Answer:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
Step-by-step explanation:
For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2018, but statisticians might be more interested in the processes behind exit polling and the rellabllity of thelr results.
When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents.
Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a random telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed
(a) What type of sampling methods are used in selecting people for exit polls?
a. Simple Random Sampling
b. Cluster Sampling
c. Stratified Sampling
d. Convenience Sampling
e. Systematic Sampling
(b) Why do the polllng companles randomly select the preclncts to vislt?
a. Randomly selecting precincts to assign pollsters ensures that the companies can conclude a cause and effect relationship between the voters' beliefs and their voting pattern
b. There are too many precincts to manually select, so they are forced to randomly select them
c. Randomly selecting precincts increases the likelihood that the people polled represent the population well.
Answer:
A) cluster sampling ( b ) and systematic sampling ( e )
B ) Randomly selecting precincts increases the likelihood that the people polled represent the population well. ( c )
Step-by-step explanation:
Cluster sampling is a type of sampling plan used when there is an internally heterogeneous groups can be found inside a population that is supposed to be mutually homogeneous . while systematic sampling is a type of probability sampling that involves the selection of samples from a larger population at random but using a specific interval. to get the systematic sample the larger population is divided by the sample size.
from the information available in the report it is very evident that not all voters can be captured at once hence cluster sampling and systematic sampling would be employed .
B) the company will randomly select precinct to increase the likelihood of the sample size representing the entire population very well
Convert decimal +61 and +27 to binary using the signed 2’s complement representation and enough digits to accommodate the numbers. Then perform the binary equivalent of (27) + (-61), (-27) + (+61), and (-27) + (-61). Convert then answers back to decimal and verify that they are correct.
Answer:
the sum is 01011000₂ = 88
Step-by-step explanation:
For numbers of magnitude less than 128, it is convenient to use an 8-bit representation. I find it works will to convert back and forth through the octal (base-8) representation, as each base-8 digit converts nicely to three (3) base-2 bits.
61 = 8·7 +5 = 075₈ = 00 111 101₂
27 = 8·3 +3 = 033₈ = 00 011 011₂
Then ...
[tex]\begin{array}{cc|ccc}&61&&00111101\\+&27&+&00011011\\ &\overline{88}&&\overline{01011000}\end{array}[/tex]
__
Starting from the right, we can convert the binary back to octal, then to decimal by considering 3 bits at a time:
01 011 000₂ = 130₈ = 1·8² +3·8 +0 = 64 +24 = 88
The binary sum is the same as the decimal sum.
Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
[tex]x=35^\circ[/tex]
Step-by-step explanation:
From the diagram which I have drawn and attached below:
[tex]56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ[/tex]
Next, in the triangle, the sum of the three interior angles:
[tex]y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ[/tex]
The value of angle x is 35 degrees.
If the general term of a sequence is 4, then the sequence is
A)4,4,4,4,
B)4,16,64.216
C)4, 8, 12, 16,
Answer:
Correct answer is A) 4,4,4,4
Simon makes 30 cakes he gives 1/5 of the cakes to sali he gives 10 percent of the 30 cakes to jane what fraction of the 30 cakes does he have left
Answer:
7/10 or 70% left
Step-by-step explanation:
total cakes= 30
Gave to Sali
30*1/5= 6 cakesGave to Jane
30*1/10= 3 cakesCakes left:
30- (6-3)=21Cakes left fraction:
21/30= 7/10 or 70 %Answer:
7/10
Step-by-step explanation:
Cakes Simon gave to Sali = 30*1/5
= 6
Cakes Simon Gave to Jane = 30 * 1/10
= 3
Cakes left = 30 - (6-3)
= 21
21 cakes were left, so in terms of a fraction, it'd be 21/30, which can be reduced to 7/10
Hope this helps!
A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 108 inches. Suppose you want to mail a box with square sides so that its dimensions are h by h by w and its girth is 2 h plus 2 w. What dimensions will give the box its largest volume?
Answer:
18×18×36
Step-by-step explanation:
According to the Question
108≥ 4h + w
Volume V is given by
V = wh^2
⇒V= (108-4h)h^2
⇒V= 108h^2 - 4h^3
Now differentiating and keeping = 0 we get
V' = 216h - 12h^2 = 0
h = 216/12 = 18
w = 108 - 4×18 = 36
V = 36×18^2 = 11664 from a box of 18×18×36.
please hurry I’ll make brainiest
The number of people at a concert can be modeled by the following
equation where p is the number of people and t is the time passed in
minutes.
P = 30(1.10) + 20
Based on the model, which of the following statements is true?
Answer:
There were 30 people attending at the start of the concert
Step-by-step explanation:
The coefficient of the value raised to an exponent in these types of functions is always the "starting" value. In your case, '30' is the coefficient, so it is the starting value. FYI: 1.10 is the rate at which the people increase, t is time passed, 20 is a constant, and P is the total number of people after the time goes by.
Answer:
There were 30 people attending at the start of the concert.
Step-by-step explanation:
30 is the coefficient, so that's your starting point, basically.
A quick quiz consists of a multiple-choice question with 5 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Report the answer as a percent rounded to two decimal place accuracy. You need not enter the "%" symbol. Probability = %
Answer:
Probability = 4%
Step-by-step explanation:
For each answer, there are only two possible outcomes. Either it is correct, or it is not. The probability of an answer being correct is independent of other answers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has 5 possible answer:
The person guesses, so [tex]p = \frac{1}{5} = 0.2[/tex]
2 questions:
This means that [tex]n = 2[/tex]
Find the probability that both responses are correct.
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.2)^{2}.(0.8)^{0} = 0.04[/tex]
As a percent:
Probability = 4%
Jeanie wrote the correct first step to divide 8z2 + 4z – 5 by 2z.
Which shows the next step?
A.4z + 2 –
B.4z2 + 2 –
C.4z2 + 2 –
D.4z + 2 –
Answer:
4z + 2 - 5/2z
Step-by-step explanation:
8z^2 + 4z -5
divided by 2z
8z^2 /2z = 4z
4z/2z =2
5/2z = 5/2z
Putting them back together
4z + 2 - 5/2z
Answer:
A 4z + 2 - 5/2z
Step-by-step explanation:
Please answer number 3 I will give brainliest thank you!
Answer:
Skewed to right
Step-by-step explanation:
there is no explanation, it just is, just like how 1+1 is 2
Brainleist! as you promised!
Answer:
Yeah no skewed right, like the guy said.
Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.
How much is in her account at the end of one year?
Answer:
$ 1,060.00
Step-by-step explanation:
A = $ 1,060.00
A = P + I where
P (principal) = $ 1,000.00
I (interest) = $ 60.00
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Can anybody help me with this one?
Answer:
12 cm
Step-by-step explanation:
The rule regarding secants and/or tangents is that the product of distances from their common point to the two intersection points with the circle is the same.
For the tangent the "two" intersection points with the circle are the same point, so ...
product of tangent lengths = product of secant lengths
(8 cm)(8 cm) = (4 cm)(4 cm +x)
Dividing by 4 cm gives ...
16 cm = 4 cm + x
12 cm = x
A line intersects the point (-11, 4) and has
a slope of -2. What are the inputs to the
point-slope formula?
y - [?] = [ ](x-[])
Answer: Point slope form is y-y1=m(x-x1)
Step-by-step explanation:
Here y1=4
x1=-11
m i.e slope=-2
And there you go.
. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answer:
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 1/2 = 0.5
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.5 = 0.5
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.5)^8 × (0.5)^2
P(X) = 0.0039 x 0.25
P(X) = 0.00098 = 0.098%
Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?
Answer:
The best estimate of the mean of the population is 50,000 miles, which is the sample mean.
To make a better inference, we know that the 95% confidence interval for the mean is (49,306; 50,694).
Step-by-step explanation:
The unbiased point estimation for the population mean tread life is the sample mean (50,000 miles), as it is the only information we have.
Although, knowing the standard deviation, we can calculate a confidence interval to make a stronger inference.
We calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=50000.
The sample size is N=100.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3500}{\sqrt{100}}=\dfrac{3500}{10}=350[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=100-1=99[/tex]
The t-value for a 95% confidence interval and 99 degrees of freedom is t=1.98.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.98 \cdot 350=694.48[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 50000-694.48=49306\\\\UL=M+t \cdot s_M = 50000+694.48=50694[/tex]
The 95% confidence interval for the mean is (49306, 50694).
Please help me with this question!!!
Answer:
θ = ±2π/3 +2kπ . . . . . for any integer k
Step-by-step explanation:
2·cos(θ) +1 = 0
cos(θ) = -1/2 . . . . . subtract 1, divide by 2
The cosine function has the value -1/2 for θ = ±2π/3 and any integer multiple of 2π added to that.
θ = ±2π/3 +2kπ . . . . . for any integer k
Lucas and Erick are factoring the polynomial 12x3 – 6x2 + 8x – 4. Lucas groups the polynomial (12x3 + 8x) + (–6x2 – 4) to factor. Erick groups the polynomial (12x3 – 6x2) + (8x – 4) to factor. Who correctly grouped the terms to factor? Explain.
Answer:
Lucas groups the polynomial (12x^3 + 8x) + (–6x^2 – 4) to factor → 2 (2 x - 1) (3 x^2 + 2)
Step-by-step explanation:
Factor the following:
12 x^3 - 6 x^2 + 8 x - 4
Hint: | Factor out the greatest common divisor of the coefficients of 12 x^3 - 6 x^2 + 8 x - 4.
Factor 2 out of 12 x^3 - 6 x^2 + 8 x - 4:
2 (6 x^3 - 3 x^2 + 4 x - 2)
Hint: | Factor pairs of terms in 6 x^3 - 3 x^2 + 4 x - 2 by grouping.
Factor terms by grouping. 6 x^3 - 3 x^2 + 4 x - 2 = (6 x^3 - 3 x^2) + (4 x - 2) = 3 x^2 (2 x - 1) + 2 (2 x - 1):
2 3 x^2 (2 x - 1) + 2 (2 x - 1)
Hint: | Factor common terms from 3 x^2 (2 x - 1) + 2 (2 x - 1).
Factor 2 x - 1 from 3 x^2 (2 x - 1) + 2 (2 x - 1):
Answer: 2 (2 x - 1) (3 x^2 + 2)
Answer:
Both students are correct because polynomials can be grouped in different ways to factor. Both ways result in a common binomial factor between the groups. Using the distributive property , this common binomial term can be factored out. Each grouping results in the same two binomial factors.
Step-by-step explanation:
this is the sample response provided by edge
George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 9 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 14 seconds.
After running for 4 minutes, how far east of his starting point is George?
Answer:
George is 43.20 ft East of his starting point.
Step-by-step explanation:
Let Paula's speed be x ft/s
George's speed = 9 ft/s
Note that speed = (distance)/(time)
Distance = (speed) × (time)
George takes 50 s to run a lap of the track at a speed of y ft/s
Meaning that the length of the circular track = y × 50 = 50y ft
George and Paula meet 14 seconds after the start of the run.
Distance covered by George in 14 seconds = 9 × 14 = 126 ft
Distance covered by Paula in 14 seconds = y × 14 = 14y ft
But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track
That is,
126 + 14y = 50y
50y - 14y = 126
36y = 126
y = (126/36) = 3.5 ft/s.
Hence, Paula's speed = 3.5 ft/s
Length of the circular track = 50y = 50 × 3.5 = 175 ft
So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of
9 × 240 = 2160 ft.
2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.
Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft
So, 60 ft along a circular track subtends an angle θ at the centre of the circle.
Length of an arc = (θ/360°) × 2πr
2πr = total length of the circular track = 175
r = (175/2π) = 27.85 ft
Length of an arc = (θ/360) × 2πr
60 = (θ/360°) × 175
(θ/360°) = (60/175) = 0.343
θ = 0.343 × 360° = 123.45°
The image of this incomplete lap is shown in the attached image,
The distance of George from his starting point along the centre of the circular track = (r + a)
But, a can be obtained using trigonometric relations.
Cos 56.55° = (a/r) = (a/27.85)
a = 27.85 cos 56.55° = 15.35 ft
r + a = 27.85 + 15.35 = 43.20 ft.
Hence, George is 43.20 ft East of his starting point.
Hope this Helps!!!
HURRY! WILL GIVE BRAINLIEST! HURRY
[tex]answer \\ = - 0.5 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
Step-by-step explanation:
Insurance Underwriters have established that the probability of city experiencing disasters in the next five years is 0.3 for a Tornado, 0.4 for Hurricane, and 0.1 for both Tornado and Hurricane. A) What is the probability of city experiencing only a Tornado in the next five years?B) What is the probability of city experiencing neither a Tornado nor Hurricane in the next five years?
Answer:
a. 20%
b. 40%
Step-by-step explanation:
We have the following from the statement:
P (T) = 0.3
P (H) = 0.4
P (T n H) = 0.1
Thus:
a. Tornado-only probability would be the probability of a tornado minus the probability of both tornado and hucaran
P (only T) = P (T) - P (T n H)
replacing:
P (only T) = 0.3 - 0.1
P (only T) = 0.2
In other words, the probability that only one tornado will occur is 20%
b. The probability that there is neither of the two would be the complement of the union between both events, that is:
P (T U H) '= 1 - P (T U H)
and the union is equal to:
P (T U H) = P (T) + P (H) - P (T n H)
replacing:
P (T U H) = 0.3 + 0.4 - 0.1
P (T U H) = 0.6
now if replacing in P (T U H) ':
P (T U H) '= 1 - 0.6
P (T U H) '= 0.4
That is to say that the probability that neither of the two happens is 40%
The line y = kx + 4, where k is a constant, is
graphed in the xy-plane. If the line contains the
point (c,d), where c ≠ 0 and d ≠ 0, what is the slope
of the line in terms of c and d ?
Answer:
(d - 4) / c
Step-by-step explanation:
The slope of the line in terms of c and d is (d - 4) / c.
Here, we have,
To find the slope of the line in terms of the coordinates of the point (c, d), we can use the slope-intercept form of a line, y = mx + b, where m represents the slope.
In the given equation, y = kx + 4, we can see that the coefficient of x is k, which represents the slope of the line.
Since the line contains the point (c, d), we can substitute these values into the equation:
d = kc + 4
To isolate the slope term, we rearrange the equation:
d - 4 = kc
Now, divide both sides by c:
(d - 4) / c = k
Therefore, the slope of the line in terms of c and d is (d - 4) / c.
To learn more on slope click:
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what is the solution for this equation [3y+7]=13
Answer:2
Step-by-step explanation:
3y+ 7= 13
3y= 13 - 7
3y= 6
Y = 6/3
Y= 2
Z=1.23 z=0.86 WHAT is the area of the shaded region between the two
Answer:
The area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.
Step-by-step explanation:
To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.
We need to having into account that a z-score is given by the following formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
Where
x is a raw score from the distribution that we want to standardize using [1].[tex] \\ \mu[/tex] is the mean of the normal distribution.[tex] \\ \sigma[/tex] is the standard deviation of the normal distribution.A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above [tex] \\ \mu[/tex], and conversely, a negative that x is below [tex] \\ \mu[/tex].
The standard normal distribution is a normal distribution with [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex], and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).
Using the cumulative standard normal table, for [tex] \\ z = 1.23[/tex], the corresponding cumulative probability is:
[tex] \\ P(z<1.23) = 0.89065[/tex]
The steps are as follows:
Consult the cumulative standard table using z = 1.2 as an entry. Z-scores are in the first column of the mentioned table. In the first row of it we have +0.00, +0.01, +0.02 and, finally, +0.03. The probability is the point that result from the intersection of z = 1.2 and +0.03 in the table, which is [tex] \\ P(z<1.23) = 0.89065[/tex].Following the same procedure, the cumulative probability for [tex] \\ z = 0.86[/tex] is:
[tex] \\ P(z<0.86) = 0.80511[/tex]
Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):
[tex] \\ P(0.86 < z < 1.23) = 0.89065 - 0.80511[/tex]
[tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex]
Therefore, the area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.
We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, [tex] \\ N(0, 1)[/tex], and [tex] \\ z = 0.86[/tex] and [tex] \\ z = 1.23[/tex].
