Answer:
Step-by-step explanation:
Given that :
A web page is accessed at an average of 20 times an hour.
Therefore:
a. he rate parameter λ of the distribution of the time until the first hit = 20
b. What is the expected time between hits?
Let consider E(Y) to be the expected time between the hits; Then :
E(Y) = 1/λ
E(Y) = 1/20
E(Y) = 0.05 hours
E(Y) = 3 minutes
(c.) What is the probability that there will be less than 5 hits in the first hour?
Let consider X which follows Poisson Distribution; Then,
P(X<5) [tex]\sim[/tex] G(∝=5, λ = 20)
For 5 hits ; the expected time will be :
Let 5 hits be X
E(X) = ∝/λ
E(X) = 5/20
E(X) =1/4
E(X) = 0.25 hour
E(X) = 15 minutes
From above ; we will see that it took 15 minutes to get 5 hits; then
[tex]P(\tau \geq 0.25) = \int\limits^{\alpha}_{0.25} \dfrac{\lambda^{\alpha}}{\ulcorner^{\alpha}} t^{a\pha-1} \ e^{-\lambda t} \, dt[/tex]
[tex]P(\tau \geq 0.25) = \int\limits^{5}_{0.25} \dfrac{20^{5}}{\ulcorner^{5}} t^{5-1} \ e^{-20 t} \, dt[/tex]
[tex]\mathbf{P(\tau \geq 0.25) =0.4405}[/tex]
Probability equation need help again. worded problem-the table below displays the number of siblings for students. at one school. Find the probability that a randomly selected students has 2 siblings.
The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 3.5 to 4.75 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 4.4 millimeters?
Answer:
The probability is 0.28
Step-by-step explanation:
Here, we want to calculate the probability that the ball bearing randomly selected has a diameter greater then 4.4 mm
I.e P(X> 4.4)
P(X>4.4) = (4.75-4.4)/(4.75-3.5) = 0.35/1.25 = 0.28
What is m Please help me
Answer:
Angle BCA = 70
Angle CAB = 20
Step-by-step explanation:
Not sure what angle you meant, so I'll give you all of them <3
Angle BCA = 70 degrees, because If two angles form a line, they add up to 180. (110+x=180, x = 70)
Angle CAB = 20 degrees, because there are 180 degrees in a triangle, so 90+70+x=180, x = 20
Hope it helps <3
Answer:
BCA = 70
CAB = 20
ABC=90
Step-by-step explanation:
ABC is 120 because the square indicates that
BCA = 70 because angles on a straight line add up to 180.
110+x=180
x=180-110
=70
Angle CAB = 20 degrees, because angles in a triangle add up to 180
90+70+x=180
x = 180-(90+70)
=180-160
=20
Please mark as brainliest
Find the distance between the points (–9, 0) and (2, 5). Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance, we use the following formula
d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( -9-2) ^2 + ( 0-5) ^2)
sqrt( ( -11) ^2 + ( -5) ^2)
sqrt( 121+25)
sqrt( 146)
Graph a line that contains the point (-7,-4)and has a slope of - 2/3
Hi there! :)
Answer:
Given the information, we can write an equation in slope-intercept form
(y = mx + b) to graph the line:
Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the
x-coordinate given for 'x':
-4 = -2/3(-7) + b
-4 = 14/3 + b
Solve for b:
-12/3 = 14/3 + b
-12/3 - 14/3 = b
-26/3 = b
Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)
Some points on the line include:
(-7, -4)
(-4, -6)
(0, -26/3)
(2, -10)
(5, -12)
i will give brainliest and 50 points pls help ASAP
Answer:
answer is 2.3 hope you get the answer
Change -4Y - 3X = -8 to the slope-intercept form of the equation of a line.
Answer:
y=-3/4x+2
Step-by-step explanation:
Add +3x both sides.
Divide each side by -4
-8/-4=2
Slope = -3/4
Y-intercept= 2
Math question, need help
In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.
Answer:
[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]
First answer is correct.
Step-by-step explanation:
we know that,
[tex] {x}^{a} = {x}^{b} [/tex]
[tex]a = b[/tex]
So, according to that,
[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]
Therefore,
[tex]2x - 1 = 5x - 14[/tex]
CAN ANYONE HELP ME PLEASE? Two numbers total of 52 and have a difference of 30. Find the two numbers. The larger number is ? and the smaller number is ?
Answer:
41 and 11.
Step-by-step explanation:
Let's say the 2 numbers are x and y.
Since they add up to 52, x + y = 52.
Seeing as the difference is 30, x - y = 30 assuming x is the larger number.
We have left:
x + y = 52
x - y = 30
By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82
Therefore x = 41.
Since x + y = 52
41 + y = 52
Therefore y = 11
Therefore we have: the larger number is 41 and the smaller number is 11.
Translate into an algebraic expression and simplify if possible. The value of a number whose units digit is x and whose tens digit is three more than the units digit.
Answer: 11x + 30
Step-by-step explanation: Algebraic expression is a way of use letters to express relationships between algarisms.
For this question:
Units digit = x
Tens digit = 10(x + 3)
The number in question is:
10(x + 3) + x
10x + 30 + x
To simplify, add, subtract, multipy or divide similar terms:
As x is of the first order:
10x + x + 30
11x + 30
The simplified algebraic expression is 11x + 30
Stella bought a dinette set on sale for $725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount?
Answer:
40%
Step-by-step explanation:
1299-725= 574
574/1299 x 100 = 44.19%
The rate of discount on the dinette set = 44.2%.
What is a discount?Often, goods are sold at a price that is lower than their marked price. The price at which the good is sold is called the selling price and the difference between the marked price and the selling price is the discount.
Discount = Marked Price - Selling Price.
Rate of Discount = Discount/Marked Price * 100%.
How to solve the given question?In the question, we are given that Stella bought a dinette set on sale for $725. The original price was $1,299.
We are asked to calculate the rate of discount on the dinette set.
The marked price of the dinette set = $1299.
The selling price of the dinette set = $725.
∴ The discount on the dinette set = the marked price of the dinette set - the selling price of the dinette set = $1299 - $725 = $574
∴ The rate of discount on the dinette set = the discount on the dinette set/the marked price of the dinette set *100%
or, The rate of discount on the dinette set = 574/1299 * 100%
or, The rate of discount on the dinette set = 0.4418 * 100%
or, The rate of discount on the dinette set = 44.18% ≈ 44.2% (to the nearest tenth of a percent)
∴ The rate of discount on the dinette set = 44.2%.
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Find the domain for the rational function f of x equals quantity x end quantity divided by quantity x minus 5 end quantity.
Answer:
All real numbers except for 5.
Step-by-step explanation:
[tex]f(x)=\frac{x}{x-5}[/tex]
The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.
Thus, we need to find the zero(s) of the denominator to determine the domain.
[tex]x-5=0[/tex]
[tex]x=5[/tex]
Therefore, the domain of the rational function is all real numbers except for 5.
In set builder notation, this is:
[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]
Select the correct answer. Consider matrices A, B, and C:
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
Find the measure of angle angle AGE in the figure below. Enter only the number.
Help please!
Answer:
AGE = 129 degrees
Step-by-step explanation:
Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.
Thus, the measure of the angles can be rewritten as,
∠AGC + ∠AGE = 180°
51° + ∠AGE = 180°
∠AGE = 180° - 51°
∠AGE = 129°
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To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called:____________
Answer:
Convenience sampling.
Step-by-step explanation:
To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called convenience sampling.
Convenience sampling can be defined as a sampling method which involves the researcher selecting or collecting data that is easily available or choosing the individuals who are easiest to reach in a population. It is a type of non-probability method of sampling where the first or easiest available data source is being used by the researcher without other requirements.
In this scenario, to gather information on customer satisfaction, the researcher went to the store most likely situated in a shopping mall to collect data from six (6) customers in each stores.
Some of the advantages of convenience sampling are low cost, data are collected quickly, lesser rules etc.
limit xtens to 0 x^2logx^2 what is the ans of interminate forms?
Rewrite the limit as
[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]
Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get
[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]
The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $150 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 17 tons of sugar.
Answer:
C = $6050
Equation:
To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:
[tex]3500+150(S)=C[/tex]
3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.
Solving the equation
To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.
[tex]3500+150(17)=C[/tex]
150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.
Our answer is: C = $6050
a student showed the steps below while solving the equation 14=log5(2x-3) by graphing. which step did the student make the 1sr error
Answer:
[tex]x= \frac{5^{14}+3}{2}[/tex]
Step-by-step explanation:
The correct steps to solve the equation are:
[tex]14=log_5(2x-5)[/tex]
[tex]5^{14}=5^{log_5(2x-3)}[/tex]
Because [tex]a^{log_am}=m[/tex]
So, solving we get:
[tex]5^{14}=2x-3[/tex]
Sum 3 on every side:
[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]
Dividing by 2 into both sides:
[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]
So, the answer is [tex]x= \frac{5^{14}+3}{2}[/tex]
Answer: Step 2
Step-by-step explanation:
This is correct according to Edge 2021
In the search to determine if car 1 is slower to accelerate than car 2, the mean time it takes to accelerate to 30 miles per hour is recorded (Note: a car is slower to accelerate if it takes more time to accelerate). Twenty trials of the acceleration time for each car are recorded, and both populations have normal distributions with known standard deviations. What are the hypotheses used in this test
Answer:
Step-by-step explanation:
The happiest used in a test in statistics are the null and the alternative hypothesis. The null hypothesis is usually the default statement while the alternative hypothesis is thevopposite of the null hypothesis.
In this case study, the null hypothesis is u1 = u2: the average mean time it takes to accelerate to 30 miles per hour for car 1 is the same as that for car 2.
The alternative hypothesis is u1 > u2: the mean time it takes to accelerate to 30 miles per hour is greater than that for car 2 thus car 1 is slower to accelerate as it takes more time.
If the average American sleeps 8 hours a night, with a standard deviation of 1 hour, and I plan on gathering a sample of 12 college students to compare to this population, find the following:
mu =
sigma =
mu_x bar =
sigma_x bar =
Answer:
8 hours
1 hour
8 hours
0.288675
Step-by-step explanation:
We complete the answer as follows;
mu = mean = 8 hours
sigma = standard deviation= 1 hour
Mu_x bar = mu = 8 hours
sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675
A train travels 45 feet in 1/10 if a second. How far will it travel in 3.5 seconds
Answer:
1575 ft
Step-by-step explanation:
Convert 1/10 to decimal to make the math simpler.
1/10 = 0.1
Divide 3.5 by 0.1.
3.5/0.1 = 35
Multiply 35 by 45.
35 × 45 = 1575
The train will travel 1575 feet in 3.5 seconds.
The distance covered by the train in 3.5 seconds will be 1575 feet.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
A train travels 45 feet in 1/10 in a second.
Then the speed will be
Speed = 45 / (1/10)
Speed = 45 x 10
Speed = 450 feet per second
The distance covered by the train in 3.5 seconds will be
Distance = 450 x 3.5
Distance = 1575 feet
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There are 45 balloons: 15 are blue; 20 are green; 10 are red. 3 balloons are selected for the float. Leaving your answers in combinatorics format, how many ways can all 3 be selected such that they are the same color.
Answer: Required number of ways = 1715
Step-by-step explanation:
Given, there are 45 balloons: 15 are blue; 20 are green; 10 are red.
3 balloons are selected for the float.
Number of combinations to select r things out of n things : [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
So, the number of ways to select 3 ballons such that they are the same color = (Ways to select all blue ) x (Ways to select all green ) x (Ways to select all red)
[tex]^{15}C_3+^{20}C_3+^{10}C_3\\\\=\dfrac{15!}{12!\times3!}+\dfrac{20!}{17!\times3!}+\dfrac{10!}{7!\times3!}\\\\=\dfrac{15\times14\times13}{6}+\dfrac{20\times19\times18}{6}+\dfrac{10\times9\times8}{6}\\\\=455+1140+120\\\\=1715[/tex]
Hence, Required number of ways = 1715
Find the number of four-digit numbers which are not divisible by 4?
Answer: without trying each calculation individually, 6750 4-digit numbers are not divisible by 4
Step-by-step explanation: From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.
Eliminate all the odd numbers 9000/2 = 4500
Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250
9000 - 2250 = 6750.
subtract 2-3/4-1 1/10=
Answer:
23/20
Step by step Explanation
Answer:
3/20Step-by-step explanation:
[tex]2-\frac{3}{4}-1\frac{1}{10}=x\\x=2-\frac{3}{4}-\frac{11}{10}\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\x=\frac{2}{1}-\frac{3}{4}-\frac{11}{10}\\1,\:4,\:10\\\mathrm{Prime\:factorization\:of\:} ;\\1=1\\4=2\times \:2\\10=2\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:2\times \:2\times \:5=20\\Adjust\: fractions\: based\: on\: their\: LCM ;\\\frac{2}{1}=\frac{2\times \:20}{1\times \:20}=\frac{40}{20}\\\\\frac{3}{4}=\frac{3\times \:5}{4\times \:5}=\frac{15}{20}\\[/tex]
[tex]\frac{11}{10}=\frac{11\times \:2}{10\times \:2}=\frac{22}{20}\\\mathrm{Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\\mathrm{Subtract\:the\:numbers:}\:40-15-22=3\\\\x=\frac{3}{20}[/tex]
need help thanksssss
Before we can find any of the three items mentioned, we need the height. The diameter is 10, so the radius is 5. A right triangle with hypotenuse 13 and leg 5 forms. The height is h. Use the pythaogrean theorem to solve for h
5^2+h^2 = 13^2
25+h^2 = 169
h^2 = 169-25
h^2 = 144
h = sqrt(144)
h = 12
The height is 12. We now have enough info to find the volume, the lateral area and surface area.
-------------------------------------------------------------------
Volume
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*5^2*12
V = 314 cubic cm
-------------------------------------------------------------------
Lateral Area
LA = pi*r*L
LA = 3.14*5*13
LA = 204.1 square cm
-------------------------------------------------------------------
Surface Area
SA = 2*pi*r + pi*r*L .... note how we add on the lateral area to the bottom circular area
SA = 2*3.14*5 + 3.14*5*13
SA = 235.5 square cm
Find the value of a A.130 B.86 C.58 D.65
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.18.
1. Which of the following is a type I error?
a. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
b. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
c. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
d. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
2. Which is the following is a type II error?
a. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
b. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
c. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
d. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Answer:
Type I error: Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
Type II error: Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Step-by-step explanation:
We are given the following hypothesis below;
Let p = proportion of people who write with their left hand
Null Hypothesis, [tex]H_0[/tex] : p = 0.18 {means that the proportion of people who write with their left hand is equal to 0.18}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.18 {means that the proportion of people who write with their left hand is different from 0.18}
Type I error states that we would reject the null hypothesis given the fact that the null hypothesis was actually true. Or in other words, the probability of rejecting a true hypothesis.
So, according to our question, Type I error is to Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
Type II error states that we would accept the null hypothesis given the fact that the null hypothesis was actually false. Or in other words, the probability of accepting a false hypothesis.
So, according to our question, Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting or . (b) Compute the probability of randomly selecting or or . (c) Compute the probability of randomly selecting or .
Answer: See answer in the attached file
Step-by-step explanation:
The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows:
Houses Sold (x) Probability P(x)
0 0.24
1 0.01
2 0.12
3 0.16
4 0.01
5 0.14
6 0.11
7 0.21
Find the mean of the given probability distribution.
A. μ = 3.35
B. μ = 3.50
C. μ = 3.60
D. μ = 3.40
Answer:
C. μ = 3.60
Step-by-step explanation:
Two tables have been attached to this response.
One of the tables contains the given data and distribution with two columns: Houses Sold and Probability
The other table contains the analysis of the data with additional columns: Frequency and Fx
=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,
When the number of houses sold = 0
F = P(0) x Total number of houses sold
F = 0.24 x 28 = 6.72
When the number of houses sold = 1
F = P(1) x Total number of houses sold
F = 0.01 x 28 = 0.28
=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,
When the number of houses sold = 0
Fx = F * x
F = 6.72 x 0 = 0
Now to get the mean, μ we use the relation;
μ = ∑Fx / ∑F
Where;
∑Fx = summation of the items in the Fx column = 100.8
∑F = summation of the items in the Frequency column = 28
μ = 100.8 / 28
μ = 3.60
Therefore, the mean of the given probability distribution is 3.60
The mean of the discrete probability distribution is given by:
C. μ = 3.60
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:
[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]
Hence option C is correct.
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Lisa is 34 years old. Two years ago, she was twice as old as her brother. How old is her brother now?
Answer:
18
Step-by-step explanation:
Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.