The probability that headway is within 1 standard deviation of the mean value is 0.890.
What is mean value?
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
The mean of a discrete probability distribution of a random variable X is equal to the sum over all possible values weighted by the likelihood of each value. To calculate the mean, one must multiply each potential value of X by its probability P(x), then add all of these products.
Given mean value is P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995).
The cdf for the distribution is
[tex]F(x)=\left \{ {{1 -\frac{1}{x^6} ,x > 1} \atop {0,x\le 1}} \right.[/tex]
Now calculate the value of F(1.445) and F(0.995).
F(1.445) = 1 - (1/(1.445)⁶)
F(0.995) = 0
Now putting the value of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995):
P( 0.995 ≤ x ≤ 1.445)
=1 - (1/(1.445)⁶) - 0
=0.890
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f(1) = 12 +10 |1| me pueden ayudar porfavor
Answer:
Your answer is 22.
Tu respuesta es 22. Además, no hablo español, usé Translate
an important problem in industry is shipment damage. a windshield factory ships its product by truck and determines that it cannot meet its profit expectations if, on average, the number of damaged items per truckload is greater than 12. a random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 9.4 with a calculated sample of variance of 0.64. select a 99% confidence interval for the true mean of damaged items.
99% confidence interval would be (10.78,11.82) for the true mean of the damaged items.
What is meant by Variance?Variability is measured by the variance. It is determined by averaging the squared deviations from the mean.
The degree of dispersion in your random sample collection is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.
You may determine the average distance between each number and the mean using the standard deviation, which is obtained from variance. It is the variance's square root.
Both metrics capture distributional variability, although they use different measurement units:
Standard deviation is represented in the same units as the initial values (e.g., meters).
Larger units are used to express variation.
How to solve?
n = 12
Average = 11.3
Variance = 0.49
Standard deviation = √0.49=0.7
so, we need to find 99% confidence interval.
At 99% confidence , z = 2.58
So, interval would be
x±z* σ/√n = 11.3 ±2.58* 0.7/√12
=11.3±0.521
=(11.3 - 0.521,11.3 +0.521
= (10.78, 11.82)
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An ant travels at a constant rate of 30 cm every 2 minutes. at what pace does the ant travel per centimeter?
The ant travels at a pace of 1/15 mins per centimeters.
What is Pace?
Meaning of pace is rate of movement.
Pace is the inverse of speed.
If speed is measured in units of distance per unit of time then pace is measured in units of time per unit of distance.
We know speed is total distance travelled in the total time taken
speed = distance/time
According to the given question:
Ant travels 30cm in every 2 minutes
Distance travelled by ant = 30 cm
Time taken to travel this distance = 2 minutes
Therefore, speed of the ant is
30/2 = 15 cm per min
Now pace = inverse of speed
pace = 1/15 min per cm
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write the equation of the parabola in vertex form
vertex (4,4), point (3,-2)
f(x)=?
Hence, the equation of parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] is
[tex]y=-6(x-4)^2+4[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
The parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] .
Here [tex](x,y)=(3,-2)[/tex] and [tex](x_1,y_1)=(4,4)[/tex]
The general formula is
[tex]y=a(x-x_1)^2+y_1[/tex] ....[tex](1)[/tex]
Substitue the given values in the equation [tex](1)[/tex], we get
When [tex](x_1,y_1)=(4,4)[/tex]
[tex]y=a(x-4)^2+4[/tex]
When [tex](x,y)=(3,-2)[/tex]
[tex]-2=a(3-4)^2+4\\\\-2=a(-1)^2+4\\\\-2=a+4\\\\a+4+2=0\\\\a+6=0\\\\a=-6[/tex]
So, the equation is of thr form
[tex]y=-6(x-4)^2+4[/tex]
Hence, the equation of parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] is
[tex]y=-6(x-4)^2+4[/tex].
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Find the missing value in each row. Use the percent equation. Principal (P) $100 $500 $200 :1 1. Interest Rate (r) 5% 4% 10% Time in Interest years (1) years (1) Earned (1) 3 7 2 $20 $35 $6
The missing values are as shown below:
A.) 15
B.) 1 year
C.) $50
D.) 1.5%
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The percentage equation goes thus:
Interest earned = principal * rate * time
A)
Principal: $100 Interest rate: 5% Time in years: 3 Interest earned
Interest earned = $100 * 0.05 * 3
Interest earned = $15
B.)
Principa;" $500 Interest rate: 4% Time in years: interest earned: $20
Interest earned = principal * rate * time
20 = 500 * 0.04 * time
20 = 20 * time
Time = 20 / 20 = 1
Time = 1 year
C.)
Principal: Interest rate:10% Time in years: 7 Interest earned:$35
Interest earned = principal * rate * time
$35 = principal * 0.1 * 7
$35 = principal * 0.7
Principal = $35 / 0.7
Principal = $50
D.)
Principal: $200 Interest rate: Time in years:2 Interest earned: $6
Interest earned = principal * rate * time
$6 = $200 * rate * 2
$6 = $400 * rate
Rate = $6/$400
Rate = 0.015 = 1.5%
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A new crew of painters takes two times as long to paint a small apartment as an experienced crew. Together, both crews can paint the apartment in 4 hours. How many hours does it take the new crew to paint the apartment?
It takes hours for the new crew to paint the apartment.
It will take the new crew 8 hours to paint the new apartment.
what is inverse proportion?Two quantities are said to be in inverse proportion if an increase in one leads to a decrease in the other quantity and a decrease in one leads to an increase in the other quantity". In other words, if the product of both the quantities, irrespective of a change in their values, is equal to a constant value, then they are said to be in inverse proportion.
if it takes both crews 4 hours to paint the crew and both crew worked at same rate.
Then it will take the new crew 4 x 2 hours to complete the apartment which is 8 hours.
In conclusion, the new crew will complete the apartment in 8 hours
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if the racetrack publishes that the odds in favor of a horse winning a race are 2 to 6, what is probability that the horse will not win the race? a) 0.1667 b) 0.2500 c) 0.7500 d) 0.0833 e) 0.5000 f) none of the above.
The probability that the horse will not win the race is 0.7500.
The mathematical branch known as probability deals with determining the possibility of an event occurring. The conversions between probability and odds are feasible. This is because the odds are determined by dividing the likelihood that an event will occur by the likelihood that it won't.
Here, the odds of a horse winning a race are given as 2 to 6. Then, the probability of winning the horse race is calculated as,
[tex]\begin{aligned}\text{Odds}&=\frac{p}{1-p}\\\frac{2}{6}&=\frac{p}{1-p}\\2(1-p)&=6p\\2-2p&=6p\\2&=6p+2p\\8p&=2\\p&=\frac{2}{8}\\&=\frac{1}{4}\end{aligned}[/tex]
Then, the probability of not winning the horse race is,
[tex]\begin{aligned}q&=1-p\\&=1-\frac{1}{4}\\&=\frac{3}{4}\\&=0.75\end{aligned}[/tex]
The answer is 0.75. Therefore, the correct option is option c.
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A large university, except 70% of the students to apply. All the students at the university acceptance, 30% actually enroll. If 10,000 series apply, how many actually enroll?
The amount that actually enrol is 3000
How to determine the amount that actually enrol?From the question, we have the following parameters that can be used in our computation:
Expected enrolment = 70%
Actual enrolment = 30%
Number of applicants = 10000
This means that
Actual = Actual enrolment * Number of applicants
Substitute the known values in the above equation, so, we have the following representation
Actual = 30% * 10000
Evaluate
Actual = 3000
Hence, the amount is 3000
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26/5 as a mixed number
Answer:
5 1/5
Step-by-step explanation:
you set up the fraction in the division bracket with the denominator staying the same in the final answer. The denominator will go on the inside, and the 5 on the outside.
5 1/5 :)))))))))))))))))))))))))))))))))))))))))))
A child stands on a bathroom scale while riding in an elevator. The child's weight when the elevator is not moving is 100 Ibs. What does the scale read when the elevator accelerates upward while travelling downward?
The scale reads more than 100 pounds of force when the elevator speeds upward while moving downward.
Explain the term gravitational force?The gravitational force, which is what pushes mass-containing objects toward one another. We frequently consider the pull of gravity from the Earth. Your body is kept on the ground by this force.However, all mass-bearing objects are pulled toward one another by gravity.Gravity pulls downward while the lift is not in motion, as shown by the reading on the scale of;
F = m g
F = 100 lbs force.
When the lift begins to rise quickly, the child's normal response force increases by (ma)
Net weight on the scale becomes;
F = m g + m .
Scale will thus display weight that is larger than 100 lbs. force.
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g in a class of 30 children, 20 take latin, 14 take greek, and 10 take hebrew. if no child takes all three languages and eight children take no language, how many children take greek and hebrew?
The number of children take greek and hebrew = 2
In this question, we have been given that in a class of 30 children, 20 take latin, 14 take greek, and 10 take hebrew.
So, n(s) = 30
Let set a: children taking Latin language
n(a) = 20
set b: children taking Greek language
n(b) = 14
set C: children taking Hebrew language
n(c) = 10
no child takes all three languages
⇒ n(a ∩ b ∩ c) = 0
And eight children take no language
⇒ n(S) - n(a ∪ b ∪ c) = 8
So, n(a ∪ b ∪ c) = 8
This means, 22 children taking languages.
Of those 22 kids, 14 take Greek and 10 take Hebrew.
14+10 = 24
This means, at least 2 children must taking Greek and Hebrew.
Since no child takes all three languages, the children taking Greek and Hebrew can't be taking Latin. Since 20 of the 22 kids are taking Latin, that means at most 2 are taking Greek and Hebrew.
Therefore, 2 children take greek and hebrew
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Suppose that R(x) is a polynomial of degree 13 whose coefficients are real numbers.
Also, suppose that R(x) has the following zeros.
2, -4, 3i, -4+i
Answer the following.
(a) Find another zero of R(x).
(b) What is the maximum number of real zeros that R(x) can have?
(c) What is the maximum number of nonreal zeros that R(x) can have?
Answer:
(a) Other zeros: 3i and -4-i
(b) 9
(c) 10
Step-by-step explanation:
Given information:
Polynomial function with real coefficients.Degree: 13Zeros: 2, -4, 3i, -4+iPart (a)For any complex number [tex]z=a+bi[/tex], the complex conjugate of the number is defined as [tex]z^*=a-bi[/tex] .
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if R(x) is a polynomial with real coefficients, and 3i is a root of R(x)=0, then its complex conjugate -3i is also a root of R(x)=0.
Similarly, if -4+i is a root of R(x)=0, then its complex conjugate -4-i is also a root of R(x)=0.
Part (b)The degree of the polynomial is the greatest of the exponents of its various terms.
The degree of R(x) with just the given roots (including the complex conjugates) is 6, which includes 2 real zeros.
As the actual degree of R(x) is 13, the maximum number of real zeros would be 7 more than the given real zeros.
Therefore, the maximum number of real zeros that R(x) can have is 9.
Part (c)For each complex root there is also a complex conjugate root.
We have been given 2 complex zeros and 2 real roots, so when we include the complex conjugates, the degree of R(x) is 6.
The actual degree of R(x) is 13, so the maximum number of non-real zeros is 6 more (as they come in pairs) than the already given 4 non-real zeros. Therefore, the maximum number of non-real zeros that R(x) can have is 10.
7. Gabriela goes to dinner with some
friends and pays the bill. Each person
orders a meal that cost $14.95. Gabriela
gave the server a $11.96 tip. The total bill,
including the tip, was $71.76. How many
friends did Gabriela pay for?
A bus leaves Deltaville at 11:32 it’s a travels at an average speed of 42 km/h if it arrives in eastwich at12:42 what is the distance between the two towns ?
Help pls I have a test after tomorrow
The distance between the two towns is 49 km
What is average speed?
Average speed is calculated by dividing distance by time (eg miles/hour).
The entire distance traveled by the object in a specific amount of time is its average speed. A scalar quantity, average speed, exists. The magnitude serves as its representation, and it lacks direction.
A body's average speed is its mean value over a given amount of time. Since a moving body's speed fluctuates over time and is not constant, an average speed formula is required. The total time and total distance numbers can be used, even with fluctuating speed, and with the aid of the average speed formula, we can get a single value to represent the entire motion.
Difference in times = 12:42 - 11:32 = 1.17 hours
Formula:
Distance = speed * time
= 42 * 1.17
= 49 km
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Suppose you have two bank accounts. In Account A you deposit $200 In Account B you deposit $400. Account A has a simple interest rate of 3.9%. Account B has a simple interest rate of 2.7%. One year later, you get a bank statement from each bank and one of the statements shows an incorrect amount of interest. The interest for Account A is $7.80. The interest for Account B is $1,080. Which account statement is incorrect? Find the bank's likely error.
The account in which there was a mistake in the calculation of the simple interest is account B.
What is the account statement that is incorrect?We know that the interest is an amount of money that is obtained on top of the initial money that was deposited. The initial money that you deposit in the account is called the principal. The rate is the percentage at which the interest is calculated and the time is the period that has elapsed since the deposit was made.
Given that;
I = PRT/100
I = interest
P = principal
R = rate
T = time
For account A
I = 200 * 3.9 * 1/100
I = $7.8
For account B;
I = 400 * 2.7 * 1/100
I = $10.8
We can see that there must have been a calculation error as the interest in account B was being calculated.
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What is the length of the diameter of the base of the cone?
a
56 cm
b
112 cm
c
139 cm
d
278 cm
The length of diameter of the base of the cone will be 112 cm. Hence, option b is correct.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
Use the equation of Pythagoras's theorem,
106² = 90² + r²
r² = 106² - 90²
r = √3136
r = 56 cm.
Then, the diameter will be,
D = 2r
D = 2(56)
D = 112 cm.
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in order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. how large a sample must he select if he wants to be 99% confident that the true average time is within 15 minutes of the sample average? assume the standard deviation of all times is 30 minutes.
The value of n is 25 according to standard deviation in the question.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
s = 30 minutes
C.I. = 99%
mean = 15 minutes
z value for 99% = 2.58
mean = z*s/√n
15 = 2.58 * 30 / √n
√n = 5.06
n = 25
Hence the value of n is 25 .
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Which answers are equivalent to the ratio 13 to 25?
Select all that apply.
13:25
25/13
25:13
13/25
Please help I'm majorly confused!!
The ratio of 13 to 25 is 13/25 because 13 is a prime number
RatioThe ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.
In this question, we have to find the ratio between 13 to 25
To do this, we simply divide 13 by 25
13÷25 = 13/25
This is so because the two numbers are not divisible as 13 is a prime number.
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please help i cant solve this problem
In triangle def, m∠d = (2x 19)°, m∠e = (3x 24)°, and m∠f = 87°. determine the degree measure of the exterior angle to ∠d. 54° 39° 141° 126°
The exterior angle with angle d is equivalent to 141 degrees, and the value of x is equal to 10.
Explain the term exterior angle?Whenever a side of a triangle is extended, an external angle of the triangle is created.We must keep in mind that the total of all the angles in a triangle equals 180 degrees in order to solve this puzzle.
The given angles are-
m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°.Using that formula in this case;
Thus, sum of all angles is 180°.
m < d + m < e + m < f = 180°
(2x + 19)° + (3x + 24)° + 87° = 180°
x = 10°
But if angle D is on a straight line, it is possible to find its exterior angle because angle D plus its exterior angle add up to 180 degrees.
Suppose y = external angle.
m < d + y = 180°
2x + 19 + y = 180°
And x = 10°
2(10) + 19 + y = 180°
y = 141°
Thus, the measure of the degree measure of the exterior angle is found as 141°.
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The correct question is-
In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.
54°
39°
141°
126°
Find the sum of the interior angles of a 22-sided polygon.
Group of answer choices
1,980°
2,160°
3,360°
3,600°
Answer:
3600°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 22 , then
sum = 180° (22 - 2) = 180° × 20 = 3600°
Answer:
3360°
Step-by-step explanation:
180n-360= sum of interior angles
question what is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2.
We can infer that those assertions do not provide us with adequate details on the hundredths in the decimal system.
What do we mean by a decimal?The decimal numeral system is widely used to express both integer and non-integer numbers.
The Hindu-Arabic number system has been expanded to include non-integer values.
The way of representing numbers in the decimal system is known as decimal notation.
(1) Since 2 is the eleventh digit of 100z, we may begin writing 100z.
10z = 100(a.bcd)
The decimal point is moved two places to the right by multiplying by 100, giving us the value of:
10z = 100abc.d
Then we shall have d = 2 if the tenths of 100z equal 2.
We have so far: z = a.bc2
(2) Since 1000z's units digit is 2, we may begin writing 1000z.
1000z = 1000a.bc2
We need to move the decimal point three places to the right so that we have order to multiply by 1000:
1000z = abc2
As a result, we can now confirm that the unit digit is actually 2.
However, the number is as follows: z = a.bc2
Therefore, we can infer that those assertions do not provide us with adequate details on the hundredths in the decimal system.
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Use technology to find points and then graph the line y=2x-1, following the instructions below.
Answer: 1st point : 0,-1 second point : 1,0
Step-by-step explanation: the y intercept is -1. The slope is 2/1 rise over run. Two rise 1 over
(Solving Equations Using Square and Cube Roots LC)
Solve z3 = 8.
The value of z after solving the equation z³ = 8 is 2.
Define cube root.The result of a number (x) being multiplied three times is referred to as the cube of that number. The phrase "cube root" in mathematics means "the number that needs to be multiplied three times in order to acquire the original number." Let's now examine the cube root formula, in which y is equal to the cube root of x. ∛x = y. Any integer can be represented as the cube root by the radical sign ∛, which has a little 3 written on the top left of the sign. Writing 1/3 as a number's exponent is another method to represent a cube root.
The given equation
z³ = 8
The number 8 can be written as
8 = 2 × 2 × 2
= 2³
So,
z³ = 2³
So, comparing both sides, we get
z = 2
This is the solution to the equation.
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Write and solve an equation for the following situation: mia was getting ready to go back to school. She purchased 7 pens and a binder that cost $1. 25. She spent a total of $7. 90. How much did each pen cost?.
Answer: $0.95
Step-by-step explanation:
7.90 - 1.25 = 6.65
6.65 divided by 7 = 0.95
A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys. Since it is true that some boys do better than girls and some girls do better than boys, the researcher must use a two tailed test.
True OR False
The statement of the given hypothesis is False.
What is hypothesis testing?
Hypothesis testing is a statistical analysis that looks at a sample to see if the findings are representative of the population. Depending on the type of data used and the goal of the research, the analyst will choose a certain approach.
Given: A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.
">" sign implies that right-tailed test i.e., one-tailed right-sided.
Hence, the given statement is False.
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a bank pay is 7% interest on 3 years certificates of deposit what is the value of a $500 certificate after one year give your answer to the nearest cent
The value of a $500 certificate after one year is $525.
if integer polynomials p and q satisfy p(x)/q(x) is an integer for infinitely many integer inputs x, does it follow that q(x) divides p(x)?
The condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).
What are integer polynomials?In mathematics, a polynomial with integer values (also called a numerical polynomial) has an integer value for each integer n.
Contrary to popular belief, every polynomial with integer coefficients has integer values.
For instance, when t is an integer, the polynomial takes on integer values.
So, polynomials are the sums of terms of the form kˣⁿ, where k is any number and n is a positive integer.
A description of polynomials, such as the polynomial 3x+2x-5.
The concepts of degree, standard form, monomial, binomial, and trinomial are all covered in this section.
Therefore, the condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).
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after collecting the data, douglas finds that the finishing times for cyclists in a race is normally distributed with mean (μ) 149 minutes and standard deviation (σ) 16 minutes. what is the probability that a randomly selected race participant had a finishing time of less than 165 minutes? use the empirical rule provide the final answer as a percent.
Probability which is randomly selected race participants with finishing time less than 165 minutes is equal to 0.84.
As given in the question,
Mean 'μ' = 149 minutes
Standard deviation 'σ' = 16 minutes
Probability of randomly selected race for finishing time less than 165 minutes
⇒ P( X < 165 ) = P [(X - μ)/σ < (165 -149)/16]
= P [(X - μ)/σ < 1]
= P ( z < 1 )
Probability is associated with 1,2,3 standard deviation of 68%, 95% and 99.7%
Empirical rule = 68 - 95 - 99.7
P ( z < 1 ) = 0.5 + 0.68/2
= 0.5 + 0.34
= 0.84
Therefore, the probability for randomly selected participants whose finishing time is less than 165 minutes is 0.84.
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Answer:
Step-by-step explanation:
84% is the answer for Knewton Alta Stats
Which best describes the meaning of the statement "If A, then B'?
Answer: If A is true, then B must be true.