Messages arrive to a computer server according to a poisson distribution with a mean rate of 10 per hour. determine the length of an interval of time such that the probability that no messages arrive during this interval is 0.90.
A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?
To find the speed at which the rider is rising, we use trigonometry and differentiation to calculate the rate of change of the height with respect to time. The speed is approximately -8.14 m/min.
Explanation:To find the speed at which the rider is rising, we need to find the rate of change of the height of the rider with respect to time. This can be done using the concept of trigonometry and differentiation.
Since the Ferris wheel completes one revolution every 2 minutes, the angular speed is given by 2π radians per 2 minutes, which simplifies to π radians per minute.
The height of the rider can be represented by a sinusoidal function, and by taking the derivative of this function, we can find the rate of change of the height with respect to time. In this case, the derivative would be -13sin(t), where t is the time in minutes.
Substituting t = 18 minutes into the derivative equation, we can calculate the rate at which the rider is rising. Plugging in the value, we get a speed of -13sin(18) m/min, which is approximately -8.14 m/min.
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Molly bake 24 blueberry muffins and 18 banana muffins she wants to package them for a bake sale each package will have the same number of each kind of muffin what is the greatest number of packages that molly can make if she wants to use all of the muffins
Use an algebraic rule to describe a translation right 4 units and down 2 units.
if 60 blimps each had 70 people on board,how many people would be riding on the blimp
By multiplying the number of blimps (60) with the number of people on each blimp (70), we find that a total of 4200 people would be riding on the blimps.
Explanation:This is a simple multiplication problem, where you simply need to multiply the number of blimps by the number of people on each blimp to get the total number of people. In this case, we have 60 blimps each carrying 70 people. So we multiply 60 blimps by 70 people to get the total number of people, which is 4200 people. Therefore, if 60 blimps each had 70 people on board, a total of 4200 people would be riding on the blimps.
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How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed
0 through 6 is 7 total numbers
1st digit can be 0-6 = 7 numbers
2nd digit can be 0-6 = 7 numbers
3rd digit can be 0-6 = 7 numbers
4th digit can be 0-6 = 7 numbers
7 * 7 *7 *7 = 2401 different combinations
Which equation could you use to solve for x in the proportion 4/5=9/x ?
Answer:
4x = 45 Chi3 is completely wrong
Step-by-step explanation:
To solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction, you can use the cross multiplication method.
First, multiply the numerator of the left fraction (4) by the denominator of the right fraction (x). Then, multiply the denominator of the left fraction (5) by the numerator of the right fraction (9).
This gives you the equation: 4x = 5 * 9.
Simplifying the equation, you get: 4x = 45.
To isolate x, divide both sides of the equation by 4: x = 45/4.
So, the correct equation to solve for x in the given proportion is 4x = 45.
The ____ function can be used to ensure that a number has the appropriate number of decimal places.
A machine is set to fill the small-size packages of m&m candies with 56 candies per bag. a sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. to test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?
In statistics, the amount of degrees of freedom is the quantity of values in the final computation of a statistic that are free to differ. In this case, you can get the answer by adding the number of bags and subtracting 1.
So in computation, this would look like: 3 + 2 + 1 + 2 - 1 = 7
Therefore, 7 is the degrees of freedom.
Final answer:
The number of degrees of freedom for the hypothesis test that the mean candies per bag is 56 is 7, calculated by subtracting one from the total number of sampled bags.
Explanation:
To calculate the number of degrees of freedom for the hypothesis test that the mean candies per bag is 56, we use the sample size minus one. The sample size is the number of observations, which is the total count of bags sampled. In this case, we have a total of 8 bags (three bags of 56, two bags of 57, one bag of 55, and two bags of 58). Therefore, the degrees of freedom for this test would be 8 - 1 = 7.
What is the sum of 1.53 + 2.786 + 3.3 written with the correct number of significant figures?
Answer:
1.53 + 2.786 + 3.3 = 7.6
Step-by-step explanation:
Significant figures is the number of digits that carry precision in a number.
In mathematical operations involving significant figures, an answer is no more precise that the least precise number used to get the answer.
For addition, look at the places to the decimal point. Add in the normal fashion, then round the answer to the least number of places to the decimal point of any number in the problem.
To find the sum of 1.53 + 2.786 + 3.3 you must:
[tex]1.53 + 2.786 + 3.3\\4.316 + 3.3\\7.616\\[/tex]
Because 3.3 is the number with the smallest sig figs, the result should have as many decimal places as the number with the smallest sig figs. Therefore, 7.6.
Kathy can clean 12 house in 10 hrs. If she goes at a steady pace. How many hrs. will it take her to clean 27 houses?
What inequality represents the verbal expression? 1. all real numbers less than 69?
A childcare center charges $150 per week during the school year In the summer, parents can pay a prorated amount based on the number of days of attendance How much do parents pay per day
what is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3
Express 9.21212121212... as a rational number, in the form pq
what is the factor expression of 27 + 33
Which unit would you use to measure the length of a football field mm cm m or km?
What is the perimeter of a parallelogram if it has a base width of 3x+9 and it has a height length of 4x-5?
a square has a perimeter of 6x - 20 units. What is the value of x?
We wish to choose 7 cards from a usual deck of 52 playing cards. In how many ways can this be done if we are required to choose the cards in the following ways?
(a) with no restriction.
(b) all cards come from the same suit.
(c) exactly 3 Aces and exactly 3 Kings are chosen.
(d) all 7 cards have values between 2 and 7 inclusive.
(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).
The cost function for a particular product is given by C(x)=0.0001 x^3−0.015x^2+13.1x+120 dollars, where 0≤x≤60. Find the minimum marginal cost of the product, rounded to the nearest cent.
Final answer:
To find the minimum marginal cost, differentiate the cost function to get the MC function, find its critical points, and evaluate it at these points within the interval.
Explanation:
To find the minimum marginal cost of the product, we need to differentiate the cost function C(x) with respect to x to find the marginal cost function, then find the critical points within the given interval by setting the derivative to zero and solving for x.
The cost function is C(x) = 0.0001x^3 - 0.015x^2 + 13.1x + 120. The marginal cost (MC) function, MC(x), is the first derivative of the cost function with respect to x:
MC(x) = dC/dx = 0.0003x^2 - 0.03x + 13.1.
To find the minimum marginal cost, we need to differentiate the MC function to find its critical points:
dMC/dx = 0.0006x - 0.03
Setting dMC/dx equal to zero and solving for x gives us:
0.0006x - 0.03 = 0
x = 50
After finding the critical point, we check if it is within the interval [0,60] and evaluate the MC function at x = 50 to find the minimum MC. Rounding it to the nearest cent, we have:
MC(50) = 0.0003(50)^2 - 0.03(50) + 13.1
The final minimum marginal cost of the product is calculated and rounded to determine the minimum cost to produce one more unit of output.
1. which expression is equivalent to 8 × 8 × 8 × 8?
A. 8 × 4
B. 8^5
C. 8^4
D. 4^8
2. which expression is equivalent to 4 × 4 × 4 × 4 × 4 × 4 × 4?
3. which expression is equivalent to 7 × 7 × 7 × 7 × 7 × 7?
4. which expression is equivalent to 4 × 4 × 4?
5. which expression is equivalent to 3 × 3?
74,137 rounded to the nearest thousands is
explain how you could find 3/8% of 800
Add: 3 cups 6 oz + 2 cups 9 oz
6 cups 7oz is your answer
5x^7y^4+25xy^2+15xy^3/5xy^3
On Wednesday, Miguel's bank account balance was -$55. On Thursday, his balance was less than that. Use absolute value to describe Miguel's balance on Thursday as a debt. In this situation, -$55 represents a debt of _________. On Thursday, Miguel had a debt of _____________than $55.
In this situation, the -$55 represents the debt of $55, since this happens when Miguel does not have enough money in his account to cover payments or transactions. On Thursday, he has a debt of more than $55. The explanation behind this is if an account balance is less than -55 dollars, it exemplifies a debt bigger than 55 dollars.
y varies directly as x when x= 3 and y =12 find y when x =12
Which ordered pair would form a proportional relationship with the point graphed below?
(–10, 30)
(30, –15)
(–30, 10)
(80, –30)
The (–30, 10) ordered pair would form a proportional relationship with the point graphed option (C) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
The point (60, -20) is shown in the graph:
As we know from the definition of the proportional relationship:
y = kx
Here k is the constant of proportionality.
k = y/x
k = -20/60
k = -1/3
y = -x/30
Plug x = -30
y = 10
(–30, 10)
Thus, the (–30, 10) ordered pair would form a proportional relationship with the point graphed option (C) is correct.
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if a cylinder has a V=3053.6 cubic inches and a radius of 9 inches, what is the height of the cylinder to the nearest inch?
Answer:
12
Step-by-step explanation:
12 inches