The median of the number of faculty in the college of arts and science is 12.
What is median?When a group of values is sorted from smallest to greatest, the median is the number in the middle of the range.
Given that,
Number of faculties in 9 departments of arts and science in the college
= 8, 12,9, 15, 17, 11, 13, 14, and 7
To find median number of the faculty in the college of arts and science,
Arrange number in increasing order,
= 7, 8, 9, 11, 12, 13, 14, 15, 17
The middle number of the sequence is 12.
So, the median of the sequence will be 12.
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At 1 P.M., there were 16 seagulls on the beach. At 3p.m., there were 40 seagulls. What is the constant rate?
20 less than 5 times a number
3.4−2.8d+2.8d−1.3 Combine like terms to simplify the expression
5,550 divide 10 to the power of 3
This would be 5.55
5550÷10^3=5.55
Hope this helps
The solution involves dividing 5,550 by 1,000, which gives 5.55. The expression 10³ represents 1,000, simplifying the division. Therefore, 5,550 divided by 10 to the power of 3 equals 5.55.
To solve the problem 5,550 divided by 10 to the power of 3, follow these steps:
First, understand that 10 to the power of 3 is equivalent to 10³.Calculate 10³: 10 × 10 × 10 = 1,000. Now, divide 5,550 by 1,000: 5,550 ÷ 1,000 = 5.55.Therefore, 5,550 ÷ 10³ = 5.55.
Joanne deposits $4,300 into a one-year CD at a rate of 4.3%, compounded daily. How much interest does she earn?
In this case, Joanne's interest earned by depositing $4,300 into a one-year CD at a rate of 4.3%, compounded daily can be calculated by plugging the values into the formula.
To calculate the interest earned, use the formula for compound interest: I = P(1 + r/n)^nt - P, where I is the interest earned, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per time period, and t is the number of time periods.
Substitute the values into the formula to find the interest earned: I = $4,300(1 + 0.043/365)^(365*1) - $4,300
If a snail can move 3/10 of a meter every 1/12 hour, what is the speed of the snail, in meters per hour?
1/4
5/18
1 1/2
3 3/5
The speed of the snail, in meters per hour 3 3/5 meters/hour.
Given that, a snail can move 3/10 of a meter every 1/12 hour.
We need to find the speed of the snail, in meters per hour.
What is speed?Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took. The formula for speed is Speed = Distance ÷ Time.
Now, speed = 3/10 ÷ 1/12
=3/10 × 12/1
=18/5
=3 3/5
Therefore, the speed of the snail, in meters per hour 3 3/5 meters/hour.
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How do you construct a line segment perpendicular to the segment given through the point given?
PLEASE HELP ME!!!! WORTH 10 POINTS!!
Write the point-slope form of the given line that passes through the points (-4, -1) and (3, -3). Identify (x1, y1) as (-4, -1).Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Answer:
[tex]y-(-1)=-\frac{2}{7}(x-(-4))[/tex]
Step-by-step explanation:
We know that the line passes through (-4,-1) and (3,-3), where [tex](x_{1} ,y_{1} )[/tex] is [tex](-4,-1)[/tex] and [tex](x_{2} ,y_{2} )[/tex] is [tex](3,-3)[/tex].
First, we need to find the slope with the formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Replacing given points
[tex]m=\frac{-3-(-1)}{3-(-4)}=\frac{-3+1}{3+4}=\frac{-2}{7}[/tex]
Then, we use the slope, one point and the slope-point form
[tex]y-y_{1} =m(x-x_{1} )\\y-(-1)=-\frac{2}{7}(x-(-4))\\ y+1=-\frac{2}{7}x+\frac{8}{7} \\y=-\frac{2}{7}x+\frac{8}{7}-1\\y=-\frac{2}{7}x+\frac{8-7}{7} \\y=-\frac{2}{7}x+\frac{1}{7}[/tex]
The slope-intercept form is
[tex]y=-\frac{2}{7}x+\frac{1}{7}[/tex]
The point-slope form is
[tex]y-(-1)=-\frac{2}{7}(x-(-4))[/tex]
Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable with 2r degrees of freedom by showing that
To show that the moment generating function (mgf) of a random variable y = 2px converges to that of a chi-squared random variable with 2r degrees of freedom as p approaches 0, we need to find the mgf of y using the definition of the mgf and substitute the new random variable. Then, by applying the limit as p approaches 0, we can demonstrate the convergence.
In this question, we are asked to define a new random variable, y = 2px, and show that as p approaches 0, the moment generating function (mgf) of y converges to that of a chi-squared random variable with 2r degrees of freedom.
To show this, we need to find the mgf of y by using the definition of the mgf and substituting the new random variable.
Then, as p approaches 0, we need to simplify the mgf and show that it converges to the mgf of a chi-squared random variable with 2r degrees of freedom.
By applying the limit as p approaches 0, we can demonstrate that the mgf of y converges to the mgf of a chi-squared random variable with 2r degrees of freedom.
Show why the function f(x) = 3rad x is not differentiable at x=0
Find the measure of Angle 1
Answer:
66º
Step-by-step explanation:
From the picture we know that AB║CD. Therefore, the line BD is a transversal line between two parallels.
We know that in these cases, the alternate interior angles are the same.
In the picture, angle 1 and the angle that measures 66º are alternate interior angles. Therefore, angle 1 measures 66º as well.
∠1 = 66º
Mary bought 20 bowls and plates for $96. each bowl cost $4.50 and each plate cost $1.50 more than a bowl. she bought more bowls than plates. how many bowls and how many plates did she buy?
If f(x)=-2(5)^x what is f(2)
Billy picked 18 oranges. Taylor picked 3 times as many oranges as Billy did. They want to put them in bags with 9 oranges in each bag.
How many bags will they need for all the oranges?
in february,Robbins and Myers,Inc.executed a 2-for-1 split.janine had 470 shares before the spilit.each share was worth $69.48. A.how many shares did she hold after the split? B.what was the post-split price per share? C.show that the split was a monetary non-event for janine?
Janine held 940 shares after the split. The post-split price per share was $34.74. The split was a monetary non-event as the total value of Janine's shares remained the same.
Explanation:A 2-for-1 split means that for every one share of stock owned, an investor receives two shares in return. In this case, Janine had 470 shares before the split. After the split, she would have 470 x 2 = 940 shares.
The pre-split price per share was $69.48. Since the split was 2-for-1, the post-split price per share would be $69.48 / 2 = $34.74.
To show that the split was a monetary non-event for Janine, we can calculate the total value of her shares before and after the split. Before the split, Janine's shares were worth 470 x $69.48 = $32,621.60. After the split, her 940 shares would be worth 940 x $34.74 = $32,621.60. Therefore, the total value of her shares remained the same.
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Before a sale, an item’s price was $38.00. After the sale discount, the price became $32.30. What was the percent of the sale discount
Answer:
15%
Step-by-step explanation:
Before a sale, an item’s price was $38.00.
Original price, p = $38.00
After the sale discount, the price became $32.30.
After discount price, q = $32.30
Difference of sale = 38.00 - 32.30
= $5.70
% of sale distance [tex]=\dfrac{difference}{original price}\times 100[/tex]
[tex]=\dfrac{5.70}{38.00}\times 100[/tex]
[tex]=15\%[/tex]
Hence, The sale discount is 15%
Before a sale, an item’s price was $38.00. After the sale discount, the price became $32.30. The percentage of the sale discount is 15%.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Before a sale, an item’s price was $38.00.
Original price, p = $38.00
After the sale discount, the price became $32.30.
After discount price, q = $32.30
Difference of sale = 38.00 - 32.30
= $5.70
The percent of the sale discount = difference/ original x 100
= 5.70 / 38.00 x 100
= 15%
Thus, The percentage of the sale discount is 15%.
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WHO IS GOOD AT MATH!!!!! Solve this problem.
326-9²+32= ?
If it takes 4 men 6 hours to repair a road, How long will it take 7 men to do the job if they work at the same rate ?
Given: p: 2x = 16 q: 3x – 4 = 20 Which is the converse of p → q?
Answer:
If q:3x-4=20 then p:2x=16
Step-by-step explanation:
We are given that two statement p and q
p:2x=16
q:3x-4=20
We have to find the converse of given statements.
Converse:
If p then q.
Converse statement
If q then p.
[tex]q\implies p[/tex]
Therefore, definition of converse
q: 3x-4=20
p: 2x=16
If q:3x-4=20 then p:2x=16
Please help and show all work.
What is the doubling time of prices which are increasing by 7 percent per year?
The doubling time of prices increasing at a rate of 7% per year can be calculated using the Rule of 70, which states that the doubling time of a variable undergoing exponential growth is approximately 70 divided by the growth rate. Thus, the doubling time for these prices would be about 10 years.
Explanation:The question pertains to the concept of doubling time in the field of finance and economics, specifically how quickly something (prices, in this case) doubles in size or value at a constant growth rate. The doubling time for a variable growing at a 7% annual growth rate can be calculated using the Rule of 70. This rule states that the doubling time of a variable undergoing exponential growth is approximately 70 divided by the growth rate (in this case, 7).
So, to calculate:
Doubling Time = 70 / 7
Doubling Time = 10 years
This means that the prices will double approximately every 10 years if they increase at a constant rate of 7% per year.
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The parent function of a graph is f(x) = x2. The graph shifts a units to the left and down b units. Which function models the transformed function?
A) y = x2 - a + b
B) y = (x - a)2 - b
C) y = (x + a)2 - b
D) y = (x - b)2 - a
B was incorrect, whats answer?
Audrey has $120 dollars to spend on a tennis racket and lessons. The racket costs $45 and the lessons cost $15 dollars per hour. Define a variable. The write and solve an equation to find how many hours of lessons she can afford.
does this equation describe a linear function
Y=2/x-28
What is the percent increase of 2826 to 3324?
The answer is provided in the image attached.
Have a great day!
Martene got a small aquarium for her birthday. The aquarium is a right rectangular prism 18.5cm long by 15cm wide. Martene put 3885 cm3 of water in the aquarium. How deep is the water in the aquarium -
PLease Help!
A number x is no more than 9 units away from 8. Write and solve an absolute-value inequality to show the range of possible values of x.
1. |x + 9| ≤ 8
−17 ≤ x ≤ −1
2. |x + 8| ≤ 9
−17 ≤ x ≤ 1
3. |x − 9| ≤ 8
1 ≤ x ≤ 17
4. |x − 8| ≤ 9
−1 ≤ x ≤ 17
The top of a manhole cover is shaped like a circle. The area of the manhole cover is 380 square inches. What is the circumference of the manhole cover, to the nearest inch?
need to find the radius first
area = pi*r^2
380 = PI *r^2
380/PI = r^2
r^2 = 121
r = sqrt(121) = 11 inches
radius is 11 inches
now calculate circumference:
c = 2*PI*r
C = 2 * 3.14 * 11
circumference = 69.08 = 69 inches
HELP ME PLZ PPL!!!!
Solve for x: |x − 2| + 10 = 12 (1 point)
x = −20 and x = 4
x = −4 and x = 0
No solution
x = 0 and x = 4
The revenue from selling x shirts is r(x) = 15x.
The cost of buying x shirts is c(x) = 7x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
A. p(x) = 22x – 20
B. p(x) = 22x + 20
C. p(x) = 8x – 20
D. p(x) = 8x + 20
The profit function, p(x) is the difference between the revenue and cost function of the shirt sales, Hence, the profit function is 8x - 20
Given the Parameters :
Revenue function, R(x) = 15x Cost function, C(x) = 7x + 20The profit function can be expressed thus ::
Revenue function - Cost FunctionP(x) = R(x) - C(x)
P(x) = 15x - (7x + 20)
P(x) = 15x - 7x - 20
P(x) = 8x - 20
Therefore, the profit function is 8x - 20.
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