Answer:
2.28% of faculty members work more than 58.6 hours a week.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average full-time faculty member in a college works an average of 53 hours per week. Standard deviation of 2.8 hours.
This means that [tex]\mu = 53, \sigma = 2.8[/tex]
What percentage of faculty members work more than 58.6 hours a week?
The proportion is 1 subtracted by the p-value of Z when X = 58.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{58.6 - 53}{2.8}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
1 - 0.9772 = 0.0228
0.0228*100% = 2.28%
2.28% of faculty members work more than 58.6 hours a week.
What is the median of the data set? 32, 41,43,50,70,73,80,88
Answer:
60
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
1) Find the two middle numbers: 50 and 70.
2) Take the average of both #'s to get your answer: 60.
What is 1/8 * 1/8 in fraction? PLEASE HELP
Answer:
1/64
Step-by-step explanation:
See image below:)
Two pools are being drained. To start, the first pool had 3650 liters of water and the second pool had 4166 liters of water. Water is being drained from the first pool at a rate of 27 liters per minute. Water is being drained from the second pool at a rate of 39 liters per minute. Let be the number of minutes water has been drained. (a) For each pool, write an expression for the amount of water in the pool after minutes. (b) Write an equation to show when the two pools would have the same amount of water.
Step-by-step explanation:
(a) Let's start with the first pool. It has 3650 liters of water. For every minute, 27 liters are being drained. Thus, we can write its equation as 3650 liters - 27 liters per minute = end amount of liters. If we write minutes as m, we can say 3650-27m is our expression. Similarly, for the second one, we have 4166-39m as our answer
(b) For this, we just have to make the two expressions equal, so
4166-39m = 3650-27m
The solution is:
(a)
Amount of water in the first pool (in liters) = 3650 liters - 27 liters per minute * x minutes
Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes
(b)
3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here, we have,
(a) With x being the minutes after which you want to calculate the amount of water in the pool, to calculate this amount of water you must subtract the water drained from the initial amount of water that the pool contains.
Knowing that, for example, the water from the first pool drains at a rate of 27 liters per minute, then after x minutes, the total water drained will be 27 liters per minute * x minutes. Then:
Amount of water in the first pool (in liters) = 3650 liters - 27 liters per minute * x minutes
Reasoning in the same way:
Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes
(b) Now want to know when the two pools would have the same amount of water. If they have the same amount of water then you can express:
Amount of water in the first pool = Amount of water in the second pool
Replacing the expressions found in (a):
3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes
To learn more on equation click:
brainly.com/question/24169758
#SPJ2
Determine whether the triangles are similar. If so, write a similarity
statement.
Answer:
[tex]\triangle FED\sim \triangle JEH[/tex]
Step-by-step explanation:
Both pairs of vertical angles formed at point E are equal. Therefore, the two triangles share two angles. If two triangles share two angles, they must also share the third angle, since the sum of the interior angles of a triangle add up to 180 degrees. Therefore, all three angles of the two triangles are equal, which is a proof of similarity. [tex]\implies \boxed{\triangle FED\sim \triangle JEH}[/tex]
9514 1404 393
Answer:
ΔDEF ~ ΔHEJ
Step-by-step explanation:
The vertical angles at E are congruent, and the marked angles at F and J are congruent. The two triangles are similar by the AA postulate.
The given portion of the similarity statement names the angles in the order "unspecified", "vertical", and "50°". If we name those angles in the same order in the other triangle, the similarity statement becomes ...
ΔDEF ~ ΔHEJ
On a radar screen, a plane located at A(-2, 4) is flying toward B(4,3). Another plane, located at C(-3, 1), is flying toward D(3,0). Are the planes' paths perpendicular?
Answer:
yes they are perpendicular
hope this helps
have a good day :)
Step-by-step explanation:
Find the volume of cone pictured below. Use 3.14 for π
.
Round your answer to the nearest hundredth.
Answer:
V≈718.38
Step-by-step explanation:
The volume of this cone is 718.38 cubic centimeters.
Have a nice day!
hkiojhguyhvjln kiuhbjv hgvytcf gv
Answer:we had in dog C criminal seyyyyy and hbu have a dog in a car accident in a dog and he got to the house to go back and he said
Step-by-step explanation:
Which statement describes the solution set of function f? f(x)= 3x^2 - 4x - 2
Answer:
Vertex form
( 2 /3 , − 10 /3 )
x and y intercepts
Y intercept ( 2 + √ 10 /3 , 0 ) , ( 2 − √ 10/ 3 , 0 )
X intercept ( 0 , − 2 )
Step-by-step explanation:
The correct statement that describes the solution set of the function f is Two real solutions. So, correct option is C.
To determine the solution set of the function f(x) = 3x² - 4x - 2, we can consider the nature of the solutions by examining the discriminant of the quadratic equation.
The discriminant, denoted as Δ, is calculated as b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, the quadratic equation is 3x² - 4x - 2 = 0. Comparing it to the general form, we have a = 3, b = -4, and c = -2.
The discriminant is given by Δ = (-4)² - 4(3)(-2) = 16 + 24 = 40.
Based on the value of the discriminant (Δ = 40), we can determine the nature of the solutions:
If Δ > 0, there are two distinct real solutions.
If Δ = 0, there is one real solution.
If Δ < 0, there are two complex solutions.
Since Δ = 40, which is greater than 0, the correct statement that describes the solution set of the function f is:
C- Two real solutions.
To learn more about function click on,
https://brainly.com/question/29046119
#SPJ2
Complete question is:
Which statement describes the solution set of function f? f(x) = 3x² - 4x - 2
A- One real solution and one complex solution
B- Two complex solutions
C- Two real solutions
D- One real solution
What is the volume of a square pyramid with a height of 4cm and a base with a side of 9 cm?
Answer:
108cm³
Step-by-step explanation:
Seeing that the base is a square, we first have to calculate the area of the base. This is equal to 9x9, in other words 81cm squared. Now, we multiply the base area to the vertical height divided by 3, which becomes 81x(4/3), which is then 108cm³.
:))))))))))
Suppose a random sample of size 50 is selected from a population with μ = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). Round your answers to two decimal places.
a. The population size is infinite.
b. The population size is N = 50,000.
c. The population size is N = 5000.
d. The population size is N = 500.
In the question, it's σ = 10 and not μ = 10.
Answer:
A) σ_x = 1.4142
B) σ_x = 1.4135
C) σ_x = 1.4073
D) σ_x = 1.343
Step-by-step explanation:
We are given;
n = 50
σ = 10
A) Formula for standard error of the mean for infinite size is;
σ_x = σ/√n
Thus;
σ_x = 10/√50
σ_x = 1.4142
B) When population is finite, we use correction factor and thus, we have;
σ_x = [√((N - n)/(N - 1)] × σ/√n
N = 50,000
Thus;
σ_x = [√((50000 - 50)/(50000 - 1)] × 10/√50
σ_x = 1.4135
C) N = 5000
Thus;
σ_x = [√((5000 - 50)/(5000 - 1)] × 10/√50
σ_x = 1.4073
D) N = 500
Thus;
σ_x = [√((500 - 50)/(500 - 1)] × 10/√50
σ_x = 1.343
Joe has 23 carnival ride tickets and it takes 3 tickets to ride the roller coaster how many times can he ride the coaster how many tickets will he have left over
Answer:
JIKA ANDA YANG
Step-by-step explanation:
yang bales anak yang
[tex]5 { \frac{3 \frac{ + > }{?} }{?} }^{?} [/tex]
Answer:
20
Step-by-step explanation:
He has 23 carnival ride tickets and it takes 3 tickets to ride a roller coaster
so 23 - 3 = 20
The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed. Suppose, that the mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.4 fluid ounce. (a) At what value should the mean be set so that 99.9% of all cans exceed 12 fluid ounces
Answer: At a value of 12.3 the mean should be set so that 99.9% of all cans exceed 12 fluid ounces.
Step-by-step explanation:
Let us assume that X is a normal rando variable with a mean value [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].
Hence, random variable Z will be introduced as follows.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
(a) Set the value [tex]\sigma = 0.1[/tex] and the equation will be written down as follows.
[tex]0.999 = P (X \geq 12) \\= P (Z \geq \frac{12 - \mu}{0.1})\\= 1 -\phi (\frac{12 - \mu}{0.1})\\\phi (\frac{12 - \mu}{0.1}) = 0.001[/tex]
According to the tables,
[tex]\frac{12 - \mu}{0.1} = -3\\\mu = 12.3[/tex]
Thus, we can conclude that at a value of 12.3 the mean should be set so that 99.9% of all cans exceed 12 fluid ounces.
In order to safely land, the angle that a plane approaches the runway should be no more than 15°. A plane is approaching Ottawa Macdonald–Cartier International Airport to land. It is at an altitude of 500 m and a horizontal distance of 3 km from the start of the runway. At what angle is the plane approaching and is it safe for the plane to land?
9514 1404 393
Answer:
9.5°, yes
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
The distance opposite the angle of elevation is the plane's height, 500 m. The distance adjacent to the angle of elevation is the horizontal distance to the plane, 3 km = 3000 m. Then the angle is found from ...
tan(α) = 500/3000 = 1/6
α = arctan(1/6) ≈ 9.46°
The plane is approaching at an angle of 9.46°. It is safe to land, since that angle is less than 15°.
_____
Additional comment
The usual descent angle for most commercial air traffic is 3°. Some airport geography demands it be different (steeper). A higher descent angle can put undue stress on the landing gear.
I don’t get this one but the question was something about finding the equation.
9514 1404 393
Answer:
y = -(x -3)^2 +2
Step-by-step explanation:
The vertex form of the equation for a parabola is ...
y = a(x -h)^2 +k
where the vertex is (h, k) and the value 'a' is a vertical scale factor.
The value of 'a' can be found by looking at the y-value of points ±1 either side of the vertex relative to the vertex. Here, the vertex y-value is +2 at x=3, and either side goes down 1 unit (to y=1) for 1 unit to the right or left. So, a = -1.
Using the values we've read from the graph for the vertex (h, k) = (3, 2) and the scale factor a = -1, we can write the equation as ...
y = -(x -3)^2 +2
what is equivalent to 4 to the power of 3
Answer:
64
Step-by-step explanation:
because you multiply 4 by it self
A number - _______ = previous number
Answer:
1
Step-by-step explanation:
When we substract 1 from any number then will get just previous number.
Example :
Let any number 17
17-1 =16
16 is the just previous number of 17
Therefore, A number -1 = previous number
Answer will be 1
Which figure can be formed from the net?
6 cm
4 cm
4 cm
6 cm
4 cm
4 cm
6 cm
6 cm
Answer:
It's the fourth option, the bottom right one
The last one is the answer to the right. look at the base you can understand it from there, the net that shows from the question is a square base pyramid so that means you have to look for square base and that will give you the correct answer.
Solve rational equations 5/6+3/b=1/3
Explain why the sum of the interior angles in a regular pentagon is 540?
Answer:
Step-by-step explanation:
formula to find the sum of interior angle of a regular pentagon is
(n-2)*180 degree
here n means no of sides .since pentagon has 5 sides replace it by 5
=(5-2)*180
=3*180
=540 degree
Solve for y.
O 10
O 12
O 15
O 18
Answer:
first option
Step-by-step explanation:
3x = 90 degree (being perpendicular)
x = 90/3
x = 30 degree
substitute the value of x
2x + 3y = 90 degree (being perpendicualr)
2*30 + 3y = 90
60 + 3y = 90
3y = 90 - 60
y = 30/3
y = 10 degree
Answer:
that's easy its letter a number 10
What is the value of 2 - 1.25 as a fraction?
Answer:
3/4
Step-by-step explanation:
2 - 1.25 - 0.75
0.75 = 3/4
Your answer is 3/4.
I hope this helps, have a nice day.
Answer:
[tex] \frac{3}{4} [/tex]Step-by-step explanation:
[tex]2 - 1.25[/tex]
[tex]0.75[/tex]
[tex]0 \frac{75}{100} [/tex][tex] \frac{75}{100} [/tex][tex] \frac{25(3)}{25(4)} [/tex][tex] \frac{25 \times 3}{25 \times 4} [/tex][tex] \frac{3}{4} [/tex]Hope it is helpful...Do 8feet + 10feet + 12feet make a right triangle
9514 1404 393
Answer:
no
Step-by-step explanation:
If triangle side lengths are an arithmetic sequence (have a common difference), they must have the ratios 3:4:5 to make a right triangle. Here, the ratios of the side lengths are 4:5:6, so will not be a right triangle.
A public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds. A sample of 15 babies is studied. Round the answers to three decimal places. Part 1 of 4 (a) What is the probability that exactly 5 of them weigh more than 20 pounds
Answer:
0.206 = 20.6% probability that exactly 5 of them weigh more than 20 pounds.
Step-by-step explanation:
For each baby, there are only two possible outcomes. Either they weigh more than 20 pounds, or they do not. The probability of a baby weighing more than 20 pounds is independent of any other baby, which means that the binomial probability distribution is used 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.
A public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds.
This means that [tex]p = 0.3[/tex]
A sample of 15 babies is studied.
This means that [tex]n = 15[/tex]
What is the probability that exactly 5 of them weigh more than 20 pounds
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.3)^{5}.(0.7)^{10} = 0.206[/tex]
0.206 = 20.6% probability that exactly 5 of them weigh more than 20 pounds.
In an experiment, the population of bacteria is increasing
at the rate of 100% every minute. The population is
currently at 50 million.
How much was the population of bacteria 1 minute
ago?
million
25 million
number of bacteria doubles every minute
At the beginning of the week, Josh had 323232 computer games, 133\33, percent as many computer games as Peter had. By the end of the week, Josh gave 25\%%, percent of his computer games to Peter. How many computer games did Josh and Peter each have by the end of the week
Answer:
[tex]Josh =24[/tex]
[tex]Peter = 32[/tex]
Step-by-step explanation:
Given
Beginning of Week
[tex]Josh = 32[/tex]
[tex]Josh = 133\% * Peter[/tex]
First, we calculate the amount Peter has at the beginning of the week
[tex]Josh = 133\% * Peter[/tex]
Make Peter the subject
[tex]Peter = \frac{Josh}{133\%}[/tex]
[tex]Peter = \frac{32}{133\%}[/tex]
[tex]Peter = \frac{32}{1.33}[/tex]
[tex]Peter = 24[/tex]
When Josh gave out 25%.
The number (n) of computers is:
[tex]n = Josh * 25\%[/tex]
[tex]n = 32 * 25\%[/tex]
[tex]n = 8[/tex]
This means that Josh gave out 8 computers.
So, the amount they both have is:
[tex]Josh =32 - 8[/tex]
[tex]Josh =24[/tex]
[tex]Peter = 24+8[/tex]
[tex]Peter = 32[/tex]
From her eye, which stands 1,61 meters above the ground, Savannah measures the
angle of elevation to the top of a prominent skyscraper to be 24°. If she is standing at
a horizontal distance of 340 meters from the base of the skyscraper, what is the
height of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary
Answer:
152.99 m
Step-by-step explanation:
Using the solution diagram attached below :
We can obtain the height, h of skyscraper to the position of her eye level using trigonometry ;
Tan θ = opposite / Adjacent
Tan 24 = h / 340
h = tan 24 * 340
h = 151.37775
Hence, the height will be (h + distance from eyelevel to ground)
151.37775 + 1.61
= 152.98775
= 152.99 m
Answer:
132.6 meters tall
Step-by-step explanation:
it gave me the answer
Which ordered pairs would appear on the graph of the equation y = 1/2x +
6?
(-6, 3) and (0,6)
(10, 8) and (0,6)
(6, 3) and (0,6)
(10, 11) and (0,6)
Mac traveled to three cities on one highway. The total distance one way was 320 miles. The distance from his original location to the first city was 20 miles more than half the distance from the first city to the second city. The distance from the second city to the third city was 75 miles less than the distance from the first city to the second city. Let x represent the distance from the original location to the first city, y represent the distance from the first city to the second city, and z represent the distance from the second city to the third city. Place the correct sets of column entries in the augmented matrix that models Mac's situation
Answer:
827
Step-by-step explanation:
this is the answer !!
What is the length of a diagonal in the given picture? Round your answer to the nearest whole number. Write the numerical value
What is the probability of the spinner landing on 1 or 3
Answer:
Assuming there are 3 possibilities for the spinner, the answer is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
