Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
[tex]\frac{x}{3} + z = 14[/tex]
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
[tex]x + y = 44[/tex]
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
[tex]\frac{x}{3} + z = 14[/tex]
[tex]\frac{x}{3} = 14 - x[/tex]
[tex]x = 3(14 - z)[/tex]
[tex]x = 42 - 3z[/tex]
And
[tex]y = z + w[/tex]
In which
[tex]w = 10 + z[/tex]
So
[tex]y = z + 10 + z[/tex]
[tex]y = 2z + 10[/tex]
Replacing:
[tex]x + y = 44[/tex]
[tex]42 - 3z + 2z + 10 = 44[/tex]
[tex]-z + 52 = 44[/tex]
[tex]z = 52 - 44[/tex]
[tex]z = 8[/tex]
The number of female faculty in the Department with a PhD is 8.
PLEASE ANSWER FAST!
PROBABILITY QUESTION
Answer:
1/3
Step-by-step explanation:
There are 3 cards and out of the three you only have one one third chance of picking each number
Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate the flux of F across S. F(x, y, z) = x2yi + xy2j + 3xyzk, S is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x + 2y + z = 2.
Answer:
-14 / 3
Step-by-step explanation:
- Divergence theorem, expresses an explicit way to determine the flux of a force field ( F ) through a surface ( S ) with the help of "del" operator ( D ) which is the sum of spatial partial derivatives of the force field ( F ).
- The given force field as such:
[tex]F = (x^2y) i + (xy^2) j + (3xyz) k[/tex]
Where,
i, j, k are unit vectors along the x, y and z coordinate axes, respectively.
- The surface ( S ) is described as a tetrahedron bounded by the planes:
[tex]x = 0 \\y = 0\\x + 2y + z = 2[/tex]
[tex]z = 0\\[/tex]
- The divergence theorem gives us the following formulation:
[tex]_S\int\int {F} \,. dS = _V\int\int\int {D [F]} \,. dV[/tex]
- We will first apply the del operator on the force field as follows:
[tex]D [ F ] = 2xy + 2xy + 3xy = 7xy[/tex]
- Now, we will define the boundaries of the solid surface ( Tetrahedron ).
- The surface ( S ) is bounded in the z - direction by plane z = 0 and the plane [ z = 2 - x - 2y ]. The limits of integration for " dz " are as follows:
dz: [ z = 0 - > 2 - x - 2y ]
- Now we will project the surface ( S ) onto the ( x-y ) plane. The projection is a triangle bounded by the axes x = y = 0 and the line: x = 2 - 2y. We will set up our limits in the x- direction bounded by x = 0 and x = 2 - 2y. The limits of integration for " dx " are as follows:
dx: [ x = 0 - > 2 - 2y ]
- The limits of "dy" are constants defined by the axis y = 0 and y = -2 / -2 = 1. Hence,
dy: [ y = 0 - > 1 ]
- Next we will evaluate the triple integral as follows:
[tex]\int\int\int ({D [ F ] }) \, dz.dx.dy = \int\int\int (7xy) \, dz.dx.dy\\\\\int\int (7xyz) \, | \limits_0^2^-^x^-^2^ydx.dy\\\\\int\int (7xy[ 2 - x - 2y ] ) dx.dy = \int\int (14xy -7x^2y -14 xy^2 ) dx.dy\\\\\int (7x^2y -\frac{7}{3} x^3y -7 x^2y^2 )| \limits_0^2^-^2^y.dy \\\\\int (7(2-2y)^2y -\frac{7}{3} (2-2y)^3y -7 (2-2y)^2y^2 ).dy \\\\[/tex]
[tex]7 (-\frac{(2-2y)^3}{6} + (2-2y)^2 ) -\frac{7}{3} ( -\frac{(2-2y)^4}{8} + (2-2y)^3) -7 ( -\frac{(2-2y)^3}{6}y^2 + 2y.(2-2y)^2 )| \limits^1_0\\\\ 0 - [ 7 (-\frac{8}{6} + 4 ) -\frac{7}{3} ( -\frac{16}{8} + 8 ) -7 ( 0 ) ] \\\\- [ \frac{56}{3} - 14 ] \\\\\int\int {F} \, dS = -\frac{14}{3}[/tex]
Which expression is equivalent to 2 (5) Superscript 4?
2 times 5 times 4
2 times 5 times 5 times 5 times 5
2 times 4 times 4 times 4 times 4 times 4
10 times 10 times 10 times 10
Answer:
b
Step-by-step explanation:
The given expression can be rewritten as 2 × 5 × 5 × 5 × 5 and is equal to 1250. The correct option is (B).
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given expression is 2 × 5⁴.
It can be simplified using the rule of indices as follows,
The expression 5⁴ can be written as 4 times 5 as below,
5⁴ = 5 × 5 × 5 × 5.
Then, the expression can be evaluated as
⇒ 2 × 5 × 5 × 5 × 5
⇒ 1250
Hence, the expression can be simplified to obtain 1250.
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a mathematical statement regarded as undecided or cannot be proved to be true or false is called what
Answer: axiom
Step-by-step explanation:
Which geometric series converges?
Answer:
B
Step-by-step explanation:
Geometric series converge if |r| < 1.
A) r = 3
B) r = 1/2
C) r = -4
D) r = 2
Only B has |r| < 1.
The converging sequence of geometric progression is given by the relation A = 1 + 1/2 + 1/4 + 1/8 ... where the common ratio r = 1/2
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A = 1 + 1/2 + 1/4 + 1/8 ...
Now , the common ratio r of the GP is
r = second term / first term
On simplifying , we get
r = ( 1/2 ) / 1
r = 1/2
So , when | r | < 1 , the GP is a converging series
Hence , the GP is converging series
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Which equation is part of solving the system by substitution? 4(y + 11)2 – 3y2 = 8 4(11 – y)2 – 3y2 = 8 4(y – 11)2 – 3y2 = 8 4(–11y)2 – 3y2 = 8
Answer: B
Step-by-step explanation:
A cell phone company
charges a $20 fee every
month and $0.01 for ten
minutes spent talking on
the phone. Write an
equation to model the cost
of a monthly cell phone bill
for the linear function.
Answer:
C = 20 + 0.001x
C = $20 + $0.001x
Step-by-step explanation:
Let x represent the number of minutes spent talking on the phone.
Given;
Fixed monthly charge F = $20
Charge per 10 minutes V = $0.01
Charge per minute = V/10 = $0.01/10 = $0.001
The equation to model the cost of a monthly cell phone bill;
Total cost = fixed cost + variable cost
C = F + (V/10)x
Substituting the values;
C = 20 + 0.001x
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money fro
the account. Which equation below gives the amount of money you will have in the account after tyears?
Al = 2,000 20.05
Al = 2,000(1.5)
A10 = 2,000(105)
A1 = 2.000 e5
Answer:
[tex]A(t) = 2,000(1.05)^{t}[/tex]
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
You invest $2,000
This means that [tex]P = 2,000[/tex]
Compounded anually
Once a year, so [tex]n = 1[/tex]
Interest rate of 5%.
This means that [tex]r = 0.05[/tex]
Amount after t years:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 2,000(1 + \frac{0.05}{1})^{t}[/tex]
[tex]A(t) = 2,000(1.05)^{t}[/tex]
Which pair of complex numbers has a real-number product?
Answer:
Step-by-step explanation:
the complex number and its conjugate
Answer:
(1+3i)(1-3i)
Step-by-step explanation:
are all the rectangles faces the same size
Answer:
A rectangle is a 2 dimensional figure, it is in a plane, so it has two faces, and yes, they are equals.
Find the function value. cos150°
Answer:
[tex]cos150 = -\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Recall the unit circle. At 150 deg, the point value is (-sqrt3/2, 1/2)
Remember the cosine is always the x-value, and sine is always the y-value.
This means that cosine will be -sqrt3/2.
Write an expression for "the quotient of z and 4
Answer:
z/4
Step-by-step explanation:
you divide the numerator by the denominator
Answer:
z/4 is the answer
please brainliest me
Step-by-step explanation:
and can me divide which is also (/)
Name the numerator and the denominator in each fraction 11⁄12
. 7⁄512
. 12⁄10
0⁄78
Answer:
numerators: 11 7. 12. 0
_ _ _. _
denominators. 12 512. 10. 78
Step-by-step explanation:
Answer:
11/12 n:11 d:12
7/512 n:7 d:512
12/10 n:12 d:10
0/78 n:0 d:78
Step-by-step explanation:
n=numerator
d=denominator
lect the best answer for the question.
3
1. Find the value of y in the equation
-=8.
y-2
3
A. y = 2
8
B. y=-2-
3
8
5
C. y=-1
8
5
D. y =
loo
The equation h = 7m + 8 models the growth of a plant after it was put into a flowerbed. If
m is the number of months since it was planted and h is the plant's height in
centimeters, which statement is valid?
The vertical axis on a graph would
represent the number of months the plant
has been in the flowerbed.
The height of the plant is the dependent
variable.
The domain of the function represents the
height of the plant.
The variable m could be represented as
f(h).
Answer:
2
Step-by-step explanation:
the vertical axis would be h, the plant's height, and the horizontal axis would be m, the number of months. This would make statement 2 the only valid statement.
statement 1: Incorrect, as the vertical axis is the height
statement 2: correct, as h depends on m
statement 3: incorrect, as the domain is the horizontal and represents the number of months
statement 4: incorrect, as h = f(m)
Find the total amount of interest on a savings account if the principal is $9400 and the bank gives a rate of 6% compounded quarterly for the next 6 years.
Answer:
4037.3264$
Step-by-step explanation:
Total amount of money after 6 years:
A = P x (1 + rate)^time
= 9400 x ( 1 + (6/100)/4)^(6 x 4)
= 13437.3264$
=> Total amount of interest after 6 years:
I = A - P = 13437.3264 - 9400 = 4037.3264$
Area of composed figure. Parallelogram, square and a rectangle
Answer:
126 in²
Dude just trust me
Which function models the number of deer?
Answer:
Step-by-step explanation:
Hi,
for n =0, so at the beginning we have 125 individuals
for n=1 the population is decreasing by 4%
it means that we got 125 - 124*0.04 = 125*(1-0.04)=125*0.96
for n = 2 we got [tex]125*0.96*0.96=125*0.96^2[/tex]
for n >= 1 we got [tex]125*(0.96)^n[/tex]
so the correct answer is A
do not hesitate if you need further explanation
hope this helps
a cone has the diameter of 3 inches. the cone holds 12 cubic inches of water. to the nearest inch, what is the height of the cone?
Answer:
The height is about 5 inches.
Step-by-step explanation:
The volume for a cone is [tex]\frac{1}{3}[/tex] × π × r² × h
The radius of the cone is 1.5
12= [tex]\frac{1}{3}[/tex] × π × 1.5² × h
12= [tex]\frac{1}{3}[/tex] × π × 2.25 × h
12=0.75×π×h
Divide both sides by 0.75
16=π×h
Divide both sides by π
5≈h
The height is about 5 inches.
From which point of view is the story told?
Answer:
there are 5 types of point of views
please brainliest me
Step-by-step explanation:
1rst person: Writing in first person means writing from the author's point of view or perspective. This point of view is used for autobiographical writing as well as narrative.
2 person: The second-person point of view belongs to the person (or people) being addressed. This is the “you” perspective. Once again, the biggest indicator of the second person is the use of second-person pronouns: you, your, yours, yourself, yourselves.
3 person: In the third-person point of view, a narrator tells the reader the story, referring to the characters by name or by the third-person pronouns he, she, or they.
4 person: The term fourth person is also sometimes used for the category of indefinite or generic referents, which work like one in English phrases such as "one should be prepared" or people in people say that..., when the grammar treats them differently from ordinary third-person forms."
5 person:From a fifth person perspective, one starts to “feel” the system in a different way, recognizing that one's own perspective on and in the Anthropocene is merely a perspective, which itself is a perspective, which in turn is a perspective.
Which system of linear inequalities is represented by the
graph?
O y2x - 2 and y = x + 1
O y< x-2 and y> x + 1
O y < x-2 and y? x + 1
O y> x-2 and y < x + 1
Answer:
answer c.
y <= x - 2 and y >= x + 1
Step-by-step explanation:
You wrote the given answers wrong. Here are the right choices that are given as possible solutions:
O y >= x - 2 and y <= x + 1
O y < x - 2 and y > x + 1
O y <= x - 2 and y >= x + 1
O y > x - 2 and y < x + 1
The graph clearly shows two lines and the intended area is shaded and it is clearly including the lines.
Because the lines are included in the solution, by that alone, you can exclude two answers b and d.
Now you still need to decide between the in equalities in answer a and c. Both lines have a gradient of 1, so that does not help to distinguish...
The y intercept of the top line is at y= +1 and the shaded area is bigger then that....
So y >= x + 1 is the right inequality.By now it is absolutely clear that answer c must be the right answer and you are done!
EXTRA
Although you have deduced beyond any doubt, that answer c must be the right answer, you still can check your findings 'to be sure' by looking and checking for the bottom line...
BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?
By double checking yourself, it will sort of "undermine" your appproach. Basically you are doing something which is strictly spoken not nessasary any more. So I urge you to basically step over the urge to check yourself, and stick to your answer.
However, if you can not resit the temptation of checking to see if you actually found the right answer, you could test the y intercept of the bottom line, which is at y= -2 and the shaded area is smalller then that....
So y <= x - 2 is the right inequality.So again, it is now confirmed that answer c is indeed the right answer.
The correct system of linear inequalities is represented by the graph are,
⇒ y > x - 2
⇒ y < x + 1
What is mean by Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The system of linear inequalities is shown in graph.
Hence, By graph;
The value of y - intercepts are,
⇒ - 2 and - 1
Hence, The correct system of linear inequalities is represented by the graph are,
⇒ y > x - 2
⇒ y < x + 1
Thus, The correct system of linear inequalities is represented by the graph are,
⇒ y > x - 2
⇒ y < x + 1
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For problems 3 and 4, find the missing side of the triangle. Leave answers in simplest radical form.
Answer: 3. 4[tex]\sqrt{13}[/tex] 4. [tex]\sqrt{225}[/tex]
Step-by-step explanation:
8^2 + 12^3 = c^2
64 + 144 = c^2
208 = c^2
√208
[tex]4\sqrt{13}[/tex]
The final answer is the square root of 208
8^2 + b^2 = 17^2
64 + b^2 = 289
-64 64
b^2 = 225
[tex]\sqrt{225}[/tex]
Parker marks sixths on number line. He writes 5/6 just before 1. What fraction does he write on the first mark to the right of 1?
Answer: 7/6
Step-by-step explanation:
If he is writing sixths, then we have multiples of 1/6.
this is:
0*(1/6) = 0
1*(1/6) = 1/6
.
.
.
5*(1/6) = 5/6 (the numer he wrote at the left of 1)
6*(1/6) = 6/6 = 1
7*(1/6) = 7/6
So the number next to 1, (at the right of 1) must be 7/6.
You also can find it by adding 1/6 to 1.
1/6 + 1 = 1/6 + 6/6 = 7/6.
Answer:
[tex]7/6[/tex]
Explanation:
[tex]1/6 \approx 0.16666[/tex]
[tex]2/6 \approx 0.33333[/tex]
[tex]3/6 = 0.5[/tex]
[tex]4/6 \approx 0.66666[/tex]
[tex]5/6 \approx 0.83333[/tex]
[tex]6/6=1[/tex]
[tex]7/6 \approx 1.16666[/tex]
Which of the following is most likely the next step in the series?
Answer:
B
Step-by-step explanation:
They are increasing by 1 vertically. Hope this helps!! :)
15=3(2x+4)-3 prove x=1
Answer:
X=1
Step-by-step explanation:
6x+12-3=15
6x+9=15
6x+9-9=15-9
6x=6
X=1
Answer:
see below
Step-by-step explanation:
15=3(2x+4)-3
Distribute
15 = 6x +12 - 3
Combine like terms
15= 6x +9
Subtract 9 from each side
15 -9 = 6x+9-9
6 = 6x
Divide each side by 6
6/6 = 6x/6
1 =x
Chris has been hired to assess a new version of a college entrance exam. He randomly assigns 100 high school juniors to take the new exam and 100 high school juniors to take the old exam. So that the participants were unaware of the two versions, the new exam was administered in the school gym while the old exam was administered in the school auditorium. The students taking the exam in the gym complained about the smell, the temperature and the uncomfortable seats. The students taking the exam in the auditorium made no complaints. Chris calculated a statistically significant difference between the two versions of the exam (t(198)= 3.1, p< 0.005) and concluded that the new exam was not a valid substitute for the old exam. There is a problem with validity. Which validity is weak in this example?
a. external validity
b. construct validity
c. statistical validity
d. internal validity
Answer:
Internal validity
Step-by-step explanation:
The internal validity here is weak
Internal validity describes the extent to which an evidence weighs the cause and effect claim. In this study, the internal validity that brought about failure in the new exam is mainly due to the environment where the exam was written and not the new exam itself.
So this validity is weak in claiming that the new exam is not a good substitute for the old exam.
Putting them in the same good environment might help the researchers to draw a better conclusion.
You have been hired to assist in the data analysis at the court level (judge-level analysis will be done at a later time). You must use your knowledge of probability and conditional probability to help determine the likelihood of appeal and reversal for cases handled by different courts. Which outcome has the highest probability of occurring based on the data? a. A case in Domestic Relations Court being reversed b. A case in Common Pleas Court being reversed c. A case in Municipal Court being reversed d. There is not enough information to determine the answer
ANSWER: "There is not enough information to determine the answer". Option D is correct.
Step-by-step explanation:
For a case that was ruled by a court to be reversed by a higher court, they must be conditions in the ruling of the lower court that has been reconsidered by the higher court. This is regardless of the jurisdiction of the court or judge that ruled the case.
A case from all the courts in the options can be reversed by a higher court if the courts judgement lacks merit by the higher court, at any given times, irrespective of the court.
A scale drawing of a rectangular painting has a scale factor of 1:4 which statements are true
Answer:
object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .
Step-by-step explanation:
What a scale factor of 1:4 means.
Simply it means that the reals size of the object on land have been reduced in the drawing in the paper.
Now for scale factor of 1:4 in particular it means that the object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .
Example if the drawing has measurements of 4 inches on paper, then on land it will be 16 inches
An amusement park had 56,437 visitors the first year and 48, 319 visitors the second year it was open . What was the total number of visitors for both year
Answer:
the total number is 104756
Step-by-step explanation:
You need to add 56437 with 48319 which equals 104756
Awnser is 104,756 if you add the 2 numbers
For the given set, first calculate the number of subsets for the set, then calculate the
{5, 13, 17, 20}
The number of subsets is ]
The number of proper subsets is .
Answer:
[tex]\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}[/tex]
Step-by-step explanation:
Given:
The set A = {5, 13, 17, 20}
Question:
Find the number of subsets of A
Find the number of proper subsets of A
Simple solution by counting:
Subset of A that has 0 element:
{∅} - 1 set
Subset of A that has 1 element:
{5}, {13}, {17}, {20} - 4 sets
Subset of A that has 2 elements:
{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets
Subset of A that has 3 elements:
{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets
Subset of A that has 4 elements:
{5, 13, 17, 20} - 1 set
In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16
The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15
Key-point:
The counting method might be used for finding the number of subsets when the original set contains few elements.
The question is that, for a set that contains many elements, how to find out the number of subsets?
The answer is that: there is a fix formula to calculate the total number ([tex]N[/tex]) of subsets of a set containing [tex]n[/tex] elements: N = [tex]2^{n}[/tex]
With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.
=> Number of subsets of A: N = [tex]2^{4} = 16[/tex]
(same result as using counting method)
Brief proof of formula: N = [tex]2^{n}[/tex]
Each element of original set is considered in 2 status: existed or not.
If existed => fill that element in.
If not => leave empty.
For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.
=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are [tex]n[/tex] elements in total. => There are [tex]2^n}[/tex] ways to select, or in other words, there are [tex]2^{n}[/tex] subsets.
Hope this helps!
:)
