Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that the average salary of a group of 16 randomly selected ph.d. students is more than $13,000.
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Related Questions
One factor of f(x)= 4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
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f(x)=4x^3-4x^2-16x+16=x^3-x^2-4x+4.
We could divide f(x) by (x-2) and solve the resulting quadratic equation.
We could, however, use another property of f(x).
We are given that.................................................... (x-2) is a factor
Knowing that the constant term is +4, and using the factor theorem, we can try (x+2) as a factor.
f(-2)=-8-4+8+4=0......................................................(x+2) is a factor
We note that f(x) has a sum of coefficients 1-1-4+4=0, equal to zero, this means that f(1)=0, or (x-1) is a factor...................................................(x-1)
Therefore all the factors of the function are (x+2)(x-2)(x-1)
and the roots are x={1,2,-2}
Is the answer to your problem
Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A
Answers
Answer:
C ✔️
Step-by-step explanation:
"16 inches"
A baker has a bin filled with 30 cups of flour. His signature cake requires one and a half cups of flour. Determine which graph and which equation represent the amount of flour in the bin, F, after he bakes c signature cakes.
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The equation for the flour left in the bin after baking c number of cakes is F = 30 - 1.5*c. This equation can be graphed with flour left, F, on the vertical axis and the number of cakes, c, on the horizontal axis, producing a downward sloping line.
Explanation:The subject of this question is mathematics and it focuses on linear equations and graphical representations. To answer this question, consider that the baker uses one and a half cups of flour for each cake. So, if he bakes 'c' amount of cakes, then the total flour used will be 1.5*c cups. If he started with 30 cups of flour in the bin, after making 'c' cakes, the flour remaining, F, in the bin will be given by the equation F = 30 - 1.5*c. This is a linear equation and its graph would be a line with a negative slope (because the amount of flour decreases as more cakes are baked). On the graph, the vertical axis (y-axis) could be the amount of flour left 'F', and the horizontal axis (x-axis) would be the number of cakes 'c'. The line would start from the point (0,30) (since initially, when no cakes are baked, there are 30 cups of flour) and slope downwards.
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find the length of arc ac, cb=60degrees, ab=12ft(diameter)
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Radius= diameter ÷2 =12÷2=6
And put in ur values to obtain the answer
Final answer: arc ac = 120
what is the factored form of 64g^3+8
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Jen has 2 meters of taffy. She wants to give each of her 3 best friends an equal amount of taffy. How many centimeters of taffy will each friend get?
Write your answer as a mixed number in the form a b/c.
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Answer:
[tex]66\frac{2}{3}[/tex] centimeters.
Step-by-step explanation:
Jen has 2 meters of taffy.
She wants to give each of her 3 best friends an equal amount of taffy.
First we convert 2 meters to centimeters.
1 meter = 100 centimeters
2 meters = 100 × 2 = 200 centimeters.
Now divide 200 cm to 3 friends
Each friend get = [tex]\frac{200}{3}[/tex]
= [tex]66\frac{2}{3}[/tex]
Each friend will get [tex]66\frac{2}{3}[/tex] centimeters of taffy.
which best describes your ability to calculate the volume of prisms, cylinders, pyramids, and cones?
A.I know the correct formulas to find the volumes of a ll of these figures.
B.I know the correct formulas to find the volume of at least half of these figures.
C.I can find the volume of these figures when the formulas are given to me.
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Prism:
Surface area multiplied by height, or more simple:
[tex]( \frac{1}{2} \times l \times w) \times h[/tex]
Cylinders:
Surface area multiplied by height, more simple again:
[tex]\pi \times {r}^{2} \times h[/tex]
Pyramids:
[tex] \frac{1}{3} \times l \times w \times h[/tex]
Cones:
[tex] \frac{1}{3} \times \pi \times r^{2} \times h[/tex]
I know the correct formulas to find the volumes of a ll of these figures. best describes to calculate the volume of prisms, cylinders, pyramids, and cones
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Volume of prism is Surface area multiplied by height, or more simple:
V=1/2×(l×w×h)
Volume of cylinder = πr²h
where r is the radius of cylinder and h is the height of the cylinder
Volume of pyramid = 1/3×l×w×h
Where l is length of pyramid, w is width of pyramid and h is height of the pyramid.
Volume of cone = 1/3πr²h
r is the radius of cone and h is the height of the cone
Hence, I know the correct formulas to find the volumes of a ll of these figures. best describes to calculate the volume of prisms, cylinders, pyramids, and cones
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The graph shown is the solution set for which of the following inequalities?
y ≥ x + 1
y ≥ |x| + 1
y ≥ |x - 1|
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The lines represented are the line y=x-1 and the line y=x-1 itself in the positive section of the graph (absolute value).
Answer:
The correct option is C) [tex]y\geq |x+1|[/tex]
Step-by-step explanation:
The graph of [tex]y=|x|[/tex] is shown in figure-1
In option (1) [tex]y\geq x+1[/tex] .....(2)
the graph of equation (2) is shown in figure-2
In option (2) [tex]y\geq |x|+1[/tex] .....(3)
the graph of equation (3) is shown in figure-3
In option (3) [tex]y\geq |x+1|[/tex] .....(4)
the graph of equation (3) is shown in figure-4
As this is shifted 1 unit to right side
So, this figure is correct as it is matches the provided figure
Therefore, the correct option is C) [tex]y\geq |x+1|[/tex]
How many ways can a person select 3 videotapes from a collection of 10 tapes?
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C(10,3)=10!/(3!(10-3)!)=10!/(3!7!)=10*9*8/(1*2*3)=120
ways to select three videotapes out of 10.
Mr Richards science class is conducting a variety of expirements with projectiles and falling objects DROP DOWN ANSWERS ARE GROUPS A-D
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a = g
vf = g * t + vo
rf = (1/2) * g * t ^ 2 + vo * t + ro
g: gravity
t: time
vf: final speed
Vo: initial speed
For this case what we should do is to choose the equation that best suits each statement.
We have then:
GroupA: h (t) = - 4.9 * t ^ 2 + 19 * t
Group B: h (t) = - 16 * t ^ 2 + 50 * t
Group C: h (t) = - 4.9 * t ^ 2 +19
Group D: h (t) = - 16 * t ^ 2 +50
PLEASE HELP WILL GIVE 30 POINTS AND BRAINLIEST.
Write the statement for the problem in mathematical language. Use x for the tens digit and y for the unit digits in the two digit numbers.
Find the two-digit number which is greater than the product of its digits by 26
The statement is ?
The number is ?
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There are thee (3) sets of numbers that satisfy this.
.. (x, y) = (3, 2) . . . . the number is 32
.. (x, y) = (5, 6) . . . . the number is 56
.. (x, y) = (9, 8) . . . . the number is 98
If you solve the equation for y, you get
.. y = 10 -16/(x -1)
so x-1 is a 1-digit factor of 16: 2, 4, 8. These give rise to the solutions above.
One is dollar is currently worth 84.1 Japanese yen. If you exchange 4,205 for US dollars, how much will you have?
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yen/yen per dollar=dollar
Luis wants to buy a home priced at $315,000. He plans to finance this amount less the down payment required. His mortgage payment would then be $2100. Luis has an annual income of $91,500 and $65,000 in savings. Luis has a car payment of $370, a student loan payment of $165 and a credit card payment of $45. Use a 20% down payment and the 28/36 ratio to determine if Luis is eligible for a loan. What would you advise him to do if he is not eligible?
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Solution:
Annual income of Luis= $ 91,500
[tex]\frac{28}{36}[/tex] ratio states that maximum of 28 % of your gross monthly income should be spent on housing finances and not more than 36% of your total monthly income should be spent on loans.
36% of $ 91,500= 0.36 × 91,500=$ 32,940(Annualy)
Total money that luis can use for loan as a monthly payment =$ [tex]\frac{32940}{12}=2745[/tex] $
Amount that Luis spent on loan Monthly =car payment of $370, a st udent loan payment of $165 and a credit card payment of $45= $ 370 + $ 165 + $ 45=$ 580
Amount that can be used for housing debt = $ 2745 - $ 580= $2165
Down Payment =
20 % of $315,000=0.20 × 315,000 =$ 63,000
Remaining amount for home that Luis has to pay = $ 315,000 - $ 63,000= $252,000 (not given in how many months or years Luis has to pay this amount )
Mortgage payment = $ 2100
Calculated Mortgage payment on $ 91,500 using 28% rule = 0.28 × 91,500=$25620 (Yearly)
Amount that Luis can use for Mortgage payment monthly=$ [tex]\frac{25620}{12}=2135[/tex] $(Calculated) Monthly
So, Money saved = 2135-2100=$ 35
If Monthly income allowable for Debt(i.e if $ 252,000 is divided into months) > or exceeds $ 2165, then Luis is not eligible for Loan.
If Monthly income allowable for Debt (i.e if $ 252,000 is divided into months )< or Less than $ 2165, then Luis is eligible for Loan.
The advise that i will give to Luis is that he should make full payment of his car debt, and stop being Extravagant i.e start saving more money if he wants to Possess a home.
suppose a new car that cost 20 000 depreciates by 15% each year. in how many year till the car costs 7500. use the equation 7500=(20,000)(0.85)^x
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3 = 8 * (0.85)^x => 0.85^x = 3/8
next, we can take the log() on both sides, and use the fact that log(a^b)=b*log(a)
log(3/8) = log(0.85^x) => log(3/8) / log(0.85) = x
If you calculate this, you find x ≈ 6.03
Find the equation of the plane which has intercepts of (4,0,0) and (0,−2,0) and no z-intercept.
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First step: find direction vector of the two points:
V = <4-0, 0-(-2), 0-0> = <4,2,0>
Since there is no z-intercept, Π must be orthogonal to the z-axis, hence the unit normal vector is Z=<0,0,1>.
To find the normal vector of the plane Π, we take the cross-product of V & Z, i.e.
Π =
i j k
4 2 0
0 0 1
= <2*1, -4*1, 0>
= <2,-4,0>
The corresponding equation of the plane through (4,0,0) is then
2(x-4)-4y+0(z-0)=0 => 2x-4y=8
Answer: The equation of the plane is 2x-4y=8
The equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
A plane is represented by the following expression:
[tex]A\cdot x + B\cdot y + C\cdot z = 1[/tex] (1)
Where [tex]A,B, C[/tex] are real coefficients.
We need three distinct points to determine all coefficients of the plane. If we know that [tex](x_{1}, y_{1}, z_{1}) = (4,0,0)[/tex], [tex](x_{2}, y_{2}, z_{2}) = (0,-2,0)[/tex] and [tex](x_{3}, y_{3}, z_{3}) = (0, 0, 0)[/tex], then we have the following system of linear equations:
[tex]4\cdot A = 1[/tex] (2)
[tex]-2\cdot B = 1[/tex] (3)
[tex]0 \cdot C = 1[/tex] (4)
Then, the solution of this system is [tex]A = \frac{1}{4}[/tex], [tex]B = -\frac{1}{2}[/tex] and [tex]C = 0[/tex].
And the equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
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Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
a. $273.60
b. $1,080.00
c. $1,800.00
d. $2,073.60
Would It Be D?
Answers
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Answer:
Yes the Answer is
"D" $2,073.60
Step-by-step explanation:
Correct on edg. 2021
which of the following function is f(x) if f^-1(x)=5x-19
Answers
Answer: F(x)=x-19/5
Step-by-step explanation:
The table represents the temperature of a cup of coffee over time.
Which model best represents the data set?
A) exponential, because there is a relatively consistent multiplicative rate of change
B) exponential, because there is a relatively consistent additive rate of change
C) linear, because there is a relatively consistent multiplicative rate of change
D) linear, because there is a relatively consistent additive rate of change
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temperature thrice. If you compare time=0 until time=30, you will get this table
t(10)- t(0)= 180-200= -20
t(20)-t(10)= 163-180= -17
t(30)-t(20)= 146-163= -17
t(40)-t(30)= 131- 146= -15
t(50)-t(40)= 118-131= -13
t(50)-t(40)= 107-118= -11
There is something weird about the 2nd and 3rd value because it was same -17., but there seems to be a +2 change to the difference. So, the graph would be exponential with a relatively consistent multiplicative rate of change
Answer:
A on E2020
Step-by-step explanation:
A bag contains 5 gray tiles and 2 blue tiles. Jenny reached into the bag and picked a tile randomly, and then without replacing it, picked a second tile. If you know that she picked a blue tile with her first pick, what is the probability that she picked a gray tile with her second pick? A) 1 6 B) 1 7 C) 5 6 D) 5 7
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Answer:
the anwer would be c
if the apr on a credit card is 22.2% what is the monthly interest rate
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Solution:
APR =Annual Percentage rate
It is the amount of money charged as interest on a sum that you borrow from bank.The interest can be paid monthly or annualy. If you pay the balance at the end of each month that you have borrowed from credit card ,there is no need to pay interest.To find the monthly interest rate , we just divide the value of APR by 12 .
As Yearly interest rate i.e APR on credit card = 22 .2 %
Then , Monthly interest rate = [tex]\frac{22.2}{12}= 1.85[/tex]%
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
Answers
Final answer:
To find the mass of each box in this scenario, calculate the total mass of the cans first, then divide by the number of boxes. Each box weighs 10 grams.
Explanation:
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
To find the mass of each box, we first calculate the total mass of the 3 cans: 3 cans * 30 grams/can = 90 grams. Since the 3 cans have the same mass as 9 identical boxes, each box's mass is: 90 grams / 9 boxes = 10 grams per box.
How do you figure how far Leanne walks if she walks a speed of
3 and one third miles in two hours
Answers
3 1/3 x 2 hours = 6 2/3 total miles
Which is an odd monomial function? A.y=2x^3 B.1/x C.5x^-9 D.3
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Monomy: Algebraic expression that consists of a single term or in which the terms that form it are related by the product operation.
Odd function: A function is odd if, for each x in the domain of f, f (- x) = - f (x).
The function y = 2x ^ 3 complies with both definitions.
Answer:
an odd monomial function is:
A.y = 2x ^ 3
The function f(x)=15000(0.96)^x represents the value in dollars of a vehicle x years after it has been purchased new. What is the average decrease in value per year between years 5 and 10? Please show all work!
Answers
Value of the car after 5 years will be:
[tex]f(5)=15000 (0.96)^{5}=12230.59 [/tex]
Value of the car after 10 years will be:
[tex]f(10)=15000 (0.96)^{10}=9972.49 [/tex]
The decrease in the value of car will be:
[tex]f(5)-f(10)=2258.10 [/tex]
Average decrease in the value of car will be:
[tex] \frac{2258.10}{10-5}=451.62 [/tex]
Thus, on average the value of car decreases by $451.62 between year 5 and 10.
To find the average decrease in value per year between years 5 and 10 of a vehicle, we plug in x=5 and x=10 into the given function, subtract the values, and divide by 5.
Explanation:To find the average decrease in value per year between years 5 and 10, we need to calculate the difference in value between those two years and then divide it by the number of years.
First, we find the value of the vehicle in year 5 by plugging in x = 5 into the function:
f(5) = 15000(0.96)^5
solving this equation gives us the value of the vehicle in year 5.
Next, we find the value of the vehicle in year 10 by plugging in x = 10 into the function:
f(10) = 15000(0.96)^10
solving this equation gives us the value of the vehicle in year 10.
Finally, we subtract the value in year 10 from the value in year 5 and divide by 5 (the number of years) to get the average decrease in value per year.
In the figure below, triangle ABC is similar to triangle PQR, as shown below: What is the length of side PQ?
A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.
Answers
The corresponding side of QR is BC
BC = 2 and QR = 12
As you can see QR is 6 times longer than BC and so PQ should be proportional to AB by the same factor.
if AB is 4 then multiply that by 6:
4 x 6 = 24
Line PQ is 24
Answer:
Line PQ is 24
△FSB∼△ZDR .
What is the value of x?
Enter your answer.
How many units?
Answers
---------------------------------------------------------
Explanation:
The triangles are similar, so we know the corresponding sides form ratios that are equal.
Note how...
FS and ZD are the first two letters of FSB and ZDR respectively
FB and ZR are the first & last letters of FSB and ZDR respectively
Based on those two facts above, we can form this proportion
FS/ZD = FB/ZR
38/15.2 = 55/x
Solve for x
38/15.2 = 55/x
38*x = 15.2*55
38*x = 836
x = 836/38
x = 22
△FSB∼△ZDR
What is the value of x?
Enter your answer in the box.
____UNITS
Which is equivalent to (−2m + 5n)2, and what type of special product is it? 4m2 + 25n2; a perfect square trinomial 4m2 + 25n2; the difference of squares 4m2 − 20mn + 25n2; a perfect square trinomial 4m2 − 20mn + 25n2; the difference of squares
Answers
It expands to the trinomial 4m^2 -20mn +25n^2, a "perfect square trinomial."
A equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
What is expression?"It is a mathematical statement which consists of numbers, variables and some mathematical operations."
What is trinomial?"It is a polynomial which has only three terms."
What is perfect square trinomial?"When a trinomial can be factored into a binomial multiplied to itself, then its is a perfect square trinomial."
For given question,
We have been given a quadratic expression [tex](-2m + 5n)^2[/tex].
We need to find to find an equivalent expression to given expression.
Consider given expression,
[tex]\Rightarrow (-2m + 5n)^2 = (2m)^2-2(2m)(5n)+(5n)^2\\\\\Rightarrow (-2m + 5n)^2 =4m^2-20mn+25n^2[/tex]
We can observe that a trinomial [tex]4m^2-20mn+25n^2[/tex] is a perfect square trinomial.
Therefore, an equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
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At a wedding, there are 456 people spread out amongst 45 tables. There are no empty seats. The reception hall has tables that sit 12 people or 8 people. Write a system of equations that can be used to find the number of each type of table the restaurant has.
Answers
The system of equations is [tex]\[ \begin{cases} x + y = 45 \\ 12x + 8y = 456 \end{cases} \][/tex]
How did we arrive at this equation?
Let's denote the number of 12-person tables as [tex]\( x \)[/tex] and the number of 8-person tables as [tex]\( y \)[/tex]. Since there are 45 tables in total, we can express the first equation as:
[tex]\[ x + y = 45 \][/tex]
Now, considering the total number of people seated, we know that each person at a 12-person table occupies one seat, and each person at an 8-person table occupies one seat as well. The total number of people is 456. Therefore, the second equation is:
[tex]\[ 12x + 8y = 456 \][/tex]
So, the system of equations is:
[tex]\[ \begin{cases} x + y = 45 \\ 12x + 8y = 456 \end{cases} \][/tex]
These equations represent the conditions that the total number of tables is 45 and the total number of people seated is 456, with no empty seats.
-2⁄3 a − 6 = 12 a =?????????????/
Answers
-6=12a+2/3a
-6=38/3a
3/38*-6=a
-18/38=a
a=-9/19
a=-0.47
How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun?
Answers
The spinner can have the outcomes 1, 2, 3.
The total number of outcomes is the product of the individual numbers of outcomes.
2 * 2 * 3 = 12
Here's a way of thinking about it:
The coins can have these four outcomes:
HH
HT
TH
TT
For each of the 4 outcomes of the two coins, there are 3 different outcomes of the spinner, so the total number of possible outcomes is 4 * 3 = 12.
Answer:
12
Step-by-step explanation: