Answer:
[tex]Pr = 0.4286[/tex]
Step-by-step explanation:
Given
Let
[tex]U \to\\[/tex] Undergraduates
[tex]G \to[/tex] Graduates
So, we have:
[tex]U = 3; G =5[/tex] -- Total students
[tex]r = 4[/tex] --- students to select
Required
[tex]P(U =2)[/tex]
From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.
First, we calculate the total possible selection (using combination)
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
So, we have:
[tex]Total = ^{U + G}C_r[/tex]
[tex]Total = ^{3 + 5}C_4[/tex]
[tex]Total = ^8C_4[/tex]
[tex]Total = \frac{8!}{(8-4)!4!}[/tex]
[tex]Total = \frac{8!}{4!4!}[/tex]
Using a calculator, we have:
[tex]Total = 70[/tex]
The number of ways of selecting 2 from 3 undergraduates is:
[tex]U = ^3C_2[/tex]
[tex]U = \frac{3!}{(3-2)!2!}[/tex]
[tex]U = \frac{3!}{1!2!}[/tex]
[tex]U = 3[/tex]
The number of ways of selecting 2 from 5 graduates is:
[tex]G = ^5C_2[/tex]
[tex]G = \frac{5!}{(5-2)!2!}[/tex]
[tex]G = \frac{5!}{3!2!}[/tex]
[tex]G =10[/tex]
So, the probability is:
[tex]Pr = \frac{G * U}{Total}[/tex]
[tex]Pr = \frac{10*3}{70}[/tex]
[tex]Pr = \frac{30}{70}[/tex]
[tex]Pr = 0.4286[/tex]
Una empresa que trabaja en un mercado de competencia perfecta tiene una función de costos totales CT=Q^3-45Q^2+600Q+1.200 Las funciones de oferta y demanda de este mercado son: Qo=5P-300 y Qd=2.860-8P. Recuerde que la condición para maximizar beneficios dice que la empresa habrá de producir una cantidad tal que haga igualar sus costos marginales con el precio de equilibrio de mercado.
Answer:
La cantidad producida para maximizar las ganancias es de 915 unidades
Step-by-step explanation:
Pregunta: Calcule cuánto producirá para maximizar las ganancias.
La función de costo dada se presenta de la siguiente manera;
CT = Q³ - 45 · Q² + 600 · Q + 1200
La función de suministro es Qo = 5 · P - 300
La función de demanda es Qd = 2860 - 8 · P
A precio de equilibrio, tenemos;
Qo = Qd
Por lo tanto;
5 · P - 300 = 2860 - 8 · P
13 · P = 2.860 + 300 = 3.160
P = 3160/13
Por lo tanto;
Q = 2860 - 8 × (3160/13) = 11900/13 ≈ 915,38
La cantidad producida que maximiza las ganancias es de aproximadamente 915 unidades.
El costo total CT = 915³ - 45 × 915² + 600 × 915 + 1200 = 728,935,950
find k so that x^2+2x+k is a factor of 2x^4+x^3-14x^2+5x+6. also find all the zeroes of the two polynomial
Compute the quotient and remainder,
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]
The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means
[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]
and
[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]
Only k = -3 makes both remainder terms vanish.
Then the previous result reduces to
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]
so that
[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]
and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.
Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
201.1 km^3
Step-by-step explanation:
The volume of a cylinder is V=πr2h. In this problem, our radius is 8, and our heigh is 4. Plugging in our values we get:
V=π(8)(2)(4)=64π, which is approximately 201.1.
Hope this helped,
~cloud
Answer:
804.2 km^3
Step-by-step explanation:
Volume of cylinder = πr^2h
π(8)^2(4)
= 804.247719319
Rounded of to nearest 10th = 804.2 km^3
Answered by G a u t h m a t h
A 10-foot ladder rests against a vertical wall. Let x be the distance from the bottom of the ladder to the wall and y be the distance from the floor to the top of the ladder. If the bottom of the ladder slides away from the wall, how fast does the top of the ladder fall down the wall with respect to x
Answer:
The rate of change of the top of the ladder with respect to x is -x/y
Step-by-step explanation:
The given parameters are;
The length of the ladder = 10 ft.
The horizontal distance of the bottom of the ladder from the wall = x
The distance of the top of the ladder from the floor = y
By Pythagoras's theorem, we have;
10 = y² + x²
Therefore, we have;
x² = 10 - y²
d(x²)/dx = 2·x = d(10 - y²)/dx = -2·y·dy/dx
∴ 2·x = -2·y·dy/dx
dy/dx = 2·x/(-2·y) = -x/y
Therefore, the rate of change of the top of the ladder with respect to x, dy/dx = -x/y.
1. Write three different solutions of 4x - 2y = 8. plzz answer fast
Answer:
y=-4+2x
x=(4+y)/2
2x-y=4
Find cos A and cot B exactly if a=15 and b=11 , what will Cos A be and Cot B be?
Answer:
D. <15/√346>
Have a nice day! :)
Find the interior angle sum for the following polygon
Find the area of the shaded regions:
Answer:
84.78
Step-by-step explanation:
Used calculator and formula
what is the mass of raisins in a package
Answer:
Step-by-step explanation:
12
Find the value of y. Round
the nearest tenth.
Answer: 178.3
Step-by-step explanation:
Use cos to find the value of x: cos(27)=350/x
You will find x = 392.81
Using this value, find sin(27): Sin(27)=y/392.81
You will find y=178.33
Rounding to the nearest tenth, you get 178.3
james cuts his neighbor's lawn the first is 1000 m long and 100 m wide what is the area
Answer:
100,000 m²
Step-by-step explanation:
the area = l x w = 1000 x 100 = 100,000 m²
hlpppppp plesaseeeeeeeeeeeeeeeee
Answer:
50
Step-by-step explanation:
Given,
96 + 2² / 2
96 + 4 / 2
100 / 2
50
determine the dimension of cube when the volume is 1.468mcube
Answer:
1.137 m
Step-by-step explanation:
The volume of a cube is given as the cube of the side. A cube is a 3 dimensional shape with equal sides and 6 faces. If the volume is V and the side is s then
V = s * s * s
Given that the volume is 1.468mcube then
s^3 = 1.468
s = cube root of 1.468
= 1.137 m
(4,-5) with slope of 2
that's a point slope form so
y +5 = 2(x -4)
You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
No; the red marble was not replaced, so it has an effect on drawing a second marble.
Yes; you may not get a red marble again.
No; you do not know which marble you will draw next.
Yes; the red marble was kept out, so you can not draw it again.
Answer:
the red marble was kept out so you can not draw it again
Answer:
Yes; you may not get a red marble again.
Step-by-step explanation:
there is a chance to get a red marble but it is not high
How many solutions exist for the mixed-degree system graphed below?
Answer:
The answer is one.
Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two
Answer:
The shortest side of the triangle is 18
Step-by-step explanation:
Let the sides the triangle be x, y and z.
From the question, the perimeter of the rectangle is 64, that is
x + y + z = 64 ...... (1)
Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)
The third side, z, is 20 less than the sum of the other two, that is
z + 20 = x + y ...... (3)
Substitute equation (3) into (1)
Then,
z + 20 + z = 64
2z +20 = 64
2z = 64 - 20
2z = 44
z = 44/2 k
z = 22
From equation (3)
z + 20 = x + y
Then, k
22 + 20 = x +y
42 = x + y
x = 42 - y ...... (4)
Substitute this into equation 2
3x = 4y
3(42-y) = 4y
126 - 3y = 4y
4y + 3y = 126
7y = 126
y = 126/7
y = 18
Substitute this into equation (4)
x = 42 - y
x = 42 - 18
x = 24
∴ x = 24, y = 18 and z = 22
Hence, the shortest side of the triangle is 18.
Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. Suppose that we select random samples from this population of American adults ages 25 and older. For each sample we then calculate the proportion that had never been married.
For which of the following sample sizes will the sampling distribution be approximately normal?
Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center. http://www.pewsocialtrends.org/2014/09/24/record-share-of-americans-have-never-married/
A) 25
B) 50
C) 75
Answer:
B. 50
Step-by-step explanation:
Central limit theorem is used to calculate the sampling distribution of the given case. The number of adults who are 25 years of age or above and not married is 20% of the samples selected. The standard deviation is 0.06 while the sample size should be 50 to conclude the results.
Find the missing segment in the image below
Answer:
Step-by-step explanation:
What is the sum of the interior angles of the octagon below?
Select one:
a. 360°
b.720°
C. 1,080
d. 800
Answer:
Option C, 1,080
Step-by-step explanation:
sum of the interior angles of the octagon,
(8-2)×180
= 6×180
= 1080
Answered by GAUTHMATH
PLEASE HELP! DUE TODAY :))
Step-by-step explanation:
do like the picture I sent
In the adjoining fig. In a circle with centre C and chord DE ,ahe CF perpendicular to chord DE.If diameter of a circle is 20cm and DE=16cm,then CF=?GIVE REASON
DC=CF
Diameter=20cmRadius=20/2=10cmWe know
[tex]\boxed{\sf L=\dfrac{\theta}{180}\times πr}[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{90}{180}\times \dfrac{22}{7}\times 10[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{1}{2}\times \dfrac{220}{7}[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{110}{7}[/tex]
[tex]\\ \large\sf\longmapsto L=15.5[/tex]
Now
[tex]\\ \large\sf\longmapsto CF=L+r-DE[/tex]
[tex]\\ \large\sf\longmapsto CF=15.7+10-16[/tex]
[tex]\\ \large\sf\longmapsto CF=25.7-16[/tex]
[tex]\\ \large\sf\longmapsto CF=9.7cm[/tex]
[tex]\large\sf\red{⟼L=18090×722×10}[/tex]
[tex]\begin{gathered}\\ \large\sf\red{ ⟼ L=\dfrac{1}{2}\times \dfrac{220}{7}}\end{gathered}[/tex]
[tex]\begin{gathered}{ \large\sf\red{⟼ L=\dfrac{110}{7}}\end{gathered}[/tex]
⟼ L=15.5
Now
⟼ CF=L+r−DE
⟼ CF=15.7+10−16
⟼ CF=25.7−16
⟼CF=9.7cmLet g(x) = f (x+1) - 2, find when g(x) = 12
I don't know how to evaluate this since I have both g(x) and an f(x).
Answer:
f(x +1 ) =14
Step-by-step explanation:
12= f(x +1) -2
f(x +1) = 12 +2
f (x+1 ) = 12
Which lists all of the shapes that are in a two-dimensional net of a square pyramid? 6 squares 4 triangles 1 square and 3 triangles 1 square and 4 triangles
Answer:
4 triangles and 1 square
Step-by-step explanation:
Required
The shapes in two-dimensional net of a square pyramid
To do this, I will attach an attachment of a 2D net of a square pyramid (see attachment)
From the attachment, we can see that:
The 2d shape of the pyramid is made of 4 triangles and 1 square
Answer:
D
Step-by-step explanation:
58×62 without actual multiplication
Answer:
3596
Step-by-step explanation:
Use long multiplication to evaluate.
Answer:
3596
Step-by-step explanation:
(58*10) = 580
580*6 = 3480
58 * 2 = 116
3480 + 116 = 3596
is 23/17 a rational number?
Answer:
rational number
Step-by-step explanation:
a rational number can be written as a/b where a and b are integers
23/17 = a/b where a = 23 and b = 17
This is a rational number
15) The sum of one-fourth, one-ninth and one- third of a number is 25. Find the number.
Answer:
Step-by-step explanation:
(1/4 + 1/9 + 1/3)x = 25.
x = 36
Answer:
Let the number be x
(1/4 + 1/9 + 1/3) * x = 25
25/36 * x = 25
25x = 25*36
x = 25*36/25
x = 36
Step-by-step explanation:
What is 200% of 20? Thanks!
Answer:
40
Step-by-step explanation:
200% x 20
200/100 x 20
(200 ÷ 100) x 20
200 x 20 ÷ 100
4,000 ÷ 100 = 40
I need help solving this
Answer:
E. 248
Step-by-step explanation:
1 to 500 in set A, 250 to 750 in set B
500 - 250 = 250
100 and 200 are divisible by 100.
250 - 2 = 248
Find the value of x. PLEASE HELP ASAP!
A.4
B. 16
С. 5
D. 12
Answer: x>12
so i think x is 16.
