If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct characters (letters or numbers)
There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.
For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.
Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is
[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]
Pettit printing company has a total market value of $100 million, consisting of 1 million shares selling for $50 per share and $50 million of 10 percent perpetual bonds now selling at par. the company's ebit is $13.24 million, and its tax rate is 15 percent. pettit can change its capital structure by either increasing its debt to 70 percent (base on market value) or decrease it to 30 percent. if its decides to increase its use of leverage, it must call its old bonds and issue new ones with a 12 percent coupon. if it decides to decrease its leverage, it will call in its old bonds and replace them with new 8 percent coupon bonds. the company wills ell or repurchase stock at the new equilibrium price to complete the capital structure change. the firm pays out all earnings as dividends; hence; its stock is a zero growth stock. its current cost of equity, rs; is 14 percent. if it increases leverage rs will be 16 percent. if it decreases leverage, rs will be 13 percent. what is the firm's wacc and total corporate value under each capital structure?
The weighted average cost of capital for the firm will be 11.25%.
How to calculate the WACC?The weighted average cost of capital is the calculation of the cost of capital for a firm where each category of capital is weighted.
Here, the weighted average cost of capital will be:
= 0.5(10%)(1 - 15%) + 0.5(14%)
= 0.5(0.1)(0.85) + 0.5(0.14)
= 11.25%
The corporate value at 70% debt when WACC is 11.94% will be:
= (EBIT)(1 - T)/WACC
= (13.24)(1 - 0.15)/0.1194
= $94.26 million
The corporate value at 30% debt when WACC is 11.14% will be:
= (EBIT)(1 - T)/WACC
= (13.24)(1 - 0.15)/0.1114
= $101.02 million
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Using a trial and improvement method, find x correct to 1 decimal place.
3x² - x = 30
Answer:
x = 10/3
x = -3
Step-by-step explanation:
3x² - x = 30
3x² - x - 30 = 0
multiply 3 and -30 which =
-90
what are 2 numbers that when multiplied make
-90
and that when added make
-1
(-1 is the number in -x in the equation)
they are the numbers 9 and 10
namely -10 and +9
3(x-10/3)(x+9/3)=0
divide both sides by 3
(x-10/3)(x+9/3)=0
then split factors being multiplied
(x-10/3)=0
(x+9/3)=0
x = 10/3
x = - 9/3 = -3
Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]
So, the most specific classification is a rectangle
A fogpole casts a 13-foot shadow on the ground when the sun is at a 68° angle of elevation. Which of the following expressions can be used to determine the height (h), in feet, of the fogpole? (Assume the flagpole is perpendicular to the ground.) Draw a picture
Answer:
see below
Step-by-step explanation:
You didn't include the choices but here is a solution
tan 68 = opp/adj = height / 13
13 Tan 68 = height of pole
What is the summation notation for the geometric series 1/2+2+8+32+128?
Answer ( k=1 ∑ 5 ) 1/2(4)^k-1
The summation notation is ∑ [tex](4^{n} -1)\\[/tex]/2.
What is geometric progression?The common ratio multiplied here to each term to get the next term is a non-zero number.
Given: 1/2+2+8+32+128
Using,
[tex]a_n= a_1r^{n-1}[/tex]
We have,
a1 =1/2 and r= 4
notation is : An= ∑ [tex](4^{n} -1)\\[/tex]/2
Hence, the notation is An= ∑ [tex](4^{n} -1)\\[/tex]/2.
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Examine the steps used to solve the equation.
2
-3y += 2y-4
3
2
1.
3 = 5y-4
2
14=5y
3
14
(²) ¹/4 = (3) 5y
5
Intro
3.
Evaluate the steps used to solve the equation, and
then describe each step.
What is the solution to the equation?
Answer:
step1:add 3y to both sides
step2:add 4 to both sides
step3:multiply both sides by(1/5)
14/15
Step-by-step explanation:
What is the range of the function [tex]y=\sqrt[3]{x+8}[/tex]?
A. -∞ < y < ∞
B. -8 < y < ∞
C. 0 ≤ y < ∞
D. 2 ≤ y < ∞
Answer:
-∞ < y ∞
The range is all real numbers.
Segment BD is a median. Solve for x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
Answer: 10
Step-by-step explanation:
By definition, the point at which a median intersects the side of the triangle opposite from the vertex from which it is drawn is the midpoint of that side.
If x and y are supplementary angles, then x is _____ obtuse.
answer choices - always, sometimes, or never.
Answer:
sometimes
Step-by-step explanation:
a supplementary angle is "either of two angles whose sum is 180°".
So, x or y could be any degree, (less than 180 of course) and either one could be obtuse (>90) or acute (<90).
What is the quotient? startfraction t 3 over t 4 endfraction divided by (t squared 7 t 12)
A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The quotient of [tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}[/tex] can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,
t² + 7t + 12
= t² + 4t + 3t + 12
= t(t+4) +3(t+4)
= (t+4)(t+3)
Now, quotient will be,
[tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}[/tex]
Hence, the quotient of the fraction is 1/(t+4)².
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Give the domain and range.
X
-2
0
2
y
-1
0
1
a.
b.
domain: (2, 0, 2), range: (1, 0, 1)
domain: {-2, 0, 2), range: {-1, 0, 1)
domain: {-1, 0, 1), range: (-2, 0, 2}
d. domain: {1, 0, 1), range: {2, 0, 2)
C.
DI
at the host answer from the choices provided
1
2
3
4
5
Answer:
(b) domain: {-2, 0, 2}, range: {-1, 0, 1}
Step-by-step explanation:
For the function defined by the table ...
[tex]\begin{array}{|cccc|}\cline{1-4}x&-2&0&2\\\cline{1-4}y&-1&0&1\\\cline{1-4}\end{array}[/tex]
we want the function's domain and range.
__
domainThe domain is the list of x-values for which the function is defined. Here, that list is ...
domain = {-2, 0, 2}
__
rangeThe range is the list of y-values the function produces. Here, that list is ...
range = {-1, 0, 1}
_____
The domain and range sets are most conveniently listed in order, with duplicates removed.
How do i add and subtract
Answer:
take the dots and either put them together or rake them away
Step-by-step explanation:
Example: .....+..=....... five dots plus two dots equals seven dots.
......-...=... six dots minus three dots equals three since you are taking away three
i hope u found this helpful.
7. Write the equation -3x +2y = 7 in slope-intercept form.
Answer:
y = 3/2x + 7/2
Step-by-step explanation:
Slope-intercept form is when y is the subject. So we make y the subject:
Add 3x to both sides :
2y = 3x + 7
Now we divide both sides by 2 :
y = 3/2x + 7/2
This is our final answer.
Hope this helped and brainliest please
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to write the equation -3x+2y=7 in slope-intercept form.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The equation for slope-intercept form is y=mx+b, where m= slope (gradient) of the line, b=y-intercept of the lineSo let's write this equation, -3x+2y=7, in slope-intercept form...
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\///\\\////\\\///\\\///\\\////\\\\////\\\\
First, we add -3x to both sides of the equal sign:
[tex]\large\pmb{2y=7+3x}[/tex]
We can switch the order of the terms:
[tex]\large\pmb{2y=3x+7}[/tex]
This is starting to look like the slope-intercept equation. In fact, all we have to do is divide both sides by 2:
[tex]\large\pmb{y=(3x+7)\div2}[/tex]
Which simplifies to...
[tex]\large\pmb{y=\cfrac{3}{2}x+\cfrac{7}{2}}[/tex]
That's the equation in slope-intercept form.
Hope this helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Chester scored 84, 88, and 80 on his first 3 math tests. How can you find Chester's mean, or average, score on these tests?
Answer:
Add and Divide.
Mean = 84
Step-by-step explanation:
Mean ( math word) and average (common usage word) tell us to ADD up the numbers in the list of data and DIVIDE by the number of pieces of data.
Here we add:
(80 + 84 + 88)
then divide by 3, because there's 3 numbers in this list.
(80 + 84 + 88)/3
= 252/3
= 84
The mean, or average is 84.
The length of a rectangle is units greater than twice its width. if its width is w, which expression gives the perimeter of the rectangle in terms of w?
a. 2(5w/2) + w
b. 5w/2 + w
c. 3w + 10/2
d. 6w + 5
please help me quickly
Answer:
d
Step-by-step explanation:
the length is how many units greater than twice the width ?
you skipped that information from us.
so, all we can say
length = 2×width + x
the perimeter is
2×length + 2×width
with width = w we get by using the first equating in the second :
2×(2×w + x) + 2×w = 4w +2x + 2w = 6w + 2x
so the right answer must be d.
it is the only option with "6w".
it means that 2x = 5 and x = 2.5.
so it was that the length is 2.5 units greater than twice the width
−4(4x-6)= 3(-7x-1)
How do I solve this step by step when trying to solve for x?
[tex]-4(4x-6)=3(-7x-1)[/tex]
[tex]-16x+24=3\left(-7x-1\right) [/tex]
[tex]-16x+24=-21x-3 [/tex]
[tex]-16x+24+21x=-3 [/tex]
[tex]5x+24=-3 [/tex]
[tex]5x=-3-24 [/tex]
[tex]5x=-27 [/tex]
[tex]x=\frac{-27}{5} [/tex]
[tex]x=-\frac{27}{5} [/tex]
Explanation:
#CarryOnLearning
Sequence A: 4;9;16;25;36; ... ; ...
a) write the next two numbers
b) describe how sequence A is being formed
Answer:
49,64
Step-by-step explanation:
Every time the number changes there is an addition of two. for instance, from 4 to 9 the was an addition of 5 and from 9 to 16 there was an addition of 7. Thats how it works
Make f the subject of
m² = 3 ef
Answer:
below
Step-by-step explanation:
f. =. m²
------
3e
hope makes sense dive both sides by 3e to get f alone
Which number(s) below belong to the solution set of the equation? Check all
that apply.
X+ 6 = 45
A. 45
B. 39
C. 35
D. 3
E. 51
F.0
If ABCD is a parallelogram, which of the following statements must be true? (
Answer:
AB=CD and BC=AD because both of them are visually paired with the same longitude.
Answer:
AB = CD, BC = AD
Step-by-step explanation:
According to parallelogram properties,
Angle A = 180-Angle B; False
AB!=BC; False
AC==BD is only true when AB = BC, False
AB ==CD, BC == AD; True
HURRY GIVING BRAINLIEST
Answer:
12 or 7??
Step-by-step explanation:
it depends if they are being spinned at the same time because then you can get for eg. 'A,1' 'A2' etc.
Charlotte is buying milk. She can get 64 oz. for $3.00 or 80 oz. for $4.50. Which is the better deal, 64 oz. or 80 oz.?
Answer:
80 oz
Step-by-step explanation:
The Bloomington Bank has a height of 163 meters. Molly is making a scale model of this building using a scale of 125 meters: 1 meter. To the nearest tenth of a meter, what will be the height of the scale model?
The height of the scale model 1.304 scale units.
What is unit conversion?Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
Given:
The Bloomington Bank has a height of 163 meters.
Molly is making a scale model of this building using a scale of 125 meters.
125 meters = 1 scale unit
1 meter = 1/125 scale unit
So, for 163 meters = 1/125* 163
= 1.304 scale units.
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find the height of the trapezoid
Answer:
h = 19
Step-by-step explanation:
The are is given so we can use the area to find the height because the area of a trapezoid is calculated by the following formula:
1/2 * (a+b)*h (a: base, b: base, h: height)
We already know the bases; 37 and 51
1/2*(37+51)*h = 836 first multiply both sides by 2
(37+51)*h = 1672 now divide both sides by 88 (sum of bases)
h = 19
The equation of the line with slope = 3, going through point (2, 4) is:
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10[/tex]
1. How many ways can Grant arrange 3 of his 10 plants on a window ledge?
2. A parade organizer received 8 entries for floats. How many ways can he arrange 4 floats out of the 8 entries?
3. Express 4! in expanded form.
4. The number of ways 15 members of a 24-member club can be arranged. ( use permutation notation). PLEASE HELP ME!! and thankyou
The number of ways that Grant can arrange 3 of the 10 plants is 120 ways and the number of ways that 4 floats out of 8 can be arranged is 70 ways.
How can these combination problems be solved?Grant can arrange 3 out of 10 plants in the following number of ways:
= 10!/ ((10! - 3!)3!)
= ( 10 x 9 x 8) / (3 x 2)
= 120 ways
The parade organizer can arrange 4 floats out of 8 as:
= 8!/((8! - 4!)4!)
= (8 x 7 x 6 x 5) / (4 x 3 x 2)
= 70 ways
When 4! is written in expanded form, it comes out as:
= (4 x 3 x 2)
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Find the circumerference
Circumference = diameter x PI
Circumference = 8 in x Pi
Circumference = 8PI in. (Exact)
Or as a decimal answer: 25.12 in.
Answer:
25.1 in (nearest tenth)
Step-by-step explanation:
Formula
Circumference = πd (where d is the diameter)
From inspection of the diagram:
Diameter (d) = 8 in⇒ Circumference = 8π
= 25.1 in (nearest tenth)
I can write a system of linear equations and inequalities from context.
One smartphone plan costs $40 per month and an
extra $3.50 per gigabyte of data used each month.
Another smartphone plan costs $75 per month and
$0.50 per gigabyte of data used each month.
Let c represent the cost of a phone plan, m represent
number of months, and g represent the number of
gigabytes of data used each month. Write a system of
two linear equations that could be used to determine
the number of gigabytes used in a month so that the
two phone plans cost the same amount.
Equation 1:
Equation 2:
An equation is formed of two equal expressions. The number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let c represent the cost of a phone plan, m represent the number of months, and g represent the number of gigabytes of data used each month.
Equation1: C = 40m + 3.5mg = (40+3.5g)m
Equation2: C = 75m + 0.5mg = (75+0.5g)m
Equating C,
(40+3.5g)m = (75+0.5g)m
40 + 3.5g = 75 + 0.5g
3g = 35
g = 11.6667 gigabyte of data per month
Hence, the number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.
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Find the slope of the line graphed below.
to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]