Answer:
[tex]27,\!405[/tex] if:
The cards are drawn without replacement, All cards in this set are distinct from one another, andThe ordering of the four chosen cards does not matter.Step-by-step explanation:
[tex]\displaystyle \genfrac{(}{)}{0}{}{30}{4} = \frac{30 \times 29 \times 28 \times 27}{4 \times 3 \times 2 \times 1} = 27,\!405[/tex].
Assume for now that the ordering of the four cards does matter. Hands like [tex]\verb!A!\, \verb!B!\, \verb!C!\, \verb!D![/tex] and [tex]\verb!A!\, \verb!B!\, \verb!D!\, \verb!C![/tex] would then be considered different from one another.
There would [tex]30[/tex] choices for the first card. Since the first card was not returned to the pile, there would be only [tex]29[/tex] choices for the second card. Likewise, there would be [tex]28[/tex] choices for the third card and [tex]27[/tex] for the fourth.
By this reasoning, there would be [tex]30 \times 29 \times 28 \times 27 = 657,\!720[/tex] different ways to draw a hand of four cards from this set when the ordering of these four cards do matter.
However, in many card games, once a hand of cards is drawn, the ordering of cards within that hand does not matter. In other words, hands like [tex]\verb!A!\, \verb!B!\, \verb!C!\, \verb!D![/tex] and [tex]\verb!A!\, \verb!B!\, \verb!D!\, \verb!C![/tex] would not be considered as distinct from one another.
In that case, the [tex]30 \times 29 \times 28 \times 27 = 657,\!720[/tex] ways of drawing cards would include a large number of duplicates.
There are be [tex]4 \times 3 \times 2 \times 1 = 24[/tex] ways to arrange a hand of four cards when the order matter. Hence, when the ordering within a hand no longer matters, each hand of four cards would have been counted [tex]24[/tex] times among those [tex]30 \times 29 \times 28 \times 27 = 657,\!720[/tex] ways.
Therefore, when the ordering of cards within a set does not matter, [tex]\displaystyle \frac{30 \times 29 \times 28 \times 27}{4 \times 3 \times 2 \times 1} = 27,\!405[/tex] would give the number of distinct ways to draw a hand of four out of this set of thirty distinct cards.
In the 30-60-90 triangle below, side s has a length of__and side q has a
length of
30°
g
8
90°
60"
S
O A. 16-3,5
OB. 1613, 16-3
O C. 4,8-13
O D. 8-5, 16
O E. 4, 4.5
O F. 4/2, 412
Answer:
Option E, 4, 4√3
Step-by-step explanation:
s = 4
q = 4√3
How to find Joint and Combined variation?
Answer:
W is multiplied by 8
Step-by-step explanation:
If W varies jointly with x, y, and z, we can say that
W = k (xyz), with k being a constant for our original equation. We are asked what will happen to W if x, y, and z are each doubled. To figure this out, we can go back to our equation,
W = k (xyz)
First, we can double x, meaning that we multiply it by 2. Doing this, we get
W = k (2x * y * z)
Then, we can double y and z in a similar fashion, resulting in
W = k (2x * 2y * 2z)
W = 8 * k (xyz)
The new W, after all the doubling, is equal to 8 * k * x * y * z. The old W is equal to k * x * y * z. It can be determined that the new W is equal to 8 * the old W, so W is multiplied by 8
Find hyperbola equation. center (0,0) vertex (-2,0) focus (-5,0)
[tex] \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{21} = 1[/tex]
[tex] \frac{(x - h)^{2} }{ {a}^{2} } - \frac{(y - k) ^{2} }{ {b}^{2} } = 1 \\ [/tex]
a= (–2, 0) ; Center =(0,0)[tex]distance = \sqrt{(x2 - x1)^{2} + (y2 - y1) ^{2} } \\ a = \sqrt{(( - 2) - 0)^{2} + (0 - 0) ^{2} } \\ a = \sqrt{ {2}^{2} } \\ a = 2[/tex]C = (–5,0) ; Center =(0,0)[tex]distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } \\ c = \sqrt{(( - 5) - 0)^{2} + (0 - 0) ^{2} } \\ c = \sqrt{ {5}^{2} } \\ c = 5[/tex]
C²= a²+ b²(5)²= (2)² + b²b²= 25–4 —> b² = 21[tex]b = + \sqrt{21} , - \sqrt{21} [/tex]
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{0 - 0}{0 - ( -5 )} = 0[/tex]
[tex] \frac{(x - h)^{2} }{ {a}^{2} } - \frac{(y - k) ^{2} }{ {b}^{2} } = 1 \\ [/tex]
[tex]\frac{(x - 0)^{2} }{ {2}^{2} } - \frac{(y - 0) ^{2} }{ { \sqrt{2} }^{2} } = 1 \\ [/tex]
[tex] \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{21} = 1[/tex]
I hope I helped you^_^
Pls give this anwere with explanation spammer will be reported
Answer:
Whole number —> X
Twice the square of the number —> 2X²
X + 2X² = 10
2X²+X –10 =0
(2x + 5) ( x–2) =0
2x +5=0 —> 2x= – 5 —> x= – 5/2 = —> x= - 2.5 (rejected)
x–2=0 —> x= 2
So Ans ; X= 2 ( the number )
I hope I helped you^_^
Is the relationship shown by the data linear? If so, model the data with an equation.
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
What is the volume of a cylinder with a radius of 2 ft and a height of 8 ft.
Use 3.14 for pi, round your answer to the nearest hundredth if necessary, and do not include units.
Answer:
100.48
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = 3.14 ( 2)^2 * 8
V = 3.14 (4)(8)
V = 100.48
A person of height 2m observes the angle of elevations of the top of a Pole 62m height which is in front of him and finds it to be 45. find the distance between the person end the pole .
I need the answer explained
Answer:
1.33
Step-by-step explanation:
62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.
find the value of x. help with geometry pls
Answer:
Find the value of x:-
To find Y, use Pythagorean theorem:- [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex](2.1)^{2} =y^{2} +(1.4)^{2}[/tex]
[tex]2.1^{2}=4.41[/tex]
[tex]1.4^{2} =1.96[/tex]
[tex]4.41=y^{2} +1.96[/tex]
subtract 1.96 from both sides
[tex]2.45=y^{2}[/tex]
[tex]y=1.5652[/tex]
Now, to find x:-
[tex]x=y+y[/tex]
[tex]= 1.5632+1.5652[/tex]
[tex]x=3.1 \: ft[/tex]
~OAmalOHopeO
how many 50 cents coins are there in $10:50
Question:- how many 50 cents coins are there in $10.50
Answer:-
Total amount-> $ 10.50
So amount in cents
$ 1 is equal to 100 cents
$10.50 is equal to 1050 cents
According to the question
[tex]Number \: of \: the \: 50 \: cents= \frac{ Total \: cents}{ 50 \: cents } \\ [/tex]
[tex]Number \: of \: the \: 50 \: cents = \frac{1050}{50} \\ Number \: of \: the \: 50 \: cents = 21 \: [/tex]
Hi! Can you help me answer this?
Answer:
[tex]C'(x)=-\frac{148}{x^2}[/tex]
[tex]R'(x)=-0.06[/tex]
Step-by-step explanation:
Marginal average Cost function:
[tex]\frac{d}{dx}(\frac{148+6.3x}{x})=-\frac{148}{x^2}[/tex]
Marginal average Revenue function:
[tex]\frac{d}{dx}(\frac{3x-0.06x}{x})=-0.06[/tex]
Answer:
Step-by-step explanation:
yess
Write the equation of the line that passes through the points (- 4, - 3) and (3, - 5) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Help:(
Answer:
y = (-2/7)x - (29/7)
Step-by-step explanation:
look at the image below
Answer:
1520.5 yd²
Step-by-step explanation:
Surface area of a sphere = 4πr², where r is the radius
so,
4πr²
= 4×π×11²
= 484π
= 1520.5 yd²
PLEASE HELP
-6/5k = 12
Show your work in details if you can, I have a hard time understanding this.
[tex] \begin{cases}\large\bf{\green{ \implies}} \tt \: \frac{6}{5} \: k \: = \: 12 \\ \\ \large\bf{\green{ \implies}} \tt \: \frac{6k}{5} \: = \: 12 \\ \\ \large\bf{\green{ \implies}} \tt \: 6k \: = \: 12 \: \times \: 5 \\ \\ \large\bf{\green{ \implies}} \tt \: 6k \: = \: 60 \\ \\ \large\bf{\green{ \implies}} \tt \: k \: = \: \cancel\frac{60}{6} \\ \\ \large\bf{\green{ \implies}} \tt \: k \: = \: 10 \end{cases}[/tex]
Answer:
k = -10
Step-by-step explanation:
In order to solve for k, we need to isolate the variable. This means we need k to be on one side of the equation by itself.
We are given:
[tex]-\frac{6}{5}k=12[/tex]
The first thing I would do is multiply both sides of the equation by 5:
[tex](5)-\frac{6}{5}k=12(5)[/tex]
This leaves us with:
[tex]-6k=60[/tex]
Now, in order to get k by itself, we need to divide by -6 on both sides:
[tex]\frac{-6k}{-6}=\frac{60}{-6}[/tex]
Therefore:
[tex]k=-10[/tex]
Previous studies suggest that use of nicotine-replacement therapies and antidepressants can help people stop smoking. The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment.
In this experiment researchers randomly assigned smokers to treatments. Of the 162 smokers taking a placebo, 28 stopped smoking by the 8th day. Of the 272 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day.
Calculate the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment). (The standard error is about 0.0407. Use critical value z = 2.576.)
( ), ( )
Round your answer to three decimal places. Put lower bound in the first box and upper bound in the second box.
Using the z-distribution, it is found that the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm zs[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.s is the standard error.In this problem, we are given that z = 2.576, s = 0.0407. The sample mean is the difference of the proportions, hence:
[tex]\overline{x} = \frac{28}{162} - \frac{82}{272} = -0.129[/tex]
Then, the bounds of the interval are given by:
[tex]\overline{x} - zs = -0.129 - 2.576(0.0407) = -0.234[/tex]
[tex]\overline{x} + zs = -0.129 + 2.576(0.0407) = -0.024[/tex]
The 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
More can be learned about the z-distribution at https://brainly.com/question/25890103
simplify using distributive property
2396 X 78 + 2396 X 22
Answer:
239600Step-by-step explanation:
2396 × 78 + 2396 × 22 =2396 × (78 + 22) =2396 × 100 =239600[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]
[tex]\\ \sf\longmapsto 2396\times 78 +2396\times 22[/tex]
[tex]\\ \sf\longmapsto 2396(78+22)[/tex]
[tex]\\ \sf\longmapsto 2396(100)[/tex]
[tex]\\ \sf\longmapsto 239600[/tex]
The sum of twice a number and 3 times the same number as 40. What is the number?
Answer:
Let the number be x
According to Question ,
2x + 3x = 40
5x = 40
x = 8
therefore , the number is 8
hope that helps uh...☺
Please Help I will give you a lot of points if you do!
Recall that a ⇒ b ⇔ ¬a ∨ b. So we can write
q ⇒ (p ∧ r ) ⇔ ¬q ∨ (p ∧ r )
Then the negation of this would be, for instance,
¬(¬q ∨ (p ∧ r )) ⇔ ¬(¬q) ∧ ¬(p ∧ r )
… ⇔ q ∧ (¬p ∨ ¬r )
… ⇔ (¬p ∧ q) ∨ (q ∧ ¬r )
… ⇔ ¬(p ∨ ¬q) ∨ (q ∧ ¬r )
… ⇔ (p ∨ ¬q) ⇒ (q ∧ ¬r )
It's impossible to tell what kind of statement your program is expecting, but since there are 5 slots available, my money would be on q ∧ (¬p ∨ ¬r ), so long as ¬p and ¬r are options.
solve and reduce to lowest term 7/13+3/13
Answer:
Step-by-step explanation:
10/13
Answer: 10/13
Explanation:
= 7/13 + 3/13
Its like fraction
= 10/13
Its already in lowest terms
Must click thanks and mark brainliest
Sets L and M are defined as follows.
L={-1,1,4,5,7,8)
M={1,2,7)
Answer each part below. Write your answer in roster form or as Ø.
(a) Find the union of L and M.
(b) Find the intersection of L and M
Answer:
the union of l and m is minus 1,1,2,4,5,7,8.....and the intersection of l and m is 1.......
help please I need help
pls
Answer:
23. -9+2y
24. 6x=5
Step-by-step explanation:
27-6y/-3
3(9-2y)/-3
-(9-2y)
-9+2y
2(6x+5)/2 . cancel 2
6x+5
Answer: (Depends what grade you're in)
Step-by-step explanation:
HLP HLP 10 10 10 HLP HLP HLP
W
Answer:
A. 6²¹
Step-by-step explanation:
When you have a number raised to the power in that form, you have to multiply the powers:
(6⁷)³
7×3 = 21
(6⁷)³ = 6²¹
Answer:
A. 6 raise to 21
Step-by-step explanation:
its a formula if:
a raise to m whole raise to n = a raise to m×n
so here
6 raise to 7 × 3
that is 6 to the power of 21
the perimeter of a square room is 48m,how much square carpet is requried to cover it ?
Answer:
144
Step-by-step explanation:
perimeter of square=48 ( formula= 4*a )
a= 48/4
= 12
area= a*a
=12*12
=144
if chaka,ada and ese are to share 120 oranges with the ratio of 1:2:3 respectively. How many oranges does ada have?.
Answer:
40
Step-by-step explanation:
1+2+3=6
1/6×120=20
2/6×120=40
3/6×120=60
I need step by step solution.
Answer: it is an exponential decay function
Step-by-step explanation:
Since 0.3 is less than 1 then increasing the value of the x will lead to the decrease of the value function y
please help me!
find x
Answer:
√13 miles
Step-by-step explanation:
Using Pythagorean Theorem,
h^2=p^2+b^2
Here,
h=x
p=2miles( taking the angle opposite to 2miles as reference)
b=3miles
Now,
x^2=2^2+3^2
x=√(4+9)
x=√13 miles
(a + b + c) power of 10 - abc
Tip
A=1
B=2
C= -3
[tex]\\ \rm\longmapsto (a+b+c)^{10}-abc[/tex]
[tex]\\ \rm\longmapsto (1+2-3)^{10}-(1)(2)(-3)[/tex]
[tex]\\ \rm\longmapsto (3-3)^{10}+6[/tex]
[tex]\\ \rm\longmapsto 0^{10}+3[/tex]
[tex]\\ \rm\longmapsto 0+3[/tex]
[tex]\\ \rm\longmapsto 3[/tex]
(a+b+c)^10-abc
= (1+2-3)^10-(1×2×-3)
= 0- (-6)
=6 answer.....
8th grade math
A box of chocolates contains 3 milk chocolates 2 dark chocolates, and 1 white chocolate You randomly select and eat three chocolates What is the probability that the first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate
Answer:
10 Milk chocolates
8 dark chocolates
6 white chocolates
24 TOTAL
\frac{10}{24} Probability that Hanissa choose a milk chocolate
Now, since she has already eaten one chocolate, then what's left is 23 chocolates.
So, since the second one should be a white chocolate and there are 6 of them, then
\frac{6}{23} - probability of choosing a white chocolate.
Then, multiply,
( \frac{10}{24} )( \frac{6}{23} )= \frac{60}{552} or \frac{5}{46}
Answer: 5/46 or 10.87%
Step-by-step explanation:
Answer: there is 1/2 chance of your first being milk chocolate, 1/3 chance your second will be drake and 1/6 chance it will be white chocolate
Step-by-step explanation:
Convert 16,000 feet per second into kilometers per hour. step by step
Factor the following
9t^2-42t+49
Answer:
(3t -7)²
Step-by-step explanation:
We know that the square of a binomial is ...
(a -b)² = a² -2ab +b²
So, when we see the first and last terms are both perfect squares, we suspect that the trinomial is a perfect square trinomial.
9t² = (3t)²
49 = 7²
-42t = -2(3t)(7) . . . . confirming we have a perfect square
The factorization is ...
(3t -7)²
