Answer:
A) 1/n²
B) (n - 1)/n²
C) Probability = (1 - (1/n))/2
Step-by-step explanation:
A) We are told that a ticket is drawn at random from the box. Thereafter, the ticket is replaced in the box and a second ticket is now drawn at random.
This means the events of the first and second tickets are independent.
Probability of first ticket = 1/n
Probability of 2nd ticket = 1/n
Probability of both together = 1/n × 1/n = 1/n²
B) The number on the 2 tickets are consecutive integers.
This means number of cases will be (n - 1)
From a above, we see that for the two tickets the denominator is n²
Thus, in this case, the probability that both that the numbers on the two tickets are consecutive integers = (n - 1)/n²
C) if we assume that the first ticket is b, then the number of correct selections for the 2nd ticket is (n - b).
Thus, number of correct selections is;
(n_Σ_k=1) (n - b) = n² - (n(n - 1)/2)
Simplifying this gives;
(2n² - n² - n)/2
>> ½(n² - n)
There are n² selections in total, thus let's factorize n² out and then the remaining part in bracket will be the probability. Thus;
>> n²(1 - (1/n))/2
Probability = (1 - (1/n))/2
Caroline puts $400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is the time in years. Solve algebraically after how many years she will get $1200 in her account (round it to the nearest year).
Answer: 19 years
Step-by-step explanation:
Given
Amount invested [tex]\$400[/tex]
Rate of interest [tex]R=6\%[/tex]
after 1-year amount becomes
[tex]A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400\times 1.06\\A=\$424[/tex]
After n years it is
[tex]A=400\left (1.06\right)^n[/tex]
Sum accumulated is [tex]\$1200[/tex]
[tex]\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=\dfrac{\ln 3}{\ln 1.06}\\\\\Rightarrow n=18.85\approx 19\ \text{years}[/tex]
There are 2,598,960 possible 5-card hands that can be dealt from an ordinary 52-card deck. In a 5-card hand of poker, a flush is a hand where all 5 cards are of the same suit. Assuming a well-shuffled deck of cards and a random deal, what is the probability of being dealt a flush
Answer:
The answer is "0.0019808"
Step-by-step explanation:
[tex]\to \text{P(deall a flush) =P(select one of 4 suits and then select 5 out of 13 cards from this suit)}[/tex]
[tex]=(4\ C_1)\times \frac{(13\ C_5)}{(52\ C_5)} \\\\=4\times \frac{1287}{2598960}\\\\=0.0019808[/tex]
2x is subtracted from the square of a number
Answer:
let the number be x
x²-2x=0
here it is your quadratic equation
Tim's grandmother recently gave him 25 shares of
preferred stock. Tim would like to figure out the actual
dollar amount of the dividend, which is a percentage of
the par value of the sock.
The par value of each share is $45.00
The dividend rate is 8%
What is the total dollar amount that Tim should receive
each year?
Answer:
According to the stock certificates that Kwame's grandmother gave to him, the par value of each share is $45 and the dividend rate is 6 ...
Step-by-step explanation:
correct me if I'm wrong. C:
#CARRYONLEARNINGIvan wants to fill with foam the empty space left in a cube-shaped box after he places a basketball in the box. How many cubic inches of foam is needed if the radius of the basketball is 4.75 in. and the sides of the box are each 9 in.? Use 3.14 for π, and round your answer to the nearest whole number. in.3
Answer:
280 cubic inches
Step-by-step explanation:
Cubic inches of foam required = volume of the box - volume of the basketball
The box has a shape of a cube, so that;
volume of the box = [tex]l^{3}[/tex]
where l is the length of the sides of the box.
volume of the box = [tex]9^{3}[/tex]
= 729 cubic inches
volume of the box = 729 cubic inches
The basketball has the shape of a sphere, so that;
volume of the basketball = [tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x 3.14 x [tex](4.75)^{3}[/tex]
= 448.693
volume of the basketball = 448.693 cubic inches
Thus,
cubic inches of foam required = 729 - 448.693
= 280.307
The cubic inches of foam to be used is 280 cubic inches.
describe and correct the error in solving the equations below
9514 1404 393
Answer:
19. wrong multiplier was used, and used incorrectly; x = -324
20. wrong multiplier was used, and used incorrectly; y = 5
Step-by-step explanation:
In each case, the equation was multiplied by the coefficient of the variable, instead of divided. In each case, the square of the coefficient was evaluated incorrectly (so the error wasn't noticed).
__
19) As described above.
(-36)(9) = (x/9)(9)
-324 = x
__
20) In addition to the errors described above, the variable was changed from y to x.
15/3 = (3y)/3
5 = y
In ΔWXY, the measure of ∠Y=90°, YX = 40, XW = 41, and WY = 9. What ratio represents the cosine of ∠W?
Answer:
[tex]\cos(W) = \frac{9}{41}[/tex]
Step-by-step explanation:
Given
[tex]\angle Y = 90^o[/tex]
[tex]YX = 40; XW = 41; WY = 9[/tex]
Required
Determine [tex]\cos(W)[/tex]
The question is illustrated with the attached image.
So:
[tex]\cos(W) = \frac{Adajacent}{Hypotenuse}[/tex]
[tex]\cos(W) = \frac{WY}{XW}[/tex]
This gives:
[tex]\cos(W) = \frac{9}{41}[/tex]
Bag A has five red marbles and two green ones. Bag & has seven red
marbles and three green ones.
Which bag has the greater probability of drawing a green marble?
Answer:
bag B
Step-by-step explanation:
bag A: 5R and 2G
bag B: 7R and 3G
Bag A probability for green is 2/7
bag B probability for green is 3/10
if we convert the fractions to have a common denominator:
bag A: 20/70
bag B: 21/70
so bag B has the greater probability of drawing a green marble
What is the best description of the data?
Height Tally Frequency
65" | 1
66" | 1
67" |||| 9
68" ||| 8
69" ||| 3
70" || 2
71" | 1
Six students are taller than 68 inches.
Most of the students are 67 inches tall.
One student is 65 inches tall.
Most of the students are 67 or 68 inches tall.
Answer: Most of the students are 67 or 68 inches tall.
Step-by-step explanation:
From the information given, option A is correct as six students are taller than 68 inches.
Also, most of the students are 67 inches tall since there are 9 students who are 67 inches tall. Also, only one student is 65 inches tall.
The best description of the data is that most of the students are 67 or 68 inches tall. 9 students are 67 inches tall while 8 students are 68 inches tall. This means 17 out of 25 students have those heights. Therefore, most of the students are 67 or 68 inches tall is the correct option.
Only six students (24 percent) are taller than 68 inches.
According to provided data set consisting of height measurements for a group of students.
The data has been organized into a tally chart,
with each tally representing one student's height falling within a particular category.
To analyze this data further,
we can calculate the cumulative frequency for each height category.
The cumulative frequency is the sum of the frequencies up to and including the current category.
Using the provided data,
we can calculate the cumulative frequency as follows,
65" | 1 |
cf = 1 66" | 1 |
cf = 2 67" |||| 9 |
cf = 11 68" ||| 8 |
cf = 19 69" ||| 3 |
cf = 22 70" || 2 |
cf = 24 71" | 1 |
cf = 25
Based on this data,
we can make several observations.
Firstly, there is only one student who is 65 inches tall.
Secondly, most of the students (44% or 11 out of 25) are 67 inches tall, with a similar number (32% or 8 out of 25) being 68 inches tall.
Finally, only six students (24%) are taller than 68 inches.
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How high is the end of the ladder against the building?
Answer:
D.
Step-by-step explanation:
its a right triangle, so we can use the pythagorean theorem to find h
(pythagorean theorem is a^2+b^2=c^2, c is the hypotenuse)
h^2+4^2=13^2
h^2+16=169
h^2=153
h=sqrt153
h≈ 12.4ft
NO LINKS!! PART 2a. Find the measure of the arc or angle indicated.
9514 1404 393
Answer:
2) 198°
4) 99°
6) 90°
Step-by-step explanation:
The relevant relations are ...
an inscribed angle is half the measure of the arc it interceptsthe total of arcs around a circle is 360°__
2) Arc WXY = 2×angle WDY = 2(99°) = 198°
__
4) Arc CLE is 2×angle CDE = 2(97°) = 194°
Arc DE = 360° -72° -194° = 94°
angle C = (arc DE +arc EL)/2 = (94° +104°)/2 = 99°
__
6) angle C = (360° -arc EC -arc CD)/2 = (360° -71° -109°)/2 = 90°
Answer:
2.
Given:
m arc WXY=2×99°=198°[central angle is equal to the twice of its inscribed angle]
4.Arc CLE =2x< CDE = 2×97° = 194°[central angle is equal to the twice of its inscribed angle]
again
Arc DE =360° -72° -194° = 94°[from complete turn]
and
angle C =½ (arc DE +arc EL) =½ (94° +104°) = 99°
6) angle C =½ (360° -arc EC -arc CD)
=½ (360° -71° -109°)= 90°
Can someone help me out with my grades are bad
What is the volume of the rectangular prism?
consider the series 1/4+1/16+1/64+1/256
The expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
What is a series?A sequence is defined as an arrangement of numbers in a particular order. A series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers.
For the given situation,
The series is 1/4 + 1/16 + 1/64 + 1/256.
⇒ [tex]\frac{1}{4}+\frac{1}{16} +\frac{1}{64} +\frac{1}{256}[/tex]
⇒ [tex]\frac{1}{4}+\frac{1}{4^{2} } +\frac{1}{4^{3} } +\frac{1}{4^{4} }[/tex]
Thus the sum of this series can be obtained by the expression,
[tex]S_{n}= \lim_{n \to \infty} (\frac{1}{4^{n}})[/tex]
⇒ [tex]S_{n}= \lim_{n \to \infty} (\frac{1}{4})^{n}[/tex]
Hence we can conclude that the expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
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HELP 50 POINTS
FOX ≅ ∆ELK… so what’s m?
Find the slope of the line graphed below
Answer:
the answer to this equation is
4,4
plz solve this question mhanifa
Answer:
(3 - 4i) / (3 + 4i) + (3 + 4i) / (3 - 4i) = [(3 - 4i)² + (3 + 4i)²] / (3 + 4i)(3 - 4i) = 2(3² + 4²i²) / (3² - 4²i²) = 2(9 - 16) / (9 + 16) =-14/25Correct choice is C
f(x) = (2x + 5)(x+3)(3x – 10) (2x - 8) has zeros at x = -3, x =-5/2, x=10/3
and x = 4.
What is the sign of f on the interval
-5/2
Choose 1 answer:
A) f is always positive on the interval
B) F is always negative on the interval
C) f is sometimes positive and sometimes negative on the interval.
Answer:f is sometimes positive and sometimes negative on the interval
Step-by-step explanation:
What is 3 to the power of 7 times 92 divided by 3.369
Answer:i dont know maybe 699
Step-by-step explanation:dont judge cause i guessedhope its right
Hello can someone help me with these four questions!!!
Please no fake answers, I need these to pass my class. <3 :) Ty! Math
Answer:
1) A = 27 square units, P = 24 units; 2) 276 mm; 3) A = 8, B = 4, C = 3, D = 5, 108 square feet; 4) 5.
Step-by-step explanation:
1) The sides of the rectangle are 9, 9, 3, and 3.
2) 40 + 40 + 70 + 70 + 28 + 28
3) 32 + 6 + 6 + 24 + 40 = 108
4) 24 + 24 + 20 + 20 + 30 + 30 = 148
740/148 = 5
Your homeowner’s policy has a premium of $150, a deductible of $5000, and a limit of $300,000. Your home suffers $500,000 in damages. How much will you pay?
The amount that the person get after he home suffers $500,000 in damages is $20000.
What is deductible amount?Deductible amount is the amount which is paid by one in the starting of any policy.
The homeowner’s policy has a premium of $150. Thus, the amount paid in a year is,
[tex]150\times12=1800[/tex]
The home suffers $500,000 in damages and the deductible is of $5000. Thus, the amount remain is,
[tex]A=500000-5000\\A=495000[/tex]
The limit of the policy is $300000. Thus, the amount will be remained as,
[tex]A=495000-300000\\A=195000[/tex]
If we include the deductible amount, then,
[tex]A=195000+5000\\A=200000[/tex]
This amount does not include the premium paid by the homeowner. Hence the amount that the person get after he home suffers $500,000 in damages is $20000.
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f(x)= square root of x-5. find f-1 (x) and it’s domain
Answer:
Option B.
Step-by-step explanation:
Inverse function:
Suppose we have a function y = f(x). To find the inverse function, we exchange x and y on the original function, and then isolate y.
The domain of the inverse function(x values) is the range of the original function(y values).
Original function:
[tex]f(x) = \sqrt{x} - 5[/tex]
Domain is [tex][0,\infty)[/tex], and when [tex]x = 0, f(x) = -5[/tex]. So the range is [tex][-5,\infty][/tex], that is, [tex]y \geq -5[/tex]
Inverse function:
[tex]y = \sqrt{x} - 5[/tex]
Exchanging x and y
[tex]x = \sqrt{y} - 5[/tex]
[tex]\sqrt{y} = x + 5[/tex]
[tex](\sqrt{y})^2 = (x+5)^2[/tex]
[tex]y = (x+5)^2[/tex]
The inverse function is [tex]f^{-1}(x) = (x+5)^2[/tex]
Domain:
Range of the original function is [tex]y \geq -5[/tex], so the domain of the inverse function is [tex]x \geq -5[/tex]. The correct answer is given by option B.
Answer:
B. f ^ -1 (x) = (x + 5) ^ 2;
x > -5
Step-by-step explanation:
Ap e x
evaluate the expression (4×5)2-6+3
Answer:
40x - 3
Step-by-step explanation:
4x(5)(2)−6+3
=40x+−6+3
=40x+−6+3
=(40x)+(−6+3)
=40x+−3
If Lisa were to plant six apple trees and only four of them were successful, she would have minus two apple trees. How many apple trees would Lisa have if she added fourteen more to the lasting apple trees?
Answer:
18
Step-by-step explanation:
the spinner shown below has 12 congruent sections. the spinner spun 150 times. what is a reasonable prediction for the number of items the spinner will land on an even number. (pls help asap!!)
Answer:45
Step-by-step explanation:
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
120 x 3/8 = 360/8 = 45
The answer would be 45 times.
Choice 1: Angela and Kellie went to lunch. Their bill before tax was $20.00. Tax is 8%. How much tax should
they expect to pay?
Please help ASAP and anything would help thank you:)PS: these are percentages
Answer:
$1.60
Step-by-step explanation:
Amount of tax paid = percentage of tax to be paid x bill before tax
0.08 x $20 = $1.60
50 POINTS
What is the correct reason for statement 2?
somebody help me please in the photo
Answer:
93 degrees
Step-by-step explanation:
alternate interior angles are congruent so 39+x=132 x=93
Answer:
Step-by-step explanation:
According to Alternate Interior Angles Theorem (in a graph that shows a transversal crossing two parallel lines, the alternate interior angles are congruent), The angle that includes the sum of 39° and x° is congruent to 132°.
So: 39° + x° = 132°, and x = 93
convert the angle 0=230 degrees to radians. express your answer exactly
Answer:
(23/18)π radians
Step-by-step explanation:
180º = π radians
230º * (π/180)
(23/18)π radians
Answer:
O=4.0rad
Step-by-step explanation:
230° to radians
(pie/180°)*230
23pi/18
4.0 rad
Grahg x= 5. Plz il do anything
Answer:
Y=5 and x=0
XENICAL AND THE REST
Answer:
ta-da!
the red line is x=5
the blue line is y=5