Answer:
answer is 1/1
Step-by-step explanation:
How many randomly chosen guests should I invite to my party so that the probability of having a guest with the same birthday as mine is at least 2/3?
Answer:
At least 401 chosen guests
Step-by-step explanation:
Represent those with same birth day with Same
So:
[tex]P(Same) > \frac{2}{3}[/tex]
Represent number of people with n
There are 365 days in a year and 364 days out of these days is not your birthday.
So, there the probability that n people do not share your birthday is [tex](\frac{364}{365})^n[/tex]
i.e.
[tex]P(none) = (\frac{364}{365})^n[/tex]
Solving further, we have that:
[tex]P(same) + P(none) = 1[/tex]
[tex]P(same) + (\frac{364}{365})^n = 1[/tex]
[tex]P(same) = 1 - (\frac{364}{365})^n[/tex]
We're calculating the probability that [tex]P(Same) > \frac{2}{3}[/tex].
So, we have:
[tex]1 - (\frac{364}{365})^n > \frac{2}{3}[/tex]
Collect Like Terms
[tex]1 - \frac{2}{3}> (\frac{364}{365})^n[/tex]
[tex]\frac{3-2}{3}> (\frac{364}{365})^n[/tex]
[tex]\frac{1}{3}> (\frac{364}{365})^n[/tex]
[tex]3^{-1} > (\frac{364}{365})^n[/tex]
Take natural logarithm (ln) of both sides
[tex]ln(3^{-1}) > ln((\frac{364}{365})^n)[/tex]
[tex]-ln\ 3 > n\ ln\ (\frac{364}{365})[/tex]
Apply laws of logarithm
[tex]-ln\ 3 > n\ (ln(364) - ln(365))[/tex]
Multiply through by -1
[tex]ln\ 3 < n\ (ln(365) - ln(364))[/tex]
Solve for n
[tex]\frac{ln\ 3}{(ln(365) - ln(364))} < n[/tex]
Reorder
[tex]n > \frac{ln\ 3}{(ln(365) - ln(364))}[/tex]
[tex]n > \frac{1.09861228867}{(5.89989735358 - 5.89715386764)}[/tex]
[tex]n> \frac{1.09861228867}{0.00274348594}[/tex]
[tex]n > 400.443928891[/tex]
[tex]n > 400[/tex] (approximated)
This implies that n = 401, 402, 403 .....
i.e
[tex]n \geq 401[/tex]
So, at least 401 people has to be invited
What is the value of the expression 3/19 7/2
Answer:
It is 2/15
Step-by-step explanation:
[tex]\frac{3}{19\frac{7}{2} } =\frac{3}{\frac{45}{2} }\\=\frac{2}{15}[/tex]
Dont know if this helps but here you go :)
If an object moves in a straight line with position function s = f(t), then the average velocity between t = a and t = b is
f(b) − f(a)/b − a
and the velocity at t = c is f '(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f '(c) is equal to the average velocity. For instance, if a car traveled 150 km in 2 hours, then the speedometer must have read km/h at least once.
In general, the Mean Value Theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval.
Answer:
75 km/hr
Step-by-step explanation:
So, if a car travels 150 km in 2hours.
Then;
f(t=0) = 0
f(t = 2 hours) = 150 km
Therefore;
f'(c) (speedometer reading) = f(t=2)-f(t=0)/(2-0)
f'(c) (speedometer reading) = 150/2 km/hr
f'(c) (speedometer reading) = 75 km/hr
The slope of the line is ?
Answer:
slope= 4,
Step-by-step explanation:
y = 4x-6
f(1) = 6 f(n) = f(n – 1) – 5 for integer values of n > 1
Solve the equation and describe what your answer. What happens? 5x-7=2x+1+3x
Answer: The Answer is 0
Step-by-step explanation:
The key here is combining like terms. Here:
1) 5x-7=2x+1+3x
2) 5x-7=5x+1
Then you add 7 to both sides anywhere that there is no variable. You also subtract 5x to the other 5x
3) 0x=8
When you divide by zero on both sides, your answer should be 0
Which of the following describes the roots of the polynomial function f (x) = (x + 2) squared (x minus 4) (x + 1) cubed?
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4
Answer:
A
Step-by-step explanation:
[tex]f(x) = (x + 2)^2(x-4)(x + 1)^3[/tex]
x+2=0
x+2-2=0-2
x=-2.....(x+2) was squared...exponent of 2...multiplicity of 2
x-4=0
x-4+4=0+4
x=4....(x-4) has no visible exponent which means it is essentially to the power of 1...multiplicity of 1
x+1=0
x+1-1=0-1
x=-1....(x+1) was cubed...exponent was 3...multiplicity of 3
The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct.
What are the roots of an equation?The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.
For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.
As per the given function,
f(x) = (x + 2)²(x - 4)(x + 1)³
The roots are the points at which the value of the function is zero.
f(x) = 0
(x + 2)²(x - 4)(x + 1)³ = 0
(x + 2)² = 0
x = -2 (with a multiplicity of 2)
(x - 4) = 0
x = 4 (with a multiplicity of 1)
(x + 1)³ = 0
x = -1 (with a multiplicity of 3)
Hence "The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct".
To learn more about the roots of equations,
https://brainly.com/question/12029673
#SPJ6
What is the slops of the line passing through (-1, 2) and (-3, -2)? PPPPLLLZZZ HELP!!!!
A. 2
B. -1/2
C. 1/2
D. -2
Answer:
A. 2
Step-by-step explanation:
Count the steps to get to the both points.
From (-3, -2) to (-1, 2), it gets up by 4 and move to the right by 2.
Rise ÷ Run = 4 ÷ 2 = 2
Answer:
I think it's D
Step-by-step explanation:
because it's same to another one so D only
Eighty percent of students surveyed said they feel more focused after exercising. Nine hundred fifty students were surveyed. How many students said they feel more focused after exercising? 380 570 760 930
Answer:
760
Step-by-step explanation:
Answer:
760
Step-by-step explanation:
To find 7% of a total you can multiply the total by
(1) 7 (3)
(2) 0.7
(3) 7/10
(4) 0.07
please help will give brainlyest again
Answer:
8
_
12 I think
that's it it you can cross multiple it will be 7/10
The Jimenez family is bringing 12 packages of hamburger and hotdog buns to the neighborhood picnic. The hamburger buns cost $2.00 per package. The hot-dog buns cost $1.50 per package. They spent $20 for the buns. Create and solve a system of equations that can be used to find the number of packages of each type of bun purchased.
Answer:
The system of equations is x + y = 12 and 2x + 1.5y = 20
The number of packages of the hamburger is 4
The number of packages of the hotdog is 8
Step-by-step explanation:
Assume that they bringing x packages of hamburger y packages of hotdog
∵ x represents the number of packages of hamburger
∵ y represents the number of packages of hotdog
∵ Jimenez family is bringing 12 packages of hamburger and hotdog buns
∴ x + y = 12 ⇒ (1)
∵ The hamburger buns cost $2.00 per package
∵ The hot-dog buns cost $1.50 per package
∵ They spent $20 on the buns
∴ 2x + 1.5y = 20 ⇒ (2)
The system of equations is x + y = 12 and 2x + 1.5y = 20
Let us solve it to find x and y
→ Multiply equation (1) by -1.5 to make the coefficients of y equal in
values and different in signs to eliminate it
∵ -1.5(x) + -1.5(y) = -1.5(12)
∴ -1.5x - 1.5y = -18 ⇒ (3)
→ Add equations (2) and (3)
∵ (2x + -1.5) + (1.5y + -1.5y) = (20 + -18)
∴ 0.5x = 2
→ Divide both sides by 0.5 to find x
∴ x = 4
→ Substitute the value of x in equation (1) or (2) to find y
∵ 4 + y = 12
→ Subtract 4 from both sides
∴ 4 - 4 + y = 12 - 4
∴ y = 8
∴ The number of packages of the hamburger is 4
∴ The number of packages of the hotdog is 8
List the transformations of the function. *
5 points
f(x)= (1/2(- 1/4(x-3))+1
Answer:
Transformations of function f(x) = 1/2(-1/4(x-3)) + 1 :
vertical compressionhorizontal stretchreflection across y-axistranslates righttranslates upHelp me pleaseeeee:(((
Answer:
1.25
Step-by-step explanation:
if you paid 7.50 for 6 feet of rope we can figure out how much each foot of rope is by example 750 divided by 6 which equals 1.25 .
Answer:
$62.50
Step-by-step explanation:
Proportions:
$7.50 ⇔ 6ft
$R ⇔ 50ft
R = 7.5*50/6
R = $62.5
Find the circumference of a circle whose
area is 49pi sq units.
Answer: C=2πr
r Radius
The 7th grade class took a survey on their faviorte ice cream. 58 people said they perfer vanilla, while 28 people said they pefer chocolate. Write a ratio comparing chocolate to vanilla.
If the average price of a new one-family home is $246,300 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 60% of the market. Assume that the variable is normally distributed.
Answer:
Step-by-step explanation:
P(-a<z<a)=0.60, from the symmetry of normal distribution, P(z<a) = 0.60+ (1-0.60)/2 =
0.60+0.4/2
0.60+0.2
= 0.8
Considering the standard normal distribution table, we have a = 0.80, thus
z =(x-m)/std = 0.80
the maximum x = m + 0.80×std =
Where m = 246300
Std = 15000
246300+0.80×15000
= 246300+12000
= 258300
For the minimum x
x = m - 0.80×std
x = 246300-0.80×15000
246300-12000
= 234300
The square shown has sides of length 6z^7 decimeters. Find it’s area
Answer:
49z^10 dm^2
Step-by-step explanation:
what is principal in simple intrest
Solve this system for m and b 342=23m+b 147=10m+b
Answer:
b = − 3
m = 5 ( 39 + 2 m ) /23
What is the answer for 2/5x5/8 ?
James deposited $575 into a bank account that earned 5.5% simple interest each year. No money was deposited into or withdrawn from the account. How much money was in the account after 2 1/2 years? Round your answer to the nearest cent.
Answer:
$654.06
Step-by-step explanation:
ジオメトリヘルプミープリーズは、速くて正しい場合に最も頭が良くなります
関係のドメインは？ 1）関係の出力（y）値2）関係の入力（x）値3）入力値をペアにするポイントのセット…
f（x）= 16 – x ^ 2、g（x）= 4 –xとします。 （fg）（x）とその定義域を見つけます。
助けてくださいお願いします
助けてください
Answer: the answer would be 79.06
Step-by-step explanation:
Bella is learning to type. She typed a letter to her teacher but misspelled 8 words. If she misspelled 25% of the words she typed. how many words did she type in her letter I'm taking a test I need this ASAP
Answer:
She typed 32 words in her letter
Step-by-step explanation:
Assume that the letter has x words
∵ She typed x words in her letter
∵ She misspelled 8 words
∵ She misspelled 25% of the words she typed
∴ She misspelled 25% of x
→ That means 8 is equivalent to 25% of x
∴ 25% of x = 8
∴ 25% × x = 8
→ Change 25% to decimal by divide it by 100
∵ 25% = 25 ÷ 100 = 0.25
∴ 0.25 × x = 8
∴ 0.25x = 8
→ Divide both sides by 0.25
∵ [tex]\frac{0.25x}{0.25}[/tex] = [tex]\frac{8}{0.25}[/tex]
∴ x = 32
∵ x represents the number of words that she typed in the letter
∴ She typed 32 words in her letter
This is for someone that i was suppost to give brainliest to lol
Answer:
ok does that mean me dont get brainliest
Step-by-step explanation:
Suppose babies born in a large hospital have a mean weight of 3685 grams, and a variance of 330,625. If 113 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 50 grams? Round your answer to four decimal places.
its not greater than 50 grams. and the answer rounder to the four decimal places is 32.6106
What is the maximum for: P = 3x + 2y
Answer:
The maximum value of the function P= 3x + 2y
There is an accompanying graph in this problem. In the graph, there are 4 points to consider. I'll just assign letters on each point.
Point O is found in x = 0 ; y = 0 or (0,0)
Point A is found in x = 8 ; y = 0 or (8,0)
Point B is found in x = 6 ; y = 5 or (6,5)
Point C is found in x = 0 ; y = 8 or (0,8)
We will substitute x and y in the equation by its values per point.
Point A = 3(8) + 2(0) = 24 + 0 = 24
Point B = 3(6) + 2(5) = 18 + 10 = 28
Point C = 3(0) + 2(8) = 0 + 16 = 16
-4q= 52
HELP!!!!!!!!!!!!!!!!!!!!!
Algebra 1
hi
-4q= 52
q = 52/ -4
a = -13
Answer:
-13
Step-by-step explanation:
-4q=52
divide both side by -4
-4q/-4=52/-4
q=-13
Given g(x)=−x−4, find g(5)
Answer:
-9
Step-by-step explanation:
Plug it in
g(x)=-x-4
g(5) meaning that x=5
Thus,
-5-4=-9
Hope it find it helpful :)
Answer:
-1
Step-by-step explanation:
Given g(x) = -x + 4, find g(5)
g(x) = -x+4
g(5) = -(5) + 4 Plug input into x
-5 + 4 Negate
-1 Add
complete the sequence:1,1,2,3,5,_,_,_
Answer:
8,13,21
Step-by-step explanation:
Basically,add the previous number to next number
Answer:8,13,21
Step-by-step explanation:
Please help thanks :)
Answer:
Distributive Property
Step-by-step explanation:
[tex]x(8x+3y)\\We\ multiply\ the\ term\ outside\ brackets\ with\ terms\ inside\ the\ bracket\ equally,\\through\ the\ distributive\ property\ method\ .\\\\Hence,\\x(8x+3y)\\=8x*x+3y*x\\=8x^2+3xy[/tex]