To find the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x), you can use the following steps:
Set y equal to 0 and solve for x to find the x-intercepts of the graph.
Since the graph of y = cos(12x) + cos(16x) is periodic with period 2π/12 = π/6 and 2π/16 = π/8, respectively, you only need to consider x-intercepts in the interval [0,π/6).
Use the identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b) to rewrite the equation y = cos(12x) + cos(16x) as:
y = 2cos(4x)cos(8x) - sin(4x)sin(8x)
Set y equal to 0 and solve for x to find the x-intercepts. This will give you the x-coordinates of all the x-intercepts of the graph.
Sort the x-coordinates in increasing order and take the first three smallest positive values to find the 3 smallest positive x-intercepts.
For example, if you set y equal to 0 and solve for x, you get:
0 = 2cos(4x)cos(8x) - sin(4x)sin(8x)
This equation can be rewritten as:
cos(4x)cos(8x) = sin(4x)sin(8x)
Using the identity cos(a) = sin(π/2 - a) and substituting this into the equation above, we get:
sin(4x)sin(8x) = sin(4x + π/2)sin(8x)
This equation simplifies to:
sin(4x)sin(8x) = sin(4x)cos(8x)
Dividing both sides by sin(4x) and rearranging, we get:
sin(8x) = cos(8x)
This equation holds for all values of x that satisfy sin(8x) = cos(8x), so we can find the x-intercepts by setting these two functions equal to each other and solving for x:
sin(8x) = cos(8x)
sin^2(8x) = cos^2(8x)
sin^2(8x) - cos^2(8x) = 0
1 - cos(16x) = 0
cos(16x) = 1
Thus, the x-intercepts of the graph are at x = 0, x = π/16, x = π/8, x = 3π/16, and so on. Since we are only interested in the 3 smallest positive x-intercepts, we can take the first three values in this list: x = 0, x = π/16, and x = π/8.
Therefore, the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x) are [0, π/16, π/8].
a fair coin is flipped nultiple times until it lands on heads if the probability of landing on heads is 50% what is the probability of first landing on heads on the fourth attempt
If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.
what is probability ?There are four primary categories of probability: classical, empirical, subjective, and axiomatic. Since possibility and probability are equivalent, you may define probability as the likelihood that a specific event will occur.
given
A fair coin is repeatedly flipped until it comes up heads.
The coin is impartial.
On the third try, we need to calculate the likelihood of the first landing being on heads.
We are aware that each flip of a fair coin is independent of the others, and that each effort results in P(H) = P(T) = 0.5.
Required probability is the likelihood that the third attempt's first landing will be on heads.
= Chance of (I two trials result in tail and third result in head)
=P(I head) P(II head) P(III tail) (since each trial is independent)
= ( 1 /2 ) (1/2)(1/2) = (1/8 )
If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.
To know more about probability visit :-
https://brainly.com/question/30034780
#SPJ4
Solve for a:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Answer:
its 14
Step-by-step explanation:
50 didvdied by 20 is 18 so here u go
A Naval Carrier dropped anchor off the coast. The massive anchor drops at 3.5 m/s and will be 52.5 meters under the surface of the water after 20 seconds.
How high above the surface of the water does the anchor begin to drop? Round to the nearest meter.
The height the anchor begins to drop is 17.5 m
How to find how high above the surface of the water does the anchor begin to drop?Since a Naval Carrier dropped anchor off the coast. The massive anchor drops at 3.5 m/s and will be 52.5 meters under the surface of the water after 20 seconds.
Let
h = the height the anchor begins to drops, h' = height of anchor below water surface = 52.5 mThe total height the anchor drops is thus H = h + h'
Now, the total height the anchor drops H = vt where
v = speed of anchor = 3.5 m/s and t = time anchor drops = 20 sSo, equating both equations, we have
vt = h + h'
Making h subject of the formula, we have that
h = vt - h'
Given that
v = 3.5 m/s, t = 20 s and h' 52.5 mSubstituting the values of the variables into the equation, we have that
h = vt - h'
h = 3.5 m/s × 20 s - 52.5 m
h = 70 m - 52.5 m
h = 17.5 m
So, the anchor drops 17.5 m
Learn more about height anchor drops here:
https://brainly.com/question/28706489
#SPJ1
You and a friend both draw a card from a standard deck of 52 cards.If you draw a card, put it back, and then your friend draws, what is the probability you both draw a heart?
Step-by-step explanation:
sign of truelove or truefriendship is the probability of both draw a heart
pls help asap negative two and one third times negative five and fifteen hundredths
Answer:
Step-by-step explanation:
the product between the mixed numbers is equal to 12 and 1 over 60, which is the first option.
How to find the product between two mixed numbers?
A mixed number is a number that is written as the addition of a whole number and an improper fraction.
Remember that the mixed number "negative two and one third" is written as:
-2 ¹/₃ = (-2 - 1/3)
Here we want to solve the product:
(-2 - 1/3)*(-5 - 15/100)
Notice that all the signs are negative, so the outcome will be positive:
(-2 - 1/3)*(-5 - 15/100) = 2*5 + (1/3)*5 + 2*(15/100) + (1/3)*(15/100)
= 10 + 5/3 + 30/100 + 5/100
= 10 + 5/3 + 3/10 + 1/20
= 10 + 3/3 + 2/3 + 6/20 + 1/20
= 11 + 2/3 + 7/20 = 11 + 40/60 + 21/60
= 11 + 61/60 = 11 + 60/60 + 1/60 = 12 + 1/60
Then the product between the mixed numbers is equal to 12 and 1 over 60, which is the first option.
Answer:
12 1/60
Step-by-step explanation:
-2 1/3 × (-5 15/100) =
= -7/3 × (-5 3/20)
= 7/3 × 103/20
= 721/60
= 12 1/60
either roll or a 7 or 11 on the first roll, or match the point value on a subsequent roll. what's the likelihood of winning after one roll? explain your answer.
The likelihood of winning after one roll in a game is 1/6. This is because there are only two ways to win on the first roll: by rolling a 7 or an 11.
What is Probability?The possibility that an event will occur is gauged by probability. It is a mathematical idea that measures the probability or possibility that a specific event will occur. Probability is expressed as a number between 0 and 1, where 0 denotes that the event is highly unlikely to occur and 1 denotes that it will definitely happen. Making predictions and judgments based on the likelihood of an event occurring is a common use of probability in many disciplines, including statistics, economics, and gambling. The number of successful outcomes is divided by the total number of possible outcomes to determine probability. For example, if a coin is flipped and has a 50% chance of landing on heads, the probability of the coin falling on chiefs is 0.5.
How to solve?
Since there are 6 possible outcomes on a single roll of a pair of dice (1, 2, 3, 4, 5, 6), the likelihood of winning on the first roll is 1/6.
To learn more about probability, visit:
https://brainly.com/question/20164508
#SPJ4
In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.
there are no pictures. Will give brainlest.
A caino only ha red playing chip for $10 each and blue playing chip for $5 each. Jack paid $400 to purchae 50 playing chip at the cahier' window. How many red playing chip were given to him?
30 red playing chip were given to him.
Let m be the number of red playing chips and n be the number of blue playing chips.
since Jack purchased 50 playing chips, we get an equation.
m + n = 50 .............(1)
He pais $400 for these 50 chips, so we get an equation,
10m + 5n = 400 ........(2)
From equation (1) we get,
m = 50 - n ...............(3)
Substitute above value of m in equation (2),
10(50 - n) + 5n = 400
500 - 10n + 5n = 400
-5n = -100
n = 20
Substitute above value of n in equation (3),
m = 50 - 20
m = 30
Therefore, the number of red playing chips = 30
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ4
The life in hours of a battery is known to be approximately normally distributed with standard deviation σ = 1. 25 hours. A random sample of 10 batteries has a mean life of x =40. 5hours. A. Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0. 5. B. What is the P-value for the test in part (a)? c. What is the β-error for the test in part (a) if the true mean life is 42 hours? d. What sample size would be required to ensure that β does not exceed 0. 10 if the true mean life is 44 hours? e. Explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life
a)[tex]$z=\frac{40.5-40}{\frac{1.25}{\sqrt{10}}}=1.265$[/tex]
Now we can calculate the p value since we have a right tailed test the p values is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .
b) [tex]$p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029$[/tex]
c) [tex]$\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$[/tex]
d) We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:
[tex]n=\frac{\left(z_\alpha+z_s\right)^2 \sigma^2}{(x-\mu)^2}[/tex]
The true mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:
[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]
e) For this case we can calculate a one sided confidence interval given by:
[tex]$\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)$[/tex]
And if we replace we got:
[tex]$40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152$[/tex]
And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]
And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.
What is null hypothesis?
In a scientific setting, a hypothesis (plural: hypotheses) is a testable claim about the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.
Part a
We have the following data given:
n=10 represent the sample size
[tex]$\bar{x}=40.5$[/tex] represent the sample mean
[tex]$\sigma=1.25$[/tex]represent the population deviation.
We want to test the following hypothesis:
Null: [tex]$\mu \leq 40$[/tex]
Alternative: [tex]$\mu > 40$[/tex]
The significance level provided was [tex]$\alpha=0.05$[/tex]
The statistic for this case since we have the population deviation is given by:[tex]z=\frac{\bar{x}-\mu}{\frac{-\mu}{\sqrt{n}}}$[/tex]
If we replace the values given we got:
[tex]$z=\frac{40.5-40}{\frac{1.24}{\sqrt{10}}}=1.265$[/tex]
Now we can calculate the p value since we have a right tailed test the p values is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .
Part b
The p value on this case is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
Part c
For this case the probability of type II error is defined as the probability of incorrectly retaining the null hypothesis and is defined like this:
[tex]\beta=P\left(Z < z_\alpha-\frac{(x-\mu) \sqrt{n}}{\sigma}\right)[/tex]
Where [tex]$z_\alpha=1.645$[/tex]represent the critical value for the test that accumulates 0.05 of the area on the right tail of the normal standard distribution.
The true mean on this case is assumed [tex]$\mu=42$[/tex], so then we can replace like this:
[tex]\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$$[/tex]
Part d
We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:
[tex]n=\frac{\left(z_\alpha+z_\beta\right)^2 \sigma^2}{(x-\mu)^2}[/tex]
The ture mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:
[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]
Part e
For this case we can calculate a one sided confidence interval given by:
[tex]\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)[/tex]
And if we replace we got:
[tex]40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152[/tex]
And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]
And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.
To learn more about null hypothesis visit:https://brainly.com/question/28920252
#SPJ4
11
Write an equation in slope-intercept form that models the situation. In order to go bowling,
you must pay a one-time fee of $10 for rental shoes, and then pay $3 per game. Let y
represent the total cost of bowling after playing x games. (5 Points)
y = - 10x + 3
y = 10x + 3
y = 10x - 3
y=-3x + 10
y = 3x + 10
Answer:
y=3x+10
Step-by-step explanation:
The formula for an equation in slope-intercept is y=mx+b. m is the slope and b is the y-intercept
The 3 is the slope because it says that you have to pay that amount per game so that is the rate. 10 is the y-int because it says that you have to pay a one-time fee and a y-intercept is just once and isn't a rate.
Given J = 2hr + 2b, solve for h.
Answer: [tex]h = \frac{J-2b}{2r}[/tex]
Work Shown:
[tex]J = 2hr + 2b\\\\J - 2b= 2hr\\\\h = \frac{J-2b}{2r}[/tex]
Explanation:
In the 2nd step, we isolate the "2hr" by subtracting both sides by 2b. This is do unto the +2b done to the right side initially. We want 2hr all by itself since it contains h.
Then to fully isolate h, we divide both sides by 2r. It might help to think of 2hr as 2r*h so you can pull out the terms easier. The division is done to undo the multiplication.
If writing out the final step using a keyboard, then you would say (J-2b)/(2r). Use parenthesis to indicate which terms are being divided.
Need help answering this question
The measure of ∠JKM is 145°.
What is exterior angle theorem?The measure of an exterior angle of a triangle is bigger than either of the measures of the distant interior angles, according to the external angle theorem, Proposition 1.16 in Euclid's Elements.
Because the parallel postulate is not required for its proof, this is a fundamental conclusion in absolute geometry. Three of a triangle's corners are its vertices.
Two angles are produced by a triangle's sides (line segments) meeting at its apex (four angles if you consider the sides of the triangle to be lines instead of line segments). An interior angle of the triangle is the only one of these angles that has the third side of the triangle inside of it.
Here it is given that, ∠JLK= 70°
∠LJK = x°
(2x-5)°= 70°+x°
now applying exterior angle theorem,
x=75°
substitute 75 for x in 2x-5 to find m∠JKM.
=2x-5
=2×75-5
=145°
Hence, The measure of ∠JKM is 145°
To learn more about angle theorem refer to:
https://brainly.com/question/27962469
#SPJ1
sketch the solution to each system of inequalities.
y<=-x-2
y>=-5x+2
Answer:
Where you see the colors overlap is the answer.
Step-by-step explanation:
Desmos is a free graphing calculator.
Please help me ASAP. I will give brainliest after 2 people comment.
Answer: x= 18
Step-by-step explanation:
9 divided by 6 = 1.5
That is the rate change
So take 12 times 1.5 = 18
x= 18
If you can please give me a Brainliest, thank you!
Answer:
18
Step-by-step explanation:
See attached worksheet.
A scaled figure will have dirrent dimensions, but with the same proportions. The ratio of the two sides in Figure A is 2/1 (Side/Top). That same ratio will apply to Figure B. So we could write:
x/9 = 2
x = 18
-5(-4/7) as a simplified mixed fraction
Answer:
[tex]2\frac{6}{7}[/tex]
Step-by-step explanation:
-5(-4/7)
First:
A negative multiplied by a negative is positive, so we can remove the negative symbols.
5(4/7)
Multiply:
[tex]\frac{5(4)}{7}[/tex]
20/7
Convert into a mixed number:
2 6/7
PLEASE MARK AS BRAINLIEST!!Diana arrives late at the theater for a play.
Her ticket entitles her to sit anywhere in Circle
G. She had hoped to sit in Seat D, which she
thought would give her the widest viewing
angle of the stage. But Seat D is taken, as
are all the other nearby seats in Circle G. The
seating chart for the theater is shown.
Identify two other spots where Diana can sit
that will give her the same viewing angle she
would have had in Seat D. Explain how you
know how your points would provide the
same viewing angle, and support your claim
by showing the viewing angles on the
drawing.
We have to set ∠AMN equal to ∠D.
What are angles?
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
Label the rows (A nearest the screen, through G at back) and the seat numbers (starting with 1 on the far left of the diagram) and count towards the right.
The seat is not equal to 1 and will align to point D.
Viewing angle is in terms of another angle
Set ∠AMN equal to ∠D.
Hence, we have to set ∠AMN equal to ∠D.
To learn more about angles, visit:
https://brainly.com/question/25716982
#SPJ1
Suppose your parents agree to pay you
one cent today, two cents tomorrow (the first day after today), four cents the next day (second day after today), and so forth. Each time they double the amount they pay you. Write an equation expressing amount paid in terms of number of days after today. What kind of function is this? How much will they pay you the 30th day? Surprising?! Show that the amount paid today (0 days after today) agrees with the definition of zero exponents.
They will pay You $5368709.12 on the 30th day
What does the term "compound interest" mean?
Compound interest is when you receive interest on both your interest income and your savings.
You start with a one cent.
You have $0.01 x 2 the following day.
You have $0.01 x 2 x 2 the following day.
and so forth
You will have $0.01 x 2^n-1 on day n.
This means that on the 30th day, you have $0.01 x 2^29 = $5 368 709.12.
That is compound interest at work! It equates to daily payments of 100% interest. It immediately soars to inconceivable heights with even a penny as your initial investment!
Learn more about compound interest
https://brainly.com/question/24274034
#SPJ1
B.
5x + 2 = 2x + 14
WITH SOLUTION
i also need it rn-
Answer:
4
Step-by-step explanation:
5x + 2 = 2x + 14
or, 5x - 2x = 14 - 2
or, 3x = 12
or, x = 12/3
.
. . x = 4
solve it HURRY if if u can
Answer:
y= 0.25x
Step-by-step explanation:
First, use the slope formula to calculate the slope.
Second, solve for the y-intercept using the slope and one of the points.
Finally, once you've determined m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to obtain the equation for the line.
Solve each system of equations without graphing.
5x + 14y = -5
-3x+10y = 72
Answer:
To solve a system of equations without graphing, you can use one of several methods, such as substitution or elimination. Here's how you can solve this system using substitution:
First, solve one of the equations for one of the variables in terms of the other variable. For example, you can solve the first equation for y:
5x + 14y = -5
y = (-5 - 5x) / 14
Substitute this expression for y into the second equation, to get an equation in terms of x:
-3x + 10((-5 - 5x) / 14) = 72
Simplify this equation to get an equation in terms of x:
-3x - 50 - 35x = 72
-38x - 50 = 72
-38x = 122
x = -3.316
Substitute this value for x back into one of the original equations to solve for y:
y = (-5 - 5(-3.316)) / 14
y = (5 + 16.58) / 14
y = 21.58 / 14
y = 1.546
So the solution to the system of equations is (x, y) = (-3.316, 1.546).
Alternatively, you could solve the system using elimination. To do this, you would add the two equations to eliminate one of the variables, and then solve the resulting equation for the remaining variable.
in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
The American adults who believes in alien as per given 95% of confidence interval and the given sample surveyed is in the range of
( 0.657 , 0.783 ).
As given in the question,
Number of American adults surveyed (sample size) 'n' = 200
Percentage of people who believes in aliens 'p'= 72%
= 0.72
Percentage of people who don't believes in aliens ' 1 - p' = 1 - 72%
= 28%
= 0.28
95% Confidence interval that represents percent of people believes in aliens
Z - score of 95% confidence interval = ± 1.96
Margin of error = (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × 0.28)/ 200
= 1.96 ( 0.032)
= 0.06272
= 0.063
Lower limit = p - Margin of error
= 0.72 - 0.063
= 0.657
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.783
Therefore, for the given 95% confidence interval and sample size the Americans who believes in alien are in range of ( 0.657 , 0.783 ).
Learn more about confidence interval here
brainly.com/question/24131141
#SPJ4
At the start of 2014, Jim's house was worth £240,000.
The value of the house increased by 5% every year.
Work out the value of his house at the start of 2017.
Answer: $146,410
Step-by-step explanation:
which graph represents the solution of the system of inequalities
2x+6y < 6
x + 3y > 12
Compare √18 and 23/5 using >, <, or =.
23/5<√18
23/5 = √18
√18 > 23/5
√18<23/5
Answer: Thus, sqrt 18 < 23/5
Step-by-step explanation:
23/5=4.6
4.6x4.6=21.16
18<21.16
mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has
a. rs 11
b. rs 10
c. rs 14
d. rs 9
Answer:
a. 11
Step-by-step explanation:
Mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has:
a. 11
b. 10
c. 14
d. 9
3.5 * 3 = 10.5 cost
She has 11.
Find an equation of the line that has a slope of -1 and a y intercept of 5. Write your answer in the form
y = mx + b.
y =
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
there are different levels and combinations of concerns among individual students. what is the rationale that supports this statement?
The rationale that supports this statement is:
Situational experiences are interpreted differently.
Now, According to the question:
Let's Know:
What is the Rationale of the Study?
The rationale of the study explains the reason why the study was conducted (in an article or thesis) or why the study should be conducted (in a proposal). This means the study rationale should explain to the reader or examiner why the study is/was necessary.
We know that :
There are different levels and combinations of concerns among individual students.
Hence, The rationale that supports this statement is:
Situational experiences are interpreted differently.
In the question;
There are different levels and combinations of concerns among individual students.
what is the rationale that supports this statement?
Learn more about Rationale at:
https://brainly.com/question/28788724
#SPJ4
a jar contains 10 blue marbles and 11 red marbles. two marbles are drawn without replacement. what is the probability of getting two red marbles?
0.2620 is the probability of getting two red marbles.
What is probability?Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
a jar contains 10 blue marbles and 11 red marbles.
So, there total 21 marbles are present.
Now among 21 marbles, 11 are red marble. So, odds of a red on the first are 11/21
Next, there are 20 marbles are present and 10 are red. So odds of a red on the second is 10/20.
For, probability both are red, just multiply
= (11/21) x (10/20)
= 0.2620.
To know more about probability refer to:
brainly.com/question/24756209
#SPJ4
six distinct integers are selected at random from 2018 2019 2020 2027 what is the probability that among those selected the second smallest in 2020
The probability that among those selected the second smallest in 2020 is 1/3
In this question, we have been given six distinct integers are selected at random from 2018, 2019, 2020, . . . , 2027
We need to find the probability that among those selected the second smallest in 2020.
Here, total integers are: 10
The total number of ways to choose six distinct integers :
10C6
= 10!/6!(10 - 6)!
= 210
Assume 2020 is the second-lowest number.
There are 5 numbers left to choose, 4 of which must be greater than 2020.
This is equivalent to choosing 4 numbers from the seven numbers larger than 2020, and 1 number from the two numbers less than 2020
using combination formula,
7C4 * 2C1
= 35 * 2
= 70
So, the probability would be,
P = 70/210
P = 1/3
Therefore, the required probability is 1/3
Learn more about the probability here:
https://brainly.com/question/11234923
#SPJ4
At the grocery store it costs $2.50 per pound of Mac n cheese how much Mac and cheese could you get per dollar?
Please give good example
Answer: 5.6 kg of Mac n cheese per dollar.
Step-by-step explanation:
1 pound = 0.45 kg
So take 2.50 divided by 0.45 = 5.6 kg of Mac n cheese per dollar.