The two rolls of the number cube are independent events because
the result of 1 roll does not affect the result of the other roll.
To find the probability of two independent events, we first find
the probability of each event, then we multiply the probabilities.
We can find the probability of an event using the following ratio:
number of favorable outcomes/total number of outcomes
Since there is only one way to roll a 3 and there are six
possible outcomes, 1, 2, 3, 4, 5, and 6, the probability of rolling a 3 is 1/6.
Since there is also only one way to roll a 2 and there are
six possible outcomes, the probability of rolling a 2 would be 1/6.
Now we multiply the probabilities.
1/6 x 1/6 is 1/36.
So the probability of rolling a 3 and a 2 is 1/36.
Answer:
1/36
Step-by-step explanation:
Probability of rolling 3 in a dice = 1/6.
Probability of rolling 2 = 1/6
Since, 2 should be followed after 3; we multiply 1/6 and 1/6
1/6 x 1/6 = 1/36.
A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.
Answer: a=24
Step-by-step explanation:
Lets find the line's formula (equation of the line).
As known the general formula of any straight line (linear function) is
y=kx+b
Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7
(Xb;Yb)- are the coordinates of point B
(Xa;Ya) are the coordinates of point A
Now lets find the coefficient b. For this purpose we gonna use the coordinates of any point A or B.
We will use A
7=-2/7*3+b
7=-6/7+b
b=7 6/7
So the line' s equation is y= -2/7*x+7 6/7
Now we gonna find the value of a usingcoordinates of point C.
Yc=1, Xc=a
1=-2/7*a+7 6/7
2/7*a= 7 6/7-1
2/7*a=6 6/7
(2/7)*a=48/7
a=48/7: (2/7)
a=24
Answer:
a=24
Step-by-step explanation:
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
Use the definition of continuity and the properties of limits to show that the function f(x)=x sqrtx/(x-6)^2 is continuous at x = 36.
Answer:
The function is continuous at x = 36
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]
The point at which continuity is tested is x = 1
Now from the definition of continuity ,
At function is continuous at k if only
[tex]\lim_{x \to k}f(x) = f(k)[/tex]
So
[tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]
[tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]
[tex]= 7.2[/tex]
Now
[tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]
[tex]f(36) = 7.2[/tex]
So the given function is continuous at x = 36
because
[tex]\lim_{x \to 36}f(x) = f(36)[/tex]
The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county
Answer:
[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
Step-by-step explanation:
number of counties = 159
n number of people are mutually independent and equally likely home locations
considering the details given in the question
n ≤ 159
The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]
since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in
therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
What's the exact value of tan 15°?
Answer:
The answer is 0.267949192
Step-by-step explanation:
I hope that is enough numbers.
Pablo rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 80 cents for each mile driven. Pablo had to pay
$221.59 when he returned the truck. For how many miles did he drive the truck?
Answer:
252 miles
Step-by-step explanation:
19.99 + .80x = 221.59
,80x = 201.60
x = 252
given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9
Answer:
f(g(9)) = 945/16
Step-by-step explanation:
To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).
g(x) = x + 3/4
f(x) = x² - 4x - 3
f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3
f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3
f(g(x)) = x² - 5/2x + 9/16 + 3 - 3
f(g(x)) = x² - 5/2x + 9/16
Now, put a 9 wherever there is an x in f(g(x)).
f(g(9)) = (9)² - 5/2(9) + 9/16
f(g(9)) = 81 - 5/2(9) + 9/16
f(g(9)) = 81 - 45/2 + 9/16
f(g(9)) = 117/2 + 9/16
f(g(9)) = 945/16
the ration of men to women in a certain factory is 3 to 4. there are 204 men. how many workers are there?
Answer:
476 workers
Step-by-step explanation:
Men: women : total
3 4 3+4 = 7
We want 204 men
204/3 =68
Multiply each by 68
Men: women : total
3*68 4*68 7*68
204 272 476
Answer:
There are 476 workers
Step-by-step explanation:
I really need help please answer!
Answer:
-2, b, a+c
Step-by-step explanation:
Answer:
-2, b, a+c
Step-by-step explanation:
By looking at where A and C are on the number line, we can tell that A is a negative number close to zero and C is a positive number a little greater than four. This means that if we add the two together, we'll get a positive number a little below four.
By looking at the number line, we can tell that the value of B is a positive number a little below the number three.
Now that we know that B is less than A+C, and we know where -2 is on the number line (two marks to the left of zero) we can decide the least to greatest values.
Since negatives are always less than positives, we know that -2 has the smallest value. Next, we know that B is lower on the number line than A+C. So, in order, from least to greatest, the answer is:
-2, B, A+B
Hope this helps!! <3 :))
Find the domain of the Bessel function of order 0 defined by [infinity]J0(x) = Σ (−1)^nx^2n/ 2^2n(n!)^2 n = 0
Answer:
Following are the given series for all x:
Step-by-step explanation:
Given equation:
[tex]\bold{J_0(x)=\sum_{n=0}^{\infty}\frac{((-1)^{n}(x^{2n}))}{(2^{2n})(n!)^2}}\\[/tex]
Let the value a so, the value of [tex]a_n[/tex] and the value of [tex]a_(n+1)[/tex]is:
[tex]\to a_n=\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}[/tex]
[tex]\to a_{(n+1)}=\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}[/tex]
To calculates its series we divide the above value:
[tex]\left | \frac{a_(n+1)}{a_n}\right |= \frac{\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}}{\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}}\\\\[/tex]
[tex]= \left | \frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2} \cdot \frac {2^{2n}(n!)^2}{(-1)^2n x^{2n}} \right |[/tex]
[tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)!^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |[/tex]
[tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\= \left | \frac{x^{2n}\cdot x^2}{2^{2n} \cdot 2^2(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\[/tex]
[tex]= \frac{x^2}{2^2(n+1)^2}\longrightarrow 0 <1[/tex] for all x
The final value of the converges series for all x.
At an airport, 76% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.
Answer:
The probability is [tex]P( X \le 4 ) = 0.0054[/tex]
Step-by-step explanation:
From the question we are told that
The percentage that are on time is p = 0.76
The sample size is n = 11
Generally the percentage that are not on time is
[tex]q = 1- p[/tex]
[tex]q = 1- 0.76[/tex]
[tex]q = 0.24[/tex]
The probability that no more than 4 of them were on time is mathematically represented as
[tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]
=> [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]
[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]
[tex]P( X \le 4 ) = 0.0054[/tex]
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?
Answer:
There are 80 10th graders in the school
Step-by-step explanation:
Let the number of 10th graders be x
There are 25% fewer 11th graders
That mean x - 25% of x
x -0.25x = 0.75x
There are 20% more 11th graders than 12th graders
So if number of 12th graders = y, then
0.75x = y + 20/100 * y = y + 0.2y = 1.2y
Since ;
0.75x = 1.2y
then y = 0.75x/1.2 = 0.625x
So let’s add all to give 190
x + 0.75x + 0.625x = 190
2.375x = 190
x = 190/2.375
x = 80
Nina skated for 2 hours and 14 min she stop at 8:24 pm when did Nina start skating
Answer:
6:10 pm
Step-by-step explanation:
she skate for 2 h and 14 min so,
8:24- 2:14
=6:10 pm
A bag contains 12 blue marbles, 5 red marbles, and 3 green marbles. Jonas selects a marble and then returns it to the bag before selecting a marble again. If Jonas selects a blue marble 4 out of 20 times, what is the experimental probability that the next marble he selects will be blue? A. .02% B. 2% C. 20% D. 200% Please show ALL work! <3
Answer:
20 %
Step-by-step explanation:
The experimental probability is 4/20 = 1/5 = .2 = 20 %
. line containing ( −3, 4 ) ( −2, 0)
Answer:
The equation is y= -4x -8
Step-by-step explanation:
The -4 is the slope and the -8 is the y intercept
Answer:
Slope: -4
Line type: Straight and diagonal from left to right going down.
Rate of change: a decrease by 4 for every x vaule
y-intercept is: (0,-8)
x-intercept is: (-2,0)
Step-by-step explanation:
Slope calculations:
y2 - y1 over x2 - x1
0 - 4
-2 - ( -3) or -2 + 3
=
-4/1 =
-4
More slope info on my answer here: https://brainly.com/question/17148844
Hope this helps, and have a good day.
24. After a vertical reflection across the x-axis, f(x) is
Options:
A. –f(x)
B. f(x – 1)
C. –f(–x)
D. f(–x)
Answer:
A. –f(x)
Step-by-step explanation:
The transformation of a reflection about the x-axis is
f(x) -> -f(x).
So the answer is
A. –f(x)
f(x)=−5x^3−4x^2+8x and g(x)=−4x^2+8, find (f−g)(x) and (f−g)(−2).
Answer:
see explanation
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) , that is
f(x) - g(x)
= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1
= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms
= - 5x³ + 8x - 8
Substitute x = - 2 into this expression, thus
(f - g)(- 2)
= - 5(- 2)³ + 8(- 2) - 8
= - 5(- 8) - 16 - 8
= 40 - 16 - 8
= 16
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent
The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]
where T is the set
[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]
(a) I've attached an image of the integration region.
[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]
(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]
[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]
Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.
Brandon is paid 150% of his regular hourly rate for overtime hours. He is paid \$45.00 an hour for overtime hoursWhat is his regular hourly rate?
Answer:
Regular hourly rate for Brandon is $30
Step-by-step explanation:
Let the payment for regular hours be $x
given that
Brandon is paid 150% of his regular hourly rate for overtime hours
payment for overtime hours = 150% of payment for regular hours
payment for overtime hours = 150/100 * x = 3x/2
Given that He is paid \$45.00 an hour for overtime hours
thus,
3x/2 = 45
=> x = 45*2/3 = 30
Thus, regular hourly rate for Brandon is $30
What is the area of polygon EFGH?
Answer:
C. 42 square units
Step-by-step explanation:
This is a rectangle and to calculate the area of a rectangle we multiply length and width
The length of this rectangle is 7 units and the width is 6 units
6 × 7 = 42 square units
area to the right of z=0.72
I don’t have a graphing calculator and I couldn’t find one online. I’m completely clueless on this one.
Answer:
Desmos could come in handy
A train goes at a speed of 70km / h. If it remains constant at that speed, how many km will it travel in 60 minutes?
Answer:
Total distance travel by train = 70 km
Step-by-step explanation:
Given:
Speed of train = 70 km/h
Total time taken = 60 min = 60 / 60 = 1 hour
Find:
Total distance travel by train
Computation:
Distance = Speed × Time
Total distance travel by train = Speed of train × Total time taken
Total distance travel by train = 70 × 1
Total distance travel by train = 70 km
if 280 is to be shared between iyene and nokob in the ratio 2:3. in how many equal part will thE money be shared
Answer:
5
Step-by-step explanation:
There will be five equal part because Iyene takes 2 parts and nokob takes 3 parts
Thus, the total parts which have been shared is 2+3=5
Further more, every part is
[tex] \frac{280}{5} = 56[/tex]
Hence, there is 5 parts have been shared and every part is 56 dollars
Answer:
5 equal parts
Because one of the dudes will get 2 and the other one will get 3 parts
3+2 is 5
280/5=56 (1 part)
so iyene will get 56*2=112 and nokob will get 56*3=168
7. Over the past 50 years, the number of hurricanes that have been reported are as follows: 9 times there were 6 hurricanes, 13 times there were 8 hurricanes, 16 times there were 12 hurricanes, and in the remaining years there were 14 hurricanes. What is the mean number of hurricanes is a year
Answer:
Step-by-step explanation:
Let us first generate the frequency table from the information given:
Hurricane number(X) Frequency(f) f(X)
6 9 54
8 13 104
12 16 192
14 12 168
Total ∑(f) = 50 ∑f(x) =518
In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:
Let the last frequency be f
9 + 3 + 16 + f = 50
38 + f = 50
f = 50 - 38 = 12
Now, calculating mean:
[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]
Therefore mean number of hurricanes = 10.4 (to one decimal place)
Find the product of all solutions of the equation (10x + 33) · (11x + 60) = 0
Answer:
18
Step-by-step explanation:
Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:
10x + 33 = 0 or 11x + 60 = 0
10x = -33 or 11x = -60
x = -33/10 or x = -60/11
Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.
Circle O has a circumference of 36π cm. Circle O with radius r is shown. What is the length of the radius, r? 6 cm 18 cm 36 cm 72 cm
Answer:
18 cm.
Step-by-step explanation:
The circumference of a circle is found by calculating 2 * pi * r.
In this case, the circumference is 36 pi cm.
2 * pi * r = 36 * pi
2 * r = 36
r = 36 / 2
r = 18 cm.
Hope this helps!
Answer:
18 centimeters
Step-by-step explanation:
The circumference of a circle can be found using the following formula.
[tex]c=2\pi r[/tex]
We know the circumference is 36π cm, therefore we can substitute 36π in for c.
[tex]36\pi= 2 \pi r[/tex]
We want to find r, the radius. Therefore, we must get r by itself. First, divide both sides of the equation by pi.
[tex]36\pi / \pi = 2 \pi r / \pi\\\\36= 2 \pi r / \pi\\\\36=2r[/tex]
Next, divide both sides of the equation by 2.
[tex]36=2r \\\\36/2=2r/2\\\\36/2=r\\\\18=r\\\\r=18 cm[/tex]
The radius of Circle O is 18 centimeters.
find the slope of the line that passes through the two points (0,1) and (-8, -7)
Answer:
The slope of the line is 1Step-by-step explanation:
The slope of a line is found by using the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
where
m is the slope and
(x1 , y1) and ( x2 , y2) are the points
Substituting the above values into the above formula we have
Slope of the line that passes through
(0,1) and (-8, -7) is
[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]
The slope of the line is 1Hope this helps you
Please help! Stuck on this question!!
Answer:
The 2 Gallon Tank is Enough
Step-by-step explanation:
A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.
There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.
[tex]8 * 2 = 16[/tex]
So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.
Answer:
2 gallon tank
Step-by-step explanation:
16 pints is the same as 2 US gallons
