Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and 0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.
a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.
b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)
Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,
P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228
P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392
P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269
P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093
P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016
P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011
d) The mean and standard deviation of the distribution is given by:
mean = n*p = 5*0.256 = 1.28
standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995
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expand the trinomial 10x2 - 61x + 72
The expansion of the trinomial 10x² - 61 x + 72 is (2x - 9) (5x - 8).
What is trinomial?An algebraic expression known as a trinomial has three non-zero terms and more than one variable. An example of a trinomial is a polynomial having three terms. An algebraic expression with one or more terms is called a polynomial.
Given:
10x² - 61 x + 72
Calculate the roots of the trinomial as shown below,
10x² - 16 x - 45 x + 72
2x (5x - 8) - 9(5x - 8)
(2x - 9) (5x - 8)
Thus, the expansion of the trinomial is (2x - 9) (5x - 8).
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which is the equation of the line shown in the graph A.y = 3x + 1/2 B. y = 3x + 2 C. y = 3x + 1/2 D. y = 1/2x + 3
Answer: D. y = 1/2x + 3
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 1/2
y-intercept: (0,3)
x|y
0|3
2|4
Hope this helps :D
What is the system with atleast one solution?
The System of Linear Equations with at least one solution is called as Consistent .
Consider the two linear equations , [tex]a_{1}x +b_{1}y =c_{1}[/tex] and [tex]a_{2}x +b_{2}y =c_{2}[/tex] ;
Case(i) If the ratio is [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex] ,
then we say that the system of linear equations has a unique solution and the solutions are called as consistent .
Case(ii) If the ratio is [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex] ,
then we say that the system of linear equations has infinitely many solution and the solutions are called as consistent .
Case(iii) If the ratio is [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex] ,
then we say that the system of linear equations has No Solution and the solutions are called as inconsistent .
So , if the system has at least one solution , then the solutions are consistent .
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Please help I'm really stuck
Answer:
7
Step-by-step explanation:
Answer:
7
If this help please set brainliest.
Step-by-step explanation:
To find the length between Point A (-3,4) and Point B (4,4), we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = √((4 - (-3))^2 + (4 - 4)^2)
Simplifying this, we get:
distance = √(7^2 + 0^2)
Simplifying further, we get:
distance = √49
So the distance between Point A and Point B is approximately 7.
What is the slope of the line joining (1, 4) and (-3, 2)?
Answer:
1/2
Step-by-step explanation:
The slope of a line is defined as the change in y-value divided by the change in x-value between two points on the line. To find the slope of the line joining (1, 4) and (-3, 2), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two points, we get:
slope = (2 - 4) / (-3 - 1)
slope = -2 / -4
slope = 1/2
So the slope of the line joining (1, 4) and (-3, 2) is 1/2.
Answer:
1/2
Step-by-step explanation:
derive an expression for the electric field at points on the x-axis, where −a
An expression for the electric field at points on the x-axis is [tex]$\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)$[/tex]
The electric field at a point P on the x-axis for which X is much larger than the distance between the charges.
Let us consider two charge -q and +q separated by small distance 2d.
P is a point along the axial line of the dipole at a distance X from the midpoint O of the electric dipole.
The electric field at the point P due to +q placed at B
[tex]E_1=\frac{1}{4 \pi \epsilon_0} \frac{q}{(X-d)^2}[/tex]...(I)
The electric field at the point P due to -q placed at A
[tex]E_2=-\frac{1}{4 \pi \epsilon_0} \frac{-q}{(X+d)^2}[/tex]...(II)
We need to calculate the magnitude of resultant of electric field
Using formula of electric field
[tex]E=E_1+\left(-E_2\right)[/tex]
Put the value into the formula
[tex]& E=\frac{1}{4 \pi \epsilon_0} \frac{q}{(X-d)^2}-\frac{1}{4 \pi \epsilon_0} \frac{q}{(X+d)^2} \\[/tex]
[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{1}{(X-d)^2}-\frac{1}{(X+d)^2}\right) \\[/tex]
[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 X d}{\left(X^2-d^2\right)^2}\right)[/tex]
If the point P is far away from the charges, and X is much larger than the distance between the charges
The electric field will be
[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 X d}{X^4}\right) \\[/tex]
[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)[/tex]
Hence, the electric field will be [tex]$\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)$[/tex]
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Derive an expression for the electric field at a point P on the x-axis for which X is much larger than the distance between the charges.
Graph h(x) = 7 sin x
Use 3.14
Graph of a sine function ,The sinusoidal graph, often known as the sine graph, is an up-down graph that repeats every 360 degrees, or at 2[tex]\pi[/tex]. Amplitude is 7
What is sine graph?Graph of a sine function ,The sinusoidal graph, often known as the sine graph, is an up-down graph that repeats every 360 degrees, or at 2[tex]\pi[/tex].
Trigonometric functions include sine functions. Keep in mind the intercepts, maximum points, and minimum points throughout one period if you wish to sketch the graph of the fundamental sine function. As a result, the graph is h(x) = 7 sin x depicted in the image below.
h(x) = 7 sin x
Those intercepts are
(0 0) , ([tex]\pi[/tex] ,0) , and (2[tex]\pi[/tex], 0)
A maximum of:
([tex]\pi[/tex]/2 , 7)
Minimum score:
(3[tex]\pi[/tex]/2 , -7)
Period:
2[tex]\pi[/tex]
Amplitude = 7
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Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is $\tfrac{1}{2}$, independently of what has happened before. What is the probability that Larry wins the game
The probability that Larry wins the game is [tex]$\tfrac{1}{2}$[/tex].
The probability that Larry knocks the bottle off the ledge on his first throw is
[tex]$\tfrac{1}{2}$.[/tex]
The probability that Larry knocks the bottle off the ledge on his second throw, given that he did not knock it off on his first throw, is
[tex]$\tfrac{1}{2}$[/tex]
Therefore, the probability that Larry wins the game is
[tex]$\tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{2}$.[/tex]
By the law of total probability, we have:
[tex]$P(W) = P(W|F)P(F) + P(W|F^c)P(F^c)$[/tex]
[tex]$P(W) = 1 \times \tfrac{1}{2} + \tfrac{1}{2} \times \tfrac{1}{2}$[/tex]
[tex]$P(W) = \tfrac{1}{2}$[/tex]
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find the volume of the given solid. bounded by the cylinders x2 + y2 = 16r2, y2 + z2 = 16r2
Answer: {1024/3 r^3
Step-by-step explanation:
Similar Question
Mother used 62.5% of a bag of flour weighing 4.8kg to make a loaf of bread. How much flour will she need to make 5 loaves of bread?
Answer:
15 kg
Step-by-step explanation:
.625 x 4.8 = 3
It takes 3 kg of flour to make 1 loaf of bread.
3 x 5 = 15
Find the area of the following triangle:
Enter the exact answer.
Do not round
13cm, 5.7cm, and 4cm
Answer:
To find the area of a triangle, you use the following formula:
[tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 13 x 4
= 6.5 x 4
= 26
Which statement is true by the ASA Postulate? CBA = DEA CBA = ADE CBA = CAB CBA = ABC
The two triangles that are congruent by by ASA congruency postulate are; ΔCBA ≅ ΔDBA
How to prove triangle congruence postulate?There are different triangle congruence postulates such as;
SAS which means Side - Angle - Side
SSS which means Side - Side - Side
ASA which means Angle - Side - Angle
AAS which means Angle - Angle - Side
HL which means Hypotenuse Leg Congruence Postulate
Now, we want to look for the triangles that are congruent by Angle - Side - Angle Congruence Postulate.
Looking at triangles ABC and AED, we can see that;
∠ACB ≅ ∠ADE
∠ABC ≅ ∠AED
BC ≅ ED
Thus, we have 2 congruent angles and the included side and as such ΔCBA ≅ ΔDBA by ASA congruency postulate.
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PLEASE I BEGGGGG IN A RUSH
The circle with the equation
(x-1)^2 + (y-k)^2 =50 passes through the point (2,3)
find the possible values for k
The possible values of k for the equation of circle are -4 and 7.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
The equation of a circle is (x - 1)² + (y - k)² = 50
The equation of the circle passes through the point (2, 3) = (x, y).
Now,
(2 - 1)² + (3 - k)² = 50
1 + (3 - k)² = 50
(3 - k)² = 50 - 1
3 - k = √49
3 - k = ±7
Now,
3 - k = 7
3 - 7 = k
k = -4
3 - k = -7
3 + 7 = k
k = 10
Thus,
The possible values of k are -4 and 10.
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Pretend your homeowners policy has a premium of $150, a deductible of $5,000, and a limit of $300,000. Your home suffers $170,000 in damages. How much will you pay for the damages?.
The total amount the homeowner would pay for the damages would be $5,150.
In this situation, the homeowner would pay $5,000 for the deductible, plus the premium of $150. The remaining amount of $165,000 would be covered by the policy up to the limit of $300,000. Therefore, the total amount the homeowner would pay for the damages would be $5,150.
To calculate this, we can use the following formula:
Total Cost = Deductible + Premium + (Damages - Limit)
Total Cost =[tex]$5,000 + $150 + ($170,000 - $300,000)[/tex]
Total Cost =[tex]$5,000 + $150 + (-$130,000)[/tex]
Total Cost = [tex]$5,150[/tex]
The total amount the homeowner would pay for the damages would be 5,150.
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find a formula for rn for the function f(x) = (5x)2 on [−1, 5] in terms of n.
RN=RN=
Compute the area under the graph as a limit.
limN→[infinity]RN
The Riemann sum formula to find RN is RN = (5/n) × Σ(i=1 to n) [f(x_i) × (5/n)], and the area under the graph as a limit is 400.
The function f(x) = (5x)² is a polynomial function, and we can use the formula for the nth Riemann sum to find RN. The formula for the nth Riemann sum is:
RN = (5/n) × Σ(i=1 to n) [f(x_i) × (5/n)]
where x_i = -1 + (i-1)(5/n) and f(x_i) = (5x_i)²
Substituting these values into the formula, we get:
RN = (5/n) × Σ(i=1 to n) [(5x_i)² × (5/n)]
RN = (5/n) × Σ(i=1 to n) [(25x_i²) × (1/n)]
Therefore the formula for RN is (5/n) × Σ(i=1 to n) [(25x_i²) × (1/n)]
To find the area under the graph as a limit, we take the limit as n approaches infinity:
limN→[infinity] RN = limN→infinity × Σ(i=1 to n) [(25x_i²) × (1/n)]
The function is defined on the closed interval [-1,5], so the definite integral is the definite integral from -1 to 5 of (25x²) dx
limN→[infinity] RN = (25/3) × 5³ - (25/3) × (-1)³
limN→[infinity] RN = (25/3)×(125 -1)
limN→[infinity] RN = 400
Therefore, limN→[infinity] RN = 400
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Write the integer that represents the opposite of each real world situation. In words, write the meaning of the opposite. Then, choose one of the examples and represent the integer and its opposite on a vertical number line. On a number line, locate and label a credit of $38 and a debit for the same amount from a bank account. What does zero represent in this situation?
The integer that represents the exact opposite of the real-world situation; "a credit of $38" is; -$38 which represents a debit for the same amount.
Which Integer represents the opposite of the given real world situation?As evident in the task content; the integer which correctly represents the opposite of the given real world problem is required to be determined.
Since the given real-world problem is; $38 which represents a credit.
The exact opposite of that which represents a debit for the same amount is; -$38.
On this note, the number line representation of both integers is as represented in the attached image.
The number, zero represents a point of neither credit nor debit in this situation.
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1. The area of a rectangular parking lot is 6264 m^2 .
If the length of the parking lot is 87 m , what is its width?
2. The perimeter of a rectangular pool is 342 m .
If the width of the pool is 78 m , what is its length?
Answer:
72 m
93 m
Step-by-step explanation:
1) A = length x width
6264 m² = (87 m)w
w = 6264 m²/87 m = 72 m
2) P = 2l + 2w
342 m = 2l + 2(78 m)
342 m - 156 m = 186 m = 2l
l = 186 m/2 = 93 m
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
The focus of a parabola is (0,-1). The directrix is the line y = 0. What is the equation of the parabola in vertex form?
(-k)² +h, the value of pis
In the equation y =
The vertex of the parabola is the point (
The equation of this parabola in vertex form is y =
2²-1
The equation of this parabola in vertex form is y = ( -1/2) x² - 0.5
What are Functions?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
We are given that Focus (0,-1), Directrix is the line y=0
so, we have a vertical parabola open downward
Remember that the distance from the vertex to the directrix must be the same that the distance from the vertex to the focus
This means that the vertex is the point (0,-0.5)
The midpoint between the focus and the directrix
Find out the value of p (focal distance)
p=0.5
The equation of the parabola is given by
y =( -1/2) x² - 0.5
The vertex is (0,-0.5)
The value of p=0.5
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round off 4 067.23 to the nearest ten
4,067.2
Step-by-step explanation:
—4067.23
You rounded to the nearest tenths place. The 2 in the tenths place rounds down to 2, or stays the same, because the digit to the right in the hundredths place is 3.
4,067.2
When the digit to the right is less than 5 we round toward 0.
4067.23 was rounded down toward zero to 4,067.2
Shirley buys 5 bottles of soda. She has a coupon for 0.55 dollars off the regular price of each bottle. After using the coupons, the total cost is 5.20 what is the regular price of the soda.
The regular price of the soda is $1.59
How to determine the regular price of the soda.From the question, we have the following parameters that can be used in our computation:
Number of bottles = 5
Total cost = 5.20
Coupon = 0.55
Using the above as a guide, we have the following:
Total cost = Number of bottles * (Regular price - Coupon)
Substitute the known values in the above equation, so, we have the following representation
5 * (Regular price - 0.55) = 5.20
So, we have
Regular price - 0.55 = 1.04
Add 0.55 to both sides
Regular price = 1.59
Hence, the regular price is 1.59
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A firm has the short-run total cost function c(y) = 4y 2 100. it marginal cost is mc(y) = 8y. at what quantity of output is short-run average cost minimized? a. 5 b. 2 c. 25 d. 0.40
A firm has the short-run total cost function c(y) = 4y^2 + 100; its marginal cost is mc(y) = 8y. At the A: 5 quantity of output the short-run average cost is minimized.
AC=c/y, where y is the output produced
AC= c/y= (4y^2 + 100)/y
= 4y+100/y
To minimize AC, the first derivative of the AC function is determined
dAC/dy= 4 -100/y^2
4 -100/y^2=0
4 = 100/y^2
y^2 = 100 /4
y^2 = 25
y = 5
At y=5 we find the second derivative of the AC function to ascertain if AC is minimized.
d(dAC/dy)= -200/y^3
-200/(5)^3= 1.6, revealing that AC is minimized at y=5.
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Co-efficient of y in - 2x ^ 2 * y ^ 2 * z is
Please help!
Give step by step explanation
The coefficient of y in the expression -2x² * y² * z is 0
How to determine the coefficient of y in the expressionFrom the question, we have the following parameters that can be used in our computation:
An algebraic expression
The algebraic expression is given as
- 2x ^ 2 * y ^ 2 * z
Express the exponents as proper subscripts
So, we have the following representation
-2x² * y² * z
There is no term in the expression with the variable y
Instead, the term has a y² as its variable
This means that the coefficient of y is 0
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Ahmad obtained a car loan of RM 700000 from a bank with an interest rate of 3.2% per annum for 9 years. Calculate the loan amount that Ahmad needs to repay.
The loan amount that Ahmad needs to relay will be RM 901600
How to calculate the interest?From the information, Ahmad obtained a car loan of RM 700000 from a bank with an interest rate of 3.2% per annum for 9 years.
The interest based on the information will be:
= Principal × Rate × Time
= 700000 × 3.2% × 9
= $201600
The loan amount that Ahmad needs to relay will be:
= 700000 + 201600
= 901600
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The temperature was `-13`℉ and then rose `5` degrees.
What was the final temperature?
Answer:The answer is -18
Step-by-step explanation: Add -13+5 and you will get the correct answer.
It takes a cook 3 min 45 sec to make 3 sandwiches and 3 salads. It takes him 8 min 30 sec to make 6 sandwiches and 8 salads. How long does it take to make each sandwich
The time taken by cook to make one sandwich is equals to forty-five seconds.
let "x" be the time (in seconds) to make 1 sandwhich and " y " be the time (in seconds) to make 1 salad. Now, it takes 3 min 45 sec to make 3 sandwiches and 3 salads.
time in seconds , 3 min 45 sec = 225 sec
so, 3x + 3y = 225
=> x + y = 75 --(1)
Also, it takes 8 min 30 sec to make 6 sandwiches and 8 salads, i.e ,8min 30sec = 510 sec
so, 6x + 8y = 510
=> 3x + 4y = 255--(2)
We have a system of linear equations consists equation (1) and (2). We solve this system of equations by using Substitution,
Substitute the value of x = 75 - y in equation (2),
3x + 4y = 255
=> 3(75- y) + 4 y = 255
=> 225 - 3y + 4y = 255
=> y = 255 - 225 = 30
from equation (1) , x = 75 - 30 = 45.
So, it takes 45 seconds to make one sandwich and 30 seconds for one salad .
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Point c is on line segment \overline{bd} bd. Given bd=2x,bd=2x, cd=8,cd=8, and bc=x,bc=x, determine the numerical length of \overline{bd}. Bd.
The numerical length of BD is 16 units
as given in the question,
There is a line segment BD
and a point lies on the line segment BD which is point C
but we don't know the exact position where the point C lies on the line segment BD
from the details given
The distance between C and B is x
the distance between B and D is 2x
the distance between C and D is 8
let the point C be a arbitrary point in the line segment BD
now ,
BC + CD = BD
x + 8 = 2x
x = 8
now BD is 2x that is 2( 8) is 16
The length of BD is 16.
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The numerical length of [tex]\overline{bd}[/tex] is 16 units.
Using the formula for the length of a line segment, we can calculate the length of segment BD. The formula is
Length = [tex]√((x2-x1)^2+(y2-y1)^2)[/tex]
We know that BD = 2x so x2 = 2x and x1 = 0. We also know that CD = 8 and BC = x so we can calculate y2 and y1. y2 = 8 - 2x and y1 = x - 0.
Therefore, plugging in these values we get:
Length =[tex]√((2x-0)^2+(8-2x)^2)[/tex]
Solving for the length of BD we get:
Length = [tex]√(4x^2 + 64)[/tex]
Substituting in the value of x = 8, we get:
Length = [tex]√(4*8^2 + 64)[/tex]
Length = [tex]√(256 + 64)[/tex]
Length = [tex]√320[/tex]
Length = 16 units.
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Ahmad needs to memorize words on a vocabulary list for French class. He has 9 words to memorize, and he is one-third done. How many words has Ahmad
memorized so far?
Answer: 3 words
Step-by-step explanation:
what is 9 in a fraction
How many segments can be drawn using 4 points?
Answer:
6
Step-by-step explanation:
Drag each tile to the correct box
Find the distance between pairs of points, and arrange them in increasing order.
C and D
D and E
B and C
F and A
E and F
A and B
The distance between two points is D and E, E and F, C and D, A and B, B and C, when the points are arranged in increasing order.
How to find the distance between the following pairs of points?Discover the distance formula, a Pythagorean theorem application, to determine the separation between two places. To get the separation between any two points, we can rewrite the Pythagorean theorem as [tex]d= \sqrt{x_{2} -x_{1} + y_{2} -y_{1} }[/tex]
In geometry, distances are always positive unless the points are exactly adjacent. The distance between A and B is equal to the distance between B and A. We consider two points A(a,b) and B to get the formula for the distance between two points in the plane (c,d).
[tex]d= \sqrt{x_{2} -x_{1} + y_{2} -y_{1} }[/tex]
The distance is provided in the following equation as
A and B are [tex]\sqrt{39}[/tex] miles apart.
B and C are [tex]\sqrt{41}[/tex] miles apart.
C and D are five miles apart.
D and E are four miles apart.
E and F are [tex]\sqrt{17}[/tex] miles apart.
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Answer:
Step-by-step explanation:
you have to count the distance between each point then list them from smallest to greatest. The other answers on here made it more convoluted than necessary.
A coin is tossed three times. What is the probability that the first toss and the last toss yield different outputs?.
There is a 0.5 probability that the first toss and the last toss yield different outputs.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The sample space for a coin tossed three times is:
P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}
Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.
The sample space for this is:
P = {HHT, HTT, THH, TTH}
The probability is:
[tex]P = \frac{4}{8} = \frac{1}{2}[/tex]
Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.
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There is a 0.5 probability that the first toss and the last toss yield different outputs.
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What is probability and example?
It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.
The sample space for a coin tossed three times is:
P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}
Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.
The sample space for this is:
P = {HHT, HTT, THH, TTH}
Probability = Number of Favorable Outcomes / Total Number of Outcomes.
P = 4/8 = 1/2
Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.
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