Answer:
[tex]P(X = 0) = 0.03125[/tex]
[tex]P(X = 1) = 0.15625[/tex]
[tex]P(X = 2) = 0.3125[/tex]
[tex]P(X = 3) = 0.3125[/tex]
[tex]P(X = 4) = 0.15625[/tex]
[tex]P(X = 5) = 0.03125[/tex]
Step-by-step explanation:
For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Fair coin:
Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]
5 tosses:
This means that [tex]n = 5[/tex]
Probability distribution:
Probability of each outcome, so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]
[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]
[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]
[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
if a pendrive is bought for 1200 and sold at 25% profit find the profit amount
Answer: Profit = $300
Step-by-step explanation:
Given information
Original Price = $1200
Profit rate = 25%
Given expression
Profit amount = Profit rate × Original price
Substitute values into the expression
Profit amount = 25% × 1200
Profit amount = $300
Hope this helps!! :)
Please let me know if you have any questions
A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 10 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy
Answer:
50/60 = .8333= 83.33%
Step-by-step explanation:
The probability that the call arrived when the switchboard was not fully busy is 0.75.
What is Normal Distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Given:
Here X follows uniform distribution with parameter a and b.
Where,
a = 0 and b = 1.
Then,
The density function of Y is given by:
P( 15 < Y ≤ 60)
or, P( 0.25 < Y ≤ 1)
So, P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]
= [tex][y]^1 _ {0.25}[/tex]
= (1- 0.25)
= 0.75
Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.
Learn more about Normal Distribution here:
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1. Which of these sentences are propositions? What are the
truth values of those that are propositions?
a) Boston is the capital of Massachusetts.
b) Miami is the capital of Florida.
c) 2 + 3 = 5. d) 5 + 7 = 10.
e) x + 2 = 11. 1) Answer this question.
Answer:I have the same problem
Step-by-step explanation
For an ordered pair left parenthesis x comma y right parenthesis in a relation, the x element represents the
Answer:
the x éléments représente the domain
x represents the value on the x-axis and the coordinate is also known as abscissa.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).
Here x represents the value on the x-axis and the coordinate is also known as abscissa.
More about the coordinate geometry link is given below.
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Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
OAmalOHopeO
find the two intersection points
(x+1)^2 +(y+2)^2 = 16
3x+ 4y = 1
Show your steps please
Answer:
Our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Step-by-step explanation:
We want to find where the two graphs given by the equations:
[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]
Intersect.
When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.
Since the linear equation is easier to solve, solve it for y:
[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]
Substitute this into the first equation:
[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]
Simplify:
[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]
Square. We can use the perfect square trinomial pattern:
[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]
Multiply both sides by 16:
[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]
Combine like terms:
[tex]25x^2+-22x+97=256[/tex]
Isolate the equation:
[tex]\displaystyle 25x^2 - 22x -159=0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 25, b = -22, and c = -159. Substitute:
[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]
We have our two x-coordinates.
To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:
[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]
And:
[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]
Thus, our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
A data set includes data from student evaluations of courses. The summary statistics are n=89, x=3.44, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
H0: μ=3.50
H1: μ>3.50
B.
H0: μ=3.50
H1: μ<3.50
C.
H0: μ≠3.50
H1: μ=3.50
D.
H0: μ=3.50
H1: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)
We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0
The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.
We go with answer choice D to form the null and alternative hypotheses.
The sign ≠ in the alternative hypothesis tell us that we have a two tail test.
---------------------------------------
Let's compute the test statistic
z = (xbar - mu)/(s/sqrt(n))
z = (3.44 - 3.50)/(0.67/sqrt(89))
z = -0.84483413122896
z = -0.84
The test statistic is roughly -0.84
---------------------------------------
Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.
Use a calculator or a Z table to determine that
P(Z < -0.84) = 0.2005
which is approximate
Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401
The p-value is roughly 0.401
-----------------------------------------
Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.
The conclusion based on that means that μ=3.50 must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50
Solve for y 2y+1>-9/5y-6
Answer: All real numbers
Step-by-step explanation:
Let's find the critical points of the inequality.
2y2+1=
−9
5
y−6
2y2+1−(
−9
5
y−6)=
−9
5
y−6−(
−9
5
y−6)(Subtract (-9)/5y-6 from both sides)
2y2+
9
5
y+7=0
For this equation: a=2, b=1.8, c=7
2y2+1.8y+7=0
y=
−b±√b2−4ac
2a
(Use quadratic formula with a=2, b=1.8, c=7)
y=
−(1.8)±√(1.8)2−4(2)(7)
2(2)
y=
−1.8±√−52.76
4
Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *
12/24
Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.
Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24
Step Three: Add our new fractions: 3/24+8/24= 12/24
Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten
I hope I've help!
Suppose that appearances of a foe to battle (that is, a random encounter) in a role-playing game occur according to a Poisson process, and the average rate equals one appearance per two minutes. Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
Answer:
Rate parameter of [tex]\mu = 0.5[/tex]
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
One appearance per two minutes.
This means that [tex]m = 2[/tex]
Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
[tex]\mu = \frac{1}{m} = \frac{1}{2} = 0.5[/tex]
So
Rate parameter of [tex]\mu = 0.5[/tex]
A(3, 7), B(5, 7), C(3-7), D(5, -7)
what is the area ?
Answer:
28 square units.
Step-by-step explanation:
This is a rectangle with sides (7 - (-7) and (5 - 3)
= 14 by 2
= 28 unit^2.
What is the length of the missing leg??
Answer:
12.04 cm
Step-by-step explanation:
Pythagoras in general :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90 degree angle).
a and b are the side legs.
so, in our example here
17² = 12² + b²
289 = 144 + b²
145 = b²
b = sqrt(145) = 12.04 cm
Working at home: According to the U.S Census Bureau, 34% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 170 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Answer:
The answer is "0.340".
Step-by-step explanation:
[tex]n = 500\\\\x = 170[/tex]
Using formula:
[tex]\to \hat{p} = \frac{x}{n} = \frac{170}{500}=\frac{17}{50} =0.340[/tex]
An item is regularly priced at $70. Keiko bought it on sale for 80% off the regular price. How much did Keiko pay? $
Answer:
$14
Step-by-step explanation:
80% of $70 is $14, saving him $56
The other person has a great answer. Here's another approach.
If the discount is 80%, then you have to pay the remaining 20% (the two percentages add to 100%)
20% of 70 = 0.20*70 = 14
The sale price is $14 which is the amount Keiko pays
We see that Keiko saves 70-14 = 56 dollars.
Write 3^7/2 in surd form.
Answer:
[tex]\sqrt[2]{3^7}[/tex]
Step-by-step explanation:
[tex]\sqrt[2]{3^7}[/tex]
The top number is the power and the bottom of the fraction is the root
Complete the equation describing how
x and y are related.
X
-2
-1
D
у
12
8
0
-8
E 12
y = [? ]x
Enter the answer that belongs in [?]
Answer:
y= -(4x)
Step-by-step explanation:
Process control and acceptance sampling procedures are most closely related to _____. a. analysis of variance procedures b. hypothesis testing procedures c. interval estimation procedures d. linear regression procedures
10 times as much as 9
Answer:
90
Step-by-step explanation:
10 x 9
=> 90
10 times 9 is 90.
A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.
Answer:
About 6,785 people will be infected about nine months.
Step-by-step explanation:
We can write an exponential function to represent the situation. The standard exponential function is given by:
[tex]\displaystyle f(x) = a(r)^x[/tex]
Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.
3,124 people have already been infected. Thus, our initial value a = 3124.
And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.
Hence, our function is:
[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]
Then after nine months, the total amount of infected people will be f(9):
[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]
Use a calculator:
[tex]\displaystyle f(9) \approx 6785[/tex]
About 6,785 people will be infected about nine months.
Answer:
7,022
Step-by-step explanation:
How many x intercepts does the graph of y=2x^2+4x-2have
Answer:
2
Step-by-step explanation:
x intercepts are at y=0
therefore
0= 2x^2+4x-2
Simplify by 2
0=x^2+2x-1
the determinant
D= 2^2 - 4 (1)(-2) = 4 + 8 = 12 > 0
therefore the graph has two intercepts
Please help out explanation need it
For this you just look at the sides.
Soh cah toa
This is good to remember.
Sin = opposite/ hypotenuse
Cos= adjacent/ hypotenuse
Tan = opposite/ adjacent
In this case you have TanZ, the side adjacent to the angle is 10 and the opposite to the angle is 24. So tanZ is 24/10 which simplifies to 12/5.
The hypotenuse is always the longest side, but the opposite and adjacent sides can change depending on the angle.
Answer:90 = ... 42 + 48) - 360
Step-by-step explanation:
Bill's father is three times Bill's age. Three years ago, Bill's father was four times Bill's age.
By forming two equations, find Bill's age now.
Answer:
12 and 36
Step-by-step explanation:
Call the age of both Bill and his father is a and b, respectively
we have:
b=3a
b-3=4(a-3) ->b=4a-12 -> 3a=4a-12 ->a =12 -> b=36
on a 25 square grid how many squares need to be shaded to make 60% shaded
Answer:
15 squares
Step-by-step explanation:
60/100 * 25 = 15
Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.
Answer:
Step-by-step explanation:
The remainder when f(x) is divided by x + 3 would be 76.
What is remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x).
We have been given a function;
[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]
We need to find the remainder when f(x) is divided by x + 3.
So, Let p(x) = x + 3
p(x) = 0
x + 3 = 0
x = -3
Substitute in the given function f(x);
[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]
Thus, the remainder when f(x) is divided by x + 3 would be 76.
Learn more about remainder;
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Which polynomial function is best represented by the graph?
ƒ(x) = –x(x – 1)4
ƒ(x) = x2(x + 1)3
ƒ(x) = x2(x – 1)3
ƒ(x) = x(x – 1)4
Answer: ƒ(x) = x2(x – 1)3
a contractor charges $1200 for 100 square feet of roofing installed. at this rate how much does it to have 1,100 square feet installed
Answer:
$13,200
Step-by-step explanation:
if 100 square feet = $1,200
1,100 square feet = $13,200
1500 to the nearest hundred
Answer:
1500.
There is no need to round here, it is already exact.
Which expression is equivalent to sqrt of (6x^5 z)^3/ 4x^4 z^2
Answer:
[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]
I hope I helped you^_^
What's the measure of an arc with a central angle of 90°?
1) 90°
2) 360°
3) T°
4) 180°
Answer:
1.) 90° degrees becausemeasure of an arc is equal to the measure of an arc's central angle.
Express 18 hours to 2 days in its lowest term
Answer:
1 : 3
Step-by-step explanation:
We know that 1 days is 24 hours
2 days = 2*24 = 48 hours
16 hours : 48 hours
Divide each by 16
16/16 : 48/16
1 : 3
Answer:
[tex]3 : 8[/tex]
Step-by-step explanation:
[tex]18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8[/tex]
