Answer:
a) [tex] P(X=3) = 0.1[/tex]
b) [tex] P(X\geq 3) =1-P(X<3) = 1-P(X\leq 2) = 1-[P(X=0) +P(X=1)+P(X=2)][/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4[/tex]
c) [tex] P(X=4) = 0.3[/tex]
d) [tex] P(X=0) = 0.2[/tex]
e) [tex] E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2[/tex]
f) [tex] E(X^2)= \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4[/tex]
And the variance would be:
[tex] Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4[/tex]
And the deviation:
[tex] \sigma =\sqrt{2.4} = 1.549[/tex]
Step-by-step explanation:
We have the following distribution
x 0 1 2 3 4
P(x) 0.2 0.3 0.1 0.1 0.3
Part a
For this case:
[tex] P(X=3) = 0.1[/tex]
Part b
We want this probability:
[tex] P(X\geq 3) =1-P(X<3) = 1-P(X\leq 2) = 1-[P(X=0) +P(X=1)+P(X=2)][/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4[/tex]
Part c
For this case we want this probability:
[tex] P(X=4) = 0.3[/tex]
Part d
[tex] P(X=0) = 0.2[/tex]
Part e
We can find the mean with this formula:
[tex] E(X)= \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2[/tex]
Part f
We can find the second moment with this formula
[tex] E(X^2)= \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4[/tex]
And the variance would be:
[tex] Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4[/tex]
And the deviation:
[tex] \sigma =\sqrt{2.4} = 1.549[/tex]
what is the slope-intercept equation of the line shown below?
Slope = 3, y intercept = 2
============================================================
Work Shown:
Find the slope of the line through (x1,y1) = (-2,-4) and (x2,y2) = (1,5)
m = (y2 - y1)/(x2 - x1)
m = (5 - (-4))/(1 - (-2))
m = (5 + 4)/(1 + 2)
m = 9/3
m = 3 is the slope
Plug m = 3 and (x1,y1) = (-2,-4) into the point slope formula. Solve for y.
y - y1 = m(x - x1)
y - (-4) = 3(x - (-2))
y + 4 = 3(x + 2)
y + 4 = 3*x + 3*2 ... distribute
y + 4 = 3x + 6
y + 4 - 4 = 3x + 6 - 4 ... subtracting 4 from both sides
y = 3x + 2 is the slope intercept equation
Which of the following statements about trapezoids is true?
O A. Opposite angles are equal
B. One pair of opposite sides is paralel.
C. Opposite sides are equal
O D. Both pairs of opposite sides are parallel
Answer:
B
Step-by-step explanation:
Trapezoids have only one pair of parallel lines.
What is y - 8 = 4(x - 4) in slope intercept form?
Answer:
y=4x-8
Step-by-step explanation:
First you must use the distributive property and get y-8=4x-16.
Then you have to add 8 on both sides so just y is left on the left side.
This will get you y=4x-8 in slope-intercept form.
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 120 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population?
Required:
a. State the random variable, population parameter, and hypotheses.
b. State the Type I and Type II errors in the context of this problem.
Answer:
(a) H₀: p = 0.11 vs. Hₐ: p > 0.11.
(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
Step-by-step explanation:
A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus.
From past data, it is believed that 11% of all Americans are left-handed.
The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handed people than the general American population.
(a)
The hypothesis can be defined as follows:
H₀: The percentage of left-handed people in the college is 11%, i.e. p = 0.11.
Hₐ: The percentage of left-handed people in the college is more than 11%, i.e. p > 0.11.
(b)
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this case, a type I error would be committed if it is concluded that the percentage of left-handed people in the college is more than 11% when in fact it is 11%.
And, a type II error would be committed if it is concluded that the percentage of left-handed people in the college is 11% when in fact it is more than 11%.
PLEASE HELP ME!! A hexagon has vertices (3,1) and (4,1). The hexagon is dilated. The new hexagon has vertices (6,1) and (10,1). {In the same spots as the old hexagon}. What is the center of dilation? What is the dilation factor? I can try to add information.
Answer:
( 2,1) is the center of dilation and 4 is the scale factor
Step-by-step explanation:
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
3,1 becomes 6,1
6,1 = k( 3-a) +a, k( 1-b)+b
6 = 3k -ka+a
1 = k -kb +b
4,1 becomes 10,1
10,1 = k( 4-a) +a, k( 1-b)+b
10 = 4k -ka+a
1 = k -kb +b
Using these two equations
6 = 3k -ka+a
10 = 4k -ka+a
Subtracting the top from the bottom
10 = 4k -ka+a
-6 = -3k +ka-a
------------------------
4 = k
Now solving for a
6 = 3k -ka+a
6 = 3(4) -4a+a
6 =12 -3a
Subtract 12
6-12 = -3a
-6 = -3a
Divide by -3
-6/-3 = -3a/-3
2 =a
Now finding b
1 = k -kb +b
1 = 4 - 4b+b
1 =4 -3b
Subtract 4
-3 = -3b
Divide by -3
1 = b
Answer:
Dilation factor: 4.
Center of dilation: (2, 1).
Step-by-step explanation:
The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.
Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.
In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.
10 = 4(4 – a) + a
10 = 16 – 4a + a
10 = 16 – 3a
-3a + 16 = 10
-3a = -6
a = 2
1 = 4(1 – b) + b
1 = 4 – 4b + b
1 = 4 – 3b
-3b + 4 = 1
-3b = -3
b = 1
And so, your center of dilation will be (2, 1).
Hope this helps!
Expand and simplify (4x+3)(2x-5)
Answer:
4x(2x-5)+3(2x-5)
8x^2-20x+6x-15
8x^2-14x-15
Ryan called each school in the district to determine whether or not they have a recycling program. What is true about Ryan’s data collection?
Answer:
A. Ryan conducted a survey where he asked about qualitative data.
Step-by-step explanation:
Surveys when carried out on people as the subjects are meant for the purpose of extracting some specific information from them. Observational studies involve close monitoring of the subject under evaluation. Quantitative data mainly deal with numbers and figures obtained from measurements or calculations. Qualitative data on the other hand is basically descriptive in nature and could sometimes be quite detailed.
Ryan's data collection would require a yes or no answer from the schools involved, and this information is descriptive or qualitative in nature. It also does not involve observation or close monitoring as he relies on the information provided by the school.
Answer: A
Step-by-step explanation:
Have a nice day
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl
Answer: 7/8
Step-by-step explanation:
Let the boy is letter B and the girl is letter G.
So the possible outcomes are as follows below
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
SO the number of possible outcomes is 8
The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7
So the probability, that family with 3 kids has at least 1 girl is
P(number of girls >=1)= 7/8
Select the correct answer from each drop-down menu. The given equation has been solved in the table.
Answer:
1). SUBTRACTION property of equality
2). MULTIPLICATION property of equality
Step-by-step explanation:
Step 2:
When we subtract the same number from both the sides of an equation it represents the subtraction property of equality.
[tex]\frac{x}{4}+5-(5)=23-(5)[/tex]
Here 5 has been subtracted from both the sides.
Therefore, SUBTRACTION property of equality was applied.
Step 4:
If the same number is multiplied to both the sides of an equation, multiplication property of equality is applied.
[tex]4\times \frac{x}{4}=4\times (18)[/tex]
Here 4 has been multiplied to both the sides.
Therefore, MULTIPLICATION property of equality was applied.
6x+15=6x+15 ❤️Solve the equation correctly to get brainliest and thanks! :)❤️
Answer:
Hey there!
6x+15=6x+15
Subtract 15 on both sides
6x=6x
Divide by 6 on both sides
x=x
Thus, x can be any number and there is an infinite amount of solutions.
Hope this helps :)
3. Find the measure of x.
a 18°
b. 54°
C 126
d. 45
Answer:
18 degrees
Step-by-step explanation:
The triangle is an iscoceles right triangle.
The angles in a triangle add up to 180.
90+2y (iscoceles) =180
2y=90
y=45
So the angles of the right triangle are 45. However, you have to take away 27 because you are solving for only a part of 45. 45-27=18
plz answer question in screen shot
Answer: 342.32
Step-by-step explanation: sin(25) = h/a
Sin(25)= h/27
27*sin(25) = h
b*h = area
i need this asap guys im giving brainliest
An aquarium is in the shape of a rectangular prism. How much water will it take to fill the aquarium if the dimensions are 2ft by 4ft by 3ft? 12 cubic feet 24 cubic feet 36 cubic feet 8 cubic feet
Answer:
24 cubic feet.
Step-by-step explanation:
What we need to do here, is to find the volume of the aquarium.
The Aquarium is a rectangular prism.
The volume of a rectangular prism is length*width*height (we just multiply the dimensions together)
2*4*3=8*3=24
The volume of the aquarium is 24 cubic feet, and therefore 24 cubic feet of water is required to fill the tank.
Answer:
Hello! :) The answer will be under “Explanation”
Step-by-step explanation:
The answer will be 24 cubic feet.
Work:
LxWxH
(Length,Width,Hight)
So you the question is asking about volume, we need to do the formula (length,width, and hight)
Now we have to multiply
2x4=8
8x3=24
So the answer will be 24 cubic feet.
Hope this helps! :)
A company buys a machine for $575,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n)
Answer:
[tex]V(n) = 575000(0.7)^{n}[/tex]
Step-by-step explanation:
The value of the machine after n years is given by an exponential function in the following format:
[tex]V(n) = V(0)(1-r)^{n}[/tex]
In which V(0) is the initial value and r is the yearly rate of depreciation, as a decimal.
A company buys a machine for $575,000 that depreciates at a rate of 30% per year.
This means, respectively, that: [tex]V(0) = 575000, r = 0.3[/tex]. So
[tex]V(n) = V(0)(1-r)^{n}[/tex]
[tex]V(n) = 575000(1-0.3)^{n}[/tex]
[tex]V(n) = 575000(0.7)^{n}[/tex]
In the xy-plane, what is the y-intercept of the graph of the equation y=V4-?
O a. 2
O b.4
O c. 16
O d. There is no y-intercept.
Answer:
D
Step-by-step explanation:
There isn't enough information to find a y-intercept.
the commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. if a random sample of 37 workers is taken and results in a sample mean of 31 minutes and sample standard deviation of 5 minutes, find a 95% confidence interval estimate for the population mean using the student's t-distribution.
Answer:
The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 37 - 1 = 36
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 36 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0262
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0262\frac{5}{\sqrt{37}} = 1.67[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 31 - 1.67 = 29.33 minutes
The upper end of the interval is the sample mean added to M. So it is 31 + 1.67 = 32.67 minutes.
The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.
Find the value of x geometry
Answer:
x = 22
Step-by-step explanation:
Since the the 2 bisectors are equal, that means the chords are also equal. Since bisector splits into 2 equal parts, 11 + 11 equals 22
Can anyone help me with the question I attached below?
Answer:
The range in the average rate of change in temperature of the substance is from a low temperature of -22 ºF to a high of 16 ºF.
Step-by-step explanation:
Sine function is a bounded function whose range is between -1 and 1. The lowest average rate of change in temperature occurs when sine function is equal to 1 and the highest when this function is equal to -1. Then, the minimum and maximum average rate of changes in temperature are:
Minimum
[tex]f_{min} = -19 -3[/tex]
[tex]f_{min} = -22[/tex]
Maximum
[tex]f_{max} = 19-3[/tex]
[tex]f_{max} = 16[/tex]
The range in the average rate of change in temperature of the substance is from a low temperature of -22 ºF to a high of 16 ºF.
please help! the number of candies consumed varies inversely with the number of children present
Answer:
The answer is
210 candiesStep-by-step explanation:
Let n represent the number of children
Let c represent the number of candies
The above variation is written as
[tex]c = \frac{k}{n} [/tex]
when n = 12 c = 140
So we have
[tex]140 = \frac{k}{12} [/tex]
Cross multiply
That's
k = 1680
So the formula for the variation is
[tex]c = \frac{1680}{n} [/tex]
when n = 8
[tex]c = \frac{1680}{8} [/tex]
c = 210
Therefore there are 210 candies consumed when there are 8 children
Hope this helps you
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
53 in.
Step-by-step explanation:
to find the area u do 8 times 6 and 1/2 2(5)
triangle = 1/2bh
rectangle = bh
hope this helps
Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined. z=x8+3y+xy.
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined. z=[tex]x^{8}[/tex]+[tex]3^{y}[/tex]+[tex]x^{y}[/tex]
a) Zx b) Zy
In differentiation, if y = axⁿ, y' = [tex]nax^{n-1} \ where \ n\ is\ a\ constant[/tex]. Applying this in question;
Given the function z = x⁸+[tex]3^{y}[/tex]+[tex]x^{y}[/tex]
[tex]Z_x = \frac{\delta z}{\delta x} = 8x^{7} + 0 + yx^{y-1} \\\frac{\delta z}{\delta x} = 8x^{7} + yx^{y-1} \\[/tex]
Note that y is treated as a constant since we are to differentiate only with respect to x.
For Zy;
[tex]Z_y = \frac{\delta z}{\delta y} =0+ 3^{y} ln3 + x^{y}lnx \\\frac{\delta z}{\delta y} = 3^{y} ln3 + x^{y}lnx } \\[/tex]
Here x is treated as a constant and differential of a constant is zero.
What is the next item in the sequence −10,−3,4,11
Answer:
18
Step-by-step explanation:
The pattern in this sequence is that you add 7 from the previous number to get the next number (-10 + 7 = -3, -3 + 7 = 4, etc). The next item will be 11 + 7 + 18. Hope this helps!
The next item in the sequence is 18.
What is sequence and series ? A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.A number sequence is a collection of numbers that move from term to term according to a specific pattern or rule.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.
The sequence is -10 ,-3, 4, 11,........
this sequence is following pattern ,you add 7 from the previous number to get the next number
First term = -10 + 7 = -3,
Second term =-3 + 7 = 4, .
The next item will be 11 + 7 = 18.
Therefore, The next item in the sequence is 18.
Learn more about sequence brainly.com/question/12474324 here
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What is the serving of coffee? 1 quart, 1 ml, or 1 c
Can somebody help me with this question?
Answer:
86 yd
Step-by-step explanation:
the area of the shaded region is 2924 yd²
let b the doted side next y :
the area of the total triangle is :
A = (y+b)*68/2 = 2924+ b*68/2
[tex]\frac{(y+b)*68}{2}[/tex] = [tex]\frac{b*68}{2}[/tex] + 2924 [tex]\frac{68*(y+b-b)}{2}[/tex] = 2924 68*y/2 = 2924 68y = 2*2924 y= (2*2924)/68 y= 86 ydwhat is the answer to this ??
Answer:
[tex] A.\angle 1\: \\\\D. \angle 3[/tex]
Step-by-step explanation:
[tex] \angle 1\: \&\: \angle 3[/tex] are remote interior angles of [tex] \angle 6[/tex]
what is 8/5plus 2x?please answer this for me
The intensity of a hurricane is a random variable that is uniformly distributed on the interval [0, 3]. The damage from a hurricane with a given intensity y is exponentially distributed with a mean equal to y. Calculate the variance of the damage from a random hurricane.
Answer:
3.75
Step-by-step explanation:
We have that x is the random variable denoting damage and y is the variable denoting intensity:
they tell us that the interval is [0.3], the variance in this case is the same:
var (x) = var * [E (x | y)] + E * [var (x | y)]
from here we have to:
var (x) = var (y) + E (y ^ 2)
we know that var (y) = E (y ^ 2) - E ^ 2 (y), we replace
var (x) = E (y ^ 2) - E ^ 2 (y) + E (y ^ 2)
var (x) = 2 * E (y ^ 2) - E ^ 2 (y)
We have that E (y ^ 2) = integral from 0 to 3, from 1/3 y ^ 2 * dy
we solve and we are left with:
1/9 and ^ 3, from 0 to 3
(1/9) * (3 ^ 3) - (1/9) * (0 ^ 3) = 3
We also know that E (y) = 3/2
replacing we have:
var (x) = 3 * 2 - (3/2) ^ 2
var (x) = 3.75
Therefore the variance is 3.75
Jerry has a miniature model of a boat. He knows that the model is 3 3/4 inches wide and 5 1/2 inches long. What is the actual length of the boat if the actual width is 15 feet
Answer:
22 feet
Step-by-step explanation:
Change 15 feet into inches using the conversion
1 foot = 12 inches, thus
15 ft = 15 × 12 = 180 inches
scale factor = 180 ÷ 3.75 = 48
Thus the actual dimensions of the boat are 48 times the model.
actual length = 48 × 5.5 = 264 inches = 264 ÷ 12 = 22 feet
Please help ASAP thanks in advance
Answer:
Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)
Step-by-step explanation:
can someone pleaseee help me??