Answer:
[tex]E(X^2)=32.5\\V(X)=7.5\\E[X(X-1)]=E(X^2)-E(X)\\V(X)=E(X^2)-[E(X)]^2[/tex]
Step-by-step explanation:
We have the following properties:
[tex]E( X + Y ) = E(X) + E(Y)\\V(X) = E(X^2)-[E(X)]^2[/tex]
So, if we have that E[X(X-1)] = 27.5, we can write them using the first property as:
[tex]E(X(X-1))=27.5\\E(X^2-X)=27.5\\E(X^2)-E(X)=27.5[/tex]
Then, replacing E(X) by 5 and solving for [tex]E(X^2)[/tex], we get:
[tex]E(X^2)-5=27.5\\E(X^2)=27.5+5\\E(X^2)=32.5[/tex]
Finally, using the second property and replacing [tex]E(X)[/tex] by 5 and [tex]E(X^2)[/tex] by 32.5, we get that V(X) is equal to:
[tex]V(X) = 32.5 - 5^2\\V(X) =32.5 - 25\\V(X) = 7.5[/tex]
How to read a ruler?
Answer:
Look at the numbers on the sides. If they are not spaced out very far, it's centimeters. If they are spaced out very far, it's inches
Step-by-step explanation:
this is how you read a ruler
Answer:
Start at 0
Step-by-step explanation:
Start at 0, then see how far the object goes.
In Triangle ABC, AB = 10. AC = 14, and angle A = 51°. Find the length of BC to the nearest hundredth
Answer:
BC ≈ 10.94
Step-by-step explanation:
Base on the triangle we were given 2 sides and an angle. We were also asked to find the last length BC.
we can use cosine rule to find the side BC.
Base on cosine rule
a² = b² + c² - 2bc cos A
a = BC
b = AC = 14
c = AB = 10
a² = 14² + 10² - 2 × 14 × 10 cos 51°
a² = 196 + 100 - 280 cos 51°
a² = 296 - 280 × 0.62932039105
a² = 296 - 176.209709494
a² = 119.790290506
square root both sides
a = √119.790290506
a = 10.9448750795
BC ≈ 10.94
Answer:
BC = 10.94
Step-by-step explanation:
its a las of cosines
a² = b² + c² - 2bc cos A
AB = 10
AC = 14
angle A = 51°
BC² = 10² + 14² - (2 * 10 * 14 cos 51°)
BC = sqrt 119.8
BC = 10.94
Estimate the indicated probability by using the normal approximation as an approximation to the binomial distribution. (PROBLEMS 4 & 5) 4. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective.
5. In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.
Answer:
4
[tex]P(X \ge 219 ) = 0.093[/tex]
5
[tex]P(X \ge 219 ) = 0.1038[/tex]
Step-by-step explanation:
From the question we are told that
The percentage of hair dryers that are defective is p=2% [tex]= 0.02[/tex]
The sample size is [tex]n =10000[/tex]
The random number is x = 219
The mean of this data set is evaluated as
[tex]\mu = n* p[/tex]
substituting values
[tex]\mu = 10000 * 0.02[/tex]
[tex]\mu =200[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]
substituting values
[tex]\sigma = \sqrt{[200 (1 -0.02)]}[/tex]
[tex]\sigma = 14[/tex]
Since it is a one tail test the degree of freedom is
df = 0.5
So
[tex]x_l = x- 0.5[/tex]
[tex]x = 219 - 0.5[/tex]
[tex]x = 218.05[/tex]
Now applying normal approximation
[tex]P(X \ge 219 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]
substituting values
[tex]P(X \ge 219 ) = P(z > \frac{218.5 - 200}{14} )[/tex]
[tex]P(X \ge 219 ) = P(z > 1.32} )[/tex]
From the z-table
[tex]P(X \ge 219 ) = 0.093[/tex]
Considering Question 5
The random number is x = 90
The mean is [tex]\mu = n * p[/tex]
Where n = 100
and p = 0.85
So
[tex]\mu = 0.85 *100[/tex]
[tex]\mu = 85[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]
substituting values
[tex]\sigma = \sqrt{[85 (1 -0.85)]}[/tex]
[tex]\sigma = 3.5707[/tex]
Since it is a one tail test the degree of freedom is
df = 0.5
Now applying normal approximation
[tex]P(X \ge 90 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]
substituting values
[tex]P(X \ge 219 ) = P(z > \frac{89.5 - 85}{3.5707} )[/tex]
[tex]P(X \ge 219 ) = P(z > 1.2603} )[/tex]
From the z-table
[tex]P(X \ge 219 ) = 0.1038[/tex]
A simple random sample of size nequals17 is drawn from a population that is normally distributed. The sample mean is found to be x overbar equals 56 and the sample standard deviation is found to be sequals10. Construct a 95% confidence interval about the population mean. The lower bound is nothing. The upper bound is nothing. (Round to two decimal places as needed.)
Answer:
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Step-by-step explanation:
Step(i):-
Given random sample of size 'n' =17
Given mean of the sample 'x⁻' = 56
Given standard deviation of sample 's' = 10
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 17-1 =16
t₀.₀₅ = 1.7459 (from t-table)
Step(ii):-
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]
( 56 - 4.2344 , 56 + 4.2344)
(51.7656 , 60.2344)
Conclusion:-
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
College students were given three choices of pizza toppings and asked to choose one favorite Results are shown in the table toppings Sremam 15 24 28 28 15 1 11 23 28 cheese meat 23 15 veggie Estimate the probability that a randomly selected student who is a junior or senior prefers veggie. Round the answer to the nearest thousandth
A. 371
B. 220
C. 395
D. 662
Answer:
B. 0.220
Step-by-step explanation:
The table is presented properly below:
[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]
Number of junior students who prefers veggies =23
Number of senior students who prefers veggies =28
Total =23+28=51
Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie
=51/232
=0.220 (to the nearest thousandth)
The correct option is B.
When would you need to arrange polynomials
Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0).
Answer:
x + y + z = 14
Step-by-step explanation:
If the points are designated A, B, C, then ...
AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).
That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...
(1, 1, 1)·(x, y, z) = (1, 1, 1)·A
x + y + z = 14
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x + 4 x + y ≤ 6
Answer:
Graph is attached.
Step-by-step explanation:
We are to graph the following inequalities:
y > 2x + 4 ... (i)
x + y ≤ 6 ... (ii)
We can graph these inequalities on an online graphing calculator but its recommended that you graph them on your physical graph book.
Your graph is attached below. The shaded region is the required part.
The graph of a system of inequalities represents the solution of the inequalities
The solution to the system of inequalities is [tex]\mathbf{y > \frac 23}[/tex] and [tex]\mathbf{x \le \frac{16}3}[/tex]
The system of inequalities is given as:
[tex]\mathbf{y > 2x + 4}[/tex]
[tex]\mathbf{x + y \le 6 }[/tex]
See attachment for the graphs of [tex]\mathbf{y > 2x + 4}[/tex] and [tex]\mathbf{x + y \le 6 }[/tex]
From the graph, we have:
[tex]\mathbf{y > \frac 23}[/tex]
[tex]\mathbf{x \le \frac{16}3}[/tex]
Read more about system of inequalities at:
https://brainly.com/question/19526736
If the coefficient of realism alpha equals 1, then the criterion of realism will yield the same result as the maximax criterion.
A. True
B. False
Answer:
True
Step-by-step explanation:
Coefficient of realism called alpha which is a decimal number between 0 and 1. This number provides the optimistic view. The number 1 - [tex]\alpha[/tex] is amount of emphasis that is placed in pessimistic outcome. If the coefficient of realism alpha is 1 then criterion of realism will yield same result as maxi max criterion.
8. What should be subtracted from 360 to make
it a perfect cube?
Answer:
17
Step-by-step explanation:
The closest perfect cube (to 360) is 343 (7^3) .
360-343 = 17
Subtract 17.
Answer:
You should subtract 17 from 360 to make a perfect cube
Step-by-step explanation:
help with this I don't know how to solve plz greatly appreciate
Answer:
cos∅ = 16√481/481
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
cos∅ = adjacent/hypotenuse
tan∅ = opposite/adjacent
Step 1: Find hypotenuse
15² + 16² = c²
c = √481
Step 2: Find cos∅
cos∅ = 16/√481
cos∅ = 16√481/481
The second statement is the ___ of the first. a⇒b b⇒a A) converse B) contrapostive C) contradition D) inverse
Answer:
A. converse
Step-by-step explanation:
Let's first define some concepts:
Statement If p , then q
Converse If q , then p
Inverse If not p , then not q
Contrapositive If not q , then not p
From the statement we have:
a ⇒b
b ⇒a
if you look at the definitions then:
The second statement is the converse of the first
Answer:
Converse
Step-by-step explanation:
Got Correct On ASSIST.
A biologist samples and measures the length of the fish in a lake. What is the level of measurement of the data?
Answer:Ratio
Step-by-step explanation:
The ratio data because length has a true zero, and ratios of lengths are meaningful.
If the ratio of red hairbands to green hair bands is 5 to 9 with a total of 70 hairbands, how many of them are green?
Answer:
45
Step-by-step explanation:
This can be written as 5r:9g. Add 5 and 9 to get the total of 14. You can write a ratio of 9 green: (out of) 14 total = x green: (out of) 70 total. Multiply 9 and 14 by 7 to get 45:70. Therefore, if there are 70 hairbands, 45 are green.
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=7, x=3, p=0.65
Answer:
P(X = 3) = 0.1442
Step-by-step explanation:
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.
In this problem we have that:
[tex]n = 7, p = 0.65[/tex]
We have to find P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{7,3}.(0.65)^{3}.(0.35)^{4} = 0.1442[/tex]
Find the lateral area of a regular square pyramid if the base edges are of length 12 and the perpendicular height is 8.
Answer:
Lateral area of the pyramid = 120 square units
Step-by-step explanation:
In the figure attached,
A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.
Lateral area of a pyramid = Area of the lateral sides
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
= [tex]\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})[/tex] [Since l = [tex]\sqrt{r^{2}+h^{2}}[/tex]]
= [tex]\frac{1}{2}(6)(\sqrt{6^2+8^2})[/tex]
= [tex]3\sqrt{100}[/tex]
= 30 units²
Now lateral area of the pyramid = 4 × 30 = 120 square units
Answer: 240 units^2
Step-by-step explanation:
LA= 1/2 Pl
P= perimeter of base
l= lateral height
l= 8^2 + (12/2)^2 = 10^2
P= 12 x 4 = 48
48 x 10 = 480
480/2 = 240
240 units^2
In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B?
Answer:
a) The student cannot receive an A in the class.
b) The student must score 119 in the third exams to make an A. This is clearly not possible, since he cannot make 119 in a 100-points exam.
c) The student can make a B but he must score at least 84 in the third exam.
Step-by-step explanation:
To make an A, the student must score 315 (350 x 90%) in both home and the three exams.
The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.
To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.
B ≥ 280 and < 315.
Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.
If f(x) = 4x – 8 and g(x) = 5x + 6, find (f - g)(x).
Answer:
(f - g)(x) = -x - 14
Step-by-step explanation:
Step 1: Plug in equations
4x - 8 - (5x + 6)
Step 2; Distribute negative
4x - 8 - 5x - 6
Step 3: Combine like terms
-x - 14
Answer:
-x-14
Step-by-step explanation:
Hope this helps
The weights of beagles have a mean of 25 pounds and a standard deviation of 3 pounds. A random sample of 50 beagles is collected. What is the probability that a sample of this size has a mean weight below 26 pounds?
Answer:
[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]
And we can find the probability using the normal distribution table and we got:
[tex] P(z<2.357) =0.9908[/tex]
Step-by-step explanation:
Let X the random variable of interest and we can find the parameters:
[tex] \mu =25, \sigma= 3[/tex]
And for this case we select a sample size n =50. And since the sample size is higher than 30 we can use the central limit theorem and the distribution for the sample mean would be given by:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
We want to find the following probability:
[tex] P(\bar X <26)[/tex]
And we can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]
And we can find the probability using the normal distribution table and we got:
[tex] P(z<2.357) =0.9908[/tex]
An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 47.0. Assume the population standard deviation is known to be 1.9. A level of significance of 0.02 will be used.
A. Find the value of the test statistic.
B. State the null and alternative hypotheses.
Answer:
A
The test statistics is [tex]t = -1.7[/tex]
B
The Null and Alternative hypothesis are
[tex]H_o : \mu = 47.2[/tex] and [tex]H_a : \mu \ne 47.2[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47.2 miles/gallon(MPG)[/tex]
The sample size is [tex]n = 250 \ van[/tex]
The sample mean is [tex]\= x = 47.0[/tex]
The sample standard deviation is [tex]\sigma = 1.9[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then
The Null Hypothesis is
[tex]H_o : \mu = 47.2[/tex]
The alternative Hypothesis is
[tex]H_a : \mu \ne 47.2[/tex]
The test statistics can be mathematically evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]
[tex]t = -1.7[/tex]
Find the exact value
sin 79° cos 19° - cos 79° sin 19°
Step-by-step explanation:
Using the trigonometric identity
sin(a - b) = sin a cos b - cos a sin b
So sin 79° cos 19° - cos 79° sin 19° can be written as
sin ( 79 - 19) = sin 60
And
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
Hope this helps you
(a) Which unit fraction 1/n for n s 50 has the decimal expansion of longest period?
(b) Justify your reasoning
Answer:
0.02
Step-by-step explanation:
If n is 50, 1/n is equivalent to 1/50. 1/50 as a decimal is 0.02.
what is the answer?!?!??!
Answer:
Option D
Step-by-step explanation:
It forms a linear pair (Angles on a straight line) with one of the interior angles of the triangle.
Answer:
D
Step-by-step explanation:
A linear pair of angles is when two angles add up to 180 degrees on a line.
Interior angles and exterior angles form a linear pair.
please answer this question
Answer:
c
Step-by-step explanation:
next
In a survery of 154 households, a Food Marketing Institute found that 106 households spend more than $125 a week on groceries. Please find the 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries.
Answer:
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
What is 1(y), when y=-7/12?
Answer: -7/12
Step-by-step explanation: an number multiplied by 1 is itself
Find the perimeter of the following trapezoid:
6 ft
2.5 ft/ 12 ft
2.5 ft
8 ft
Answer:
31ft
Step-by-step explanation:
6 ft + 2.5 ft + 12 ft + 2.5 ft + 8 ft = 31ft
I assumed the slash in the space between 2.5ft and 12ft was an error, so I ignored it in the solution to this problem.
Besides that, perimeter is found by adding all sides of the shape or figure together, and the sum of that is the perimeter.
The basic formula for perimeter is:
base + height + base + height.
I do not think you square perimeter as you do area (e.g. 31ft^2).
Using Volume Formulas: Tutorial
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Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
identical volumes? There is more than one correct answer.
B
TUX
X
Font Sizes
A. A
E JE
Square Pyramids
Rectangular Pyramid
Volume
Base Length Height
Volume
Volume x4 Base Length Base Width Height
(2x)
3
(lxwh
3
I
Characters used: 110 / 15000
Submit
Answer:
For the Square
Base length is 6 units
Height is 4 units
Volume is 48 cubic units
Volume of 4 square pyramids is 192 cubic units
(Rectangular)
Base length is 12 units
Base width is 8 units
Height is 6 units
Volume is 192 cubic units
Step-by-step explanation:
Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.
Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people in a restaurant that has a capacity of 300. (b) The weight of a Upper T dash bone steak.
Answer:
a) Discrete random variable
b) Continous random variable.
Step-by-step explanation:
a) As the number of people can take only integer values, from 0 to n (0, 1, 15, 256, for example, but not 5.6) and not decimals values, we can say that it is a discrete variable.
b) In this case, the weight of a Upper T dash bone steak is a physical variable and can take decimals positive values (0.645 lbs for example).
Then, this variable is a continous variable.
Marko drovev75mile in 1 1/2 hours .how many mile can he he drive in 1 hour
Answer: 50 miles
Step-by-step explanation:
75 miles in one and half hours.
That's 25 miles per half hour
So, in 1 hour, he will drive 50 miles