Answer:
a) the probability that the first non-defective engine will be found on the second trial is 0.09
b) probability that the third non-defective engine will be found on the fifth trial is 0.00486
c) the Mean is 1.1111 and Variance is 0.1235
d) the Mean is 3.3333and Variance is 0.3704
Step-by-step explanation:
Firstly;
Let x be the number of trail on which the rth defective occurs
Also let the probability that an occurrence of a defective be p = 0.10
Here, x follows negative binomial distribution with parameters r and p
The probability mass function of X is as follows:
P(X = x) = [ x -1 p^r ( 1 - p)^(x-r) ; x = r, r + 1, r + 2, ...
r - 1 ]
= [ x -1 (0.10)^r ( 1 - 0.10)^(x-r)
r - 1 ]
= [ x -1 (0.10)^r ( 0.9)^(x-r) ..........n 1..... let this be equatio
r - 1 ]
This represents the probability that the rth success occurs on the xth trail.
a)
probability that the first non-defective engine will be found on the second trial?
Substitute r = 1 and x = 2 in equation 1
P(X = 2) = [ 2 - 1 (0.10)¹ ( 0.90 )²⁻¹
1 - 1 ]
= (0.10) × (0.90)
= 0.09
Therefore, the probability that the first non-defective engine will be found on the second trial is 0.09
b)
probability that the third non-defective engine will be found on the fifth trial?
So we substitute r = 3 and x = 5 in equation 1
P(X = 5) = [ 5 - 1 (0.10)³ ( 0.90)⁵⁻³
3 - 1 ]
= [ 4 (0.10)³ ( 0.9)²
2 ]
= 0.00486
Therefore, probability that the third non-defective engine will be found on the fifth trial is 0.00486
Now the formula for the mean of the negative binomial distribution is as follows:
Mean u = r / p ------- let this be equation 2
The formula for the variance of the negative binomial distribution also is as follows:
Variance α² = rq / p² ---------- let this be equation 3
so
c)
the mean and variance of the number of trials on which the first non-defective engine is found.
First, let the probability that non-defective engine found be p = 0.90
And q = (1 - p) = 1 - 0.90 = 0.10
Now we substitute r = 1, p = 0.90 and q = 0.10 in equation 2 & 3simultaneously,
the mean and variances are as follows;
Mean = r/p = 1/0.90 = 1.1111
Variance = rq/p² = (1)(0.10) / (0.90)² = 0.1235
Therefore the Mean is 1.1111 and Variance is 0.1235
d)
the mean and variance of the number of trials on which the third non-defective engine is found
Let the probability that non-defective engine found be p = 0.90
And q = (1 - p) = 1 - 0.90 = 0.10
Now we substitute r = 3, p = 0.90 and q = 0.10 in equation (2) and (3) simultaneously,
the mean and variances are;
Mean = r/p = 3/0.90 = 3.3333
Variance = rq/p² = (3)(0.10) / (0.90)² = 0.3704
Therefore the Mean is 3.3333 and Variance is 0.3704
Can someone help me with this.. It is timed I WILL MARK YOU AS BRAINLIEST
Answer:
1) dividend
2) divisor
3) quotient
An angle measures 79.4 degrees more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
The angles are: 50.3 and 129.7
Step-by-step explanation:
The sum of supplementary angles is 180°.
Let x be one angle then the other angle will be x+79.4
Using the supplementary angle sum
[tex]x+x+79.4 = 180\\2x+79.4 = 180\\2x = 180-79.4\\2x = 100.6\\\frac{2x}{2} = \frac{100.6}{2}\\x = 50.3[/tex]
For the measurement of 2nd angle
x+79.4 => 50.3+79.4 => 129.7
Hence,
The angles are: 50.3 and 129.7
The fourth term of a geometric progression is 4 and the seventh term is 32/125. Find the first term, the common ratio and the sum of the first nth terms. Hence, deduce the sum to infinity.
Answer:
common ratio is 2/5
First term is 125/2
The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]
Step-by-step explanation:
The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:
[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]
Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:
[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]
So, the common ratio is 2/5
we can now determine the first term:
[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]
The sum of the first n terms is given by the formula:
[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
and therefore, the infinite sum is:
[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]
Would you please help me on this question?
Answer:
x = 2
Step-by-step explanation:
Given that the measure of segment BC must equal the addition of the measure of segment BA plus the measure of segment AC, we can write this in equation form:
BC = BA + AC
then we replace them with the measure information they provide:
12 x + 4 = 7 x - 4 + 8 x + 2
and we solve for x in the equation:
12 x + 4 = 15 x - 2
subtract 12 x from both sides:
4 = 15 x - 12 x - 2
4 = 3 x - 2
add 2 on both sides
4 + 2 = 3 x
6 = 3 x
x = 6/3
x = 2
Completing the Square
Solve each equation by completing the square.
1) 7x2 + 14x - 65--9
Answer:
2(30-7x)
Step-by-step explanation:
=14+14x-65-9
=14+14x-79
=60+14x
=2(30-7x)
Hint : Add togheter and =180
Answer:
100 + 80
Step-by-step explanation:
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 90 yd, find its length and width.
Answer:
Length of rectangle = 36 yd and width of rectangle = 9 yd
Step-by-step explanation:
Let width of rectangle = w
Length of rectangle = 4w (four times the width)
Perimeter of rectangle = 90 yd
We need to find length and width of rectangle.
The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]
Where l is length and w is width
Putting values and finding length and width of rectangle
[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]
So,width (w) of rectangle is w= 9 yd
Finding length of rectangle = 4w = 4*9 = 36 yd
So, length of rectangle = 36 yd and width of rectangle = 9 yd
In a video game, Agnes scored 20% fewer than Amy. Amy scored 860
points. How many points did Agnes score? *
Answer:
[tex]\huge\boxed{\sf Agnes\ Score = 688\ points}[/tex]
Step-by-step explanation:
[tex]\sf = 20 \% \ of \ 860 \\\\= \frac{20}{100} * 860\\\\= 2 * 86\\\\= 172 \ points[/tex]
Since, Agnes scored 20 % fever than Amy.
So,
Agnes Score = Amy's Points - 20 % of Amy's Points
Agnes Score = 860 - 172
Agnes Score = 688 points
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807
Solve the equation 3(x + 4.5) = 36.
If you get stuck, use the diagram. first one and with an explanation will get brainllest
Answer:
.75
Step-by-step explanation:
there is prof
Solve for n: n/3 > 66 2/3
Answer: The 2 answers are inequality form and interval notation: n>200, and (200, ∞).
Step-by-step explanation: To solve for n, you’ll need to simplify the both sides of the inequality, and then isolating the variable.
Find the value of r.
Answer:
r=0
Step-by-step explanation:
the line passes through the origin which means there is no y-intercept
what is 12+12 and give good reson why
Answer:
24
Step-by-step explanation:
you have 12 of something and Are adding 12 to it.
12 divide 4 x 7 - 18 =
Answer:
20
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
HELP FOR 40 POINTS PLEASE AND BRAINLIST
Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?
After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.
Answer:
the price of each pound of pretzels is 4.20
Step-by-step explanation
1 pound · [tex]\frac{10.50}{2.5 pound} = 4.20$\\[/tex]
Answer:After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.
Step-by-step explanation:
What is the perimeter of this square?
aaaaaaaaaaaaaa
11 in
Answer:
44 in
Step-by-step explanation:
Perimeter is adding up all the sides together and since we know it is a square that means each side is equal
11 in + 11 in + 11 in + 11 in = 44 in
Is that a perfect square
Answer:
im gonna go with yes
Step-by-step explanation:
Answer:
is what a perfect square?
Step-by-step explanation:
there is no pic attached
The two triangles are similar, What is the length of DE?
Answer:
If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.
I hope this might help you
Mark it as brainliest answer and follow me
Now move vertices A, B, and C of ∆ABC to create a triangle of your choice. (Note: the tool will allow you to create only certain kinds of triangles.) Does the relationship between the base angles change as the vertices change? If so, how?
Answer:
The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.
Step-by-step explanation:
Here is the answer from Plato. Hope this helps :)
Answer:
The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.
Step-by-step explanation:
Exact Edmentum sample answer
Sofia used these steps to find the inverse of function f
She made a mistake in step__(2,6,4,3,5)?
She should have_____
.dived each side by 8 instead of multiplying
.replaced x with f(x)
.divided each side by 3 instead of multiplying
.added 4 to each side instead of subtract
.restricted the domain to x>0
Answer:
Step-by-step explanation:
Step 1 f(x) = [tex]\frac{3x+4}{8}[/tex] Given
Step 2 y = [tex]\frac{3x+4}{8}[/tex] Change f(x) to y
Step 3 x = [tex]\frac{3y+4}{8}[/tex] Switch x and y
Step 4 8x = 3y + 4 multiply each side by 8
Step 5 8x - 4 = 3y Subtract 4 from each side
Step 6 [tex]\frac{8x-4}{3}=y[/tex] Divide by 3 on each side
Step 7 [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex] Replace y by [tex]f^{-1}(x)[/tex]
Therefore, inverse of the function will be,
[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]
Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.
Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.
The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].
It is required to calculate the inverse of the function.
So, the steps involved in finding the inverse of the function will be,
Step 1:
Write the given function as,
[tex]f(x)=\dfrac{3x+4}{8}[/tex]
Step 2:
Change the function f(x) to y as,
[tex]y=\dfrac{3x+4}{8}[/tex]
Step 3:
Switch x and y as,
[tex]x=\dfrac{3y+4}{8}[/tex]
Step 4:
Multiply each side of the equation by 8 as,
[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]
Step 5:
Now, subtract 4 from each side of the equation as,
[tex]8x-4=3y+4-4\\8x-4=3y[/tex]
Step 6:
Now, it is required to divide each side by 3.
[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]
Step 7:
Now, replace y with [tex]f^{-1}(x)[/tex] as,
[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]
So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].
Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.
For more details, refer to the link:
https://brainly.com/question/19606498
HELP ME HELP HELP Josiah has a mask collection. He keeps 117 of the masks on his wall, which is 65% of
his entire collection. What is the total number of masks in Josiah's collection?
Answer:
x=180
Step-by-step explanation:
Let us have x represent the entire mask collection
We know that 117 is 65% of his collection. We want to know the total number of masks he has
The equation we set up is:
117 is 65% of x: this translates to
117=0.65x, then we solve for x by dividing 0.65 by both sides
180=x
The total number of masks Josiah has is 180.
When playing the lottery game Cash4Life, you must choose a cash ball number from 1 through 4. What is the probability that the randomly drawn cash ball is at least 2?
A. 0.50
B. 0.75
C. 0
D. 0.25
Answer:
[tex]P(At\ least\ 2) = 0.75[/tex]
Step-by-step explanation:
Given
Balls = 1 to 4
Required
Determine the probability of selecting ball numbered at least 2
Here, we'll assume that all numbers have the same probability.
The probability of each ball will be:
[tex]Probability = \frac{1}{4}[/tex]
So:
[tex]P(At\ least\ 2) = P(2) + P(3) + P(4)[/tex]
Recall that
[tex]Probability = \frac{1}{4}[/tex] --- for each ball
So, the equation becomes
[tex]P(At\ least\ 2) = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(At\ least\ 2) = \frac{3}{4}[/tex]
[tex]P(At\ least\ 2) = 0.75[/tex]
what number is represented by this number discs
Answer:
15
Step-by-step explanation:
Simplify (6x ^ 2 + 11x - 3) + (2x ^ 2 - 17x - 4) . (1 point)
1 ) 8x ^ 2 + 6x - 1
2) 8x ^ 2 - 6x - 7
3 ) 8x ^ 2 + 6x + 1
4 ) 8x ^ 2 - 6x + 7
Answer:
2) 8x^2 -6x-7 hope this helps
Simplify the expression using the properties of operations.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is
Answer:
Step-by-step explanation:
5.23x+3.76-3.67x+6.39
x(5.23-3.67) +(3.76+6.39)
1.56x + 10.15
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
What is the graph of the function rule?
1. y= 3x - 2 (1 point)
Algebra 1
This should be what you're looking for.
Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation.
"The sum of a number and its opposite is always 1."
Answer:
Never applies
Step-by-step explanation:
Given
Argument: The sum of a number and its opposite is always 1
Assume a positive number x
The opposite of the number is negative x (i.e. -x)
The sum of both numbers is:
[tex]Sum = x + (-x)[/tex]
Open Bracket
[tex]Sum = x -x[/tex]
[tex]Sum = 0[/tex]
Now, take for instance.
[tex]Number = 5[/tex]
Opposite would be
[tex]Opposite = -5[/tex]
Their sum is:
[tex]Sum = 5 + (-5)[/tex]
[tex]Sum = 5 -5[/tex]
[tex]Sum = 0[/tex]
Another instance is:
[tex]Number = -8[/tex]
Opposite would be
[tex]Opposite = 8[/tex]
Their sum is;
[tex]Sum = -8 + 8[/tex]
[tex]Sum = -0[/tex]
Hence, the argument never applies because the sum is never 1
Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page
Answer:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
Answer:
26
Step-by-step explanation:
13 in 1/2 hour
13:1/2
26:1
Understand the question explain and u will be brainiest
Please help me please and fast
Answer:
b
Step-by-step explanation:
sorry if wrong
Write an equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).
Line CD is shown. C is at 1, 1. D is at 3, 5.
y = −0.5x − 5.5
y = −0.5x + 5.5
y = 2x + 13
y = 2x − 13
Answer:
its b
Step-by-step explanation:
i took the test
y = - 0.5x + 5.5 is the equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).
What is the slope-intercept form of a straight line?The slope-intercept form of a straight line is y = mx + c.
Here, x and y are coordinates, m is the slope and c is the y-intercept of the line.
Given, two points are C(1, 1) and (3, 5).
Therefore, equation of the line CD is:
[tex]\frac{x - x_{1} }{y-y_{1} }[/tex] = [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]
⇒ [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{1-3}{1-5}}[/tex]
⇒ [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{-2}{-4}}[/tex]
⇒2(x - 1) = (y - 1)
⇒ y = 2x - 1
Let, line AB is perpendicular to the line CD and passes through the point (-1, 6).
Therefore, slope of the line CD is = 2.
We know, slope of CD × slope of AB = -1
Therefore, slope of AB = -1 / slope of CD = [tex]-\frac{1}{2}[/tex].
Now, line AB has a slope of [tex]-\frac{1}{2}[/tex] and passes through the point (-1, 6).
Therefore, equation of the line AB is:
(y - y₁) = m(x - x₁)
⇒ [y - (6)] = [tex]-\frac{1}{2}[/tex][x - (- 1)]
⇒ 2(y - 6) = (-x - 1)
⇒ 2y - 12 + x + 1 = 0
⇒ x + 2y = 11
⇒ y = - 0.5x + 5.5
Learn more about slope-intercept form of a straight line here: https://brainly.com/question/12763756
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