Answer: base width = 27 in
Step-by-step explanation:
Base width = 3 x (V / hl)
3 x (1296 / 24 x 6)
3 x (1296 / 144)
3 x 9 = 27
What is the coefficient in this expression? 5 minus 4.7 minus 2 x + StartFraction 5 over 8 EndFraction
Answer:
2 is the coefficient
Step-by-step explanation:
2 is the coefficient bc a coefficient is the number next to a variable (such as x) and 2 is next to x and is the only one in the equation
Answer:
-2
Step-by-step explanation:
It is known that 40% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the expected number of adult workers with a high school diploma? (That is, what is E(X)?) Round to the whole number. Do not use decimals. Answer:
Answer:
The expected number of adult workers with a high school diploma is 4.
Step-by-step explanation:
This random variable X can be modeled with the binomial distribution, with parameters n=10 (the sample size) and p=0.4 (the probability that a adult worker have a high school diploma).
The expected value of X is then the mean of the binomial distribution with the parameters already mentioned.
This is calculated as:
[tex]E(X)=\mu_b=n\cdot p=10\cdot0.4=4[/tex]
Solve for x. whats the solutions from least to greatest. 4x^2 + 48x + 128 = 0
Answer:
[tex]\boxed{\sf \ \ \ x = -8 \ or \ x = -4 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]4x^2+48x+128=0\\<=> 4(x^2+12x+32)=0\\<=> x^2+12x+32=0\\<=> (x+6)^2 - 36 + 32= 0\\\\<=> (x+6)^2-4=0\\<=> (x+6+2)(x+6-2)=0\\<=> (x+8)(x+4) = 0\\<=> x = -8 \ or \ x = -4[/tex]
vouch, i confirm that -8, -4 are the answers
Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $500
Answer:
[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]
And we can find this probability using the normal standard distribution and we got:
[tex] P(z<-2.22) =0.0132[/tex]
Step-by-step explanation:
For this case we have the foolowing parameters given:
[tex] \mu = 520[/tex] represent the mean
[tex] \sigma =90[/tex] represent the standard deviation
[tex] n = 100[/tex] the sample size selected
And for this case since the sample size is large enough (n>30) we can apply 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]
And we want to find this probability:
[tex] P(\bar X <500)[/tex]
We can use the z score formula given by:
[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]
And we can find this probability using the normal standard distribution and we got:
[tex] P(z<-2.22) =0.0132[/tex]
A Student select a marble from a bag, keeps it and select another. The bag contains 5 Green marbles 4 black marbles and 2 blue marbles. Find the probability of selecting a green marble on the first trial and a black marble on the second trial.
Answer:
Yes because yes.
Step-by-step explanation:
Y + e + s = Yes
Alex is paid $30/hr at full rate, and $20/hr at a reduced rate. The hours of work are paid at a ratio of 2:1, full rate : reduced rate. For example, if he worked 3 hours, he would be paid 2 hours at full rate and 1 hour at reduced rate. Calculate his pay for 4 hours of work.
Answer:
$106.67
Step-by-step explanation:
Using the example, for 3 hours work, Alex would be paid ...
(2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80
At the same rate of pay, for 4 hours work, the pay would be ...
pay/(4 hr) = $80/(3 hr)
pay = $80(4/3) ≈ $106.67
Alex's pay for 4 hours of work is $106.67.
outline any four views of how people approach curriculum
Answer:
they may like it
they may dislike it
Step-by-step explanation:
they amy think ots essentiall
they may think its unescary
Please answer this correctly.
Answer:
m=(3+f)/(f-4)
Step-by-step explanation:
To make m the subject of the formula, we want to isolate m. That is, we want to move m to one side of the equation.
First, the fractions need to be taken away. Multiply both sides by m-1 to get: f(m-1)=4m+3.
The distributive property of subtraction tells us a(b-c)=ab-ac. Thus, from this equation we have fm-f=4m+3.
Subtracting 4m, we have fm-4m-f=3
Now, we work the distributive property backwards, where we have ab-ac=a(b-c). Rearrange the terms of fm and 4m, to get mf, and m4. Thus, this can be simplified to m(f-4).
Going back to the equation, we have m(f-4)-f=3.
Add f on both sides, so we have m(f-4)=3+f.
Divide by f-4, so we have m=(3+f)/(f-4)
Juan told Sylvia he got a $0.50 raise this week and his new hourly rate will be $10.25 an hour. Sylvia wants to know what Juan’s hourly rate was before his raise. Which equation and solution can be used to solve this problem? r minus 10.25 = 0.50: Add 10.25 to both sides. The answer is $10.75. r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75. r minus 0.50 = 10.25: Subtract .50 from both sides. The answer is $10.75 r + 10.25 = 0.50: Subtract .50 from both sides. The answer is $9.75.
Answer:
The correct answer is:
r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.
This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).
Answer:
$9.75
Step-by-step explanation:
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
[tex] \frac{4 {x }^{2} - 17x - 9 }{ {x}^{3} - 7 {x}^{2} + 7x + 15 } [/tex]
Step-by-step explanation:
In the picture.
I hope I am correct
I hope it helps :)
PLEASE HELP ASAP Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6
Answer:
Step-by-step explanation:
Step 1: Consider P(1) that is n = 1
[tex]1^2 = \frac{1(1+1)(2*1+1)}{6}=\frac{6}{6}=1 \checkmark[/tex]
Step 2: Suppose the equation is true up to n. That is
[tex]1^2 + 2^2+3^2+........+n^2 = \dfrac{n(n+1)(2n+1)}{6 }[/tex]
Step 3: Prove that the equation is true up to (n+1). That is
[tex]1^2 + 2^2+3^2+........+n^2 + (n+1)^2 = \dfrac{(n+1)(n+2)(2n+3)}{6 }[/tex]
The easiest way to prove it is to expend the right hand side and prove that the right hand side = the right hand side of step 2 + (n+1)^2
From step 2, add (n+1)^2 both sides. The left hand side will be the left hand side of step 3, now, the right hand side after adding.
[tex]\dfrac{n(n+1)(2n+1)}{6 }+(n+1)^2 = \dfrac{2n^3+3n^2+n}{6}+\dfrac{6n^2+12n+6}{6}[/tex]
[tex]=\dfrac{2n^3+9n^2+13n+6}{6}[/tex]
If you expend the right hand-side of the step 3, you will see they are same.
Proof done
Answer:
see below
Step-by-step explanation:
1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6
Step1
Verify it for n=1
1^2= 1(1+1)(2*1+1)/6= 1*2*3/6= 6/6=1 - correct
Step2
Assume it is correct for n=k
1^2+2^2+3+2+...+k^2= k(k+1)(2k+1)/6
Step3
Prove it is correct for n= k+1
1^2+2^2+3^2+...+(k+1)^2= (k+1)(k+2)(2k+2+1)/6
prove the above for k+1
1^2+2^2+3^2+...+k^2+(k+1)^2= k(k+1)(2k+1)/6 + (k+1)^2=
= 1/6(k(k+1)(2k+1)+6(k+1)^2)= 1/6((k+1)(k(2k+1)+6(k+1))=
=1/6((k+1)(2k²+k+6k+6))= 1/6(k+1)(2k²+4k+3k+6))=
= 1/6(k+1)(2k(k+2)+3(k+2))=
=1/6(k+1)(k+2)(2k+3)
Proved for n= k+1 that:
the sum of squares of (k+1) terms equal to (k+1)(k+2)(2k+3)/6
Mary pays income tax according to the graduated schedule shown below. A 3-column table with 6 rows. Column 1 is labeled If taxable income is over with entries 0 dollars, 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars. Column 2 is labeled but not over with entries 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars, no limit. Column 3 is labeled the tax is with entries 10 percent of the amount of 0 dollars, 782 dollars and 50 cents plus 15 percent of the amount of 7,825 dollars, 4,386 dollars and 25 cents plus 25 percent of the amount of 31,850 dollars, 15,698 dollars and 75 cents plus 28 percent of the amount over 77,100 dollars, 39,148 dollars and 75 cents plus 33 percent of the amount of 160,850 dollars, 101,469 dollars and 25 cents plus 35 percent of the amount over 349,700 dollars. If Mary’s taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
Answer:
$13564
Step-by-step explanation:
[tex]\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\% of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|[/tex][tex]\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\% of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\% of the amount over 77,100\end{array}\right|[/tex]
[tex]\left|\begin{array}{c|c|c}160,850 &349,700 &$39,148.75 plus 33\% of the amount over 160,850 \\349,700 &$no limit&$101,469.25 plus 35\% of the amount over 349,700\end{array}\right|[/tex]
Mary’s taxable income= $68,562
From the table, If taxable income is over $31,850 but not over $77,100
The tax = $4386.25 + 25% of the amount over 31,850
Amount over $31,850=$68,562-$31,850
=$36,712
Therefore:
Mary's tax = $4386.25 + (25% of $36,712)
=$4386.25 +9,178
=$13564.25
=$13564 (to the nearest dollar)
Income tax is the tax charged on individual's or entities' income
Mary owes $13564 income tax
Given that the taxable income is $68,562.
Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100
So, the tax is $4386 added to 25% of the excess over $31850
This is calculated as:
[tex]Tax = \$4386 + 25\% \times (Income -\$31850)[/tex]
Substitute $68,562 for income
[tex]Tax = \$4386 + 25\% \times (\$68562 -\$31850)[/tex]
Solve the expression in the bracket
[tex]Tax = \$4386 + 25\% \times \$36712[/tex]
Evaluate the product
[tex]Tax = \$4386 + \$9178[/tex]
Add the terms of the expression
[tex]Tax = \$13564[/tex]
Hence, Mary owes $13564 income tax
Read more about income tax at:
https://brainly.com/question/1720419
What is the value of X ?
14
17
24
28
Answer:
24
Step-by-step explanation:
Use the Pythagorean theorem.
Where the sum of the two legs squared is equal to the hypotenuse squared.
10² + x² = 26²
100 + x² = 676
x² = 576
x = √576
x = 24
The value of x is 24.
Please answer this correctly
Answer:
The range will decrease by 1
Step-by-step explanation:
Range: Largest no. - Smallest no.
The range with the original numbers is 7 -1 =6
The range when 1 is replaced by 6,the smallest no. becomes 2 which makes the range 7-2= 5
So 1st range - 2nd range =6 - 5 = 1
An animal shelter has 5 times as many cats as it has dogs. There are 75cats at the shelter
Answer: 15 dogs
Step-by-step explanation:
75 / 5 = 15
Answer:
15 dogs
Step-by-step explanation:
Let the number of dogs be x
number of cats be y
5 times the number of cats = number of dogs
y = x*5
Since y = 75
75 = 5x
Bring 5 to the other side n divide
x= 75/5
= 15
Rasheeda sees a garden in a book. She changes the scale because she wants a garden with different dimensions. The figure below shows both scales and a scale drawing of the garden.
Book scale: 1 inch = 2 feet. Rasheeda's Scale: 2 inches = 3 feet. A rectangle with length A of 18 inches and width B of 6 inches.
Which statements about the gardens are true? Select three options.
Answer:
B. Length A of Rasheeda’s garden is 27 ft.
C. Length B of the book’s garden is 12 ft.
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
Step-by-step explanation:
step 1
Find the dimension of the book's garden
we know that
Book scale: 1 inch = 2 feet
That means
1 inch in the drawing represent 2 feet in the actual
To find out the actual dimensions, multiply the dimension in the drawing by 2
so
Length A of the book’s garden
Width B of the book’s garden
step 2
Find the dimension of Rasheeda’s garden
we know that
Rasheeda's Scale: 2 inch = 3 feet
That means
2 inch inches the drawing represent 3 feet in the actual
To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2
so
Length A of Rasheeda's garden
Width B of Rasheeda's garden
Verify each statement
A. Length A of the book’s garden is 18 ft.
The statement is false
Because, Length A of the book’s garden is 36 ft (see the explanation)
B. Length A of Rasheeda’s garden is 27 ft.
The statement is true (see the explanation)
C. Length B of the book’s garden is 12 ft
The statement is true (see the explanation)
D. Length B of Rasheeda’s garden is 6 ft.
The statement is false
Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
The statement is true
Because the difference between 36 ft and 27 ft is equal to 9 ft
F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.
The statement is false
Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.
taffy927x2 and 22 more users found this answer helpful
Answer:
B. Length A of Rasheeda’s garden is 27 ft.
C. Length B of the book’s garden is 12 ft.
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
(second, third, and fifth choices)
Explanation: I did the quiz and got it right.
Hope this Helps!
Help me please!!!
10pts
Answer:
-7/2
Step-by-step explanation:
To find the y coordinate of the midpoint and the y coordinates together and divide by 2
(2+-9)/2
-7/2
Answer:
2 goes in green box
Step-by-step explanation:
(9,2) (-7,-9)
(x1, y1) (x2,y2)
Midpoint is (x1+x2)/2 , (y1+y2)/2
(9-7)/2= 1
(2-9)/2 = -7/2
Write the equation of the line that is parallel to the x-axis and goes through the point (1, 4).
Answer:
y=4
Step-by-step explanation:
A line that is parallel to the x-axis would have an equation of y= ______.
This is because a horizontal graph has a gradient of zero, thus the value of m in y=mx+c is zero.
y=0x +c
y= c
Since it passed through the point (1,4):
When x=1, y=4,
4= 0(1) +c
c= 4
Thus, the equation of the line is y=4.
Answer:
y =4
Step-by-step explanation:
Parallel to x axis means a horizontal line
Horizontal lines are of the form
y =
Since it goes through the point (1,4)
y =4
A multiple-choice examination has 20 questions, each with five possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least seventeen questions correctly? (Round your answer to three decimal places.)
Answer:
The probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].
Step-by-step explanation:
Let the random variable X represent the number of correctly answered questions.
It is provided all the questions have five options with only one correct option.
Then the probability of selecting the correct option is,
[tex]P(X)=p=\frac{1}{5}=0.20[/tex]
There are n = 20 question in the exam.
It is also provided that a student taking the examination answers each of the questions with an independent random guess.
Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.
The probability mass function of X is:
[tex]P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...[/tex]
Compute the probability that the student answers at least seventeen questions correctly as follows:
[tex]P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)[/tex]
[tex]=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}[/tex]
Thus, the probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].
Quadrilateral J K L M is shown. A diagonal is drawn from point J to point L. Sides K L and J M are parallel. Sides J K and L M are congruent. The length of J L is 18, the length of J K is 16, and the length of J M is 40. Angle M is 45 degrees.
If KM is drawn on this quadrilateral, what will be its length?
Answer:
KM is 52.55
Step-by-step explanation:
Given that JKLM is a quadrilateral with a diagonal drawn from J to L, we have;
Sides KL is parallel to side JM
Side JK is congruent to side LM
Therefore, sides JK and LM are parallel being the equal distances between two parallel lines
JL = 18, JK = 16, therefore, LM = 16, JM = 40 therefore, KL = 40 (equal distances between parallel lines JK and LM)
∠M = 45° ∴ ∠L = 180° - 45° = 135° (sum of adjacent interior angles of a parallelogram)
By cosine rule, we have;
KM² = LM² + KL² - 2×KL×LM×cos(∠M) = 16² + 40² - 2×16×40×cos(135°)
KM² = 2761.0967
KM = √(2761.0967) = 52.55 units.
Answer:
18
Step-by-step explanation:
Edg 2021
A consumer group surveyed 146 airplane travelers after a flight and found that 132 of them would fly that airline again. Find the standard error for the sample proportion of airline travelers who would fly on that airline again. Enter your answer as a decimal rounded to three decimal places.
Answer:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p =\frac{132}{146}= 0.904[/tex]
And for this case the standard error assuming normality would be given by:
[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]
Step-by-step explanation:
For this problem we know the following notation:
[tex] n= 146 [/tex] represent the sample size selected
[tex] X= 132[/tex] represent the number of airplane travelers who after a flight would fly that airline again
The estimated proportion for this case would be:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p =\frac{132}{146}= 0.904[/tex]
And for this case the standard error assuming normality would be given by:
[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]
paulina plays both volleyball and soccer .the probability of her getting injured playing soccer is 1.10 and the probability of her getting injured playing soccer is 0.20 .which of the event is more likely
In our decimal system, we distinguish odd and even numbers by looking at their ones (or units) digits. If the ones digit is even (0, 2, 4, 6, 8), the number is even. If the ones digit is odd (1, 3, 5, 7, 9), the number is odd. Determine whether this same criterion works for numbers expressed in base four
Answer:
Yes. In base 4 numbers if a number ends with 0 or 2 then it is an even number. If it ends with 1 or 3 then it is an odd number.
Step-by-step explanation:
The first 13 numbers in base 4 are written in brackets next to their corrsponding decimal number below
decimal number 0(0) ,1 (1) ,2(2), 3(3), 4(10), 5(11), 6(12), 7(13), 8,(20), 9(21), 10(22), 11(23), 12(30), 13(31) and so on
From above we can deduce that in base-4 any number ending with 0 or 2 is an even nmuber and any number ending with 1 or 3 is an odd number
The endpoints of the directed line segment AB are A(−7, 4) and B(8, 9). Find the coordinates of point P along line segment AB so that the ratio of AP to PB is 2 to 3. pls help
Answer:
(-1,5)
Step-by-step explanation:
When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:
The coordinates of x and y are:
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
Given:
[tex]A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3[/tex]
The coordinates of P is:
[tex](x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)[/tex]
If three times a number, added to 2 is divided by the number plus 5, the result is eight thirds.
Answer:
Number = 34
Step-by-step explanation:
We are looking for our mystery "number". I will call this number N.
We can find out what our equation looks like based on what the question tells us.
"three times a number" is 3N
"added to 2" is + 2
Which so far is 3N + 2
"divided by the number plus 5" is ÷ [tex]{N+5}[/tex]
Combined with the first two parts to give us (3N + 2) ÷ (N + 5)
"the result is eight third" So the above equation is equal to 8/3
Combining all these comments together to get the following equation
(3N + 2) ÷ (N + 5) = 8/3
Rearrange by multiplying both sides of the = by (N+5)
3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)
Simplify
3N + 2 = 8/3 × (N + 5)
3N + 2 = 8N/3 + 40/3
Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =
3N + 2 - 2 = 8N/3 + 40/3 - 2
Simplify
3N = 8N/3 + 34/3
and then subtracting 8N/3 from both sides
3N - 8N/3 = 8N/3 - 8N/3 + 34/3
Simplify
1N/3 = 34/3
Simplify for our final answer by multiplying both sides of the = by 3
1N/3 x 3 = 34/3 x 3
N = 34
Many of these steps can be skipped when solving for yourself but I wanted to be thorough
Please answer this correctly
Answer:
1-5: Make it 5 units tall
6-10: Make it 4 units tall
11-15: Make it 2 units tall
16-20: Make it 0 units tall (Don't do anything to it)
21-25: Make it 4 units tall
Step-by-step explanation:
1-5: 2, 3, 3, 3, 5 (5 numbers)
6-10: 6, 6, 8, 10 (4 numbers)
11-15: 11, 13 (2 numbers)
16-20: (0 numbers)
21-25: 22, 23, 24, 24 (4 numbers)
Answer:
The heights of the missing bars are the following:
1- 5 ⇒ 5
6-10 ⇒ 4
11-15 ⇒ 2
16-20 ⇒ 0
21-25 ⇒ 4
two technicians regularly make repairs when breakdowns occur on an automated production line. the first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair. the second technican, who services 60% of the breakdowns, has 3% chance of making an incomplete repair. given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
Answer:
52.63% probability that thids intial repair was made by the first technican
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Incomplete repair
Event B: Made by the first technican.
The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.
This means that [tex]P(B) = 0.4, P(A|B) = 0.05[/tex].
Probability of an incomplete repair:
5% of 40%(first technican) or 3% of 60%(second technican). So
[tex]P(A) = 0.05*0.4 + 0.03*0.6 = 0.038[/tex]
Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
[tex]P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263[/tex]
52.63% probability that thids intial repair was made by the first technican
a realtor uses a lock box to store the keys to a house that is for sale. the access code for the lock consist of five digits. the first digit cannot be 1 and the last digit must be even. how many different codes are avaible
Answer:
45,000 codes
Step-by-step explanation:
Given:
Code of 5 digits
Condition
First digit can't be 1Last digit must be evenRequired
Calculate the number of codes available
Digits = {0,1,2....9}
n(Digits) = 10
Let the format of the code be represented as follows;
ABCDE
From the conditions given
A can't be 1;
This means that A can be any of 0,2,3,4....9
This implies that A can be any of the above 9 digits
n(A) = 9
There's no condition attached to BCD;
This means that B can be any of 10 digits
This means that C can be any of 10 digits
This means that D can be any of 10 digits
n(B) = n(C) = n(D) = 10
Lastly, E must be an even number;
This means that E can be any of 0,2,4,6,8
This implies that E can be any of the above 5 digits
n(E) = 5
So,
Number of available codes = n(A) * n(B) * n(C) * n(D) * n(E)
Number of available codes = 9 * 10 * 10 * 10 *5
Number of available codes = 45,000
Hence, there are 45,000 available codes
Choose the correct simplification of a to the 5th power times b to the 6th power all over a to the 4th power times b to the 4th power. a9b10 ab2 1 over a times b to the 2nd power 1 over a to the 9th power times b to the 10th power
Answer:
ab²
Step-by-step explanation:
Step 1: Write out the expression
[tex]\frac{a^5b^6}{a^4b^4}[/tex]
Step 2: Cross out like terms
The a's cancel out, leaving a in the numerator
The b's cancel out, leaving b² in the numerator
Step 3: Finalize
ab²
And you have your final answer!
Answer:
the answer is ab^2
Step-by-step explanation:
hope this helps
A sport analyst wants to determine the mean salary of a Baseball player for 2015. He believes an estimate of this average salary using a confidence interval is sufficient. How large a sample should he take to be within $497,000 of the actual average with 80% confidence? He calculates the standard deviation of salary for all baseball players for 2015 is about $5,478,384.55. Round your answer to whole number.
Answer:
The large sample size 'n' = 199.6569≅ 200
Step-by-step explanation:
Step(i):-
Given Standard deviation of salary for all baseball players for 2015 is about $5,478,384.55
Standard deviation of of salary for all baseball players for 2015
(S.D ) σ = $5,478,384.55
Given estimate of this average salary for all baseball players for 2015
= $497,000
Given Margin of error of error is = $497,000
Level of significance ∝ = 80%
The critical value Z₀.₂₀ = 1.282
Step(ii):-
Margin of error of error is determined by
[tex]M.E = \frac{Z_{0.20} S.D}{\sqrt{n} }[/tex]
[tex]497,000 = \frac{1.282 X 5,478,384.55}{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = \frac{1.282 X 5,478,384.55}{497,000 }[/tex]
On calculation , we get
√n = 14.13
Squaring on both sides, we get
n = 199.6569
Conclusion:-
The large sample size 'n' = 199.6569≅ 200