Simplify 3 + 3 to 6
6^2/10 - 4 × 3
Simplify 4 × 3 to 12
6^2/10 - 12
Simplify 10 - 12 to -2
6^2/-2
Simplify 6^2 to 36
36/-2
Move the negative sign to the left
-36/2
Simplify 36/2 to 18
= -18
Consider the following sets of sample data: A: $29,400, $30,900, $21,000, $33,200, $21,300, $24,600, $29,500, $22,500, $35,200, $20,800, $39,800, $22,300, $35,700, $25,100 B: 4.53, 4.17, 4.48, 3.73, 3.83, 2.91, 2.99, 4.67, 4.21, 4.68, 3.38 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
The coefficient of variation (CV) is calculated as the standard deviation divided by the mean, expressed as a percentage. Calculate the mean and standard deviation for each set of data, then use these to calculate the CV. Round to one decimal place.
Explanation:The coefficient of variation (CV) is a measure of relative variability. It's calculated as the ratio of the standard deviation to the mean, and it's often expressed as a percentage. We first need to calculate the mean and standard deviation for both sets of data, A and B.
Let's take Set A as an example: Add all the values together and divide by the count (the total number of values) to get the mean. Next, subtract each value by the mean and squared it, then sum all those squared differences. Divide that by the count minus one to get the variance. The standard deviation is the square root of the variance. Finally, the CV is (standard deviation / mean) x 100.
Repeat these steps for Set B.
Remember to always round to one decimal place as requested in the question.
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Which number is rational?
Answer:
5.(3)
Step-by-step explanation:
5.(3)=16/3
Answer:
d
Step-by-step explanation:
The average age of doctors in a certain hospital is 45.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 8.0 years. If 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 46.9 years. Assume that the variable is normally distributed.
Answer: 0.7619
Step-by-step explanation:
Given : Mean : [tex]\mu=45.0 [/tex]
Standard deviation : [tex]\sigma =8.0[/tex]
Sample size : [tex]n=9[/tex]
We assume that the variable is normally distributed.
The value of z-score is given by :-
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
a) For x= 46.9 years
[tex]z=\dfrac{46.9-45.0}{\dfrac{8}{\sqrt{9}}}=0.7125[/tex]
The p-value : [tex]P(z<0.7125)=0.7619224\approx0.7619[/tex]
Hence, the probability that the average age of those doctors is less than 46.9 years =0.7619
The question relates to probability in a normally distributed population. We calculated the standard error and z-score, then used the z-table to find that there is approximately a 76.11% chance that the average age of 9 randomly chosen doctors from this hospital will be less than 46.9 years.
Explanation:The subject of this question pertains to Probability and Statistics, specifically the application of the Normal Distribution in the context of calculating the probability of a particular outcome in a real-world scenario. We'll apply the rule for the Central Limit Theorem (CLT) since the sample size is reasonably large (n = 9).
The first step is to calculate the standard error (SE). The SE of the mean can be calculated by dividing the standard deviation by the square root of the number of doctors:
SE = 8.0/sqrt(9) = 8.0/3 = 2.67.
Next, you would calculate the z-score. The z-score of 46.9 is obtained by subtracting the population mean from 46.9 and then dividing by the SE:
Z = (46.9 - 45.0)/2.67 = 0.71.
To determine the probability that the average age is less than 46.9 years, you will want to look up the z-score of 0.71 in a z-table, which gives a value of 0.7611, or 76.11%. So there is approximately a 76.11% chance that the mean age of the 9 doctors chosen will be less than 46.9 years old.
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Find the interest rate needed for an investment of $10,000 to grow to an amount of $11,000 in 4 years if interest is compounded quarterly. (Round your answer to the nearest hundredth of a percent.) %
Answer:
[tex]2.39\%[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=4\ years\\ P=\$10,000\\A=\$11,000\\ r=?\\n=4[/tex]
substitute in the formula above
[tex]11,000=10,000(1+\frac{r}{4})^{4*4}[/tex]
[tex]1.1=(1+\frac{r}{4})^{16}[/tex]
Elevated both sides to (1/16)
[tex]1.005975=(1+\frac{r}{4})[/tex]
[tex]0.005975=\frac{r}{4}[/tex]
[tex]r=0.005975*4=0.0239[/tex]
Convert to percent
[tex]0.0239*100=2.39\%[/tex]
Peter kim wanted to buy a new car.To help finance the purchase he decided to sell his organic markets bond in the secondary market.Peters bond had a par value of $ 10,000 and a coupon of 6 percent.Current interests were 3 percent.What would peters bond sell for?
A student's course grade is based on one midterm that counts as 15% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 83, his project score is 97, his homework score is 82, and his final exam score is 63. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but < 90 is a B, and so on.
Answer:
Overall final score = 77.75% ; Grade = C.
Step-by-step explanation:
The approach to solve this question is to realize that the marks have to be converted into the respective percentages of the whole course. This means that the marks of all the components have to be normalized according to the grading breakdown.
Project Marks = 97/100. Weightage = 15%. So 97*15/100 = 14.55/15.
This means that the student received 14.55 marks in the project out of 15.
Similarly for other components:
Mid-Term Marks = 83/100. Weightage = 15%. So 83*15/100 = 12.45/15.
Homework Marks = 82/100. Weightage = 35%. So 82*35/100 = 28.7/35.
Finals Marks = 63/100. Weightage = 35%. So 63*35/100 = 22.05/35.
After the conversion process, add up the normalized marks, which are now acting as the percentages earned in all the components.
Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%.
According to the grade scale, the student receives a C because 70 is less than 77.75 and 77.75 is less than 80.
Summarizing, the student receives a C at 77.75%!!!
The student gets the Grade 'C' because the aggregate percentage is greater than 70 and less than 80 and this can be determined by using the given data.
Given :
A student's course grade is based on one midterm that counts as 15% of his final grade.One class project counts as 15% of his final grade.A set of homework assignments that counts as 35% of his final grade.A final exam that counts as 35% of his final grade. His midterm score is 83, his project score is 97, his homework score is 82, and his final exam score is 63.A student's project marks are 97 out of 100 but the weightage of the project marks is 15%. That is:
[tex]=\dfrac{97\times 15}{100}[/tex]
[tex]=14.55[/tex]
So, the project marks are 14.55 out of 15.
A student's homework assignments marks are 82 out of 100 but the weightage of the project marks is 35%. That is:
[tex]=\dfrac{82\times 35}{100}[/tex]
= 28.7
So, homework assignments marks are 28.7 out of 35.
A student's midterm marks are 83 out of 100 but the weightage of the project marks is 15%. That is:
[tex]=\dfrac{83\times 15}{100}[/tex]
= 12.45
So, midterm marks are 12.45 out of 15.
A student's final exam marks are 63 out of 100 but the weightage of the project marks is 35%. That is:
[tex]=\dfrac{63\times 35}{100}[/tex]
= 22.05
So, final exam marks are 22.05 out of 35.
So, the aggregate percentage is given by:
Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%
The student gets the Grade 'C' because the aggregate percentage is greater than 70 and less than 80.
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Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 53 and, in a separate drawing, you must also select the correct single number between 1 and 45. Find the probability of winning the jackpot.
[tex]|\Omega|={_{53}C_3}\cdot 45=\dfrac{53!}{3!50!}\cdot45=\dfrac{51\cdot52\cdot53}{2\cdot3}\cdot45=1054170\\|A|=1\\\\P(A)=\dfrac{1}{1054170}\approx0.00000095\%[/tex]
Write the standard equation of a circle that passes through (-5 5) with center (-10 -5) brainly
Answer:
The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form
Step-by-step explanation:
* lets study the standard form of the equation of a circle
- If the coordinates of the center of the circle are(h , k) and its radius
is r, then the standard equation of the circle is:
(x - h)² + (y - k)² = r²
* Now lets solve the problem
∵ The coordinates of the center of the circle are (-10 , -5)
∵ The standard form of the equation is (x - h)² + (y - k)² = r²
∵ h , k are the coordinates of the center
∴ h = -10 , k = -5
∴ The equation of the circle = (x - -10)² + (y - -5)² = r²
∴ The equation of the circle = (x + 10)² + (y + 5)² = r²
- To find the value of the radius lets use the point (-5 , 5) to
substitute their coordinate instead of x and y in the equation
∵ The circle passes through point (-5 , 5)
∵ (x + 10)² + (y + 5)² = r²
- Use x = -5 and y = 5
∴ (-5 + 10)² + (5 + 5)² = r² ⇒ simplify
∴ (5)² + (10)² = r²
∴ 25 + 100 = r²
∴ r² = 125
* Now lets write the equation in standard form
∴ (x + 10)² + (y + 5)² = 125
* The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form
What is the average rate of change of the function over the interval x=0 to x=4?
f(x)=2x-1/3x+5
Enter your answer, as a fraction, in the box.
(To whoever is looking for the answer)
Step-by-step explanation:
The average rate of change of a function f(x) over an interval [a, b] is:
(f(b) − f(a)) / (b − a)
(f(4) − f(0)) / (4 − 0)
(7/17 − -1/5) / 4
(52/85) / 4
13/85
Answer:
yes thank you so much i was struggling so much with this tysm
Step-by-step explanation:
A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight equals negative 5.33 plus 0.1926 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?
The residual for the newborn is -0.9148 kg, indicating he is lighter than what the model predicts for his length.
To calculate the residual for the newborn's weight, we first use the least squares regression line equation, which is weight = -5.33 + 0.1926 * length. We then input the newborn's length of 48 cm into the equation to predict the weight.
Predicted weight = -5.33 + (0.1926 * 48) = -5.33 + 9.2448 = 3.9148 kg
The residual is the difference between the actual weight and the predicted weight, so for this newborn, the residual = actual weight - predicted weight = 3 kg - 3.9148 kg = -0.9148 kg.
The negative residual indicates that the newborn weighs less than what the regression model predicts for a boy of 48 cm in length. This could suggest that the child is lighter than average for his length
If an increase in one variable causes a decrease in another variable, there is A. a negative relationship. B. a dependent relationship. C. a direct relationship. D. an independent relationship.
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given a situation that
If an increase in one variable causes a decrease in another variable,
Then, there is inverse relationship.
When one variable is increased whereas other variable falls.
There will be inverse relationship.
Since inverse relation has negative relation.
Then, there is a negative relationship.
Hence, Option 'A' is correct.
An increase in one variable causing a decrease in another indicates a negative relationship between the two variables, characterized by opposite directional movements and graphically represented by a line with a negative slope.
Explanation:When discussing the correlation between two variables, it is important to consider the direction and type of relationship they share. If an increase in one variable causes a decrease in the other variable, this is defined as a negative relationship. In a negative relationship, the two variables move in opposite directions, meaning that as one variable increases, the other decreases and vice versa.
The relationship is depicted graphically as a line with a negative slope on a graph, where the line descends as it moves from left to right. This situation should not be confused with dependent, direct, or independent relationships, which describe different aspects of variable interaction.
Help ASAP!! See screenshot below.
ANSWER
The relation is not a function.
EXPLANATION
The relation is not a function because we have an x-coordinate mapping on to more than one y-coordinate.
This occurs at x=1.
The ordered pairs (1,1) and (1,3) disqualify the relation from being a function.
Hence the relation is not a function.
The probability that a college student belongs to a health club is 0.3. The probability that a college student lives off-campus is 0.4. The probability that a college student belongs to a health club and lives off-campus is 0.12. Find the probability that a college student belongs to a health club OR lives off-campus. Tip: P(A or B) = P(A) + P(B) - P(A and B) 0.54 0.58 0.70 0.82
Answer:
The correct option is 2.
Step-by-step explanation:
Let A be the event that the college student belongs to a health club and B be the event that the college student lives off-campus.
The probability that a college student belongs to a health club is 0.3.
[tex]P(A)=0.3[/tex]
The probability that a college student lives off-campus is 0.4.
[tex]P(B)=0.4[/tex]
The probability that a college student belongs to a health club and lives off-campus is 0.12.
[tex]P(A\cap B)=0.12[/tex]
The probability that a college student belongs to a health club OR lives off-campus is
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]P(A\cup B)=0.3+0.4-0.12[/tex]
[tex]P(A\cup B)=0.58[/tex]
The probability that a college student belongs to a health club OR lives off-campus is 0.58. Therefore the correct option is 2.
Help Algebra!!
10. To solve a system of equations using the matrix method, use elementary row operations to transform the augmented matrix into one with _______. Then, proceed back to substitute.
A. zeros in its final column
B. an inverse
C. zeros below the diagonal
D. Gaussian elimination
Answer:
C. zeros below the diagonal
Step-by-step explanation:
Upper echelon form (zeros below the diagonal) corresponds to a system of equations that has one equation in one variable, one equation in two variables, and additional equations in additional variables adding one variable at a time.
The single equation in a single variable is easily solved, and that result can be substituted into the equation with two variables (one of which is the one just found) to find one more variable's value. This back-substitution proceeds until all variable values have been found.
The process of producing such a matrix is called Gaussian Elimination.
__
The back-substitution process effectively makes the matrix be an identity matrix (diagonal = ones; zeros elsewhere) and the added column be the solution to the system of equations.
To solve a system of equations using the matrix method, you transform the augmented matrix to have zeros below the diagonal through Gaussian elimination. Then, you substitute back into the equations to find the solution.
Explanation:To solve a system of equations using the matrix method, you use elementary row operations to transform the augmented matrix into one with zeros below the diagonal. This is achieved through a method called Gaussian elimination. The goal is to reduce the matrix to its row-echelon form, which leaves zeros below the diagonal. After this reduction, you can then proceed to substitute back into the equations to find the solution.
For example, let's take the system of equations:
x+2y=7
3x-4y=11
This can be represented as an augmented matrix:
[1 2 | 7]
[3 -4 | 11]
Using Gaussian elimination, we can eliminate the '3' below the diagonal by subtracting 3x the first row from the second, getting you:
[1 2 | 7]
[0 -10 | -10]
By substituting, we then find the solutions for the system of equations.
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A psychologist wishes to conduct a study on the effects of music deprivation on high school students. A high school class consists of the 30 students numbered in the list below. The researcher establishes a treatment group of 15 students who will have their portable music players replaced by experimental players that present the sound of water running. The control group of 15 students will all get regular portable music players, stuffed full of their favorite songs. 00 Aaron 01 Buffy 02 Chandler 03 Cindy 04 Drusilla 05 Eric 06 Fallon 07 Graham 08 heather 09 Hsin-chi 10 Ismail 11 Jasmine 12 Kiefer 13 Lucia 14 Monte 15 Naomi 16 Otis 17 Polly 18 Quincy 19 Rachael 20 Sarah 21 Stacy 22 Tasha 23 Tuan 24 Ukiah 25 Valerie 26 Wahib 27 Xavier 28 Yolanda 29 Zachary Use the line of random numbers below to select the first 5 students to receive the treatment. What is the name of the fifth student selected? 59784 44312 15954 09233 00046 74318 02610 57396 16843 38454.
Answer:
Quincy
Step-by-step explanation:
Each student is assigned a two digit number, so let's split the random number line into two digit numbers:
59, 78, 44, 43, 12, 15, 95, 40, 92, 33, 00, 04, 67, 43, 18, 02, 61, 05, 73, 96, 16, 84, 33, 84, 54
Now let's identify the numbers between 00 and 29.
59, 78, 44, 43, 12, 15, 95, 40, 92, 33, 00, 04, 67, 43, 18, 02, 61, 05, 73, 96, 16, 84, 33, 84, 54
So the fifth student in the list is #18, or Quincy.
Answer:
Quincy is the answer
Step-by-step explanation:
The diagram represents the polynomial 4x2 + 23x – 72.
What is the factored form of 4x2 + 23x – 72?
(4x + 8)(x – 9)
(4x – 8)(x + 9)
(4x + 9)(x – 8)
(4x – 9)(x + 8)
For this case we must factor the following expression:
[tex]4x ^ 2 + 23x-72[/tex]
We rewrite the middle term as a sum of two terms whose product is [tex]4 * (- 72) = - 288[/tex] and whose sum is 23. These numbers are -9 and +32. So:
[tex]4x ^ 2 + (- 9 + 32) x-72\\4x ^ 2-9x + 32x-72[/tex]
We factor the highest common denominator of each group.
[tex]x (4x-9) +8 (4x-9)[/tex]
We factor taking into account the common term [tex](4x-9):[/tex]
[tex](4x-9) (x + 8)[/tex]
Finally, the factored expression is:
[tex](4x-9) (x + 8)[/tex]
Answer:
Option D
Answer:
The correct answer option is D. (4x – 9)(x + 8).
Step-by-step explanation:
We are given the following polynomial and we are to find its factored form:
[tex]4x^2+23x-72[/tex]
Finding factors of (-72 * 4 = ) -288 such that when added they give a result of 23 and when multiplied it gives a product of -288.
[tex] 4 x ^ 2 + 3 2 x - 9 x - 7 2[/tex]
[tex] 4 x ( x + 8 ) - 9 ( x + 8 ) [/tex]
[tex] ( 4 x - 9 ) ( x + 8 )[/tex]
Simplify 16m^2/m^2+5/4m/3m^2+15
Answer:
12m
Step-by-step explanation:
We are given the following expression where a fraction is divided by another fraction:
[tex]\frac{\frac{16m^2}{m^2+5} }{\frac{4m}{3m^2+15} }[/tex]
To change this division into multiplication, we will take reciprocal of the fraction in the denominator and then solve:
[tex] \frac { 1 6 m ^ 2 } { m^2+5} } \times \frac{3m^2+15}{4m}[/tex]
Factorizing the terms to simplify:
[tex] \frac { 4 m ( 4m ) } { m ^ 2 + 5 } \times \frac { 3 ( m ^ 2 + 5 ) } { 4 m } [/tex]
Cancelling the like terms to get:
12m
Answer: [tex]12m[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{\frac{16m^2}{m+5}}{\frac{4m}{3m^2+15}}[/tex], we can rewrite it in this form:
[tex](\frac{16m^2}{m+5})(\frac{3m^2+15}{4m})[/tex]
Now we must multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:
[tex]=\frac{(16m^2)(3m^2+15)}{(m^2+5)(4m)}}[/tex]
According to the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
And the Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then, simplifying, we get:
[tex]=\frac{3(m^2+5)(4m)(4m)}{(m^2+5)(4m)}}\\\\=3(4m)\\\\=12m[/tex]
If F(x,y) = x^2sin(xy), find Fyx.
Answer:
[tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]
Step-by-step explanation:
We need to find out the partial differential [tex]F_{yx}[/tex] of [tex]F(x,y)=x^{2}sin(xy)[/tex]
First, differentiate [tex]F(x,y)=x^{2}sin(xy)[/tex] both the sides with respect to 'y'
[tex]\frac{d}{dy}F(x,y)=\frac{d}{dy}x^{2}sin(xy)[/tex]
Since, [tex]\frac{d}{dt}\sin t =\cos t[/tex]
[tex]\frac{d}{dy}F(x,y)=x^{2}cos(xy)\times \frac{d}{dy}(xy)[/tex]
[tex]\frac{d}{dy}F(x,y)=x^{2}cos(xy)\times x[/tex]
[tex]\frac{d}{dy}F(x,y)=x^{3}cos(xy)[/tex]
so, [tex]F_y=x^{3}cos(xy)[/tex]
Now, differentiate above both the sides with respect to 'x'
[tex]F_{yx}=\frac{d}{dx}x^{3}cos(xy)[/tex]
Chain rule of differentiation: [tex]D(fg)=f'g + fg'[/tex]
[tex]F_{yx}=cos(xy) \frac{d}{dx}x^{3} + x^{3} \frac{d}{dx}cos(xy)[/tex]
Since, [tex] \frac{d}{dx}x^{m} =mx^{m-1}[/tex] and [tex] \frac{d}{dt} cost =-\sin t[/tex]
[tex]F_{yx}=cos(xy)\times 3x^{2} - x^{3} sin(xy)\times \frac{d}{dx}(xy)[/tex]
[tex]F_{yx}=cos(xy)\times 3x^{2} - x^{3} sin(xy)\times y[/tex]
[tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]
hence, [tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]
At a certain school, intro to economics and intro to calculus meet at the same time, so it is impossible for a student take both classes. If the probability that a student takes intro to economics is 0.57, and the probability that a student takes intro to calculus 0.17, what is the probability that a student takes intro to economics or into to calculus?
Answer:
0.74
Step-by-step explanation:
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.57 + 0.17 - 0
P(A∪B) = 0.74
The probability of A∩B is zero because the classes are mutually exclusive.
if f(x)=2x-1+3 and g(x)=5x-9, what is (f-g)(x)?
Answer:
[tex]\large\boxed{(f-g)(x)=-3x+11}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x-1+3=2x+2\\g(x)=5x-9\\\\\text{Substitute:}\\\\(f-g)(x)=(2x+2)-(5x-9)\\\\=2x+2-5x-(-9)\\\\=2x+2-5x+9\qquad\text{combine like terms}\\\\=(2x-5x)+(2+9)\\\\=-3x+11[/tex]
Twenty switches in an office computer network are to be connected so that each switch has a direct connection to exactly three other switches. How many connections will be necessary?
Answer:
30 connections
Step-by-step explanation:
20 switches with 3 connections each will have a total of 20×3 = 60 connections. That counts each connecting link twice, so only 30 connecting links are required.
Answer:
30 Connections!
Step-by-step explanation:
I did this on AoPs :)
Suppose that 3 cards from a standard deck of 52 playing cards are successively drawn at random without replacement (a) Find the probability that all 3 are queens (b) Find the probability that all 3 are spades (a) The probability that all 3 are queens is (Type an integer a simplified fraction) or (b) The probability that all 3 are spades is (Type integer simplified fraction) an or a
[tex]|\Omega|=52\cdot51\cdot50=132600[/tex]
a)
[tex]|A|=4\cdot3\cdot2=24\\P(A)=\dfrac{24}{132600}=\dfrac{1}{5525}[/tex]
b)
[tex]|A|=13\cdot12\cdot11=1716\\P(A)=\dfrac{1716}{132600}=\dfrac{11}{850}[/tex]
a. Probability of all 3 cards being queens:
Number of ways to choose 3 queens from 4: 4C3 = 4.Number of ways to choose 3 cards from 52: 52C3 = 22100.Probability = 4/22100 = 1/5525.b. Probability of all 3 cards being spades:
Number of ways to choose 3 spades from 13: 13C3 = 286.Number of ways to choose 3 cards from 52: 52C3 = 22100.Probability = 286/22100 = 13/1001.Fill in the blank with a digit such that the resulting number is divisible by 11.
(a) 362,375,__35
(b) 82,919,__21
(c) 57,13__,473
Answer: Hence, a) 0, b) 2, and c) 0
Step-by-step explanation:
As we know that If the difference of sum of odd places values and sum of even places value is divisible by 11, then the number is itself divisible by 11.
(a) 362,375,__35
Sum of odd places values : 3+2+7+5+x=17+x
Sum of even places values : 6+3+5+3=17
Difference between them is 17+x-17=x
So, x should be 0 to get divisible by 11 as 0 is divisible by 11.
(b) 82,919,__21
Sum of odd places values : 8+9+9+2=28
Sum of even places values : 2+1+x+1=4+x
Difference between them is 28-(4-x)=24-x
So, x should be 2 so, that it becomes 24-2=22 which is divisible by 11.
(c) 57,13__,473
Sum of odd places values : 5+1+x+7=13+x
Sum of even places values : 7+3+4+3=17
Difference between them is 17-(13+x)=4-x
So, x should be 4 so that it becomes 4-4=0 which is divisible by 11.
Hence, a) 0, b) 2, and c) 0
The number of typing errors made by a typist has a Poisson distribution with an average of two errors per page. If more than two errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped? (Round your answer to three decimal places.)
Answer: 0.6767
Step-by-step explanation:
Given : Mean =[tex]\lambda=2[/tex] errors per page
Let X be the number of errors in a particular page.
The formula to calculate the Poisson distribution is given by :_
[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]
Now, the probability that a randomly selected page does not need to be retyped is given by :-
[tex]P(X\leq2)=P(0)+P(1)+P(2)\\\\=(\dfrac{e^{-2}2^0}{0!}+\dfrac{e^{-2}2^1}{1!}+\dfrac{e^{-2}2^2}{2!})\\\\=0.135335283237+0.270670566473+0.270670566473\\\\=0.676676416183\approx0.6767[/tex]
Hence, the required probability :- 0.6767
Harry operates a coffee shop. One of her customers wants to buy two kinds of beans. Arabian mocha and Columbian decaf. If she wants twice as much Arabian mocha as Columbian decaf how much of each can she buy for a total of $181.50?
The customer can buy ____ lbs of arabian mocha
And ______ lbs of Columbian decaf
Answer:
11 lbs of Arabian Mocha5.5 lbs of Columbian DecafStep-by-step explanation:
Since we want twice as much Mocha as Decaf, we can create a "bag" that contains 2 lbs of Mocha (at 11.50 each) and 1 lb of Decaf (at 10). The value of this "bag" is then 2×11.50 +10.00 = 33.00. For 181.50, we can buy ...
181.50/33.00 = 5.5
"bags". This amount is ...
11 lbs of Arabian Mocha and 5.5 lbs of Columbian Decaf
The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
Answer:
3x -4y = 2
Step-by-step explanation:
A plot of the points makes it clear that the longest diagonal is BD. The 2-point form of the line through those points can be found by filling in ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-2))/(6 -(-2))(x -(-2)) +(-2) . . . . . fill in points B and D
y = (6/8)(x +2) -2
4y = 3(x +2) -8 . . . . . . multiply by 4
3x -4y = 2 . . . . . . . . . . add 2-4y
Line m is parallel to line n. The measure of angle 4 is 109°. What is the
measure of angle 6?
A) 71°
B) 109°
C) 95°
D 101°
The answer is A, 71°.
180-109=71
Since m and n are parallel, angles 4 and 6 will add up to 180 degrees - just like angles 4 and 2. Remember that 180 degrees is a straight line: if angles 4 and 6 are put together, they will make a straight line.
Solve the following system of equations, 3x +5y+2-0
Answer:
3x+5y+2
Step-by-step explanation:
remove the 0
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting aa clubclub or spadespade. (b) Compute the probability of randomly selecting aa clubclub or spadespade or heartheart. (c) Compute the probability of randomly selecting aa twotwo or diamonddiamond.
Answer:
a) 1/2 = 50%
b) 3/4 = 75%
c) 1 / 52 or 1,9%
Step-by-step explanation:
In a standard deck of cards, there are 52 cards in total:
13 are hearts, 13 are diamonds, 13 are clubs and 13 are spades.
(a) Compute the probability of randomly selecting a club or spade
How many cards are a club or a spade?
C = 13 clubs + 13 spades = 26 cards
Out of the 52 total, that means that:
P (club or spade) = 26/52 = 1/2 = 50%
(b) Compute the probability of randomly selecting a club or spade or heart.
How many cards are a club or a spade?
C = 13 clubs + 13 spades + 13 hearts = 39 cards
Out of the 52 total, that means that:
P (club or spade or heart) = 39/52 = 3/4 = 75%
(c) Compute the probability of randomly selecting a two or diamond.
There's only ONE two of diamond in regular deck of cards, so...
P(2 of diamond) = 1 / 52 or 1,9%
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.Step 1 of 2 : Suppose a sample of 523 suspected criminals is drawn. Of these people, 172 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer: The required proportion is [tex]\dfrac{172}{523}[/tex] in fraction and [tex]0.329[/tex] in decimals.
Step-by-step explanation:
Since we have given that
Number of suspected criminals is drawn = 523
Number of criminals were captured = 172
We need to find the proportion of people who were caught after being on the 10 Most wanted list.
So, Proportion of people who were caught is given by
[tex]\dfrac{172}{523}\\\\=0.3288\\\\\approx 0.329[/tex]
Hence, the required proportion is [tex]\dfrac{172}{523}[/tex] in fraction and [tex]0.329[/tex] in decimals.
The estimated proportion of suspected criminals caught after being on the FBI's 10 Most Wanted list is 0.329, or 32.9%, based on a sample where 172 out of 523 individuals were captured.
Explanation:To estimate the proportion of people who were caught after being on the FBI's 10 Most Wanted list, we can use the sample data provided. In the sample, 523 suspected criminals were monitored and 172 were captured. The estimated proportion of individuals caught is calculated by dividing the number of people captured by the total number in the sample.
To find this proportion, we perform the following calculation:
Proportion = Number of people captured / Total number of suspected criminals
Proportion = 172 / 523
Proportion = 0.329 (rounded to three decimal places)
So, the estimated proportion of people who were caught after appearing on the list is approximately 0.329, or 32.9%.