Answer:
Step-by-step explanation:
For first game PA = 1/3
For second game PA = 1/3 ( If A is not lost in first game )
= 2/5 (If A is lost in first game )
For conclusion of game in three matches :
If A wins , the probability is
PA , PB , PA = 1/3 X 2/3 X 3/5 = 6/45
PB , PA , PA = 2/3 X 3/5 X 1/3 = 6/45
If B wins
PA, PB, PB = 1/3 X 2/3 X 2/5 = 4/ 45
PB, PA , PB = 2/3 X 3/5 X 2/3 = 4 / 15
Total probability of conclusion of game in 3 matches
= 6/45 +6/45 + 4/45 +4/15 = 28/45
b )
For the game concluding in 2 matches , the probability are as follows
PA,PA = 1/3 X 1/3 = 1/9
PBPB = 2/3 X 2/5 = 4 / 15
Total probability
= 1/9 + 4/15 = 17/45
So PA = 1/9 / 17/45
= 5/17
A student earned grades of Upper AA, Upper DD, Upper AA, Upper CC, and Upper BB. Those courses had the corresponding numbers of credit hours 44, 22, 22, 33, and 11. The grading system assigns quality points to letter grades as follows: Aequals=4; Bequals=3; Cequals=2; Dequals=1; Fequals=0. Compute the grade point average (GPA) as a weighted mean and round the result with two decimal places. If the Dean's list requires a GPA of 3.00 or greater, did this student make the Dean's list? The grade point average is nothing. (Round to two decimal places as needed.) Did this student make the Dean's list? A. Yes because at least two of the student grades are B or above B. No because the students GPA is not 4.0 C. NoNo because the student has at least one grade lessless than 3 D. NoNo because the student's GPA is lessless than 3.0
Answer:
The grade point average is 2.92The student didn't make the Dean's list because the student's GPA is less than 3.0Step-by-step explanation:
I take the grades as A,D,A,C,B not AA,DD,AA,CC,BB.I take numbers of credit hours as 4,2,2,3,1 not as 44, 22, 22, 33, and 11.Since quality points to letter grades are A=4; B=3; C=2; D=1; F=0, weighted mean is the sum of the qulity points times corresponding credit hours divided by the total credit hours:
[tex]\frac{(4*4) + (1*2) + (4*2) + (2*3) + (3*1)}{12}[/tex] ≈ 2.92
Since 2.92<3.0, the student is not in Dean's list.
You and your friend play a game. You answer 80% of the questions correctly and your friend answers 0.60 of the questions correctly. What is the minimum number of questions in the game?
Answer:
5
Step-by-step explanation:
Assuming both players can answer the same question, the minimum number of questions is the smallest number that when multiplied by either 0.60 or 0.80 yields a whole number.
Let x be the number of questions, solving by trial and error:
[tex]if\ x=2\\x*0.8=1.6\\x*0.6=1.2\\\\if\ x=3\\x*0.8=2.4\\x*0.6=1.8\\\\if\ x=4\\x*0.8=3.2\\x*0.6=2.4\\\\if\ x=5\\x*0.8=4\\x*0.6=3\\\\[/tex]
Therefore, the minimum number of questions in the game is 5.
To find the minimum number of questions in a game where one person answers 80% correctly and another answers 60% correctly, calculate the LCM of the fractions' denominators. The result is 5 questions.
You and your friend have different accuracy rates when answering questions in a game. You answer 80% of the questions correctly, while your friend answers 60% of the questions correctly. To find the minimum number of questions in the game, we need to ensure that both percentages can correspond to whole numbers of questions.
Convert the percentages to fractions: You: [tex]\( \frac{80}{100} = \frac{4}{5} \)[/tex] and your friend: [tex]\( \frac{60}{100} = \frac{3}{5} \)[/tex]To find the smallest number of questions (N) that allows both fractions to be whole numbers, find the Least Common Multiple (LCM) of the denominators (5 in both cases).The LCM of 5 is 5 since it’s the same for both.Thus, the minimum number of questions in the game is 5.In a game with 5 questions:
You would answer 4 out of 5 questions correctly (80%).Your friend would answer 3 out of 5 questions correctly (60%).Therefore, the minimum number of questions in this game is 5.
Based on a poll, a newspaper reported that between 52% and 68% of voters would be likely to vote for a schoolbond issue. What is the margin of error of the poll?
Answer:
The margin of error of the poll is 8%.
Step-by-step explanation:
This is a confidence interval. A confidence interval has both a lower end and an upper end.
The true proportion is the midpoint between the two ends.
The margin of error is the absolute difference between the proportion and the ends(which is the same, upper end - proportion = proportion - lower end),
In this problem, we have that:
The lower end is 52%.
The upper end is 68%.
The proportion is (52 + 68)/2 = 60%.
The margin of error is 60 - 52 = 68 - 60 = 8%.
Find the vector representing the area of the triangle ABC where A=(4,5,6), B=(6,4,5) and C=(5,4,6) oriented so that it faces upward.
Answer: Area of triangle is √3 / 2
Step-by-step explanation:
The explanation can be found in the attached in picture
How many 7/8 cup servings are in 1/2 of a cup of juice? (in simplest fraction form)
The result is [tex]\frac{4}{7}[/tex]
Step-by-step explanation:
In this problem, we are asked to find how many 7/8 cup servings are in 1/2 of a cup of juice.
Mathematically, this is equivalent to divide 1/2 by 7/8. So we can write:
[tex]\frac{1/2}{7/8}[/tex]
This can be rewritten as a multiplication by reversing the denominator:
[tex]\frac{1}{2}\cdot \frac{8}{7}[/tex]
Now we can perform the multiplication of both the numerator and the denominator:
[tex]\frac{1\cdot 8}{2\cdot 7}=\frac{8}{14}[/tex]
And simplifying (dividing by 2),
[tex]\frac{8}{14}=\frac{4}{7}[/tex]
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There are 4/7 servings of 7/8 cup in 1/2 cup of juice.
To determine the number of 7/8 cup servings in 1/2 of a cup of juice, divide the 1/2 cup of juice by 7/8 cup.
Now, the reciprocal of 7/8 and multiplying it by 1/2.
Reciprocal of 7/8 = 8/7
Now, perform the multiplication:
= (1/2 cup) * (8/7)
= (1 * 8) / (2 * 7)
= 8/14
= 4/7
Therefore,4/7 servings of 7/8 cup in 1/2 cup of juice.
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1) Find an equation of the line that passes through the point and has the indicated slope m. (Let x be the independent variable and y be the dependent variable.) (1, 8); m = -1/2
2) Find an equation of the line that passes through the points. (2, 4) and (3, 7)
3) Find an equation of the line that has slope m and y-intercept b. (Let x be the independent variable and y be the dependent variable.) m = −2; b = −1
4) Write the equation in the slope-intercept form.y − 7 = 0 _____________ Then find the slope of the corresponding line _______ then find the y-intrcept of the corresponding line (x,y)= ( ______ )
Answer:
1) The equation of a line is [tex]y=-\frac{1}{2}x+\frac{17}{2}[/tex].
2) The equation of the line that passes through the points (2,4) and (3,7) is [tex]y=3x-2[/tex]
3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is [tex]y=-2x-1[/tex]
4) The slope-intercept form of [tex]y-7=0[/tex] is [tex]y=7[/tex], where the slope is zero and the y-intercept is (0, 7).
Step-by-step explanation:
1) The equation of a line with slope m, passing through the point [tex](x_1,y_1)[/tex], is
[tex]y-y_1=m(x-x_1)[/tex]
We know that [tex]m = -\frac{1}{2}[/tex] and the point is (1,8). Therefore, the equation of the line is
[tex]y-8=-\frac{1}{2} (x-1)\\\\y-8+8=-\frac{1}{2}\left(x-1\right)+8\\\\y=-\frac{1}{2}x+\frac{1}{2}+8\\\\y=-\frac{1}{2}x+\frac{17}{2}[/tex]
2) The equation of a line is typically written as
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
The slope of a line is a measure of how fast the line "goes up" or "goes down" and is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
To find the equation of the line that passes through the points (2, 4) and (3, 7), the first step is to find the slope.
Applying the definition of the slope, we get that
[tex]m=\frac{7-4}{3-2}=3[/tex]
Now, we find the y-intercept with the help of point (2, 4) and the general form of the equation of a line
[tex]4=3(2)+b\\b=-2[/tex]
The equation of the line that passes through the points (2,4) and (3,7) is [tex]y=3x-2[/tex]
3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is
[tex]y=-2x-1[/tex]
4) The slope-intercept form of [tex]y-7=0[/tex] is [tex]y=7[/tex], where the slope is zero and the y-intercept is (0, 7).
Final answer:
An equation of a line through the point (1, 8) with a slope of -1/2 is y - 8 = (-1/2)(x - 1). A line with a slope of -2 and a y-intercept of -14 is represented by y = -2x - 14. The equation y - 7 = 0 represents a horizontal line with a slope of 0 and a y-intercept of (0, 7).
Explanation:
Equations of Lines: Slope and Y-Intercept
To find an equation of a line that passes through the point (1, 8) with a slope m of -1/2, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point. Plugging in the values, we get:
y - 8 = (-1/2)(x - 1)
For a line with a slope m of −2 and a y-intercept b of −14, we can write the equation directly in slope-intercept form, which is y = mx + b. Therefore, the equation is:
y = -2x − 14
For the equation y − 7 = 0, this is a horizontal line where the slope is 0 because there's no change in y as x varies. The y-intercept of this line is (0, 7), as the line crosses the y-axis at y = 7.
Which table represents the graph of a logarithmic function with both an x-and y-intercept?
Answer:
The answer is B
Step-by-step explanation:
Answer:
B. The second graph
Step-by-step explanation:
edge 2021 math assignment
In an election in a small town, everybody voted for one of the three candidates. The winner received
8392 votes, and the second-place candidate got 7480 votes. If 20900 people voted in the election,
how many people voted for the third candidate?
PLEASE SHOW WORK!
Answer:
The answer to your question is 5028 votes
Step-by-step explanation:
Data
Winner 8392 votes
Second-place = 7480 votes
Total votes = 20900
Third candidate = ?
Process
1.- Write an equation
Total votes = Winner + Second-place + Third-place
Solve for Third-place
Third-place = Total votes - Winner - Second-place
2.- Substitution
Third-place = 20900 - 8392 - 7480
3.- Simplification
Third-place = 20900 - 15872
4.- Result
Third-place = 5028 votes
Answer:
5028
Step-by-step explanation:
If everyone in the town voted for 3 candidates and the total vote is 20900, then
a + b + c = 20900
If stands for the first contestant, b for the second contestant and c for the last contestant.
If a = 8392
b = 7480
c = 20900-(a+b)
c = 20900-15872
c = 5028
Let A and B be subsets of R. (a) If x ∈ (A ∩ B)c, explain why x ∈ Ac ∪ Bc. This shows that (A ∩ B)c ⊆ Ac ∪ Bc. 12 Chapter 1. The Real Numbers (b) Prove the reverse inclusion (A ∩ B)c ⊇ Ac ∪ Bc, and conclude that (A ∩ B)c = Ac ∪ Bc. (c) Show (A ∪ B)c = Ac ∩ Bc by demonstrating inclusion both ways.
Answer:
answer is -3 just subtract 4 from each side
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
B ⊂ A
Hope it helps!
Part of the analysis we routinely do with datasets is to identify whether or not any of the variables included are Binomial or Poisson in nature.
Discuss why it can be helpful to do this?
Answer:
This is useful to choose which calculation to perform.
Step-by-step explanation:
1) Firstly, let's consider that the Binomial Distribution tends to the Poisson Distribution given certain conditions:
[tex]n\rightarrow \infty, p\rightarrow 0, \lambda =np[/tex]
Roughly, they tend to the same value.
2) The Binomial Probability is calculated through this formula:
[tex]Binomial: P(X=x)=\binom{n}{x}p^{x}(1-p)^{n-x}[/tex]
Poisson Distribution this way:
[tex]Poisson:P(X=x)=\frac{\lambda^{x} e^{-\lambda }}{x!}[/tex]
3) If we plug
[tex]p=\frac{\lambda }{n}[/tex]
In the Binomial formula, given an "n" a very large quantity we'll have a closer outcome to Poisson.
[tex]P(X=x)=\binom{n}{x}\left ( \frac{\lambda }{n} \right )^{x}(1-\frac{\lambda }{n})^{n-x} \approx \frac{\lambda^{x} e^{-\lambda }}{x!}[/tex]
4) This is useful especially due to the convenience of calculating.
Because operating with exponentials and factorials, is hard and sometimes 'n' and 'p' may also be unknown, and sometimes the known parameter is the Mean.
Final answer:
Identifying if dataset variables follow a Binomial or Poisson distribution aids in selecting appropriate statistical models and sampling methods for ecological count data, leading to more accurate analyses and conclusions.
Explanation:
Identifying whether variables in datasets are Binomial or Poisson in nature can be incredibly helpful in statistical analyses, particularly in the field of ecology where data often consists of counts of organisms. These statistical models help determine appropriate sampling protocols and confirm the distribution of the observed data, which is essential for choosing the correct statistical tests and making accurate probability statements.
The Binomial distribution is used for data representing the number of successes in a fixed number of independent trials with a constant success probability, such as sex ratios or ratios of juveniles to adults. Conversely, the Poisson distribution is suitable for data representing counts over an interval of time or space, and is typically applied to model random occurrences in a fixed interval, like the count of organisms in a particular habitat.
Logistic regression is another analytical tool used for binary (yes/no) categorical data. It is based on a different premise, allowing researchers to predict occurrence probabilities by modeling the relationship between species detection and various explanatory variables. When using any statistical model, it is crucial to validate that the data align with the assumptions inherent to the model chosen. This is because using inappropriate statistical models could lead to incorrect conclusions, affecting research validity and the understanding of the ecological phenomena being studied.
A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.64 + 0.01 D."What is the slope of the regression line? __________?(Round your answer to the nearest hundredth.)
Answer:
The slope of the regression line is 0.01.
Step-by-step explanation:
The given regression equation for this bird is
[tex]DD=2.64+0.01D[/tex] .... (1)
where, DD is dive duration measured in minutes, and D is depth in meters.
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept.
On comparing equation (1) and (2), we get
[tex]y=DD,x=D,m=0.01,b=2.64[/tex]
Since, m=0.01, therefore the slope of the regression line is 0.01.
If there are 50 trees per acre in an orchard and the orchard is 1.7 x 2.2 km, how many trees are in the entire orchard?
Answer:
187 trees
Step-by-step explanation:
50 trees per acre in an orchard and
the orchard is 1.7 x 2.2 km,
we calculate the orchard dimension = 1.7 x 2.2km = 3.74
to calculate how many trees are in the entire orchard = 3.74 x 50 = 187 trees
The number of trees in the entire orchard will be 46,208.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
If there are 50 trees per acre in an orchard and the orchard is 1.7 x 2.2 km.
The area of the entire orchard will be
A = 1.7 x 2.2
A = 3.74 square km
We know that 1 square km = 247.105 acre
A = 3.74 x 247.105
A = 924.17
Then the number of trees in the entire orchard will be
⇒ 50 x 924.17
⇒ 46,208
The number of trees in the entire orchard will be 46,208.
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Find the sales tax and total cost of a Sony Playstation that costs $172.99. The tax rate is
4%. Round your answer to the nearest cent.
Answer:
all work is shown and pictured
Answer:The total cost of the Sony Playstation is $179.9096
Step-by-step explanation:
The initial or regular cost of the Sony Playstation is $172.99.
The tax rate is 4%. Therefore, the value of the sales tax would be
4/100 × 172.99 = 0.04 × 172.99 = $6.9196
The total cost of the Sony Playstation would be the sum of the regular price and the sales tax. It becomes
172.99 + 6.9196 = $179.9096
Three times each day, a quality engineer samples a component from a recently manufactured batch and tests it. Each part is classified as conforming (suitable for its intended use), downgraded (unsuitable for the intended purpose but usable for another purpose), or scrap (not usable). An experiment consists of recording the categories of the three parts tested in a particular day.
a. List the 27 outcomes in the sample space.
b. Let A be the event that all the parts fall into the same category. List the outcomes in A.
c. Let B be the event that there is one part in each category. List the outcomes in B.
d. Let C be the event that at least two parts are conforming. List the outcomes in C.
Answer:
Step-by-step explanation:
Hello!
Three samples of components manufactured are taken per day. They are classified as:
D: "Conforming (suitable for its use)"
E: "Downgraded (unsuitable for the intended purpose but usable for another purpose)"
F: "Scrap (not usable)"
This classification includes the three events that may occur in your sample space S. The experiment consists in recording the categories of the three parts tested in a day.
a. List the 27 outcomes in the sample space.
The possible outcomes in the space sample are the combinations of the three events. To avoid using the same letters as in the following questions I've named the evets as D, E, and F
S={DDD, DED, DFD, DEF, DFE, DEE, DFF, DDE, DDF , EDE, EEE, EFE, EED, EEF, EDF, EFD, EDD, EFF , FDF, FEF, FFF, FFE, FFD, FDE, FED, FDD, FEE}
b. Let A be the event that all the parts fall into the same category. List the outcomes in A.
A: "All the parts fall into the same category"
You have three possible outcomes for this event, that the three compounds are conforming, "DDD", that the three are unconforming, "EEE", or that the three compounds are scrap, "FFF". There are only three possible outcomes for this event.
S={DDD, EEE, FFF}
c. Let B be the event that there is one part in each category. List the outcomes in B.
B: "There is a part in each category"
This means, for example, The first one is conforming "D", the second one is unconforming "E" and the third one is scrap "F", then the first one may be unconforming "E", the second one is conforming "D" and the thirds one is scrap "F", and so on, you have 6 possible outcomes for this event:
S={DEF, DFE, EDF, EFD, FDE, FED}
d. Let C be the event that at least two parts are conforming. List the outcomes in C.
C: "At least two parts are conforming"
For this event, you can have two of the compounds to be considered conforming or the three of them.
S={DDD, DED, DFD, DDE, DDF , EDD, FDD}
A total of 7 combinations fit this event.
I hope you have a SUPER day!
5th grade math lesson 7.9 a vet weighs 2 puppies. The small puppy weighs 4 1/2 pounds. The large puppy weighs 42/3 times as much as the small puppy. How much does the small puppy weigh
The large puppy weighs 4 1/2 x 42/3 pounds.
4 1/2 x 42/3 = 9/2 x 42/3 = 63 pounds
answer: 63 pounds for the large puppy
Answer:the large puppy weighs 63 pounds.
Step-by-step explanation:
A vet weighs 2 puppies. The small puppy weighs 4 1/2 pounds. Converting 4 1/2 pounds to improper fraction, it becomes 9/2 pounds.
The large puppy weighs 42/3 times as much as the small puppy. This means that the number of pounds that the large puppy weighs would be
42/3 × 9/2 = 63
Find the average of 2.605, 24.04, 13.3, and 201.64. Express your answer using the proper number of significant figures.
Answer:
average =60.39625Step-by-step explanation:
The average of 2.605, 24.04, 13.3, and 201.64 is gotten by adding the values and dividing by 4 since we are dealing with 4 digits.
[tex]Average =\frac{2.605+24.04+13.3+201.64}{4}[/tex]
average = 241.585/4
average=60.39625
Let V be the vector space of all 2 X 2 matrices over the field F. Prove that V has dimension 4 by exhibiting a basis for V which has four elements.
Answer:
See the proof below.
Step-by-step explanation:
We can define a basis of V with the following elements:
[tex]X_1=\begin{matrix}1 & 0 \\0 & 0 \end{matrix} [/tex]
[tex]X_2=\begin{matrix}0 & 1 \\0 & 0 \end{matrix} [/tex]
[tex]X_3=\begin{matrix}0 & 0 \\1 & 0 \end{matrix} [/tex]
[tex]X_4=\begin{matrix}0 & 0 \\0 & 1 \end{matrix} [/tex]
So then if we define the basis X as following:
[tex] X = [X_1, X_2, X_3, X_4][/tex]
[tex]X =[\begin{pmatrix}1 & 0\\0 & 0\end{pmatrix},\begin{pmatrix}0 & 1\\0 & 0 \end{pmatrix},\begin{pmatrix}0 & 0\\1 & 0\end{pmatrix},\begin{pmatrix}0 & 0\\0 & 1 \end{pmatrix}[/tex]
We see the the dimension for X is 4 [tex] dim (V) = 4[/tex] since the basis have a dimension of 4 [tex] dim (X) =4[/tex]
Final answer:
The vector space V of all 2 x 2 matrices over a field F has a basis consisting of four matrices which are linearly independent and span V. This basis demonstrates that V has a dimension of 4.
Explanation:
In order to prove that the vector space V of all 2 x 2 matrices over a field F has dimension 4, we need to exhibit a basis for V that consists of four linearly independent elements, which also span V. Consider the following 2 x 2 matrices as the candidate basis elements:
⬑ 1 0 ⬑These matrices are linearly independent and span the vector space of all 2 x 2 matrices. To show linear independence, assume that a linear combination of these matrices equals the zero matrix:
a ⬑ 1 0 ⬑ + b ⬑ 0 1 ⬑ + c ⬑ 0 0 ⬑ + d ⬑ 0 0 ⬑
⬑ 0 0 ⬑ ⬑ 0 0 ⬑ ⬑ 1 0 ⬑ ⬑ 0 1 ⬑
= ⬑ 0 0 ⬑
⬑ 0 0 ⬑
This equation leads to a = b = c = d = 0, which verifies the linear independence. Since we can represent any 2 x 2 matrix as a linear combination of these four basis matrices, they also span V, fulfilling both criteria for a basis. Hence, there are four basis elements, and therefore, the dimension of V is 4.
A person has a 35 percent chance of winning on a scratch-off lottery ticket. What is the probability she first wins of the sixth ticket? (0.65)3 (0.35) (0.65)3 (0.35) (0.35)3 (0.65) () (0.35) (0.65) 0.35
Final answer:
To calculate the probability of winning on the sixth ticket, multiply the probability of not winning on the first five tickets by the probability of winning on the sixth ticket.
Explanation:
To calculate the probability of winning on the sixth ticket, we multiply the probability of not winning on the first five tickets (0.65)^5 by the probability of winning on the sixth ticket (0.35). Here's the step-by-step calculation:
Probability of not winning on the first five tickets: (0.65)^5
Probability of winning on the sixth ticket: 0.35
Overall probability of first winning on the sixth ticket: (0.65)^5 * 0.35Therefore, the probability of first winning on the sixth ticket is equal to (0.65)^5 * 0.35.
Find the equation of the plane that is parallel to the vectors left angle 3 comma 0 comma 3 right angle and left angle 0 comma 1 comma 3 right angle, passing through the point (2 comma 0 comma negative 1 ).
Answer:
[tex]x + 3y -z - 3 = 0[/tex]
Step-by-step explanation:
We have to find the equation of plane that is parallel to the vectors
[tex]\langle 3,0,3\rangle, \langle0,1,3\rangle[/tex]
The plane also passes through the point (2,0,-1).
Hence, the equation of plane s given by:
[tex]\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0[/tex]
It is the required equation of plane.
For wages less than the maximum taxable wage base, Social Security contributions (including those for Medicare) by employees are 7.65% of the employee's wages.
(a) Find an equation that expresses the relationship between the wages earned (x) and the Social Security taxes paid (y) by an employee who earns less than the maximum taxable wage base.
Answer:
y = 0.0765x
Step-by-step explanation:
We have that:
y is the total taxes paid.
x is the total wages earned.
The total taxes paid is a function of the total wages earned.
For wages less than the maximum taxable wage base, Social Security contributions (including those for Medicare) by employees are 7.65% of the employee's wages.
So 7.65% of the total wages earned are paid in taxes. We write the percentage as a decimal, so 7.65/100 = 0.0765
So the answer for a) is:
y = 0.0765x
The relationship between the wages earned (x) and the Social Security taxes paid (y) can be expressed as a linear equation. The equation is y = 0.0765x, which means for every dollar earned, 7.65 cents are paid towards Social Security taxes.
Explanation:The relationship between the wages earned (x) and the Social Security taxes paid (y) can be expressed as a linear equation. Since the contribution is 7.65% of the wages, the equation becomes y = 0.0765x, where x stands for the wages earned, and y represents the employee's Social Security taxes paid.
This equation means that for every dollar earned, 7.65 cents are paid towards Social Security taxes. So, if an employee earns $1000, you would substitute x with 1000 to find the taxes payable. That is y = 0.0765 * 1000, which equates to $76.50
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The Honolulu advertiser stated that in Honolulu there was an average of 661 burglaries per 400,000 households in a given year. In the Kohola drive neighborhood there are 317 homes. Let r be the number of homes that will be burglarized in a year. Compute the probability for r > or equal to 2 round your answer to the nearest ten thousandth.
A)0.3010
B) 0.1013
C) 0.0144
D) 0.0902
E) 0.0369
Answer:
D) 0.0902
Step-by-step explanation:
Data provided in the question:
Probability of burglary, p = [tex]\frac{661}{400,000}[/tex]
= 0.00165
q = 1 - p
or
q = 1 - 0.00165
or
q = 0.99835
Now,
P(r ≥ 2) = 1 - P(r < 2)
= 1 - [ P(0) + P(1) ]
= 1 - [ [tex]^{317}C_0(0.00165)^0(0.99835)^{317-0}+^{317}C_1(0.00165)^1(0.99835)^{317-1}[/tex] ]
[ as P(x) = [tex]^nC_rp^rq^{n-r}[/tex]]
= 1 - [ 0.593 + 0.3168]
= 1 - 0.9098
= 0.0902
Hence,
Option (D) 0.0902
In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find the length of the angle bisector of angle ∠A.
The length of the angle bisector of angle ∠A is approximately 4.62 feet.
To find the length of the angle bisector of angle ∠A in triangle ΔABC, we can use the Angle Bisector Theorem, which states that in a triangle, the angle bisector of a vertex divides the opposite side into segments proportional to the adjacent sides.
In triangle ΔABC, let AD be the angle bisector of ∠A, where D lies on BC. According to the Angle Bisector Theorem:
AC/CD = AB/BD
Given AC = 5 ft and AB = 13 ft, we can plug in these values:
5/CD = 13/BD
To find BD, we use the Pythagorean theorem:
BD = √(AB² - AD²) = √(13² - 5²) = √(169 - 25) = √144 = 12 ft
Now, using the Angle Bisector Theorem:
5/CD = 13/12
Cross-multiply:
5 × 12 = 13 × CD
CD = (5 × 12) / 13 = 60 / 13 ≈ 4.62 ft
If the world population is 7.0 billion in 2012, and the growth rate is constant at 1.4%, calculate the population in 2030. If the growth rate is constant for another 30 years, what will be the population in 2060
Answer:
The world population in 2030 will be of 9.0062 billion.
The would population in 2060 will be of 13.71 billion.
Step-by-step explanation:
The exponential model for population growth is as follows.
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(t) is the population in t years from now, P(0) is the population in the current year and r(decimal) is the growth rate.e = 2.71 is the Euler number.
If the world population is 7.0 billion in 2012.
2012 is the initial year, so P(0) = 7.
P(t) will be measured in billions of people.
The growth rate is constant at 1.4%.
This means that [tex]r = 0.014[/tex]
Calculate the population in 2030.
2030 is 2030-2012 = 18 years after 2012, so this is P(18).
[tex]P(t) = 7e^{rt}[/tex]
[tex]P(18) = 7e^{0.014*18} = 9.0062[/tex]
So the world population in 2030 will be of 9.0062 billion.
What will be the population in 2060.
This is 2060-2012 = 48 years after 2012. So this is P(48).
[tex]P(t) = 7e^{rt}[/tex]
[tex]P(48) = 7e^{0.014*48} = 13.71[/tex]
The would population in 2060 will be of 13.71 billion.
Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers in set notation.Enter EMPTY or∅for the empty set.)(a) What are the 16 outcomes in?=(b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rate?(c) Which outcomes are in the event that all four mortgages are of the same type?(d) Which outcomes are in the event that at most one of the four is a variablerate mortgage?(e) What is the union of the events in parts (c) and (d)?
Answer:
a) FFFF, FVFF, FFVF, FFFV,
FVFV, FFVV,FVVF,VVFF,
VFVF, VFFF,VFFV,FFVV
VVVV, VFVV, VVFV, VVVF
b) FVFF, FFVF, FFFV,VFFF
c) VVVV or FFFF
d) FFFF, FVFF, FFVF, FFFV, VFFF
e) FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV
Step-by-step explanation:
For this case we define some notation:
F= mortgage classified as fixed rate
V= mortgage classified as variable rate
We select a sample of 4 mortgages.
Part a
We have 2*2*2*2= 16 possible combinations defined below:
FFFF, FVFF, FFVF, FFFV,
FVFV, FFVV,FVVF,VVFF,
VFVF, VVFF,VFFV,FFVV
VVVV, VFVV, VVFV, VVVF
Part b
Which outcomes are in the event that exactly three of the selected mortgages are fixed rate
We need to see in the possible outcomes from part a) how many we have exactly three F's .If we analyze the possible options the possible combinations are:
FVFF, FFVF, FFFV, VFFF
Part c
Which outcomes are in the event that all four mortgages are of the same type?
For this case we have just two possible values: VVVV or FFFF
Part d
Which outcomes are in the event that at most one of the four is a variable rate mortgage?
We need to see in the possible outcomes from part a) how many have at least one V. After analyze we see that the possible values:
FFFF, FVFF, FFVF, FFFV, VFFF
Part e
The union represent all four mortgages are of the same type or outcomes are in the event that at most one of the four is a variable rate. So we are looking for the possible outcomes VVVV and FFFF and the outcomes with just one V ( FVFF, FFVF, FFFV ,VFFF) so then the union would be:
FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV
Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the y-axis.
y= square root of (x/2) , y=0 , x=2
Answer:
3.2 pi
Step-by-step explanation:
Given 3 curves are:
y = square root ( x / 2)
y = 0
x = 2
Use washer method for hollow volumes.
Step 1: Compute A (y)
A ( y ) = pi * ( f_1 (y) ^2 - f_2 (y) ^2)
where,
f_1 (y) is the function further away from y axis
f_2 (y) is the function closer to y axis
f_1 (y) = 2
f_2 (y) = 2*y^2
A ( y ) = pi * ( 2 ^2 - (2*y) ^2)
A (y) = pi * (4 - 4*y^2)
A (y) = 4*pi * (1 - y^2)
Step 2: Compute V (y)
[tex]V = \int\limits^1_0 {A (y)} \, dy \\V = 4*pi\int\limits^1_0 {1 - y^2} \, dy\\\\V = 4 * pi* (y - 0.2 y^5) \limits^1_0\\\\V = 4*pi*(1 - 0.2)\\\\V = 3.2 pi[/tex]
Answer: V = 3.2 pi
When the price of a glass of lemonade at lemonade stand was $1.75, 400 glasses were sold.Assume that the demand function is linear and that the marginal and fixed cost are $0.10, and $25 respectively
AFind the profit p as a function of x, the number of glasses of lemonade sold
B Use graphing utility to graph p and comment about slopes of P when X=300 and X=700
C Find the marginal profit when 300 glasses are sold and when 700 of lemonade glasses are sold
Answer:
Step-by-step explanation:
A. Price is 1.75
Total revenue, if number of galsses equals X is 1.75X
Total cost function of X glasses of lemonade is 25+0.1X
Profit function is Revenue - Cost, P=1.75X-25-0.1X=1.65X-25
C. Marginal profit= d/dx(1.65x-25) = 1.65-0=1.65
X=300 glasses, P'(300)=1.65
X=700 glasses, P'(700)=1.65
what is the common ratio for the geometric sequence? (look at image below)
Answer:
The common factor is -1/4
Step-by-step explanation:
Let's find out the common ratio for the geometric sequence:
24, - 6, 3/2, -3/8
Relationship between first and second term:
24 * -1/4 = -24/4 = -6
Relationship between second and third term:
-6 * -1/4 = 6/4 = 3/2
Relationship between third and fourth term:
3/2 * -1/4 = -3/8
The common factor is -1/4
The population model given in (1) in Section 1.3 dP/dt \propto P or dP dt = kP (1)
fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t > 0. (Assume the constants of proportionality for the birth and death rates are k1 and k2 respectively. Use P for P(t).)
dP dt = __.
Answer:
[tex] \frac{dP}{dt}=k_1 P -k_2 P= P(k_1 -k_2)[/tex]
Step-by-step explanation:
For this case we know that the birth rate is given by [tex]b[/tex] and the death rate is given by [tex] d[/tex].
We also know that these rates are proportional to the population size, so then we have this:
[tex] b \propto P(t) [/tex]
[tex] d \propto P(t)[/tex]
And in order to have expression with the sign= we have the proportional constants given [tex]k_1[/tex] for b and [tex]k_2[/tex] for d, so then we convert the system of equations on this:
[tex] b = k_1 P(t) [/tex]
[tex] d = k_2 P(t) [/tex]
And then the change in the population respect to the time would be calculated on this way:
[tex] \frac{dP}{dt} = b-d[/tex]
And if we replace what we found we got:
[tex] \frac{dP}{dt}=k_1 P -k_2 P= P(k_1 -k_2)[/tex]
And we can solve the differential equation reordering the terms like this:
[tex] \frac{dP}{P}= (k_1 -k_2) dt[/tex]
And if we integrate both sides we got:
[tex] ln |P| = (k_1 -k_2) t +C[/tex]
Using exponentials we got:
[tex] P(t) = e^{(k_1 -k_2)t} *e^c[/tex]
And we can rewrite this expression like this:
[tex] P(t) = P_o e^{(k_1 -k_2)t}[/tex] where [tex] e^c = P_o[/tex]
Final answer:
The differential equation for the population change accounting for both birth and death rates when both are proportional to the population at time t is given by dP/dt = k1P - k2P, where k1 is the birth rate constant, k2 is the death rate constant, and P is the population at time t.
Explanation:
The question concerns the modeling of a population where the rate of change in population (dP/dt) is considered to be the difference between the birth rate and the death rate, both of which are proportional to the current population. This is a scenario often explored in the field of ecology and employs principles of differential calculus. If we let k1 be the proportionality constant for the birth rate and k2 be the proportionality constant for the death rate, the differential equation representing the rate of change in population can be expressed as follows:
dP/dt = k1P - k2P
In this model, P represents the population at time t, where t > 0. Here, k1P represents the total birth rate and k2P represents the total death rate in the community. As such, the net change in population (dP/dt) is determined by the intrinsic rate of increase (r), which is k1 - k2.
Suppose we want to choose 4 objects, without replacement, from 16 distinct objects (a) How many ways can this be done, if the order of the choices is not relevant? (b) How many ways can this be done, if the order of the choices is relevant?
Answer:
a) 1820 ways
b) 43680 ways
Step-by-step explanation:
When the order of the choices is relevant we use the permutation formula:
[tex]P_{n,x}[/tex] is the number of different permutations of x objects from a set of n elements, given by the following formula.
[tex]P_{n,x} = \frac{n!}{(n-x)!}[/tex]
When the order of choices is not relevant we use the combination formula:
[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]
In this problem, we have that:
[tex]x = 4, n = 16[/tex]
(a) How many ways can this be done, if the order of the choices is not relevant?
[tex]C_{16,4} = \frac{16!}{4!(12)!} = 1820[/tex]
(b) How many ways can this be done, if the order of the choices is relevant?
[tex]P_{16,4} = \frac{16!}{(12)!} = 43680[/tex]
We can choose 4 objects from 16 in 1820 ways if order doesn't matter (combination), and in 43680 ways if order does matter (permutation).
Explanation:The subject of this question is combinatorial mathematics. You're being asked to calculate combinations and permutations.
(a) If the order of the choices is not relevant, we are dealing with a combination. The formula for a combination is C(n, r) = n! / [r!(n-r)!], where n is the number of objects and r is the number of objects chosen. In this case, n = 16 and r = 4, so C(16, 4) = 16! / [4!(16-4)!] = 1820 combinations.
(b) If the order of the choices is relevant, we are dealing with a permutation. The formula for a permutation is P(n, r) = n! / (n-r)!. Again, n = 16 and r = 4, so P(16, 4) = 16! / (16-4)! = 43680 permutations.
Learn more about Combinations and Permutations here:https://brainly.com/question/19917646
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Suppose 60% of homes in Miami have a swimming pool and 30% have both a swimming pool and a Jacuzzi. What is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool?
Answer:
0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.
Step-by-step explanation:
We are given the following in the question:
S: Homes in Miami have a swimming pool
J: Homes in Miami have a jacuzzi
[tex]P(S) = 60\% = 0.6\\P(S\cap J) = 30\% = 0.3[/tex]
We have to find the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.
Thus, we have to calculation the conditional probability of having a jacuzzi given the house has a swimming pool.
[tex]P(J|S) = \dfrac{P(J\cap S)}{P(S)}\\\\P(J|S) = \displaystyle\frac{0.3}{0.6} = 0.5[/tex]
0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.