Answer:
a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.375)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
Part b
[tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2?
Each side of the square would have to be 6 cm to have an area of 36 cm^2. However, as a side can never be 0, and you never gave a starting size for the square, the question is unanswerable.
Which of the following represents a coefficient from the expression given?
9x – 20 + x2
Answer:
1 or 9.
Step-by-step explanation:
A coefficient is "a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy)".
So, in this case, the coefficient of 9x would be 9.
The coefficient of x^2 would be 1.
Hope this helps!
In the given quadratic expression 9x - 20 + x, 1, 9, and -20 are the coefficients.
What are coefficients in a quadratic expression?In a quadratic expression of the standard form ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
How to solve the given question?In the question, we are asked to identify the coefficients from the given quadratic expression 9x - 20 + x².
First, we try to express the given quadratic expression, 9x - 20 + x², in the standard form of a quadratic expression, ax² + bx + c.
Therefore, 9x - 20 + x² = x² + 9x - 20.
Comparing the expression x² + 9x - 20 with the standard form of a quadratic expression ax² + bx + c, we get a = 1, b = 9, c = -20.
We know that in a quadratic expression ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
Thus, we can say that in the given quadratic expression 9x - 20 + x², 1, 9, and -20 are the coefficients.
Learn more about quadratic expressions at
https://brainly.com/question/1214333
#SPJ2
What is the complete factorization of x^2+4x-45?
Answer:(x-5)(x+9)
Step-by-step explanation:
You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.
Answer: (x - 5)(x + 9)
If you have to solve, x=5 or x= -9
Step-by-step explanation: You need two numbers that multiply to be 45.
(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.
9 - 5 =4, so use those. -45 has a negative sign, so one of the factors must be + and the other - Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.
So (x -5)(x + 9) are your factors. You can FOIL to be sure
x × x += x² . x × 9 = 9x . -5 × x = -5x . -5 × 9 = -45 .
Combine the x terms: 9x -5x = +4x
In a Classroom, 1/6 of the students are wearing blue shirts, and 2/3 are wearing white shirts. There are 12 students in the classroom. How many students are wearing shirt other than blue shirts or white shirts?
Answer:
2
Step-by-step explanation:
firstly...you have to find the number of students wearing blue and white shirt and subtract from the total number of students to get the number if students that neither wears blue or white shirt as follows :
no wearing blue = 1/6 × 12 = 2
no.wearing white = 2/3 × 12 = 8
total number wearing blue and white = 8+2 =10
number of students not putting on either of the two colours include...= 12-10 = 2
.....
.....
.....
MARK BRAINLIEST will be appreciated please...thanks in advance
if p+4/p-4, what is the value of p
Answer:
p = 2
Step-by-step explanation:
p + 4/p - 4
multiplying through by p,
p×p + 4/p ×p - 4×p
p² + 4 - 4p = 0
p² - 4p + 4 = 0
factorizing,
p(p - 2) -2(p - 2) =0
(p -2)(p -2) =0
p-2 =0
p=2
PLEASE HELP. FINAL TEST QUESTION!!!!
Devon is having difficulty determining if the relation given in an input-output table is a function. Explain why he is correct or incorrect.
Step-by-step explanation:
input x , output y
if x= x1 then y=y1 and y1 is the only value then it is a function
if we get multiple values of y then it is not a function
The mean monthly car payment for 123 residents of the local apartment complex is $624. What is the best point estimate for the mean monthly car payment for all residents of the local apartment complex?
Answer:
The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
We apply the inverse Central Limit Theorem.
The mean monthy car payment for 123 residents of the local apartment complex is $624.
So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.
While the Pareto distributions are continuous, they tend to be used to model discrete data in humanities and actuarial sciences. Moreover, with its roots in power functions, Pareto distributions may be used in the growing popularity of the studies of networks. The probability density function (PDF) for a Pareto distribution is
Answer:
Step-by-step explanation:
While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.
The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.
The probability density function (PDF) for a Pareto Distribution is:
Xn = 1
for various Alpha levels
Where Xn is the probability value of X
As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]
Where ¶ is the Dirac Delta function.
Use ￢, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together
Sameer chose 12 different toppings for his frozen yogurt sundae, which was Three-fourths of the total number of different toppings available at the make-your-own sundae shop. To determine the number of different toppings available at the shop, Sameer set up and solved the equation as shown below.
Three-fourths = StartFraction x over 12 EndFraction. Three-fourths (12) = StartFraction x over 12 EndFraction (12). 9 = x.
Which best describes the error that Sameer made?
Sameer did not use the correct equation to model the given information.
Sameer should have multiplied both sides of the equation by Four-thirds instead of by 12.
The product of Three-fourths(12) is not equal to 9.
The product of Four-thirds and StartFraction 1 over 12 EndFraction should have been the value of x.
Answer: B. Sameer did not use the correct equation
Step-by-step explanation:
12 IS three-fourths OF x
IS: equals
OF: multiplication
[tex]12=\dfrac{3}{4}x[/tex]
48 = 3x
16 = x
Answer:
it's b in Edg
Step-by-step explanation:
if jonny has 3 × 6 amounts of dish soap, how much dish soap does he have?!
a(I dont know)
b(18)
c(12)
d(6)
look up a skit called what's 6×3 before answering.
Answer: 18 (b)
Step-by-step explanation:
3x6=18
Answer:
18
Step-by-step explanation:
you can use a visual for a short answer or organize 3 dots in six groups, count in total
F =9/5 C + 32 A) constants B) units C) variables D) numbers
Answer:
a) 32
b) none?
c) C & F
D) 9/5, 32?
Step-by-step explanation:
HELP PLEASE!!What method can you use to find the area of the composite figure. Check ALL that apply.
Answer:
C
Step-by-step explanation:
The reason we can use this method is because we are given a composite figure with a house shape with one triangle on top. We can use the guidance of the dotted lines to make out that a rectangle can be used to find the figure. We can see that apart from the figure, there are two congruent triangles. To find the area we would do -
First find the missing height of the smaller triangles. We would use the pythagorean theorem to find that the missing height is√5
We could do 8(4) = 32 to find the area of the rectangle.
Then, we could do 2√5/2 to find one missing triangle. We could then add the triangles to find the measures of the combined triangles as 2√5. Then, we could do 32 - 2√5 to find the area as 27.5.
Hope this helps :)
Answer:
it is A,B,D
Step-by-step explanation:
i got it right on edge
A superintendent of a school district conducted a survey to find out the level of job satisfaction among teachers. Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.
z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction
The superintendent wishes to construct a significance test for her data. She find that the proportion of satisfied teachers nationally is 18.4%.
What is the z-statistic for this data? Answer choices are rounded to the hundredths place.
a. 2.90
b. 1.15
c. 1.24
d. 0.61
Answer:
b. 1.15
Step-by-step explanation:
The z statistics is given by:
[tex]Z = \frac{X - p}{s}[/tex]
In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.
This means that [tex]X = \frac{13}{53} = 0.2453[/tex]
She find that the proportion of satisfied teachers nationally is 18.4%.
This means that [tex]p = 0.184[/tex]
Standard error:
p = 0.184, n = 53.
So
[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]
Z-statistic:
[tex]Z = \frac{X - p}{s}[/tex]
[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]
[tex]Z = 1.15[/tex]
The correct answer is:
b. 1.15
Which angles are pairs of alternate exterior angles
Answer:
when a straight line cuts two or more parallel lines then the angles forming on the side of transversal line exteriorly opposite to eachother is called exterior alternative angle.
for eg if AB //CD and EF is a transversal line meeting the parallel lines at G abd H then the exterior alternative angle are angle EGB = angle CHF and angle AGE=angle DHF are two pairs of exterior alternative angle .
hope its helpful to uh !!!!!!
Evaluate the expression.........
Answer:
9
Step-by-step explanation:
p^2 -4p +4
Let p = -1
(-1)^1 -4(-1) +4
1 +4+4
9
Complete the square to rewrite y = x2 - 6x + 16 in vertex form. Then state
whether the vertex is a maximum or minimum and give its coordinates.
Answer:
y = x² + 6x + 16
= (x² + 6x + 9) - 9 + 16
= (x + 3)² + 7 ← vertex form
Therefore, vertex is (-3, 7) and since the coefficient of (x + 3)² is positive the vertex is a minimum.
Answer:
minimum (3,7)
Step-by-step explanation:
If (a+1) and (a-1)= 35 what is a?? Helpppppppppp
Answer:
There is no real number that can satisfy this equation
Step-by-step explanation:
a+1=35 and a-1=35 ⇒ a+1=a-1⇒ a-a = -1-1⇒ 0= -2 That's absurd so a has no real solutionI got the answer but I really don’t know if it’s correct or not, please help this is due today
show that 7 1/2 - 4 2/3 = 2 5/6
Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]
We need to check whether the left hand side is equal to right hand side.
These are in the form pf mixed fraction we can convert them to the improper fraction.
[tex]7\frac{1}{2}=15/2[/tex]
[tex]4\frac{2}{3}=\frac{14}{3}[/tex]
So Let us subtract 24/3 from 15/2
15/2-14/3
LCM of 2 and 3 is 6
45-28/6
17/6
This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]
Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Help please!!
What quadrant does the terminal side of this angle lie in?
Answer:
QIII
Step-by-step explanation:
Simple linear equations
Check Whether the value given in the brackets is the root of the given equation or not (nessessary steps is needed)
a) 4x = -4 [x=-1]
b) 2(x-3) =-12 [x=3]
c) 8x - 4x = 24 [x = 1/2]
d) 9x - 4x = 24 [x=18]
Answer: Evaluate the Function, right?
Hello!
~~~~~~~~~~~~~~~~~~
A) 4x = -4 [x=-1] =
4x = -4 =
x = -1 = x = -1
( The steps : Substitute the given value into the function and evaluate.)
B) 2(x-3) =-12 [x=3] =
2 ( x - 3) = -12 = x = -3
x = 3 = x = 3
( The steps : Substitute the given value into the function and evaluate.)
C) 8x - 4x = 24 [x = 1/2] =
8x - 4x = 24 = x = 6
x = 1/2 = x = 1/2
( The steps : Substitute the given value into the function and evaluate.)
D) 9x - 4x = 24 [x=18] =
9x - 4x = 24 = x = 24/5
x = 18 = x = 18
( The steps : Substitute the given value into the function and evaluate.)
~~~~~~~~~~~~~~~~~~
Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.
Hope this helped you!
What is the volume of a cubed shaped box with edges 6 cm. in length?
Answer:
216 cm³
Step-by-step explanation:
The volume of a cube is denoted by V = s³, where s is the side length.
Here, the side length is 6 centimetres, so plug this into the formula to find V:
V = s³
V = 6³ = 6 * 6 * 6 = 216
The answer is thus 216 cm³.
~ an aesthetics lover
Answer:
216
Step-by-step explanation:
6³ = 216
An election ballot asks voters to select six city commissioners from a group of 24 candidates in how many ways can this be done? Six city commissioners can be selected from a group of 24 candidates in blank different ways
Answer:
134,596 diffrent ways.
Step-by-step explanation:
Combination has to do with selection. When n object is to be selected from n objects, this can be achieved using the combination formula as shown; \
nCr = n!/(n-r)!r!
If an election ballot asks voters to select six city commissioners from a group of 24 candidates, then the selection can be done in 24C6 different ways.
Applying the formula above:
24C6 = 24!/(24-6)!6!
24C6 = 24!/18!6!
24C6 = 24*23*22*21*20*19*18!/18!*6*5*4*3*2
24C6 = 24*23*22*21*20*19/24*30
24C6 = 23*22*21*20*19/30
24C6 = 134,596 different ways.
Hence, Six city commissioners can be selected from a group of 24 candidates in 134,596 different ways
which point is a solution to the inequality shown in the graph? (3,2) (-3,-6)
The point that is a solution to the inequality shown in the graph is:
A. (0,5).
Which points are solutions to the inequality?The points that are on the region shaded in blue are solutions to the inequality.
(3,2) and (-3,-6) are on the dashed line, hence they are not solutions. Point (5,0) is to the right of the line, hence it is not a solution, and point (0,5) is a solution, meaning that option A is correct.
More can be learned about inequalities at https://brainly.com/question/25235995
#SPJ1
The two triangles are similar. What is the value of x? Enter your answer in the box. x =
Answer:
the value of x=12
Step-by-step explanation:
d) the answer is d on edg.
2{ 3[9 + 4(7 -5) - 4]}
Answer:
2{3[9+4(7-5)-4]}
2{3[9+4(2)-4]}
2{3[13(2)-4]}
2{3[26-4]}
2{3[22]}
2{66}
132
Step-by-step explanation:
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Answer:
paper = $4 and stapler = $7
Step-by-step explanation:
let p represent paper and s represent stapler, then
3p + 4s = 40 → (1)
5p + 6s = 62 → (2)
Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p
15p + 20s = 200 → (3)
- 15p - 18s = - 186 → (4)
Add (3) and (4) term by term to eliminate p
2s = 14 ( divide both sides by 2 )
s = 7
Substitute s = 7 into either of the 2 equations and evaluate for p
Substituting into (1)
3p + 4(7) = 40
3p + 28 = 40 ( subtract 28 from both sides )
3p = 12 ( divide both sides by 3 )
p = 4
Thus package of paper costs $4 and stapler costs $7
Duran Manufacturing uses a process costing system and manufactures its product in three departments. Which of the following is NOT a way in which Duran can use the cost per unit of each process? A) Duran can look for ways to cut the costs when actual process costs are more than planned process costs. B) Duran needs to set the selling price to cover the costs of making the product and provide a profit. C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period. D) Duran needs to know the ending balances in the following accounts: Work-In-Process Inventory, Finished Goods Inventory, and Cost of Goods Sold.
Answer:
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
Step-by-step explanation:
Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.
A committee has ten members. There are two members that currently serve as the board's chairman and vice chairman. Each member is equally likely to serve in any of the positions. Two members are randomly selected and assigned to be the new chairman and vice chairman. What is the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and reassigning them to their current positions?
Answer:
1/90 = 1.11%
Step-by-step explanation:
We have that the number of ways of total selections and assignments possible is a permutation.
We know that permutations are defined like this:
nPr = n! / (n-r)!
In our case n = 10 and r = 2, replacing:
10P2 = 10! / (10 - 2)! = 10! / 8!
10P2 = 90
In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,
Probability would come being the following:
P = 1/90 = 1.11%