Answer:
a)
{FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV,VVFV,FVVF,FFVF,VFVF,VVVF,FVFF,FFFF,VFFF,VVFF}
b)
{FFFV,FFVF,FVFF,VFFF}
c)
{FFFF,VVVV}
d)
{FFFV,FFVF,FVFF,FFFF,VFFF}
e)
{FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
{FFFF}
f)
{FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
{ }
Step-by-step explanation:
a)
The 16 outcomes for a sample of four home mortgages classified as fixed and variable rate are
Sr.No Outcomes
1 FVVV
2 FFVV
3 VFVV
4 VVVV
5 FVFV
6 FFFV
7 VFFV
8 VVFV
9 FVVF
10 FFVF
11 VFVF
12 VVVF
13 FVFF
14 FFFF
15 VFFF
16 VVFF
b)
Let A be the event that exactly three are fixed rate. Thus, event A consists of following outcomes
A={FFFV,FFVF,FVFF,VFFF}
c)
Let B be the event that all four are of same type. The event B consists of either all fixed rate or all variable rate. Thus, event B consists of following outcomes
B={FFFF,VVVV}
d)
Let C be the event that at most one of four is variable rate. The event C consists of less than and equal to one variable rate. Thus, event C consists of following outcomes
C={FFFV,FFVF,FVFF,FFFF,VFFF}
e)
Let union of part(c) and part(d) can be represented as BUC. The union represents all the outcomes in event B and event C.
B∪C={FFFF,VVVV}∪{FFFV,FFVF,FVFF,FFFF,VFFF}
B∪C={FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
Let intersection of part(c) and part(d) can be represented as B∩C. The intersection represents the common outcomes in event B and event C.
B∩C={FFFF,VVVV}∩{FFFV,FFVF,FVFF,FFFF,VFFF}
B∩C={FFFF}
f)
Let union of part(b) and part(c) can be represented as AUB. The union represents all the outcomes in event A and event B.
A∪B={FFFV,FFVF,FVFF,VFFF}∪{FFFF,VVVV}
A∪B={FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
Let intersection of part(b) and part(c) can be represented as A∩B. The intersection represents the common outcomes in event A and event B.
A∩B={FFFV,FFVF,FVFF,VFFF}∩{FFFF,VVVV}
A∩B={ }
So intersection of part(b) and part(c) is an empty set as there is no common outcome in these two sets.
Sample of four homes.
The sample of 4 homes is on a mortgage and has been classified as a fixed rate of F and a variable rate of V. The mortgage is thus an agreement between the lender of the money and the borrower. The lender has the right to take away the property.
Thus answer is given below.
The set of 16 outcomes of the variable and the fixed rates is given as {FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV, and VVFV,FVVF,FFVF,VFVF,VVVF,and the FVFF,FFFF,VFFF,VVFF}. The outcomes in the events that exactly is of 3 of the selected mortgages at a fixed rate is about {FFFV, FFVF,FVFF, VFFF}The outcomes of the events that all four mortgages are of the same type are about {FFFF, VVVV} The union of events in parts of c and d are as {FFFV, FFVF, FVFF, FFFF, VFFF}.Learn more about the sample of four homes.
brainly.com/question/14565659.
The perimeter of the rectangle is 56 cm. Find the value of x.
10 cm
3x cm
What is the equation of a vertical line passing through the point (-4, 7)?
EFGH is a rhombus. Rhombus E F G H is shown. Diagonals are drawn from point E to point G and from point F to point H. All sides are congruent. Given EG = 16 and FH = 12, what is the length of one side of the rhombus? 6 units 8 units 10 units 14 units
Answer:
10 units
Step-by-step explanation:
The diagnonals of a rhombus meet at right angle to their selves and bisect each other.
So one quarter will form a right angle triangle of base 6 and height 8.
Let The length of one side of the rhombus be x
X²= 8²+6²
X²= 64+36
X²= 100
X= √100
X= 10 units
Answer:
answer is C. 10 units. Just took the test
Step-by-step explanation:
Solve for the indicated variable: ⅖(z + 1) = y for z.
Answer:
z = 5/2y -1
Step-by-step explanation:
We observe that z has ...
1 addedthe sum multiplied by 2/5To solve for z, we undo these operations in reverse order.
[tex]\dfrac{2}{5}(z+1)=y\qquad\text{given}\\\\z+1=\dfrac{5}{2}y\qquad\text{multiply by 5/2}\\\\\boxed{z=\dfrac{5}{2}y-1}\qquad\text{subtract 1}[/tex]
Step-by-step explanation:
Above is the solution....
I’m having a bit of trouble with this
There are 45 children in a class. If
9 of them are absent, what
percentage of the class is absent?
Answer:
20%
Step-by-step explanation:
Total = 45
Absentees = 9
Percentage = (No. of absentees / total) × 100
= 9 / 45 × 100
= 0.2 × 100
= 20%
Answer:
20% of the children are absent
Step-by-step explanation:
Number of children absent = 9
Total children in the class = 45
Percent of absent children / total children is defined as the quotient 9/45 multiplied by 100. That is;
[tex]\frac{9}{45} \,*\,100 = 0.2 \,*\,100=20\,%[/tex]
SO the percentage is 20%
how many times does 3/4 go into 4.5
Answer:
6 times
Step-by-step explanation:
Turn that fraction into a decimal. 3/4=0.75
Divide!
4.5/0.75=6
A number 4.5 is 6 times of number 3/4.
We have to given that,
To find how many times does 3/4 go into 4.5.
Let us assume that,
x times does 3/4 go into 4.5.
Hence, It can be written as,
⇒ x × 3/4 = 4.5
Solve for x,
⇒ 3x /4 = 4.5
⇒ 3x = 4.5 × 4
⇒ 3x = 18
Divide by 3;
⇒ x = 18/3
⇒ x = 6
Therefore, 4.5 is 6 times of number 3/4.
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Look at the factors of 18 and 30. What is the greatest common factor? factors of 18: 1, 2, 3, 6, 9, 18 factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Answer:
is number 6
Step-by-step explanation:
the greatest common factor is the largest common factor of those.
The greatest common factor of 18 and 30 is 6.
To find the greatest common factor (GCF) of 18 and 30, we can list their factors and identify the largest factor they have in common.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The common factors between 18 and 30 are 1, 2, 3, and 6.
The largest common factor is 6.
Therefore, the greatest common factor of 18 and 30 is 6.
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Karen Sullivan delivers newspapers for the Tribune Dispatch. She
receives 18.2 cents per paper, 6 days a week (for the daily paper),
and 70 cents for the Sunday paper. She delivers 124 daily papers each
day and 151 Sunday papers each week. What is her total pay?
The correct answer is $241.1 each week and $964.4 each month
Explanation:
To calculate the amount Karen should receive, it is required to calculate the money she earned from Monday to Saturday and then the money she earned on Sunday as the amount paid per paper is different on Sunday.
Monday to Sunday:
Karen delivers 124 papers each day from Monday to Sunday. This means she delivers a total of 744 papers (124 papers each day x 6 days = 744 papers). Now, let's find the money she earned from Monday to Sunday:
744 papers x 18.2 cents = 13540 cents or 135.4 dollars (each dollar is equivalent to 100 cents, which means if you divide the cents into 100 you get the equivalent in dollars)
This means the total Karen earned from Monday to Saturday is $135.4
Sunday:
Karen delivers 151 Sunday papers and with each of these she earns 70 cents
151 papers x 70 cents = 10570 cents or 105.7 dollars
Total per week:
$135.4 + $105.7 = $241.1 each week, which is equivalent to $964.4 a month ($241.1 x 4 weeks = $964.4 )
Is this correct ? I think part of it is correct but I’m not sure
Answer: no
Step-by-step explanation:
Compute the critical value z Subscript alpha divided by 2 that corresponds to a 96% level of confidence.
Complete Question
Compute the critical value [tex]Z_{\frac{\alpha }{2} }[/tex] that corresponds to a 96% level of confidence.
Answer:
The value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.04}{2} }= 2.326[/tex]
Step-by-step explanation:
From the question we are told that
The confidence level [tex]C = 96\%[/tex]
Generally the level of significance is mathematically represented as
[tex]\alpha = (100 -96)\%[/tex]
[tex]\alpha = 0.04[/tex]
Now from the normal distribution table the critical value for [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.04}{2} }= 2.326[/tex]
55 points! Need asap
Answer:
FG = 18
Step-by-step explanation:
to find the length FG
FG + 31 = 49
FG = 49 - 31
FG = 18
Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges? F. H. G. J. CARDS, c 2 9 11 15 DOLLARS, d 9 40.5 50.5 67.5 CARDS, c 9 18 27 36 DOLLARS, d 2 4 6 8 CARDS, c 2 4 7 10 DOLLARS, d 9 18 31.5 45 CARDS, c 2 3 4 5 DOLLARS, d 9 10 11 12
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
Jill says that
23
1
,
000
can be written as 0.23. Which explains whether or not Jill is correct?
Answer:
Jill is incorrect
Step-by-step explanation:
Given
[tex]\frac{23}{1000}= 0.23[/tex]
Required
Determine if Jill is correct or incorrect
Start by solving the expression on the left hand side:
[tex]\frac{23}{1000} = 0.023[/tex]
The result of [tex]\frac{23}{1000}[/tex] gives 0.023 and not 0.23 as Jill as said;
Hence;
Jill is incorrect and the expression is false;
3n(5+3n-8-3n) what is the answer
Answer:
-9n
Step-by-step explanation:
3n(5 + 3n - 8 - 3n)
First we combine the like terms inside the parenthesis:
3n(-3)
Because 5 -8 = -3 and 3n - 3n = 0
Now we multiply:
-9n
because 3n × -3 = - 9n
So the answer is -9n
Find the radius of a circle with the equation:
x2 + y2 – 18x – 14y + 124 = 0
Answer:
The radius of [tex]x^{2}+y^{2}-18\cdot x - 14\cdot y +124 = 0[/tex] is [tex]\sqrt{6}[/tex].
Step-by-step explanation:
The given expression must be converted into the standard form of a circle, which is described by:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Location of center, dimensionless.
[tex]r[/tex] - Radius, dimensionless.
The expression is modified algebraically as follows:
1) [tex]x^{2}+y^{2}-18\cdot x - 14\cdot y +124 = 0[/tex] Given
2) [tex](x^{2}-18\cdot x)+(y^{2}-14\cdot y)+124 = 0[/tex] Commutative and associative properties.
3) [tex](x^{2}-18\cdot x+81)+(y^{2}-14\cdot y +49)+124 = 81+49[/tex] Commutative and associative properties/Compatibility with addition
4) [tex](x-9)^{2}+(y-7)^{2} + 124 = 130[/tex] Perfect square binomial/Definition of sum
5) [tex](x-9)^{2}+(y-7)^{2} = 6[/tex] Compatibility with addition/Existence of additive inverse/Modulative property/Result
Given that [tex]r^{2} = 6[/tex], the radius of the circle is [tex]\sqrt{6}[/tex].
Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why?
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs 38 12
Subject Is Not a drug user 19 29
Answer:
probability of a false positive test result = 0.010 The non-drug user will suffer from the result since it is positiveStep-by-step explanation:
The probability that the test result is a false positive
total number of cases studied (n) = 38 + 12 + 19 + 29 = 98
number of false positive cases ( x ) = 1
probability of false positive result = x / n = 1/98 = 0.010
The non-drug user will suffer from the result since it is positive
Look at the picture so you know what the problem is.
Excuse me, is this I ready because you know you can get reported right... just try your best, it's not a real grade! :)
& possibly delete this question because a bot can track and report this to your school. People at my school did that and got in 3 days detention...
A local diner has started selling cupcakes and is using the bar chart given below to keep track of how many are sold each day. How many cupcakes will be sold on day n?
Answer: 4n-3
================================================
Explanation:
day 1 = 1 sold
day 2 = 5 sold
day 3 = 9 sold
day 4 = 13 sold
Each time we're going up by 4. This is effectively the slope of the line since it represents the rate of change. The starting amount sold (1) is the y intercept
So we go from y = mx+b to y = 4x+1
Afterward, replace x with n to get 4n+1
On day n = 0, we have 4n+1 = 4(0)+1 = 1 sold. While this is correct, it doesn't really help to start with day 0 and it's better to start with day 1 instead.
What we can do is replace n with (n-1) and then simplify
4(n-1)+1 = 4n-4+1 = 4n-3
Now plugging in n = 1 leads to 4n-3 = 4(1)-3 = 1
Plugging in n = 2 leads to 4n-3 = 4(2)-3 = 5
and so on.
A farmer harvests 15 cucumbers for every 45 carrots. Which of the following ratios represents the ratio of cucumbers to carrots, in simplest form? 4 3 please help
Answer:
1 : 3.
Step-by-step explanation:
15 : 45
Divide both numbers by 15 , we get:
1 : 3.
Define and give a visual example of the Commutative Property. 2. Explain the process ( Every Step ) that you would use to simplify the following expression. 7 ( c + 3 ) + -4 (3c -2 )
Answer:
The Commutative Property is a property that states the order of the numbers in addition and multiplication don't matter. 2+3+7 = 7+2+3
Step-by-step explanation:
7(c+3)+ -4(3c-2)
Distribute the 7 and the -4 to each of their parentheses.
7c+21-12c+8
You can use the Commutative Property to move the terms to places where they can be easily simplified.
7c-12c+21+8
Simplify.
-5c+29
Problem 1
Imagine a rectangle that is 2 by 3. You would have an area of 2*3 = 6 and it is the same as saying 3*2 = 6. The order of multiplication doesn't matter. Visually, we can rotate the rectangle to have the shorter side be horizontal and then make it vertical, and the area is still the same. All we're doing is shifting things around.
Another example is say you had a marching band with 10 rows and 2 columns. That gives 10*2 = 20 people total. Then we could easily form the same number of people into 2 rows and 10 columns. The order of rows and columns doesn't matter because we get the same total number as a result.
======================================================
Problem 2
7(c+3) + -4(3c-2) ..... is the original expression
7(c+3) - 4(3c - 2) .... adding a negative is the same as subtracting
7*c + 7*3 - 4*3c - 4*(-2) .... distributive property
7c + 21 - 12c + 8 .... multiply
(7c-12c) + (21+8) .... group like terms
-5c + 29 ... combine like terms
The original expression simplifies to -5c+29
An architect is redesigning a rectangular room on the blueprints of the house. He decides to double the width of the room, increase the length by 48 %, and increase the height by 18 %. By what factor has the volume of the room increased
Answer:
3.4928.Step-by-step explanation:
Initial volume of the rectangular room = Length * Width * Height
V = LWH .............1
If the width is doubled then new width W2 = 2W
If the length is increased by 48%, the new Length L2 = L + 0.48L = 1.48L
If the height is increased by 18%, the new height H2 = H + 0.18H = 1.18H
The new volume after increasing all the dimensions will be;
V2 = L2W2H2
V2 = (1.48L)(2W)(1.18H)
V2 = 3.4928LWH ................2
Now we will divide equation 2 by 1 to have;
V2/V = 3.4928LWH/LWH
V2/V = 3.4928
V2 = 3.4928V
This means that the volume of the room has increased by the factor of 3.4928.
given the sequence -2,-8/3,-10/3,-4,-14/3 find the recursive formula
Step-by-step explanation:
-2, -8/3, -10/3, -4, -14/3
Write as multiples of 1/3.
-6/3, -8/3, -10/3, -12/3, -14/3
This is an arithmetic sequence where the first term is -6/3 and the common difference is -2/3.
Therefore, the recursive formula is:
aᵢ₊₁ = aᵢ − 2/3, a₁ = -2
(-2,5) and (4,10) slope of the line containing points
Answer:
Step-by-step explanation:
(10-5)/(4+2) = 5/6
y - 5 = 5/6(x + 2)
y - 15/3 = 5/6x + 10/3
y = 5/6x + 25/3
Can anyone please help me solve this question? (If you can, of course)
Answer:
[tex]\frac{4}{9}[/tex]
Step-by-step explanation:
Create 2 equations with the repeating number after the decimal point, then subtract the equations to eliminate the repeating number.
let x = 0.4444.... → (1) ← multiply both sides by 10
10x = 4.4444.... → (2)
Subtract (1) from (2) eliminating the repeater
9x = 4 ( divide both sides by 9 )
x = [tex]\frac{4}{9}[/tex]
Thus 0.444444... = [tex]\frac{4}{9}[/tex]
To know which power of 10 to multiply by
The power of 10 is the value to ensure the repeating 4 is after the decimal point.
Here it was [tex]10^{1}[/tex] as we required 0.4444.. → 4.444...
The 17 students on the math team want to raise $483.62 to buy practice books. They have already raised $218.25. If each student raises the same amount, how much money must each student raise?
Can you think of a situation where it would make the most sense to express your birth year in binary numbers?
Answer:
Yeah I've thought of it and have an example with the year 2000 as the birth year
So 2000 In binary= 11111010000
Step-by-step explanation:
Binary numbers consist of only 0 and 1
So to convert a number to binary we divide by 2
Let's assume a birth year of 2000
Now let's convert it to binary
2000/2= 1000 R 0
1000/2= 500 R 0
500/2= 250. R 0
250/2= 125. R 0
125/2 = 62. R 1
62/2= 31. R 0
31/2= 15. R 1
15/2 = 7. R. 1
7/2= 3. R 1
3/2 = 1. R 1
1/2 = 0. R 1
Where R signifies the remainder
So we'd pick the remainder from the bottom and that becomes our binary number
So 2000 In binary= 11111010000
There are 15 students in the preschool class. For every 7 kids there is 1 teacher. Which ratio shows the number of teachers to the number of students in the class?
15=2
7+7=14+1=15=2
sooooooooo just going to keep righting
The ratio of student to teacher is 1:7
What is a ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given: There are 15 students in a preschool class and for every 7 students there is 1 teacher. Clearly the ratio is 1:7
Hence, The ratio of student to teacher is 1:7
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Polygon A has one side that is 1.5 and two sides 2.5. How can I figure out how many times larger Polygon B is?
My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. Find the total cost of the fencing as a function of the length of a side x.
Answer:
The total cost of the fencing as a function of side is [tex]C = 8\cdot x[/tex].
Step-by-step explanation:
Dimensionally speaking, the total cost is equal to the product of length and cost per length. Given that orchid garden has a square form, there is only an input: Side ([tex]x[/tex]), measured in feet. Therefore, the total cost of fencing is represented by the following formula:
[tex]C = (c_{west} + c_{south} + c_{east})\cdot x[/tex]
Given that [tex]c_{west} = c_{east} = 2\,\frac{\$}{ft}[/tex] and [tex]c_{south} = \$\,4\,\frac{\$}{ft}[/tex], the total cost of the fencing as a function of side is:
[tex]C = 8\cdot x[/tex]