Answer:
See explanation
Step-by-step explanation:
Given
[tex]A = (-1,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]C =(4,-2)[/tex]
Solving (a): [tex]P(0,0) \to Q(1,3)[/tex]
This means that:
[tex](x,y) \to (x+1,y+2)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1 + 1,1+2)[/tex]
[tex]A' = (0,3)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3 + 1,3+2)[/tex]
[tex]B'= (4,5)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+1,-2+1)[/tex]
[tex]C' = (5,-1)[/tex]
Solving (b): [tex]P(0,-1) \to Q(4,-2)[/tex]
This means that:
[tex](x,y) \to (x+4,y-1)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1+4,1-1)[/tex]
[tex]A' = (3,0)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3+4,3-1)[/tex]
[tex]B'= (7,2)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+4,-2-1)[/tex]
[tex]C' = (8,-3)[/tex]
Solving (c): [tex]P(-1,-2) \to Q(-2,-2)[/tex]
This means that:
[tex](x,y) \to (x-1,y)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1-1,1)[/tex]
[tex]A' = (-2,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3-1,3)[/tex]
[tex]B'= (2,3)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C'= (4-1,-2)[/tex]
[tex]C'= (3,-2)[/tex]
A certain manufacturing process yields electrical fuses of which, in the long run
15% are defective. Find the probability that in a random sample of size n=10, fuses
selected from this process, there will be
(i) No defective fuse
(ii) At least one defective fuse
(iii) Exactly two defective fuses
(iv) At most one defective fuse
Answer:
i) 0.1969 = 19.69% probability that there will be no defective fuse.
ii) 0.8031 = 80.31% probability that there will be at least one defective fuse.
iii) 0.2759 = 27.59% probability that there will be exactly two defective fuses.
iv) 0.5443 = 54.43% probability that there will be at most one defective fuse.
Step-by-step explanation:
For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
15% are defective.
This means that [tex]p = 0.15[/tex]
We also have:
[tex]n = 10[/tex]
(i) No defective fuse
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]
0.1969 = 19.69% probability that there will be no defective fuse.
(ii) At least one defective fuse
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
We already have P(X = 0) = 0.1969, so:
[tex]P(X \geq 1) = 1 - 0.1969 = 0.8031[/tex]
0.8031 = 80.31% probability that there will be at least one defective fuse.
(iii) Exactly two defective fuses
This is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{10,2}.(0.15)^{2}.(0.85)^{8} = 0.2759[/tex]
0.2759 = 27.59% probability that there will be exactly two defective fuses.
(iv) At most one defective fuse
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]
[tex]P(X = 1) = C_{10,1}.(0.15)^{1}.(0.85)^{9} = 0.3474[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1969 + 0.3474 = 0.5443[/tex]
0.5443 = 54.43% probability that there will be at most one defective fuse.
What is the value of x?
Answer:
Step-by-step explanation:
(2x - 5)° + 45° = 180°
2x - 5 + 45 = 180
x = 70
find two factors of the first number such that their product is the first number and their sum is the second number.
70,17
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Answer:
7, 10
Step-by-step explanation:
It often works well to look at the factor pairs that form the product.
70 = 1×70 = 2×35 = 5×14 = 7×10
The sums of these are 71, 37, 19, 17. The last pair of factors is the one of interest:
7 and 10.
Determine if the sequence below is arithmetic or
geometric and determine the common difference / ratio in
simplest form.
3, 8, 13, ..
(PLEASE HELPP)
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Answer:
arithmetic; common difference of 5
Step-by-step explanation:
It usually works well to check differences first. Here, they are ...
8 -3 = 5
13 -8 = 5
These are the same value, so the sequence is arithmetic with a common difference of 5.
Which equation represents the parabola with focus (8, 4) and vertex (8, 2)
Answer:
Step-by-step explanation:
The focus lies above the vertex, so the parabola opens upwards.
At Joe's Restaurant, 80 percent of the diners are new customers (N), while 20 percent are returning customers (R). Fifty percent of the new customers pay by credit card, compared with 70 percent of the regular customers. If a customer pays by credit card, what is the probability that the customer is a new customer?
Answer:
0.7407 = 74.07% probability that the customer is a new customer.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Pays by credit card
Event B: New customer.
Probability of a customer paying by credit card:
50% of 80%(new customers).
70% of 20%(regular customers). So
[tex]P(A) = 0.5*0.8 + 0.7*0.2 = 0.54[/tex]
Probability of a customer paying by credit card and being a new customer:
50% of 80%, so:
[tex]P(A \cap B) = 0.5*0.8 = 0.4[/tex]
What is the probability that the customer is a new customer?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.54} = 0.7407[/tex]
0.7407 = 74.07% probability that the customer is a new customer.
Help me! Thanks! Show work too! Please!
Answer:
(2, 79) (12, 24)
24-79/12-2=-55/10
m=-0.55
24=-6,6+b
30.6=b
y=-0.55x+30.6
Step-by-step explanation:
you multiply
using the equation to represent your answer
URGENT!!!!!! 15 POINTDS
Answer:
Option C
Step-by-step explanation:
thankful that there are graphing tools. see screenshot
Peter, Jan, and Maxim are classmates. Their total score for the last test was 269. Peter's score was more than the sum of Jan's and Maxim's scores. What could be Peter's least possible score?
Answer:
135
Step-by-step explanation:
Given that :
Total score obtained by Peter, Jan and Maxim = 269
Let :
Peter's score = x
Jan's score = y
Maxim's score = z
x + y + z = 269
x > (y + z)
For x to be greater Than y + z ;
Then x > (269 / 2) ; x > 134.5
The least possible x score is 135
Hence, Peter's least possible score is 135.
a.
What is 46.7% of
4/5?
Answer:
0.3736
Step-by-step explanation:
46.7 percent of [tex]\frac{4}{5}[/tex] is 0.3736.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.What is a fraction?A number is stated as a quotient in mathematics when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.Solution -To find 46.7% of [tex]\frac{4}{5}[/tex].
So,
[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]
[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]
⇒ [tex]0.3736[/tex]
Therefore, 46.7% of [tex]\frac{4}{5}[/tex] is 0.3736.
Know more about percentages here:
https://brainly.com/question/24304697
#SPJ2
The diameter of the circle is 2”. What is the area of the circle
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
1. 2/2 =1 1 is the radius
2. [tex]A = \pi r^2[/tex]
3. [tex]A=\pi 1^2[/tex]
4. [tex]A=\pi[/tex]
a plane can fly 450 miles in the same time it takes a car to go 150 miles. if the car travels 100 mph slower than the plane, find the speed (in mph) of the plane
Answer:
The speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Step-by-step explanation:
Since a plane can fly 450 miles in the same time it takes a car to go 150 miles, if the car travels 100 mph slower than the plane, to find the speed (in mph) of the plane the following calculation must be performed:
450 to 150 is equal to 3: 1, that is, the plane travels three times the distance of the car.
Therefore, since 100/2 x 3 equals 150, the speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Complete the input-output table:
x 3x + 7
0
4
8
14
Step-by-step explanation:
When x = 0,
3x + 7
= 3 ( 0 ) + 7
= 0 + 7
= 7
When x = 4,
3x + 7
= 3 ( 4 ) + 7
= 12 + 7
= 19
When x = 8,
3x + 7
= 3 ( 8 ) + 7
= 24 + 7
= 31
When x = 14,
3x + 14
= 3 ( 14 ) + 14
= 14 ( 3 + 1 )
= 14 ( 4 )
= 56
Two minor league baseball players got a total of 390 hits. Washington had 2 more hits than Sanchez. Find the number of hits for each player.
Washington had
hits. Sanchez had
hits
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Answer:
Washington had 196 hitsSanchez had 194 hitsStep-by-step explanation:
Let s represent the number of hits Sanchez had. Then Washington had (s+2) hits, and their hit total was ...
s +(s+2) = 390
2s = 388 . . . . . . subtract 2
s = 194 . . . . . . . . divide by 2
Sanchez had 194 hits; Washington had 196.
HELP PLEASE BE CORRECT
Answer:
12
Step-by-step explanation:
Scale factor of 4
CD = 3
3 · 4 = 12
Length of C'D' is 12 units
Answer:
12 units
Step-by-step explanation:
The original segment CD = 3 units
Scale factor is 4.
3 x 4 = 12
What is the other dimension of the rectangular cross section that is perpendicular to the base (the face that is shaded) and passes through the midpoints of the 10 cm edges?
________ centimeters by 18 centimeters
PLZ PLZ HELP
A rectangular prism with length of 10 centimeters, width of 8 centimeters, and height of 18 centimeters.
A. 2
B. 8
C. 10
D. 18
The gross domestic product (GDP) of the United States is defined as
Answer:
the market value of all final goods and services produced within the United States in a given period of time.
the angle between two lines is 60 degree. if the slope of one of them is 1. find the slope of other line
Answer:
-3.73
Step-by-step explanation:
solution:
Given:
Angle between two lines=60⁰
slope of first line=1
Or, tanA=1
Or, A= tan inverse (1)
so, A=45⁰
so, angle of inclination of first line=45⁰
Now,
angle of inclination of second line= A+ 60⁰
= 45⁰+60⁰
=105⁰
so, slope of second line = tan105.
= -3.73
what's a divisor a dividend and a quotient
Find mBFE, help ASAP!!!
Answer: C
<BFE is 148 degrees
Step-by-step explanation:
We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?
1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same
2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.
3. Now, we have all the angles we need to find out <BFE.
4. <BFC+<CFD+<DFE=<BFE
5. Substitute to get
57+34+57=<BFE
91+57=<BFE
148=<BFE
6. Now we know that the answer is 148 degrees.
Ming rented a bike from Ted's Bikes. It cost $13 plus $3 per hour. If Ming paid $31,
then he rented the bike for how many hours?
A)7.
B)10.3333
C)6
D)10
Answer:
C, 6
Step-by-step explanation:
31-13 is 18, 18/3 is 6.
Answer:
6
Step-by-step explanation:
31-13= 18
18÷3 = 6
Answer from Gauthmath
Domain and range problem Help
Answer:
Range y≤-1
Domain all reals
Step-by-step explanation:
The range is the output values (y)
Y is less than or equal to -1
y≤-1
The domain is the values that the input can take
the arrows on the ends of the graph tells us x can take all real numbers
The range is the span of y-values. What is the smallest possible y-value and what is the largest possible y-value?
For this problem, the y-values start at -1 and decrease infinitely. Therefore, the range is y <= -1.
The domain is the span of x-values. What is the smallest possible x-value and what is the largest possible x-value?
For this problem, the parabola will keep expanding horizontally (or to the left and right). Therefore, the range is all real numbers.
Hope this helps!
Use the figure to find y.
Tanθ =sin /cos
tan θ = 5/2 / y
tan (30°) = 5/2 /y
[tex]y = \frac{5 \sqrt{3} }{2} [/tex]
y=4.33
Pls answer , If you do tysm
Answer:
Step-by-step explanation:
ypu bhave to mulitply each by a percentage, for example, the percentage it says you mulitply it by
PLEASE HELP
Identify the 15th term of the arithmetic sequence in which a. = 10 and ao = 20.
Answer:
The 15th term is 160
Step-by-step explanation:
The details are not clear. So, I will make the following assumptions
[tex]d = 10[/tex] ---- common difference
[tex]a_1 = 20[/tex] ---- first term
Required
The 15th term
This is calculated as:
[tex]a_{n} = a + (n - 1) * d[/tex]
Substitute 15 for n
[tex]a_{15} = a + (15 - 1) * d[/tex]
[tex]a_{15} = a + 14 * d[/tex]
Substitute values for d and a
[tex]a_{15} = 20 + 14 * 10[/tex]
[tex]a_{15} = 20 + 140[/tex]
[tex]a_{15} = 160[/tex]
If f(x) = x
2−3x+1
x−1
find f(-1) and f(-3)
Answer:
f(-1) = 2-3(-1) +1
= 7
f(-3)= 2-3(-3)+1
= 12
f(-1) = -1-1
= -2
f(-3) = -3-1
= -4
QUESTION 20
The patient's weight is 245 lbs. If the patient loses 1 kg every week for 5 weeks:
a. How much will the patient weight in pounds?
b. How much will the patient weight in kilograms?
.Answer:
The answer is below
Step-by-step explanation:
The patient loses 1 kg every week for 5 weeks.
1 kg = 2.2 lbs
Therefore the patient loses 2.2 lbs every week for 5 weeks.
a) The weight of the patient after 5 weeks = 245 lbs. - (5 weeks)(2.2 lbs per week)
The weight of the patient after 5 weeks = 245 lbs. - 11 lbs. = 234 lbs.
b) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs. = 234 lbs.
1 kg = 2.2 lbs.
234 lbs. = 234 lbs. * 1 kg per 2.2 lbs. = 106.36 kg
SOMEONE HELP PLEASE ASAP PLES DONT LEAVE UR ANSWER AS AN IMAGE SOMETIMES I CANT SEE IMAGES. THANK YOU VERY MUCH! WILL MARK BRAINLIEST :)))
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Answer:
x = -2/5 or -1
Step-by-step explanation:
The last two terms of the expression on the left can be factored also.
(5x+2)² +3(5x+2) = 0
And the common factor can be factored out:
(5x+2)(5x +2+3) = 0
5(5x +2)(x +1) = 0
Solutions to the equation make the factors zero:
5x +2 = 0 ⇒ x = -2/5
x +1 = 0 ⇒ x = -1
The values of x that are solutions to the equation are x = -2/5 and x = -1.
_____
Once you realize that (5x+2) is a factor, you know one solution is x = -2/5. The rest is just fluff to find the second solution. It is not required in order to answer the question.
suppose two soccer teams consist of players with a combined average height of 66 inches. if team a has an average height of 68 inches and has twice as many members as team b, what is the average height of team b
Answer:
The average height of team b is 62 inches.
Step-by-step explanation:
Mean:
The mean of a data-set is the sum of all values in the data-set divided by the number of values, that is:
[tex]M = \frac{s}{n}[/tex]
Sum:
Team a: Mean of 68 inches, 2x members.
Team b: Mean of y inches, x members.
So
[tex]s = 68*2x + yx = x(136 + y)[/tex]
Number of athletes:
[tex]n = 2x + x = 3x[/tex]
What is the average height of team b?
[tex]66 = \frac{x(136+y)}{3x}[/tex]
[tex]66 = \frac{136 + y}{3}[/tex]
[tex]136 + y = 198[/tex]
[tex]y = 198 - 136 = 62[/tex]
The average height of team b is 62 inches.
Why lines e and f must be parallel
