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Write an equation for the piecewise function over the domain
The equation of piecewise function is [tex]y=-\frac{1}{2} x+2[/tex]
Equation of piecewise function:From given graph of function, we have to write function for the domain of [tex]-2\leq x\leq 2[/tex].
It is observed that, in the particular domain graph of function is a straight line, which passes through the points [tex](-2,3)[/tex] and [tex](2,1)[/tex].
Equation of line is,
[tex]y-3=\frac{1-3}{2+2}(x+2) \\\\y-3=-\frac{1}{2} (x+2)\\\\y=-\frac{1}{2} x-1+3\\\\y=-\frac{1}{2} x+2[/tex]
The equation of piecewise function is [tex]y=-\frac{1}{2} x+2[/tex]
Learn more about the equation of function here:
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How far apart would Mars and Jupiter be if they were on opposite sides of the Sun?
Answer:
approximately 550,390,000 km
Step-by-step explanation:
Answer:
approximately 550,390,000 km
Step-by-step explanation:
sorry im late
Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 55% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 15% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis. (Round your answer to three decimal places.)
Answer:
0.71 = 71% probability that she or he used the lab on a regular basis.
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: Student got an A
Event B: Used the lab on a regular basis.
Probability of an student getting an A:
55% of 40%(go to the lab on a regular basis).
15% of 100 - 40 = 60%(do not go to the lab on a regular basis).
So
[tex]P(A) = 0.55*0.4 + 0.15*0.6 = 0.31[/tex]
Probability of getting an A and using the lab on a regular basis:
55% of 40%, so:
[tex]P(A \cap B) = 0.55*0.4 = 0.22[/tex]
Probability that she or he used the lab on a regular basis.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.22}{0.31} = 0.71[/tex]
0.71 = 71% probability that she or he used the lab on a regular basis.
One plus a number y is no more than - 13.
Answer: 1 + y ≤ -13
Step-by-step explanation:
Select all that may be correct
Answer:
Option (2) and Option (6)
Step-by-step explanation:
Expression representing the error can be given by,
Expected value = Original value ± percentage error
If original value of the ice cream filled in the container = 64 ounce
Percentage error to fill the ice cream in each container = 1.5%
So net error = ± 1.5% of 64
= [tex]64(\frac{1.5}{100})[/tex] ounce
= 64(0.015) ounce
Therefore, expression that can show the maximum maximum amount of ice cream in the container will be
= 64 + 64(0.015) Option (6)
= 64(1 + 0.015)
= 64(1.015) Option (2)
Therefore, Option (2) and Option (6) are the correct options.
the volume of a rectangular prism is 21/12 ft3 , and the height of the prism is 3/4 ft. determine the area of the base
What's the GCF of 77?
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 99 people in the 18-21 age bracket and finds that 84 of them respond and 15 refuse to respond. When 276 people in the 22-29 age bracket are contacted, 257 respond and 19 refuse to respond. Assume that 1 of the 375 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond.
Answer:
The probability of getting someone in the 18-21 age bracket or someone who agreed to respond [tex]= 0.365[/tex]
Step-by-step explanation:
The counts are as follows
Age Group No of people contacted No of refusals Total
18-21 88 8 96
22-29 240 42 282
Total 328 50 378
The probability of getting some one in the age bracket of 18-21 or some one who refused to respond is
[tex]= \frac{96}{378} + \frac{50}{378} - \frac{8}{378} \\= \frac{96+50-8}{378} \\= \frac{138}{378} \\= 0.365[/tex]
Can you conclude that these triangles are congruent?
yes or no?
Which expression is equivalent to 6(-4f + 5)?
Answer:
-24f + 30
Step-by-step explanation:
Use the distributive property.
Malik earns an average of 412 points on his daily quizzes. Near the end of the quarter, his average decreases by 34 points.
Write and then evaluate a subtraction expression (in fraction form) to find his current quiz grade average.
Answer: Required expression= 412-34
Current quiz grade average = 378
Step-by-step explanation:
Given: The average points on daily quizzes = 412
The average decreases by 34 points. (Near the end of the quarter)
Current quiz average = (Average points on daily quizzes) - (Average decreases)
i.e. Current quiz average =412-34 [ i.e. Required expression= 412-34]
i.e. Current quiz average =378
Hence, his current quiz grade average = 378
Jack decides to invest $300 per quarter into an annuity. How long would he have to keep investing if the annuity is paying 8% annually and he wants to accumulate $10,000?
Answer:
25.95 quarters which is about 6.5 years
Step-by-step explanation:
Classify each pair of numbered angles
Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more
than once
*
linear pair
vertical
adjacent
none of these
Answer:
Vertical and thats it
The oldest child in a family of four children is twice as old as the yougest. The two middle children are 12 and 16 years old. If the average age of the children is 15.25 , how old is the youngest child?
The age of the youngest child will be 11 years old.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The oldest child in a family of four children is twice as old as the youngest.
Let x be the age of the youngest child and y be the age of the oldest child. Then the equation is given as,
y = 2x ...1
The two middle children are 12 and 16 years old. If the average age of the children is 15.25. Then the equation is given as,
(x + 12 + 16 + y) / 4 = 15.25
x + y = 33 ...2
From equations 1 and 2, then we have
x + 2x = 33
3x = 33
x = 11
The age of the youngest child will be 11 years old.
More about the solution of the equation link is given below.
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You are randomly assigned a password consisting of 7 different characters chosen from the digits 0 to 9 and the letters A to Z. As a percent, what is the probability that you are assigned a password consisting of only letters? Round the answer to the nearest tenth of a percent.
Answer:
It would be 50%.
Step-by-step explanation:
beacuse its half numbers and half letters
Answer:
7.9%
Step-by-step explanation: I got it wrong for you :)
Two candles were lit and are burning. Candle A has
an initial height of 10 inches and burning down at a
rate of 1.5 inches per hour. Candle B is burning down
at a rate of 0.5 inches per hour and has an initial
height of 6 inches. Let t represent time in hours and
h represent the total height of the candle.
Answer:
A - 6 hours and 40 minutes
B - 12 hours
Step-by-step explanation:
Candle A - After 6 hours: the candle will be 1 inch tall, because 6 times 1.5 = 9. You need an extra 40 minutes for the candle to burn completely, because 10/1.5 = 6 and 2/3
Candle B - After 12 hours, the candle will be completely burned, because 6/.5 = 12.
Equation - Initial height/inches burned per hour = time it takes for cnadle to burn down completely
Look at the formula for finding distance. Which of the following is the formula to find time? [picture included]
Answer:
A.
Step-by-step explanation:
Answer:
[tex] \huge \: \boxed { \boxed{ \red{ a)t = \frac{d}{r}}}}[/tex]Step-by-step explanation:
to understand thisyou need to know about:equationPEMDASgiven:[tex]d = rt[/tex]to find[tex]t[/tex]let's solve:[tex]step - 1 :define[/tex]
[tex]d = rt[/tex]
[tex]step - 2 : solve[/tex]
[tex]rewrite : \\ rt = d[/tex][tex]divide \: both \: sides \: by \: r : \\ \frac{rt}{r} = \frac{d}{r} [/tex][tex]simplify : \\ t = \frac{d}{r} [/tex][tex] \huge \: \boxed { \boxed{ \red{ \therefore t = \frac{d}{r}}}}[/tex]
(5 + 7) = x
In word form
Answer:
Five plus seven equals x
Step-by-step explanation:
Answer:
Five plus seven equals x
Step-by-step explanation:
What quadrilateral has both diagonals bisecting each other but they are not congruent or perpendicular?
Answer:
A parallelogram with different side lengths.
Step-by-step explanation:
If we consider a parallelogram (not rectangle, not square, and not a rhombus), then its diagonals will bisect each other but would be not congruent or perpendicular. See attached image.
Name two ways you can figure out an area of a composite figure.
Answer: they contain valuable items and are very interesting
Step-by-step explanation:
Can someone explain how you do this?
please look at the photo below and answer the question(s)
Answer:
Mean - 79
Median- 81
Range- 11
Step-by-step explanation:
Mean aka average = add all the numbers together and divide it by the number of numbers there were to find the mean of something.
in this case : 81 + 82 + 84+ 75+73+75 + 83 = 553 divided by 7 = 79
Median - Rearrange the set of numbers from least to greatest or greatest to least and find the middle number to find the median
In this case : 73, 75, 75, 81, 82, 83, 84 = The median is 81
Range - Substract the highest and the lowest number from the set of numbers to find the range.
In this case : 84 - 73 = 11
find the perimeter of a rectangle whose sides are 8 1/2cm by 4 1/2cm.
Answer:
26 cm
Step-by-step explanation:
To find the perimeter with the side lengths, you can use this formula: 2(L+W) because it's the measure of the distance around the rectangle. So,
2(8.5+4.5)
2(13)=26
Answer:26
Step-by-step explanation:
Round 0.41826923 to the nearest tenth
Answer:
0.4
Step-by-step explanation:
A factory can make 120 backpacks in 3 hours.
How long would it take to make 600 backpacks?
15 h
20 h
30 h
40 h
Find the number that makes the ratio equivalent to 2:7.
6:?
Answer:
6:21
Step-by-step explanation:
2 was multiplied by 3, so 7 should also be multiplied by 3. The answer is 6:21. Hope this helps!
Which statement is NOT TRUE when solving 5x - 4 = 26 *
O I need to add 4 to both sides of the equation.
O I need to divide both sides of the equation by 5.
O My answer is that x = 6
O My answer is that x = 4.4
Answer:
My answer is that x = 4.4
Step-by-step explanation:
The answer to the equation is 6, so the false one is the last one. All the other ones are true.
margo has sandwich cut into 1/3 pieces . if she needs to serve 11 people how many whole sandwiches will she need?
Answer:
she needs 4 and will have 1/3 of a sandwich left
Step-by-step explanation:
Answer:
12 pices remainder 1
Step-by-step explanation:
Because if u split a sandwich in 12 pices u get 1 extra sandwich left over and 12 is good enough for 11 ppl hope I helped
Need help please I would be grateful
Answer:
The correct answer is given by option A.
Step-by-step explanation:
A function is said to be increasing for intervals of x in which the values of y are increasing, that is, it trends upwards, and decreasing for intervals of x in which the values of y are decreasing, that is, it trends downwards.
In this question:
It trends upwards from the start, at negative infinity, until 0.
It trends downwards from 0, until the end, at positive infinity.
So the correct answer is given by option A.
2u+15 less than or equal to 55
Answer:
less than i dont know
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