The function notation will be:
f(x) = 3x - 2
Since y (the output) can be replaced with f(x).
How to use function notation?First, we know that a relationship between two variables x and y maps the first variable (called the input) into the second variable (called the output)
In this case, the relationship between x and y is linear, and is of the form:
y = 3x - 2
Particularly, if for each value of "x" that we use we get only one value of y as the output, then the relationship is called a function, and in that case we can write:
y = f(x).
So here to use function notation we just write:
f(x) = 3x - 2
And in that way we know that we have a function.
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if during a typical week susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?
The probability that the average score for the week is between 220 and 228 = 0.7641
Susan's score on bowling follows Normal Distribution.
Average score or mean, μ = 225
Standard Deviation, σ = 13
Number of times Susan bowled, n = 16
Since the scores follows Normal Distribution, the z-score = (x-μ)√n/σ
When the score, x = 220,
z = (220-225)√16/13
= -20/13
= -1.538
When the score, x = 228,
z = (228-225)√16/13
= 12/13
=0.923
Hence The probability that the average score for the week is between 220 and 228 = P(220 < x < 228)
= P(-1.538 < z < 0.923)
= P(z < 0.923) - P(z < -1.538)
= (0.5 + 0.3212) -( 0.5 - 0.4429) [From the z-tables]
= 0.7641
The question is incomplete. Find the complete question below:
Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?
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PLS HELP GEOMETRY WILL GIVE BRAINLIEST
Given: line c is parallel to line d, and angle 1 is congruent to angle 7,
Prove: line a is parallel to line b
By corresponding angle we prove a parallel line a ║ b .
What is an example of parallel lines?
Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. They may be vertical or horizontal. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.Lines that are always the same distance apart in a plane are said to be parallel. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Given, c ║d
∠1 ≅ ∠7
∠1 = ∠3 ( corresponding question)
∠5 = ∠7 ( corresponding question)
then a ║ b
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Find the 60th term of the arithmetic sequence −29, -49, −69,
We see, the second number is 20 less than the first number, the third number is 20 less than the second number, ..
So, the pattern is : We minus 20 from a term to get the next term right after.
From the 1st term to the 60th term, there are 59 spaces.
Therefore, the 60th term = -29 - 59 x 20 = -1209
Jack is baking a cake. the recipe says that it must bake for 2 1/2 hours it has been baking for 3/4 hours how much longer must to bake? PLEASE HELP AND EXPLAIN TYSM
Answer:
Step-by-step explanation:
60 divided by 4 is 15 so 1/4 of an hour is 15 minutes. so three fourths is 45 minutes and one hour and a half is the extra hour that has not been touched so add the last 15 min from the 3/4 onto that so it still has 1 hour and 45 minutes to bake
Answer:
It still has to bake for 1 3/4 hours
Step-by-step explanation:
So, the way I do it, you start by making 2 1/2 an improper fraction, which would be 5/2. Then, you have to get it so 5/2 and 3/4 have common denominators. The fastest way to do this is to multiply the denominator 2 by 2, which means you have to do the same to the numerator. So, you have 10/4-3/4, which equals 7/4. Now, you can simplify. 7/4 = 1 3/4
HELLP me asap giving brainlyest to right answer
Answer:
Answer is y + 5 = -1(x-7)
Step-by-step explanation:
First find the slope, m = y2 - y1 / x2 - x1
so -5 -6 = -11, 7- (-4) = 11
m = -11/11 = -1
then plug into equation y-y1 = m(x-x1) so
Answer: The correct answer is the second one.
Step-by-step explanation:
That is the answer
p/3> 9 anyone know this??
Answer:
p > 37
Step-by-step explanation:
Multiply both sides by 3 so 9 x 3 is 27 so p > 37
Treat it like an equal sign and solve, but if you were to divide by a negative you would need to switch the sign, you don't need to though because you didn't divide by a negative in this one
Multiply.
3c^6(9c+4c^3)
Simplify your answer as much as possible
Answer:
[tex]12c⁹+27c⁷[/tex]
Step-by-step explanation:
3c⁶(9c+4c³)
=(3c⁶)(9c+4c³)
=(3c⁶)(9c)+(3c⁶)(4c³)
=27c⁷+12c⁹
=12c⁹+27c⁷
Given that lines an and b are parallel and that m<6=65 , find m
factor out the GCF -2x^2 - 4x - 6
The Greatest Common factor(GCF) of -2x^2-4x-6 is -2(x+1)(x-3)
What is Greatest Common Factor?The greatest common factor (GCF) is the largest factor two or more numbers have in common
From the question,
-2x^2-4x-6
By collecting like terms
-2(x^2-2x-3)
By factoring x^2-2x-3
-2(x^2-3x+1x-3)
Collecting like terms
-2(x^2-3x)+(x-3)
-2(x(x-3)+1(x-3))
-2(x+1)(x-3)
hence -2(x+1)(x-3) is the Greatest Common factor of -2x^2-4x-6 is
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A football team scored 3 touchdowns 3 extra points and 4 field goals write an expression to represent the total points the football team scored
Expression to represent the total points 3t + 3e + 4f
What is Algebra?
Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.
Let t represent the number of points for a touchdown, e represent the number of points for the extra point and f represent the number of points for a field goal.
Total points = 3(t) + 3(e) + 4(f)
= 3t + 3e + 4f
Hence, Expression to represent the total points the football team scored
3t + 3e + 4f
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PLSS HELP ASAP!!!!!!!!!!Which of the following is true? (1 point)
a
|–7| < 6
b
|–6| < |–7|
c
|–7| < |6|
d
|–6| < –7
I will give brainiest!!!!!!!!!!!!!!
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (2,3) and (2,5).
ok
P1 = (2, 3)
P2 = (2, 5)
1.- Find the slope
slope = m = (y2 - y1) / (x2 - x1)
-Substitution
m = (5 - 3) / (2 - 2)
m = 2/0
The slope is a horizontal line because does not exist.
2.- Find the equation of the line
y - y1 = m(x - x1)
y - 3 = 0
y = 3 This is the standard form of your question.
Electrical power (P) is measured in watts using the formula P = V · I where V is the voltage in volts and I is the current in amperes.
If there are 60 volts running to a light bulb of 174 watts, how much current is flowing through the light bulb?
current flowing through the light bulb is 2.2 Amperes
Step by step explanation:
Step 1:
Given the voltage = 60 Volts and power = 174 Watts.
Find the current using the formula , P = V . l
=> l = P/V=60/174= 0.3448275862
i really need help!
4) At 5:00am in the morning, the temperature was -14.8 degrees Fahrenheit. By noon, the temperature increased to 6.2 degrees Fahrenheit. How much did the temperature change? Write an equation and then solve. Show all your steps.
Answer:
21 degrees
Step-by-step explanation:
Let the change in temp. be y.
-14.8 + y = 6.2
y = 21
Therefore, the change in temp. is 25 degrees.
Given f(x) = 2x - 2, find f(-3).
Answer:
-8
Step-by-step explanation:
f(-3) = 2(-3) -2
f(-3) = -6 -2
f(-3) = -8
If x > 6, then -7 is a solution.
True
False
Answer:
false
Step-by-step explanation:
because
i dont know how to explain but hope this help you
-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6
as you know,negative number also know the smallest number compared to positive number, but but sometimes negative number can be the big number such as : x > -7 then the answer is -1 because -1 near at 0, imagine you went in deep sea 0 between the sky and the sea, and 6 above the sky, -7 bottom of the sea, if you go down,means that your going bottom of the sea,while if you go up,itll increase cuz youre going up
the further a negative number is from the origin, the smaller the value of the number, the further away the positive number, the greater the value of the number
HOPE THIS HELP E
Answer:
The answer is False.
Question
What is the slope of this graph?
Responses
1 fourth
negative 4
negative 1 fourth
4
Answer: The slope of the graph is negative 4.
The ounces of soda consumed by an adult next month are an example of a discrete random variable.
a. True
b. False
The ounces of soda consumed by an adult next month are examples of a discrete random variable, False
A discrete random variable are known as counts. This is because it takes on only a countable number of distinct values. This means a random variable can only be considered to be discrete if it can take on values that are countable in an interval, otherwise it can be continuous.
Now on the question of ounces of soda consumed by an adult next month is considered not to be discrete random variable. This is because ounces of soda or volume of soda consumed are countless and infinite in number.
Hence, the statement that says ounces of soda consumed by an adult next month are an example of a discrete random variable is False.
Choice b(False) is correct.
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ten is ________ of two and 5
Ten is the product of two and five.
What does product mean?Product is the result of the multiplication process. Multiplication is a mathematical operation that entails adding a number repeatedly over a number of times. The sign that is used to represent multiplication is ×.
In order to determine the product of 2 and 5, add to five times.
2 + 2 + 2 + 2 + 2 = 10
This is usually written as 2 x 5 = 10
Other mathematical operations are addition, subtraction and division. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of finding the difference between two or more numbers. Division is the process of determining the quotient of a number.
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Of the following situations, which is best represented by the product
5x-3
A
The amount of money a snack bar earns for selling 333 sandwiches for $555 per sandwich
B
The change in elevation of a submarine as it sinks 333 meters every second for 555 seconds
C
The change in temperature as it decreases 555 degrees every hour for 333 hours
D
The height of a child who grew 333 inches each year for 555 years
i need the answer fast pls
Answer: b
Step-by-step explanation:
Which expression is equivalent to the given expression?
6y - 12
Answer: Y - 2
Step-by-step explanation: (6Y / 6) - (12 / 6) = Y - 2
22 Here is a right-angled triangle.
Work out the value of x.
4 cm
8.5 cm
xcm
x = 7.5 cm is value of v by Pythagorean theorem.
What is the Pythagorean theorem ?
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the total of the squares on the legs.For an acute triangle, c2 a2 + b2, where c is the side across from the acute angle, given the Pythagorean Theorem that states a2 + b2 = c2. For a right triangle, c is the side of the 90-degree angle and c2 = a2 + b2.use Pythagorean theorem in triangle,
8.5² = 4² + x²
72.25 = 16 + x²
72.25 - 16 = x²
56.25 = x²
x = √56.25
x = 7.5 cm
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In which relation is y not a function of x?
Write an equation that expresses the following relationship: x varies directly as a and inversely as the difference between y and z. Then solve the equation for y
Write an equation that expresses the given relationship. Use k as the constant of variation.
Answer:
Where is question
Step-by-step explanation:
Sorty
Explain how you know that the sum of 26.541 and 14.2 will be greater than 40.
The sum of 26.541 + 14.2 is greater than the integer 40, as the sum is equivalent to 40 + 0.741.
How to prove that the sum of two real numbers is greater than an integer
In this problem we need to compare the sum of two real numbers with an integer, also a real number. The two real numbers can be written as the sum of an integer and excess decimal part. Then, the given sum can be rewritten as:
x = 26.541 + 14.2
x = (26 + 0.541) + (14 + 0.2)
This sum must be compared with an integer, 40.
x = (26 + 14) + (0.541 + 0.2)
x = 40 + 0.741
Then, by direct comparison, we see that the sum of 26.541 + 14.2 is greater than 40.
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Use long division to find the quotient below.
(4x³ + 11x² +9) + (x+3)
OA. 4x²+2x+3
OB. 4x²-x+3
OC. 4x²+x+3
OD. 4x²-2x+3
Option B: 4x²-x+3
(4x³ + 11x² + 0x + 9) + (x+3) [here, we will include 0x to do long division]
Divide 4x³ by x to get first term of the quotient, 4x³
Then, take 4x² and multiply it with 3 and you will get 4x² + 12
Subtract 4x² + 12 from 4x³ + 11x².
Then, you will get the remainder as -x² + 0x
Now you have to repeat the same same process, divide -x² by x to get second term of quotient, -x
Then take -x and multiply with 3 and you will get -x²- 3x
You will get the remainder as 3x+ 9
Divide 3x by x to get the third term of quotient, 3
Then, take 3 and multiply with 3 and you will get 3x + 9
Subtract and you will get the remainder as 0.
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You are completing a math assessment. The number of questions you complete and the time it takes you to complete them have a proportional relationship, as shown in the table. Number of Questions 4 7 Time (in minutes) 6 ? How much time does it take to complete 7 questions? 3 minutes 5 minutes, 30 seconds 9 minutes 10 minutes, 30 seconds
Through direct proportionality, we calculated that Seven questions will be answered in 10 minutes and 30 seconds.
Seven questions will need to be answered in 10 minutes and 30 seconds.
Direct proportionality: What is it?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. In mathematics, a straight line is used to express direct proportionality, and its equation is of the form y = kx , k = y/x, where [k] is the constant.
The assumption is that the time it takes to finish each question and the number of completed questions [y] are inversely proportional to one another.
The time [x] it takes to complete them is directly proportional to the number of questions [y] that are answered. As a result, y = kx, k = y/x, and y is directly proportional to x.
Thus, we can write:
y₁/x₁ = y₂/x₂
Substituting the values,
4/6 = 7/x₂
x₂ = (7 x 6)/4
x₂ = 21/2
x₂ = 10.5
x₂ = 10 minutes 30 seconds
Therefore, Seven questions will be answered in 10 minutes and 30 seconds.
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1. Here is the recursive definition of a sequence: f(1) = 10, f(n) = f(n-1)-1.5 for
nz 2.
a. Is this sequence arithmetic, geometric, or neither?
b. List at least the first five terms of the sequence.
c. Graph the value of the term f(n) as a function of the term number n for at least
the first five terms of the sequence.
sno ritw nobin
Answer:
Below in bold.
Step-by-step explanation:
f(1) = 10
f(2) = f(2-1) - 1.5 = 10 - 1.5 = 8.5
f(3) = f(2) - 1.5 = 7.
a. This is Arithmetic.
b. The first 5 terms are:10. 8.5. 7, 5.5, 4.
c. The first point on the graph will (1, 10).
It will be a straight line descending to the right.
Fill in the information about the absolute value functions below.
EXPLANATION:
We are given the absolute value functions below;
[tex]\begin{gathered} y=3|x| \\ y=-\frac{3}{4}|x| \\ y=-\frac{1}{2}|x| \\ y=-1|x| \end{gathered}[/tex]Note that for this function, we have a v-shaped graph, since the values of the output is always positive (absolute value) and the vertex is at (0, 0). Also, if the value of a in the function;
[tex]y=a|x|[/tex]is positive, the graph opens upwards, and if the value of a is negative;
[tex]y=-a|x|[/tex]then it opens downwards.
Therefore,
ANSWER;
[tex]\begin{gathered} y=3|x|\text{ Opens upwards} \\ y=-\frac{3}{4}|x|\text{ Opens downwards} \\ y=-\frac{1}{2}|x|\text{ Opens downwards} \\ y=-1|x|\text{ Opens downwards} \end{gathered}[/tex][tex]\begin{gathered} The\text{ equation with the narrowest graph;} \\ y=3|x| \end{gathered}[/tex][tex]\begin{gathered} The\text{ equation with the widest graph;} \\ y=-\frac{1}{2}|x| \end{gathered}[/tex]could you help answer 1-12
1. The unit cost of red potatoes is $1.45/pound
2. The unit cost of white potatoes is $1.81/pound
3. Red potatoes bag is a better buy as it is cheaper than white potatoes while giving the same values of product.
What is unit cost?A price is referred to as a unit cost when it is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can. Divide the ratio's terms if you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price.
For example,
$5.50 ÷ 5 pounds = $1.10 per pound
4) 4/1.8 5) 5/6
= 2.9 = 0.83
6/2.4 12/14
=2.5 = 0.86
6 envelopes is better buy 5 songs download is a bette buy
6) 3/9 7) 12/6
= 0.3 = 2
5/12 100/28
= 0.42 = 3.57
3 games of laser tag is better buy 12 gifts is a better buy
8) 20/5 9) 16/3.04
= 4 = 5.26
100/20 24/5.04
= 5 = 4.76
20 arcade tokens is better buy 24 bottles of water is a better buy
10) 2/3.50 11) 100/2
= 0.57 = 50
5/6.75 145/4.35
= 0.74 = 33.3
2 pounds box is better buy 145 napkins is a better buy
12) 12/2.88 13) 250/40
= 4.16 = 6.25
15/3.30 600/138
= 4.54 = 4.35
12-ounce box is better buy 600 GB Hard drive is a better buy
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