Answer:
[tex]g(x)=\dfrac{x^2+1}{3}[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}[/tex]
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (f o g)(x) means to substitute function g(x) in place of the x in function f(x).
[tex]\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}[/tex]
Therefore:
[tex]\boxed{g(x)=\dfrac{x^2+1}{3}}[/tex]
Math
Seventh grade L.9 Solve percent equations: word problems JS6
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pins
Pam ordered a set of red and yellow pins. She received 1,000 pins, and 91% of them were
red. How many red pins did Pam receive?
Submit
Skill plans
You have prizes
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After solving percent equation ,the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins.
What is percent equation?Eventually, we'll run into a problem that requires us to calculate a percentage of something. The percent equation is the formula we'll employ and it goes like this: part = percent x whole.
The symbol for percent (%) denotes a percentage of one hundred.
You'll need to convert between a percent and a decimal to express these numbers, so let's take a moment to go over that. When you see a percentage, it means 40 out of 100, or 40/100, and that is our fraction. When you divide 40 by 100, you get the decimal 0.40. Remember that 0.40 is the same as 40/100, which means 40%, when converting a decimal to a percent.
Pam ordered a set of red and yellow pins. She received 1,000 pins, and 91% of them were red, so the amount of red pins is
red pins = 91/100 × 1000
red pins = 910
Thus, the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins
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Find the length of the third side. If necessary, round to the nearest tenth-
5
3
Answer:
The third side is 4cm
Step-by-step explanation:
[tex] {3}^{2} + {a}^{2} = {5}^{2} [/tex]
a=25-9
a=16
a=4
Can someone help me?? I really need the help and I would appreciate it! Thank you so much in advance! :)
y= -1/2 x - 5 write in slope intercept form.
Answer:
Hii! This is already written in slope intercept form.
For a refresher, slope intercept form is [tex]y=mx+b[/tex]
[tex]y[/tex] = y-coordinate
[tex]m[/tex] = slope
[tex]x[/tex] = x-coordinate
[tex]b[/tex] = y-intercept
In this equation,
[tex]m[/tex] is [tex]-1/2[/tex]
[tex]b[/tex] is [tex]-5[/tex]
Hope this answers your questions.
Find the exact value of y
Answer:
3√2
Step-by-step explanation:
We have an isoceles right triangle, so the length of the hypotenuse is √2 the length of each leg.
[tex]y \sqrt{2} = 6[/tex]
[tex]y = \frac{6}{ \sqrt{2} } ( \frac{ \sqrt{2} }{ \sqrt{2} } ) = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]
i dont even know what to put
Answer:
first one (2*2*2*3*3)
Step-by-step explanation:
2*2*2*3*3=72
Zachary purchased a computer for $1,700 on a payment plan. Seven months after he purchased the computer, his balance was $790. Eight months after he purchased the computer, his balance was
$660. What is an equation that models the balance y after x months?
The equation that models the balance y after x months is;
y = 1,700 - 130x
What is Equation of line?
The equation of line with slope m and y intercept at point b is given as;
y = mx + b
Given that;
Zachary purchased a computer for $1,700 on a payment plan.
Seven months after he purchased the computer, his balance was $790.
Eight months after he purchased the computer, his balance was $660.
Now, Let months is represented by x and models the balance is represented by y.
So, We get;
For 0 months, balance is $1,700.
For 7 months, Balance is $790
For 8 months, balance is $660.
So, Slope = (1,700 - 790) / 7
= 910/7
= 130
And, Slope = (1,700 - 660) / 8
= 1,040/8
= 130
So, The equation with slope 130 and starting balance $1,700 will be;
y = 1,700 - 130x
Thus, The equation that models the balance y after x months is;
y = 1,700 - 130x
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x + 3.5 = 4 1/3
×=4/5
×=5/6
×=47/6
Answer:
Step-by-step explanation:
x=0.83
The graph of the function f(x) = x - 3x² - 4 is shown below. Choose the best description of
the roots.
&
5
0
OTwo real roots and one non-real roots.
O Four real roots and no non-real roots.
O Two real roots and no non-real roots.
O Two real roots and two non-real roots.
5
The description which represents the roots is Four real roots and no non-real roots.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph is given below;
The function can be written as;
f(x) = [tex]x^4[/tex] - 3x² - 4
Then the values of x for which the value of the function is zero will be;
f(x) = 0
f(x) = [tex]x^4[/tex] - 3x² - 4 = 0
Then the function will be f(x) = [tex]x^4[/tex] - 3x² - 4. Then Four real roots and no non-real roots.
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The table of values shows the output values of three different equations for the same input values, x. Drag the correct expression to each row to complete each equation.
The expression to represent the equation is given by y = x + 3 .
An algebraic expression is one that was created in mathematics utilizing integer variables, constant, and algebraic procedures (accumulation, deletion, multiplication, separation, and exponentiation by a rational exponent).
However, since they are not produced by using integer constants and algebraic operations, transcendental numbers like the same and e are not algebraic.The production of is commonly stated as a geometric expression, although the definition of e requires an endless amount of algebraic operations.An expression can be reduced to a rational fraction by using the characteristics of arithmetic operations ( commutative properties and associative properties of addition and multiplication, distributive property and rules for the various operations on the given fractions).The required expressions are :
y₁ = x + 3
y₂ = 3x²
y₃ = 3ˣ
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The direct distances in kilometres between six different towns are given in the table below. A dash indicates that there is no direct route available and the journey must be made via other towns.
(a) What is the total distance for the shortest possible route from Anglemouth to Doncatry? [1] WORK NEEDS TO BE INCLUDED :)
The shortest total distance for the route from Anglemouth to Doncatry is 15 units.
How to identify the shortest distance from Anglemounth to Doncatry?On the table, we can see that there is a dash in the section of:
"Anglemouth to Doncatry"
So there is not a direct route, so we need to try another way.
If we go from Anglemouth to Covenham, we have a distance of 10 units.
If now we go from Covenham to Doncatry, we have a distance of 5 units.
Adding these two distances we get:
Total distance = 10 + 5 = 15 units.
This is also the shortest total distance between the two towns.
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When Shaq first checked the temperature, it was 13 degrees. He
checked again later and it was 10 degrees. Express the change in
temperature as an integer.
> |×
Y
label optional
2
X² f(x)/x Xn
(X) X ≤
IV
skill code: 41103
TT
Initial temperature T₀ = 13°c
second Temperature T₁= 10°c
Change in Temperature T₂ = T₀ - T₁ = 13°c - 10°c = 3°c
TemperatureUsing any of a number of arbitrary scales, temperature is a measure of hotness or coldness that shows the direction in which heat energy is moving. When converting from degrees Celsius to Fahrenheit, multiply the result by 1.8 (or 9/5) and then by 32.To learn more about Temperature calculation refer:
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Graph each equation by using the x and y intercepts
Question 2: 5x-2y=7
The x and y intercepts are (7/5, 0) and (0, -7/2) respectively.
What are x and y intercepts?A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.We can graph linear equations by considering intercepts.Since the x-intercept lies on the horizontal axis, it is also known as the horizontal intercept.Since the y-intercept lies on the vertical axis, it is also referred to as the vertical intercept.Given equation is 5x-2y = 7.
To find the x-intercept substitute y = 0 in the equation and then solve,
5x - 0 = 7
x = 7/5
So the x-intercept is (7/5, 0).
Similarly, to find the y-intercept substitute x = 0 in the equation and then solve,
0 - 2y = 7
y = -7/2
So the y-intercept is (0, -7/2).
Now, graph the intersections of (7/5, 0) and (0, -7/2).
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Name the property of equality that justifies going from the first statement to the second statement first statement: 5x = 20 second statement: x = 4 a. addition property of equality b. division property of equality c. reflexive property of equality d. substitution property of equality
b. Division property of equality justifies going from the first statement: 5x = 20 to the second statement: x = 4.
Division property is a type of property of equality that states that if both sides of an equation are divided by the same number except 0, then that equation will remain true.
This property can be proved for the given statements as follows;
5x = 20
According to the division property of equality, we divide both sides by the same number which in this case is 5. Therefore;
5x = 20
5x/5 = 20/5
x = 4
As x = 4 is the second statement, therefore property of equality that justifies going from the first to the second statement is the division property of equality.
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What is 12b-9=??? if b=24?
Answer: The answer is 279
Step-by-step explanation:
12 x 24=288
288-9=279
12(24)-9=279
A line has a slope of – 3 and includes the points (5, – 6) and (s, – 3). What is the value of s?
Answer:
4
Step-by-step explanation:
[tex]\frac{(-6) - (-3)}{s - 5} = -3\\-3(s-5)=-3\\s-5=-1\\\\s=4[/tex]
Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
5(y + 1) = 5
y + 1 =
Divide both sides by 5
Subtract 1 from both sides
Answer:
Step-by-step explanation:
5(y + 1) = 5
Divide both sides by 5
=> 5(y + 1)/5 = 5/5
=> y + 1 = 1 [ 5 in numerator and 5 in denominator cancel]
Subtract 1 from both sides
y + 1 -1 = 1 - 1
y + 0 = 0
=> y = 0
2
The stem-and-leaf diagram shows the
heights of the students in a class.
Heights of students
18 1
17 0 4 4
16
0 1
3
15
3778
14 9
13 4
6
7 8
6 7 8
Key 13 | 4 means 134 cm
a) Find three different averages and three
different measures of spread.
b) Which average and which measure of
spread would you use to represent this
dataset? Give reasons.
Eggs are sold in cartons containing one dozen eggs. If a farmers’s hens laid 660 eggs, how many cartons of eggs could the farmer sell?
Answer:
the farmer can sell 55 cartons
Step-by-step explanation:
1 carton = 12 eggs
660 decided by 12 = 55
Which relation is a function?
The relation that is a function from the given option is Graph A.
Relations and functionsIn mathematics, a relation is a group of ordered pairs that expresses the relationship between two sets.
Function contains both domain and codomain which are also known as dependent and independent variables
For the relation to be a function, two or more of the coordinates must not lie on the same line.
From the given graphs, the relation that is a function is Graph A since two points does not lie on the same vertical line.
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a small barber shop has a single chair and an area for waiting, where only one person can be in the chair at a time, and no one leaves without getting their hair cut. so the system is roughly: entrance → wait → haircut → exit assume customers arrive at the rate of 7 per hour and stay an average of 0.6 hour. what is the average number of customers in the barber shop?
There are 6 customers in the barber shop on an average.
What is average in ?
In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.As per the Little's law, the average number of costumers or individuals in a system (L) can be calculated by multiplying the average arrival rate (λ) and the average time each customer spends in the system (W).
The algebraic expression, is as follows:
L = λW
Here,
L=inventory or average number of customers in the system.
λ=arrival rate = 10
W=flow time average customer spends in the system = 0.6
L = 0.6 * 10 = 6
Thus, there are 6 customers in the barber shop on an average.
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!!! Trigonometry emergency !!!
Answer:
2.4
Step-by-step explanation:
tan(theta) is defined as: [tex]tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
in the given diagram we only have the opposite and hypotenuse, but we can use the Pythagorean Theorem to solve for the other two missing sides.
Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse.
Plugging in known values we get the following:
[tex]a^2+12^2=13^2[/tex]
in this case the missing side, or the adjacent side is simply "a"
from here we simplify the bases with exponents
[tex]a^2+144=169[/tex]
now subtract 144 from both sides
[tex]a^2=25[/tex]
take the square root of both sides
[tex]a=5[/tex]
So now we know the adjacent side so we can plug it into the tan equation
[tex]tan(z)=\frac{12}{5}\\\\tan(z)=2.4[/tex]
Morgan scored 41 points in 3 games. How many points would you expect him to make in an 11 game season?
Morgan will score 150.7 points in 11 season
How to calculate the number of points that Morgan will score ?The first step is to calculate the number of point that Morgan will score in one season
41= 3
x= 1
cross multiply both sides
3x= 41
x= 41/3
x= 13.7
The number of points he will score in 11 game season can be calculated as follows
= 13.7 × 11
= 150.7
Hence Morgan will score 150.7 points in 11 game season
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Which value of x is the solution of the equation 2(x - 4) + 7 = 3?
so the answer is x=2
Answer:
x=2
Step-by-step explanation:
2(x-4)+7=3
First, multiply the 2 to x-4.
2x-8+7=3
Simplify.
2x-1=3
Add x on both sides.
2x=4
Divide 2 on both sides.
x=2
The graph of the function f(x) = -10x² + 700x - 600 shows the profit a company earns for
selling headphones at different prices. What is the maximum profit the company can expect to earn?
The maximum profit which this company can expect to earn is $11,650.
What is the maximum value of a function?The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.
In order to determine the maximum profit which this company can expect to earn, we would differentiate the given function as follows:
f(x) = y = -10x² + 700x - 600
y' = -20x + 700
-20x + 700 = 0
20x = 700
x = 700/20
x = 35.
Substituting the parameter into the formula, we have;
f(x) = -10x² + 700x - 600
f(35) = -10(35)² + 700(35) - 600
f(35) = -12250 + 24,500 - 600
f(35) = $11,650.
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Hamid has gained weight. He now weighs 88 kg, which is 10% higher than his normal weight. What is Hamid's normal weight?
Answer:
Hamid's original weight was 80 kgs
lloyd's cereal company packages cereal in 1 pound boxes (16 ounces). a sample of 25 boxes is selected at random from the production line every hour, and if the average weight is less than 15 ounces, the machine is adjusted to increase the amount of cereal dispensed. if the mean for 1 hour is 1 pound and the standard deviation is 0.1 pound, what is the probability that the amount dispensed per box will have to be increased?
The probability that the amount dispensed per box will have to be increased is 0.0062.
Consider the provided information.
Sample of 16 boxes is selected at random.
If the mean for 1 hour is 1 pound and the standard deviation is 0.1
1 Pound = 16 ounces , then 0.1 Pound = 16/10 = 1.6 ounces
Thus: μ = 16 ounces and σ = 1.6 ounces.
Compute the test probability
z= x−μ/σ/[tex]\sqrt{n}[/tex]
z= 15-16/ 1.6/4
z= -1/ 0.4
z= -2.5
By using the table.
Probability p value = P(Z<-2.50) = 0.0062
Thus, the probability that the amount dispensed per box will have to be increased is 0.0062.
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A retail company is studying the number of employees, based on job classification, such as employee, manager, and senior manager. Which of the following displays could be used to represent the data, and why?
O Bar chart; because job classification is categorical
O Box plot; because job classification is categorical
O Circle graph; because job classification is numerical
O Histogram, because job classification is numerical
The display to represent the data of the number of employees based on job classification is A. Bar chart; because job classification is categorical.
What is categorical data?Categorical data refers to the data types that can be grouped instead of calculated numerically.
Some examples of categorical data include sex, age group, educational level, job classification, and racial categories.
Bar charts and histograms are handy for representing categorical data because they use rectangular bars with heights or lengths to represent proportional values.
Thus, the correct display for the categorical data of job classification is Option A.
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Answer:
A
Step-by-step explanation:
Bar Chart
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800. The law firm designated twice as many partners as associates to the case and was able to charge the client $17600 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.
The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800. The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.
EquationLet variable x = number of associates, assigned to the case
Let variable y = number of partners assigned to the case.
The system of equations to describe this are:
800 x + 1800 y = 17600
y = x + 2
Plugging equation 2 in equation 1, we get,
800 x + 1800(x+ 2) = 17600
2600 x + 3600 = 17,600
Collect like terms
2400 x = 14,000
Divide both side by 2400x
x = 14,000 / 2400
x = 5.8
x = 6 (Approximately)
So,
y = x + 2
y = 5.8 +3
y = 7.8
y = 8 (Approximately)
Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.
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Which is the complete factorization of 6x3
+ 12x2
Information to answer the question.
This data represents the number of jumps in a row 10 students made during a jump-rope competition.
30, 36, 38, 45, 57, 60, 77, 86, 88, 88
What is the interquartile range? Enter the answer in the box.
Jumps
The interquartile range of the number of jumps of the 10 students during the competition is 38.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. The interquartile range is used to determine the variation of a data set.
Th first step is to determine the median of the first half of the dataset. The median of the first half is the first quartile.
First half of the data set: 30, 36, 38, 45, 57
Median = first quartile = 38
The next step is to determine the median of the second half of the dataset. The median of the second half is the third quartile.
Second half of the data set: 60, 77, 86, 88, 88
Median : third quartile = 86
Interquartile range = third quartile - first quartile
86 - 38 = 48
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