Composite Functions for : f [ g (x) ] = 3 g(x) + 7 will be f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8
Common functions typically have a subset of the real numbers as their domain. Any integer from the domain may be used to replace a variable.
The domain of a composite function is determined by another function, not by a collection of numbers. We refer to it as "a result of another function. Example:
If: . f (x) = 3x + 7 . f [g(x)] must be found and simplified. g(x) = 5x - 5. Due to the fact that the domain of this function is a function of another function, f (x) is a simple function or just a function.
Let's make the example I gave previously simpler.
G (x) signifies in f "Replace x with g (x) in the function f (x). The Composite function f [g (x)]
we have : f [ g (x) ] = 3 g(x) + 7 . but . g( x) = 5x - 5
replace x in f[ g(x ) ] . by. 5x - 5 and simplify
f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8 **
Know more about Composite Functions
https://brainly.com/question/10687170
#SPJ4
The question seems to be wrong
Evaluating Composite Functions for : f [ g (x) ] = 3 g(x) + 7
A rectangular garden has a length of 57 m and a width of 42 m. How many m2 will decrease the area of a garden, if the ornamental fence with a width of 60 cm will be planted inside its perimeter?
The area of the rectangular garden can be calculated as follows: 57 m * 42 m = 2406 m^2.
The ornamental fence with a width of 60 cm has a width of 0.6 m. If the fence is planted inside the perimeter of the garden, the length of the garden will decrease by 2 * 0.6 m = 1.2 m and the width of the garden will decrease by 2 * 0.6 m = 1.2 m.
So, the new length and width of the garden will be 57 m - 1.2 m = 55.8 m and 42 m - 1.2 m = 40.8 m, respectively.
The new area of the garden can be calculated as follows: 55.8 m * 40.8 m = 2270.784 m^2.
Finally, the decrease in area can be calculated as follows: 2406 m^2 - 2270.784 m^2 = 35.216 m^2.
Therefore, the area of the garden will decrease by 35.216 m^2.
Answer:
The width of the ornamental fence is 60 cm, which is equal to 60/100 = 0.6 meters.
The total length of the ornamental fence that will be planted inside the perimeter of the rectangular garden is 2 * (57 m + 42 m) = 2 * 99 m = 198 m.
The decrease in the area of the garden due to the ornamental fence is 0.6 m * 198 m = 118.8 m^2.
Show that the triangles are similar and write a similarity statement.
Answer:
im sorry bro i
Step-by-step explanation:
i just need points
A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population. T/F
A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population.
The following statement is True.
A variable is a trait that can be measured and has several values. Variables include height, age, income, province or country of birth, school grades, and kind of dwelling. Variables can be divided into two types: category and numeric.
A "sampling frame" is a list of all population items to be researched. Probability and nonprobability are the two primary types of sampling methodologies. A simple random sample is a sample drawn from the population in which every member has an equal probability of being chosen.
For more questions on Population
https://brainly.com/question/28523401
#SPJ1
What is the domain of the graph
below?
Answer:
A
Step-by-step explanation:
[tex]4\leq x < 4[/tex]
Focusing on the left end of the graph, the x value corresponding to the graph is -4. The circle present at this end of the graph is coloured in, which indicates that -4 is included in the domain.
Focusing on the right end of the graph, the x value corresponding to the graph is 4. The circle present at this end of the graph is NOT coloured in, which indicates that 4 is NOT included in the domain.
HELP FAST WILL GIVE BRAINLYS IF ANSWER IS RIGHT!
You work in a dentist’s office. You record the number of X-ray plates used each day of the week that the dentist works, as shown: 15, 13, 16, 18, 13, and 22. The dentist then calculates the mean by dividing the number of X-ray plates used (97) by the number of days in the week (5).
What was the dentist’s mistake in the calculation?
The dentist counted 13 twice.
The dentist counted too few days.
The dentist counted too many days.
The dentist divided instead of multiplying.
The dentist did not sum the number of plates used correctly.
Answer:
Dentist counted to few days.
Step-by-step explanation:
Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average of the survival times of the 16 batteries is computed. If the claim is true, the average life of 16 batteries should EXCEED what value for 99% of the time?
53 is the value of the 99% of the time.
What is a normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center
Given, Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average survival times of the 16 batteries are Comput.
μ = 50
σ² = 25
n = 16
So, the Population standard deviation
σ² = 25
σ = 5
To find the value 99% of the time
The z-score will be
P(z <Z) = 0.999
P(z < 2.326) = 0.999
Z = 2.326
To find a z score corresponding to a known probability, select fx, Statistical, NORMSINV, and enter the total area to the left of the given value.
Now we determine the z-score using the z-score formula
x = μ + (Z *σ / √n)
x = 53
Therefore, the value of 99% of the time is 53.
Learn more about normal distribution here:
https://brainly.com/question/29509087
#SPJ1
Complete question:
find the function of the form y= A sin(kx)+C or y= A cos (kx) +C
Answer:
[tex]y \: = 2cos \: ( \frac{\pi}{5} x) - 3[/tex]
Two numbers are in a ratio 3:5. What is the ratio between their squares?
Answer:
let the two numbers be x and y.
Given ,
[tex] \underline{\underline{\frac{x}{y} = \frac{3}{5}}} \\ [/tex]
To find - ratio of squares of the two numbers.
[tex]\longrightarrow \: \frac{ {x}^{2} }{ {y}^{2} } = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ \\ \longrightarrow \: \boxed{\frac{ {x}^{2} }{ {y}^{2} } = \frac{9}{25} }[/tex]
Therefore ,
[tex] \underline{\underline{ratio \: of \: the \: squares \: of \: two \: numbers \: = \: 9 \: : \: 25}} [/tex]
hope helpful! :)
help asap its timed cmon
When the center angle is 60 degrees, the arc length is measured in 1.047 units.
What is arc?An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference. An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference. An arc is a kind of curve.
Here,
angle=60°
in triangle BCD,
cos 60=CB/DB
DB= 2 units
radius=1 unit
arc length=2πr*(θ/360)
=2*3.14*1*60/360
=1.047 units
The measure of arc length when central angle is 60 degree is given by 1.047 units.
To know more about arc,
https://brainly.com/question/20294211
#SPJ1
Y=601(1.05)^18 rounded to the nearest hundredth
The value of y is 1446.38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
y = 601 [tex](1.05)^{18}[/tex]
Now,
y = 601 x 2.4066192336911
y = 1446.3781
y = 1446.38
Thus,
y = 1446.38
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Please help me with this question.
The solution of the equation can be obtained as x = 1.
How do we solve the exponential equation?
We have to note that the exponential equation can be solved in the form of a quadratic equation and then we can be able to obtain the values that can be able to sort out the equation.
We know that;
e^2x + e^x - 12= 0
Let p represent e^x we would then have
p^2 + p - 12 = 0
If we solve the quadratic we would have;
p = 3 or p = -4
If we discard the negative answer;
e^x = 3^1
x = 1
The solution of the equation x = 1.
Learn more about exponential equation:https://brainly.com/question/29506679
#SPJ1
The chart to the right shows a country'sannual egg production. Model the data in the chart with a linear function,using the points (1995,52.7)and (1999,61.3).Let x represent the year,where x=0 represents 1995,x=1 represents 1996,and so on,and let y represent the egg production (inbillions). Predict egg production in 2001.
The predicted egg production in 2001 is given as follows:
65.6 billion.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the yearly change.The intercept b represents the production in 1995.The production in 1995 was of 52.7, hence the intercept b is given as follows:
b = 52.7.
In 4 years, the production increased to 61.3, hence the slope m is given as follows:
m = (61.3 - 52.7)/4
m = 2.15.
Hence the function is of:
y = 2.15x + 52.7.
2001 is 6 years,hence the estimate is given as follows:
y = 2.15(6) + 52.7
y = 65.6 billion.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Please help me with this
Extra points
The equation that represents the second step of solution process is 12x-3+27=-24. Thus, option A is correct.
What is simplex method of equation ?The simplex method is a widely used linear programming methodology for addressing optimization problems. These problems typically involve a function and a number of constraints that are stated as inequalities.
Step 1: 3(4x-1)+27=-24
Step 2: 12x-3+27=-24
Step 3: 12x+24=-24
Step 4: 12x=-48
Step 5: x=-4
A. 12x-3+27=-24.
Learn more about equation here:
https://brainly.com/question/1529522
#SPJ1
Which line has a constant of proportionality between y and x of 3?
Cinema A sells a twelve-pack of movie passes for $66. Cinema B sells a five-pack of movie passes for $29. Find the unit cost for each movie pack and determine.
The unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.
How to determine the unit ratesTo find the unit cost of each movie pack, we need to divide the total cost by the number of passes in each pack.
The unit cost for Cinema A's twelve-pack can be calculated as follows:
unit cost for Cinema A = $66 / 12 passes = $5.50 per pass
The unit cost for Cinema B's five-pack can be calculated as follows:
unit cost for Cinema B = $29 / 5 passes = $5.80 per pass
So, the unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.
Read more about unit rates at
https://brainly.com/question/19493296
#SPJ1
Given a set of seven distinct positive integers, prove that there is a pair whose sum or whose difference is a multiple of 10. you may use the fact that if the one digit is a 0 it is divisible by 10. hint: create six categories of integers based on their ones digit. I cant figure out the six categories.
Six categories of integers based on their ones digit are:
Integers ending in 0 or 5.Integers ending in 1 or 9.Integers ending in 2 or 8.Integers ending in 3 or 7.Integers ending in 4 or 6.Prove Pair Sum/Diff Multiple of 10The cases when sum or difference of the pair is divisible by 10:
If the integers have the same units digit (e.g. both end in 5 or both end in 0), then their sum is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 1 or 9, then their difference is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 2 or 8, then their sum is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 3 or 7, then their difference is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 4 or 6, then their sum is a multiple of 10.Therefore, no matter which seven integers we choose, there is always a pair that meets the condition.
Learn more about Prove Pair Sum/Diff Multiple of 10 here:
https://brainly.com/question/14280621
#SPJ4
A system has three computers. Computer 1 works with a probability of 0.65; computer 2 works with a probability of 0.65; computer 3 works with a probability of 0.87. Suppose that the operations of the computers are independent of each other. Suppose that the system works only if at least one computer is working. What is the probability that the system works? Round your answer to four decimal places.
Probability that the system works is approximately 0.9841.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Let the three events be C₁, C₂ and C₃.
Probability that computer 1 works = P(C₁) = 0.65
Probability that computer 1 does not work = P(C₁') = 1 - 0.65 = 0.35
Probability that computer 2 works = P(C₂) = 0.65
Probability that computer 2 does not work = P(C₂') = 1 - 0.65 = 0.35
Probability that computer 3 works = P(C₃) = 0.87
Probability that computer 3 does not work = P(C₃') = 1 - 0.87 = 0.13
Let the event that at least one of the computer is working is S.
P(S) = 1 - P(no computer is working)
P(no computer is working) = P(C₁' ∩ C₂' ∩ C₃')
We have the operations of the computers are independent of each other.
P(C₁' ∩ C₂' ∩ C₃') = P(C₁') × P(C₂') × P(C₃')
= 0.35 × 0.35 × 0.13
= 0.015925
P(no computer is working) = 0.015925
P(S) = 1 - 0.015925
= 0.984075 ≈ 0.9841
Hence the required probability is 0.9841.
To learn more about Probability, click on the link :
https://brainly.com/question/30034780
#SPJ1
A ∪ B ∪ C
A union B union C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
A ∪ B ∪ C is the set of all items in sets A, B, or C.
Region V: Items in A, B, and C
What does A ∪ B ∪ C represent?In set theory, the union of two or more sets is a new set that contains all the elements from each of the original sets. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∪ B = {1, 2, 3, 4}.
In this case, A ∪ B ∪ C represents the set of all elements that belong to at least one of the sets A, B, or C.
Therefore, A ∪ B ∪ C represents the set of all items in sets A, B, or C.
Learn more about set theory on:
brainly.com/question/13458417
#SPJ1
The movies charges 16$ for adults and 16$ for children. The revenue total was 672$ determine the number of each tickets sold if the number of children tickets sold was half the number of the adults.
Answer:
7 child tickets
14 adult tickets
Step-by-step explanation:
Let a = the number of adult tickets
Let c = the number of child tickets
16a + 16c + 672
2c = a Substitute 2c for a
15a + 16c = 672
16(2a) + 16c = 672
32a + 16c = 672 Combine like terms
48a = 672 Divide both sides by 48
a = 14
2c = a
2c = 14 Divide both sides by 2
c = 7
Evaluate the expression. 8+12x7
Answer:
92
Step-by-step explanation:
We first do 12x7 which equals to 84
Then we add 8 which equals to 92
Find the value of X and the length of YZ
Answer: x = 8 and YZ = 19
Step-by-step explanation:
mb i focused on the x between a and y and i forgot the x they were talking about was the x in the equations..
since its a bisector, we know that az = yz therefore 2x + 3 = 3x - 5
2x + 3 = 3x - 5
2x + 8 = 3x
8 = x
now we know the value of x, we can plug it into the equation for yz
3(8) - 5
24 - 5
19
therefore, x = 8 and yz = 19
A new appliance salesperson sold an average of $12,000 per day for the first 3 days they worked.
On the next 4 days they worked, they sold an average of $9,000 per day. How much did they sell on average per day over the entire 7 days?
Kelly works two jobs. She usually works at a retail store for 7 hours during the day and is paid $12 per hour by the store. In the evening she works at a restaurant as a manager for 5 hours and is paid $20 per hour. How much does she make on average per hour for the day?
7. Henry worked for 10 consecutive days, earning an average wage of $120 per day at his dog walking business. During the first 5 days, Henry averaged $100 per day and his average earned for the next 4 days was $130 per day. How much did he earn on the last day?
Marcus has a slugging average of .484 and has had 18 singles, 33 doubles, 2 triples, and 54 homeruns. How many at-bats has Marcus had?
It is Tyler's first season playing baseball with the Diamondbacks. He has had 383 at-bats. So far, he has 74 singles, 13 doubles, 11 triples and 4 homeruns. What is Tyler's current Slugging Percentage? What is Tyler's Batting Average?
Tyler's current Slugging Percentage is 546 and current Batting Average is 192.
What is Slugging Percentage?Slugging percentage is a statistic used in baseball and softball to measure a batter's total number of bases per at bat. It is calculated by dividing the total number of bases earned by the number of at-bats. This statistic is often used to compare batters since it takes into account the number of bases earned in addition to the number of hits. Slugging percentage is an important statistic to consider when evaluating batters since it provides an overall picture of how well a batter is performing. Slugging percentage is usually expressed as a decimal or a percentage, with a higher percentage indicating better performance.
Tyler's current Slugging Percentage is .546. This is calculated by adding the total number of bases earned (74 + 2*13 + 3*11 + 4*4 = 194) and dividing that by the total number of at-bats (383).
Tyler's current Batting Average is .192. This is calculated by dividing the total number of hits (74 + 13 + 11 + 4 = 102) by the total number of at-bats (383).
To learn more about Slugging Percentage
https://brainly.com/question/14626722
#SPJ1
Find the equation of the line passing through the points (8, -16) and (1, 5).
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{8}}} \implies \cfrac{5 +16}{-7} \implies \cfrac{ 21 }{ -7 } \implies - 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{8}) \implies y +16 = - 3 ( x -8) \\\\\\ y+16=-3x+24\implies {\Large \begin{array}{llll} y=-3x+8 \end{array}}[/tex]
Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.) Round your answer to two places, where applicable. Side AB Side BC Side AC ? 12 19
The length of the unknown side or, the length of AC = 22.62.
To calculate the length of the unknown side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides or, in familiar algebraic notation, a2 + b2 = c2.
In this Question, side AC is the hypotenuse, so we can use the Pythagorean theorem to find the length of side AC:
AC^2 = AB^2 + BC^2
We know that AB = 12 and BC = 19, so we can substitute these values into the equation:
AC^2 = 12^2 + 19^2
AC^2 = 144 + 361
AC^2 = 505
To find the length of AC, we can take the square root of 505:
AC = √505
Rounded to two decimal places, the length of AC = 22.62.
Learn more about the Pythagorean theorem,
https://brainly.com/question/343682
Of all the metals, Mercury has the lowest melting point at
-37.8 degrees Celsius. Write an inequality to show all of the possible melting points for any other metal.
Mercury, gallium, and caesium often have low melting points, except gold. The only liquid metal with a 38 °C melting temperature is mercury.
What are the possible melting points for any metal?They have high melting and boiling points because melting and boiling require a lot of energy to break through the strong metallic connections present in a metal's massive structure.
Brass: 930 °C (1710 °F) Aluminium Bronze*: 1027-1038 °C (1881-1900 °F) Chromium: 1860 °C (3380 °F) Copper: 1084 °C (1983 °F).
In general, aluminium is an easy metal to melt, and it is easy to get your hands on. To make aluminum metal shapes, many people melt discarded soda cans made of aluminum. The aluminum should be heated until it melts completely.
Therefore, the melting or boiling point will be higher the more energy is required. Varying metals have different melting and boiling points because the force of attraction between the metal ions differs between them.
Learn more about metal here:
https://brainly.com/question/28199316
#SPJ1
7 raised to the power 2 divided by 7 raised to the power 3
The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Given expression,
7 raised to the power 2 divided by 7 raised to the power 3
7 ^ 2 / 7 ^ 3
The value of a ^ m / a ^ n = a ^ m-n
= 7 ^ (2-3)
= 7 ^ ( -1)
= 1 / 7 .
Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7
To learn more about Algebraic expression from given link.
https://brainly.com/question/953809
#SPJ1
Based on the completed Form 1040 and 2018 Taxable Income Tiers, what is the total tax
that the employee is responsible for paying?
Answer in complete sentences.
By assuming that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be: $17,836.
What are tax bracket or income tiers?A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.
In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.
Read more about tax bracket
brainly.com/question/29196852
#SPJ1
The population of a certain town is 158,260 and increases exponentially at the rate of 6% every year. Which equation best represents the population after x years?
The equation for the population after x years can be represented using P(x) = 158,260 * (1 + 0.06)^x
Which equation best represents the population after x years?From the question, we have the following parameters that can be used in our computation:
Initial, a = 158260
Rate, r = 6%
The function is represented as
P(x) = a(1 + r)^x
This means that
P(x) = 158,260 * (1 + 0.06)^x
Read more about exponential function at
https://brainly.com/question/2456547
#SPJ1
As part of a survey, 300 girls were asked to name their favorite sport. 12 of the girls named bowling as their favorite. Based upon the results, how many of the next 200 girls surveyed would you expect to choose bowling as their favorite sport?
The number of girls in the next 200 girls surveyed that would choose their favorite sport as bowling are 8 girls.
What is percentage?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given that 300 girls were asked to name their favorite sport. 12 of the girls named bowling as their favorite.
The percentage of girls that selected the sport is thus:
12/ 300 (100) = 4%
For the next 200 girls, calculate the 4% of the number to get the number of girls who like bowling:
200 (4%) = N
N = (200)(4/100)
N = 8
Hence, the number of girls in the next 200 girls surveyed that would choose their favorite sport as bowling are 8 girls.
Learn more about percentage here:
https://brainly.com/question/14801224
#SPJ1
A tourist asked a zookeeper how many birds and lions are in the zoo. The zookeeper replied there are 31 heads and 96 feet. Find the number of each.
By concept of linear equations, The number of birds is 14 and number of lions is 17.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Let no. of birds=x and no. of lions=y
Given heads=31
and feet=96
Therefore, the equations will be
x+y=31 and 2x+4y=96
from given equations x=14 and y=17.
Hence,
The number of birds is 14 and number of lions is 17.
To know more about linear equations visit the link
https://brainly.com/question/29739212?referrer=searchResults
#SPJ1
