To find the composition we need, let's first find the general expression:
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(2x-1) \\ =(2x-1)^2+1 \\ =4x^2-4x+1+1 \\ =4x^2-4x+2 \end{gathered}[/tex]Hence:
[tex](g\circ f)(x)=4x^2-4x+2[/tex]Now we can evaluate when x=1/2:
[tex]\begin{gathered} (g\circ f)(\frac{1}{2})=4(\frac{1}{2})^2-4(\frac{1}{2})+2 \\ =4(\frac{1}{4})-2+2 \\ =1-2+2 \\ =1 \end{gathered}[/tex]Therefore:
[tex](g\circ f)(\frac{1}{2})=1[/tex]A triangle has angle measurements of 72, 34 and 74 . what kind of triangle is it?
We can give two classifications to that triangle
It's a scalene triangle, because all the sides are different (because all the angles are different). Also, it's a acute triangle because all the angles are less than 90°
A stack of one dozen cookies of diameter 2.5 in. exactly fits in a cylindrical container of volume 29.452 in3. Which is the thickness of each cooke?
The volume of a cylinder is given by:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=29.452in^3_{} \\ r=\frac{d}{2}=\frac{2.5}{2}=1.25 \end{gathered}[/tex]solve for h:
[tex]\begin{gathered} 29.452=\pi\cdot(1.25)^2\cdot h \\ h=\frac{29.452}{\pi(1.25)^2} \\ h=5.999912171 \end{gathered}[/tex]divide the height by 12:
[tex]\frac{h}{12}=0.499992681in[/tex]The thickness of each cookie is 0.499992681in or approximately 0.5in
Rewrite the following percents as decimals. i. 4% ii. 76% ii. 120% iv. 100% V. 32.5%
Answer
i) 4% = 0.04
ii) 76% = 0.76
iii) 120% = 1.20
iv) 100% = 1.00
v) 32.5% = 0.325
Explanation
The key to writing percents as decimals is to divide the percents by 100 to get the decimal equivalent.
i) 4% = (4/100) = 0.04
ii) 76% = (76/100) = 0.76
iii) 120% = (120/100) = 1.20
iv) 100% = (100/100) = 1.00
v) 32.5% = (32.5/100) = 0.325
Hope this Helps!!!
Ubicar las siguientes fracciones en la recta numérica: 3/9
The most appropriate choice for Number line will be given by -
The number line has been shown in the figure attached.
What is a number line?
A visual representation of the real numbers can be shown on a diagrammatic representation of graduated straight lines. The visual representation of the real numbers is known as the number line. Number line can be used for addition or subtraction of two numbers.
Here,
The number line has been attached
[tex]\frac{3}{9}[/tex] lies between 0 and 1
So the space between 0 and 1 is divided into 9 equal parts as the denominator of the given fraction is 9
Now the third small line is the required value i.e [tex]\frac{3}{9}[/tex] as 3 is in the numerator of the given fraction
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Question
Solve 6x+3y=−1 for y
The required solution of the given equation 6x + 3y = −1 for y would be the value of equation y = -2x - 1/3.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
The equation is given in the question below as:
6x + 3y = −1
We have to determine the solution of the equation 6x + 3y = −1 for y.
⇒ 6x + 3y = −1
Rearrange the terms of the variable in the above equation,
3y = - 6x - 1
Divided by 3 both sides of the equation to get
y = -2x - 1/3
Hence, the required solution of the given equation 6x + 3y = −1 for y would be the value of equation y = -2x - 1/3.
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Last year, Carlos opened an investment account $5,200 with. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in his account at the end of last year?
ANSWER
[tex]\begin{gathered} 338 \\ 5538 \end{gathered}[/tex]EXPLANATION
The Principal is $5200;
Increase rate is; 6.5%
The increase in dollar is;
[tex]\begin{gathered} \frac{6.5}{100}\times5200 \\ =338 \end{gathered}[/tex]Hence, the amount in the account at the end of the year;
[tex]\begin{gathered} A=P+I \\ =5200+388 \\ =5538 \end{gathered}[/tex]Therefore, the increase in dollar is $338 while the amount in the account at the end of the year is $5538
What can I do to decrease my bill by $25.00 per month?"
Employee: "Your bill is currently __________ per month, so we'll make a change to a less expensive option that will result in a 30% decrease in your monthly payment."
If he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33
The percentage decrease in the monthly payment = 30%
The amount of decrease in the bill per month = $25
Consider the current bill amount as x
Then the equation will be
x × (30/100) = $25
Solve the equation
0.3x = $25
x = 25/0.3
x = $83.33
Hence, if he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33
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Find the distance between the two points in simplest radical form.
(-6, 5) and (-3, 7)
Answer: [tex]\sqrt{13}[/tex]
Step-by-step explanation:
Using the distance formula,
[tex]\sqrt{(-6-(-3))^2 +(5-7)^2}=\sqrt{13}[/tex]
I need help with this question but no one is helping me! Can someone please help me
Answer:
a) 0.0187
b) 0.0943
c) 0.2959
Step-by-step explanation:
a) 9/31 * 8/30 * 7/29 = 0.0187
b) 10/31 * 9/30 * 8/29 + 12/31 * 11/30 * 10/29 + 9/31 * 8/30 * 7/29 = 0.0943
c) 21/31 * 20/30 * 19/29 = 0.2959
You are 37 years old have accumulated 150000 in your savings account. You intend to add a fixed amount each month for twenty years. For first 5 years you add 100 at the end of each month.
On Monday, 365 students purchased a hot lunch in the cafeteria. On Friday, 429 students
purchased a hot lunch. What was the percent increase in students buying hot lunches?
OA 1.75%
O B 2.5%
OC 8.5%
O D 17.5%
The percent increase of the students in the cafeteria that bought hot lunches is 17.5%
How to calculate the percent increase ?On Monday 365 students purchased hot lunch
On Friday 429 students purchased hot lunch
The first step is to calculate the percent change
429-365
= 64
The percent increase can be calculated by dividing the percent change by the original value and then multiply by 100
64/365 × 100
= 0.175 × 100
= 17.5
Hence the percentage increase in the students purchasing lunch is 17.5%
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.What are the odds against exactly 5 cars passing over the bridge in that time?
A probability is the number of outcomes divided by the number of total outcomes.
An odd is given by a:b, in which a is the number of successes and b is the number of failures.
From the question, the probability of 5 cars will pass over a small bridge is 0.16
That means the total outcomes is 100 and the outcomes of successes are 16
Then to find the failures subtract 16 from 100
The failures = 100 - 16 = 84
Successes = 16
a = 16
Failures = 84
b = 84
Odds = a: b
Odds = 16: 84
Divide each term by 4 to simplify
Odds = (16/4): (84/4)
Odds = 4: 21
The answer is 4: 21
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Vince is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $5 per kilogram for the lobster he picks. At the second restaurant, Vince would pay $8 per kilogram for the lobster, in addition to $33 for the meal. Vince realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Vince pay for his dinner? What is the weight?Dinner would cost $ at either restaurant if Vince's lobster weighed kilograms.
Based on the given situation, if x is number of kilograms of lobster, you can write the following expressions:
51 + 5x cost in the first restaurant
33 + 8x cost in the second restaurant
In order to determine the value of x which makes the cost the same in both restaurants, equal the previous expressions and solve for x:
51 + 5x = 33 + 8x subtract 33 both sides and 5x subtract both sides
51 - 33 = 8x - 5x simplify
18 = 3x divide by 3 both sides
18/3 = x
6 = x
x = 6
Hence, the weight of the lobster is 6 kg.
The cost of the dinner is:
51 + 5(6) = 51 + 30 = 81
Hence, the cost of the dinner is $81
Can I get help? Please show your work and steps.
1) -14 = -4(9x-1)
Number 2
⬇️⬇️⬇️
Question 1
[tex]-14=-4(9x-1)\\\\-14=-36x+4\\\\-18=-36x\\\\x=\frac{1}{2}[/tex]
Question 2
Multiplying both sides by 12,
[tex]4x-7x=8\\\\-3x=8\\\\x=-\frac{8}{3}[/tex]
True or false?
In centrally planned economies, the distribution of goods costs nothing to administer
The following statement "In centrally planned economies, the distribution of goods costs nothing to administer" is true.
A centrally planned economy, often known as a command economy, is an economic system in which a government agency makes economic choices affecting the production and distribution of products. Centrally planned economies vary from market economies in that these decisions are the outcome of hundreds of choices made by producers and consumers.
State-owned corporations provide goods and services in planned economies, however, independent firms may occasionally be brought into economic planning. Prices, salaries, and production schedules are often set by a centralized bureaucracy.
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Pls help (give right answer)!!
seems hard very xd oihfoidhfoidshfodjsklfdsfdsfsdfdsf
Veronika has 3 daughters. Today the eldest is 7 years older the the second who is 2 years older than the youngest. The sum of their ages 12 years from now will be 56. How old are they today?
We define the following variables:
• x = age (in years) of the eldest,
,• y = age (in years) of the second,
,• z = age (in years) of the youngest.
From the statement, we know that:
0. the eldest is 7 years older than the second → , x = 7 + y,,
,1. the second is 2 older than the youngest → ,y = 2 + z,,
,2. the sum of the ages 12 years from now will be 56 → x + y + z + 12 = 56 → ,x + y + z = 56 - 12 = 44,.
We have the following system of equations:
[tex]\begin{gathered} x=7+y, \\ y=2+z, \\ x+y+z=44. \end{gathered}[/tex]i) Replacing the second equation in the first one, we have:
[tex]x=7+y=7+(2+z)=9+z\text{.}[/tex]ii) Summing the ages of the three daughters, we have:
[tex]x+y+z=(9+z)+(2+z)+z=11+3z\text{.}[/tex]iii) Equalling the last equation with the third one, we have:
[tex]\begin{gathered} 11+3z=44, \\ 3z=44-11=33, \\ z=\frac{33}{3}=11. \end{gathered}[/tex]Replacing the value of z in the equation of x and y, we get:
[tex]\begin{gathered} x=9+11=20, \\ y=2+11=13. \end{gathered}[/tex]Answer
The ages of the daughters are 20, 13 and 11.
3 9/13 to a improper fraction
Answer:
48/13
Step-by-step explanation:
To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction
3 * 13/13 = 39/13
Then add it to the rest of the fraction
39/13 + 9/13
= 48/13
Answer: 48/13
Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.
Some researchers developing a new Intelligence test are trying to decide how much time to allow to complete the test. The researchers have recorded the times(in minutes) for completion of 26 people who took the test for practice. The frequency distribution below summarizes the completion times recorded by theresearchers.Time for completion(in minutes)Frequency9 to 1112 to 14715 to 1785318 to 2021 to 233Based on the frequency distribution, using the midpoint of each data class, estimate the mean completion time of the people who took the test. For yourintermediate computations, use four or more decimal places, and round your answer to one decimal place.
To find the mean of grouped data, we need to use the next formula:
[tex]Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}[/tex]First, we need to find the midpoint of each interval:
The midpoint of interval = 1/2 (lower class limit + upper-class limit)
Then:
Time for competition (in minutes) ----- frequency ---- midpoint
9 -11 8 1/2(9+11) = 10
12 -14 7 1/2(12+14) = 13
15-17 5 1/2(15+17)= 16
18 - 20 3 1/2(18+20) = 19
21-23 3 1/2(21+23) = 22
Now, multiply the frequency of each interval by its midpoint:
10 * 8 = 80
13* 7 = 91
16 * 5 = 80
19 * 3 = 57
22 *3 = 66
Summ all the results 80 + 91 +80+57+66= 374
Then, sum all the frecuencys = 8 + 7 +5 +3 +3 = 26
Use the mean formula =
[tex]Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}[/tex][tex]Mean\text{ of a gruop data =}\frac{374}{26}=14.38461[/tex]The mean is given using five decimals.
Help me! i need this answer now i am so dead. if i get it worng please help
Answer:
[tex]260 \: {cm}^{2} [/tex]
Step-by-step explanation:
hope it helped, have a nice day!: )
Which of the following could be a cross-section of a triangular prism? circle o hexagon O octagon O rectangle
A triangular prism have two possible cross sections: A triangle and a rectangle
msMario bought 3 yeard of ribbon for 1.50 how much would 5 yards of the same ribbon cost? explain how u got your answer
For 3 yards, it costs, 1.50.
So for one yard,
[tex]\frac{1.50}{3}=0.5[/tex]Therefore for 5 yards,
[tex]5\times0.5=2.5[/tex]Ann and Tom want to establish a fund for their grandson's education. what lump sum must they deposit at a 7% annual interest rate compounded monthly in order to have $60,000 in the fund at the end of 10 years?
Formula to calculate Principal with clompound interest:
[tex]\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{n\cdot t}} \\ \\ A=\text{Amount} \\ r=\text{Interest rate (decimals)} \\ n=\text{ number of times per unit t} \\ t=time \end{gathered}[/tex]For the given situation:
A= 60,000
r= 7% =7/100= 0.07
n= 12 (as it is compounded monthly and a year has 12 months)
t= 10 years
[tex]\begin{gathered} P=\frac{60,000}{(1+\frac{0.07}{12})^{12\cdot10}} \\ \\ =\frac{60,000}{(1+\frac{0.07}{12})^{120}} \\ \\ \approx29,855.78 \end{gathered}[/tex]Then, they must deposit approximately $29,855.75
The table shown represents a linear relationship.
x 0 1 3 4
y −8 −6 −2 0
Based on the table, what is the equation of the linear relationship in slope-intercept form?
y = 2x − 8
y = 2x + 8
y = −2x + 4
y = −2x − 4
Answer: y = 2x - 8
Step-by-step explanation:
When x = 0, y = -8. This is the y-intercept.
As x increases by 1, y increases by 2. This makes 2 the slope.
The equation for the linear relationship given, in slope-intercept form is y = 2x-8
What is slope-intercept form?The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers.
Given that, coordinates representing a linear relationship.
x → 0, 1, 3, 4
y → -8, -6, -2, 0
We need to find an equation for the given linear relationship in slope-intercept form,
Considering points, (0, -8) and (4, 0)
We know that, the equation of a line passing through, two points is given by,
y-y₁ = (y₂-y₁) / (x₂-x₁) (x-x₁)
Here, y₁ = -8, y₂ = 0, x₁ = 0, x₂ = 4
Therefore, the equation is =
y+8 = 8/4(x-0)
y+8 = 2x
y = 2x-8
Hence, the equation for the linear relationship given, in slope-intercept form is y = 2x-8
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17. MTR Model Problems Place points on the number line to show 4 equal lengths from 0 to 1.8. How long is each length?
Answer:
4.5
Step-by-step explanation:
4.5 + 4.5 + 4.5 + 4.5 = 18
You write it like this in the number line:
4.5, 9, 13.5, 18
ASAP i need help rn before i finish this test
The triangles shown are congruent.
What is a correct congruence statement for the triangles shown?
Answer:
SAS= Side, Angle, Side
Step-by-step explanation:
According to the image, GB congruent to XP, and LB congruent to PF. So, it means that both triangle have the same angle since they both have two congruent side.
The recommended dosage of a drug for pediatric patients is 200 mg per kilogram of a patient's weight. If Janine weighs 102 lb, how much of the drug should she receive? Use the fact that 1 lb = 0.45 kg
Janine should receive about ____ milligrams of the drug.
(Round to the nearest milligram as needed.)
Answer: 9180 mg
Step-by-step explanation:
First we must convert the patients weight from lb to kg.
102lb x [tex]\frac{0.45kg}{1lb}[/tex] = 102 x 0.45 kg = 45.9 kg
Now to calculate the amount of the drug she should receive.
45.9 kg x [tex]\frac{200mg}{kg}[/tex] = 9180 mg
a. On what interval(s) of x is f(x) positive?
b. On what interval(s) of x is f(x) negative?
c. On what interval(s) of x is f(x) increasing?
d. On what interval(s) of x is f(x) decreasing?
e. On what interval(s) of x does f have positive concavity?
f. On what interval(s) of x does f have negative concavity?
On (-∞, -2) ∪ (3,∞) f(x) is positive, On (-∞, -0.5) it is negative, On (0.5, ∞) it is increasing, in none of the intervals it is having positive concavity, On (-∞, ∞) it has negative concavity.
What X intervals are beneficial for fx?Seeing as how f (x) = 0 there. A function’s “positive regions” are those times when it is above the x-axis. Y-values that are positive are where it is (not zero).
The portions of a function that are below the x-axis are known as its negative regions.
How can I determine the time intervals where f is positive?You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.
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For the following, find f(2.1) and f(4).
Answer:
A
Step-by-step explanation:
Comment
The tricky part is f(4)
Log part
That is defined by log_2 which means that the base used for the log is 2.
We don't have log_2 on our calculators so you have to create it.
Substitute 4 for x
log_2 (4) = log_10(4)/ log_10 (2) Which your calculator can handle
log_2 (4) = Log(4)/ log(2) = 2
f(x) = 1/2 x^2
x = 2.1
Only answers a and b are correct, but which one is right? 2.1 is between 2 and 4. So you choose f(x) = 1/2 x^2
1/2 2.1^2 = 1/2 4.41 = 2.205
Answer
A
Answer:
(a) f(2.1) = 2.205 and f(4) = 2
Step-by-step explanation:
You want to evaluate a piecewise-defined function to find f(2.1) and f(4).
DomainThe first step in evaluating a piecewise defined function is to match the argument value with the appropriate domain.
for f(2.1), you want to use the definition for the domain 2 < x < 4for f(4), you want to use the definition for the domain 4 ≤ x < 8Function evaluationOnce you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.
f(2.1) = 1/2(2.1)² = 1/2(4.41) = 2.205f(4) = log₂(4) = log₂(2²) = 2The desired function values are f(2.1) = 2.205 and f(4) = 2.
What is the value of x + y² when x = 1 and y = 9?
Answer:
=82
Step-by-step explanation:
the value of
x + y²
putting x=1,y=9
we get,
1+(9)^²
=1+81
=82