The function [tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex] is continuous on (-∞, ∞).
As per the given data the function f(x) is given by:
[tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]
Here we have to determine that the function f(x) is continuous on (-∞, ∞)
If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)
What are continuous function?
A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.
To show f(x) is continuous at x = 1
[tex]\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}[/tex] f(x)
[tex]\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\[/tex]
= 1 - 1
= 0
[tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\[/tex]
= ln 1
= 0
Therefore [tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0[/tex].
Hence f(x) is continuous on (-∞, ∞)
For more questions on Limits
https://brainly.com/question/20067425
#SPJ4
PLEASE HELP GUYS THANK YOU IN ADVANCED
Answer:
x=3.5
Step-by-step explanation:
Answer:
x=sqrt(12) or 2sqrt(3)
Step-by-step explanation:
You can just use pythagorean theorem for this.
We can do 4^2+x^2=8^2
This gives us 16+x^2=64.
Simplify: x^2=48
x=sqrt(48)
Now, we can find x!
We just have to do 6^2+x^2=sqrt(48).
We get 36+x^2=48
simplify: x^2=12
Now, x=sqrt(12) or 2sqrt(3)
Select the correct answer.
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to
test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has NO
oil and the test shows that there is no oil?
OA. 0.09
OB. 0.11
OC. 0.44
OD. 0.36
Answer:
the answer is A. 0.09
Step-by-step explanation:
internet :)
Answer:
C. 044Step-by-step explanation:
Probability of oil:
P(oil) = 45%Probability of no oil:
P(no oil) = 100% - 45% = 55% = 0.55Probability of testing for no oil:
P(test no oil) = 0.55*0.8 = 0.44Correct choice is C
9. The diagram below shows a plan for a park. ABCD is a rectangle. APB and DQC are semicircles
centred at X and Y. Given AB = 7 cm and AC = 25 cm. Calculate the perimeter of the park in cm.
Answer:
this is the answer please give brainliest
Mariana spent $166.50 on games played at a laser tag arena
last year. If the laser tag arena charges $4.50 per game, how
many games did Mariana play at the arena last year?
Answer: 37
Step-by-step explanation:
divide the total that she spent over how much each game is (166.50/4.50). this will give you the number of games that she played.
What is m∠CDE?
A circle with center point A and four chords BE,ED,DC,CB joins to make a trapezoid. The angle at BED is given as 62 degree and also arc angles BE and BC measuring 90 degree and 64 degree respectively
A. 45
B. 62
C. 64
D. 77
Answer:
45°
Step-by-step explanation:
Angle CDE is half of a right angle
1. 90°/2 = 45°
I'm not good at this stuff i need help quick pleaseeeeee
In the function, f(x) = 3 − sin(x + π), three transformations have been applied. Briefly describe the three transformations.
Answer:
The three transformations used are -
Vertical shift
Phase shift
Period
Step-by-step explanation:
Given - Given the function, f(x) = 3 − sin(x + π)
To find - In the function, three transformations have been applied. Briefly describe the three transformations.
Proof -
Given that, The function is f(x) = 3 − sin(x + π)
We know the
The general form of sine function is -
y = Asin(Bx + C) + D
where
A is the Amplitude
The period is [tex]\frac{2\pi }{B}[/tex]
Phase (Horizontal) shift is C
Vertical Shift id D
Here, The function is f(x) = 3 − sin(x + π)
By Comparing with General form of sin function, we get
-1 is the Amplitude
The period is 2[tex]\pi[/tex]
Phase (Horizonal) shift is [tex]\pi[/tex]
Vertical shift is 3
The three transformations used are -
Vertical shift
Phase shift
Period
A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of so trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described? + 0 1 + 3 N + 4 5 6 7 8 9 10 • : 6 0 1 + 2 w+ 4 5 6. + 8 9 7 10 0 10 20 30 40 50 60 70 80 90 100 D 0 10 20 30 40 50 60 70 80 90 100 0 1 2 + +0 다. 4 D+ + ••• 00+ 6 10
The dot plot in option E is correct.
What is sample size?
Choosing the number of observations or replicates to include in a statistical sample is the process of determining sample size. Any empirical study whose objective is to draw conclusions about a population from a sample must take the sample size into consideration.
Finding your sample size in five steps
Clarify the term "population size" or "people"
Specify your error margin.
Decide how confident you are.
Calculate the expected variance.
Decide on the sample size.
As long as it doesn't go over 1,000, 10% of the population serves as a good maximum sample size.
The dot plot in option E is correct.
Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.
On X axis, we take no. of successes out of 10.
Hence it having 0 to 10 numbering.
Hence, the dot plot in option E is correct.
To know more about sample size, click on the link
https://brainly.com/question/28583871
#SPJ4
combine like terms:
Like terms for the given data are: 17x² and 3x²; -3xy and -2xy. Combining the like terms we get: 20x² and -5xy
What is like terms?In algebra, the term "equal terms" refers to words with the same variable to the same power.
Similar variables and powers are called similar words in algebra. Matching coefficients is not required. When two or more words do not share the same variable or power, they are called inequal terms. The order of both variables is irrelevant unless there is a power. All of these have the same terminology.
17x² and 3x²
-3xy and -2xy
Combine the same terms obtained.
17x² + 3x² = 20x²
-3xy + (-2xy)
= -3xy -2xy
= -5xy
To know more about like terms refer to:
https://brainly.com/question/4680455
#SPJ1
What is the median for the following set of data?
5, 7, 8, 10, 12, 12
A.12
B.10
C.9
D.7
Answer:
C.)9
Step-by-step explanation:
You add up all your data to get 54 and divide by the amount of numbers you had in the data which was 6. So if you divide 54 by 6 you get 9.
Will mark brainlist if answered right =)
Answer:
Hello! answer: 1/2 and reduction
Step-by-step explanation:
a scale factor of 1/2 was applied because you do 3.4 ÷ 2 = 1.7 so thats 1/2 scale factor and its a reduction because the triangle is getting smaller then the original triangle hope that helps!
together Larry and Lenny have $\$$35. Larry has two-fifths of Lenny's amount. How many more dollars than Larry does Lenny have
The answer which we get after calculating from the data given is that Larry has 15 dollars more than Lenny.
Let the amount which Lenny is having be x
then the amount which Larry is having will be (2/5)x
and on combining them it makes $35 .
Which means, x + 2x/5 = 35
On simplifying this equation we will get ,
(7/5)x= 35 ,
multiplying both the sides by 5/7
x= (5/7)*35 = $25
Therefore , Lenny is having 4 25.
So Larry must be having , $(35 - 25) = $10
So , we can conclude that Lenny has more dollars. The difference is of 15 dollars.
To learn more about equations
brainly.com/question/29168024
#SPJ4
would you earn a greater total commission with Sara or Ravi?
The current ratio of Sara's sales to Ravi's sales is 100:2
Sara's pieces of art sell for $25 each your commission is 60%
Ravi's pieces of art sell for $2000 each your commission is 25%
as a professional artist assume you will make pieces of art that sell at the same sales ratio as the artist with whom you apprenticed. would you earn more as a professional after apprenticed for Sara or Ravi?
As a professional artist and judging from the current sales ratio and commission rates, one would earn more if one apprenticed for Sara.
Which of Sara and Ravi guarantees more earnings after apprenticeship?As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.
Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.
Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.
Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.
Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.
On this note, one would earn more if one apprenticed for Sara.
Read more on commission percent;
https://brainly.com/question/22258082
#SPJ1
Finn jumped 200 times in 10 hours. At what rate, how many times would he jumped in 12 minutes?
Answer: 4 times
Step-by-step explanation: I got 4 times. Here's how to solve it:
Set up a proportional relationship, but first, we need to convert 10 hrs into mins:
1 hour = 60 mins
To find how many minutes are in 10 hours, we multiply 60 by 10, which equals 600.
So, therefore there are 600 mins in 10 hours. Now, we can set up our proportional relationship:
[tex]\frac{200}{60} = \frac{?}{12}[/tex]
So, if we know 12 is a factor of 60, we should divide 60 by 12, and we should get 5. So, now we do the same with the 200. We do 200 / 50, and we get 4. I hope this helps!
Nic borrowed $350 to buy a bow. The finance charge on the loan was $25 and the
term on the loan was 45 days. What was the APR for Nic's loan?
1 pts
In answering the question, we discovered that a sample size of 20 was required in order to reach this conclusion.
How big a sample is it?The sample size is the number of observations used to estimate a certain population. The population was used to determine the sample size.
The act of promoting a product to increase sales is known as advertising. Based on the scenario given, the advertisement is misleading for the following reasons:
For this finding to be reliable, a sample size of 20 samples is rather small. Although the company was aware that the fertilizer treatment might get rid of weeds in approximately 2 weeks, customers said it would take 4 weeks for all of the weeds to die.
To know more about sample size, visit:
brainly.com/question/25894237
#SPJ1
9) The dog pen at doggy daycare has a length of 29 feet and a width of 18 feet.
What is the area of the dog pen?__
What is the perimeter of the dog pen?_
Answer:
The area of the dog pen is 522 [tex]ft^2[/tex]. (feet squared)
The perimeter of the dog pen is 94 feet
Step-by-step explanation:
Area
Here is the formula for the area of a rectangle.
[tex]A=lw[/tex]
We are given
[tex]l=29\\w=18[/tex]
Lets evaluate [tex]A[/tex].
[tex]A=29*18\\A=522[/tex]
Perimeter
Here is the formula for the perimeter of a rectangle.
[tex]P=2w+2l[/tex]
We are given
[tex]l=29\\w=18[/tex]
Lets evaluate [tex]P[/tex].
[tex]P=2l+2w\\P=(2*29)+(2*18)\\P=58+(2*18)\\P=58+36\\P=94[/tex]
Which equation below best models the line of best fit for the data?
y=2x+1
y=-2x+1y=−2x+1
y=2x+20y=2x+20
y=-2x-20y=−2x−20
Answer:
y=-2x-20y=−2x−20
Step-by-step explanation:
best models the line of best fit for the data
which expression is equivalent to -3(4x-2)-2x
Answer:
d
Step-by-step explanation:
-3(4x+2)-2x
-12x+6-2x
-14x+6
Answer:
*error* error* This account is here to assist CodeName: ELA/ LANGUAGE ARTS/ ENGLISH. Please say RESET in order for me to go back to ELA/ LANGUAGE ARTS/ ENGLISH.
Step-by-step explanation:
-7x+y=-19 In standard form
Answer: x= 1/7y + 19/7 (Standard form will be:7x−y=19)
Step-by-step explanation:
Step 1: Add -y to both sides.
−7x+y+−y=−19+−y
−7x=−y−19
Step 2: Divide both sides by -7.
−7x/−7
= −y−19/−7
x= 1/7y + 19/7
How fast is a motorcycle that is going 6 miles in 4 minute?
Answer:90
Step-by-step explanation:
Write an equation in slope-intercept form of the line that passes through the points (-5,-12) and 2,9) .
The equation is y=
Answer:
y=3x+3
Step-by-step explanation:
PLEASE HELP
G(Ax)) may not be equal to HG(x)).
O A. True
O B. False
Answer:
A. True
・ᗜ・ ¯\_(ツ)_/¯
Please help me with this
Answer:
2. David practices the most hours of soccer.
3. Jessie and Victor.
Step-by-step explanation:
3. On the x-axis, it shows that David practices the most hours out of all the friends.
2. This is just self explanatory!
Answer:
1. Title: Number of Hours Soccer was Practiced
Label X: Hours Label Y: Names of Maria's Friends
3. David practices the most
4. Jessie and Victor
Find the area of the right triangle below.
9m
4m
Area = 1/2*base*height = 1/2*9*4 = 18 sq.m
The length and breadth of the three rectangles are as given below:(a) 9 m and 6 m(b) 17 m and 3 m(c) 4 m and 14 mWhich one has the largest area and which one has the smallest?Solution:
We will be using the area of rectangle formula to calculate the areas of the three rectangles given.
(a) Length(l) = 9 m and Breadth(b) = 6 m
Area of rectangle = l × b
= 9 × 6
= 54 m2
(b) Length(l) = 17 m and Breadth(b) = 3 m
Area of rectangle = l × b
= 17 × 3
= 51 m2
(c) Length(l) = 4 m and Breadth(b) = 14 m
Area of rectangle = l × b
= 4 × 14
= 56 m2
Therefore, the area of the rectangle with the dimensions 4m and 14m having an area of 56 m2 that is (c) has the largest area whereas, the area of the rectangle with dimensions 17m and 3m having an area of 51 m2 that is (b) has the smallest area.
To be learn more about rectangle refer to:
https://brainly.com/question/29123947?referrer=searchResults
#SPJ1
T h e r e a r e 235 seven t h - g r a d e st u d e n t s g o i n g o n a fi e l d t r i p . T h e sc h o o l h a s 5 b u se s t o t a k e t h e st u d e n t s. E a c h b u s h a s 22 se a t s, a n d 2 st u d e n t s c a n si t i n e a c h se a t . B a se d o n t h i s i n f o r m a t i o n , h o w m a n y st u d e n t s w i l l n o t b e a b l e t o r i d e o n a b u s f o r t h e fi e l d t r i p ?
The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of students for the trip = 235 students
The number of buses = 5 buses
The number of students in a bus be = B
Now , each seat on the bus can occupy = 2 students
So , 22 seats can occupy = 22 x 2 students
22 seats in the bus can occupy = 44 students
So , the number of students in a bus B = 44 students
And , the total number of students in 5 buses = 5 x number of students in a bus B
Substituting the values in the equation , we get
The total number of students in 5 buses = 5 x 44
The total number of students in 5 buses = 220 students
So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses
Substituting the values in the equation , we get
The remaining number of students A = 235 - 220
The remaining number of students A = 15 students
Therefore , the value of A is 15 students
Hence , the number of students is 15 students
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
The entrance fee for the carnival is $7and the cost for a ticket for a
ride is $.25.
a. Write an equation for the total cost (C) if you go to the carnival
and ride r number of rides.
b. What is the total cost if you ride 15 rides?
Answer:
Step-by-step explanation:
Consider the following:
a) y=0.25x+7
b) $10.75
Explanation:
a)
y=mx+b is the slope-intercept form.
B is our Y intercept meaning any fee or initial charge that adds to total cost. In this situation, the initial fee of $7 is our Y-Intercept. . Our mx is the slope. A slope increases based on the amount (x) of certain things you have. In this situation, you are buying maybe 1, 2 or 3 tickets and each ride costs $0.25.
Our x remains the same, that is where we plugin the amount of tickets we will buy (x). The M value is the price per ticket which as said, is $0.25 per. Our slope therefore will be 0.25x.
Combining our Y-Intercept and our Slope will leave us with y (total cost) = 0.25x + 7
b)
We have found our slope, 0.25x+7
Now, we have to plugin our number of rides (x) which is 15.
If done correctly it should be 0.25(15)+7 and that is equal to $10.75 for 15 rides.
knowing the difference between an experimental group and a control group is most relevant to understanding the nature of: group of answer choices random sampling. replication. hindsight bias. independent variables.
The experimental group is given the experimental treatment, and the comparison group is statistically significant.
Which three attitudes are the basis of the scientific viewpoint?Curiosity, scepticism, and humility are described by historians of science as the three attitudes that form the bedrock of the scientific viewpoint. Larger, more representative sample sizes aid in the production of accurate and valid data.When random sampling is used, every member of the population has an equal chance of being chosen, resulting in the collection of a representative sample. The odds of generalising the study's findings to the population increase with the use of a random sample. The study's margin of error is reduced with higher study sample sizes.) Researcher control over the possibility of reporting false-negative or false-positive findings is made possible by larger sample sizes. Results will be more precisely predicted with a larger sample size.To learn more about random sampling refer to :
https://brainly.com/question/24466382
#SPJ4
Solve for s.
Give an exact answer.
63 – 4= 8(2+1/4s)
Answer:
s=5
Step-by-step explanation:
6s-4=8(2+1/4s)
6s-4=16+2s
4s-4=16
4s=20
s=5
Answer:
5
Step-by-step explanation:
6s-4=8x2 + 8x1/4s
6s -4 =16+2s
6s-2s = 16 +4
4s=20
s=5
HELP PLSSS I NEED THIS QUICK!!!!!
Answer: Its B
Step-by-step explanation:
What is the area of the shaded region in the archery target? Use 3.14 for pi.
Answer:
690.8 in^2
Step-by-step explanation:
First find the area of the three circles, by doing 3.14 r^2
With the innermost circle, 3.14 6^2 --> 113.04
With the second circle, 10 inches + 6 inches (inner circle radius), 3.14 16^2 --> 803.84.
With the outermost circle, you don't need it for the problem.
Then, we do subtraction to find the area of the shaded region, removing the "dount hole".
803.84 - 113.04 = 690.8 in^2