Answer:
Non-existent is the answer.
Answer: Choice D is correct. The limit does not exist.
========================================================
Explanation:
Let's see what happens when we approach 0 from the left side.
So we could start at x = -1 and get closer to 0, but never actually get to that exact value.
If x = -1, then
\(\frac{x}{|x|}=\frac{-1}{|-1|}=\frac{-1}{1} = -1\)
Now let's try x = -0.5
\(\frac{x}{|x|}=\frac{-0.5}{|-0.5|}=\frac{-0.5}{0.5} = -1\)
You should find that any negative x value will lead to an output of -1.
You can make a table of values to help see this.
-----------------------
In short, as x approaches 0 from the left, the y value will approach -1.
We would then write
\(\displaystyle \lim_{x\to 0^{-}}f(x) = -1\)
This is the left hand limit which I'll abbreviate as LHL.
-------------------------
For similar reasoning, the RHL (right hand limit) is
\(\displaystyle \lim_{x\to 0^{+}}f(x) = 1\)
Because the LHL and RHL aren't the same value, this means that the limit at x = 0 does not exist. The two sides do not approach the same meeting point. It's like two cars, on two separate roads, that don't meet up. The roads need to connect.
Check out the graph below.
Side note: we avoid division by zero errors when we specifically state that x is nonzero for the first piece of that piecewise function.
Can anyone prove this?
Answer:
Rewrite \(csc^4x-cot^4x\) by applying exponent rule \(a^{bc}=(a^b)^c\):
\(\implies (csc^2x)^2-(cot^2x)^2\)
Apply difference of two squares formula \(x^2-y^2=(x+y)(x-y)\):
\(\implies (csc^2x+cot^2x)(csc^2x-cot^2x)\)
Using trig identity \(1+cot^2x=csc^2x \implies 1=csc^2x-cot^2x\)
\(\implies (csc^2x+cot^2x)(1)\)
\(\implies csc^2x+cot^2x\)
Select the possible dimensions of a rectangular prism with volume of 48 in.
Answer:
6 in * 4 in * 2 in
Step-by-step explanation:
Given the following data;
Volume of rectangular prism = 48 in³
To find its possible dimensions;
Volume of rectangular prism = length * breadth * height
48 = length * breadth * height
From the given options, option B is most likely to be its dimensions.
Where;
Length = 6 in
Breadth = 4 in
Height = 2 in
Substituting into the formula, we have;
48 in = 6 * 4 * 2
48 in = 48 in
WILL GIVE BRAINLIEST PLEASE HELP!
The correct statement regarding the angle measures is given as follows:
m < 1 + m < 4 > m < 3.
How to obtain the angle measures?The given angle measure is as follows:
m < 3 = 119º.
Angles 3 and 4 form a linear pair, meaning that they are supplementary, that is, the sum of their measures is of 180º.
Hence the measure of angle 4 is given as follows:
m < 4 + m < 3 = 180º.
m < 4 = 180º - 119º
m < 4 = 61º.
Angles 1 and 4 are opposite by the same vertex, hence they are congruent, thus the measure of angle 1 is given as follows:
m < 1 = m < 4
m < 1 = 61º.
Hence:
m < 1 + m < 4 = 2 x 61
m < 1 + m < 4 = 122º
122º > 119º
m < 1 + m < 4 > m < 3.
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plssss helppp meeeee
Answer:
890 1/2 or 890.5
Step-by-step explanation:
Answer:
890.5 ft²
Step-by-step explanation:
Formula to find rectangular area
Area = A = L × W
So put values
R 1 A 1 = 24.5 × 18 = 441
R 2 A 2 = 14.5 × 18.5 = 268.25
R 3 A 3 = 12.5 × 14.5 = 181.25
Add them up
441 + 268.25 + 181.25 = 890.5
A house on the market was valued at $365,000. After several years, the value increased by 8%. By how much did the house's value increase in dollars? What is
the current value of the house?
Answer:
394,200
Step-by-step explanation:
You have to multiply the house value by 1.08 or 108%
365,000*1.08=394,200
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables show the distribution responses?
answer choices
Graph i
Graph ii
Graph iii
Graph iv
Graph v
Graph ii shows that 150 people preferred eating ice cream from a cone, while 60 people preferred eating ice cream from a cup. There was no association between age and preferred method of eating ice cream.
Graph ii is a table that shows the distribution of responses to the survey about preferred method of eating ice cream. The table shows that out of the 210 people surveyed, 70 were adults and 140 were children. Of the 210 people surveyed, 150 indicated the cone as the preferred method of eating ice cream, while 60 indicated the cup as the preferred method. This table indicates that there is no association between age and preferred method of eating ice cream, as the responses were evenly distributed between adults and children. This information can be used to determine the preferences of customers at the ice-cream store and can help inform decisions about how to serve the ice cream. For example, the store may choose to provide more cones than cups based on the survey results. Additionally, this table can be used to compare the preferences of different demographic groups, although in this case the survey showed that there was no association between age and preferred method of eating ice cream.
Adults: 70 people surveyed, 35 preferred cone, 35 preferred cup
Children: 140 people surveyed, 115 preferred cone, 25 preferred cup
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Ryan orders a pizza with a 20 inch diameter and asks for a cheese stuff crust along its border . The cheese filled border measures blank inches
The measure of angle 1 is 56 degrees. If angle 4 is vertical find it’s measure
The measure of angle 4 is 56 degrees.
What is a vertical angle?Vertical angles are the angles that are formed when two lines intersect each other. These are angles on the opposite side of the intersection. These angles are equal.
The measure of angle 4 can be found as shown below:The measure of angle 1 is given as 56 degrees.
It is given that angle 4 is a vertical angle with respect to angle 1.
We know that vertical angles are equal in measurement.
Therefore, we can come to the conclusion that angles have the same measure. We can thus confirm that angle 4 = angle 1 = 56 degrees.
Thus, we have found that the measure of angle 4 is 56 degrees.
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What’s the answer I need help with this last problem
Answer:
Hope the picture will help you
Verify the identity.
sin x/1-cos x = csc x + cot x
Answer:
See below for proof
Step-by-step explanation:
\(\displaystyle \frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{(1-\cos x)(1+\cos x)}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{\sin^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\frac{1}{\sin x}+\frac{\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\csc x+\cot x\)
You are considering to invest in a franchise for a coffee shop in your neighborhood. To understand the revenue potential, you decide to visit a coffee shop from the same chain next to your neighborhood. In the next few months, you visit this coffee shop at random times between 6am and 9am. You observe that the line (queue) averages about 13 customers and it takes about 3 minutes to get in and out of the coffee shop. Assuming this is a typical experience and each customer spends about $5 per visit, what is the revenue potential per hour of this coffee shop? Hint: Calculate the number of customers arriving per minute (i.e., λ). Convert this to customers per hour. Then, calculate the revenue from these customers (each customer spends about $5, on average)
Based on the information given, the computation shows that the revenue from the customers will be $1300.
How to calculate the revenueThe following can be deduced from the information given:
Line average = 13 customers.Time taken to get in and out = 3Amount spent by each customer = $5Therefore, the number of visits in an hour will be:
= 60/3
= 20 visits
Therefore, the revenue every hour will be:
= 20 × $5 × 13
= $1300
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is this a function?
Answer:
yes srry if I'm wrong
.................
...
Which of the following are disadvantages of the mode?
For many sets of data there are multiple modes.
The mode is affected by extremely large and small values.
For many sets of data there is no mode.
the mode can only be computed for interval-level data or higher
The disadvantages of the mode are: For many sets of data there is no mode.
The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.
However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.
The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.
The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.
The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.
The correct option is: For many sets of data there is no mode.
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2/3% of 300
Find the percent by making a proportion.
Answer:
Step-by-step explanation:
try this
take a calculator and do 2 divided by 3
you get 0.66666666666666666666
but now, immediately press the multiplication button,
and type 300 and press enter
the answer is 200
epic
What are the slope and y-intercept in the equation y = 7 + 5x + 2x + 4?
Answer: slope is 7 and y-intercept is 11
Step-by-step explanation:
y = 7 + 5x + 2x + 4
combine like terms
y = 11 + 7x
rearange
y = 7x + 11
slope is 7 and y-intercept is 11
\(\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}\)
What is the slope of the line y=7+5x+2x+4? What about the y-intercept?
\(\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}\)
First, we need to combine like terms:-
\(\Large\text{y=7+4+5x+2x}\)
\(\bigstar\) On simplification,
\(\Large\text{y=11+7x}\)
\(\bigstar\) We can rearrange the terms a little:-
\(\Large\textit{y=7x+11}\)
Now we can easily determine the slope and the y-intercept of the line.
Slope = number multiplied by x
y-intercept = a number added to or subtracted from x
Henceforth, we conclude that
\(\Large\text{Slope=7 \& y-intercept=11}\)
Good luck with your studies.#TogetherWeGoFar
\(\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}\)
Brooklyn is going to invest in an account paying an interest rate of 3.5% compounded continuously. How much would Brooklyn need to invest, to the nearest ten dollars, for the value of the account to reach $64o in 9 years?
Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.
To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:
A = \(Pe^(^r^t^)\)
where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:
640 = \(Pe^(^0^.^0^3^5^*^9^)\)
640 = Pe^0.315
P =\(640/e^0^.^3^1^5\)
P = 432.43
Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.
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If there are
12 books in the rack, a person has to choose 5
out of them. In how many ways
can he choose books,if one
book is never selected?
Answer:
462 ways
Step-by-step explanation:
One book never selected means 12 - 1 = 11.
So to find the number of ways, 11C5 which equals to: 11!/(5!(11-5)!) = 462
In planning her retirement, Liza deposits some money at 4% interest, with twice as much deposited at 4.5%. Find the amount deposited at each rate if the total annual interest income is $2080.
She deposited $___ at 4% and $____ at 4.5%.
She deposited $16,000 at 4% and $32,000 at 4.5%
She deposited $16,000 at 4% and $32,000 at 4.5%.
Let's assume Liza deposited an amount x at 4% interest. According to the given information, she deposited twice as much, which is 2x, at 4.5% interest.
To calculate the interest income from the deposits, we'll use the formula: Interest = Principal × Rate × Time.
At 4% interest, the interest earned is 0.04x (4% expressed as a decimal multiplied by x).
At 4.5% interest, the interest earned is 0.045(2x) (4.5% expressed as a decimal multiplied by 2x).
We know that the total annual interest income is $2080. Therefore, we can write the equation:
0.04x + 0.045(2x) = 2080
Simplifying the equation:
0.04x + 0.09x = 2080
0.13x = 2080
x = 2080 / 0.13
x ≈ 16,000
Liza deposited approximately $16,000 at 4% interest, and since she deposited twice as much at 4.5% interest, she deposited approximately $32,000 at 4.5% interest.
Therefore, she deposited $16,000 at 4% and $32,000 at 4.5%.
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Please Help me!!!!!!!!!
Answer:
I THINK it’s function
Step-by-step explanation:
A store has clearance items that have been marked down by 50%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.
Let's assume the original price of an item is $100.
The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.
The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.
Therefore, the final price you end up paying after both discounts is $22.50.\
To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:
Percent of original price = (final price / original price) * 100
In this case, the final price is $22.50 and the original price is $100:
Percent of original price = ($22.50 / $100) * 100
= 0.225 * 100
= 22.5%
Therefore, you end up paying 22.5% of the original price after the discounts.
It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.
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Mark and Jacob share 5 yards of ribbon equally. How much ribbon will each get?
Answer:
2.5 each
Step-by-step explanation:
dividing by 2......
Answer:
2.5 yards of ribbon.
Step-by-step explanation:
5 divided by 2= 2.5
Hope this helps :)
Write x^2 - 8x + 10 in the form
(x + a)^2 + B
\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)
three blocks are placed together as shown below. 3.8cm 8.7cm 9.4cm
Which is the coefficient? 10x-6
Explanation:
The coefficient is the number multiplying a variable. If there's a number alone - not multiplying a variable - that's called a constant
Answer:
The coefficient is 10
11 over 7=6 over v what is v
Answer:
42/11
Step-by-step explanation:
11/7 = 6/v
cross multiply:
11v = 6x7 = 42.
v = 42/11 ≈ 3.81
Please help its very important to me ( dont guess or steal) ( give proof of answer for brainiest)
Answer:
I say A if you need anymore help just tell me!!!
What is the inverse of f(x) = 1/3x + 2 ?
A. h(x) = 1/3x + 2
B. h(x) = 1/3x - 2
C. h(x) = 3x - 2
D. h(x) = 3x - 6
Pls provide an explanation. I need help, and I will mark the person who helps me understand this Brainliest.
Answer:
D
Step-by-step explanation:
We are given the function:
\(\displaystyle f(x) = \frac{1}{3} x + 2\)
And we want to find its inverse h.
To find the inverse of a function, we can switch the y and x variables and solve for the new y. This will be our inverse.
We begin with:
\(\displaystyle f(x) = y = \frac{1}{3} x+ 2\)
Switching the variables yield:
\(\displaystyle x = \frac{1}{3}y + 2\)
And solving for y yields that:
\(\displaystyle y = h(x) = 3x - 6\)
In conclusion, the inverse function to f is 3x - 6. Our answer is D.
To understand why we switch the variables, recall that by the definition of inverse functions, if f(a) = b, then f⁻¹(b) = a. So, by switching the variables, we are essentially solving for f⁻¹(x).
3/5x+1/4=-1/2 standard form
Answer:
Hello there your answer is 12 x + 5 y = − 10!
Evaluate the function rule for the given value y=12•3x for x=-2
Answer:
-72
Step-by-step explanation:
We just have to plug in -2 for x so the answer is 12 * 3 * (-2) = -72.
Your score = 68, Need 78 or higher to score earn an A, Class mean = 72.5, Standard deviation = 4.3
With the given mean, you need a score of 78 or higher for an A, and your score is below that, you will not receive an A in the class.
What is mean?
In statistics, the mean is the numerical average of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.
To determine your performance relative to the class, we can use z-scores, which indicate the number of standard deviations your score is away from the mean.
First, we need to calculate the z-score for your score:
z = (your score - class mean) / standard deviation
z = (68 - 72.5) / 4.3
z = -1.0465
Your z-score is -1.0465.
We can interpret this z-score using a standard normal distribution table or calculator. Approximately 15.9% of the distribution falls below a z-score of -1.0465, meaning your score is below about 15.9% of the class.
To determine the grade you will receive, we need to know the grading scale for the class. Assuming an A is 90 or above, the grade cutoffs might look something like this:
A: 90 or above
B: 80-89
C: 70-79
D: 60-69
F: below 60
Since you need a score of 78 or higher for an A, and your score is below that, you will not receive an A in the class.
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