Using the definition of continuity and the properties of limits to show that the function is continuous at the given number f(x)=-5
continuity of a real function is provided generally in a calculus’s introductory course in terms of a limit’s idea.
First, a function f with variable x is continuous at the point “a” on the real line, if the limit of f(x), when x approaches the point “a”, is equal to the value of f(x) at “a”, i.e., f(a).
Second, the function (as a whole) is continuous, if it is continuous at every point in its domain.
We know that the value of f near x to the left of a, i.e. left-hand limit of f at a and the value of f near x to the right f a,
i.e. right-hand limit are equal, then that common value is called the limit of f(x) at x = a. Also,
a function f is said to be continuous at a if limit of f(x) as x approaches a is equal to f(a).
A function f is continuous at a number a if
[tex]\lim_{x \to\n} f( x) = f(a)[/tex]
f(x) = [tex]x ^3x^4 5[/tex]
= [tex]\lim_{x \to \ a} x^3 * \lim_{x \to \ a} x^4 *5\\= (-1)^3 * (-1)^4 *5\\= -1 * 1* 5\\= -5[/tex]
Using the definition of continuity and the properties of limits to show that the function is continuous at the given number f(x)=-5
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A fair coin is tossed 10 times, which of the following outcomes are contradict to the law of large numbers?A)FIVE HEADS ARE OBSERVEDB) NO TAILS ARE OBSERVEDC) SIX HEADS ARE OBSERVEDD) TWO TAILS ARE OBSERVEDE) NONE OF THE ABOVE
The outcome that contradict the law of large numbers is option E) NONE OF THE ABOVE.
The law of large numbers states that as the number of trials in a random experiment increases, the average of the results will approach the expected value.
A) FIVE HEADS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have five heads in ten tosses of a fair coin, and as the number of trials increases, the average of heads will approach the expected value of 0.5.
B) NO TAILS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have no tails in ten tosses of a fair coin, and as the number of trials increases, the average of tails will approach the expected value of 0.5.
C) SIX HEADS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have six heads in ten tosses of a fair coin, and as the number of trials increases, the average of heads will approach the expected value of 0.5.
D) TWO TAILS ARE OBSERVED: This outcome is not contradictory to the law of large numbers as it is possible to have two tails in ten tosses of a fair coin, and as the number of trials increases, the average of tails will approach the expected value of 0.5.
E) NONE OF THE ABOVE: None of the above outcomes are contradictory to the law of large numbers as each of them is possible in ten tosses of a fair coin and as the number of trials increases, the average of heads and tails will approach the expected value of 0.5.
Therefore, the answer is E) NONE OF THE ABOVE.
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Clara is training for a race in the summer. Every day she jogs the same number of miles. She also rides her bicycle 5.5 miles each day. During a 5-mile training period, she jogs and rides a total of 50 miles. How many miles does Clara jog each day during training
The required number of miles Clara jogs each day during training is 4..5 miles.
What is Miles?You can anticipate that it will take between 1 and 2.5 minutes to travel one mile because the majority of roads have speed limits between 25 and 60 mph. Do not allow algebra cause you to lose focus on the road! Also keep in mind how crucial it is to properly insure your vehicle.
According to question:Let miles does Clara jog each day during training be x.
During a 5-day training period, she jogs and rides a total of 50 miles.
5x + 5(5.5) = 50
5x + 27.5 = 50
5x = 50 - 27.5
5x = 22.5
x = 4.5 miles.
Thus, Clara jogs 4.5 miles each day.
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Sam saved $35 buying the suit at a 20% off sale what was the regular price of the suit
what does 6 1/5 i wonder what it is
Answer:
6 1/5= 31/5
Step-by-step explanation:
At a construction job for a gallery there are 33 painters. Of these painters, 21 of them
are painting the interior of the gallery. What percent of these painters are painting the
interior? Round your answer to the nearest tenth if necessary.
Answer:
63.6%
Step-by-step explanation:
21 out of 33 is what we are working with here. Divide.
21/33
= 0.636363...
Times by 100 to change from a decimal to a percent (you know "per cent" means "per hundred")
= 63.636363...
Round to the nearest tenth as per the instructions.
= 63.6%
Please help with precal problem?
The population of the world was 5.7 billion in 1995 and increases according to the exponential growth model where the growth rate is assumed to be 2%. When will the population double?
P(t) = P₁ (1+r)t
A) 2012
B) 2027
C) 2029
D) 2030
E) None of these
Answer:
D) 2030
Step-by-step explanation:
You want to know when the population will double from its value in 1995 if it increases at 2% per year.
MultiplierThe multiplier for t years is given as (1 +r)^t. We want to find t such that this value is 2 when r = 0.02.
2 = 1.02^t
log(2) = t·log(1.02)
t = log(2)/log(1.02) ≈ 35.003
The year the population doubles will be ...
1995 + 35.003 = 2030.003
The population will double in year 2030, choice D.
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Use the dropdowns to complete the following statement.
The measure of an _____ angle of a triangle is _____ the _____ of its two ____ angles.
First dropdown: corresponding, interior, exterior, alternate
Second dropdown: equal to, less than greater than
Third dropdown: sum, quotient, difference, product
Fourth dropdown: adjacent, supplementary, remote interior, exterior
A family’s expenses are $1,200. One parent makes $850. Must the other earn $400 for both incomes to equal expenses?
if 2x ≤ g(x) ≤ x4 − x2 2 for all x, evaluate lim x→1 g(x).
The limit value is equal to 2 .
Given,
2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² + 2
According to sandwich theorem,
g(x)≤ f(x) ≤ h(x)
[tex]\lim_{x \to \ a} g(x) = \lim_{x \to \ a} h(x) = L[/tex]
Then,
L= [tex]\lim_{x \to \ a} f(x) = L[/tex]
Here we have,
2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² + 2
And so if we take the limit as x→1; then
[tex]\lim_{x \to \ 1} 2x = 2\\\\ \lim_{x \to \ 1} x^{4} - x^{2} + 2 = 2\\[/tex]
Thus we can apply the sandwich theorem,
[tex]\lim_{x \to \ 1} g(x) = 2[/tex]
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Correct expression:
2x ≤ g(x) ≤ [tex]x^{4}[/tex] − x² + 2
Find the volume of a room 14 feet by 16 feet with an 8-foot ceiling.
Answer:
Below
Step-by-step explanation:
Volume = L x W x H = 14 ft x 16 ft x 8 ft = 1792 ft^3
What are the domain and range of this relation? (8,-5) (2, 1) (6,2) (-1, 6) (-10, 1)
Answer: Domain Is always the x-input, while range will be the y-output.
Step-by-step explanation:
domain- -10,-1,2,6,8
Range- -5,1,2,6
A restaurant sells meals that range from $7.25 to $12.10. A kids meal that costs $2.35 is added to the menu.
Select whether the value of the statistic will increase, decrease, or cannnot be determined (if it would likely remain the same, select cannot be determined).
Median:
Mean:
Standard Deviation:
The value of the statistic will
Median: Cannot be determined.
Mean: Increase.
Standard Deviation: Cannot be determined.
What are the mean, median, and standard deviation?
Standard deviation (σ) is defined as the square root of the variance. It measures the variability about the mean of a data set: the closer to the mean, the lower the standard deviation.
Median: Cannot be determined.
The median is the middle value in a set of data and can only change if the new value added to the menu is in the middle of the existing range.
If the new value is added to the beginning or end of the range, the median will remain unchanged.
Mean: Increase.
The mean is calculated by summing all the values and dividing by the number of values.
Adding a new value to the menu will increase the total sum and therefore increase the mean.
Standard Deviation: Cannot be determined.
The standard deviation measures the amount of variation or dispersion from the mean.
Adding a new value to the menu may increase or decrease the standard deviation, but it depends on the specific distribution of values in the existing menu and how the new value fits into that distribution.
Without more information, it is not possible to determine whether the standard deviation will increase, decrease, or remain unchanged.
Hence, the value of the statistic will
Median: Cannot be determined.
Mean: Increase.
Standard Deviation: Cannot be determined.
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Which statement is true? answer choices.
a. 4 liters 300 milliliters > 4,000 milliliters. b. 4 liters 300 milliliters < 4,000 milliliters.
Accordingly, 1 ml (milliliter) is just 1/1,000 of a liter. Consequently, 1 ml is less than 1 l.
What is the difference between liters and milliliters?Small quantities of liquid are measured in milliliters. Liters can be used to measure bigger amounts of liquid. 1 ml is equal to 0.001 liter, or 1000 milliliters. The symbol for a milliliter is either ml or mL.
The metric prefix "m" stands for "milli," which denotes "1/1,000 of" in English. Accordingly, 1 ml (milliliter) is just 1/1,000 of a liter. Consequently, 1 ml is less than 1 l.
The smallest metric unit, the milliliter, measures the tiniest amount of liquid and is a thousandth of a litre. So, 1 liter is equal to 1000 milliliters.
Therefore, the correct answer is option b. 4 liters 300 milliliters < 4,000 milliliters.
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Which statement best describes the values of a and b in the regression model?
In the power regression model, a represents the initial value and b represents the growth factor.
In the power regression model, a represents the growth factor and b represents the initial value.
In the exponential regression model, a represents the initial value and b represents the growth factor.
In the exponential regression model, a represents the growth factor and b represents the initial value.
Answer:
this question to this question is 2
Hi can someone check my work for me! im unsure of my answers, please tell me if get any wrong! PLEASE HELP ASAPPP
Answer:
Step-by-step explanation:
all of them are correct!!!!! Great Job!!!!!
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?
a. To calculate the average daily sales over the course of seven days, multiply the total sales over the course of seven days by seven.
a. How much did they sell on average per day over the entire 7 days?The salesperson generated $36,000 in revenue in the first three days by selling an average of $12,000 per day.
The following four days saw sales of $9,000 on average, for a total of $36,000 ($4 days * $9,000/day). Sales for the seven days added up to $36,000 + $36,000 = $72,000. Thus, throughout the course of the entire seven days, the average daily sales were $72,000 / seven days, or $10,285.7.
b. How much does she make on average per hour for the day?b. We must aggregate the total earnings from both jobs and divide it by the total number of hours worked in order to determine the average hourly wage. Kelly puts in a total of 12 hours of work by working 5 hours at a restaurant and 7 hours at a retail store. She is paid $12 per hour at the retail location and $20 per hour at the restaurant, so her total pay for seven hours is $104. The daily average hourly wage is $104 divided by 12 hours, or $8.67.
c. How much did he earn on the last day?c. We must first calculate Henry's total earnings for the first 10 days, then deduct those earnings from the first 9 days to arrive at his earnings on the final day. The total income for the first 10 days was $1,200 (10 days * $120/day). Five days at a rate of $100 each brought in a total of $500. The next four days' earnings came to $520 (4 days * $130/day). For the first nine days, the total earnings were $500 + $520, or $1,020. Therefore, Henry's final day earnings were $180 ($1,200 – $1,020).
d. How many at-bats has Marcus had?d. The number of singles, doubles, triples, and home runs must be added up in order to determine the total number of at-bats. Marcus has 107 hits overall, which include 18 singles, 33 doubles, 2 triples, and 54 home homers. He has now played in 107 at-bats.
e.. What is Tyler's current Slugging Percentage? What is Tyler's Batting Average?e. The total bases (one base for a single, two bases for a double, three bases for a triple, and four bases for a home run) must be added together and divided by the total at-bats in order to determine the slugging percentage. Tyler has 235 total bases, which are calculated as follows: 74 singles * 1 base/single + 13 doubles * 2 bases/double + 11 triples * 3 bases/triple + 4 home runs * 4 bases/home run. His Slugging Percentage therefore equals 235 / 383 at-bats, or 0.616. Divide the total number of hits by the total number of at-bats to obtain the batting average. 383 at-bats x 74 hits Equals 0.193 for Tyler.
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The figure below is a square. Find the length of side x to the nearest tenth.
Answer:
3.7
Step-by-step explanation:
The length of the diagonal of a square is [tex]\sqrt{2}[/tex] times the side length.
[tex]\implies x=\sqrt{7}\sqrt{2} \approx 3.7[/tex]
Can you help solve the question attached
a) The best estimate for the probability of landing on black is,
= 11/50
b) This is the best estimate because it involves the largest number of trials.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given:
Gemma spun a spinner a total of 200 times and worked out the estimated probability of it landing on black after different numbers of spins.
Her results are shown in the table below.
a) The best estimate for the probability of landing on black is,
= 11/50
b) This is the best estimate because it involves the largest number of trials.
Therefore, all the required values are given above.
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Shelley’s resolution is to bike 192 miles each week. If she rides with a average speed of 9.6 mph and plans to ride an equal amount of time each day, about how many hours a day should she plan to ride?
Answer:(192/9.6)÷7=20/7
Step-by-step explanation:
Four angles in the quadrilateral Q have the ratio 2: 3: 3: 2. Give the names of the
two possible types of quadrilateral that Q could be.
Answer:
Parallelogram, Rhombus or a regular trapezium.
Step-by-step explanation:
Since all the units add up to 10 units, which is a factor of 180 degrees, all quadrilaterials work in this case as all quadrilaterals must have angles summing up to 180 degrees.
I might be wrong though. :(
Expand & simplify 4 ( p + 6 ) + 3 ( p − 2 )
Expanding and simplifying the expression:
4 ( p + 6 ) + 3 ( p − 2 ) = 4p + 24 + 3p - 6
= 7p + 18
So, the simplified expression is 7p + 18.
Answer:
[tex]4(p + 6) + 3(p - 2) \\ \longrightarrow \: 4p + 24 + 3p - 6 \\ solving \: the \: like \: terms \: together \: we \: get \\ \longrightarrow \:\boxed{ 7p + 18}[/tex]
hope helpful! :)
The density, d, of an object can be found by using the formula d=[tex]\frac{m}{v}[/tex], where m is the mass of the object and v is its volume. What is the density of an object that has a mass of 73,430 kilograms and a volume of 7 [tex]m^{3}[/tex]
The density of an object is 10490kg/m^3.
How to find the density?Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.
Density = (Total amount available)/(total space which contains that amount)
Given;
The mass of object= 73,430 kilograms
The volume of object= 7m^3
Now
D=mass/volume
D=73430/7
D=10490
Therefore, the density will be 10490kg/m^3.
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a triangle in which two angles, called base angles have equal measure, is called an isoceles traingle. in a certain isoceles triangle, the sum of the measures of the base angles is 88 degrees less than the measure of the remaining angle. find the measure of each angle
In a certain isoceles triangle, the sum of the measures of the base angles is 88 degrees less than the measure of the remaining angle. Then the measure of each angle is 44° and 92°.
Determine the measure of each angle
These are the specified parameters:
The sum of the measures of the base angles is 88° less than the measure of the remaining angle.
Large pedestal angle
a + a = 88
2a = 88
a = 88/2
a = 44°
Peak angle
a + a + b = 180
88 + b = 180
b = 180 - 88
b = 92°
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what is the solution to this system of equations
Answer:
[tex](-1, -2)[/tex]
Step-by-step explanation:
In this problem, we are asked to solve a system of equations given two equations each containing two variables: x and y. We can solve it using the substitution method.
First, we need to solve for a variable in terms of the other using one of the equations. I will solve for x in the first equation.
[tex]4x-7y=10[/tex]
↓ add [tex]7y[/tex] to both sides
[tex]4x=7y+10[/tex]
↓ divide both sides by 4
[tex]x=\dfrac{7y+10}{4}[/tex]
Now that we have solved for x in terms of y, we can substitute the solved x-value into the bottom equation.
[tex]3x + 2y = -7[/tex]
↓ substitute in solved x-value
[tex]3\left(\dfrac{7y+10}{4}\right) + 2y = -7[/tex]
↓ distribute 3
[tex]\dfrac{21y+30}{4}\right) + 2y\left(\dfrac{4}{4}\right) = -7\left(\dfrac{4}{4}\right)[/tex]
↓ rewrite all terms as fractions over 4
[tex]\dfrac{21y+30 + 8y}{4}\right)= -\dfrac{28}{4}[/tex]
↓ cancel denominators
[tex]29y+30= -28[/tex]
↓ isolate y's
[tex]29y = -28 - 30[/tex]
↓ simplify
[tex]29y= -58[/tex]
↓ divide both sides by 29
[tex]y = -2[/tex]
Now that we have solved exactly for y, we can solve for x using the substitution value we solved for earlier.
[tex]x=\dfrac{7y+10}{4}[/tex]
↓ substitute in y-value
[tex]x=\dfrac{7(-2)+10}{4}[/tex]
↓ simplify numerator
[tex]x=\dfrac{-14+10}{4}[/tex]
[tex]x=\dfrac{-4}{4}[/tex]
[tex]x = -1[/tex]
Finally, we can put the solved x and y values into a Cartesian coordinate in the form (x, y).
[tex](-1, -2)[/tex]
to estimate the mean score of those who took the medical college admissions test on your campus you obtain an srs of students. how large of an srs must you take
The size of a Simple Random Sample (SRS) for estimating the mean score of medical college admissions test takers on your campus depends on the desired level of precision and the variability of the population.
The sample size required to estimate the mean score of a population depends on the desired level of precision, the variability of the population, and the level of confidence desired. In general, a larger sample size is needed to estimate the mean of a population with high variability or when a high level of precision is desired.
On the other hand, a smaller sample size is sufficient if the population is relatively homogeneous or if a lower level of precision is acceptable. It's important to note that a sample size that is too small may result in an imprecise estimate, while a sample size that is too large may be unnecessarily wasteful. A statistician can help determine the appropriate sample size for a given situation.
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Rabia doe not currently have a job, but declined a job offer becaue he feel her kill merit better pay and a better poition. Which term can be ued to decribe Rabia? Check all that apply. Cyclically unemployed
dometically unemployed
frictionally unemployed
tructurally unemployed
till employed
unemployed
Rabia is currently classified as unemployed, option .D since she has no job and has declined a job offer.
She falls into the category of frictionally unemployed, which means she is unemployed due to the time it takes to find a job that meets her qualifications and salary needs.
This is different from someone who is cyclically unemployed, which means they are out of work due to economic conditions, or someone who is structurally unemployed, which means they are out of work due to changes in technology or other factors that eliminated their job.
Rabia is still employed in the sense that she is actively seeking employment, but she is not employed in the sense that she has no job.
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A ray is 23 feet below sea level, what is its elevation?
The elevation of the ray is -23 feet below the sea level
How to determine the elevatin of the rayFrom the question, we have the following parameters that can be used in our computation:
Elevation = 23 feet below the sea level
The elevation of a location is its height above a certain reference point, typically sea level.
If a location is 23 feet below sea level, its elevation is -23 feet.
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30,000,000,000,000 IN SCIENTIFIC NOTATION
The answer is 3.0 x 10^13
Answer: [tex]3x10^1^3[/tex]
Explanation: When writing a number in scientific notation, the decimal point should be placed or moved until the coefficient is higher than 1 and less than 10.
find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.
Given a quadratic function y = 36 - x² , the intervals over which the function is increasing is: (-∞ , 0) and the intervals over which the function is decreasing is: (0, ∞).
The standard form of a quadratic function is given by:
f(x) = ax² + bx + c
If a > 0, the graph of the function opens upward and the extreme point is the minimum one.
If a < 0, the graph of the function opens downward and the extreme point is the maximum one.
In this case, the function is: y = 36 - x²
Since the coefficient of the quadratic term is negative, or a < 0, then the graph opens downward and has a maximum point.
y = 36 - x² is already in the form of perfect square, hence, we can immediately compute:
x-intercepts : (-6,0) and (6,0)
y-(intercept = maximum point = (0, 36)
Before the maximum point, the function is increasing, while after the maximum point, the function is decreasing.
Hence,
increasing interval = (-∞ , 0)
decreasing interval = (0, ∞)
Your question is incomplete, most likely, it was:
Find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.
y = 36 - x²
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The um of age if two boy i 18. Three year ago one boy wa wa tree time older then the other. Find their preent age
The age of first boy is 15 and age of second boy is 3.
Now, According to the question:
The x and y-axis are two important lines of the coordinate plane. The x-axis is a horizontal number line and the y-axis is a vertical number line. These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate.
"Information available from the question"
The sum of ages of two boys are 18.
Let x be the first boy
and, y be the second boy.
x +y = 18
(x +3) = 3(y+3)
Calculate the product or quotient
x + 3 = 3y + 9
x = 3y + 9 - 3
x = 3y + 6
Now,
3y + 6 + y = 18
Calculate the sum or difference:
4y + 6 = 18
4y = 18 - 6
4y = 12
y = 12/4
y = 3
So, For the value of x:
x + 3 = 18
x = 18 - 3
x = 15
Hence, The age of first boy is 15 and age of second boy is 3.
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