The 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is expressed as f(x) ≈ P3(x) = a₀ + a₁(x - 4) + a₂(x - 4)² + a₃(x - 4)³.
Here, a₀, a₁, a₂, and a₃ are the coefficients that need to be calculated. To find these coefficients, we must use the Taylor series formula and the derivatives of f(x) evaluated at 4.
The Taylor series formula is Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!) (x-a)² + (f'''(a)/3!) (x-a)³ + ... +[tex](f^(n)(a)/n!) (x-a)^n[/tex].
The derivatives of f(x) evaluated at 4 are f'(4) = 1/2, f''(4) = -1/8, f'''(4) = -1/16.
Using these values, the coefficients of the 3rd-order Taylor polynomial can be calculated as a₀ = 2, a₁ = 1/2, a₂ = -1/8, and a₃ = -1/16.
Therefore, the 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is P3(x) = 2 + (1/2)(x - 4) - (1/8)(x - 4)² - (1/16)(x - 4)³.
Using this polynomial to approximate √14.03, we have P3(14.03) = 2 + (1/2)(14.03 - 4) - (1/8)(14.03 - 4)² - (1/16)(14.03 - 4)³ ≈ 3.76401097.
Therefore, the approximation of √14.03 using the 3rd-order Taylor polynomial is 3.76401097 to 8 decimal places.
Learn more about the Taylor polynomial:
brainly.com/question/2533683
#SPJ4
A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
5 15 two and a half
7
At this rate, how much sauce and oregano will be needed to make 7 servings?
Answer: To make 7 servings of the recipe, you will need:
Sauce: 7 servings * 15 cups/5 servings = <<7*15/5=21>>21 cups
Oregano: 7 servings * (2.5 tsp/5 servings) = <<7*(2.5/5)=1.75>>1.75 tsp
So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.
Step-by-step explanation:
They will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Now, To make 7 servings of the recipe, you will need:
Sauce:
⇒ 7 × 15 /5
⇒ 21 cups
Oregano: \
⇒ 7 × (2.5 /5 )
⇒ 1.75 tsp
So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ2
According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x³-7x+11?
0 +1.1.1.5
O
11
0 + 3.1.1.5,
45, +11
5
0 0 ±, ±3. 1. ±1, , 25, ±11
Answer:
1/5
-1/5
11/5
-11/5
1
-1
11
-11
Step-by-step explanation:
The Rational Root Theorem states that if a polynomial equation with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term (in this case, 11) and q is a factor of the leading coefficient (in this case, 5).
Using this information, we can determine that the potential rational roots of the polynomial f(x) = 5x³-7x+11 are all of the following:
1/5
-1/5
11/5
-11/5
1
-1
11
-11
Note that this list includes all possible rational roots of the polynomial, but not all of these roots will necessarily be actual roots. To determine which of these potential rational roots are actual roots, we would need to test them by plugging them into the polynomial and solving for x.
Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = Vf. (If the vector field is not conservative,enterDNE) F(x, y, z)= i + sin(z)j + y cos(z)k, f(x, y, z) =
The function f such that F = ∇f does not exist, and the answer is DNE (does not exist).
What is a vector field?Generally, To determine whether or not the vector field is conservative, we need to check if its curl is zero. The curl of the given vector field is:
curl(F) = ∇ x F
= (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k
Substituting in the values of the components of F, we get:
curl(F) = (-cos(z))i + (0)j + (-y sin(z))k
Since the curl of the vector field is nonzero, the vector field is not conservative.
Therefore, the solution is DNE, and the function f such that F = f does not exist (does not exist).
Read more about vector field
https://brainly.com/question/24332269
#SPJ1
Solve the compound inequality and give your answer in interval notation
The solution set of the compound inequality is written as:
(-∞, -4] U (6, ∞)
How to solve the composite inequality?First, we need to simplify the two given inequalities, the first one is:
7x + 6 > 4x + 24
Grouping like terms we will get:
7x - 4x > 24 - 6
3x > 18
x > 18/3
x > 6
The other inequality gives:
2*(-13x - 1) - 8 ≥ -10x + 54
-26x - 2 - 8 ≥ -10x + 54
-26x - 10 ≥ -10x + 54
-10 - 54 ≥ -10x + 26x
-64 ≥ 16x
-64/16 ≥ x
-4 ≥ x
So the compound inequality is:
-4 ≥ x
x > 6
Then the solution set written as an interval is:
(-∞, -4] U (6, ∞)
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.6+4 /(t+4)^3 feet per year, where t is the time (in years).
(a) Find the number of feet that the tree will grow in the second year.
(b) Find the number of feet the tree will grow in the third year.
a.) 0.5367 feet
b.) 0.5223 feet'
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown:
[tex]\int\limits {0.5} \, + \frac{6}{(t+4)^{3} } dt[/tex]
[tex]=\int\limits {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx[/tex]
[tex]=0.5t+\int\limits6u^{-3} du \, \,where \,u=t +4 \, and \, du=dt[/tex]
[tex]=0.5t+6*\frac{u^{-3} }{-2} + C[/tex]
[tex]=0.5t-3u^{-2}+C[/tex]
[tex]=0.5t-3(t+4)^{-2} +C[/tex]
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
[tex]\int\limits^2_1 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \, =[0.5t-3(t+4)^{-2} ][/tex]
[tex]=[0.5(2)-3(2+4)^{-2} ]-[0.5-3(5)^{-2} ][/tex]
[tex]=\frac{11}{12}-\frac{1}{2}-\frac{3}{25}[/tex]
[tex]=0.9167-0.5+0.12[/tex]
[tex]=0.5367[/tex]
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
[tex]\int\limits^3_2 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \,[/tex]
[tex]=[0.5t-3(t+4)^{-2} ][/tex]
[tex]=[1.5-\frac{3}{49} ]-[1-\frac{1}{12} ][/tex]
=1.439-0.9167
=0.5223 feet
To learn more about integration follow link : https://brainly.com/question/16789471
#SPJ4
6. Writing When you add a
one-digit number to a
decade number, what do you
notice about the ones place
digit of the sum?
When one adds a one digit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added.
What is a decade number?It's important to bite that a decade number simply means the numbers that are counted when counting numbers by tens to 100.
In this situation, when one adds a one diigit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added. Any example will be:
= 10 + 2
= 12
In this case, the 2 is in the units value of the number
Learn more about numbers on:
brainly.com/question/251701
#SPJ1
For purposes of making on-campus housing assignments, a college classifies its students as Priority A (seniors), Priority B (juniors), Priority C (freshmen and sophomores). Of the students who choose to live on campus, 10% are seniors, 20% are juniors, and the rest are underclassmen. The most desirable dorm is the newly constructed Gold dorm, and 60% of the seniors elect to live there. 15% of the juniors also live there, along with only 5% of freshmen and sophomores. What is the probability that the student lived in the Gold dorm and was an underclassmen? Round to three decimals.
The probability that the student lived in the Gold dorm and was an underclassmen is of:
0.035 = 3.5%.
How to obtain a probability?A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.
The parameters for this problem are given as follows:
70% of the students are underclassmen. (freshmen and sophomores).Of the underclassmen students, 5% live in the gold dorm.Hence the probability that the student lived in the Gold dorm and was an underclassmen is calculated as follows:
p = 0.7 x 0.05 = 0.035 = 3.5%.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
help math. Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The linear function is y = 5x + 12 and the number of customers after 3 and 4 hours are 27 and 41 respectively.
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line.
m = slopeb = y-interceptUsing the data in the table, we can write can a linear function to represent it.
Taking two points;
A = (0, 12)B = (1, 17)The slope of the line is calculated as;
m = y₂ - y₁ / x₂ - x₁
m = 17 - 12 / 1 - 0
m = 5 / 1
m = 5
Using the value of the slope to calculate the y - intercept.
y = mx + b
17 = 5(1) + b
17 = 5 + b
b = 17 - 5
b = 12
The linear function is written as y = 5x + 12
a) The number of customers in the store after 3 hours is
y = 5x + 12
y = 5(3) + 12
y = 15 + 12
y = 27
b) The number of customers in store after 4 hours is
y = 5x + 12
y = 5(4) + 12
y = 20 + 12
y = 41
The linear function to model the table is y = 5x + 12
Learn more on linear function here;
https://brainly.com/question/15602982
#SPJ1
The greater of two numbers is twice the lesser. If the greater is x, what is the lesser.
Answer:
1/2x
Step-by-step explanation:
Answer:
The lesser is x/2.---------------------------------------------------
Let the numbers be x and y, where x is greater and y is lesser.
Given that x = 2y.
Find y:
x = 2y Divide both sides by 2x/2 = yy = x/2Darwin's age is 6 years greater than twice fiona's age.If darwin is 50 years old, how many years old is fiona
Answer:
22years old
Step-by-step explanation:
Let Fiona's age = x
Darwin age
2x+6 = 50
2x = 50 -6
2x = 44
x= 44/2
x = 22years old
Find the domain of the function f(x)=\sqrt{\sqrt{x^2-16}-3}$
We have to make sure that we are taking square roots of non-negative values to stay within the real number system.
You have to make sure x^2-16 ≥ 0 for the inner square root to stay in the real numbers.
You also have to make sure sqrt(x^2-16)-3 ≥ 0 for the outer square root to stay in the real numbers.
Solving x^2-16 ≥ 0 we have that x^2 ≥ 16, so either x≥4 or x≤-4.
Solving sqrt(x^2-16)-3 ≥ 0, we have
sqrt(x^2-16) ≥ 3
x^2-16 ≥ 9
x^2 ≥ 25
either x ≥ 5 or x ≤ -5.
Since that second condition is more restrictive that x ≥ 4 or x ≤ -4, we can default to just using
{ x | x ≥ 5 or x ≤ -5 }
(-infty, -5) U (5, infty)
help what is the value of y??? please help me!!
Answer: I think that y =18
Step-by-step explanation: I thought this bc the one across from it is also 18 and they look equal. I hope I helped
We have Quarterly Amazon Sales (billion dollars) starting in Quarter 3 of 2013 through Quarter 2 of 2021. In Quarter 2 of 2021 the Amazon Sales was 96.1 billion dollars. Use the output provided below to report the updated forecast for the Amazon Sales for Quarter 3 of 2021. The variable time period is coded in the following way: Start with t = 1 for Quarter 3 of 2013, t = 2 for Quarter 4 of 2013. The value of t will increase by 1 for each subsequent quarter. In this example we have created indicator variables for Quarters 1, 2 and 3. Quarter 4 is the baselevel. Using the output here for the model accounting for trend and seasonality as well as the output for the AR(1) model report the updated forecast for Amazon Sales in Quarter 3 of 2021. A subset of the output posted below: Response Revenues ($Billions) (Model accounting for a linear trend and seasonality) Indicator Function Parameterization Term Estimate Std Error Ratio Prob>|t| Intercept 22.67 2.170013 8.15 <0001* Time period 2.538 0.114582 19.54 <.0001* Quarter[1] - 10.44 2.376946 -4.39 0.0003* Quarter[2] -11.156 2.385217 -4.68 0.0001* Quarter[3] -8.773 2.290687 -3.83 0.0010* Bivariate Fit of Residual Revenues ($Billions) 2 By Lag residuals (AR(1) Model output) Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -0.0856 0.479018 -0.18 0.8598 Lag residuals 0.762 0.132836 5.74 <.0001 The Updated forecast for the Amazon Sales accounting for Trend, Seasonality and Adjusted for the Serial Correlation using the AR(1) model is: _________ billion dollars. If the answer is 75.2432 billion dollars just type 75.2432 Record your answer with at least 4 decimal places.
The AR(1) model was used to create an updated forecast for Amazon sales that account for trend, seasonality, and serial correlation is 97.6510
Accounting and revenue
Accounting is the recording of financial transactions along with storing, sorting, retrieving, summarizing, and presenting the results in various reports and analyses.Revenue in accounting refers to the entire amount of money made through selling products and services from a company's core operations. Revenue is another term for a company's earnings, also known as sales or turnover.Given that:
Equation of regression
Revenue = 22.67 + 2.538*t - 10.44*Q1 + 11.156*Q2- 8.77*Q3
t = 1 for the third quarter of 2013.
t = 33 for the third quarter of 2021
Revenue = 22.67 + 2.538*33 - 8.77 = 97.6510 billion dollars.
Therefore, Revenue = 97.6510 billion dollars
To learn more about revenue check the given link
brainly.com/question/16232387
#SPJ4
It would he quite risky for you to insure the life of a 21 -year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain $\$ 1250 dollars in premiums. But if he were to die, you would lose almost \$ 100,000$. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21 -year-old men. (b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring $\mathrm{u}$ single person's life in Exercise 14 by computing the standard deviation of the income $Y$ that the insurer will receive. Find or using the distribution and mean found in Exercise 14.
The standard deviation of the income that the insurer will receive can be determined which is 9708 using the distribution and mean.
Given in the question that the high probability would gain in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.
According to the information, the gain around is 1250
Amount would lost in case of death is 100000.The expected value with its probability is:
E(X) = ∑x ×P(x)
=(-99750) × 0.00183 + ...+ (1250) × 0.99058
= 303.35
The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is
The standard deviation of Y can be determined as
α = under root {∑x2 × P(x) - (∑x × P(x) }
= 9708
To know more about standard deviation refer to:
http://brainly.com/question/24180499
#SPJ4
….answer thank youu!!!!!!!
8/3X = 1 + 5/3X
8/3X - 5/3 = 1 + 5/3X - 5/3X
3/3X = 1
X = 1
first box = 8
second box = 8
third box = 5/3x
fourth box = 3
fifth box = 1
sixth box = 1
Given that f is increasing, f is increasing, and that the range of g is included in f what can be said about f o g?
H(x) is a decreasing function too. fog will be decreasing function.
An easy definition of a function?
As a set of inputs with one output for each, a function is defined as a relationship between them.
In plain English, a function is an association between inputs in which each input is connected to precisely one output.
Let h(x) = f(g(x))
Hence,
h'(x) = f'(g(x) ) . g(x)
h'(x) = f'g(x)) . g(x)
Now g(x) is a strictly decreasing function.
Then
g'(x) < 0 for all real x.
Hence
h'(x) < 0
since h'(X) = f'(g(X)) . g'(X) and g'(x) < 0
Therefor h(x) is a decreasing function too.
Hence fog will be decreasing function.
Learn more about function
brainly.com/question/21145944
#SPJ4
Young Professional magazine was developed for a target audience of recent college graduates who are in their first 10 years in a business/professional career. In its two years of publication, the magazine has been fairly successful. Now the publisher is interested in expanding the magazine’s advertising base. Potential advertisers continually ask about the demographics and interests of subscribers to Young Professional. To collect this information, the magazine commissioned a survey to develop a profile of its subscribers. The survey results will be used to help the magazine choose articles of interest and provide advertisers with a profile of subscribers. As a new employee of the magazine, you have been asked to help analyze the survey results.
TABLE 8.6 PARTIAL SURVEY RESULTS FOR YOUNG PROFESSIONAL MAGAZINE
age gender real estate purchases value of investments number of transactions broadband access household income children
38 female no 12200 4 yes 75200 yes
30 male no 12400 4 yes 70300 yes
41 female no 26800 5 yes 48200 no
28 female yes 19600 6 no 9300 no
31 female yes 15100 5 no 73300 yes
Prepare a managerial report summarizing the results of the survey. In addition to statistical summaries, discuss how the magazine might use these results to attract advertisers. You might also comment on how the survey results could be used by the magazine’s editors to identify topics that would be of interest to readers. Your report should address the following issues, but do not limit your analysis to just these areas.
1. Develop appropriate descriptive statistics to summarize the data.
2. Develop 95% confidence intervals for the mean age and household income of subscribers.
3. Develop 95% confidence intervals for the proportion of subscribers who have broadband access at home and the proportion of subscribers who have children.
4. Would Young Professional be a good advertising outlet for online brokers? Justify your conclusion with statistical data.
5. Would this magazine be a good place to advertise for companies selling educational software and computer games for young children?
6. Comment on the types of articles you believe would be of interest to readers of Young Professional.
We are 95% confident that the interval 29.7215 to 30.5029 includes the population mean age of all respondents.
What does a 95% confidence interval indicate?
With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
According to the given question:
Conclusions about statistical significance are possible with the help of the confidence interval. If the confidence interval does not include the value of zero effect, it can be assumed that there is a statistically significant result.
±2828.6, ±3370.3, and ±4429.6
a. A larger sample size would cause the interval to narrow.
b. Near certainty; 50.1% (a majority) is far below the 95% confidence interval for the population proportion.
To learn more about confidence interval visit
brainly.com/question/24131141
#SPJ4
In ARST, RS = ST. Solve for x. Then find the
length of RT.
The value of (a) x is 3 and (b) the length RT is= 14 units
How to find the measure of the length?The corrected question form a triangle. and the lengths of the triangle are give as
rs=9x-13
st=10x-3
rt=4x+2
Using the supporting values to find the lengths we have
s=t and rs=rt
This implies that
rs=9x-13=rt=4x+2
Equating the two equations we have
9x-13=4x+2
Collecting like terms
9x-4x=2+13
⇒5x=15
Making x the subject of the formula
x=15/5=3 units
In the same way, rs=9x-13=9(3)-13
=27-13=14 units
Also, st=10x-3
Substitute x=3 in the equation we have
10(3)-3
=30-3
=27
Recall that rt=4x+2
by substitution we have
4(3)+2
=12+2
=14 units
In conclusion, the value of (a) x is 3 units and (b) the length RT is= 14 units
Learn more about lengths of sides of a triangle on https://brainly.com/question/24273594
#SPJ1
Corrected question:
in rst, if s=t, rs=9x-13, st=10x-3, and rt=4x+2, find x and the measurement of the side rt.
coordinate geometry find the coodinates of the centroid of each triangle with the given vertices geometry answers
The Coordinates of the centroid of a triangle with the given vertices are (0, 4), (8, 10) and (6, 1) is (14/3, 5) and Centroid of triangle with vertices (1,5),(3,8),(0,2) is (4/3, 5).
What is Centroid of a triangle?The centroid of a triangle is one of the point where all three medians of the triangle intersect. The median is a line segment drawn from one vertex to the midpoint on the opposite side. Triangle centroid divides each median into individual words in a 2:1 ratio. The centroid is usually at 2/3 of the median.
If the three vertices of a triangle are A(x₁,y₁) B(x₂,y₂), C(x₃,y₃), the centroid of the triangle is given by the formula :
G(x₁+x₂+x₃/3, y₁+y₂+y₃/3 ).
We have , two triangles with vertices,
a) triangle whose vertices are A(0, 4), B(8, 10) and C(6, 0). So, the coordinates of the centroid of a triangle whose vertices are (0, 4), (8, 10) and (6 , 1) are ( (0+8+6)/3 , (4+10+1)/3 ) or (14/3, 5).
b) triangle whose vertices are P(1, 5), Q(3,8) and R(0, 2). So, the coordinates of the centroid of a ∆PQR are ( (1+3+0)/3 , (5+8+2)/3 ) or (4/3, 5).
Hence, the required coordinates of Centroid are (14/3, 5), (4/3, 5).
To learn more about centroid of a triangle, refer:
https://brainly.com/question/7644338
#SPJ4
Complete question:
Coordinate geometry find the coodinates of the centroid of each triangle with the given vertices are a) (0, 4), (8, 10) and (6, 1)
b) (1,5),(3,8),(0,2)
Identifying subgroups of the overall marketplace based on factors such as age or income level is considered:
Demographic segmentation is considered for identifying subgroups of the overall marketplace based on factors such as age or income level.
A precise method of identifying an audience is known as demographic segmentation. It is based on information such as age, gender, marital status, family size, income, education, race, occupation, nationality, and/or religion. It is one of the four primary categories of marketing segmentation and is possibly the most used approach.
By concentrating on specific qualities that may represent relevant markets for a firm, demographic segmentation joins consumers and potential customers together. The five primary demographic subgroups are :
Agegenderoccupationcultural background family statusDemographic segmentation is the process of dividing a market into subgroups based on factors such as age, gender, income level, education level, and geographic location. This is a common way for businesses to identify and target specific groups of consumers who are likely to be interested in their products or services. By understanding the characteristics of different demographic segments, businesses can tailor their marketing efforts and products to better meet the needs and preferences of these groups. This can help businesses to effectively reach and engage their target audience, and ultimately increase sales and profits.
To know more about Demographic Segmentation visit :
https://brainly.com/question/22401136?referrer=searchResults
#SPJ4
what would the graph of the equation look like? y= -3/5x + 3
The graph of the equation y=-3/5+3 will be a straight line
How to determine the graph of a straight line?The graph of a straight line is always straight. The equation is written in slope intercept for where -3/5 is the
The form of an equation in slope intercept form is y=mx+c
Here, m=-3/5
c=3
To draw the line, from the point 3 on the x-axis, rise negative 3 and run 5
The draw the line for form a straight line
Note that the formula for slope is
S=rise/run
In conclusion, the equation forms a straight line.
Learn more about equation of a line on https://brainly.com/question/21511618
#SPJ1
Find the range for the measure of the third side of a triangle given the measure of two sides.
10.5 cm, 4 cm
Oa. 4 cm
Ob. 4 cm >x> 10.5 cm
Oc. 6.5 cm >x> 10.5 cm
Od. 6.5 cm
Answer:
6.5 cm < x < 14.5 cm
Step-by-step explanation:
The length of the side of a triangle must be greater than the difference of the lengths of the other two sides and less than the sum of the other two sides.
Difference: 10.5 cm - 4 cm = 6.5 cm
Sum: 10.5 cm + 4 cm = 14.5 cm
Answer: 6.5 cm < x < 14.5 cm
the continuous function f is defined on closed interval -6
The continuous function f is defined on the closed interval −6 ≤ x ≤ 5. The figure above shows a portion of the graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3). It is known that the point (3, 3 −√5 ) is on the graph of f. 4.
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.
To learn more about continuous function f visit:
https://brainly.com/question/23542106
#SPJ4
What are the two equations to set up to solve the equation |2x - 5| = 7
Answer:
To solve the equation |2x - 5| = 7, you can set up two equations, one for the positive solution and one for the negative solution.
For the positive solution, you can start by isolating the absolute value expression on the left-hand side of the equation: |2x - 5| = 7 can be rewritten as 2x - 5 = 7. Then, you can solve this equation by adding 5 to both sides to get 2x = 12, and then dividing both sides by 2 to get x = 6.
For the negative solution, you can start by noting that the absolute value of a number is equal to its opposite if it is negative, so |2x - 5| = 7 can be rewritten as -(2x - 5) = 7. This equation can be solved by multiplying both sides by -1 to get 2x - 5 = -7, and then adding 5 to both sides to get 2x = -2. Then, dividing both sides by 2 to get x = -1.
Therefore, the two equations to solve the equation |2x - 5| = 7 are 2x - 5 = 7 and 2x - 5 = -7.
Answer:
C
Step-by-step explanation:
To solve the equation |2x - 5| = 7, we need to set up two equations, one for the case where the absolute value is equal to the positive value of the expression inside the absolute value bars, and one for the case where the absolute value is equal to the negative value of the expression inside the absolute value bars.
The first equation we need to set up is 2x - 5 = 7. In this case, the absolute value is equal to the positive value of 2x - 5, so we can simply set the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:
2x - 5 = 7
The second equation we need to set up is -(2x - 5) = 7. In this case, the absolute value is equal to the negative value of 2x - 5, so we need to set the negative of the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:
-2x+5 = 7
We can use these two equations to solve for the value of x. To solve the first equation, we can simply add 5 to both sides to get 2x = 12, and then divide both sides by 2 to get x = 6. To solve the second equation, we can first distribute the negative sign to get -2x + 5 = 7, and then add 5 to both sides to get -2x = 2. Finally, we can divide both sides by -2 to get x = -1.
Therefore, the two solutions to the equation |2x - 5| = 7 are x = 6 and x = -1.
Alternative:
2x-5 = 7
2x-5 = -7
Please help will mark brainily
Answer: C. 2x+3y=7.20 4x+2y=8.80
Step-by-step explanation: 2x and 4x = grapefruit, 3y and 2y = oranges
Which inequality statement is the same as the one given below?
x ≥ or x>2
A x≥-3
B x>-3
C x>2
The inequality statement that same as x ≥ -3 or x > 2 is option (A) x ≥ -3
The inequality statement is
x ≥ -3 or x > 2
The inequality is the mathematical statement that shows the relationship between two expression with inequality sign. The inequality signs are less than, less than or equal to, greater than, greater than or equal to etc.
The compound inequality is
x ≥ -3 or x > 2
The value of x is greater than or equal to -3 also value of x is greater than 2
Here x ≥ -3 express then values of the compound inequality
Therefore, the same inequality statement is option (A) x ≥ -3
Learn more about inequality here
brainly.com/question/20383699
#SPJ4
Given the function:
f(x) = 1/2 (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21
Answer: C
Step-by-step explanation:
It's easy! Don't worry!
f(x) = 1/2(3x+7)
f(9) = 1/2(3(9)+7)
f(9) = 1/2(27+7)
f(9) = 1/2(34)
f(9) = 17
Trust me when you finish algebra this stuff is cake not going to lie. I did it under a minute. ;)
Also, gl passing algebra!
Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (&, y) - (-x, -V)
B'
O (%, V) - (-% -x)
The rule that describes the transformation that Triangle ABC is rotated to create the image A'B'C' is; (x, y) → (-x, -y)
How to identify the transformation rule that was used?
In transformation in mathematics, there are different types such as rotation, translation, dilation, reflection e.t.c
Now, from the diagram attached showing the given transformation, we see that the coordinates of the original triangle are;
A'(-1, -1)
B(1, -1)
C(0. -4)
We now see the coordinates of the transformed triangle are;
A'(1, 1)
B'(-1, 1)
C'(0, 4)
We can see that in the transformation both x and y are negative of each other. Thus, the transformation rule is; (x, y) → (-x, -y)
Read more about transformation rule at; https://brainly.com/question/8987411
#SPJ1
a newsletter publisher believes that 64% of their readers own a personal computer. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.01 level of significance, the testing firm decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
There is sufficient warrant to rejection of the claim that 64% of the readers of the publisher own a personal computer at a = 0.01 level of significance.
What is the null hypothesis?
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
Here, we have
P = population proportion of readers, who own personal computers.
The claim of the publisher: 64% of their readers own a personal computer.
Since the claim indicates a specific value about P, it should be treated as the null hypothesis and thus the required null and alternative hypothesis would be -
H₀ : p = 0.64
H₁ : p ≠ 0.64
Now, at a = 0.01, it is decided to reject the null hypothesis.
Hence, there is sufficient warrant to rejection of the claim that 64% of the readers of the publisher own a personal computer at a = 0.01 level of significance.
To learn more about the null hypothesis from the given link
https://brainly.com/question/13135308
#SPJ1
The sum of 4 and the cube of a number.
Answer:64
Step-by-step explanation:
just trust trust