Therefore , the solution of the given problem of data plot comes out to be value (r) is roughly 0.975.
Data plot: What is it?The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear. The pinkish haze with the letter P stands in for the number 2.3.
Here,
We must compute several numbers in order to determine the Pearson correlation coefficient r for the information provided in the table.
Before anything else, we figure out the average and standard deviation of the amount of TV airings (x) and car sales (y):
mean(x) = (40 + 30 + 20 + 50 + 10) / 5 = 30
mean(y) = (30 + 20 + 10 + 40 + 20) / 5 = 24
These mean numbers allow us to determine the standard deviation:
=> SX = √ (( (40-30)² + (30-30)² + (20-30)² + (50-30)² + (10-30)²) / 4)
≈> 15.81
=> SY = √(( (30-24)²+ (20-24)² + (10-24)² + (40-24)² + (20-24)²) / 4)
≈> 8.16
Next, we determine x and y's covariance:
=> cov(x,y) =
=> [(40-30)(30-24) + (30-30)(20-24) + (20-30)(10-24) + (50-30)(40-24) + (10-30)(20-24)] / 4
≈> 125
Last but not least, we can figure out the Pearson association coefficient:
0.975 r = cov(x,y) / (s x * s y)
As a result, the table's data's Pearson correlation value (r) is roughly 0.975. This shows a significant positive correlation between the volume of car purchases and the frequency of the TV ad.
To know more about plotting data visit:
https://brainly.com/question/29096917
#SPJ1
Pls Help me with this problem, I will give brainliest to whoever answers this correctly. Answer is not x=0.1
Answer: the equation have two solutions: 0.25 and 0.75
[tex]x=\frac{1}{4}[/tex] or [tex]x=\frac{3}{4}[/tex]
Step-by-step explanation:
Notice the terms [tex]x+x^2+x^3+x^4+...+x^n[/tex] is just a geometric series (since -1<x<1)
A geometric series is given by the form
[tex]1+x+x^2+x^3+x^4+...+x^n = \frac{1}{1-x}[/tex]
This is
[tex]x+x^2+x^3+x^4+...+x^n = \frac{1}{1-x} -1[/tex]
plugging in in the equation
[tex]-1+\frac{1}{x} +\frac{1}{1-x} -1=\frac{10}{3}[/tex]
grouping terms
[tex]\frac{1}{x} +\frac{1}{1-x} =\frac{16}{3}[/tex]
groupings the fractions
[tex]\frac{1-x+x}{(x)(1-x)}=\frac{1}{(x)(1-x)} =\frac{16}{3}[/tex]
this leads to an simplified quadratic equation since X cannot be zero (notice the initial 1/x term)
[tex]3=16(x^2-x)[/tex]
the solution for this quadratic equation is just
[tex]x=\frac{1}{4}[/tex] or [tex]x=\frac{3}{4}[/tex]
Answer:
1/4 or 3/4
Step-by-step explanation:
You want the value of x in the infinite sum ...
-1 +1/x +x +x² +x³ +... = 10/3
for |x| < 1.
Geometric seriesAfter the 2nd term, this looks like a geometric series with a common ratio of x. If we define the series sum as ...
S = 1/x +1 +x +x² +x³ +...
we see that the equation of interest is ...
S -2 = 10/3
SumThe series sum is that of a geometric series with first term 1/x and common ratio x:
S = (1/x)(1/(1 -x)) = 1/(x(1-x))
Substituting for S in the above, we have the equation ...
1/(x(1-x)) -2 = 10/3
SolutionThis resolves to a quadratic that will have 2 real roots:
1/(x(1 -x)) = 16/3 . . . . add 2
x(1 -x) = 3/16 . . . . . . . invert both sides
x² -x +3/16 = 0 . . . . . . subtract the left side expression
(x -3/4)(x -1/4) = 0 . . . . . factor
Solutions are the values of x that make these factors zero:
x = 1/4 or x = 3/4
Help me! I need help with my homework !
Answer:
Rounding to the nearest hundredth, the area of the shaded region is approximately 167.91 square yards.
Step-by-step explanation:
To find the area of the shaded region between two circles with the same center, we need to subtract the area of the smaller circle from the area of the larger circle.
The area of the larger circle is:
A_outer = πr_outer^2
= π(11.9 yd)^2
≈ 445.03 yd^2
The area of the smaller circle is:
A_inner = πr_inner^2
= π(9.4 yd)^2
≈ 277.12 yd^2
Therefore, the area of the shaded region is:
A_shaded = A_outer - A_inner
≈ 445.03 yd^2 - 277.12 yd^2
≈ 167.91 yd^2
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]
A well that pumps at a constant rate of 78,000 ft³/d has achieved equilibrium so that there is no change in the drawdown with time. The well taps an unconfined aquifer that consists of sand overlying impermeable bedrock at an elevation of 260 ft ASL. An observation well 125 ft away has a head of 277 ft ASL; another observation well 385 ft away has a head of 291 ft ASL. Compute the value of hydraulic conductivity using the Thiem equation.
Therefore, the value of hydraulic conductivity using the Thiem equation is approximately 10.67 ft/day.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value. Equations are used to model relationships between variables, solve problems, and make predictions in various fields of science, engineering, economics, and mathematics. They are an essential tool in algebra, calculus, and other branches of mathematics.
Here,
To compute the value of hydraulic conductivity using the Thiem equation, we need to substitute the given values into the equation:
K = (Q / π) * ((h2 - h1) / log(r2/r1))
where:
Q = pumping rate = 78,000 ft³/d
h1 = head at the pumping well = 260 ft ASL
h2 = head at the observation well 385 ft away = 291 ft ASL
r1 = distance from the pumping well to the observation well 125 ft away = 125 ft
r2 = distance from the pumping well to the observation well 385 ft away = 385 ft
Substituting the values, we get:
K = (78,000 / π) * ((291 - 260) / log(385/125))
K = 10.67 ft/day
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
LOTS OF POINTS HELP ASAP!
The time between the injections that is injected again when the dosage reaches 9 is solved to be 1.8 to the nearest tenth
How to find the time between the injectionsThe information given by the problem include the expression
D(h) = 20e^(-0.45h)
The expression is an exponential function that shows the relationship between time and the dosage in milligrams
given that D = 9 we find h
D(h) = 20e^(-0.45h)
9 = 20e^(-0.45h)
9/20 = e^(-0.45h)
take ㏑ of both sides
㏑(9/20) = -0.45h
isolating h by dividing by -0.45
h = ㏑(9/20) / -0.45
h = 1.774
h = 1.8 to the nearest tenth
This shows that the time is 1.8 hours
Learn more about exponential function
https://brainly.com/question/2456547
#SPJ1
A health expert evaluates the sleeping patterns of adults. Each week she randomly selects 40 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 3 hours and 5% of average sleep time is more than 3.4 hours. What are the mean and standard deviation (in hours) of sleep time for the population? (Round "Mean" to 1 decimal places and "standard deviation" to 3 decimal places.)
Solving for μ and σ simultaneously gives: μ = 3.2 hours (rounded to 1 decimal place) and σ = 0.426 hours (rounded to 3 decimal places)
What is Standard Deviation ?
Standard deviation is a statistical measure that describes the amount of variation or dispersion in a set of data. It measures how spread out the data is from its mean or average.
Let the mean of the population sleep time be μ and the standard deviation be σ.
From the given information, we know that the distribution of sample means of sleep time follows a normal distribution with mean μ and standard deviation σ/√40 (since each sample size is 40).
We are also given that 5% of the sample means are less than 3 hours and 5% of the sample means are more than 3.4 hours.
Using a standard normal distribution table, we can find the corresponding z-scores for these probabilities:
P(Z < z) = 0.05 when z = -1.645
P(Z > z) = 0.05 when z = 1.645
Now we can use the formula for z-score:
z = (X' - μ) / (σ / √n)
where X' is the sample mean, n is the sample size (which is 40 in this case).
For the lower bound, we have:
-1.645 = (3 - μ) / (σ / √40)
For the upper bound, we have:
1.645 = (3.4 - μ) / (σ / √40)
Therefore, Solving for μ and σ simultaneously gives: μ = 3.2 hours (rounded to 1 decimal place) and σ = 0.426 hours (rounded to 3 decimal places)
To learn more about Standard deviation from given link.
https://brainly.com/question/23907081
#SPJ1
Mitchell is an ecologist studying bonobos, a species of ape that lives in the Congolian rainforest. When he started his study, there was a population of about 40,000 bonobos. After one year, he estimated that the population had decreased to 39,200. Based on his data, Mitchell expects the population to continue decreasing each year.
Write an exponential equation in the form y=a(b)x that can model the bonobo population, y, x years after Mitchell began studying them.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Y=?
To the nearest hundred, what can Mitchell expect the bonobo population to be 7 years after the study began?
--bonobos
Answer:
P(x)=[tex](40000)( 0.98)^x[/tex]
A=40000 B=0.98
P(7)= 34700
Step-by-step explanation:
Notice the population can be modeled as:
P(x)=[tex]A B^x[/tex]
For X=0 P(0)=40000=A (Initial population)
So A=40000
For x=1 (one year after) P=39200
[tex]39200=40000 B^1[/tex]
solving for B
[tex]B=\frac{39200}{40000} =0.98[/tex]
So B=0.98
So the population can be modeled as
P(x)=[tex](40000)( 0.98)^x[/tex]
Now at 7 years:
P(7)=[tex](40000)( 0.98)^7[/tex]= 34725.02133
Needs to be rounded to the nearest hundred
This is 34700 bonobos (7 years after the study began)
If 3000 dollars is invested in a bank account at an interest rate of 4 per cent per year,
Find the amount in the bank after 6 years if interest is compounded annually:
Find the amount in the bank after 6 years if interest is compounded quarterly:
Find the amount in the bank after 6 years if interest is compounded monthly:
Finally, find the amount in the bank after 6 years if interest is compounded continuously:
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{annually}, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{1}\right)^{1\cdot 6} \implies A \approx 3795.96 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{quarterly}, thus four} \end{array}\dotfill &4\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{4}\right)^{4\cdot 6} \implies A \approx 3809.20 \\\\[-0.35em] ~\dotfill[/tex][tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{monthly}, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{12}\right)^{12\cdot 6} \implies A \approx 3812.23 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 6} \implies A \approx 3813.75[/tex]
Identify the value for the variable.
What is the value of x in this simplified expression?
7-9-7-3-7x
x=
What is the value of y in this simplified expression?
114
= 11
118
y=
Answer: x=7 y=5
Step-by-step explanation:
I believe this is the answer to the question
Solve y=2x+1 and 2x-y=3 using the substitucion méthod
Answer:
No solution
Step-by-step explanation:
y = 2x + 1 _____(equ 1)
2x - y = 3 _____(equ 2)
from equ 1
y = 2x + 1
2x + 1 = y
2x = y - 1
x = (y - 1)/2
substitute x = (y - 1)/2 into equ 2
2x - y = 3
2((y-1)/2) - y = 3
(2y - 2)/2 - y = 3
y - 1 - y = 3
y - y = 3 + 1
0 = 4
Hello and best regards sanungapatricio1985
This equation has no solution, since -1 cannot be equal to 3. Therefore, the system has no solution.
Step-by-step explanation:We have the following equations:
⇒ y = 2x + 1
⇒ 2x - y = 3
What is the substitution method?The substitution method is a common method for solving systems of linear equations. It consists of isolating one of the variables from one of the equations and substituting the expression obtained in the other equation to eliminate that variable and obtain an equation with a single variable, which can be solved to find the value of that variable. Then, the found solution can be substituted into any of the original equations to find the value of the other variable.
From the first equation we have a good substitution candidate:
⇒ y = 2x + 1
Now we have to plug y = 2x + 1 found from the first equation, into the second equation 2x - y = 3, to find that:
⇒ 2x - y = 3
⇒ 2x - (2x + 1) = 3
⇒ 2x - 2x - 1 = 3
Based on the previous results, the system has no solution.
＼(^_^ )If you want to learn more, I share this link to complement your learning:
https://brainly.com/question/29204890
pelase help quick 25 points it 6th grade math
The median shows that the average number of students per middle school classroom in both districts is 24, while the mean shows that the average number of students per middle school classroom in one district is 24 and the other is 25.
What is median?Median is the middle value of a set of data. It is the value that divides the data set into two equal halves. It is an important measure of central tendency and is used to compare sets of data.
The difference between the mean number of students per middle school classroom in each school district is 2 students. The difference between the median number of students per middle school classroom in each school district is 0 students.
Based on the number of students shown for each school district, the median would provide the most accurate picture of the number of students in a middle school classroom, as there are some extreme values that would affect the mean but not the median.
To know more about mean, visit:
brainly.com/question/30112112
#SPJ1
Which of the following is the equation in slope-intercept form for the line that passes through the points (-4, 1) and (-3, 0)?
Answer:
y= -x - 3 is correct
Step-by-step explanation:
PLS HELP DUE TOMORROW!!
Answer:
Step-by-step explanation:
[tex]V=\pi r^2 h[/tex]
Substitute [tex]h=l,r=2,V=150,[/tex] we get
[tex]150=\pi \times 2^2 \times l[/tex]
[tex]150=4\pi l[/tex]
[tex]l=\frac{150}{4\pi}=11.94cm[/tex]
Determine the value of x.
Answer:
x = 10 (B)
Step-by-step explanation:
Use trigonometry:
[tex] \sin(30°) = \frac{5}{x} [/tex]
[tex] \frac{1}{2} = \frac{5}{x} [/tex]
Cross-multiply to find x:
[tex]x = 2 \times 5[/tex]
[tex]x = 10[/tex]
Write an expression for the sequence of operations described below:
4 increased by the quotient of 5 and 8
Answer:
4+5/8
or
5/8+4
Step-by-step explanation:
"increased by" is adding, and "quotient" id dividing two numbers.
The mathematical expression '4 increased by the quotient of 5 and 8' is written as 4 + 5/8 in standard mathematical notation, meaning you first divide 5 by 8 and then add the result to 4.
Explanation:The sequence of operations described can be converted into an expression in the following way: In terms of mathematics, the term 'increased by' refers to addition. The 'quotient of 5 and 8' refers to the result of dividing 5 by 8. Therefore, the expression can be written as '4 + 5/8'.
So, the mathematical expression '4 increased by the quotient of 5 and 8' becomes 4 + 5/8 in standard mathematical notation. This means you first divide 5 by 8 and then add the result to 4.
Learn more about Mathematical Expression here:https://brainly.com/question/34902364
#SPJ2
Two positions of an open gate are shown.
The triangles show the position of the gate in relation to its closed position. The distance from G to H in Position 1 is less than the distance from G to H in Position 2.
What can you conclude about the angles opposite these sides?
Answer: Right Picture
Step-by-step explanation:
Mark me as brainleanst
A rectangle has an area of 60 square inches and the length is 4 inches more than the width. Find the length and width of the rectangle
Answer:
w = 6in, l = 10in
Step-by-step explanation:
Area of a rectangle is [tex]A=l*w[/tex]
and [tex]l = 4 + w[/tex]
We can solve for length and width by substituting these values for the equation.
[tex]60in^2=(4+w)*w[/tex]
[tex]60in^2=4w+w^2[/tex]
[tex]0 = w^2 + 4w + 60in^2[/tex]
factor out the equation.
[tex]0= (w+10)(w-6)[/tex]
therefore w = 6in (tossing out the negative solution)
which means
[tex]l = 4 + w[/tex]
[tex]l = 6in + 4[/tex]
l = [tex]10in[/tex]
Hope this helps!
Brainliest is much appreciated!
ABC ltd is considering an investment that will cost 80000000 and have a useful life of four years.during the first two years cash flows are 25000000 per year and for the last two years are 20000000 per year.what is the payback period of this investment
Answer:
Step-by-step explanation:
To calculate the payback period of the investment, we need to find out how long it will take for the company to recover the initial investment of 80000000 through the cash flows generated by the investment.
Step 1: Calculate the cumulative cash flow for each year.
Year 1: 25000000
Year 2: 25000000 + 25000000 = 50000000
Year 3: 50000000 + 20000000 = 70000000
Year 4: 70000000 + 20000000 = 90000000
Step 2: Determine the year in which the cumulative cash flow exceeds the initial investment.
Based on the calculations above, the cumulative cash flow exceeds the initial investment of 80000000 in Year 4.
Step 3: Calculate the payback period.
The payback period is the time it takes for the cumulative cash flow to equal the initial investment. In this case, the payback period is the end of Year 3 plus the portion of Year 4 needed to recover the remaining investment, which is calculated as follows:
80000000 - 70000000 = 10000000
10000000 ÷ 20000000 = 0.5
Therefore, the payback period for this investment is 3.5 years.
To confirm this result, we can also calculate the cumulative cash flow at the end of Year 3 and check that it is less than the initial investment, while the cumulative cash flow at the end of Year 4 exceeds the initial investment:
Year 1: 25000000
Year 2: 25000000 + 25000000 = 50000000
Year 3: 50000000 + 20000000 = 70000000 (cumulative cash flow at end of Year 3)
Year 4: 70000000 + 20000000 = 90000000 (cumulative cash flow at end of Year 4)
Since the cumulative cash flow at the end of Year 3 is less than the initial investment and the cumulative cash flow at the end of Year 4 exceeds the initial investment, we can confirm that the payback period is between Year 3 and Year 4, or 3.5 years.
Maurice can weed the garden in 45 minutes. Olinda can weed the garden in 50 minutes, how long would it take them to weed the garden if they work together
Tt would take Maurice and Olinda approximately 47.37 minutes
What is work done?
Work done in physics is the dot product of force and displacement. When a force applied on an object results in a displacement, it is said to be work is done on the object.
Let's denote the time it takes both Maurice and Olinda working together to weed the garden as t.
We can use the formula: 1 / t = 1 / a + 1 / b
Plugging in the given values, we get: 1 / t = 1 / 45 + 1 / 50
1 / t = (50 + 45) / (50 * 45) = 95 / 2250
Then, we can invert both sides of the equation to get: t / 1 = 2250 / 95
Simplifying the right-hand side by dividing both the numerator and the denominator by 5, we get:
t = 2250 / 95 = 47.37 minutes (rounded to two decimal places)
Therefore, it would take Maurice and Olinda approximately 47.37 minutes to weed the garden if they work together.
To know more about work done visit,
https://brainly.com/question/8119756
#SPJ1
which one of the following greater
a, 20% of 45
b, 25% of 60
c, 2%of 800
d, 74% of 20
Answer:
2% of 800, which is 16
Can you please answer this question for me please and thank you 1/3+a=4/5
Okay so you want to make all of the fractions have a common denominator. Think of the lowest number that 3 and 5 go into, the answer you should get is 15. So 15 is the common denominator.
Now we're going to make 1/3 have a denominator of 15. 1/3 of 15 would be 5. You get that by figuring out what you have to multiply 3 by to get 15 which is 5. Then you multiply 5 and 1 and you get 5. The answer you will get will be 5/15 which is equal to 1/3.
Next we're going to make 4/5 have a denominator of 15. 4/5 of 15 would be 12/15. You can get this by figuring out what you have to multiply 5 by to get 15 which is 3. Then you take 3 and multiply it by 4 to get that 12 in 12/15. The answer 12/15 is equal to 4/5 of 15.
So now you have 5/15 + a = 12/15.
The denominator of the fraction that "a" will be is 15 because that is what we made the common denominator.
So what we have is 5/15 + x/15 = 12/15.
Think of what you have to add to 5 to get 12. (The answer is 7)
So a is equal to 7/15
Your final answer should be 5/15 + 7/15 = 12/15
which of the following is the graph of y = - sept x + 1?
Answer:
??
Step-by-step explanation:
is there a picture or something?
Which expression is equivalent to the following complex fraction? -2 5 x y 3 2 y x O O O -2y+ 5x 3x-2y 3x-2y -2y+ 5x x²y² (-2y+5x)(3x-2y) (-2y+5x) (3x-2y) 2,2 turn E.
The equivalent fraction of the given expression is: 2(y - 2x)(-5x + 3y)
How to Solve Fraction Expressions?The fraction expression is given as;
[(-2/x) + (5/y)]/[(3/y) - (2/x)]
Finding the common denominators and writing the numerators above common denominators gives:
[(2y - 4x)/xy]/[(-5x + 3y)/xy)]
Usually we divide a fraction by multiplying its' reciprocal and we have;
[(2y - 4x)/xy] * [(xy/(-5x + 3y)]
Thus, this gives us the expression:
(2y - 4x)/(-5x + 3y)
= 2(y - 2x)(-5x + 3y)
Read more about Fraction Expressions at; https://brainly.com/question/11875858
#SPJ1
Suppose you send about 12 text messages a day and your older sister sends more text messages than you do . together you send a total of about 26 messages per day. about how many text messages does she send a day ? Write an equation and solve for the unknown value
Let x be the number of text messages that your older sister sends per day. Then we can write an equation based on the given information:
x + 12 = 26
We can solve for x by subtracting 12 from both sides of the equation:
x = 26 - 12
x = 14
Therefore, your older sister sends about 14 text messages per day.
Help solve this; I'm confused. Problem 3:
Answer:
(f∘g)(1) = 2; (f∘g)'(1) = 2
(f∘g)(2) = -2; (f∘g)'(2) = -2
Step-by-step explanation:
You want (f∘g)(x) and (f∘g)'(x) for x=1 and x=2 given the function values and derivatives in the table.
(f∘g)(x)This composition means f(g(x)). The value is found by first determining the value of z = g(x), then using that to find the value of f(z).
For x=1, the value of g(1) is seen to be -2.
For x=-2, the value of f(-2) is seen to be 2.
This means f(g(1)) = 2.
For x=2, the value of g(2) is 0.
For x= 0, the value of f(0) is -2.
This means f(g(2)) = -2.
(f∘g)'(x)This is a little trickier, as you need to find the derivative of the composition:
f(g(x))' = f'(g(x))·g'(x)
In the attached table, we have made a column for f'(g(x)) to help find this product.
For x=1, f'(g(1)) = f'(-2) = 1; and g'(1) = 2, so f'(g(1))g'(1) = 1·2 = 2 = (f∘g)'(1)
For x=2, f'(g(2)) = f'(0) = 2; and g'(2) = -1, so f'(g(2))g'(2) = 2(-1) = -2 = (f∘g)'(2)
The average rate of change from x=2 to x=5
Answer:
4/3 from x = 2 to x = 5.
Step-by-step explanation:
What is Lagrange mean value theorem?
Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)
According to the given graph,
At point x = 2,
F(2) = 3
At point x = 5,
F(5) = 7
Since the formula for the average rate of change of the function between x = a and x = b is,
The average rate of change = {F(b) -F(a)}/(b-a)
Here a = 2, b = 5 and F(2) = 3, F(5) = 7
Substitute the values in the formula,
So the average rate of change = (7 - 3)/(5 - 2) = 4/3.
Hence, the average rate of change of the function is 4/3.
Check the picture below.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=2\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(2)}{5 - 2}\implies \cfrac{7-3}{5-2}\implies \cfrac{4}{3}[/tex]
What is the total interest on a 4-year term loan of
$1,700 with a simple annual interest rate of 8%?
A. $544
B. $554
C. $564
D. $574
Answer:
a
Step-by-step explanation:
The formula to calculate simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time period
Given:
Principal amount (P) = $1,700
Rate of interest (r) = 8% per annum
Time period (t) = 4 years
Using the formula of simple interest:
I = P * r * t
I = 1,700 * 0.08 * 4
I = $544
Therefore, the total interest on a 4-year term loan of $1,700 with a simple annual interest rate of 8% is $544.
Answer: A. $544
I will mark you brainiest!
What is the area of a rectangle with a length of 3 cm and a width of 4.5 cm?
A) 1.5 cm2
B) 6.75 cm2
C) 7 cm2
D) 13.5 cm2
Answer:
A equals 13.5 centimeters
a) Calculate the length x.
b) Work out the total surface area of the
frustum. Give your answer in terms of .
35 cm
7 cm
6 cm
X
a) The length of x is 5 cm. b) the total surface area of the frustum is 61[tex]\pi[/tex]√802 + 16[tex]\pi[/tex] square cm (in terms of π).
Describe Frustum?A frustum has two bases, which are usually parallel to each other and are either circular or polygonal in shape. The height of the frustum is the perpendicular distance between the two bases, and the slant height is the distance between the apex of the frustum (the point where the original cone or pyramid was cut off) and any point on the perimeter of either base.
a. To find the value of x, we can use the similar triangles formed by the two cones. Let the radius of the small cone be y cm, then we have:
y/x = (35-7)/35 [Using the similarity of triangles]
Simplifying this expression, we get:
y = x(28/35) = 4x/5
Now, we know that the difference in the areas of the two circular bases of the frustum is equal to the area of the missing part. Using this fact, we can find the value of x as:
[tex]\pi[/tex](6²) - [tex]\pi[/tex](y²) = [tex]\pi[/tex](x²) - [tex]\pi[/tex]( (4x/5)² )
Simplifying this expression and solving for x, we get:
x = 5 cm
Therefore, the value of x is 5 cm.
b. The total surface area of the frustum can be calculated as the sum of the curved surface area of the small cone and the curved surface area of the frustum itself.
Curved surface area of the small cone = [tex]\pi[/tex](y²) = [tex]\pi[/tex](4²) = 16[tex]\pi[/tex]
Curved surface area of the frustum = [tex]\pi[/tex](6² + x²) × l
where l is the slant height of the frustum. To find the value of l, we can use the Pythagorean theorem:
l² = (35-7)² + (6-x)²
l² = 784 + (6-x)²
l = √[784 + (6-x)²]
Substituting the value of x, we get:
l = √[784 + (6-5)²] = √802
Therefore, the total surface area of the frustum is:
[tex]\pi[/tex](6² + x²) × √802 + 16[tex]\pi[/tex]
= [tex]\pi[/tex](6² + 5²) × √802 + 16[tex]\pi[/tex]
= 61[tex]\pi[/tex]√802 + 16[tex]\pi[/tex]
Hence, the total surface area of the frustum is 61[tex]\pi[/tex]√802 + 16[tex]\pi[/tex] square cm (in terms of [tex]\pi[/tex]).
To know more about area visit:
brainly.com/question/28356316
#SPJ1
What does f(x)=12^x and g(x)=square root x-12 have in common?
Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
What is the Function?A relationship between a set of inputs (the domain) and a set of potential outputs (the range) is known as a function. This relationship has the feature that each input is associated to exactly one output.
The notation f(x) is often used to express a function in mathematics, where f is the name of the function and x is the input value, also known as the argument of the function. When f(x) is calculated, it indicates the function's output value for the given input value x.
First, both functions have a domain that includes all values of x greater than or equal to 12, which is expressed as [12,) in interval notation.
Second, both functions increase over the interval (12, ∞), meaning that as x increases beyond 12, the values of the functions also increase without bound. This is because the exponential function 12^x and the square root function √(x - 12) both become increasingly steep as x increases, leading to a sharp increase in their values.
Therefore, Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
To know more about domain value, visit:
https://brainly.com/question/26098895
#SPJ1
A one-topping pizza costs $12.99. This is $6.50 less than the cost of a specialty pizza. Explain how to write a subtraction equation that could be used to find the cost c of a specialty pizza.
Answer:
The cost of a specialty pizza is $19.49.
Step-by-step explanation:
To write a subtraction equation that could be used to find the cost c of a specialty pizza, we need to set up an equation that represents the relationship between the cost of a one-topping pizza and the cost of a specialty pizza.
The problem states that a one-topping pizza costs $6.50 less than a specialty pizza. Therefore, we can subtract $6.50 from the cost of a specialty pizza to get the cost of a one-topping pizza:
Cost of specialty pizza - $6.50 = Cost of one-topping pizza
We can rearrange this equation to solve for the cost of the specialty pizza:
Cost of specialty pizza = Cost of one-topping pizza + $6.50
Now, we can substitute the given value for the cost of a one-topping pizza:
Cost of specialty pizza = $12.99 + $6.50
Simplifying the expression, we get:
Cost of specialty pizza = $19.49
Therefore, the cost c of a specialty pizza is $19.49.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]