The exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3
To verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5], we need to check if the following conditions are satisfied:
f(x) is continuous on [2, 5].f(x) is differentiable on (2, 5).f(2) = f(5).Let's check each condition:
f(x) = x³ - 10x² + 31x - 30 is a polynomial function and is continuous for all real values of x. So, it is continuous on [2, 5].
To check the differentiability, we need to find f'(x):
f'(x) = 3x² - 20x + 31.
The derivative f'(x) exists and is continuous for all real values of x. So, f(x) is differentiable on (2, 5).
Now, let's evaluate f(2) and f(5):
f(2) = (2)³ - 10(2)² + 31(2) - 30 = -10
f(5) = (5)³ - 10(5)² + 31(5) - 30 = 95
Since f(2) = -10 is not equal to f(5) = 95, we can conclude that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5] after differentiable.
To find the values of c in the interval (2, 5) such that f'(c) = 0, we need to solve the equation f'(c) = 3c² - 20c + 31 = 0.
Using quadratic formula:
c = (-(-20) ± sqrt((-20)² - 4(3)(31))) / (2(3))
c = (20 ± sqrt(400 - 372)) / 6
c = (20 ± sqrt(28)) / 6
c = (20 ± 2sqrt(7)) / 6
c = (10 ± sqrt(7)) / 3
The values of c in the interval (2, 5) such that f'(c) = 0 are:
c = (10 + sqrt(7)) / 3
c = (10 - sqrt(7)) / 3
Therefore, the exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3.
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Incomplete question:
Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² +31x-30 on the interval [2, 5]. Then find all values of c in the interval such that f' (c) = 0.
Enter the exact answers in increasing order.
To enter √a, type sqrt(a)
c = ?
Which us better a 12oz for $0.85 or a 8oz for $0.50
Answer:
Step-by-step explanation:
12 oz is better
A loan of R1 000 is granted at an interest rate of 16% p.a. compounded quarterly. The loan is to be amortised by means of ten consecutive, equal quarterly payments starting one year after the granting of the loan. The balance outstanding on the loan (to the nearest cent) immediately after the seventh quarterly payment has been made is equal to R
The balance outstanding on the loan immediately after the seventh quarterly payment, using an interest rate of 16% p.a. compounded quarterly and equal quarterly payments, is R$310.39.
To calculate the balance outstanding after the seventh quarterly payment, we need to use the formula for the present value of an ordinary annuity:
P = PMT * (1 - (1 + r)^(-n)) / r
Where:
P = Principal amount of the loan (R$1,000)
PMT = Equal quarterly payment
r = Interest rate per period (16% p.a. compounded quarterly = 4% per quarter)
n = Number of periods (10 payments)
First, we calculate the equal quarterly payment (PMT) using the present value of an ordinary annuity formula rearranged to solve for PMT:
PMT = P * (r / (1 - (1 + r)^(-n)))
PMT = 1000 * (0.04 / (1 - (1 + 0.04)^(-10))) = R$129.09
Next, we calculate the balance outstanding after the seventh quarterly payment. We can consider it as the present value of the remaining three payments:
Balance = PMT * (1 - (1 + r)^(-n_remaining)) / r
Where: n_remaining = Number of remaining payments (10 - 7 = 3)
Balance = 129.09 * (1 - (1 + 0.04)^(-3)) / 0.04 = R$310.39
Therefore, the balance outstanding on the loan immediately after the seventh quarterly payment is R$310.39.
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For the solved question below, I am still unclear on how the PV Factor is figured out. What is the PV Factor formula?
The PV factor formula is given below: The formula for PV factor is: PV Factor = [1 - (1 + r)⁻ⁿ] / r
where r = discount rate, and n = number of periods.
PV factor can be used to calculate the present value of an annuity. If the amount of each payment and the number of periods are known, the present value of the annuity can be calculated using the following formula:
Present value of annuity = Payment × PV factor.
For example, suppose that you have an annuity that pays $1,000 per year for 5 years.
The discount rate is 8%. We can calculate the PV factor using the formula:
PV factor = [1 - (1 + r)⁻ⁿ] / r= [1 - (1 + 0.08)⁻⁵] / 0.08= 3.9936
The present value of the annuity can be calculated by multiplying the payment by the PV factor:
Present value of annuity = Payment × PV factor= $1,000 × 3.9936= $3,993.6
Therefore, the present value of the annuity is $3,993.6.
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what is the area of the conposite figure?
Step-by-step explanation:
Area of Rectangle = Length x Width
Area of Top Rectangle =
[tex]22 \times (31 - 18) \\ = 22 \times 13 \\ = 286 {ft}^{2} [/tex]
Area of bottom Rectangle =
[tex]18 \times 9 \\ = 162 {ft}^{2} [/tex]
Area of Composite figure = Area of top Rectangle + Area of bottom rectangle
[tex] = 286 + 162 \\ = 448 {ft}^{2} [/tex]
Jaelynn rolled a number cube that has sides labeled 1 to 6. What is the probability that she rolled a 2 or a 4?
The ratio of pears to green apples is 1:3 if there are 150 green apples how many pears are there
50. 150 divided by 3
What’s the area?? There’s a picture
Answer:
A= 12 Ft^2
Step-by-step explanation:
Reminder the Area formula is A=B(Base) times H(Height).
Take The base (6) and the Height (6) then multiply.
Hence, the reason is 12 Ft squared.
The bat population in a certain Midwestern county was 270,000 in 2012, and the observed doubling time for the population is 34 years.
Rob and Mary are planning trips to nine countries this year. There are 13 countries they would like to visit. They are deciding which countries to skip.
show me how to solve
Answer:
they will skip 4
Step-by-step explanation:
Answer:
They will have to skip the ones that are less desirable to them
A roller skating rink charges a skate rental fee and an hourly rate to skate.
The total cost to skate for 2 hours is $9.50 and for 5 hours is $18.50.
Assume the relationship is linear. Find and interpret the rate of change and
where x represents the number of hours and y represents the total cost.
initial value. Then write the equation of the function in the form y = mx + b
Answer:
The initial value, b = $3.50 is the skate rental fee
The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink
Step-by-step explanation:
From the question we have;
The charges of the roller skating rink = A skate rental fee + An hourly rate
The total cost to skate for 2 hours = $9.50
The total cost to skate for 5 hours = $18.50
The relationship between the total cost of skating and the duration in hours = Linear relationship
Let 'x' represent the number of hours skating and let 'y' represent the total cost, we have;
The form of the equation is y = m·x + b
Where;
m = The rate of change of the linear relationship
b = The initial value (y-intercept)
When x = 2, y = 9.50
Therefore, we can write;
9.50 = 2·m + b...(1)
When x = 5, y = 18.50
Therefore, we can write;
18.50 = 5·m + b...(2)
Subtracting equation (1) from equation (2) gives;
18.50 - 9.50 = 5·m - 2·m + b - b = 3·m
9.0 = 3 × m
∴ m = 9.0/3 = 3.0
The rate of change, m = 3.0
Similarly, we have;
From equation (1), we get;
9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b
9.50 = 6.0 + b
∴ b = 9.50 - 6.0 = 3.50
The initial value = 3.50
Therefore, the initial value, b = $3.50 is the skate rental fee while rate of change m = $3.0 is the hourly rate the rate.
Plzzzz help with the square ( parallelograms)
Answer:
#1=8
#2=3
Step-by-step explanation:
Which of the following box-and-whisker plots correctly displays the data set?
88 85 86 82 66 75
O
1
70 75
60 65
80 85 90
o
60 65
70 75 80 85 90
60 65 70 75 80 85 90
o
60 65
70 75 80 85
90
Answer:
1
70 75
60 65
80 85 90
o
60 65
70 75 80 85 90
60 65 70 75 80 85 90
o
60 65
70 75 80 85
90 95 105 120 125 130 135 140 145
The box and whisker plot which correctly displays the given data set is option 3.
What is Median?Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.
Given is a data set.
88 85 86 82 66 75
A box and whisker plot is used to summarize the data using boxes which shows the quartiles in the plot.
Arranging the data set in increasing order,
66 75 82 85 86 88
Highest value in the data set = 88
Lowest value = 66
The plot which correctly displays these two points are options 2 and 3.
Now, find the median of the data set.
Median is the average of 3rd and 4th element since this consist of even number of data sets.
Median = (82 + 85) / 2 = 83.5
This is correctly marked in option 3.
Hence the correct option is third one.
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The complete question is given in the image below. :
A random sample of 750 Democrats included 615 that consider protecting the environment to be a top priority. A random sample of 850 Republicans included 306 that consider protecting the environment to be a top priority, Construct a 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment.
The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is (0.41, 0.53). This means we can be 99% confident that the true difference in proportions falls within this interval.
Sample size of Democrats, n1 = 750
Number of Democrats who consider the environment as a top priority, x1 = 615
Sample size of Republicans, n2 = 850
Number of Republicans who consider the environment as a top priority, x2 = 306
Calculate the sample proportions:
Sample proportion of Democrats, p1 = x1 / n1 = 615 / 750 = 0.82
Sample proportion of Republicans, p2 = x2 / n2 = 306 / 850 = 0.36
Calculate the standard error of the difference in two sample proportions:
σd = sqrt{ [P1(1-P1) / n1] + [P2(1-P2) / n2] }
σd = sqrt{ [0.82(0.18) / 750] + [0.36(0.64) / 850] }
σd = sqrt{ 0.000180 + 0.000240 }
σd = sqrt{ 0.000420 }
σd ≈ 0.0205
Determine the level of confidence:
Given level of confidence, C = 99%
Find the critical value (z-score):
The z-score corresponding to the given level of confidence can be obtained from the standard normal table. For a 99% confidence level, the critical value is approximately z = 2.576.
Calculate the margin of error:
The margin of error is given by E = z * σd
E = 2.576 * 0.0205
E ≈ 0.0528
Construct the confidence interval:
The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is given by (D – d, D + d), where D is the difference in sample proportions and d is the margin of error.
(0.82 – 0.36 – 0.0528, 0.82 – 0.36 + 0.0528)
(0.41, 0.53)
Interpretation:
We can be 99% confident that the true difference in the percentages of Democrats and Republicans who prioritize protecting the environment falls within the interval (0.41, 0.53).
This means that there is a significant difference between the two groups in terms of the proportion that prioritize protecting the environment. The Democrats have a higher proportion compared to the Republicans.
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PLEASE HELP WILL MARK BRAINLIEST HELP QUICK!!
Answer: Your Answer would be A
Step-by-step explanation:
a) Rearrange the following formula to make x the subject.
Give your answer in its simplest form.
4(2x - 3y) = y + 5
+
Answer:
x = 13y + 0.625
Step-by-step explanation:
4(2x - 3y) = y + 5
8x - 12y = y + 5
8x = y + 5 + 12y
8x = 5 + 13y
8x ÷ 8 = 5 + 13y ÷ 8
x = 5 + 13y ÷ 8
x= 13y + 5 ÷8
x = 13y + 0.625
Elena notices that when she spends less time on social media the night before a quiz, she gets a higher score. Before one quiz, she spent 107 minutes on social media and eamed 37 points on a
quiz. Before another quiz, she spent 73 minutes on social media and eamed 11 points on a quiz
write a function to model a linear relationship between Elena's social media usage, in minutes, and her quiz scores, assuming that the total number of points on each quiz remains a constant
Respond in the space provided
Answer:
[tex] f(x) = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]
Step-by-step explanation:
Given:
Score of 37 with 107 minutes on social media.
Score of 41 with 73 minutes on social media.
The two pieces of information above can be thought of as two points on a line. Since the quiz score is a function of the number of minutes on social medial, let the number of minutes on social media be x and the score be y. The given information gives us two ordered pairs: (107, 37) and (73, 41).
Now we need to write the equation of a line that passes through these two points.
The two-point form of the equation of a line is:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have [tex] x_1 = 107 [/tex], [tex] y_1 = 37 [/tex], [tex] x_2 = 73 [/tex], and [tex]y_2 = 41[/tex].
[tex] y - 37 = \dfrac{41 - 37}{73 - 107}(x - 107) [/tex]
[tex] y - 37 = \dfrac{4}{-34}(x - 107) [/tex]
[tex] y - 37 = -\dfrac{2}{17}(x - 107) [/tex]
[tex] 17y - 629 = -2x + 214 [/tex]
[tex] 17y = -2x + 843 [/tex]
[tex] y = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]
[tex] f(x) = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]
explain how to multiply 641 by 63.
Answer:
sure
Step-by-step explanation:
1) line up 641 and 63
641
x__63_
2) multiply 3 by 1 then 4 then 6 and carry the tenths place number if there is one
1
641
x__63_
1923
3) add a zero under the 3 to hold the ones place and multiply 6 by 1 then 4 then 6 and since we’re working with the tenths place now and dont forget to carry numbers if you need to
2
641
x__63_
1923
38460
4) add your two numbers together
1 1
38460
+___1923_
40383
so that is your answer “40383”
lol sorry that this was so long
Answer:
The answer is 40,383
Step-by-step explanation:
First, you set up the multiplication. 641 is the largest number so it goes on top. 63 is the smallest number so it goes on the bottom. Draw your line. Next, you multiply 3 by 1 which is 3. Then you multiply 3 by 4 and you get 12. Since this is a two digit number, the 2 goes below the line and the 1 you place on top of the 6. Next, you multiply 3 by 6 and get 18, but don't forget the 1 you placed on top! So you get 19. Then you cross out the 1 on top of the 6 and cross out the 3. After you cross out the numbers you add a 0 under the 3 with the number that is under the line. Then you start multiplying 6x1 which is 6. 6x4 which is 24, place the 4 under the line and bring the 2 on top of the 6. Then multiply 6x6 which is 36, add the 2 you brought on top which is 38. After you did all that work, add all the numbers and your answer is 40,383! Hope this made sense and hope it helps! :3
Find the equation for the plane through Po(-5, -4,3) perpendicular to the following line. x= -5+t, y= - 4+ 3t, Z= -5t, - 00
The equation for the plane through the point Po(-5, -4, 3) and perpendicular to the line x = -5 + t, y = -4 + 3t, z = -5t is 3x + 9y - 5z = -64.
To find the equation of a plane, we need a point on the plane and a normal vector perpendicular to the plane. The given point on the plane is Po(-5, -4, 3). To find the normal vector, we can use the direction vector of the given line, which is parallel to the plane. The direction vector is (1, 3, -5). Since the plane is perpendicular to this direction vector, the normal vector of the plane is (-1, -3, 5), which is the negative of the direction vector.
Now we can use the point-normal form of a plane equation. Let (x, y, z) be any point on the plane. The vector from Po to (x, y, z) is given by (x + 5, y + 4, z - 3). We can take the dot product of this vector with the normal vector (-1, -3, 5) and set it equal to zero to get the equation of the plane:
(-1, -3, 5) · (x + 5, y + 4, z - 3) = 0
-1(x + 5) - 3(y + 4) + 5(z - 3) = 0
Simplifying the equation gives us:
-1x - 3y + 5z + 64 = 0
Rearranging the terms, we obtain the equation for the plane: 3x + 9y - 5z = -64.
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Express as a trinomial.
(x – 3)(3x – 8)
Please do this ASAP i need HELP
Answer:
3x^2 - 17x + 24
Step-by-step explanation:
(x – 3)(3x – 8)
3x^2 + (-8x) + (-9x) + 24
3x^2 - 17x + 24
Determine the approximate length of the segment AD *
Answer:
35/6
Step-by-step explanation:
The right angle triangle ABC which has another triangle BCD, the length of segment AD is, 9.73 cm
What is Pythagoras theorem?It is the most important theorem of mathematics, which tells us the relationship between sides of the right angle triangle, which are known as Base(A), Height(B), Hypotenuse(H).
Pythagoras theorem,
H² = A² + B²
Given that,
Two triangle,
ΔABC and ΔBCD
Side lengths are ,
AC = 19cm
BC = 8cm
DC = 11cm
AC² = AB² + BC²
19² = AB² + 8²
AB = 17.23
Another ΔBCD
11² = DB² + 8²
DB = 7.5
The length of AD = AB - DB
= 17.23 - 7.5
= 9.73
Hence, the length of the segment is 9.73 cm
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What is the total area of the triangle and the square?
Answer:
the answer is c or 35x^2 + 210x +315
Step-by-step explanation:
The area of the square is "d" and since it asks for the combined area of the triangle and square it has to be more than that, hope that helps.
25% of what number is 65?
HELPPPP
What is the name of the figure?
Im assuming a hexagon pyramid/cone???
Bc when you look at a square triangle its only called that becoause of its base??
Answer:
it's hexagon cone
someone said that so yeah
ILL GIVE YOU BRAINLIEST NO JOKE JUST PLEASE HELKP ME
Answer:
No
Step-by-step explanation:
She needs at least another 2 coordinate pairs to test if her evaluation is correct. For instance, the next pair could be (7,22). Then, the pattern wouldn't be increasing by 4. It would not have a constant of proportionality.
Explain the error in the solution below. What
additional step needs to be completed?
log x - log5^3 = 2log5^3
log x = 3log5 ^3
log x = log5 3^3.
x = 27
Answer:
x = 1953125
Step-by-step explanation:
log x - log 5^3 = 2 log 5^3
log x - 3 log 5 = 6 log 5
log x = 9 log 5 = log 5^9
x = 5^9
x = 1953125
in anova, the linearity assumption is assessed using a qq-plot of the residuals. t/f
False, the linearity assumption in ANOVA is not assessed using a QQ-plot of the residuals.
The linearity assumption in ANOVA refers to the assumption that the relationship between the independent variable(s) and the dependent variable is linear. This assumption is typically assessed by examining the residuals (the differences between the observed values and the predicted values) of the model. However, a QQ-plot is not specifically used to assess linearity.
A QQ-plot is commonly used to assess the assumption of normality in the residuals, which is another important assumption in ANOVA. It helps to visually compare the distribution of the residuals against a theoretical normal distribution. The linearity assumption is typically evaluated through other diagnostic plots, such as scatterplots of the residuals against the predicted values or the independent variable(s).
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Which of these could be an alternative hypothesis for a dependent samples t-test?
μ>30
μd<=0
μ1−μ2#0
μd#0
None of the above
The alternative hypothesis for a dependent samples t-test would be μd≠0.
In a dependent samples t-test, also known as a paired samples t-test, the goal is to compare the means of two related variables or measurements taken from the same sample.
The null hypothesis assumes that the mean difference between the paired measurements is zero (μd = 0). The alternative hypothesis, on the other hand, proposes that there is a significant difference between the means of the two variables.
Among the given options, μ>30 and μd<=0 do not represent the alternative hypothesis for a dependent samples t-test. These options suggest a specific value or direction of the mean, rather than a difference between means.
The option μ1−μ2≠0 is also not the correct alternative hypothesis as it represents the null hypothesis (μd = 0). The option μd ≠ 0, however, accurately represents the alternative hypothesis for a dependent samples t-test. It states that there is a significant difference between the means of the two variables being compared.
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Jacob wrote the expression shown. 10 + 5 + 4(72-6) What do these parentheses indicate in the expression? F Divide 10 by 5 before adding 4 G Multiply 4 by 72 before subtracting 6 H Add 5 and 4 together before subtracting 6 from 72 Subtract 6 from 72 before multiplying by 4
I will give brainliests
help please.............
Answer:
C
Step-by-step explanation:
CHOOSE C
Helpppppp! No links please, thank you!