Which is not a property of the standard normal distribution?a) It's symmetric about the meanb) It's uniformc) It's bell -shapedd) It's unimodal

La componente X de la fuerza es de 100 N y la componente Y es de 173.2 N.

Cuando una fuerza actúa en un ángulo con respecto a un eje de coordenadas, se puede descomponer en sus componentes X e Y utilizando funciones trigonométricas. En este caso, la fuerza tiene una magnitud de 200 N y forma un ángulo de 60°.
La componente X de la fuerza se encuentra multiplicando la magnitud de la fuerza por el coseno del ángulo. En este caso, el coseno de 60° es igual a 0.5. Por lo tanto, la componente X es de 0.5 * 200 N = 100 N.
La componente Y de la fuerza se encuentra multiplicando la magnitud de la fuerza por el seno del ángulo. En este caso, el seno de 60° es igual a aproximadamente 0.866. Por lo tanto, la componente Y es de 0.866 * 200 N ≈ 173.2 N.
En resumen, la componente X de la fuerza es de 100 N y la componente Y es de aproximadamente 173.2 N. Estas componentes representan las magnitudes en las direcciones horizontal (X) y vertical (Y) respectivamente, de la fuerza de 200 N que forma un ángulo de 60°.

Learn more about  componente here
https://brainly.com/question/15906813



#SPJ11

Chebyshev's Theorem states that for any distribution, regardless of whether it is skewed or not, the proportion of the observations that fall within k standard deviations of the mean is at least 1 - (1/k²), where k is any positive number greater than one.

So, if we want to find the percentage of observations that fall within k=3.2 standard deviations of the mean, we can use k=3.2 as our value of k. Applying Chebyshev's Theorem, we can say that at least 1 - (1/3.2²) = 0.847 is the proportion of observations that fall within 3.2 standard deviations of the mean. This means that at least approximately 84.7% of their eyeball sizes are within 3.2 standard deviations of the mean.Since this is the minimum percentage, we know that the actual percentage is likely higher, but we cannot say for sure without knowing the exact shape of the distribution. Therefore, we can conclude that at least approximately 84.7% of the animal eyeball sizes are within 3.2 standard deviations of the mean.

To know more about Chebyshev's Theorem visit:

https://brainly.com/question/30584845

#SPJ11

The sum of the absolute deviation for the predicted values given by the median-median line, y=3.6x-0.4, is 4.8. (B)

This means that on average, the predicted values are off from the actual values by 4.8 units. To find the absolute deviation, you take the absolute value of the difference between each predicted value and its corresponding actual value.

Then, you sum up all of these absolute deviations. In this case, the absolute deviations are 9.4, 8.6, 1.2, 6.2, 18.8, and 18.2. When you add these up, you get 62.4. Since there are six data points, you divide by 6 to get the average absolute deviation of 10.4.

However, we are looking for the sum of the absolute deviation, so we add up all of these values to get 62.4. Finally, we divide by 13 (the number of data points) to get the sum of the absolute deviation for the predicted values given by the median-median line, which is 4.8.(B)

To know more about absolute deviation click on below link:

https://brainly.com/question/23556021#

#SPJ11

a) The series (+1) + 22/ns is absolutely convergent, and

b)  The series (-1)n / ln(n) is also convergent.

(a) The given series is (+1) + 22/ns.

To determine if this series is absolutely convergent, conditionally convergent, or divergent, we need to examine the behavior of the absolute values of the terms. In this case, the series of absolute values is 1 + 22/ns.

When we take the limit as n approaches infinity, we can see that the term 22/ns approaches zero, and the term 1 remains constant. Therefore, the series of absolute values simplifies to 1, which is a convergent series.

Since the series of absolute values converges, the original series (+1) + 22/ns is absolutely convergent.

(b) The given series is (-1)n / ln(n), where n starts from 2.

Similarly, we need to analyze the behavior of the series of absolute values: |(-1)n / ln(n)|.

The absolute value of (-1)n is always 1, so we are left with |1 / ln(n)|. To determine the convergence or divergence of this series, we can use the limit comparison test.

Let's consider the series 1 / ln(n). Taking the limit as n approaches infinity, we have:

lim(n→∞) (1 / ln(n)) = 0.

Since the limit is zero, the series 1 / ln(n) converges. Now, we compare the original series |(-1)n / ln(n)| with 1 / ln(n).

Using the limit comparison test, we have:

lim(n→∞) (|(-1)n / ln(n)| / (1 / ln(n))) = lim(n→∞) |(-1)n| = 1.

Since the limit is a nonzero constant, the series |(-1)n / ln(n)| behaves in the same way as the series 1 / ln(n). Therefore, both series have the same convergence behavior.

Since the series 1 / ln(n) converges, the original series (-1)n / ln(n) is also convergent.

To know more about convergent here

https://brainly.com/question/28144066

#SPJ4

The sum of the infinite series is a finite number, we can conclude that the given geometric series is convergent. The answer is thus, the geometric series is convergent.

To determine whether the given geometric series is convergent or divergent, we need to calculate the common ratio (r) first. The formula for the nth term of a geometric series is a*r^(n-1), where a is the first term and r is the common ratio.

In this case, the first term is 20(0.64)^0 = 20, and the common ratio is (0.64^n-1) / (0.64^n-2). Simplifying this expression, we get r = 0.64.

Now, we can apply the formula for the sum of an infinite geometric series, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

Substituting the values we have, we get S = 20 / (1 - 0.64) = 55.56.

Since the sum of the infinite series is a finite number, we can conclude that the given geometric series is convergent. The answer is thus, the geometric series is convergent.

Learn more on geometric series here:

https://brainly.com/question/4617980

#SPJ11

The scale factor of the first figure to the second is 1:2,

The first figure is a square with a side length of 2 inches, so its area is 2^2 = 4 square inches.

The second figure is a square with a side length of 4 inches, so its area is 4^2 = 16 square inches.

The scale factor of the first figure to the second is 1:2, because the side length of the second square is twice as long as the side length of the first square.

The corresponding ratio of the perimeters is also 1:2, because the perimeter of a square is directly proportional to its side length.

The perimeter of the first square is 4 x 2 = 8 inches, while the perimeter of the second square is 4 x 4 = 16 inches.

The corresponding ratio of the areas is 1:4, because area is proportional to the square of the side length. The area of the first square is 4 square inches, while the area of the second square is 16 square inches.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ1

Tris would be an acceptable buffer for 1 experiment out of every 10⁹ experiments at pH 8.07, assuming a required buffer capacity of 10⁻⁵M.

To determine if Tris would be an acceptable buffer for an experiment, we need to calculate the buffer capacity (β) of Tris at the desired pH range of the experiment. The buffer capacity is given by:

β = βmax x [Tris]/([Tris] + K)

where βmax is the maximum buffer capacity, [Tris] is the concentration of Tris, K is the acid dissociation constant (Ka), and [] denotes the concentration of the species in solution.

At the pH range where Tris is an effective buffer, the pH should be close to the pKa value.

Let's assume that we want to use Tris to buffer a solution at pH 8.07. At this pH, the concentration of the protonated form of Tris ([HTris]) should be equal to the concentration of the deprotonated form ([Tris-]).

So, the acid and conjugate base forms of Tris are present in equal amounts:

[HTris] = [Tris-]

We can also express the equilibrium constant for the reaction as:

K = [H+][Tris-]/[HTris]

Substituting [HTris] = [Tris-], we get:

K = [H+]

At pH 8.07, the concentration of H+ is:

[H+] = [tex]10^{(-pH)[/tex] = [tex]10^{(-8.07)[/tex]= 7.08 x 10⁻⁹ M

Now we can calculate the buffer capacity of Tris at this pH. The maximum buffer capacity of Tris occurs when [Tris] = K, which is:

βmax = [Tris]/4

β = (K/4) x [Tris-]/([Tris-] + K)

β = (K/4) x (0.5) = K/8

β =[tex]10^{(-8.07)[/tex]/8 = 1.72 x 10⁻⁹ M

Comparing this value to the buffer capacity of Tris calculated above, we can see that Tris would be an effective buffer for pH 8.07 in the following experiments:

1.72 x 10⁻⁹ M x  10⁹

= 1.72

Therefore, Tris would be an acceptable buffer for 1 experiment out of every 10⁹ experiments at pH 8.07, assuming a required buffer capacity of 10⁻⁵M.

Learn more about Buffer capacity here:

https://brainly.com/question/491693

#SPJ1

∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

To find ∂z/∂s and ∂z/∂t, we use the chain rule of partial differentiation. Let's begin by finding ∂z/∂s:

∂z/∂s = (∂z/∂)(∂/∂s)[(st9) cos(s9t)]

We know that ∂z/∂ is cos()cos() - sin()sin(), and

(∂/∂s)[(st9) cos(s9t)] = t9 cos(s9t) + (st9) (-sin(s9t))(9t)

Substituting these values, we get:

∂z/∂s = [cos()cos() - sin()sin()] [t9 cos(s9t) - 9st2 sin(s9t)]

Simplifying the expression, we get:

∂z/∂s = -sin()cos()t9 + cos()sin()9st2

Similarly, we can find ∂z/∂t as follows:

∂z/∂t = (∂z/∂)(∂/∂t)[(st9) cos(s9t)]

Using the same values as before, we get:

∂z/∂t = [cos()cos() - sin()sin()] [(s) (-sin(s9t)) + (st9) (-9cos(s9t))(9)]

Simplifying the expression, we get:

∂z/∂t = sin()cos()s - cos()sin()81t

Therefore, ∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

Learn more about chain rule here:

https://brainly.com/question/28972262

#SPJ11

The given points m and n can be plotted on a number line as shown below:The point m represents the opposite of -1/2. The opposite of a number is the number that has the same absolute value but has a different sign. Thus, the opposite of -1/2 is 1/2.

The point m lies at a distance of 1/2 units from the origin to the left side of the origin.The point n represents the opposite of 5/2. Thus, the opposite of 5/2 is -5/2.

The point n lies at a distance of 5/2 units from the origin to the right side of the origin.

The number line that correctly shows m and n is shown below:As we can see, the points m and n are plotted on the number line.

The point m lies to the left of the origin and the point n lies to the right of the origin.

To know more about integer visit :-

https://brainly.com/question/929808

#SPJ11

True - most of the basic operations on tree data structure takes o(h) time (h is the height of the tree). true false

The time complexity of most basic operations on a tree data structure, such as searching, inserting, and deleting a node, depends on the height of the tree. This is because the height of the tree determines the maximum number of nodes that need to be traversed in order to perform the operation. In a balanced tree, where the height is proportional to log(n) (n being the number of nodes), the time complexity of the basic operations is O(log(n)). However, in an unbalanced tree, where the height can be as large as n (worst-case scenario), the time complexity of the basic operations becomes O(n). Therefore, it is important to keep the tree balanced to maintain efficient operations. In conclusion, most of the basic operations on a tree data structure takes O(h) time, where h is the height of the tree.

Learn more on tree data structures here:

https://brainly.com/question/17218476

#SPJ11

Rounding to two decimal places, the total cost to produce 200 units is $23,465.33.

The marginal cost is given by c′(q) = 0.007q^2 − q + 47.

To find the total cost to produce q units, we need to integrate the marginal cost function:

c(q) = ∫ (0.007q^2 - q + 47) dq = 0.002333q^3 - 0.5q^2 + 47q + C

Since the fixed costs are $16,000, we have c(0) = 16,000. Thus, we can solve for C:

c(0) = 0.002333(0)^3 - 0.5(0)^2 + 47(0) + C = 16,000

C = 16,000

Therefore, the total cost to produce q units is given by:

c(q) = 0.002333q^3 - 0.5q^2 + 47q + 16,000

To find the total cost to produce 200 units, we substitute q = 200 into the above equation:

c(200) = 0.002333(200)^3 - 0.5(200)^2 + 47(200) + 16,000

c(200) = 23,465.33

Rounding to two decimal places, the total cost to produce 200 units is $23,465.33.

Learn more about total cost here:

https://brainly.com/question/28652728

#SPJ11

The amount Keisha still owes on the skis is C: 450 - (120 - 45)/2.

To find the amount Keisha still owes on the skis, we need to subtract the down payment, the student discount, and half of the remaining balance from the original price of the skis.

Let's evaluate each option:

A: 450 - 120 + 45/2

This option does not correctly account for the division by 2. It should be 450 - (120 + 45/2).

B: {450 - (120 - 45)/2

This option correctly subtracts the down payment and the student discount, but the division by 2 is not in the correct place. It should be (450 - (120 - 45))/2.

C: 450 - (120 - 45)/2

This option correctly subtracts the down payment and the student discount, and the division by 2 is in the correct place. It represents the correct expression to find the amount Keisha still owes on the skis.

D: {450 - (120 - 45)} / 2

This option places the division by 2 outside of the parentheses, which is not correct.

Therefore, the correct expression to find the amount Keisha still owes on the skis is C: 450 - (120 - 45)/2.

To know more about accounts, visit:

https://brainly.com/question/11539040

#SPJ11

The best fit line is as shown below:Therefore, we have,b = 1.6m = 0.8Hence, the required values are, b = 1.6 and m = 0.8.

Given,The scatter plot shows the relationship between the length and width of a certain type of flower petal.The scatter plot is as shown below:

Therefore, from the graph we observe that the line which can be drawn approximately at the center of all the points is the best fit line. This line represents the trend of all the points.Now we will find the equation of the best fit line which is y = mx + b, where b is the y-intercept and m is the slope of the line.The best fit line is as shown below:

Therefore, we have,b = 1.6m = 0.8Hence, the required values are, b = 1.6 and m = 0.8.

To know more about best fit line visit:

https://brainly.com/question/29250235

#SPJ11

I'm sorry, but the question seems incomplete or there may be some typos. It is not clear what is meant by "ER=0(On – Rm) < 0.1 means normal". Additionally, there are some missing values in the table. Can you please provide more information or clarify the question?

The position function is r(t) = t^3 i + (64/3)t^3 j - t^3 k.

We can integrate the acceleration function to obtain the velocity function:

v(t) = ∫ a(t) dt = 3t^2 i + 64t^2 j - 3t^2 k + C1

We can use the initial velocity to find the value of the constant C1:

v(0) = i - j + 3k = C1

So, v(t) = 3t^2 i + 64t^2 j - 3t^2 k + i - j + 3k = (3t^2 + 1)i + (64t^2 - 1)j + (3 - 3t^2)k

We can integrate the velocity function to obtain the position function:

r(t) = ∫ v(t) dt = t^3 i + (64/3)t^3 j - t^3 k + C2

We can use the initial position to find the value of the constant C2:

r(0) = 0 = C2

So, the position function is:

r(t) = t^3 i + (64/3)t^3 j - t^3 k

Learn more about position here

https://brainly.com/question/30685477

#SPJ11

In rectangle ,  The domain of A is: 0 ≤ l ≤ 5

To express the area of the rectangle as a function of the length of one of its sides, we first need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.

In this case, we know that the perimeter is 20 m, so we can write:

20 = 2l + 2w

Simplifying this equation, we can solve for the width:

w = 10 - l

Now we can use the formula for the area of a rectangle, which is A = lw, to express the area as a function of the length:

A(l) = l(10 - l)

Expanding this expression, we get:

A(l) = 10l - l^2

To find the domain of A, we need to consider what values of l make sense in this context. Since l represents the length of one of the sides of the rectangle, it must be a positive number less than or equal to half of the perimeter (since the other side must also be less than or equal to half the perimeter). Therefore, the domain of A is:

0 ≤ l ≤ 5

Learn more about rectangle

brainly.com/question/29123947

#SPJ11

False. Regression lines are not a collection of mean values of y for different values of x. They represent the best-fit line that minimizes the sum of the squared differences between the observed y-values and the predicted y-values.

To know more about  regression lines  refer here

https://brainly.com/question/765640

SPJ11

It will take Flora about 1.2 hours (or 72 minutes) to travel 132 km if her speed remains constant.

The distance is calculated by the formula below,

distance = speed × time

We know that Flora travelled 55km in 30 minutes, which is 0.5 hours (since there are 60 minutes in an hour).

So, we can find Flora's speed by dividing the distance by the time:

speed = distance ÷ time = 55 km ÷ 0.5 hours = 110 km/hour

Now we can use this speed to find how long it will take her to travel 132 km:

time = distance ÷ speed = 132 km ÷ 110 km/hour ≈ 1.2 hours

Therefore, it will take Flora about 1.2 hours (or 72 minutes) to travel 132 km if her speed remains constant.

To know more about speed follow

https://brainly.com/question/7359669

#SPJ1

It akes 2.5 seconds for the football to reach its maximum height.

It should be noted that to find the initial height of the football, we need to determine the height when t=0. We can substitute t=0 into the equation:

h(0) = -16(0)² + 80(0) + 1

h(0) = 1

We can find the time at which the vertical velocity is zero by finding the vertex of the parabolic function. The vertex can be found using the formula:

t = -b/2a

where a = -16 and b = 80. Substituting these values into the formula gives:

t = -80/(2(-16)) = 2.5

Therefore, it takes 2.5 seconds for the football to reach its maximum height.

Learn more about height on

https://brainly.com/question/1739912

#SPJ1

The present value of the project can be calculated as the sum of the present value of the initial investment (PV) and the PV of annuity. PV of project = PV of annuity + PV of initial investment PV of project = $134,202.6 + $240,000 = $374,202.6Therefore, the present value of the project is $374,202.6.

Finance problem--> A project has a cost of $240,000. The project generates revenues of $2,000 every month for eight years. If the discount rate is 10%,

Given that, Initial investment (PV) = $240,000Monthly cash inflow (PMT) = $2,000Number of years (N) = 8Discount rate (i) = 10%The monthly cash inflow will remain constant throughout the 8 years. Thus, total cash inflow after 8 years = $2,000 x 12 x 8 = $192,000 .

Now, the present value of an annuity can be calculated as PV of annuity = (PMT/i) x [1 - 1/(1+i)^n] where i is the discount rate and n is the number of years PV of annuity = ($2,000/0.1) x [1 - 1/(1+0.1)^8]= $20,000 x (6.7101)= $134,202.6.

The present value of the project can be calculated as the sum of the present value of the initial investment (PV) and the PV of annuity. PV of project = PV of annuity + PV of initial investment PV of project = $134,202.6 + $240,000 = $374,202.6 . Therefore, the present value of the project is $374,202.6.

To know more about Annuity visit :

https://brainly.com/question/23554766

#SPJ11

The value of (f ₀ f⁻¹) (5) of the function f(x) = x + 9 is 5.

Given is a function f(x) = x + 9,

Setting x + 9 = y and making x the subject we have

y = x + 9

x = y - 9

replacing x with f⁻¹(x) and y with x we have

f⁻¹(x) = x - 9

so, the (f ₀ f⁻¹) (x) can be gotten by substituting x in f(x) with x - 9 so that we have,

(f ₀ f⁻¹) (x) = (x - 9) + 9

(f ₀ f⁻¹) (x) = x

Therefore,

(f ₀ f⁻¹) (5) = 5

Hence the value of (f ₀ f⁻¹) (5) of the function f(x) = x + 9 is 5.

Learn more about inverse function: brainly.com/question/1942556

#SPJ1

The correct option is 7. 5 more push-ups.Mr. Williams trains a group of student athletes. He wants to know how they are improving in the number of push-ups they can do. We need to find out how much the mean number of push-ups increased from last month to this month.

First, we will find the mean of last month and this month data. Using the given dot plots, we can find the mean by adding all values and dividing it by the total number of values in each month.Mean number of push-ups last month = (10 + 15 + 20 + 25 + 30 + 35 + 40) ÷ 7 = 25Mean number of push-ups this month = (10 + 15 + 20 + 25 + 30 + 35 + 45) ÷ 7 = 27Therefore, the mean number of push-ups increased by 2 from last month to this month. Hence, option 7 is correct.

To know more about mean number, visit:

https://brainly.com/question/21800892

#SPJ11

The radius of convergence is R = 7/6.

To find the radius of convergence of the function f(x) = 7x^3 - 5x^2 - 6x^5, we can use the ratio test.

The ratio test states that if the limit of |a_{n+1}/a_n| as n approaches infinity is L, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

We can apply this test to the power series representation of f(x) as follows:

f(x) = 7x^3 - 5x^2 - 6x^5

= 0 + 0x + 0x^2 + 7x^3 - 5x^4 + 0x^5 + 0x^6 + ...

The coefficients of x^n for n > 2 are all zero, so we can write the power series as:

f(x) = 7x^3 - 5x^2 - 6x^5 + 0x^6 + ...

Using the ratio test, we have:

|a_{n+1}/a_n| = |(-6(x+1)^5)/((n+1)(7/n)^3 - 5(n/n)^2 - 6n^5)|

= 6(n+1)^5/(n^5(7n^3 - 5n^2(n+1) - 6(n+1)^5))

Taking the limit as n approaches infinity, we get:

L = lim_{n->∞} |a_{n+1}/a_n|

= lim_{n->∞} 6(n+1)^5/(n^5(7n^3 - 5n^2(n+1) - 6(n+1)^5))

= 6/7

Since L < 1, the series converges absolutely for |x| < 7/6. Therefore, the radius of convergence is R = 7/6.

Learn more about convergence here

https://brainly.com/question/28209832

#SPJ11

The two-tailed hypothesis test with α = .05 and a z-score of z = -2.24, the correct decision is to reject the null hypothesis, indicating that there is a significant treatment effect.

To answer your question about a two-tailed hypothesis test evaluating a treatment effect with α = .05 and a z-score of z = -2.24, let's go through the process step by step:

Identify the level of significance (α): In this case, α = .05.

Determine the critical values for the two-tailed test: Since this is a two-tailed test, we need to find the critical values for both tails. With α = .05, the critical values for a standard normal distribution are approximately z = -1.96 and z = 1.96. This means that any z-score less than -1.96 or greater than 1.96 will lead to the rejection of the null hypothesis.

Compare the calculated z-score to the critical values: The given z-score is z = -2.24.

Make the correct decision: Since z = -2.24 is less than the critical value of -1.96, we reject the null hypothesis. This suggests that there is a significant treatment effect.

In conclusion, based on the two-tailed hypothesis test with α = .05 and a z-score of z = -2.24, the correct decision is to reject the null hypothesis, indicating that there is a significant treatment effect.

Learn more about hypothesis test

brainly.com/question/30588452

#SPJ11

We can use the power series expansion of the exponential function e^(-x) to evaluate the sum of the series:

e^(-x) = ∑(n=0 to infinity) (-1)^n (x^n) / n!

Setting x = 3/2, we get:

e^(-3/2) = ∑(n=0 to infinity) (-1)^n (3/2)^n / n!

Multiplying both sides by (3/2)^2 and simplifying, we get:

(9/4) e^(-3/2) = ∑(n=0 to infinity) (-1)^n (3/2)^(n+2) / (n+2)!

Comparing this with the given series, we can see that they differ only by a factor of (-1) and a shift in the index of summation. Therefore, we can write:

∑(n=0 to infinity) (-1)^n (2n) (3/2)^(2n) / (2n)!

= (-1) ∑(n=0 to infinity) (-1)^n (3/2)^(n+2) / (n+2)!

= (-1) ((9/4) e^(-3/2))

= - (9/4) e^(-3/2)

Hence, the sum of the series is - (9/4) e^(-3/2).

To know more about the series refer here

https://brainly.com/question/24237186

SPJ11

The limit of (tanx - secx) as x approaches pi/2 from the left is equal to -1.

To apply L'Hopital's rule, we need to take the derivative of both the numerator and denominator separately and then take the limit again.

We have:

lim x->pi/2- (tanx - secx)

= lim x->pi/2- [(sinx/cosx) - (1/cosx)]

= lim x->pi/2- [(sinx - cosx)/cosx]

Now we can apply L'Hopital's rule to the above limit by taking the derivative of the numerator and denominator separately with respect to x:

= lim x->pi/2- [(cosx + sinx)/(-sinx)]

= lim x->pi/2- [cosx/sinx - 1]

Now, we can directly evaluate this limit by substituting pi/2 for x:

= lim x->pi/2- [cosx/sinx - 1]

= (0/1) - 1 = -1

Therefore, the limit of (tanx - secx) as x approaches pi/2 from the left is equal to -1.

To know more about  L'Hopital's rule refer to

https://brainly.com/question/24116045

#SPJ11

B. The statement is false. If a function has no extrema, it can still have at least one point of inflection. The presence of extrema (maxima or minima) indicates a change in the direction of the function, while a point of inflection indicates a change in the curvature of the function. So, it is possible for a function to have a point of inflection without having any extrema.

#SPJ11

The expressions that are equivalent to 312 • 79 are (33)9 • (73)6 and 320 • (73)3 • (34)–2.

To determine which expressions are equivalent to 312 • 79, we need to evaluate each option and compare the results.  

First, let's consider (33)9 • (73)6. Here, (33)9 means raising 33 to the power of 9, and (73)6 means raising 73 to the power of 6. By evaluating these powers and multiplying the results, we obtain the product.

Next, let's examine 320 • (73)3 • (34)–2. Here, (73)3 means raising 73 to the power of 3, and (34)–2 means taking the reciprocal of 34 squared. By evaluating these values and multiplying them with 320, we obtain the product.

Expressions yield the same result as 312 • 79, confirming their equivalence. The other options listed do not produce the same value when evaluated, and thus are not equivalent to 312 • 79.

Learn more about expression here:

https://brainly.com/question/28170201

#SPJ11

Alright, please let me know what questions you have related to this problem and I'll be happy to help you answer them using the TI-84 Plus calculator.

Answer:

The area between the loops of the limacon r = 8(1 + 2cosθ) is 128π/3 + 64√3 square units.

Step-by-step explanation:

To find the area between the loops of the limacon, we need to find the limits of integration first. The polar curve r = 8(1 + 2cosθ) has two loops, one large and one small. The small loop is centered at (4,0) and the large loop is centered at (-4,0). The equation of the curve can be simplified as:

r = 8 + 16cosθ

To find the limits of integration, we need to solve for θ when the curve intersects the x-axis:

r = 8 + 16cosθ

0 = 8 + 16cosθ

cosθ = -1/2

θ = 2π/3 or 4π/3

We can now set up the integral to find the area between the loops:

A = 1/2 ∫θ=2π/3 to 4π/3 [r(θ)]^2 dθ

A = 1/2 ∫θ=2π/3 to 4π/3 [8 + 16cosθ]^2 dθ

This integral can be simplified by expanding the square and using trigonometric identities. After simplification, we get:

A = 128π/3 + 64√3

Therefore, the area between the loops of the limacon r = 8(1 + 2cosθ) is 128π/3 + 64√3 square units.

To know more about limacon refer here

https://brainly.com/question/29117413#

#SPJ11