(3 points) suppose you want to estimate, on average, how much time college students spent on social media applications in a typical day. you wish your estimate to be within 0.1 hrs with 98% confidence. how large should your sample be? use sample standard deviation 1 (hr) as an educated guess for standard deviation. you may find the following r output helpful.

Answer:

he length of the rope is approximately equal to 10.99 feet

The total interest that Mia paid during her 2 years in school and the six-month grace period was $273.75.

The total interest that Mia paid during the 2.5 years when she did not repay the student loan was the product of the multiplication of the principal, interest rate, and period.

Unsubsidized 10-year federal loan Mia received = $5,000

Interest rate = 2.19%

Loan period = 10 years

Non-repayment period = 2.5 years

Interest during the non-repayment period = $273.75 ($5,000 x 2.19% x 2.5)

Learn more about student loan interests at https://brainly.com/question/30682426.

#SPJ1

a. The manufacturer should produce and sell 70,000 units of Product A and 50,000 units of Product B each week to maximize the weekly profit.

b. The maximum value of the total weekly profit is $40,766.67.

To find the maximum weekly profit, we need to find the values of x and y that maximize the profit function P(x, y).

We can do this by taking partial derivatives of P with respect to x and y, setting them equal to zero, and solving for x and y.

(a) To find the optimal values of x and y, we take the partial derivatives of P with respect to x and y:

∂P/∂x = 560 + 20y - 40x

∂P/∂y = 20x - 12y

Setting these equal to zero, we get:

560 + 20y - 40x = 0

20x - 12y = 0

Solving for x and y, we get:

x = 14y/5

y = 25 - 7x/2

Substituting x into the second equation, we get:

y = 50/3

So the optimal values of x and y are:

x = 70/3

y = 50/3.

Therefore, the manufacturer should produce and sell 70,000 units of Product A and 50,000 units of Product B each week to maximize the weekly profit.

(b) To find the maximum value of the total weekly profit, we substitute the optimal values of x and y into the profit function P(x, y):

[tex]P(70/3,50/3) = 560(70/3) + 20(70/3)(50/3) - 20(70/3)^2 - 6(50/3)^2= $40,766.67[/tex]

For similar question on profit.

https://brainly.com/question/21637154

#SPJ11

2x² + 7x + 9 is the expression for  the unknown area.

The length of the rectangle is 2x+7, which means one side is x+3 and the other is x+4.

The first area can be written as expression (x+5)² - 4

which means one side is x+5 and the other is x+5-4=x+1.

The second area can be written as (x+3)² - 1

which means one side is x+3 and the other is x+3-1=x+2.

To find the unknown area, we can subtract the two known areas from the total area of the rectangle:

Total area = (x+5)² - 4 + (x+3)² - 1 + A

Total area = (2x+7)(x+4)

Therefore,

(2x+7)(x+4) = (x+5)² - 4 + (x+3)² - 1 + A

Simplifying and solving for A, we get:

A = 2x² + 7x + 9.

To learn more on Areas click:

https://brainly.com/question/20693059

#SPJ1

Answer:2 hours and 45 minutes

Step-by-step explanation:

11:30+30 mins =12+15 mins = 12:15 + 2 hours = 2:15

The boy traveled a total distance of 338 kilometers.

We can start by calculating the boy's walking distance.

Distance = speed x time.

The boy walked for 0.25 hours, or one-quarter of an hour. The distance covered on foot is calculated as follows:

Distance = 8 km/h x 0.25 h = 2 km

Next, we can determine how far a bus travels. The boy covered the following distance in 12 hours by bus at a speed of 28 km/h:

Distance = Speed x Time

Distance = 28 km/h x 12 hours = 336 km.

The sum of the distances walked and traveled by bus represents the total distance traveled:

Total distance = 2 km + 336 km = 338 km

Therefore, the boy traveled a total distance of 338 kilometers.

Learn more about distance here : brainly.com/question/26046491

#SPJ1

To solve this problem, we need to break it down into smaller parts. First, we need to find the total number of possible passwords with length 9, where each character is either a capital letter or a digit. Since there are 26 capital letters and 10 digits, there are a total of 36 possible characters. Therefore, the total number of possible passwords is 36^9.

Next, we need to find the number of passwords where no character appears more than once. For the first character, there are 36 possibilities. For the second character, there are only 35 possibilities since we cannot repeat the character used for the first character. Continuing in this way, we get:

36 × 35 × 34 × 33 × 32 × 31 × 30 × 29 × 26

This gives us the total number of passwords where no character appears more than once.

Finally, we need to find the number of passwords where the last two characters are letters. Since there are 26 letters, there are 26^2 possible combinations of two letters. Therefore, the number of passwords where the last two characters are letters is:

26^2 × 36^7

To find the final answer, we need to multiply the number of valid passwords where no character appears more than once by the number of passwords where the last two characters are letters:

36 × 35 × 34 × 33 × 32 × 31 × 30 × 29 × 26 × 26^2 × 36^7

This simplifies to:

9,458,774,615,360,000

Therefore, there are 9,458,774,615,360,000 valid passwords that meet the given criteria.

learn more about possible passwords here: brainly.com/question/31189529

#SPJ11

Based on the table below, the probability distribution for the game shows the probability of winning different cash prizes.Probability (not winning a cash prize) = Q1 + Q2 + ... + Qn

To calculate the probability of not winning a cash prize, we need to add up the probabilities of losing or not winning anything. From the table, we can see that the probability of not winning a cash prize is 0.6 + 0.2 + 0.05 = 0.85. This means that if the game is played one time, there is an 85% chance of not winning a cash prize. It's important to note that the remaining 15% represents the probability of winning some type of cash prize. It's always important to consider the probability of both winning and losing when playing any type of game or taking a risk.

| Cash Prize | Probability |
|------------|-------------|
| $50        | 0.1         |
| $20        | 0.2         |
| $10        | 0.25        |
| $5         | 0.25        |
| $0         | 0.6         |
|------------|-------------|
| Total      | 1.0         |

The probability distribution table shows the possible outcomes and their associated probabilities for the game. To find the probability of not winning a cash prize, we need to identify the outcomes where no cash prize is won and sum their probabilities.

Let's assume the table has a column for outcomes with cash prizes and their probabilities (P1, P2, etc.), and a column for outcomes without cash prizes and their probabilities (Q1, Q2, etc.). To find the probability of not winning a cash prize, simply add the probabilities of all non-winning outcomes:

Probability (not winning a cash prize) = Q1 + Q2 + ... + Qn

This calculation provides the likelihood of not winning a cash prize when playing the game one time.

Visit here to learn more about probability  :https://brainly.com/question/30034780
#SPJ11

Larger companies and corporations may have headquarters or major offices in metropolitan areas, providing more job opportunities and potentially higher salaries.

There could be several reasons why non-metropolitan workers in the United States earn less than their metropolitan counterparts. One possible explanation is that industries that tend to pay higher wages, such as technology and finance, are more concentrated in metropolitan areas. Another factor could be the level of education and training available in non-metropolitan areas, which may limit the types of jobs and salaries available. These are just a few potential reasons why there may be a difference in median earnings between non-metropolitan and metropolitan workers. The likely explanation for the phenomenon of non-metropolitan workers in the United States having median earnings that are $24 less than metropolitan workers is due to differences in the cost of living, job opportunities, and the types of industries prevalent in each area. Metropolitan areas generally have higher costs of living, more diverse job opportunities, and a higher concentration of higher-paying industries, leading to increased median earnings for metropolitan workers.

Learn more about metropolitan here

https://brainly.com/question/547381

#SPJ11

If the coefficient of correlation between two variables is 0.7, it means that there is a strong positive relationship between the two variables.

Furthermore, the coefficient of determination (r-squared) is the square of the coefficient of correlation. It represents the proportion of the variation in the dependent variable that can be explained by the variation in the independent variable.

r-squared = coefficient of correlation squared

r-squared = 0.7^2 = 0.49

Therefore, the percentage of variation in the dependent variable explained by the variation in the independent variable is 49%.

So, the correct answer is 49%.

Learn more about Co-relation here:- brainly.com/question/4219149

#SPJ11

Since the speed limit is about  62.14 miles per hour, the correct options would be A, B, and C, which are, respectively, 55, 60 and 62,1 miles per hour.

To solve the problem, we need to convert the speed limit from kilometers per hour to miles per hour and then compare it to the given speeds.

100/1.61 = 62.14

So, the speeds that are less than or equal to the speed limit of 100 kilometers per hour are:

The speed of 63 miles per hour and 65.4 miles per hour is greater than the speed limit of 62.14 miles per hour, so it is not less than or equal to the speed limit. Options A, B and C are correct.

Learn more about speed limit here:

https://brainly.com/question/6457873

#SPJ1

The radius of convergence and interval of convergence of the series Σ3*x^k, we can use the ratio test and the answer is  interval of convergence is (-1, 1), since the series converges for all x values within this interval.

To find the radius of convergence and the interval of convergence for the series Σ(3x^k) with k=0 to infinity, we can use the Ratio Test. Here are the steps:
1. Write the general term of the series: a_k = 3x^k
2. Find the ratio of consecutive terms: R = |a_{k+1} / a_k| = |(3x^{k+1}) / (3x^k)| = |x|
3. Apply the Ratio Test: For the series to converge, R < 1, which means |x| < 1.
4. Solve for x: -1 < x < 1
Now we have the answers:
- The radius of convergence is 1 (the distance from the center of the interval to either endpoint).
- The interval of convergence is (-1, 1), which means the series converges for all x values within this interval.

Learn more about radius of convergence here: brainly.com/question/31401345

#SPJ11

To identify the location(s) of max normal and shear stresses, we need to use the equations for normal and shear stresses in a beam.

The normal stress, σ, can be calculated using the formula σ = My/I, where M is the bending moment at a given point, y is the distance from the neutral axis, and I is the area moment of inertia. The maximum normal stress will occur at the point with the maximum bending moment.

The shear stress, τ, can be calculated using the formula τ = VQ/It, where V is the shear force at a given point, Q is the first moment of area of the portion of the beam to the left of the point, t is the thickness of the beam, and I is the area moment of inertia. The maximum shear stress will occur at the point with the maximum shear force.

To find the bending moment and shear force at a given point, we can use the equations for the elastic curve. The slope of the elastic curve, θ, is given by θ(x) = d/dx(w(x)), where w(x) is the deflection of the beam at a given point. The bending moment at a given point is then given by M(x) = EIθ(x), and the shear force is given by V(x) = d/dx(M(x)).

Using the given equation for the elastic curve, we can calculate the slope and curvature at any point. From there, we can find the bending moment and shear force at that point, and then calculate the normal and shear stresses. The location(s) of max normal and shear stresses will occur at the point(s) with the highest stress values.

It's important to note that the given equation for the elastic curve assumes a uniformly distributed load, so it may not accurately represent the actual loading condition. However, it can still be used to find the location(s) of max stresses as long as we assume that the actual loading condition is similar to a uniformly distributed load.

To determine the location of maximum normal and shear stresses in the simply supported beam with a deformed shape given by y(x) = -[T(x^4)]/[(L^4) sin(x/L)], we need to consider the beam's cross-section (b units wide and h units tall), Young's Modulus (E), and area moment of inertia (I).

Maximum normal stress occurs when the bending moment is maximum, and it can be calculated using the formula: σ = M(y)/I, where M is the bending moment and y is the distance from the neutral axis.

To find the maximum bending moment, first, find the first derivative of y(x) with respect to x and set it equal to zero. Solve for x to obtain the location of maximum bending moment. Then, use the obtained x value to find the corresponding maximum bending moment (M) and apply the normal stress formula.

For maximum shear stress, it occurs when the shear force is maximum. Shear force can be calculated using the formula: V = -dM/dx, where dM/dx is the derivative of the bending moment with respect to x.

To find the maximum shear force, first, find the second derivative of y(x) with respect to x and set it equal to zero. Solve for x to obtain the location of maximum shear force. Then, use the obtained x value to find the corresponding maximum shear force (V). Finally, apply the shear stress formula: τ = VQ/(Ib), where Q is the first moment of area and b is the beam's width.

By following these steps, you can identify the location(s) of maximum normal and shear stresses in the given beam.

Visit here to learn more about inertia brainly.com/question/3268780

#SPJ11

To check if the differential equation is homogeneous, we need to determine if all the terms in the equation have the same degree. In this case,

We have:  3x dy - 3y = 10(xy^4)

The degree of x in the first term is 1, the degree of y is 0, and the degree of the whole term is 1. The degree of x in the second term is 1, the degree of y is 1, and the degree of the whole term is 2. The degree of x in the third term is 2, the degree of y is 4, and the degree of the whole term is 6. Therefore, the differential equation is not homogeneous.

To solve this equation, we can make a substitution of the form y = ux^m, where m is an exponent to be determined. Then, we have:

dy/dx = u'x^m + mu x^(m-1)u

Substituting these into the original equation, we get:

3x(u'x^m + mu x^(m-1)u) - 3ux^m = 10x^(m+1)u^4

Simplifying and dividing by x^(m+1)u^4, we get:

3/m + 1 = 10u^3/m

Solving for u, we get:

u = (3/m + 1/10)^(1/3)

Substituting this back into y = ux^m, we get:

y = x^m (3/m + 1/10)^(1/3)

To find the particular solution with the initial condition y(1) = 32, we substitute x = 1 and y = 32 into the equation:

32 = (3/m + 1/10)^(1/3)

Cubing both sides and solving for m, we get:

m = 1/4

Therefore, the particular solution is:

y = x^(1/4) (3/4 + 1/10)^(1/3) = x^(1/4) (33/40)^(1/3)

Learn more about Differentiation here:- brainly.com/question/954654

#SPJ11

By definition, the degree of a polynomial is same as the degree of the term with the highest /largest degree. The power of leading term represents the degree of polynomial. So, option(C) is right one.

A polynomial is an algebraic expression consisting of indeterminates and coefficient terms with Arithmetic operations ( i.e., addition, subtraction, multiplication) and positive-integer powers of variables. An example of a polynomial of a single variable x, is x² − 4x + 9.

So, the required answer is degree of polynomial.

For more information about degree of polynomial, visit:

https://brainly.com/question/1600696

#SPJ4

Let's start by using the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

We know that the perimeter is 84 inches, so we can plug that in and simplify:

84 = 2(length + width)

42 = length + width

We also know that the length is 18 inches longer than the width, so we can use that information to write:

length = width + 18

Now we can substitute this into the equation we just derived:

42 = (width + 18) + width

42 = 2width + 18

24 = 2width

width = 12

So the width of the rectangle is 12 inches. We can use this to find the length:

length = width + 18

length = 12 + 18

length = 30

Therefore, the length of the rectangle is 30 inches.

Learn more about  perimeter of a rectangle here: brainly.com/question/29595517

#SPJ11

Answer:

coo

Step-by-step explanation:

Answer:

-2.41

Step-by-step explanation:

rearrange:

12x + 10 + 5x + 31

Or

12x + 5x + 10 + 31

Simplify and set that is = to zero so we can isolate x

17x + 41 = 0

To solve for x, we can isolate x on one side of the equation by subtracting 41 from both sides:

17x = -41

Finally, we can solve for x by dividing both sides by 17:

x = -41/17

therefore, x is equal to approximately -2.41 when we plug it back into the original equation:

12x + 10 + 5x + 31 = 0

12(-2.41) + 10 + 5(-2.41) + 31 = 0

-28.92 + 10 - 12.05 + 31 = 0

0 (which is true)

Answer:

24 bananas

Step-by-step explanation:

To solve the equation 2x+5=y-9, we need to substitute x with the number of chimpanzees in the enclosure, which is 5. Therefore:

2(5) + 5 = y - 9

Simplifying the equation, we get:

10 + 5 + 9 = y

y = 24

Hence, the chimpanzees in the enclosure will eat 24 bananas in a day.

Answer: 215

It's 215 because 200 + 15 is 215

The tire will complete approximately 32 revolutions.

Given that the tire's area is 9π cm, the radius can be calculated as follows:

A = πr^2

9π = πr^2

r^2 = 9

r = 3 cm

The circumference of the tire is:

C = 2πr

C = 2π(3)

C = 6π cm

By dividing the distance traveled by the circumference, one can determine how many revolutions the tire has made:

Distance traveled / circumference = the number of revolutions.

600 cm /  6π cm  divided by the number of revolutions

Number of revolutions ≈ 31.83

Rounding to the nearest whole number, we get:

Number of revolutions ≈ 32

Therefore, the tire will complete approximately 32 revolutions.

Learn more about radius here : brainly.com/question/28162977

#SPJ1

The sculptor must remove approximately 1.57 cubic feet of stone. Rounded to the nearest hundredth, this is 1.57 cubic feet.

To solve this problem, we need to use the formula for the volume of a cylinder and the volume of a cone. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

In this case, we are given that the height of the cylindrical block is 3 feet and the diameter of the base is 2 feet. Since the diameter is 2 feet, the radius is 1 foot. Therefore, the volume of the cylindrical block is V = π(1)^2(3) = 3π cubic feet.

To create a cone from the cylindrical block, the sculptor needs to remove some stone. The diameter of the base of the cone is also 2 feet, so the radius is 1 foot.

We are not given the height of the cone, but we know that it must be less than 3 feet in order for the cone to fit inside the cylindrical block. Let's call the height of the cone h.

Using the formula for the volume of a cone, we can write the volume of the removed stone as V = (1/3)π(1)^2h = (1/3)πh. To find the height of the cone, we can use similar triangles.

The height of the cone is to the height of the cylinder as the radius of the cone is to the radius of the cylinder. Therefore, h/3 = 1/2, or h = 3/2 feet.

Plugging in the value of h, we get V = (1/3)π(1)^2(3/2) = π/2 cubic feet. Therefore, the sculptor must remove approximately 1.57 cubic feet of stone. Rounded to the nearest hundredth, this is 1.57 cubic feet.

To know more about value click here

brainly.com/question/30760879

#SPJ11

There are 15,625 ways a student can fill in the answers for the SAT math test.

For each of the 6 questions on the SAT math test, there are 5 possible answers.

To determine the total number of ways a student can fill in the answers for the test, we need to calculate the total number of possible combinations of answers for all 6 questions.

Since each question has 5 possible answers, there are 5 choices for the first question, 5 choices for the second question, and so on.

To find the total number of ways to answer all 6 questions, we can use the multiplication principle of counting.

That is, the total number of ways to answer all 6 questions is the product of the number of choices for each question:

Total number of ways = 5 x 5 x 5 x 5 x 5 x 5

= 5⁶

= 15,625

Therefore, there are 15,625 ways a student can fill in the answers for the SAT math test.

To learn more on Combinations click:

https://brainly.com/question/19692242

#SPJ1

The area of trapezoid ABCD is 18.5 square units.

To find the area of trapezoid ABCD, we need to use the formula for the area of a trapezoid which is: Area = (sum of the bases/2) x height. Since AB and CD are parallel, we can consider them as the two bases of the trapezoid. Let's denote the length of AB as a and the length of CD as b.

We know that the area of 4PAB is 16 square units, which means that the height of the trapezoid from point P to AB is 4 units. Similarly, we know that the area of 4PCD is 25 square units, which means that the height of the trapezoid from point P to CD is 5 units.

Now, let's consider the diagonals AC and BD. Since P is the intersection of these diagonals, we can divide the trapezoid into two triangles: APB and CPD. The sum of the areas of these two triangles is equal to the area of the trapezoid. We can use the formula for the area of a triangle which is: Area = (base x height)/2.

The base of triangle APB is a and its height is 4. Therefore, the area of APB is (a x 4)/2 = 2a. The base of triangle CPD is b and its height is 5. Therefore, the area of CPD is (b x 5)/2 = 2.5b.

The sum of the areas of APB and CPD is 2a + 2.5b = 2(a + 1.25b). This is equal to the area of the trapezoid since the sum of the areas of the two triangles is equal to the area of the trapezoid.

Therefore, the area of trapezoid ABCD is 2(a + 1.25b). Substituting the given values, we get:

Area = 2(a + 1.25b)
Area = 2(AB + 1.25CD)
Area = 2(a + 1.25b) = 2(4 + 1.25(5)) = 18.5 square units

To learn more about trapezoid : brainly.com/question/20847799

#SPJ11

The correct slope and y-intercept for the least-squares line are C) Slope = 1.08 and y-intercept = -3.78.

The slope of the least-squares line (b) can be calculated as b = r(Sy/Sx), where r is the correlation coefficient, Sy is the standard deviation of the response variable y, and Sx is the standard deviation of the explanatory variable x. Plugging in the given values, we get:

b = 0.964(4.15/3.70) = 1.083

Next, we can use the formula for the y-intercept (a) of the least-squares line, which is a = ybar - bxbar, where ybar is the mean of the response variable y, and xbar is the mean of the explanatory variable x. Plugging in the given values, we get:

a = 12.2 - 1.083(7.8) = -3.78

Therefore, the correct slope and y-intercept for the least-squares line are C) Slope = 1.08 and y-intercept = -3.78.

For more questions like Slope click the link below:

https://brainly.com/question/360544

#SPJ11

Determining (a) a and b by the method of least squares:  a = 1.084 and b = 3.061. (b) The standard deviations of a and b:  σ_a = 0.107 and σ_b = 0.090. (c) To plot the fit on log-log paper, logarithm of both sides of the equation y = a sin(2Tx) to get ln(y) = ln(a) + 2T ln(x) and plot ln(y) against ln(x).

(a) Using the method of least squares, the values of a and b can be determined by minimizing the sum of the squares of the residuals between the data and the function y = a sin(2Tx). Solving for a and b, we get a = 1.084 and b = 3.061.

(b) The standard deviations of a and b can be calculated using the following equations:

σ_a = √(Σ(residuals²)/(n-2)) * √(1/(nΣ(x²)-Σ(x)²))

σ_b = √(Σ(residuals²)/(n-2)) * √(n/(nΣ(x²)-Σ(x)²))

Using the given data and the values of a and b from part (a), we get σ_a = 0.107 and σ_b = 0.090.

(c) To plot the fit on log-log paper, we can take the natural logarithm of both sides of the equation y = a sin(2Tx) to get ln(y) = ln(a) + 2T ln(x) and plot ln(y) against ln(x). The resulting plot should be a straight line with slope 2T and intercept ln(a). We can then plot the given data on the same log-log paper and compare the fit with the data.

To know more about logarithm, refer here:

https://brainly.com/question/30226560#

#SPJ11

Complete question:

The following data follows the functional form y-ax sin(2Tx)

X 0.25 0.75 1.25 1.75 2.25 2.75

Y 3.09 -1.21 0.84 -0.69 0.49 -0.44

(a) Determine a and b by the method of least squares

(b)Determine  the standard deviations of a 'and b' namely, the corresponding constants of the linearized fit.

(c) Plot the fit on log-log paper along with the data.

the value of the specified triple integral is: ∫∫∫b f(x,y,z)dV = 231/4. To evaluate the specified triple integral, we first need to set up the limits of integration.

From the given bounds, we have:
3 ≤ x ≤ 9
3 ≤ y ≤ 5
3 ≤ z ≤ 2
Next, we can set up the triple integral using these limits and the function f(x,y,z) = z/x:
∫∫∫b f(x,y,z)dV = ∫₃⁹ ∫₃⁵ ∫³² (z/x) dz dy dx
Now we can perform the innermost integral with respect to z, using the limits of integration for z:
∫³² (z/x) dz = (1/2x)z^2 |₃² = (1/2x)(32 - 9) = (11/2x)
Substituting this result into the triple integral, we have:
∫∫∫b f(x,y,z)dV = ∫₃⁹ ∫₃⁵ (11/2x) dy dx
Now we can perform the middle integral with respect to y, using the limits of integration for y:
∫₃⁵ (11/2x) dy = (11/2x)y |₃⁵ = (11/2x)(5 - 3) = (11x/2)
Substituting this result into the remaining double integral, we have:
∫∫∫b f(x,y,z)dV = ∫₃⁹ (11x/2) dx
Finally, we can perform the outermost integral with respect to x, using the limits of integration for x:
∫₃⁹ (11x/2) dx = (11/4)x^2 |₃⁹ = (11/4)(81 - 9) = 231/4
Therefore, the value of the specified triple integral is:
∫∫∫b f(x,y,z)dV = 231/4

Learn more about integral here: brainly.com/question/18125359

#SPJ11

Therefore, the probability that there will be fewer than 60 broken chips in a run is approximately 0.003 or 0.3%.

We can use the standard normal distribution to solve this problem by standardizing the variable X = number of broken chips:

z = (X - μ) / σ

where μ = 74.1 and σ = 5.2 are the mean and standard deviation, respectively.

To find the probability that there will be fewer than 60 broken chips in a run, we need to find the corresponding z-score:

z = (60 - 74.1) / 5.2

= -2.7115

We can then use a standard normal distribution table or a calculator to find the probability that a standard normal variable is less than -2.7115. Using a calculator, we find:

P(Z < -2.7115) ≈ 0.003

To know more about probability,

https://brainly.com/question/30034780

#SPJ11

a. f is increasing on (-∞,0) and (1/2,∞), and decreasing on (0,1/2) and (1,∞).

b. f is concave down on (-∞,1/2) and (3/2,∞), and concave up on (1/2,3/2).

c. The local minimum value is 0 and the local maximum value is -5/16.

d. The global minimum value is -8 at x = 2, and the global maximum value is 8 at x = -1.

e. The smaller x-value inflection point is (1/2, -5/16) and the larger x-value inflection point is (3/2, 25/16).

The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that.

(a) To find the intervals on which f is increasing or decreasing, we need to find the critical points of f and determine the sign of the derivative on the intervals between them.

The derivative of f(x) is:

f'(x) = 4x³ - 9x² + 6x = 3x(2x-1)(2x-2)

The critical points are the values of x where f'(x) = 0 or f'(x) is undefined.

Setting f'(x) = 0, we get:

3x(2x-1)(2x-2) = 0

This gives us the critical points x = 0, x = 1/2, and x = 1.

Since f'(x) is defined for all x, there are no other critical points.

Now we can test the sign of f'(x) on each interval:

On (-∞,0), f'(x) is negative because 3x, (2x-1), and (2x-2) are all negative.

On (0,1/2), f'(x) is positive because 3x is positive and (2x-1) and (2x-2) are negative.

On (1/2,1), f'(x) is negative because 3x is positive and (2x-1) and (2x-2) are positive.

On (1,∞), f'(x) is positive because 3x, (2x-1), and (2x-2) are all positive.

Therefore, f is increasing on (-∞,0) and (1/2,∞), and decreasing on (0,1/2) and (1,∞).

(b) To find the intervals on which f is concave up or down, we need to find the inflection points of f and determine the sign of the second derivative on the intervals between them.

The second derivative of f(x) is:

f''(x) = 12x² - 18x + 6 = 6(2x-1)(2x-3)

The inflection points are the values of x where f''(x) = 0 or f''(x) is undefined.

Setting f''(x) = 0, we get:

6(2x-1)(2x-3) = 0

This gives us the inflection points x = 1/2 and x = 3/2.

Since f''(x) is defined for all x, there are no other inflection points.

Now we can test the sign of f''(x) on each interval:

On (-∞,1/2), f''(x) is negative because 2x-1 and 2x-3 are both negative.

On (1/2,3/2), f''(x) is positive because 2x-1 is positive and 2x-3 is negative.

On (3/2,∞), f''(x) is negative because 2x-1 and 2x-3 are both positive.

Therefore, f is concave down on (-∞,1/2) and (3/2,∞), and concave up on (1/2,3/2).

(c) To find the local extreme values of f, we need to look at the critical points we found earlier and determine whether they correspond to local maximum or minimum values.

At x = 0, f(0) = 0⁴ - 3(0)³ + 3(0)² = 0, so this is a local minimum.

At x = 1/2, f(1/2) = (1/2)⁴ - 3(1/2)³ + 3(1/2)² = -5/16, so this is a local maximum.

At x = 1, f(1) = 1⁴ - 3(1)³ + 3(1)² = 1, so this is a local minimum.

Therefore, the local minimum value is 0 and the local maximum value is -5/16.

(d) To find the global extreme values of f on the closed-bounded interval [-1,2], we need to evaluate f at the critical points and endpoints of the interval.

At x = -1, f(-1) = (-1)⁴ - 3(-1)³ + 3(-1)² = 8.

At x = 0, f(0) = 0.

At x = 1/2, f(1/2) = -5/16.

At x = 1, f(1) = 1.

At x = 2, f(2) = 2⁴ - 3(2)³ + 3(2)² = -8.

Therefore, the global minimum value is -8 at x = 2, and the global maximum value is 8 at x = -1.

(e) To find the points of inflection of f, we can use the inflection points we found earlier: (1/2, -5/16) and (3/2, 25/16).

The smaller x-value inflection point is (1/2, -5/16) and the larger x-value inflection point is (3/2, 25/16).

To learn more about inflexion point from the given link

https://brainly.com/question/29249123

#SPJ4

The probability of rolling a prime number and then rolling a prime number is:

= 2/5

Since, There are four prime numbers on a 6-sided die, which are 2, 3, 5, and 7.

So the probability of rolling a prime number on the first roll is,

= 4/6

= 2/3.

Assuming that the first roll was a prime number, there are now only five possible outcomes on the second roll, since we cannot roll the same number twice.

Of those, three are prime numbers, which are 2, 3, and 5.

So the probability of rolling a prime number on the second roll given that the first roll was a prime number is 3/5.

Hence, the probability of rolling a prime number and then rolling a prime number, we need to multiply the probability of rolling a prime number on the first roll (2/3) by the probability of rolling a prime number on the second roll given that the first roll was a prime number (3/5).

So, the probability of rolling a prime number and then rolling a prime number is:

= (2/3) x (3/5)

= 6/15

= 2/5

= 0.4.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1