Please help if you are good at math!!

a) True. If f′(x∗) = 0 and f′′(x∗) = 2, it indicates that the derivative of f is zero at x∗ and the second derivative is positive at x∗. These conditions suggest that f has a local maximum at x∗.

b) False. The statement is incorrect. If x∗ is a local minimum, it means that the derivative f′(x∗) is zero, but it doesn't provide any information about the second derivative f′′(x∗). The second derivative can be positive, negative, or zero at x∗.

c) False. If x∗ maximizes the function f on the interval [0,2], it implies that f is at its maximum value at x∗. However, this doesn't necessarily mean that the derivative f′(x∗) is zero. The derivative being zero represents a critical point, but not all critical points correspond to maximum values.

d) False. If f′(x) = sin(x) + 1 for all x, the derivative is positive for some values of x and negative for others. This means that f is not strictly increasing but rather fluctuates between increasing and decreasing intervals depending on the value of x. Therefore, f is not an increasing function.

a) If f′(x∗) = 0 and f′′(x∗) = 2, it means that the slope of the function f is zero at x∗, indicating a possible extremum. Additionally, the positive value of f′′(x∗) suggests that the graph of f is concave up at x∗, reinforcing the idea of a local maximum.

b) The statement is false because the second derivative f′′(x∗) can be positive, negative, or zero at a local minimum. The second derivative test can determine the concavity of the function and provide information about whether it is a maximum or minimum, but it does not establish a direct relationship between the sign of f′′(x∗) and the nature of the extremum.

c) The statement is false. If x∗ maximizes the function f on the interval [0,2], it only implies that f achieves its maximum value at x∗. However, the derivative f′(x∗) may or may not be zero. The derivative being zero represents a critical point, but it doesn't guarantee that it corresponds to a maximum.

d) The statement is false. The derivative f′(x) = sin(x) + 1 includes the sine function, which oscillates between positive and negative values. Consequently, f′(x) is not always positive, indicating that f does not strictly increase for all x. The function f exhibits variations in its slope and does not exhibit a consistent increasing trend.

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The best-fit line to represent the black data points is the blue line.

The plot of absorbance vs. concentration shows 8 data points with 3 lines drawn to represent the data. In order to determine the best-fit line, we need to evaluate the lines based on how well they represent the data points.

(a) The red line is the middle line and goes through 1 data point, with 3 data points above it and 4 data points below it. This line has a slope that is between the slopes of the other two lines. However, it doesn't go through many of the data points and the slope is not consistent with the majority of the data points.

(b) The green line is the top line and touches 3 of the data points, with the rest of the data points below it. This line has a steeper slope compared to the red line, but it doesn't touch many of the data points and has a significant deviation from the majority of the data points.

(c) The blue line is the bottom line and has 2 data points below it and 6 data points above it. This line has a slope that is more consistent with the majority of the data points, and it has the least deviation from the data points compared to the other two lines.

In mathematical terms, the blue line has the least sum of squared residuals, meaning it has the smallest difference between the observed values and the predicted values.

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Answer:

Yes

Step-by-step explanation:

Since the lines cross over each other, yes, they do bisect each other.

~theLocoCoco

Answer:

Step-by-step explanation:

Given points

Using slope formula

Slope is 14

Correct choice is B. 14

Answer: B: 14

Step-by-step explanation:

i took the test and got that answer

Answer:

Including the tax, you would need to pay $11.05

Step-by-step explanation:

10.5/100 * 10 + 10 is the formula

The tax itself, if you had to pay $10 for something, is $1.05

Answer:

To find the volume, we must find the area of the circle and multiply it by its height, think of a cylinder as an object made up of MANY circles. So, V=pir^2h... so diameter is 6cm so radius = 3cm...

therefore, Volume = (pi)(3^2)(12) = 108(pi)

where 12 = height 3 = radius

For the surface area, we need to find the area of the 2 circles(top and bottom ) so once again,

2(pi)(r^2) = 2(pi)(9)

for the area of the rectangle(if we unfold the cylindrical can) we get D(pi)(12) where D= Diameter

so the surface area is

SA = (2)(9)(pi) + 6(pi)(12)

SA = 18pi + 72pi = 90pi

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = 2(pi)(r), where r is the radius.  If the diameter of the given cylinder is 6 cm, then the radius is 3 cm, and the circumference of the cylinder is C = 2(3.14)(3 cm) = 18.84 cm.

Note:  The wording of your question is illogical; there is no "cylinder of the base."  But it's still possible to find the circumference of the cylinder, as done above.

Answer:

I'll explain

Step-by-step explanation:

1/8 is the least because it is the smallest fraction

1/6 is the next smallest fraction

then 1/5 is the text smallest

and 1/4 is the biggest fraction

Answer:

1/8

1/6

1/5

1/4

This is in order from least to greatest starting at the top

Answer: 193 inches squared

Step-by-step explanation:

1220 - 100 = 1120

1120 + 50 = 1170

Answer: 1170

Answer:

1170

Step-by-step explanation:

HI hope you have a wonderful day.

Answer:

The percent change from 150 lbs. to 135 lbs. is a 10% change:

(135-150)/150 x 100

-15/150 x 100

-0.1 x 100

-10% change

10% decrease

Your answer is: 10% change

Answer:

Option C

Step-by-step explanation:

Any evening time on a 24 hour clock will be that hour add 12 :

3:50 pm =

3:50 + 12:00 = 15:50

Option C must be the answer

Hope this helped and brainliest please

Answer:

c.1550 hrs

Step-by-step explanation:

It Is military time to it stays going for 12:00 to 13:00 14:00 15:00 and so on

Hope This Helped

Answer:

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape with straight sides. It does not have curved sides.

Step-by-step explanation:

Step 1: Find the area of the whole circle

A = pi x r^2

A = pi x 12^2

A = 144pi units^2

Step 2: Use the given angle to find only a part of the area

---The whole circle is 360 degrees, we only want 45 degrees.

45/360 x 144pi

1.5pi

4.71 units^2

Hope this helps!

Answer:

E. None of these

Step-by-step explanation:

Sector Area = r²  (α / 2)

R = 12

a (angle) = 45

12^2 = 144

45/2 = 22.5

144 x 22.5 = 3240

This is not one of the options therefore it is E. None of these

Pls let me know if incorrect

The variance is calculated by subtract the budgeted production volume from  actual production volume, and multiply that difference by  standard cost. If the result is positive, favorable, and if it is negative, unfavorable.

The difference above the actual and budgeted production volumes, multiplied by the average cost per unit, is known as the production volume variance. The formula for calculating the production volume variance is as follows:

Production Volume Variance = (Actual Production Volume ₋Budgeted Production Volume) × Standard Cost per unit

If the actual production volume is higher than the budgeted production volume, the production volume variance will be favorable because it means that the company produced more than anticipated, which could lead to increased revenue. On the other hand, if the actual production volume is lower than the budgeted production volume, the production volume variance will be unfavorable because it means that the company produced less than anticipated, which could lead to decreased revenue.

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The compound interest on ₹ 32500 after 1 year at 12% per annum compounded half yearly is ₹ 4147.40.

The compound interest can be calculated using the formula:

A = P * (1 + (r/n))^(nt)

where,

A = amount

P = principal (₹ 32500 in this case)

r = rate of interest (12% per annum)

n = number of times the interest is compounded in a year (half yearly, so n = 2)

t = number of years (1 year in this case)

Plugging in the values,

A = 32500 * (1 + (12/100)/2)^(2*1)

A = 32500 * (1 + 0.06)^2

A = 32500 * 1.06^2

A = 32500 * 1.1236

A = 36647.40

So, the amount after 1 year at 12% per annum compounded half yearly is ₹ 36647.40.

And the compound interest can be calculated as:

CI = A - P

CI = 36647.40 - 32500

CI = 4147.40

So, the compound interest on ₹ 32500 after 1 year at 12% per annum compounded half yearly is ₹ 4147.40.

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Answer:

Step-by-step explanation:

a and c are the numbers of adult tickets and child tickets, respectively.

a+c = 1,200

c = 1,200 - a

4a + 3c = 4,500

4a + 3(1,200-a) = 4,500

a + 3,600 = 4,500

a = 900

c = 1,200-a = 300

900 adult tickets and 300 child tickets

Answer:

Answer: 250 $3 tickets and 100 $2 tickets were sold.

Answer:

Add 2 to both sides.

1/4x=2x-7

Multiply both sides by 4

x=8x-28

-8x from each side.

-7x=-28

divide both sides by -7

X=4

Answer:  x=4

1. Multiply both sides by 4 to get rid of the denominator, which gives you x-8 = 8x-36
2. Subtract 8x from both sides, which gives you x - 8 - 8x= -36

3. Add 8 to both sides, which gives you x - 8x = -36 + 8

4. Simplify, -7x = -28

5. Divide both sides by -7, x = -28/-7

6. the negative signs cancel and you just get 4

Answer:

Step-by-step explanation:

56 : x = 16 : 12

x = 56 * 12 : 16

x = 672 : 16

x = 42

The equation to convert x feet into y miles for the walking path is y = x / 5280

To convert x feet into y miles, use the following equation:

y = x / (5280)

where y = distance in miles and x = distance in feet.

For the walking path, make sure it is 1 mile long. Therefore, set up the following equation:

distance from school to park + distance from park to school = 1 mile

Let d be the distance from the school to the park, then the distance from the park to the school is also d. Using the given requirements, set up the following two equations:

distance to first water fountain = d / 3

distance to second water fountain = 2d / 3

The total distance can be expressed as:

d + (2d/3) + (d/3) = 1 mile

Multiplying both sides by 3:

3d + 2d + d = 3 miles

Simplifying:

6d = 3

d = 1/2 mile

Now, use the equation y = x / 5280 to find the distances in miles:

Distance from school to park = (1/2) mile = (1/2) x 5280 feet = 2640 feet

Distance from park to school = (1/2) mile = (1/2) x 5280 feet = 2640 feet

Distance to first water fountain = (1/2) mile / 3 = (1/6) x 5280 feet = 880 feet

Distance to second water fountain = (2/3) x (1/2) mile = (1/3) x 5280 feet = 1760 feet

Therefore, the equation to convert x feet into y miles for the walking path is:

y = x / 5280

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Circumference of circle is 2πr

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14). How do you calculate a circle's circumference? The circle's radius is necessary to calculate the circumference: To calculate the diameter, multiply the radius by two. Divide the outcome by, or an estimate of 3.14. You have now successfully determined the circle's circumference.

Given,

Radius - r

Circumference of circle:

2πr

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Answer:

x = 20

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° so we can write the following equation:

2x + 3x + 4x = 180 add like terms

9x = 180 divide bot sides by 9

x = 20

all angles have measures under 90° so it's an acute triangle and if angle measure are different from each oter e all side lengths would have different lengths so it's also a scalene triangle.

Answer:

Hello,

Step-by-step explanation:

a)

\(y=a^x*b+c\\\\if\ x- > -\infty,\ y- > -1 \ \Longrightarrow\ c=-1\\if\ x=0\ y=1\ \Longrightarrow\ 1=b-1\ \Longrightarrow\ b=2\\if\ x=1\ y=5 \ \Longrightarrow\ a*2-1=5\ \Longrightarrow\ a=3\\\\\boxed{y=2*3^x-1}\\\)

b)

\(f(x,y)=(x-a)(y-b)-k=0\ since\ hyperbola\ "\' equilat\`ere\ in\ French"\\\\\dfrac{\partial{f}}{\partial{x}} =y-b=0\ \Longrightarrow\ y=b\\\\\dfrac{\partial{f}}{\partial{y}} =x-b=0\ \Longrightarrow\ x=a\\\\Here\ center\ is\ (0,2)\ so (x-0)(y-2)=k\\\\(-3,3)\ is \ a\ point\ of \ the\ hyperbola:\\-3*(3-2)=k\ \Longrightarrow\ k=-3\\\\\boxed{x(y-2)=-3}\\\)

c)

It is parabola

y=k*(x-3)(x+3)

(1,24) is a point of the parabola:

24=k*(1²-9) => k=-3

\(\boxed{y=-3(x^2-9)}\\\)

Answer:

33.02 cm in 13inches

Step-by-step explanation:

The change in one variable related to the change in more than one other variable is measured using multiple regression analysis.

A statistical method known as multiple regression is used on datasets intended to show a link between a single response or dependent variable and a number of independent factors.

Even though linear regression is frequently employed, it can only be utilized with one independent variable and one dependent variable. Non-linear regression is not predicted by linear regression, which is also limited to the training dataset.

We employ multiple regression to account for the same restrictions. It focuses on removing one particular limitation, which is allowing for the analysis of multiple independent variables.

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The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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If the ANOVA test is statistically significant, then we can determine which groups are different by means of the F statistic, which is defined by the ratio of the mean sum square to the average square error (none of the options are correct).

The ANOVA test can be defined as a strategy to assess when differences between two or even more groups and or populations in the same are statistically significant.

Moreover, the F statistic refers to the results of the ANOVA, which is used to show statistically significant differences between groups in the sample.

Therefore, with this data, we can see that the ANOVA test is used to determine when differences between groups in the sample are significant enough to explain a given working hypothesis, and it is associated with the F statistics.

Complete question:

Your ANOVA is statistically significant. How will you determine which groups are different?

Use planned or unplanned comparisons.

Look at what the means in each group are.

Conduct Levene's test.

None of the above

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The measure of acute angle are  22.5 degree and  67.5 degree

Acute angles are those angle which is less than 90 degree.

According to the question,

Given that One acute angle in triangle is 3 times the measure of the other in Right angled triangle

Let "x" be the one acute angle

Then, the other acute angle will be = 3x

As we know , the sum of three angles in triangle is 180°

Therefore, x + 3x + 90 = 180

=> 4x = 180 - 90

=> 4x = 90

=> x = 90 / 4

=> x = 22.5°

Hence , the measure of each acute angle is 22.5 and  67.5 degree

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Answer:

12,568.75 that's the answer

Step-by-step explanation:

There will be 21 handshakes when seven people meet each other and each shakes hands only once with each of the others.

When a group of n people meet and each person shakes hands with every other person exactly once, the total number of handshakes that occur can be calculated using the formula (n * (n-1)) / 2.

To understand why this formula works, we can start by recognizing that each person will shake hands with n-1 other people, since they cannot shake hands with themselves. However, we need to divide by 2 to avoid counting each handshake twice, since each handshake involves two people.

Therefore, the total number of handshakes can be expressed as the product of the number of people (n) and the number of handshakes per person (n-1), divided by 2.

In the specific example of seven people meeting, we can substitute n=7 into the formula to find that the total number of handshakes will be (7 * (7-1)) / 2, which simplifies to 21. This means that there will be 21 handshakes when seven people meet and each shakes hands with every other person exactly once.

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