Find the absolute maximum and absolute minimum values of ƒ on the given interval.
47. f(x) = 12 + 4x - x², [0, 5]
48. f(x) = 5 + 54x − 2x³, [0,4]
49. f(x) = 2x³-3x² - 12x + 1, [-2, 3]
50. f(x) = x³- 6x² + 5, [−3, 5]
51. f(x)=3x-4x³- 12x² + 1, [2, 3]
52. f(t) = (1-4)', [-2,3]
+ → [0.2, 4]
53. f(x) = x + [0.2, 4]
54. f(x)=
I
[0,3]
55. f(1) = 1 − √1, [−1,4]
56. f(1) = [0,2]
57. f(1) = 2 cos 1 + sin 21. [0, π/2]
58. f(t)=1+ cot (1/2). Start

Answer:

3

Step-by-step explanation:

Answer:

\(d = 3h - 6\)

Step-by-step explanation:

Step 1:  Solve for d

I am assuming that you are asking for me to solve for the variable d.  Let me know if what I am doing is not what you want.

\(h = \frac{d}{3} + 2\)

\(h - 2 = \frac{d}{3} + 2 - 2\)

\((h - 2) * 3 = \frac{d}{3} * 3\)

\(3h - 6 = d\)

Answer:  \(d = 3h - 6\)

The coefficient of the x term in the expansion of f[x] best reflects the behavior of the function for x's close to 0.

The behavior of a function for x values close to 0 can be understood by examining its expansion in powers of x. When a function is expanded in a power series, each term represents a different order of approximation to the original function. The coefficient of the x term, which is the term with the lowest power of x, provides crucial information about the behavior of the function near x = 0.

In the expansion of f[x] = a0 + a1x + a2x² + ..., where a0, a1, a2, ... are the coefficients, the term with the lowest power of x is a1x. This term captures the linear behavior of the function around x = 0. It represents the slope of the function at x = 0, indicating whether the function is increasing or decreasing and the rate at which it does so. The sign of a1 determines the direction of the slope, while its magnitude indicates the steepness.

By examining the coefficient a1, we can determine whether the function is increasing or decreasing, and how quickly it does so, as x approaches 0. A positive value of a1 indicates that the function is increasing, while a negative value suggests a decreasing behavior. The absolute value of a1 reflects the steepness of the function near x = 0.

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Let's begin by listing out the information given to us:

We will caculate fºg thus:

Hence, option B is correct

Answer:

m ∠DCA

m ∠CAD = 56

m ∠CBA = 83°    

Step-by-step explanation:

A parallelogram is a polygon with two pairs of parallel lines

m ∠CDA = m ∠CBA = 83°       Opposite angles in a parallelogram are =    

m ∠CAD = m ∠ACB  = 56°     CB ║ DA and alternating interior angle are =

m ∠DCA = 180°                           The sum of the angles in a triangle = 180°

m ∠ADC + m ∠CAD + m ∠DCA = 180            Parts of the triangle

       83° +  56° + m ∠DCA = 180                     Substitution

            139° + m ∠DCA = 180°

                  m ∠DCA = 180° - 139°

                   m ∠DCA = 41°

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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Answer:

You can just switch them around, 68 + 76×

Answer:

4(19x+17)

Step-by-step explanation:

Answer:

\(m=\frac{-(f+3)}{4-f}\)

Answer:

1

log 10

Step-by-step explanation:

In e = 1

In e = log 10

Hope it helps you in your learning process.

Answer:

7

Step-by-step explanation:

There are seven t's that equal 49. So do 49 divided by 7. Therefore, t = 7.

Hi!

In the picture, we can see that 7 of the t's are equal to 49. We can set this up using an equation:

\(7t=49\)

Now, in order to solve for t, we must divide both sides by 7 to isolate the variable on one side of the equal sign:

\(\cfrac{7t}{7} =\cfrac{49}{7}\)

Simplify:

\(t=7\)

Therefore, t = 7 makes the equation true.

We can also check our work. On the scale, 7 t's are equal to 49, remember? So if there are 7 t's, and each t is equal to 7, we do 7 * 7 which is equal to 49.

49=49  ✔️

Answer:

i

Step-by-step explanation:

i

Step-by-step explanation:

   Sum = 4x³ - 3x² + 3x + 8 + (6x³ - 7x² + 4x) + (-8x³ + 7x²)     [write the terms as given by the quetion and group like terms]

⇒ Sum = (4x³ + 6x³ - 8x³) + (- 3x²  - 7x² + 7x²) + ( 3x + 4x) + 8   [complete the addition of like terms]

∴ sum = 2x³ - 3x² + 7x + 8

Answer:

2x³ - 3x² + 7x + 8

Step-by-step explanation:

We require to add

4x³ - 3x² + 3x + 8 + 6x³ - 7x² + 4x - 8x³ + 7x² ← collect like terms

= (4 + (6 - 8)x³ + (- 3 - 7 + 7)x² + (3 + 4)x + 8

= 2x³ + (- 3)x² + 7x + 8

= 2x³ - 3x² + 7x + 8

In binary representation, each bit can be either 0 or 1. Using five binary bits, we can obtain 32 different numbers. Therefore, the correct answer is (B).

With five binary bits, we have five positions, and each position can have two possibilities (0 or 1). To calculate the total number of different numbers we can obtain, we need to raise 2 to the power of the number of bits. In this case, we have \(2^5,\) which equals 32. Therefore, we can obtain 32 different numbers using five binary bits. To understand this concept, we can think of each binary bit as a switch that can be either on (1) or off (0). With five switches, we have a total of 32 different combinations or numbers that can be represented. These numbers range from 0 (all switches off) to 31 (all switches on). Therefore, the correct answer is (B), which states that we can obtain 32 different numbers using five binary bits.

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The correct option of the given statement "The present value of $5,325 to be received in one period at a rate of 6.5%" is d. 5,000.

it can be found using the formula:

PV = FV/(1 + r),

where

PV is the present value,

FV is the future value,

and r is the interest rate expressed as a decimal.

Here, FV = $5,325 and r = 0.065 (6.5% expressed as a decimal).

Substituting these values into the formula gives:

PV = $5,325/(1 + 0.065)PV

    = $5,325/1.065PV

     ≈ $5,000

Therefore, the present value of $5,325 to be received in one period if the rate is 6.5% is approximately $5,000.

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Answer:

The boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

Step-by-step explanation:

Let x be the time (in hours) that the boat traveled at 10 miles per hour, and let y be the time (in hours) that it traveled at 30 miles per hour.

We know that:

x + y = 6 (the total time the boat traveled)

We also know that the boat traveled a total distance of 140 miles, which can be expressed as:

10x + 30y = 140

We can use the first equation to solve for one of the variables in terms of the other:

y = 6 - x

Substituting this expression for y into the second equation, we get:

10x + 30(6 - x) = 140

Simplifying and solving for x, we get:

10x + 180 - 30x = 140

-20x = -40

x = 2

Therefore, the boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

The lower and upper limits of the confidence interval can be determined using the sample mean and sample standard deviation.

Given the sample readings of total calcium levels in mg/dl, we can calculate the sample mean (x) and sample standard deviation (s). Using these values, we can determine the lower and upper limits of the 99.9% confidence interval.

Calculating the sample mean:

x = (9.9 + 8.6 + 10.9 + 8.5 + 9.4 + 9.8 + 10.0 + 9.9 + 11.2 + 12.1) / 10 = 10.03 mg/dl

Calculating the sample standard deviation:

s = sqrt(((9.9 - 10.03)^2 + (8.6 - 10.03)^2 + ... + (12.1 - 10.03)^2) / (10 - 1)) = 1.16 mg/dl

To determine the 99.9%   confidence interval, we need to find the critical value corresponding to this level of confidence. Since the sample size is small (less than 30) and the population standard deviation is unknown, we can use the t-distribution. With a sample size of 10 and a desired confidence level of 99.9%, the critical value is approximately 3.250.

Calculating the margin of error:

Margin of error = critical value * (s / sqrt(n))

= 3.250 * (1.16 / sqrt(10))

≈ 1.19

The lower limit of the confidence interval is given by x - margin of error:

Lower limit = 10.03 - 1.19 ≈ 8.84 mg/dl

The upper limit of the confidence interval is given by x + margin of error:

Upper limit = 10.03 + 1.19 ≈ 11.22 mg/dl

Therefore, the 99.9% confidence interval for the population mean of total calcium in this patient's blood is approximately 8.84 mg/dl to 11.22 mg/dl.

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The error is when h is some value, the error will be when h/2.

The error of a third-order accurate numerical differentiation method scales with the fourth power of the step size, i.e. if the step size is halved, the error will decrease by a factor of 2⁴=16. So if the error is when h is some value, the error will be when h/2.

The error in numerical differentiation methods can be approximated using Taylor series expansions. For a third-order accurate method, the error term in the Taylor series would be proportional to h⁴. Hence, reducing the step size by a factor of two would reduce the error by a factor of 2⁴ = 16. This relationship between step size and error holds for small step sizes. For larger step sizes, the error may not decrease in such a simple manner and other factors such as the smoothness of the function being differentiated and the presence of singularities or discontinuities may come into play.

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Answer:

A or the first one

The algorithm for sorting a list of items by price runs in reasonable time for very large values of n, as indicated by the provided table.

The table shows the number of steps taken by the algorithm to sort lists of different sizes. As the number of items increases, the number of steps required also increases, but the relationship is not directly proportional. Instead, it appears to be quadratic, as the number of steps roughly corresponds to the square of the number of items.

For example, when the number of items is 10, the algorithm takes approximately 100 steps. When the number of items is 20, the number of steps increases to around 400, which is 4 times the number of steps for 10 items. This pattern continues, with the number of steps increasing quadratically with the number of items.

Based on this behavior, it can be inferred that the algorithm runs in reasonable time for very large values of n. Although the exact time complexity of the algorithm is not explicitly provided, the fact that the number of steps grows quadratically suggests that it can handle large lists efficiently.

Therefore, the best characterization of the algorithm for very large values of n is that it runs in reasonable time.

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Answer:

h = 14.5 ft

Step-by-step explanation:

Apply trigonometric ratio formula to find h:

reference angle = 46°

Opposite side = h

Adjacent side = 14 ft

Thus:

Tan 46 = h/14

Multiply both sides by 14

14*tan 46 = h

h = 14.4974243

h = 14.5 (nearest tenth)

Answer:

x = 5, y = 15

Step-by-step explanation:

Use substitution to solve the system of equations.

We'll replace y in x + y = 20 with 3x, since y = 3x.

x + 3x = 20

Combine like terms

4x = 20

Divide by 4 on both sides

x = 5

Now to solve for y (don't forget!)

We'll plug x = 5 back into one of the original equations

y = 3(5) = 15

Check first equation:

15 = 3(5)

15 = 15

Check second equation:

5 + 15 = 20

20 = 20

A point estimate is a single approxmate value of some parameters.

A point estimate for difference in average means is the difference between the sample means .

Point estimator :

In statistics, point estimation uses sample data to compute a single value, called a point estimate, to identify a point in a given parameter space.

Estimator Properties:

Point Estimate of Difference in Average Sales:

Point Estimate of Population Mean The calculation is the sum of all samples divided by the number of values .

Suppose we want to compare the means of two different populations . Each population has a mean and a standard deviation. Take a random sample from Population1 and label the resulting sample statistic with Index1 . Draw a sample from population2 and label its sample statistic with index 2, without reference to the first sample.

It is denoted by " μ1-μ2 " .

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The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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\(\dfrac{2ax+3}{ax+3}=-1\)

Rewrite -1 as a fraction

\(\dfrac{2ax+3}{ax+3}=\dfrac{-1}{1}\)

Cross multiply

\(2ax+3=-1(ax+3)\)

Distribute the -1

\(2ax+3=-ax-3\)

Add both sides by ax

\(3ax+3=-3\)

Subtract both sides by 3

\(3ax=-6\)

Divide both sides by 3a

\(x=-\dfrac{6}{3a}\)

Simplify

\(=-\dfrac{2}{a}\)

That's the value of x respect to a. Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

\(\frac{2ax+3}{ax+3} =-1\\2ax+3=-ax-3\\2ax+ax=-3-3\\3ax=-6\\x=-\frac{2}{a}\)

Answer: C

Step-by-step explanation:

Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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