Find the explicit equation.

The statement "If f is differentiable at a, then f is continuous at a" is true, but "If f is continuous at a, then f is differentiable at a" is false.

Differentiability and continuity are two important concepts in calculus. A function is said to be continuous at a point if the values of the function approach a finite limit as the independent variable approaches the same value. In other words, there are no sudden jumps or breaks in the function at that point.

On the other hand, a function is said to be differentiable at a point if the limit of the rate of change of the function exists as the independent variable approaches the same value. This rate of change is called the derivative of the function and it is used to determine the slope of the function at that point.

So, it is true that if a function is differentiable at a point, then it is also continuous at that point. In other words, a continuous function must be differentiable. However, the reverse is not necessarily true. A function can reach a point where it is continuous but not differentiable. For example, the absolute value function is continuous everywhere but it is not differentiable at x = 0.

Therefore, we can say that if f is differentiable at a, then f is continuous at a. But if f is continuous at a, it does not imply that f is differentiable at a.

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Let the smaller polygon have side lengths a and the larger polygon have side lengths b. Since the polygons are similar, the ratio of corresponding side lengths is the same as the ratio of their areas. That is:

b^2 / a^2 = 128 / 98

Simplifying this expression, we get:

b / a = √(128 / 98) = √(64 / 49) = (8 / 7)

Now we can use the fact that the perimeter of the smaller polygon is 42 inches:

4a = 42

a = 10.5

Substituting this into the ratio we found above, we get:

b = (8 / 7) * a = (8 / 7) * 10.5 = 12

Therefore, the larger polygon has a perimeter of:

4b = 4 * 12 = 48 inches.

The value is approximately equal to 12.0711°

While measuring angles, we use various units of measurements such as the degrees or the SI unit radians as per our convenience.

When we use the degree system, we can use the degree-minute-second or the degree decimal system as per our requirement of precision.

The angle in degree - minutes - seconds is 12°4'16"

We know that [tex]\frac{1}{60}[/tex] of a degree is minute and [tex]\frac{1}{60}[/tex] of a minute is a second.

Hence, [tex]\frac{1}{3600}[/tex] of a degree is a second.

Therefore the angle [tex]\theta[/tex] in degrees and decimal fractions of degrees will be:

[tex]\theta[/tex] = [tex]12+\frac{1}{60}[/tex] × 4 + [tex]\frac{1}{3600}[/tex] × 16

 = [tex](12+\frac{1}{15}+\frac{1}{225} )[/tex]°

The value is approximately equal to 12.0711°

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The given question is incomplete, complete question is:

The angle 12 degrees 4'16" is given in degrees, arcminutes, and arcseconds. How do you rewrite them in degrees and decimal fractions of degrees?

The correct option is, No, because HI and JK do NOT have the same slope and  HK and IJ have the same slope

Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.

Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.

Consecutive angles are supplementary: The consecutive angles of a parallelogram are always supplementary, meaning that they add up to 180 degrees.

Diagonals bisect each other: The diagonals of a parallelogram bisect each other, meaning that they intersect at the midpoint of each other.

The sum of the interior angles is 360 degrees: The sum of the interior angles of a parallelogram is 360 degrees.

No, because HI and JK do NOT have the same slope and HK and IJ have the same slope.

In order for a quadrilateral to be a parallelogram, opposite sides must be parallel, which means they have the same slope.

In this case, HI and JK do not have the same slope, and therefore, the opposite sides are not parallel.

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The complete question:

The vertices of parallelogram HUJK are H(0,-1),(2,3), J(7, -1),K(5,-5). Determine if HIJK is a parallelogram.

No, because HI and JK do NOT have the same slope and  HK and IJ have the same slope

Yes, because HI and JK have the same slope and HK and IJ have the same slope

Yes, because the image is tilted

No, because HK and JI have the same slope, but HI and JK do NOT have the same slope

The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.

AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.

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Answer:

This is false.

Step-by-step explanation:

The correct answer would be 652.5

Answer: The function has three x-intercepts.

Step-by-step explanation:

To find the x-intercepts of a function, we need to find the values of x for which the function equals zero.

So, to find the x-intercepts of the function:

F(x) = (x+5)^3(x-9)(x-1)

We need to solve the equation:

F(x) = 0

We can see that the function will be equal to zero when any of the factors on the right-hand side is equal to zero. Therefore, we need to solve the following four equations:

(x+5) = 0, which gives x = -5

(x-9) = 0, which gives x = 9

(x-1) = 0, which gives x = 1

(x+5)^3 = 0, which gives x = -5

The last equation, (x+5)^3 = 0, has a triple root at x = -5, since the factor (x+5) appears three times. Therefore, there are a total of three x-intercepts for the function:

x = -5 (with multiplicity 3), x = 1, and x = 9.

The perimeter of the actual field is 91.8 meters.

The area of the actual field is 437.4 square meters.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

The scale of a rectangular field is given in the question, as follows:

1 cm = 4.5 m

So, the dimensions of the actual field, are as:

L = 7.2 ×  4.5 = 32.4 m

W = 3 ×  4.5 = 13.5 m

The perimeter of the actual field = 2(L+W)

The perimeter of the actual field = 2(32.4 + 13.5) = 2(45.9) = 91.8 m

The area of the actual field = L × W

The area of the actual field = 32.4 × 13.5 = 437.4 m²

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if I'm Wrong Sorry And Have a Nice Day .

According to the empirical rule, the observations in a data set that can be reasonably approximated by a normal curve lie within two standard deviations of the mean is 95% .

The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical guideline that describes the approximate distribution of data that can be reasonably approximated by a normal curve. The rule states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

In other words, if a set of data is normally distributed (meaning it follows a bell-shaped curve), we can use the empirical rule to estimate the proportion of the data that falls within a certain range of values.

For example, let's say we have a data set that has a mean of 50 and a standard deviation of 10. Using the empirical rule, we can estimate that approximately:

68% of the data falls between 40 and 60 (one standard deviation from the mean)

95% of the data falls between 30 and 70 (two standard deviations from the mean)

99.7% of the data falls between 20 and 80 (three standard deviations from the mean)

It's important to note that the empirical rule is only an approximation, and it only applies to data that is approximately normally distributed. In some cases, the actual distribution

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Answer:

Step-by-step explanation:70000

The value of x and y in the given congruent triangles, are 7 and 13

The triangles which share congruent corresponding angles and sides are called congruent triangles.

Given that, Δ LMN ≅ Δ RST, ∠L = 49º, ∠M = 10x, ∠S = 70º, and ∠T = 4y + 9, we need to find the x and d,

Since, we know that, the congruent triangles have congruent corresponding angles.

Here, the congruent triangles are :

∠ L = ∠ R

∠ M = ∠ S

∠ N = ∠ T

We know that, the sum of angles of a triangle is 180°,

∠ R + ∠ S + ∠ T = 180°

∠ R + 70º + 4y + 9 = 180°

49º + 70º + 4y + 9 = 180°

128º + 4y = 180º

4y = 52º

y = 13º

∵

∠ M = ∠ S

10x = 70º

x = 7

Hence, the value of x and y in the given congruent triangles, are 7 and 13

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Answer:

He rented the bike for 5 hours.

Step-by-step explanation:

Fixed rate for renting a bike is $8 and rate per hour for renting is $5.

Amount paid by Jermaine is $33.

To find the hourly rent amount that he paid, subtract the fixed rate ($8) from total amount $33.

Rent amount for the bike = 33 - 8

                                          = $ 25

Number of hours rented = 25 ÷ 5

                                        = 5 hours

The system of equations has its solution to be (3, 4)

From the question, we have the following parameters that can be used in our computation:

2x + y = 10

3x - y = 5

Add the equations

So, we have

5x = 15

Divide by 5

x = 3

Recall that

2x + y = 10

So, we have

6 + y = 10

Evaluate

y = 4

Hence, the solution is (3, 4)

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Answer:

26.6°

Step-by-step explanation:

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.

There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).

If we know that the angle shown is a right angle, we also know that a right angle is equal to 90°. To solve for the value of c, we can use this equation:

Therefore, the value of c is 26.6°.

Answer:Step 2

Step-by-step explanation: Bc Im right

The length of the missing side of the quadrilateral shown if the perimeter is 5x+3 and sides are 8x-4 and 10x+7 and 3x+6 is -16x+12.

This is defined as the total distance around the shape.

The perimeter is the sum of the 4 sides.

Adding , 8x-4 and 10x+7 and 3x+6 , we have:

8x-4 + 10x+7 + 3x+6  = 21x+9

Subtract that from the given perimeter to get the missing side length which is:

5x+3 - 21x+9 = -16x+12

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The time it will take to do all the activities at the same time is given as follows:

60 minutes = one hour.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods of each event are given as follows:

The least common factor is obtaining factoring these numbers according to their prime factors, as follows:

15 - 12 - 10|2

15 - 6 - 5|2

15 - 3 - 5|3

5 - 1 - 5|5

1 - 1 - 1

Hence:

lcm(15,12,10) = 2² x 3 x 5 = 60 minutes.

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Answer:

200

Step-by-step explanation:

9% of 200 =

200 x 0.9 =

18

Answer:

Choice B

Step-by-step explanation:

(7/4)^11 = 471.431...

(7^11)/(4^11) =  471.431...

nswer:

Step-by-step explanation:

6*[tex]10^{6}[/tex]------100

x-------40

x=6*10^6*4*10/100=24*10^5(social media)

6*[tex]10^{6}[/tex]------100

y-------30

y=6*10^6*3*10/100=18*10^5(music)

6*[tex]10^{6}[/tex]------100

z-------25

z=6*10^6*25/100=15*10^5(games)

6*[tex]10^{6}[/tex]------100

f-------5

f=6*10^6*5/100=3*10^5(video)

The decimal form of 15/16 is 0.9375.

To convert a fraction to a decimal, you can divide the numerator by the denominator. In this case, 15 divided by 16 equals 0.9375.

Alternatively, you can also use long division to find the decimal form of a fraction.

1. Set up the long division problem with 15 as the dividend and 16 as the divisor.
2. Since 16 does not go into 15, add a decimal point and a zero to the dividend.
3. Divide 16 into 150, which equals 9 with a remainder of 6.
4. Add another zero to the dividend and divide 16 into 60, which equals 3 with a remainder of 12.
5. Add another zero to the dividend and divide 16 into 120, which equals 7 with a remainder of 8.
6. Add another zero to the dividend and divide 16 into 80, which equals 5 with no remainder.
7. The final answer is 0.9375.

So, 15/16 as a decimal is 0.9375.

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The width of the rectangular box is W = 8 inches

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangular box be V = 264 inches³

Let the height of the rectangular box be H = 3 inches

Let the length of the rectangular box be L

Let the width of the rectangular box be W

Now , L = 3 + W

And , Volume of Rectangle = Length x Width x Height

Substituting the values in the equation , we get

264 = 3 x ( W ) x ( 3 + W )

On simplifying the equation , we get

Divide by 3 on both sides of the equation , we get

3W + W² = 88

Subtracting 88 on both sides of the equation , we get

W² + 3W - 88 = 0   be equation (1)

On factorizing the equation , we get

W² + 11W - 8W - 88 = 0

Taking the common factors of the equation , we get

W ( W + 11 ) - 8 ( W + 11 ) = 0

On further simplification , we get

( W - 8 ) ( W + 11 ) = 0

The width cannot be negative , so

( W - 8 ) = 0

Adding 8 on both sides , we get

W = 8 inches

Hence , the width of the rectangular box is 8 inches

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The fraction of the £80 that you have left is 3/10.

Let's start by calculating how much money you spent at the bookshop.

40% of £80 = 0.4 x £80 = £32

£80 - £32 = £48

One third of £48 = £16

£48 - £16 = £32

£32 - £8 = £24

£24 is the same as 24/80 when expressed as a fraction.

24/80 = 3/10

So the fraction of the £80 that you have left is 3/10. This is the simplest form.

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Answer:

= 6.25 hours.

Step-by-step explanation:

If 5 hours = 12 loaves of bread

than ? = 15 loaves of bread.

therefore 15/12 × 5 hours

= 75/12

= 6. 25 hours.

The total number of ways is 45.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Ms. Kelley needs to hire one biology teacher and one chemistry teacher for the science department.

The number of ways to choose one biology teacher from a pool of 9

is 9.

The number of ways to choose one chemistry teacher from a pool of 5

is 5.

Now,

According to the multiplication principle of counting.

The total number of ways to hire one teacher from each subject.

= The number of ways to choose one biology teacher x The number of ways to choose one chemistry teacher.

= 9 x 5

= 45

Therefore,

The total number of ways Ms. Kelley can hire a staff that includes one teacher in each subject is 45.

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The required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.

Rate of change is defined as the change in value with rest to another value is called rate of change.

Here,
Given that,
f(x) = x² + 4x -15

Now, put x = -3
f(-3) = 9 - 12 - 15
f(-3) = -18

Now put x = 6
f(6)= 36 + 24 - 15
f(6) = 45

Since we know that, the rate of change of function is given as,
f'(x) = f'(a) - f'(b) / a -b

f'(x) =f'(6) - f'(-3) / a - b

f'(x) = 45 - (-18) / 6 -(-3)
f'(x) = 63 / 9
f'(x) = 7

Thus, the required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.

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In MATLAB, you can convert a string to an integer using the str2double() or str2num() function. Both functions convert a string to a double-precision floating-point number, but str2num() also supports the conversion of strings to other numeric data types.

Here's an example of how to convert a string to an integer using str2double():

str = '123';  % string to convert to integer

num = str2double(str);  % convert the string to a double-precision number

int = int32(num);  % convert the double-precision number to a 32-bit integer

In this example, the str variable contains the string '123', which we want to convert to an integer. We first use the str2double() function to convert the string to a double-precision number, which we then convert to a 32-bit integer using the int32() function.

Alternatively, you can use the str2num() function to convert the string directly to an integer:

str = '123';  % string to convert to integer

int = int32(str2num(str));  % convert the string to a 32-bit integer

In this example, we use the str2num() function to convert the string directly to a 32-bit integer, and then assign the result to the int variable.

It is important to note that if the string cannot be converted to a number, both functions will return NaN (Not a Number). Additionally, if the string represents a number that is too large to be represented by an integer, the result will be rounded or truncated.

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Answer:

31) -$1.25

32) $0.50

Step-by-step explanation:

Problem 31

[tex]E(X)=\frac{1}{4}(-5)+\frac{1}{4}(-20)+\frac{1}{2}(10)=-\frac{5}{4}-5+5=-\frac{5}{4}=-1.25[/tex]

Hence, this person would expect to gain -$1.25 (or lose $1.25) if they play this game.

Problem 32

[tex]E(X)=\frac{1}{4}(2)+\frac{1}{4}(20)+\frac{1}{2}(-10)=\frac{1}{2}+5-5=\frac{1}{2}=0.50[/tex]

Hence, this person would expect to gain $0.50 if they play this game.

Answer:

31. -$1.25

32. $0.50

Step-by-step explanation:

The expected value is the sum of the product of each probability and its corresponding winnings or loss.

31.

p(win $10) = 1/2

amount of winnings = $10

p(loose $5) = 1/4

amount of loss = $5

p(loose $20) = 1/4

amount of loss = $20

expected value = (1/2)($10) + (1/4)(-$5) + (1/4)(-$20)

expected value = -$1.25

32.

p(win $2) = 1/4

amount of winnings = $2

p(win $20) = 1/4

amount of winnings = $20

p(loose $10) = 1/2

amount of loss = $10

expected value = (1/4)($2) + (1/4)($20) + (1/2)(-$10)

expected value = $0.50