write absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that has the following solution set: x is less than or equal to 5

The derivative exists at x=0 and its value is 0. So, f'(0) = 0.

The derivative of a function can be thought of as the slope of a tangent line to the function's graph at a specific point. This tangent line represents the instantaneous rate of change of the function at that point. The derivative of a function can be used to find critical points, which are points where the function reaches a maximum or minimum value, and to find the concavity of the function, which indicates the direction in which the function is changing.

The derivative can be calculated using different methods, including the limit definition of the derivative, the power rule, the product rule, the quotient rule, and the chain rule. The derivative can also be used to calculate the slope of a curve, the velocity of a moving object, and the acceleration of an object.

To find f'(0) using the definition of a derivative, we need to use the following formula:

f'(a) = lim(h->0) [f(a+h) - f(a)]/h

where "a" is the point at which we want to find the derivative, and "h" is a small value that approaches zero.

In this case, we want to find f'(0). Let's use the formula and simplify the expression:

f'(0) = lim(h->0) [f(0+h) - f(0)]/h

= lim(h->0) [h²sin(1/h)]/h (since f(0)=0)

= lim(h->0) [hsin(1/h)]

Now, we need to evaluate this limit. We can rewrite the limit using the squeeze theorem, which says that if we have two functions, g(x) and h(x), such that g(x) ≤ f(x) ≤ h(x) for all x in some interval, and if lim(x->a) g(x) = lim(x->a) h(x) = L, then lim(x->a) f(x) = L.

In our case, we have:

-1 ≤ sin(1/h) ≤ 1 for all h≠0 (using the fact that -1 ≤ sin(x) ≤ 1 for all x)

-h ≤ hsin(1/h) ≤ h for all h≠0 (multiplying by h, which is always non-negative)

Therefore, by the squeeze theorem, we have:

lim(h->0) -h = 0 = lim(h->0) h

Since both limits are equal, we can conclude that the limit of hsin(1/h) as h approaches 0 exists and is equal to 0.

Thus, f'(0) = 0.

Therefore, the derivative exists at x=0 and its value is 0. So, f'(0) = 0.

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The table and graph is mentioned below.

In mathematics, a graph is a visual representation of a set of objects, often referred to as vertices or nodes, and the connections or edges that exist between them. Graphs are used to represent a wide range of mathematical concepts, such as functions, equations, and data sets.

A graph can be thought of as a collection of points or vertices that are connected by lines or edges. The way these vertices and edges are arranged can convey important information about the relationships between the objects being represented.

Graphs can be classified into different types, such as directed or undirected graphs, weighted or unweighted graphs, and cyclic or acyclic graphs. They can also be used to model real-world systems, such as social networks, transportation systems, and computer networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

               0                 $75.00

               10                 $95.00

               20                 $115.00

               30                 $135.00

               40                 $155.00

               50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

                0                 $5.75

                10                 $60.75

                20                 $115.75

                30                 $170.75

                40                 $225.75

                50                 $280.75

b) On the same set of axes, the graph is attached below.

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Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished.

In mathematics, a graph is a picture of a collection of things, also known as vertices or nodes, and the links or edges that join them. Numerous mathematical ideas, including functions, formulae, and data sets, are represented by graphs.

A collection of vertices or points linked by lines or edges is referred to as a graph. The arrangement of these vertices and edges can reveal crucial details about the connections between the things being represented.

Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished. Additionally, they can be used to simulate real-world systems like computer networks, transit systems, and social networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

0                 $75.00

10                 $95.00

20                 $115.00

30                 $135.00

40                 $155.00

50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

0                 $5.75

10                 $60.75

20                 $115.75

30                 $170.75

40                 $225.75

50                 $280.75

b) On the same set of axes, the graph is attached below.

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Answer: 4424.4 pesos

Step-by-step explanation:

To convert dollars to pesos, we need to multiply the number of dollars by the exchange rate:

360 dollars x 12.29 pesos/dollar = 4424.4 pesos

Therefore, Todd will get 4424.4 pesos for his trip to Mexico.

Answer:

B

Step-by-step explanation:

Answer and Explanation: Nuclear fusion takes place at very high temperature and pressure so that the two elements fuse together, forming new, heavier elements. The nuclear fusion reaction releases a massive amount of energy, and it normally takes place in the core of the stars.

hope that was the answer

Answer:

Its c it has to be because its merge and if u look it up it shows and that's what it means yw!

Step-by-step explanation:

Based on the information provided, the visibility distance for Pretoria in kilometers is 19.30 kilometers.

The table shows the visibility from Pretoria is 12, miles, while the visibility in Cape Town is 6 miles. This implies we need to change miles to kilometers. These two units are used for distance but they are not equivalent as 1 mile =  1.609 kilometers, knowing this, let's calculate the distance in kilometers:

12 miles x 1.609 =  19.30 kilometers.

Note: This question is incomplete, below I attach the missing information:

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the probability that a randomly selected light bulb will last between 675 and 825 hours is 68.26%, or 0.6826.

Probability is a measure of the likelihood of an event occurring. It is a numerical value that ranges from 0 to 1, where 0 represents an impossible event and 1 represents a certain event. A probability of 0.5 (or 50%) means that the event is equally likely to occur as not occur.

To solve this problem, we can use the standard normal distribution with a mean of 0 and a standard deviation of 1, and then convert the given values to z-scores using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For the lower value of x (675 hours), the z-score is:

z = (675 - 750) / 75 = -1

For the upper value of x (825 hours), the z-score is:

z = (825 - 750) / 75 = 1

We can then use a standard normal distribution table or calculator to find the probabilities associated with these z-scores:

P(z < -1) ≈ 0.1587

P(z < 1) ≈ 0.8413

The probability of a randomly selected light bulb lasting between 675 and 825 hours is then:

P(-1 < z < 1) = P(z < 1) - P(z < -1) ≈ 0.8413 - 0.1587 ≈ 0.6826

Therefore, the probability that a randomly selected light bulb will last between 675 and 825 hours is approximately 68.26%, or 0.6826 as a decimal.

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The complete question is:

Image is attached below.

Answer:

12/20 = 0.6

Step-by-step explanation:

The total number of cards in Kayla's hand is:

6 (spades) + 7 (hearts) + 5 (diamonds) + 2 (clubs) = 20

The number of red cards (hearts or diamonds) in Kayla's hand is:

7 (hearts) + 5 (diamonds) = 12

Therefore, the probability of randomly selecting a red card from Kayla's hand is:

12/20 = 0.6

Answer: 0.6

Step-by-step explanation: you add the total amount of cards she has which is 20(6+7+5+2) then the amount of hearts or diamonds is 7+5 for hearts and diamonds, which is =12 so the amount of hearts and diamonds divided by the total amount of cards, 12/20 which is 6/10 when divided by 2, 6/10 is 0.6, if you want to go further 6/10 can be broken down to 3/5 which is also 0.6

Answer: A

Step-by-step explanation:

The answer is A.

Answer:

0.337 or about 33.7%

Step-by-step explanation:

The number of ways to choose 1 apple out of 9 is:

C(9, 1) = 9! / (1! * (9 - 1)!) = 9

The number of ways to choose 2 oranges out of 7 is:

C(7, 2) = 7! / (2! * (7 - 2)!) = 21

So the total number of ways to choose 1 apple and 2 oranges is:

9 * 21 = 189

The total number of ways to choose 3 fruits out of 16 is:

C(16, 3) = 560

Therefore, the probability of selecting 1 apple and 2 oranges is:

189 / 560 ≈ 0.337 or about 33.7%

The woman will arrive in New York City at 11 AM.

Plane takeoff angle.

Angel

During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

Plugging this into the equation above, we get:

tan(θ) = 10/62

θ = arctan(10/62) ≈ 8.8°

Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.

Angel

Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.

Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary

Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.

From the given information, we can set up the following two equations:

tan(19°) = 7425/d1

tan(37°) = 7425/d2

Solving for d1 and d2, we get:

d1 = 7425/tan(19°) ≈ 22977.6 feet

d2 = 7425/tan(37°) ≈ 13060.2 feet

Therefore, the distance the plane traveled from point A to point B is:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.

Angel

Plane B is flying 75mph 75 ⁢ mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.

Let's start by using the formula for distance, rate, and time:

distance = rate x time

Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.

We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:

2300/r = 2600/(r + 75)

To solve for r, we can cross-multiply and simplify:

2300(r + 75) = 2600r

2300r + 172500 = 2600r

300r = 172500

r = 575 mph

Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:

distance = rate x time

2300 = 575 x time

time = 4 hours

Therefore, it takes Plane A 4 hours to travel 2300 miles.

Angel

A woman leaves at 7 AM and drive to New York City 200 miles away. If she averages 50 mph what time will she arrive at the city?

To determine the arrival time of the woman in New York City, we need to use the formula for time:

time = distance / rate

In this case, the distance is 200 miles and the rate (or speed) is 50 mph. Plugging these values into the formula, we get:

time = 200 miles / 50 mph = 4 hours

Since the woman left at 7 AM, we can simply add the travel time of 4 hours to the departure time to get the arrival time:

7 AM + 4 hours = 11 AM

Therefore, the woman will arrive in New York City at 11 AM.

Answer:

6.1 cm

Step-by-step explanation:

We have to find the hypotenuse of the orange triangle which will be the leg of the green triangle

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]4.2^{2}[/tex] + [tex]4^{2}[/tex] = [tex]c^{2}[/tex]

17.64 + 16 = [tex]c^{2}[/tex]

33.64 = [tex]c^{2}[/tex]

[tex]\sqrt{33.64}[/tex] = [tex]c^{2}[/tex]

5.8 = c

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]2^{2}[/tex] + [tex]5.8^{2}[/tex] = [tex]c^{2}[/tex]

4 + 33.64 = [tex]c^{2}[/tex]

37.64 = [tex]c^{2}[/tex]

[tex]\sqrt{37.64}[/tex] = [tex]\sqrt{c^{2} }[/tex]

6.13514466007 = c  This is a rounded number.  This is an irrational number.  It never repeats or terminates.

Rounded to 1 decimal place

6.1

Helping in the name of Jesus.

Answer:

The height of the prism is 9yd.

Step-by-step explanation:

The volume of the prism is

Vol

= BaseArea×height

The area of the base is the area of the triangle.

Area_triangle

= 1/2 b•h

= 1/2•8•7

= 28

28 is the BaseArea of the prism.

Again the volume of the prism is:

Vol = BaseArea•h

This h is the height of the prism. That is what we are looking for.

Fill in what we know or calculated already.

252 = 28•h

Divide by 28

9 = h

The height of the prism is 9yd.

I HOPE THIS HELPS

x=−7

x=−1

x

2

=−8x−7

Add 8x to both sides.

x

2

+8x=−7

Add 7 to both sides.

x

2

+8x+7=0

To solve the equation, factor x

2

+8x+7 using formula x

2

+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.

a+b=8

ab=7

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

a=1

b=7

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x+1)(x+7)

To find equation solutions, solve x+1=0 and x+7=0.

x=−1

x=−7

Answer:

5cm because you have to round off to the nearest 1000

Answer:

Step-by-step explanation:

Rectangle ABCD has diagonals AC and BD that converge at point O and

OA = 5x-7, OD = 4x-5.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X

Hence, Rectangle ABCD has diagonals AC and BD that converge at point O and

OA = 5x-7, OD = 4x-5.

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a. The probability that both of them are good is 9/16

b. Probability that one battery is good while one 3/16

c. probability that both batteries are bad is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability = sample space / total outcome

the sample space for bad batteries = 5

the sample space for good batteries = 15

Therefore

a. probability that both are good = 15/20 × 15/20 = 3/4 × 3/4 = 9/16

b. probability that a battery is good and the other is bad = 15/20 × 5/20

= 3/4 × 1/4 = 3/16

c. The probability that both are bad

= 5/20 × 5/20 = 1/4 × 1/4 = 1/16

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Answer:

The quotient is Q(x) = -2x² + x + 6 and the remainder is R(x) = 52.

Step-by-step explanation:

           -2x² + x + 6

    ------------------------

x - 7 | -2x³ + 15x² - x + 10

     -(-2x³ + 14x²)

     ---------------

              x² - x

              -(x² - 7x)

              ---------

                  6x + 10

                  -(6x - 42)

                  ----------

                          52

There are 210 ways that Janelle can choose 4 colors from 10 available colors for her art project.

Janelle needs to choose 4 colors out of 10 available colors for her art project. The order in which she chooses the colors does not matter. We can use the combination formula to determine the number of ways she can choose 4 colors from 10 available colors:

nCr = n! / r!(n - r)!

where n is the total number of colors available, r is the number of colors Janelle needs to choose, and ! denotes the factorial operation.

In this case, we have:

n = 10 (total number of colors available)

r = 4 (number of colors Janelle needs to choose)

Substituting these values into the formula, we get:

10C4 = 10! / 4!(10 - 4)!

= 10! / 4!6!

= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

= 210

Therefore, for her art assignment, Janelle can select 4 colors from a palette of 10 in 210 different ways.

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Answer:

Michael needs to purchase 6 1/4 feet of metal flashing.

Step-by-step explanation:

To determine the number of feet of metal flashing that Michael needs to purchase, we need to add the lengths of the two small pieces he already has:

3 1/8 feet + 1 3/4 feet

To add these two fractions, we need to have a common denominator. In this case, the smallest common denominator is 8:

3 4/8 feet + 1 14/8 feet = 4 18/8 feet

Now we can simplify the mixed number by converting it to an improper fraction:

4 18/8 feet = (4 x 8 + 18)/8 feet = 50/8 feet

So Michael already has 50/8 feet of metal flashing. To determine how much more he needs to purchase, we need to subtract this amount from the total amount he needs:

6 1/2 feet - 50/8 feet

To subtract these two fractions, we again need to have a common denominator. In this case, the smallest common denominator is 8:

6 4/8 feet - 50/8 feet = (6 x 8 + 4)/8 feet - 50/8 feet = 52/8 feet - 50/8 feet = 2/8 feet

So Michael needs to purchase an additional 2/8 feet of metal flashing to complete his household project, which simplifies to 1/4 feet. Therefore, Michael needs to purchase a total of:

50/8 feet + 1/4 feet = 6 1/4 feet

Answer:

34833,33 £

Step-by-step explanation:

First, we need to find how much will her sallary increase:

[tex] \frac{28500 \times 2}{9}≈ 6333.33[/tex]

And now we add this number to her old salary:

28500 + 6333,33 = 34833,33 £

The 99% confidence interval, zα/2 ≈ 2.576 and for the 94% confidence interval, zα/2 ≈ 1.88.

Hi! To find the zα/2 value for both the 99% and 94% confidence intervals, we will use the standard normal distribution table or a calculator with a z-score function.

For a 99% confidence interval, the area between the two tails (α) is 1 - 0.99 = 0.01. We need to find the value that corresponds to an area of 0.01/2 = 0.005 in each tail. Looking up this value in a standard normal distribution table or using a calculator, we get zα/2 ≈ 2.576.

For a 94% confidence interval, the area between the two tails (α) is 1 - 0.94 = 0.06. We need to find the value that corresponds to an area of 0.06/2 = 0.03 in each tail. Looking up this value in a standard normal distribution table or using a calculator, we get zα/2 ≈ 1.88.
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Answer:

[tex] \sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \sqrt{2} = 7 \sqrt{2} [/tex]

Answer:

Step-by-step explanation:

To find the mean absolute deviation (MAD), we first need to find the mean of the data set:

mean = (2 + 5 + 3 + 5 + 4 + 3 + 3 + 5 + 4 + 4) / 10

mean = 4

Next, we find the absolute deviation of each data point from the mean:

|2 - 4| = 2

|5 - 4| = 1

|3 - 4| = 1

|5 - 4| = 1

|4 - 4| = 0

|3 - 4| = 1

|3 - 4| = 1

|5 - 4| = 1

|4 - 4| = 0

|4 - 4| = 0

Then, we find the mean of these absolute deviations:

MAD = (2 + 1 + 1 + 1 + 0 + 1 + 1 + 1 + 0 + 0) / 10

MAD = 0.8

Therefore, the mean absolute deviation of the data set is 0.8.

Julia can expect to roll a 3 approximately 61 times if she rolls the die 200 times.

Probability is a means to gauge the likelihood that an event will take place. It is symbolized by the numbers 0 and 1, respectively, with 0 denoting an improbable event and 1 denoting an inescapable event. With two equally likely outcomes, switching a valid coin and coin flips have a chance of 0.5, or 50%. head or tail. A subfield of mathematics called probability theory examines random events rather than their attributes. It is employed in many different fields, including finance, science, building, and facts and statistics.

we found the best estimate for the probability of rolling a 3 to be:

p = (30 + 0.5) / 100 = 0.305

This means that the probability of rolling a 3 on any one roll of the die is 0.305.

If Julia rolls the die 200 times, we can use the formula for the expected value of a binomial distribution to find the expected number of 3's she will roll:

E(X) = np

where:

n = number of trials = 200

p = probability of success (rolling a 3) = 0.305

So, plugging in the values:

E(X) = 200 × 0.305

E(X) = 61

Therefore, Julia can expect to roll a 3 approximately 61 times if she rolls the die 200 times.

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 4000e^{0.08\cdot 25} \implies A=4000e^2\implies A \approx 29556.22[/tex]

Answer:

Step-by-step explanation: Twice means x2

Difference means subtract

A number is a unknown value so you put a variable

(Z - 4) x 2= 7

3.5 x 2= 7

(7.5 - 4) x 2= 7

Answer:

If the recipe calls for 1 1/4 pounds of beets and Sandra removes 1/2 of a pound from the scale, then the amount of beets she has left is:

1 1/4 - 1/2 = 1 - 1/4 - 1/2 = 3/4 pounds

Therefore, Sandra has 3/4 pounds of beets, which is exactly what she needs for the chocolate beet cake recipe

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