Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = In(x), then ƒ'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = = In(x) at x = 2.

Answer:

2 6/13

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

This is a two-stage problem

  for the first 12 years use cont compounding formula

        FV = PV e^(rt)     Future value  Presnt value   r = decimal int   t = years

         = 2000 e^(.05 * 12) = 3644.24    use this amount for the second stage

     Fv = pv e^(rt)  = 3644.24 ( e^(.08*8) ) = $ 6911.23

The central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

The formula for the area of a sector of a circle is [tex]A = (θ/360) * π * r^2,[/tex] where θ is the central angle in degrees, π is 3.14, and r is the radius of the circle.

Given the area of a sector of a circle is [tex]56 cm^2[/tex] and the radius is 10 cm, we can solve for θ:

[tex]56 cm^2 = (θ/360) * 3.14 * 10^2\\56 cm^2 = (θ/360) * 314\\θ = (56 * 360) / 314\\θ = 63.6[/tex]

Therefore, the central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

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The value of the expression is 18.

The value of the expression is calculated by applying the principle of order of operation as shown below.

The given expression y ÷ 4 • 3 – 6 ÷ x + 8

re-write the expression as follows;

= y/4 × 3 - 6/x + 8

where;

The value of the expression is calculated as;

= ( 16 / 4 ) x 3  -   6 / 3  + 8

= ( 4 x 3 ) - ( 2) + 8

= ( 12 ) - 2 + 8

= 12 - 2 + 8

= 18

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The complete question is below:

Given the values x = 3 and y = 16, find the value of this expression,  y ÷ 4 • 3 – 6 ÷ x + 8

Answer:

A

Step-by-step explanation:

The easiest way to see whether a table is a function is to check the Input and Output. If one Input has two outputs, then that table is not a function. So, the answer is A

The 30th term a30 of the sequence is -1445

The definition of the function is given as

arithmetic sequence of 1,-4,-9,-14

The above definitions imply that we simply subtract 5 from the previous term to get the current term

Using the above as a guide,

so, we have the following representation

First term, a = 1

Common difference, d = 5

An arithmetic sequence is represented as

a(n) = a + (n - 1)d

For the 30th term, we have

a(30) = a + 29d

So, we have

a(30) = 1 + 29 * -5

Evaluate

a(30) = -144

Hence, the value of a30 is -144

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The function with the greater initial value is (a) the function A

The complete question is added as an attachment

The initial value of a function is calculated when

x = 0

From the table of values, we have

y = 8 when x = 0

For the other function, we have

y = 4x + 3

So, the initial value is

y = 4(0) + 3

Evaluate

y = 3

8 is greater than 3

Hence, the function with the greater initial value is the table of values

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Answer:

89.28

Step-by-step explanation:

First lets find 7% of 96

96 x 0.07 = 6.72

then subtract 6.72 from 96

96-6.72=89.28

The requried, a number that is 7% smaller than 96 is approximately 89.28.

To find a number that is 7% smaller than 96, we need to calculate 7% of 96 and then subtract that value from 96.

Calculate 7% of 96.

7% of 96 = (7/100) * 96 = 0.07 * 96 = 6.72

To get a number that is 7% smaller than 96, we need to subtract the value we found in Step 1 from 96. subtract the calculated value from 96.

Number = 96 - 6.72 = 89.28

Therefore, a number that is 7% smaller than 96 is approximately 89.28.

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The new length of the living room floor would be 14.4 meters and the new width would be 6 meters.

1. Original Length = 12 meters  

2. Original Width = 5 meters

3. Increase by 20%

4. New Length = 12 + (20% of 12) = 12 + 2.4 = 14.4 meters

5. New Width = 5 + (20% of 5) = 5 + 1 = 6 meters

The original length of the living room floor was 12 meters and the original width was 5 meters. The owner decided to increase the living room dimensions by 20%, so the new length of the living room floor is 14.4 meters and the new width is 6 meters. This is calculated by adding 20% of the original length and width to the original values. For the length, this is 12 + (20% of 12) which is 12 + 2.4 = 14.4 meters. For the width, this is 5 + (20% of 5) which is 5 + 1 = 6 meters. The increase of 20% in the dimensions of the living room floor makes it look more spacious and inviting.

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As total = 4100

Insurance = 123/4100*100 = 3%

Housing = 574/4100*100 = 14%

Entertainment = 164/4100*100 = 4%

This model must be completed to represent 377 ÷ 12 as follows;

      30     1___

12 | 360  | 17 | 5.

In order to divide the given numbers by using the box method, we would write an expression to represent the number of times in which the number (377) can be divided by the number (12), while including the remainder (17) as follows;

377 ÷ 12 = (360 + 17) ÷ 12

377 ÷ 12 = (360 ÷ 12) + (17 ÷ 12)

377 ÷ 12 = 30 + (17 ÷ 12)

Note: 12 would divide 17 to give an output of one (1) remainder five (5).

In this context, the above mathematical expression would be re-written as follows;

377 ÷ 12 = 30 + 1 R 5.

Where:

The variable R represents remainder.

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There are 2,118,760 possible ways to select 6 cards from a deck of 52 cards if the spade ace must be selected.

If at all you must select the spade ace, you have 51 cards remaining from which to choose 5 more cards. The number of ways to choose 5 cards from 51 is 51C5, where C represents the number of combinations.

Using the formula for combinations, we have:

51C5 = 51! / (5! * (51 - 5)!) = 51! / (5! * 46!)

Using the factorial we can simplify this expression to:

51C5 = 51 * 50 * 49 * 48 * 47 / (5 * 4 * 3 * 2 * 1) = 2,118,760

Therefore, there are 2,118,760 possible ways to select 6 cards from a deck of 52 cards, if the spade ace must be selected.

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The number of dimes is 24.

The number of quarters is 20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

10 dimes = $1

1 dime = $0.1

4 quarters = $1

1 quarter = $0.25

Now,

Number of dimes = x

Number of quarters = (5/6)x

Now,

Duretta has collected $7.40 in all.

This means,

0.1x + 0.25(5/6)x = 7.40

0.1x + 0.21x = 7.40

0.31x = 7.40

x = 7.40/0.31

x = 23.87

x = 24

And,

(5/6)x

= 5/6 x 24

= 20

We can cross-check.

24 x 0.1 + 20 x 0.25 = 7.40

2.4 + 5 = 7.40

7.40 = 7.40

Thus,

Number of dimes = 24

Number of quarters = 5/6 x 24 = 20

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The equations that could be used to solve for the unknown lengths of △ABC are cos45° = AC/9 and sin45° = BC/9.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

The opposite side to the reference angle is BC and the adjacent is the height.

We know, cos = adjacent/hypotenuse

Therefore, To determine AC we'll use cos45° = AC/9.

Also, To determine BC we'll use sin45° = BC/9.

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The probabilities of picking an A, a B or a C is given as follows:

167/210.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes in the context of a problem.

For each event, the probabilities in this problem are given as follows:

To find the or probability, we add the probabilities of the desired outcomes, hence:

P(A) + P(B) + P(C) = 1/5 + 3/7 + 1/6 = (42 + 90 + 35)/210 = 167/210.

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Here's the completed table of values for y = 2x^2 + x

7,1,9

To find the value of y for each x, substitute x into the equation and simplify:

For [tex]x = -2: y = 2(-2)^2 + (-2) = 7[/tex]

For[tex]x = -2: y = 2(-2)^2 + (-2) = 7[/tex]

For[tex]x = 0: y = 2(0)^2 + 0 = 1[/tex]

For [tex]x = 1: y = 2(1)^2 + 1 = 4[/tex]

For[tex]x = 2: y = 2(2)^2 + 2 = 9[/tex]

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Answer:

The data points in Set 1 are more spread out than the points in set 2

he mean than the points in Set 2 because the mean absolute deviation is Larger

Step-by-step explanation:

The mean absolute deviations for two sets of data are shown.

A 2-column table with 2 rows. Column 1 is labeled Set with entries 1, 2. Column 2 is labeled M A D with entries 8.4, 0.2.

The data points in Set 1 are more_____

the mean than the points in Set 2 because the mean absolute deviation is_____

A student taking thirteen credit hours should plan for approximately 13-15 hours of work outside of class each week.

Generally, if a student is taking thirteen credit hours, they should plan for approximately 13-15 hours of work outside of class each week. This includes attending lectures, studying, and completing assignments. To calculate this, the student should take the total number of credit hours (13) and multiply it by the number of hours per credit (usually 3 hours). This would give the student 39 hours of work outside of class.

However, this number should not be taken as an exact number, as the amount of time needed to complete the course may vary based on the student's learning style, the difficulty of the course, and the amount of time required for each assignment. For example, if a student is taking a particularly difficult course, they may want to plan for more hours than the calculation suggests.

In order to ensure success, students should plan ahead, create a schedule, and stick to it. This will help them stay on track and complete their coursework in a timely manner.

A student taking thirteen credit hours should plan for approximately 13-15 hours of work outside of class each week.

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The system of equations are solved and the number of regular and premium cards are 9 and 16 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , let the regular cards be x

And , the premium cards be y

The cost of one regular card x = $ 0.40

The cost of one premium card y = $ 0.65

The total cost = $ 14

The total number of cards = 25

Substituting the values in the equation , we get

x + y = 25   be equation (1)

0.40x + 0.65y = 14   be equation (2)

Multiply by 100 on both sides of equation (2) , we get

40x + 65y = 1400

Divide by 5 on both sides of the equation , we get

8x + 13y = 280   be equation (3)

Multiply equation (1) by 8 , we get

8x + 8y = 200   be equation (4)

Subtracting equation (4) from equation (3) , we get

13y - 8y = 280 - 200

5y = 80

Divide by 5 on both sides of the equation , we get

y = 16

So , the number of premium cards is 18

Substitute the value of y in equation (1) , we get

x + 16 = 25

Subtracting 16 on both sides of the equation , we get

x = 9

So , the number of regular cards is 9

Hence , the equations are solved

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Part a: P2 processors therefore performs the best out of the three.

Part b: Number of Cycles are found.

Part c: New Clock rate for each processors is found.

High-speed data processing and intricate calculations are capabilities of high-performance computing (HPC).

1.

P1: 3GHz / 1.5 = 2 × 10^9 instructions / second

P2: 2.5GHz / 1.0 = 2.5 × 10^9 instructions  / second

P3: 4GHz / 2.2 = 1.82 × 10^9 instructions  / second

2. Number of Cycles:

P1: 3GHz × 10 = 3 * 10^10 cycles

P2: 2.5GHz × 10 = 2.5 × 10^10 cycles

P3: 4GHz ×10 = 4 ×  10^10 cycles

Number of instructions:

P1: 3GHz × 10 / 1.5 = 2 × 10^10 instructions

P2: 2.5GHz × 10 / 1.0 = 2.5 × 10^10 instructions

P3: 4GHz × 10 / 2.2 = 1.82 × 10^10 instructions

3. Execution time = (Number of instructions * CPI) / (Clock rate)

Therefore, if CPI rises by 20% but we aim to cut the execution time to 30%, we have:

Execution time × 0.7 = (Number of instructions  × CPI × 1.2) / (New Clock rate)

New Clock rate = Clock rate × 1.2 / 0.7 = 1.71 * Clock rate

New Clock rate for every processor:

P1: 3GHz × 1.71 = 5.13 GHz

P2: 2.5GHz × 1.71 = 4.27 GHz

P3: 4GHz × 1.71 = 6.84 GHz

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The correct question is-

Performance:

Consider three different processors, P1 P2 and P3, executing the same instruction set.

P1 has a 3 GHz clock rate and a CPI of 1.5. P2 has a 2.5 GHz clock rate and a CPI of 1.0.

P3 has a 4.0 GHz clock rate and a CPI of 2.2.

1. Which processor has the highest performance expressed in instructions per second?

2. If the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions.

3. We are trying to reduce the execution time by 30% but this leads to an

increase of 20% in the CPI. What clock rate should we have to get this time reduction?

The surface area is of the triangular prism is 121.8 cm²

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The surface area is gotten by adding each individual area of each surface of a three dimensional shape.

The area of the base is 6.9 cm². This is a triangular prism with height of 9 cm and each base side is 4 cm

The surface area = area of base + (9 cm * 4 cm) + (9 cm * 4 cm) + (9 cm * 4 cm) + area of base

Surface area = 6.9 + 6.9 + 36 + 36 + 36 = 121.8 cm²

The surface area is 121.8 cm²

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The quadratic regression equation is given as follows:

y = -0.02x² + 0.14x + 19.6.

Regression equations are obtained inserting the points of a data-set into a calculator.

In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.

The points for this problem are given as follows:

y = -0.02x² + 0.14x + 19.6.

Meaning that the fourth option is the correct option.

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Answer:

y = (0,-2)

Step-by-step explanation:

change in y/ change in x.

-4/4 ---> slope is -1

plug x and y coordinates AND SLOPE into y=mx+b

-3= -4/4(1)+b

-3= -1 +b

-2=b

After solving the given equation, the value of variable x is 7/2 so x+5 is not the factor of given equation.

Equation: f(x)=x3-4x*2+3x+7

Here we have equation or algebric expression to solve to check whether the given condition is correct or not.

Give:

x3-4*2+3x+7= 0

Multiply the monomials

3x- 8x+3x+7= 0

Combine like terms

-2x+7= 0

Rearrange variables to the left side of the equation

-2x= -7

Divide both sides of the equation by the coefficient of variable

x= [tex]-7/-2[/tex]

Determine the sign for multiplication or division

x= [tex]7/2[/tex]

The value of x is  [tex]7/2[/tex].

So x+5 is not a factor of f(x)=x3-4x*2+3x+7.

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Answer: 2/6 or 2/12 (Go with 2/6)

Step-by-step explanation:

1/6 probability of rolling any one number. Add the probabilities for rolling a 3 (1/6) and rolling a 6 (1/6) and there is a 2/6 chance of rolling those numbers. it can also be 2/12 if you are looking at both dice rolls like one function.

it it is 1/6 because it the probability of rolling a 3 and then rolling a 6

The simplified value of the expression  7/9 divided 578 + 2/9 + 578 is,

(27071271/46818).

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The expression 7/9 divided 578 + 2/9 + 578 is,

= 7/9 ÷ 578 + 2/9 + 578

= (7/9) × (1/578) + 2/9 + 578.

= (7/5202) + (2 + 9×578)/9.

= (7/5202) + (5204/9).

= (7×9 + 5202×5204)/(5202×9).

= (63 + 27071208)/(46818).

= (27071271/46818)

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Check the picture below.

Answer:

So if there were -4+20 the answer would be 16. When you add things, it goes to the right of the number line. When you subtract stuff it goes to the left. Simple but there are more rules like when this happens: 6--4 the two minuses turn into a plus 6+4—and other stuff. So -8 you have 8 negative signs and 20 positive signs. When a positive and a negative are added together they cancel each other out so now you have 12. This is modeled on the attachment. Hope this helped!

Step-by-step explanation: