Determine the number of terms necessary to approximate cos x to 8 significant figures using the Maclaurin series approximation cos x = 1 - x^2 / 2

Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

Any fraction that falls to the left of 1/2 on the number line is considered to be less than 0.5.

On the number line, fractions are represented as points between 0 and 1. The fraction 1/2 represents the halfway point on the number line.

Fractions to the left of 1/2 are smaller or less than 0.5.

The fraction 1/4 is to the left of 1/2, so it is less than 0.5.

This means that if you were to convert 1/4 into a decimal, it would be a number smaller than 0.5.

Similarly, the fraction 3/8 is also to the left of 1/2, so it is less than 0.5. When you convert 3/8 to a decimal, it is equal to 0.375, which is less than 0.5.

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Starting with the equation:

25,000 = 10,000(1.05)^2x

We can divide both sides by 10,000 to simplify:

2.5 = (1.05)^2x

Next, we can take the natural logarithm of both sides:

ln(2.5) = ln[(1.05)^2x]

Using the rule that ln(a^b) = b*ln(a), we can rewrite the right side as:

ln(2.5) = 2x*ln(1.05)

Now we can solve for x by dividing both sides by 2ln(1.05):

x = ln(2.5) / (2 ln(1.05))

Using a calculator, this simplifies to:

x ≈ 6.642

Therefore, the solution to the equation is x ≈ 6.642, correct to 3 decimal places.

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Answer:

its A

Step-by-step explanation:

The probability that a person consumes 2,000 to 2,500 calories in a day is 0.22.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given that:

Weight/Calories   1000-1500   1500-2000 2000-2500    Total

per Day              

120 lb.                        90            80      10        180

145 lb.                        35            143       25        203

165 lb.                        15             27         75         117

Total                       140            250        110       500

Hence, Total no. of person consumes 2000 to 2,500 calories in a day = 110

And, Total = 500

Now the probability that a person consumes 2,000 to 2,500 calories in a day :

⇒ 110 / 500

⇒ 0.22

Hence  the probability that a person consumes 2,000 to 2,500 calories in a day is 0.22.

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Answer:

it would be the first one i think

Step-by-step explanation:

Answer:

Option C: between 2.75 and 3.0

Step-by-step explanation:

Maybe this might help somewhat.

Answer: y = 3x - 8

Step-by-step explanation:

Beth drinks 7.2 ounces of orange juice, she will consume approximately 408 milligrams of potassium.

To find out how many milligrams of potassium Beth will consume when she drinks 7.2 ounces of orange juice, we can set up a proportion using the given information.

Let's set up the proportion:

12 ounces of orange juice contains 680 milligrams of potassium.

7.2 ounces of orange juice will contain x milligrams of potassium (unknown).

Using the proportion:

12 ounces / 680 milligrams = 7.2 ounces / x milligrams

Cross-multiplying, we get:

12 × x = 7.2 × 680

Simplifying:

12x = 4896

Dividing both sides by 12:

x = 4896 / 12

x ≈ 408

We may build up a percentage using the above data to determine how many milligrammes of potassium Beth will ingest when she drinks 7.2 ounces of orange juice.

Let's establish the ratio:

680 milligrammes of potassium are present in 12 ounces of orange juice.

The amount of potassium in 7.2 ounces of orange juice is x milligrammes (unknown).

Making use of the proportion

7.2 ounces / x milligrammes is equal to 12 ounces / 680 milligrammes.

The result of cross-multiplying is: 12 x = 7.2 680

To put it simply: 12x = 4896

x = 4896 / 12 x equals 408 when both sides are divided by 12.

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Answer:

The result is 0.36b

Step-by-step explanation:

Here. we want to translate the wordings into an expression of algebra.

Firstly, we decrease b by 40%

40% is same as 40/100 = 0.4

So decreasing b by 40% = b-0.4(b) = b-0.4b = 0.6b

Now we want to decrease 0.6b by another 40%

= 0.6b -0.4(0.6b)

= 0.6b - 0.24b

= 0.36b

Answer:

30.33

Step-by-step explanation:

33.70 x .10= 3.37 (discount)

33.70 - 3.37= 30.33

Kismet paid a total of $49.39 for her day at the science museum.

To find the total amount Kismet paid for her day at the science museum, we will calculate the cost of the exhibit tickets, lunch, tax, and tip separately, and then sum these costs together.

Step 1: Calculate the cost of the exhibit tickets.

Admission to the exhibit is $15.75 per person plus tax, and Kismet pays for herself and her friend.
Ticket cost for 2 people: $15.75 * 2 = $31.50

Step 2: Calculate the tax for the exhibit tickets.
Tax for tickets: $31.50 * 9.15% = $31.50 * 0.0915 = $2.88

Step 3: Calculate the cost of Kismet's lunch.
Sandwich: $7.85
Apple: $1.75
Drink: $2.39
Total lunch cost: $7.85 + $1.75 + $2.39 = $11.99

Step 4: Calculate the tax for Kismet's lunch.
Tax for lunch: $11.99 * 9.15% = $11.99 * 0.0915 = $1.10

Step 5: Calculate the tip for the server.
Tip: $11.99 * 16% = $11.99 * 0.16 = $1.92

Step 6: Calculate the total amount Kismet paid.
Total cost: (Ticket cost + Ticket tax) + (Lunch cost + Lunch tax + Tip)
Total cost: ($31.50 + $2.88) + ($11.99 + $1.10 + $1.92) = $49.39

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1000 is the amount of garbage that was initially dumped in the landfill before any additional garbage was added. i.e: It is the quantity of garbage on Day 0.

The initial function given in the problem is n = 2000x + 1000.

The definition of a function's initial value is its starting value, which is unaffected by any variables used in the function.

The given function is:

n = 2000x + 1000

where the amount of trash is n, and the number of days is x. We'll set the variable (x) equal to zero to obtain the starting value.

Therefore, initially:

n = 2000(0) + 1000 = 1000

This indicates that the trash had a value of 1000 at day zero.

Therefore 1000 represents the amount of trash that was originally present in the landfill before dumping any extra trash.

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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Answer:

The answer on the right bottom

Step-by-step explanation:

3/4 × 1/2 = 3/8

None of them have 3 shaded but the right bottom

Therefore that'd be your answer

Answer:

bottom right

Step-by-step explanation:

In order to know the answer, you have to find the product of \(\frac{3}{4}\) x \(\frac{1}{2}\).

Multiply both numerators and denominators in order to get the answer.

\(\frac{3}{4}\) x \(\frac{1}{2}\) = \(\frac{3}{8}\) (this is the lowest term already)

If you check among the choices, it is only the bottom right choice that shows correct shading of the fraction. The diagram divides the right side into 4 equal parts. If you divide the left side into 4 equal parts like this, you'll surely get 8 equal parts of the total diagram. This represents the denominator, 8. The shaded portion represents the numerator, 3.

Given function f(x) = 3x² + 5x + 2Find the slope of the tangent line to the curve y

= f(x) at the point (2,24).

= ax² + bx + c f'(x)

= 2ax + bAt point (2,24), x

= 2Therefore, slope of tangent line

= f'(2)Also, a

= 3, b

= 5 and c

= 2Thus,f'(x)

= 6x + 5 Slope of tangent line at point (2,24) is:f'(2)

= 6(2) + 5

= 12 + 5

= 17Therefore, slope of tangent line to the curve y

=f(x) at the point (2,24) is 17.

The slope of the tangent line is defined as the derivative of the function at that point. To find the slope of tangent line at a particular point, we need to find the derivative of the function and then substitute the given point in it.

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The rate at which the distance between the runner and second base changes is 28.71 ft/s.

Given, a batter hits the ball and runs toward first base at a speed of 28 ft/s. we have to find the rate (in ft/s) at which the distance between the runner and second base change when the runner has run 20 ft.

As, distance = speed × time

d = st

On differentiating both the sides

d' = s't + s

d' = 20/28 + 28

d' = 0.71 + 28

d' = 28.71

Hence, the rate at which the distance between the runner and second base changes is 28.71 ft/s.

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Answer: (0, 12)

Step-by-step explanation:

2x + 3y = 36

2(0) + 3y = 36

3y = 36

3/3 36\3

= 12

On edge

Answer:

a

Step-by-step explanation:

Answer:

5026.55

Step-by-step explanation:

A=πr2=π·402≈5026.54825ft²

Develop similarity measures by applying the Jaccard index formula to the membership degrees of the fuzzy sets and use these measures for clustering objects based on their fuzzy characteristics.

The question is asking about new similarity measures of intuitionistic fuzzy sets based on the Jaccard index and their application to clustering.

To answer the question, first, let's understand what fuzzy sets and clustering are. Fuzzy sets are a generalization of classical sets where an element can have a degree of membership ranging between 0 and 1. Clustering, on the other hand, is a technique used to group similar objects together based on their characteristics.

Now, the question specifically mentions the Jaccard index as a basis for similarity measures. The Jaccard index is a measure of similarity between two sets, which is calculated as the ratio of the intersection of the sets to the union of the sets.

To develop new similarity measures for intuitionistic fuzzy sets based on the Jaccard index, you can apply the Jaccard index formula to compare the membership degrees of the elements in the fuzzy sets. The resulting similarity measure will provide a quantitative value indicating the degree of similarity between the sets.

These new similarity measures can then be applied to clustering. In clustering, the similarity measures between objects are used to determine the groupings. By utilizing the Jaccard index-based similarity measures for intuitionistic fuzzy sets, you can cluster objects based on their fuzzy characteristics and similarities.

In summary, the question asks about new similarity measures of intuitionistic fuzzy sets based on the Jaccard index and their application to clustering. To answer this, you can develop similarity measures by applying the Jaccard index formula to the membership degrees of the fuzzy sets and use these measures for clustering objects based on their fuzzy characteristics.

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For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

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Answer:

first you divide the larger number into its separate parts. Here, 23 becomes 20 and 3.

Next, you multiply each separate part — 20 x 7 and 3 x 7.

Finally, you add all the products together. 140 + 21 equals 161, the product of 23 x 7.

Step-by-step explanation:

Answer: 4x+20

Step-by-step explanation:

4x5=20

4x1x=4x

Answer:

3.0pages

Step-by-step explanation:

If Tiffany type a page in an hour, then;;

1 page = 1 hour

To calculate the number of pages typed in 3 hours, we can express as;

x pages = 3 hours

Divide both expressions

1/x = 1/3

x* 1 = 1* 3

x = 3pages

She will type 3.0pages in 3 hours

Answer:

43.8

When you round look at the number after the one your rounding up to. If its greater than 5 round up. If its lower than 5 keep it the same number

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = M(6, - 2) and (x₂, y₂ ) = N(8, 4)

m = \(\frac{4-(-2)}{8-6}\) = \(\frac{4+2}{2}\) = \(\frac{6}{2}\) = 3

Step-by-step explanation:

1) 4 3/5 or 4.6

2) 3.833

3) 4

4) 9.866

Answer:

25 hamburger

20 hot dogs

Step-by-step explanation:

Answer:

5q+74

Step-by-step explanation:

84-94 first which equals -10

then add that by 84 which equals 74

lastly just bring the 5q and 74 together making your expression

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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