1. Find the Taylor series for f(x) = cos x centered at a = Ā. Express your answer in sigma notation.

Based on the information the cost of the product is $40,000.

Given:

Percentage earn=5% or 0.05

Amount earned=$2,000

Let x represent the cost of the product

Hence:

Formulate

.05x = $2000  

Divide both sides by .05

x=$2,000/.05

x=$40,000

Inconclusion  the cost of the product is $40,000.

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The area of the walk is 232 square feet. The area of the yard can be found by multiplying the length and width of the yard:

To find the area of the walk, we first need to calculate the area of the entire yard and the area of the inner rectangle (without the walk).

The area of the yard can be found by multiplying the length and width of the yard:
Area of yard = length * width = 26 ft * 36 ft ⇒ 936 sq ft

Next, we need to calculate the dimensions of the inner rectangle. Since the walk is 2 ft wide and goes all the way along the fence, we subtract 4 ft (2 ft on each side) from both the length and width of the yard:
Length of inner rectangle = 26 ft - 4 ft ⇒22 ft
Width of inner rectangle = 36 ft - 4 ft⇒32 ft

Now, we can calculate the area of the inner rectangle:
Area of inner rectangle = length * width = 22 ft * 32 ft ⇒ 704 sq ft

Finally, to find the area of the walk, we subtract the area of the inner rectangle from the area of the yard:
Area of walk = Area of yard - Area of inner rectangle = 936 sq ft - 704 sq ft ⇒ 232 sq ft
Therefore, the area of the walk is 232 square feet.

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The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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Answer:

y = 0.2x + 37

Step-by-step explanation:

A) Find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly of the Ringular plan.

(x, y) = (minutes, cost)

(110, 59)

(600, 157)

slope = m = dy/dx

dy/dx = change in y/change in x

m = dy/dx

m = (157 - 59)/(600-110)

m = 98/490

m = 0.2

a) the linear equation:

y - 59 = 0.2(x - 110)

y - 59 = 0.2x - 22

y = 0.2x - 22 + 59

y = 0.2x + 37

Answer:

1.00 meter.

Step-by-step explanation:

For the first day, she dug eighteen twentieth of a meter = \(\frac{18}{20}\) x 1 meter

                                                                        = \(\frac{9}{10}\) meters

The second day, she dug nine twentieth of a mater = \(\frac{9}{20}\) x 1 meter

                                                                        = \(\frac{9}{20}\) meters

Total length of the trench = \(\frac{9}{10}\) + \(\frac{9}{20}\)

                                          = \(\frac{18 + 9}{20}\)

                                          = \(\frac{27}{20}\)

                                          = 1\(\frac{7}{20}\)

                                          = 1.35 meters

Total length of the trench is 1.35 meters.

A reasonable estimate of the total length of the trench is 1.00 meter.

Answer:

It is 1 and 1 half. or C

Step-by-step explanation:

It is 18/20 + 9/20. 18 + 9 = 27, and there is (number)/20. since it is 20 it will get 1 whole. now there is just 7, and 7 you round up to 1 half because 5 and over round up, while 4 and under round down.

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The two processes that caused the puddle to form and then disappear were evaporation and infiltration.

Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.

Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.

The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.

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Given:

Angle \(\displaystyle\sf \theta\) (angle between the ladder and the ground): \(\displaystyle\sf \tan(\theta) = 2.4\)

Distance between the foot of the ladder and the wall: \(\displaystyle\sf d = 50\,cm\)

To find:

Length of the ladder: \(\displaystyle\sf x\)

Using the tangent function:

\(\displaystyle\sf \tan(\theta) = \frac{{\text{{opposite}}}}{{\text{{adjacent}}}}\)

In this case:

Opposite side is the height of the wall: \(\displaystyle\sf x\)

Adjacent side is the distance between the foot of the ladder and the wall: \(\displaystyle\sf d\)

So we have:

\(\displaystyle\sf \tan(\theta) = \frac{{x}}{{d}}\)

Substituting the given values:

\(\displaystyle\sf 2.4 = \frac{{x}}{{50}}\)

To find \(\displaystyle\sf x\), we can solve for it by multiplying both sides of the equation by 50:

\(\displaystyle\sf 2.4 \times 50 = x\)

Simplifying:

\(\displaystyle\sf x = 120\)

Therefore, the length of the ladder is 120 cm.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

If the function f(x) = \(x^2\), then the function g(x) = \(-x^2-2\)

From the given graph

The function is

f(x) = \(x^2\)

The function is the rule the shows the relationship between one variable and another variable. If one variable is independent variable and another variable will be dependent variable. We can also says that the it show the relationship between input and output of the function

We can see that the function g(x) is the reflection of the function f(x) at y = -2

The reflection of f(x) = - f(x)

= - \(x^2\)

The reflection of f(x) at y = -2 is

f(x) =  \(-x^2-2\)

Then the function g(x) = \(-x^2-2\)

Hence, If the function f(x) = \(x^2\), then the function g(x) = \(-x^2-2\)

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Answer:

x>-4

Step-by-step explanation:

Answer: In an isosceles right triangle, each leg has the same length as the hypotenuse divided by the square root of 2 (since the hypotenuse is √2 times the length of each leg).

So, the length of each leg can be found by dividing the length of the hypotenuse by √2, which gives:

length of one leg = (2√2) / √2 = 2 meters

Therefore, the length of one leg of the isosceles right triangle is 2 meters.

Step-by-step explanation:

-The coefficients in the objective function row represent the coefficients of the corresponding variables in the objective function.

To convert the given problem into a maximization problem with positive constants on the right side of each constraint, we need to change the signs of the objective function coefficients and multiply the right side of each constraint by -1.

The original problem:

Maximize z = -3x₁ + 4x₂ + 6x₃

subject to:

15x₁ + 2x₂ + y₃ ≤ 110

y₁ + 250x₂ + 1950x₃ ≥ 20

y₁ + 20x₂ + 20x₃ ≤ 250

Converting it into a maximization problem with positive constants:

Maximize z = 3x₁ - 4x₂ - 6x₃

subject to:

-15x₁ - 2x₂ - y₃ ≥ -110

-y₁ - 250x₂ - 1950x₃ ≤ -20

-y₁ - 20x₂ - 20x₃ ≥ -250

Next, we can write the initial simplex tableau by introducing slack variables:

```

 BV   |  x₁    x₂    x₃    y₁    y₂    y₃    RHS

--------------------------------------------------

  s₁  | -15    -2    0     -1    0     0    -110

  s₂  |   0   -250  -1950    0    1     0     20

  s₃  |   0   -20    -20     0    0    -1    -250

--------------------------------------------------

  z   |   3     -4    -6     0    0     0      0

```

In the tableau:

- The variables x₁, x₂, x₃ are the original variables.

- The variables y₁, y₂, y₃ are slack variables introduced to convert the inequality constraints to equations.

- BV represents the basic variables.

- RHS represents the right-hand side of each constraint.

- The coefficients in the objective function row represent the coefficients of the corresponding variables in the objective function.

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After polygon STUV is reflected across the y-axis, the coordinates of point S' are (-2, 3).

Reflecting a polygon across the y-axis is a type of transformation in geometry that involves flipping the shape over the y-axis. When reflecting a polygon across the y-axis, the x-coordinates of all the points in the shape are multiplied by -1, while the y-coordinates remain the same.

In the case of polygon STUV, point S has coordinates (2, 3). When reflected across the y-axis, the x-coordinate becomes -2, while the y-coordinate remains 3. Therefore, the image of point S after the transformation, denoted as S', has coordinates (-2, 3).

It's important to note that reflecting a polygon across the y-axis is just one of many possible transformations in geometry. Other common transformations include translations, rotations, and dilations. These transformations can be used to explore the properties of shapes and to solve problems in geometry.

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Answer:

Step-by-step explanation:

I like you pic

The value of the expression 21x + 30y is -9

The equation is given as:

7x+10y=−3

Multiply both sides by 3

3 * 7x + 3 * 10y=−3 * 3

Evaluate the product

21x + 30y = -9

Hence, the value of the expression 21x + 30y is -9

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The simplification of the trigonometric expression: \frac{\sec (x)-\cos (x)}{\tan (x)} = \frac{1/\cos (x) - \cos (x)}{\sin (x)/\cos (x)} = \frac{1 - \cos^2 (x)}{\sin (x)} = \boxed{\frac{\sin^2 (x)}{\sin (x)}} = \sin (x)

We can start by simplifying the numerator of the expression. We have $\sec (x) = 1/\cos (x)$, so we can rewrite the numerator as $1/\cos (x) - \cos (x)$. We can then use the difference of squares factor to simplify this expression:

\frac{1/\cos (x) - \cos (x)}{\sin (x)/\cos (x)} = \frac{(1/\cos (x) - \cos (x))(\cos (x) + 1)}{\sin (x)/\cos (x)} = \frac{1 - \cos^2 (x)}{\sin (x)}

Finally, we can use the identity $\sin^2 (x) + \cos^2 (x) = 1$ to simplify the denominator. This gives us $\sin^2 (x)/\sin (x) = \boxed{\sin (x)}$.

The first step is to simplify the numerator of the expression. We have $\sec (x) = 1/\cos (x)$, so we can rewrite the numerator as $1/\cos (x) - \cos (x)$. We can then use the difference of squares factorization to simplify this expression: (a - b)(a + b) = a^2 - b^2

In this case, we have $a = 1/\cos (x)$ and $b = \cos (x)$. So, we can rewrite the numerator as: \frac{(1/\cos (x))(\cos (x) + 1) - (\cos (x))^2}{\sin (x)} = \frac{1 - \cos^2 (x)}{\sin (x)}

The denominator can be simplified using the identity $\sin^2 (x) + \cos^2 (x) = 1$. This gives us $\sin^2 (x)/\sin (x) = \boxed{\sin (x)}$.

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Answer:

Y is less than or equal to 2/5x+1

Answer:

it is 100% b

Step-by-step explanation:

Answer:

I cannot confirm answer (D), but it looks correct to me.

Here's the option:

The expected yield of a crop is low whenever the number of seeds planted per square foot is small or large. A larger yield is expected when the number of seeds per square foot is around 60.

ED2021

the credit card holder paid a total of $349.26 in interest.

So the answer is not provided in the options.

To calculate the interest paid, we need to first determine the monthly interest rate, which is the annual percentage rate (APR) divided by 12:

Monthly interest rate = 11.99% / 12 = 0.9992%

Next, we can calculate the balance after each payment is made. For the first 11 months, the payment is $350 each month, so the balance after each payment is:

Month 1: $9,768.26 - $350 = $9,418.26

Month 2: $9,418.26 - $350 = $9,068.26

Month 3: $9,068.26 - $350 = $8,718.26

Month 11: $3,518.26 - $350 = $3,168.26

At the end of the 11th month, the balance is $3,168.26. This balance will accrue interest for one more month before the cardholder pays it off in full. The interest on this balance for one month is:

Interest = Balance x Monthly interest rate

Interest = $3,168.26 x 0.9992%

Interest = $31.66

Therefore, the total interest paid by the cardholder is the sum of the interest paid on the monthly balances for the first 11 months plus the interest paid on the remaining balance in the 12th month:

Total interest = (11 x $31.66) + $31.66 = $349.26

Therefore, the credit card holder paid a total of $349.26 in interest.

So the answer is not provided in the options.

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Answer:

G

Step-by-step explanation:

a + b + c = 80

Express a and c in terms of b using the ratios in fractional form, that is

\(\frac{a}{b}\) = \(\frac{2}{3}\) ( cross- multiply )

3a = 2b ( divide both sides by 3 )

a = \(\frac{2}{3}\) b

\(\frac{b}{c}\) = \(\frac{3}{11}\) ( cross- multiply )

3c = 11b ( divide both sides by 3 )

c = \(\frac{11}{3}\) b

Substitute the values for a and c into the original equation

\(\frac{2}{3}\) b + b + \(\frac{11}{3}\) b = 80 ( multiply through by 3 to clear the fractions )

2b + 3b + 11b = 240 , that is

16b = 240 ( divide both sides by 16 )

b = 15 → G

Answer:

m=3

Step-by-step explanation:

Answer:

hola grandma said holla

a) The slope of the staircase is 57/43.

b) The angle of the staircase is approximately 53.19 degrees.

To determine the slope of the staircase, we need to calculate the ratio of the rise to the run.

(a) The rise of the staircase is given as 7 1/8 inches, which can be written as a mixed number or converted to an improper fraction. Converting it to an improper fraction:

7 1/8 inches = (8 × 7 + 1)/8 inches = 57/8 inches

The run of the staircase is given as 10 3/4 inches, which can also be converted to an improper fraction:

10 3/4 inches = (4 × 10 + 3)/4 inches = 43/4 inches

Now we can find the slope by dividing the rise by the run:

slope = (rise / run) = (57/8) / (43/4) = (57/8) × (4/43) = 57/43

Therefore, the slope of the staircase is 57/43.

(b) To find the angle of the staircase, we can use trigonometry. The tangent of an angle is equal to the rise divided by the run. In this case, the tangent of the angle is equal to (57/8) / (43/4).

tan(angle) = (rise / run) = (57/8) / (43/4)

We can simplify this equation by multiplying both the numerator and denominator by 4:

tan(angle) = (57/8) × (4/43) = 57/43

To find the angle itself, we need to take the arctangent (inverse tangent) of the ratio:

angle = arctan(57/43)

Using a calculator, we can find that arctan(57/43) is approximately 53.19 degrees.

Therefore, the angle of the staircase is approximately 53.19 degrees.

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Answer:

50(4)^t

Step-by-step explanation:

The exponential function is  50 x \((4)^t\) and after 5 days the population of bacteria is 12800

An exponential function is a Mathematical function in the form f (x) = \(a^x\), where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given:

A colony of bacteria starts with 50 organisms and quadruples each day.

let the t be the number of day.

So, After t days the population of the bacteria

= 50 x \((4)^t\)

Now, After 5 days the population is

t =5

= 50 x \((4)^t\)

= = 50 x \((4)^5\)

= 50 x 256

= 12800

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Answer:

200.96

Step-by-step explanation:

Pi(8 to the power of 2)

2 Hours

this is because one pipe takes 4 hours, and if both pipes take 2 hours, that is cutting the time in half, meaning both pipes pour the same amount and take the same time.

hope this is helpful!

Answer:

2

Step-by-step explanation:

First replace x with -1

f(-1)=2+(-1)

f(-1)=1

Now plug in 1

g(1)=3-1

3-1=2

Answer:

She will have 16 begonia plants the fourth year.

Step-by-step explanation:

0   1   2   3   4

1    3   9  27  81

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Answer:

Happy holidays to you too!

add two to the rest so

year one- 3

year two-5

year three-7

year four-9

Part A: The graph consists of a solid line for 2x + 3y ≤ 15, a dashed line for x + y ≥ 3, and the shaded region above the dashed line and below or on the solid line represents the solution set.

Part B: No, the point (5, 1) is not included in the solution area as it does not satisfy the second inequality x + y ≥ 3 when substituted with x = 5 and y = 1.

Part C: Let's choose the point (2, 4) as a different point in the solution set, meaning Michael can buy 2 cupcakes and 4 pieces of fudge, ensuring he can feed at least three siblings while staying within his budget of $15.

Part A:

The system of inequalities represents the constraints on the number of cupcakes (x) and pieces of fudge (y) that Michael can buy with his $15. Let's graph the system and describe it:

First inequality: 2x + 3y ≤ 15

To graph this inequality, we can start by representing it as an equation: 2x + 3y = 15.

We can rewrite this equation in slope-intercept form: y = (-2/3)x + 5.

This equation represents a straight line with a slope of -2/3 and a y-intercept of 5.

Since the inequality is less than or equal to, we will include the line in our graph.

We will use a solid line to represent this equation.

Second inequality: x + y ≥ 3

To graph this inequality, we can rewrite it in slope-intercept form: y ≥ -x + 3. This equation represents a straight line with a slope of -1 and a y-intercept of 3.

Since the inequality is greater than or equal to, we will shade the area above the line to represent all the valid solutions.

We will use shading above the line and make it hatched to indicate that the line itself is not included in the solution.

The graph will include both lines and will have the shaded area above the second line and bounded by the first line.

Part A Solution Set Description:

The solution set is the area where the shaded region above the line y ≥ -x + 3 intersects or overlaps with the line 2x + 3y ≤ 15.

It represents all the valid combinations of cupcakes and fudge that Michael can buy with his $15, satisfying the constraints of feeding at least three siblings.

The solution set is a region in the coordinate plane that lies above the line y ≥ -x + 3 and below or on the line 2x + 3y = 15.

Part B:

To determine if the point (5, 1) is included in the solution area, we need to check if it satisfies both inequalities:

First inequality: 2x + 3y ≤ 15

Substituting x = 5 and y = 1: 2(5) + 3(1) = 10 + 3 = 13 ≤ 15

The point (5, 1) satisfies the first inequality.

Second inequality: x + y ≥ 3

Substituting x = 5 and y = 1: 5 + 1 = 6 ≥ 3

The point (5, 1) satisfies the second inequality.

Therefore, the point (5, 1) is included in the solution area for the system of inequalities.

Part C:

Let's choose a different point in the solution set, such as (3, 2). This means Michael buys 3 cupcakes and 2 pieces of fudge.

Interpretation in terms of the real-world context:

With this combination, Michael spends 3 \(\times\) $2 = $6 on cupcakes and 2 \(\times\) $3 = $6 on fudge, totaling $12.

Since $12 is less than or equal to his available $15, he can afford this combination of cupcakes and fudge.

This point represents a valid solution where Michael can feed at least three siblings by buying 3 cupcakes and 2 pieces of fudge while staying within his budget.

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The inequality of the scenario is 8.50n + 9 ≤ 43

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

Amount = $43

The cost of n books and 4 pens can be expressed as:

8.50n + 2.25(4)

We can simplify this expression:

8.50n + 9

We know the student has a total of $43 to spend, so we can set up an inequality:

8.50n + 9 ≤ 43

Subtracting 9 from both sides, we get:

8.50n ≤ 34

Dividing both sides by 8.50, we get:

n ≤ 4

Hence, the inequality that best represents the scenario is: n ≤ 4 or 8.50n + 9 ≤ 43

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Complete question

For this item, select the answers from the drop-down menus A student has $43 in total to buy books that cost \$8.50 each and pens that cost $2.25 each. The student buys n number of books and 4 pens

Complete the inequality to best represent the scenario.