Find a power series representation for the function.f(x) = x8 tan−1(x3)f(x) =[infinity] leftparen1.gifrightparen1.gifsum.gifn = 0

Answer:

12/3=4

Step-by-step explanation:

You have 12 blocks in total, and 3 sections each. It is asking you how many blocks per section.

12 blocks in total/ 3 sections each = 4 blocks per section

The number of coins which Craig collected as calculated from the given data is 49.

Given ,

percentage of foreign coin = 72%

Therefore the percentage of normal coins will be 28%.

Hence , the number of normal coins which he collected can be found out as ,

 28% of 175

= 28% × 175

= 28/100 × 175

= 0.28 × 175

= 49

When we divide a given number by 100 as a fraction , the result we get is known as percentage .

It is represented by the percentage sign which is "%".

The percentage is denoted by the letters "pct" or "pc," respectively. In other words, the percent or % is calculated at a value of around 100 and represents the proportion of one quantity made up of another.

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Answer:

C

Step-by-step explanation:

S = .6T + 331.4    

When S = 331.4:

331.4 = .6T + 331.4    <=====you should be able to see this is true when T= 0

Answer:

below

Step-by-step explanation:

Area of rectangle ( 3 x 4 )  minus the area of the circle (pi * 1^2) =

= shaded area = 8.86 cm^2

The area of the rectangle shown on the coordinate plane is 12 square units.

What is the area of the rectangle shown on the coordinate plane?

To calculate the area of a rectangle, multiply the length by the width of the rectangle.

To find the area of the rectangle shown on the coordinate plane, first, we need to calculate the distance between the points that conforms two of the sides of the rectangle (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4, 1)

2 - (-1,-2)

3 - (-3,-4)

4 - (-6, -1)

Then, calculating the length of the sides,

Consider rectangle ABCD  with vertices A(-4, 1), B(-1, -2), C(-3, -4) and D(-6, -1). The area of the rectangle is

A = length * Width

Find the length and the width:

AB = √(-1 - (-4))² + (-2 - 1)² = √9 + 9 = √18

BC = √(-3 - (-1))² + (-4 - (-2))²  = √4 + 4 = √8

Then the area of the rectangle ABCD is

A = √18 * √8

A = 12 unit²

Hence, the area of the rectangle shown on the coordinate plane is 12 square units.

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The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.

Here, we note the following

Let the person walking away from the elevator be X

Let the other person going up in the elevator be Y

Therefore after 15 seconds, their positions will be;

For X,  2 ft/sec × 15 s = 30 ft away from the elevator

For Y,  7 ft/sec × 15 s = 105 ft up in the elevator

At that instant, the distance between them is given as

d² = x² + y²

d=√ 30² +105² = 11925 ft²

d = √11925 ft²  = 109.202 ft

The rate of change of the distance between the two people, X and Y is given as

[tex]\frac{dd^2}{dt} =\frac{dx^2}{dt} +\frac{dy^2}{dt} \\Therefore,2d\frac{dd}{ydt} =2x\frac{dx}{dt} +2y\frac{dy}{dt} \\[/tex]

                (or)

[tex]d\frac{dd}{dt} =x\frac{dx}{dt} +y\frac{dy}{dt} \\[/tex]

Since dx/dt is given as 2ft/sec and dy/dt is 7ft/sec

Then [tex]d\frac{dd}{dt} =30*2+105*7=975\\\frac{dd}{dt} =\frac{795}{105*202} =7.28ft/sec[/tex]

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Answer:

Step-by-step explanation:

210x550=115500

115,500 divide 10,000=11.55?

When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   [tex]\\26 \frac{2}{5}[/tex].

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

[tex]$$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$[/tex]

Follow the PEMDAS order of operations

Multiply and divide (left to right) [tex]$12 \times \frac{6}{5}: \frac{72}{5}$[/tex]

[tex]=\frac{72}{5}+12$$[/tex]

Add and subtract (left to right) [tex]$\frac{72}{5}+12: \frac{132}{5}$[/tex]

[tex]=\frac{132}{5}$$[/tex]

Convert improper fractions to mixed numbers: [tex]$\frac{132}{5}=26 \frac{2}{5}$[/tex]

[tex]=26 \frac{2}{5}$$[/tex]

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Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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Answer:

Let x be the larger angle and y be the smaller angle

Larger angle is 2 less than 3 times the smaller angle that is x = 3y - 2

As the angles are complementary, their sum equals 90°

or, x + y = 90°

or, 3y - 2 + y = 90°

or, 4y = 92°

or, y = 23°

So, x = 3 * 23 - 2 = 67°

Larger angle = x = 67°

Smaller angle = y = 23°

Answer: -4 < n [tex]\leq[/tex] 5

Step-by-step explanation:

Labels on a line graph can make the visualization more accessible in a few ways:

Overall, labels can help make a line graph more accessible by providing additional context, improving readability, and helping the viewer quickly find the data they are interested in.

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The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

x² + 14x − 24 = 4x

Simplify the equation, then we have

x² + 14x − 24 = 4x

x² + 10x − 24 = 0

Factorize the equation, then we have

x² + 10x − 24 = 0

x² + 12x − 2x − 24 = 0

x(x − 12) − 2(x − 12) = 0

(x − 2)(x − 12) = 0

x = 2, 12

The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.

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Answer:

D. 142 degree

Step-by-step explanation:

A triangle has 180 degree

77 + 65 = 142 degree

180 - 142 = 38 degree

38 degrees is the missing angle of the triangle. This angle must add with angle 1 outside equal to 180

180 - 38 = 142 degree

So, the answer is D

The equation with x about the number thought by Natasha is (x + 2.5) × 2 = 61

Let the number thought by Natasha be x. To formulate the equation, we will perform the same operations as done by Natasha. Forming the equation now -

(x + 2.5) × 2 = 61

Performing multiplication on Left Hand Side of the equation

2x + 5 = 61

Rewriting the equation

2x = 61 - 5

Performing subtraction on Right Hand Side of the equation

2x = 56

Rewriting the equation

x = 56/2

Performing division on Right Hand Side of the equation

x = 28

Thus, the equation is (x + 2.5) × 2 = 61 and the number thought by Natasha is 28.

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Answer:

x = 6

Step-by-step explanation:

We have a 30°-60°-90° right triangle here, so the length of the hypotenuse (12) is twice the length of the shorter leg (6). So x = 6.

The value of x = 25

The measure of the angle ∠R = 101°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be TPRS

Now , the measure of ∠T = ( 4x + 1 )°

The measure of ∠S = ( 3x + 4 )°

Now , from the properties of a parallelogram ,

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

So ,

The value of ∠T = ∠R

And , value of ∠T + ∠S = 180°

Substituting the values in the equation , we get

∠T + ∠S = 180°

( 4x + 1 ) + ( 3x + 4 ) = 180

On simplifying the equation , we get

7x + 5 = 180

Subtracting 5 on both sides of the equation , we get

7x = 175

Divide by 7 on both sides , we get

x = 25

So , the value of x = 25

Now , the measure of ∠T = ( 4x + 1 )° = ∠R

So , the measure of ∠R = ( 4 x 25 + 1 )°

The measure of ∠R = 101°

Hence , The value of x = 25

The measure of the angle ∠R = 101°

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Answer:

Below

Step-by-step explanation:

27 = 3^3        and 9 = 3^2

3^3  * (3^2)^3x

3^3 * 3^6x

3^(3+6x)     so k = 3+6x

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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Answer:

m = -5/2 or -2.5

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The product of linear factors of the given polynomial are;

(x + 3 )*(x² + 2x + 50 + (−100/(x + 3)))

We are given the polynomial expression as;

g(x)= x³ + 5x² + 56x + 150

Now, we are told that  -3 is a zero. Thus, if -3 is a zero that means x = -1

and x + 3 is a factor.

Using online polynomial division calculator, the the polynomial is divided by (x + 3) to get;

(x³ + 5x² + 56x + 150)/(x + 3) = x² + 2x + 50 + (−100/(x + 3))

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The measure of one angle is 1.56° and another angle is 88.64°.

Complementary angles are two angles whose combined angle is 90 degrees.

Let's consider the smaller angle as A and the larger angle as B.

Given that the two angles are complementary, then their sum is A+B = 90°.

The angle B is 20° more than and 44 times angle A. Then B = 44A+20°. Substituting this equation in the A+B = 90° equation, we get,

A+44A+20° = 90°

45A = 90°-20°

A = 70°/45

A = 1.56°

Substitute A = 1.56°in B = 44A+20°, we get,

B = 44(1.56°)+20°

B = 88.64°

The answers are 1.56° and 88.64°. The sum of these two angles gives 90.2°. By rounding off, we will get 90°.

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option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.

First, let us study the definition of Atomic Mass,

Atomic mass -

So we can also conclude that the 1 atomic mass unit is equal to 1/12 of the mass of the C-12 atom

Therefore, option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.

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The equation becomes z + 5 = 1 and the value of the z in the given equation by completing the square is z = -4.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

z - 5 = z² - 25

z - 5 = z² - 5²

By property that A² - B² = (A + B)(A - B)

z - 5 = (z - 5)(z + 5)

z + 5 = 1    

z = - 1 / 5 = - 4

Hence "By completing the square, the equation is changed to z + 5 = 1, and the value of z in the given equation is changed to z = -4".

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Answer:

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

Given equation:

Solve it as follows:

Although part of your question is missing, you might be referring to this full question: The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm? The surface area of a sphere with radius r is given by 4πr².

The rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.

Given A = 4πr²

So, we have:

dA/dt = d/dt (4πr²)

= 4π * d/dt * (r²)

= 4π * 2r * dr/dt

= 8πr * dr/dt

Now, we have that dr/dt = 2 cm/min. So, when the radius of the ball is 8 cm, we have that:

dA/dt = 8πr * dr/dt

= 8π * 8 * 2

= 128π

Since we are measuring area, our unit is cm²/min, not cm/min.

Thus, the rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.

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Answer:

$0.39

Step-by-step explanation:

First find the unit rate for store B ( $8.84/13)

At store B Artuto spends $0.68 for one bottle of apple juice

At store A they spent $0.29

0.68-0.29= 0.39

A problem that could be solved by multiplying 4.63 x 9 is "the product of 4.63 and 9"

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

4.63 x 9

In the above expression, we can see that

4.63 and 9 are multiplied

This means that the problem is a product expression

And a problem that can represent 4.63 x 9 is "the product of 4.63 and 9"

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