Find a power series representation for the function. f(x)= 1 25+5x O a. ΣΗ. (-1)" 22 O
b. 1 25 O
C 25 -0 5*+2 2 O
d E -11 3- O e. 1 25 N O

Answer: composite

Step-by-step explanation: :)

Answer:

Im pretty sure 21 is composite

Step-by-step explanation:

Hope this helps and sorry if its incorrect

If the triangle is not precisely symmetrical, or if Johanna's fingertip is not exactly at the centroid, she may be touching another point on the triangle, allowing her to balance it.

A triangle is a closed, two-dimensional geometric shape made up of three line segments known as sides that intersect at three points known as vertices. Triangles are differentiated by thier sides and angles. Triangles can be collinear (all sides equal), rotationally symmetric, or scalene dependent on their sides. Triangles are classed as keen (all angles less than 90 degrees), correct (all angle equal to 90 degrees), or indifferent (all angles greater than 90 degrees). The area of a triangle may be determined by applying the equation A = (1/2)bh, where A is just the area, b seems to be the right triangle base, and h is the triangle's height.

If the triangle is a flat, two-dimensional object, Johanna must be touching the place where the triangle's centre of mass connects with its plane. This is known as the triangle's centroid, and it is positioned at the intersection of the triangle's medians.

If Johanna can balance the triangle exactly on her fingertip, she is most likely touching the triangle's centroid. If the triangle is not precisely symmetrical, or if Johanna's fingertip is not exactly at the centroid, she may be touching another point on the triangle, allowing her to balance it.

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Answer:

r = 17

Step-by-step explanation:

calculate: 2r=35-1

divide both sides: 2r=34

The set A' ∩ B' contains the elements 3 and 6, which are all the elements in U that are not in sets A or B.

The complement of set A, denoted by A', contains all elements in the universal set U that are not in A. Similarly, the complement of set B, denoted by B', contains all elements in U that are not in B. Therefore, we have:

A' = {3, 4, 6}

B' = {2, 3, 6, 7}

To find the intersection of A' and B', we need to find the elements that are common to both sets. In this case, the common elements are 3 and 6, so:

A' ∩ B' = {3, 6}

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Mr Palmer should use the coordinate geometry to bury the time capsule  and he should draw a x-axis and y-axis coordinate.

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and relationships of objects in space. It involves the study of points, lines, angles, surfaces, and solids, as well as their properties and relationships.

Geometry is divided into two main branches: plane geometry and solid geometry. Plane geometry deals with the study of two-dimensional shapes, such as points, lines, circles, triangles, and polygons. Solid geometry, on the other hand, deals with the study of three-dimensional shapes, such as cubes, spheres, cones, and cylinders.

Geometry has many practical applications in fields such as engineering, architecture, physics, and computer graphics. For example, architects use geometry to design buildings and structures, while engineers use it to design and build machines and structures. In physics, geometry is used to describe the shapes and movements of objects, while computer graphics use geometry to create 3D models and animations.

Geometry also has many theoretical applications. It has been used to solve problems in astronomy, such as determining the size and distance of celestial objects. It has also been used to study the properties of shapes and objects in different dimensions, such as hypercubes and higher-dimensional geometries.

Mr Palmer should use the coordinate geometry to bury the time capsule  and he should draw a x-axis and y-axis coordinate so by using it he not only able to find its location from school only but also from from the playground and basketball courts also he should name it a point P(x,y) final point and also use O(x,y) which is a reference point which can be helpful not only to calculate the distance but also the directions and also distance from the school is 10 yards which can be taken from the reference point.

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The complete question is:

Answer:

5< 10x -3

add like terms first

make sure X's are on one side and numbers on the other

Answer:

5  < 10x - 3

Step-by-step explanation:

5 - 2x < 8x - 3?

Add 2x to each side

5 - 2x+2x < 8x - 3+2x

5  < 10x - 3

The sample size must be 543 so the sample proportion is will not differ by 5%

We are given the following in the question:

Margin of error = 5%

Confidence interval:

p ±z√(p'(1 - p')/n)

Margin of error =

p = ±z√(p'(1 - p')/n)

Since no particular proportion is given, we take

p' = 0.5

Z critical at α 0.02 is ± 2.33

Putting values, we get,

p = ±z√(p'(1 - p')/n)

2.33 x √(0.5(1 - 0.5)/n)

√n = 2.33x 0.5/0.05

n = 542.89 = 543

Thus, the sample size must be 543 so the sample proportion is will not differ by 5%

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Answer:

              \(\bold{(f+g)(x)=2x^2+\frac32x-5}\)

Step-by-step explanation:

\(f(x) =\frac x2-2\quad and\quad g(x) = 2x^2 + x - 3\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=\frac12x-2+2x^2+x-3\\\\(f+g)(x)=2x^2+\frac32x-5\)

The length of the curve is approximately 0.52334 units.

To set up an integral for the length of the curve, we can use the arc length formula:

L = ∫ from y₁ to y₂  √{1 +{dx}/{dy})²} dy

In this case, we have the equation of the curve in terms of (x) and (y), but we need it in terms of (y) only.

To do this, we can solve for (x) in terms of (y) as follows:

2x = cos(3y)

x = 1/2 cos 3y

Now we can find dx/dy using the chain rule:

dx/dy = - 3/2 sin 3y

We need to find the values of (y) that correspond to the endpoints of the curve.

From the equation 2x = cos(3y), we can see that the curve starts at x = 1/2 when (y = 0), and it ends at (x = -1/2 when (y = π/6.

Therefore, we have (y₁ = 0) and (y₂ = π/6

Now we can substitute these expressions into the arc length formula and simplify:

L = ∫ from y₁ to y₂  √{1 +{dx}/{dy})²} dy

= ∫ from 0 to π/6  √{1 +(- 3/2 sin 3y)²} dy

To graph the curve, we can plug in the equation 2x = cos(3y)) into a graphing calculator or software.

Finally, we can use a graphing calculator software to evaluate the integral numerically.

Doing so, we get

L = 0.52334.

Therefore, the length of the curve is approximately 0.52334 units.

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Answer:

the value of x is twenty nine

Answer:

1. True

2. True

Step-by-step explanation:

Counter clockwise is in the opposite direction that the clock hands move, therefore, both Answers are true.

hope this helped :)

Answer:

12,1/2,81,16

Step-by-step explanation:

you just solve it

Answer:

Step-by-step explanation:

Examples

Quadratic equation

x

2

−4x−5=0

Trigonometry

4sinθcosθ=2sinθ

Linear equation

y=3x+4

Arithmetic

699∗533

Matrix

[

2

5

​

3

4

​

][

2

−1

​

0

1

​

3

5

​

]

Simultaneous equation

{

8x+2y=46

7x+3y=47

​

Differentiation

dx

d

​

(x−5)

(3x

2

−2)

​

Integration

∫

0

1

​

xe

−x

2

dx

Limits

x→−3

lim

​

x

2

+2x−3

x

2

−9

​

43 4/5 cups of cheese is needed to make 10 pizzas.

We will use the Unitary method, that is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

Given that it takes 4 3/4 cups of cheese, 7/8 cups of olives, and 2 5/8 cups of sausage to make a signature pizza.

For making one pizza, amount of cheese needed =  4 3/8 cups = 35/8  cups.

Now the total amount of cheese needed to make 10 pizzas, we need to multiply  35/8  cups by 10.

So, 350/8  cups = 43 4/5 cups

Thus,  43 4/5 cups of cheese is needed.

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Answer: Hope this helps!

Step-by-step explanation:

Area of a trapezoid formula base a+base b/2*h

Base a is the top length (22.5)

Base b is the bottom length (49.9)

Add those two lengths together (22.5+49.9=72.4)

Divide that by two (72.4/2=36.2)

Then multiply that by the height (36.2*23.8=861.56)

So your area is 861.56

Answer:

$262.5

Step-by-step explanation:

Given data

Commission earned= 7.5%

Sales for last week=  $3,500

Let us find the amount of the commission

=7.5/100* 3500

=0.075*3500

=$262.5

Hence the commission earned last week is

$262.5

When a coin is flipped 10 times, there are 1024 possible outcomes. Out of these, 286 outcomes contain at most three tails.

To calculate the number of possible outcomes containing at most three tails, we need to consider all the possible combinations of heads (H) and tails (T) in 10 flips. In each flip, we have two possibilities, so the total number of outcomes is 2^10 = 1024.

To find the number of outcomes with at most three tails, we can break it down into three cases:

1. Zero tails: There is only one outcome with all heads (HHHHHHHHHH).

2. One tail: There are 10 ways to choose the flip that results in a tail, and for each of these, the remaining flips are all heads. So, there are 10 outcomes with one tail.

3. Two tails: There are 10 choose 2 = 45 ways to choose the two flips that result in tails, and for each of these, the remaining flips are all heads. So, there are 45 outcomes with two tails.

Adding up these cases, we have 1 + 10 + 45 = 56 outcomes with at most two tails. However, this count includes the outcome with all heads, which we already counted in case 1. So, we subtract 1 to get 56 - 1 = 55 outcomes with at most three tails.

In conclusion, out of the 1024 possible outcomes when flipping a coin 10 times, there are 286 outcomes that contain at most three tails.

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By using  the sum or difference formula of cosine to solve cos(525°) we get cos(525°) = -0.465

The formula to find the value of cos(A ± B) is given as,

cos(A + B) = cosA cosB − sinA sinBcos(A − B) = cosA cosB + sinA sinB

Here, A = 450° and B = 75°

We can write 525° as the sum of 450° and 75°.

Therefore,cos(525°) = cos(450° + 75°)

Now, we can apply the formula for cos(A + B) and solve it.

cos(A + B) = cosA cosB − sinA sinBcos(450° + 75°) = cos450° cos75° − sin450° sin75°= 0.707 × 0.259 − 0.707 × 0.966= -0.465

Substituting the values in the above equation, we get

cos(525°) = 0.707 × 0.259 − 0.707 × 0.966= -0.465

Thus, cos(525°) = -0.465.

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The probability of any one undergraduate being selected in a random sample of 2550 undergraduates from a population of 25500 can be calculated using the formula:

Probability = Number of individuals in the sample / Total population

In this case, the probability would be:

Probability = 2550 / 25500 = 0.1 or 10%

Therefore, the probability of any one undergraduate being included in the random sample is 10%. This means that for every 10 undergraduates in the population, only one would be included in the sample. It is important to note that this probability assumes a truly random sampling process with no bias or influencing factors affecting the selection of individuals.

In conclusion, the probability of any undergraduate being in a random sample of 2550 undergraduates selected from a population of 25500 is 10%. This information can be useful in determining the representativeness of the sample and making inferences about the larger population based on the characteristics of the sample.

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Answer:

x - 5 = 9

x = 14

Step-by-step explanation:

On the left side, there are 5 -1's and 1 x. On the right side, there are 9 1's. Then we set them equal and solve

Problem:

x - 5 = 9

  + 5   + 5

x = 14

The term that describes a group of statements that executes as a single unit is a "block". A block of code is a program that is grouped together and treated as a single unit. So, the correct option is D.

In computer programming, a block is a group of statements or declarations that are enclosed within a set of curly braces ({ }). The block serves as a single unit that is executed together. Blocks are used to organize code and to apply control structures, such as loops and conditional statements, to multiple statements.

A block can contain any number of statements, which can include variable declarations, function calls, loops, conditional statements, and other constructs. The statements within a block are executed in sequence, one after another, unless a control statement is encountered that alters the normal sequence of execution.

For example, a while loop in Java consists of a block of code that is executed repeatedly while a certain condition is true:

while (condition) {

   // block of code to be executed while condition is true

}

In this example, the block of code inside the curly braces will be executed repeatedly while the condition specified in the while statement is true. The block can contain any number of statements, and these statements will be executed each time the loop iterates.

Another common use of blocks is to define functions or methods. A function or method is a block of code that can be called from other parts of the program, and can take inputs (arguments) and return outputs. For example, in Python, a function can be defined as follows:

def function(argument1, argument2):

   # block of code to be executed in the function

   return result

In this example, the block of code enclosed within the function definition is executed when the function is called. The function can take inputs (argument1 and argument2), which can be used within the function, and it can return a result using the return statement.

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Answer:

.2 sdfgghh 45

Step-by-step explanation:

Answer:

P(t) = 19t - 1900

Step-by-step explanation:

The factory expenses = $1900

Per toy expense = $11

The selling price of toy = $30

Now we have to convert it in the equation form. Use the below formula to convert these values in equation form.

Profit = Total revenue – total cost

Profit = TR – (variable cost + fixed cost)

Profit on truck = 30t – (11t + 1900)

Profit = 30t – 11t – 1900

P(t) = 19t - 1900

The equation will be changed into = f(x)= 32

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.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

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Answer: 1/10, 1/7, 2/9, 2/5, 7/11, 1/4, 1/10, 1/7,  1/9, 1/2 , 1/8, 1/12, 0/1, 0/0
1/13, 1/3, 1/4

Step-by-step explanation: i think i know all the answers

You can take LCM and then can add to see what's the sum.

The sum result of given expressions is given by: \(\dfrac{5}{y+5}\)

You can take LCM and then can add to see whats the sum.

\(\begin{aligned}\dfrac{3y}{y^2 + 7y + 10} + \dfrac{2}{y+2} &= \dfrac{3y}{(y+2)(y+5)} + \dfrac{2}{y+2}\\&= \dfrac{3y + 2(y+5)}{(y+2)(y+5)}\\&= \dfrac{5y+10}{(y+2)(y+5)}\\&= \dfrac{5(y+2)}{(y+2)(y+5)}\\&= \dfrac{5}{y+5}\\\end{aligned}\)

Thus, the sum of given expressions is given by:

\(\dfrac{5}{y+5}\)

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Answer:

3.5

Step-by-step explanation:

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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Answer:

1.7

Step-by-step explanation:

You can just use a calculator to make the work easier.