a girls feet are 4/5 yards from a pool. the boy's feet are 2/5 yards from the pool. Determine whose feet are closer to the pool.​

The power series cos(i)  [tex]= \sum^\infty_{n = 0} (-1)^n {\frac{i^{2n}}{(2n)!}}[/tex] and it converges to a real number 1.5308

The power series expansion of cosine function

cos(x) =>

[tex]= \sum^\infty_{n = 0} (-1)^n {\frac{x^{2n}}{(2n)!}}\\= 1 - \frac{x^2}{2!} +\frac{ x^4}{4!} - ....[/tex]

Given in the question that,

i = √(-1)

Using the power series for cos(x) , the power series for cos(i) =>

cos(i) =[tex]1 - \frac{i^2}{2!} +\frac{ i^4}{4!} - ....[/tex]

As we know ,

i² = -1 and i⁴ = 1

So, cos(i) = 1 -(-1)/2 + (1/24) - (-1 / 720) + . . .

=> 1 + 1/2 + 1/24 + 1/270+  . . .

Power series = >

cos(i) = [tex]= \sum^\infty_{n = 0} (-1)^n {\frac{i^{2n}}{(2n)!}}[/tex]

The series is convergent to the value 1.5308 which is a average of e and 1/e

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Answer: 20+.25(20)=20+5=25

Step-by-step explanation:

The half of the number is 4.5 .

Given in question as  14 is subtracted from 6 times a number.

Let us suppose a number is x.

First find 6 times of a number = 6*x.

6 times can be defined as x + x + x + x + x + x = 6*x.

We have to subtract from 6 times a number.

14 is subtracted from 6 times a number means 6x - 14.

After subtracting 14 is left.

So 6x - 14 = 40.

Add 14 both side of equal sign.

6x-14+14 = 40+14.

6x = 54.

x = 54/6.

x = 9.

Half of the number x is 9/2 = 4.5.

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Answer:

x=5

Step-by-step explanation:

-3=x-8

8-3=x

x=5

Answer/Step-by-step explanation:

Zeros are x-intercepts. (Solutions are zeros are x-intercepts!)

If you are allowed to use technology, such as a graphing calculator or an online graphing tool, input the function and look for the x-intercepts. Graphing calculators have menus to find them for you. It is a legit way to "verify the zeros" Also, since this is a third degree function (highest exponent is a 3rd power) but the leading coefficient is negative, the end behavior acts the same as:

y = -x^3

a much simpler version. Actually, even simpler:

y = -x

All of these, go up to the left and down to the right. Or some teachers/classes/books/programs want you to say:

as x goes to negative infinity, y goes to infinity (up to the left) and as x goes to infinity, y goes to negative infinity (down to the right)

SO, if you cannot use technology, put the given x-intercept into the function. And check that it gives you a value of 0. Like this:

f(x) =

-x^3-7x^2-7x+15

check by substituting -5 for x

f(-5) =

-(-5)^3-7(-5)^2-7(-5)+15

= 125 -7(25) +35+15

= 125- 175 + 35 + 15

= 0

When you use x =-5 you get y = 0. This verifies that -5 is a zero.

Check -3.

f(-3)=-(-3)^3-7(-3)^2-7(-3)+15

= 27 -7(9) +21 +15

= 27 - 63 +21 +15

= 0

Verified!

Lastly, check 1:

f(1)=-(1)^3-7(1)^2-7(1)+15

= -1 - 7 - 7 + 15

= 0

Verified!

The given expressions are equivalent.

What is equivalent expression?

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Consider the given expressions,

-(-3m + 6 - 12 + 15m) and 2(1 - 2m)

First simplify the expression -(-3m + 6 - 12 + 15m)

= 3m - 6 + 12 - 15m

= -12m + 6

Divide the expression by 3,

= -4m + 2

= 2 + 4m            ..(1)

Now, consider the expression,  2(1 - 2m)

Simplifying this,

2(1 - 2m) = 2 - 4m         ..(2)

From (1) and (2) we can see that the expressions are equivalent.

Hence, the given expressions are equivalent.

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Answer:

1. 1914 ÷ 7 = 273 R.3

2. 6365 ÷ 8 = 795 R.5

3. 7989 ÷ 2 = 3994 R.1

4. 5177 ÷ 7 = 739 R.4

5. 4178 ÷ 3 = 1392 R.2

6. 940 ÷ 9 = 104 R.4

7. 46 ÷ 3 = 15 R.1

8. 96935 ÷ 9 = 10770 R.5

9. 64 ÷ 3 = 21 R.1

10. 761 ÷ 3 = 253 R.2

Answer:6

Step-by-step explanation:

The population in 10 years will be approximately 358,528.

I'm making a table where it shows the population every year. To find how much there is that year, I multiply the previous step by 1.02, which is 102%.

(I'm multiplying by 1.02 (102%) rather than 0.02 (2%) because the population is the previous year's population plus 2%. The previous year's population is 100%, then I'm adding 2%.)

Here's what it would look like:

year 0: 300,000 (this is how the city starts)

year 1: 306,000

year 2: 312,120

year 3: 318,362.4

year 4: 324,729.648

year 5: 331,224.24096

year 6: 337,848.7257792

year 7: 337,848.7257792

year 8: 344,605.700294784

year 9: 351,497.8143006797

year 10: 358,527.7705866933

However, having 0.7705866933 of a person isn't possible, so now, you round to the nearest whole number. The number 358,527.7705866933 rounds up to 358,528 (because the decimal place is greater than 4).

And there you have your answer :) Hopefully this helps!

The amount of pizza ate by Simon, Eira and Martin is

Simon eats 3/8 of a pizza = 3/8

The amount of pizza left after Simon ate

= 1 - 3/8

= 5/8

Eira and Martin eat an equal share of the pizza that is left

that is the amount left was shared into 2

= 5/8 ÷ 2

= 5/16 each for both of them

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Answer:

[tex]\boxed{\tt y=48}[/tex]

Step-by-step explanation:

[tex]\tt \cfrac{3}{16}=\cfrac{9}{y}[/tex]

Cross multiply:-

[tex]\tt 3 \times y=(9)\times (16)[/tex]

[tex]\tt 3y=144[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3y}{3}=\cfrac{144}{3}[/tex]

Simplify:-

[tex]\tt y=48[/tex]

_________________

Hope this helps!

Answer:y=48 I hope this is helpful good luck have a good day

Step-by-step explanation:

3/16 = 9/y

Determine the defined range

3/16=9/y y=0 cross out the equal sign y=0

Simplify the equation using cross-multiplication

3y=144

Divide both sides of the equation by 3

y=48

Check if the solution is in the defined range

Answer:3940

Step-by-step explanation:

The graph y = - 0.5x + 12 has a slope of - 0.5 and decreases in nature.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, harper created a graph of a line by y = - 0.5x + 12.

∴ The graph will have a slope of - 0.5 which is decreasing in nature.

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Answer: the space shuttle

Step-by-step explanation:

The image with line segment AB is dilated from (6, 3) and (3, 3) with scale factor of 1.8

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor.

In this case, the image with endpoints of line segments AB which are (9, 4) and (5, -4) and dilated to become (6, 3) and (3, 3) would have a scale factor of;

scale factor = 9 * x = 5

x = 9 / 5 = 1.8

The scale factor is 1.8

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The probability of selecting 25 data values with a mean less than 190 is 0.6%.

What is probability?

What is mean?

Why do you use the word deviation?

Population mean = 20

Standard deviation = 20

Sample size= 25

Sample mean= 190

z = 190-200/20/5

Square root of 25 -10/4 = 2.

Corresponding term is 0.4938 P(X<190) = 0.500-0.4938

P(X<190) = 0.0062 or 0.62

P(X<190) = 0.6%

Hence, the probability of selecting 25 data values with a mean less than 190 is 0.6%.

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The probability that a point chosen at random lies in the shaded region is 0.28

From the question, we are to find the probability that a point chosen at random lies in the shaded region.

The shaded region is a triangle.

The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle

First, we will calculate the unknown side of the triangle

Let the unknown side be x.

Then, from the Pythagorean theorem, we can write that

12² = 6² + x²

144 = 36 + x²

x² = 144 - 36

x² = 108

x = √108

x = 6√3

From formula,

Area of a triangle = 1/2 × base × height

Area of the triangle = 1/2 × 6 × 6√3

Area of the triangle = 18√3 square units

Now, we will determine the area of the circle

Area of a circle = πr²

Where r is the radius

From the given information,

Diameter of the circle = 12

But,

Radius = Diameter / 2

Therefore,

r = 12/2

r = 6

Thus,

Area of the circle = 3.14 × 6²

Area of the circle = 113.04 square units

Now,

The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04

The probability that a point chosen at random lies in the shaded region = 0.2758

The probability that a point chosen at random lies in the shaded region ≈ 0.28

Hence, the probability is 0.28

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Answer:

look below

Step-by-step explanation:

Step 1: Determine the amount of pure solvent needed.

100 gallons x 0.5 (50%) = 50 gallons of pure solvent

Step 2: Determine the amount of each solution to use.

30% solution: 50 gallons of pure solvent / 0.3 = 166.67 gallons of 30% solution

80% solution: 50 gallons of pure solvent / 0.8 = 62.5 gallons of 80% solution

Step 3: Total the amount of solution used.

166.67 gallons of 30% solution + 62.5 gallons of 80% solution = 229.17 gallons total

Answer:

see explanation

Step-by-step explanation:

(a)

given y is directly proportional to x³ then the equation relating them is

y = kx³ ← k is the constant of proportion

to find k use the condition y = 20h when x = h

20h = kh³ ( divide both sides by h³ )

[tex]\frac{20h}{h^3}[/tex] = k , then

k = [tex]\frac{20}{h^2}[/tex]

y = [tex]\frac{20}{h^2}[/tex] x³ = [tex]\frac{20x^3}{h^2}[/tex]

(b)

when y = 67.5h , then

67.5h = [tex]\frac{20x^3}{h^2}[/tex] ( multiply both sides by h² to clear the fraction )

67.5h³ = 20x³ ( divide both sides by 20 )

3.375h³ = x³ ( take cube root of both sides )

[tex]\sqrt[3]{3.375h^3}[/tex] = x , that is

x = 1.5h

The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

y is directly proportional to the cube of x. Then we have

y ∝ x³

y = kx³

We have y = 20h when x = h, then

20h = k(h)³

k = 20 / h²

The formula for y in terms of x and h is given as,

y = (20 / h²)x³

y = (20 / h²)  (h³)

y = 20h

If y = 67.5 h, then we have

67.5 h = (20 / h²)x³

3.375 h³ = x³

x = 1.5h

The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.

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      idddddddddddddddkkkkkkkkkkkkkkkkkkkkkkkk annnnthinggggggg            

Answer:

A point. (3,5) represents a point that is 3 units to the right of the Y-axis (x = 3) and 5 units above the X-axis (y = 5).

Step-by-step explanation:

To plot a point, you start at origin and move however many units are specified. To do this, you can either;

 A.) Start at origin. Move along the X-axis to 3, and then go straight up five units on the Y-axis. This will plot the point.

 B.) You can also do this with your other value. Starting at origin, move along the Y-axis to 5. Go right on the X-axis three units, and you will be at the same point.

The value   of   x≥2  are: 2,4,5,6

Inequality—the state of not being equal, particularly in status, rights, and opportunities1—is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.

An inequality compares two values to determine whether one is less than, greater than, or simply not equal to the other. a b indicates that a is not equal to b.

Given ,

2x - 4≥1

State the values of x within 1 and 6

2x - 4≥1

2x ≥ 1 +4

2x ≥ 5

Divide both sides by 2

2x/2 ≥  5/2

x = 2

(1,6) is an open interval which means that 1 and 6are not inclusive of the values of x.

So:

therefore the values of   x≥2  are: 2,4,5,6

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0.302 is the probability that exactly 8 people recognize the brand

This is a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:

P(X = r) = nCr . p^r  . q^n-r

Given: number of trial (n) = 10 , probability of success (p) = 0.8, X = 8

probability of failure (q) = 1 - 0.8 = 0.2

P(X = r) = nCr . p^r  . q^n-r

P(X = 8) = 10C8 × 0.8⁸ × 0.2¹⁰⁻⁸

P(X = 8) = 45 × 0.8⁸× 0.2²

P(X = 8) =  0.302

Therefore, the probability that exactly 8 people recognize the brand is 0.302

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The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Suppose the current age of Angela is A while Khali is K.

In 5 years,

A + 5 = K

In 3 years,

K + 3 = 2(A + 3)

K + 3 = 2A + 6

K + 3 = 2(K - 5) + 6

K + 3 = 2K - 10 + 6

2K - K = 3 + 4

K = 7 years old,

A = 7 - 5 = 2 years old.

Hence "The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old".

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Answer: D

Step-by-step explanation:

      This 275 is a constant variable, meaning that the variable (in this case, w of weeks) won't change it. This means there was already 275 gallons in the tank, and was not added during the first week.

      This means the 275 in the equation represents the amount of water, in gallons, in the tank currently.

The side of the hexagonal prism is 8.77 cm

What is a hexagonal prism?

A hexagonal prism has 8 faces, 18 edges, and 12 vertices. Out of the 8 faces, 6 are parallelograms, and 2 are hexagons, and that's why it is called a hexagonal prism. These hexagons are at the base and the top as the opposite faces of a prism are the same.

Given data ,

Let the volume V of the hexagonal prism be V = 2800 cm³

Let the height of the hexagonal prism be H = 14 cm

Now , let the side of the hexagonal prism be = A cm

The volume of the hexagonal prism be V = ( ( 3 √3 / 2 ) ) a²h

where a is the side of the hexagonal base

h is the height of the hexagonal prism

Substituting the values in the equation , we get

The volume of the cube be V = ( ( 3 √3 / 2 ) ) a²h

V = ( ( 3 √3 / 2 ) ) a²h

2800 = ( 3 √3 / 2 ) x a² x 14

200 = ( 3 √3 / 2 ) x a²

Multiply by 2 on both sides of the equation , we get

400 = 3√3 x a²

Divide by 3√3 on both sides of the equation , we get

a² = 76.98

Taking square roots on both sides of the equation , we get

a = 8.77 cm

Therefore , the value of a is 8.77 cm

Hence , The side of the hexagonal prism is 8.77 cm

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The Transitive Property of Congruence allows you to say that if ∠PQR ≅ ∠RQS, and ∠RQS ≅ ∠SQT, then ∠PQR ≅ ∠SQT.

The transitive property with equivalence is another name for the transitive property. According to this rule, all variables ought to be identical if both values are closer and one of the discrete choices is equivalent to a subsequent value.

Therefore, one can assert that if ∠PQR ≅ ∠RQS, and ∠RQS ≅ ∠SQT, then ∠PQR ≅ ∠SQT uses the Transitive Property of Congruence.

This was derived from the  Property of Congruence.

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Answer: ∠PQR ≅ ∠SQT

Step-by-step explanation:

The value of car after 2 years is $17,008.8, as percent it is 28.2% and depreciation is 27.75%

Value of car after two years will be calculated by calculating the depreciation each year.

Depreciation after first year = 60,320 - 15%×60,320

Depreciation after first year = 60,320 - 9,048

Depreciation after first year = $51,272

Depreciation after second year = 51,272 - 15%×51,272

Depreciation after second year = 51,272 - 7690.8

Depreciation after second year = $43,311.2

Value after depreciation = 60,320 - 43,311.2

Value after depreciation = $17,008.8

Value of car as percentage = 17008.8/60320×100

Value of car as percentage = 28.2%

Depreciation after two years period = 9048 + 7690.8

Depreciation after two years period = 16,738.8

Depreciation as percentage = 16738.8/60320×100

Depreciation as percentage = 27.75%

The correct answers are a) $17008.8, b) 28.2% and c) 27.75%.

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The given statement exists true. A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization).

A matrix can be expressed as the union of two distinct matrices, Q and R, using the QR matrix decomposition. R is a square upper/right triangular matrix and Q is an orthogonal matrix. R is also invertible because it is square and doesn't have zeros in its diagonal entries.

A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization). Finding eigenvalues and solving linear least squares problems both use QR factorization.

A = QR. Be aware that the QR-factorization of a rectangular matrix A is sometimes understood with Q square and R rectangular rather than Q rectangular and R square, as with the MATLAB command qr.

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Answer:

1/2 x 1/10^-9

Step-by-step explanation:

(1.5x10^-5)/(3.0x10^4)

=> 1.5/3 x 10^-5/10^4

=> 1/2 x 10^-9

Answer:

= 5

Step-by-step explanation:

(1.5*10⁵) / (3.0*10⁴)

1.5*10⁵ = 15*10⁴

Then:

(1.5*10⁵) / (3.0*10⁴) = (15*10⁴) / (3*10⁴) = 15/3

= 5