Jackson is told that he will be given 1 cent for working today. However, for each day he works, he will get double the pay. So, on day 2, he gets 2 cents, on day 3, 4 cents, and so on. Jackson thinks, no way, that’s not much money. But if he agrees, how much will he make on day 20?

Answer:

D. 31/40

Step-by-step explanation:

3/8 + 2/5 =

15/40 + 16/40 =

31/40

Answer:

   39. (4) 4 1/16

Step-by-step explanation:

Simplifying

Substituting x = 4

Answer:

Perimeter = 18(1 + √3 ) cm

Step-by-step explanation:

The radius of each ball = 1/2 * 6 = 3 cm.

Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).

If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.

If the adjacent side of a triangle  ( which is part of the side of the big triangle) = x:

tan 30 = 3 / x

x = 3 / tan 30

=  3 / 1/√3

=   3√3 cm.

There are 6 of these sides in the big triangle so their total length =

18√3 cm.

The three 'middle' sides joining 2 billiard balls  each have a length of  2 radii = 6 cms   ( as they form a rectangle with the radii of 2 billiard balls).

So the perimeter of the triangle = 18√3 + 3(6)

= 18(1 + √3 ) cm

I would have liked to transfer a diagram but I can't get to copy it to this site.

Answer:

Step-by-step explanation:

(x−2)2+(y−1)2=9

This is the form of a circle. Use this form to determine the center and radius of the circle.

(x−h)2+(y−k)2=r2

Match the values in this circle to those of the standard form. The variable r

represents the radius of the circle, h represents the x-offset from the origin, and k

represents the y-offset from origin.

r=3

h=2

k=1

The center of the circle is found at (h,k)

.

Center: (2,1)

These values represent the important values for graphing and analyzing a circle.

Center: (2,1)

Radius: 3

Answer:

B is correct I hope this helps.

Answer:

1. A

2. C

Step-by-step explanation:

1. A

2. C

Answer:

40:1

Step-by-step explanation:

hope this helps:)

HOPE IT HELP (≧▽≦)(≧▽≦)(≧▽≦)

Answer:

Step-by-step explanation:

the answer is wrong its  34.3

Answer:

A.

Step-by-step explanation:

2×sqrt(48) - (2 + sqrt(12))(5 - sqrt(12))

2×sqrt(16×3) - (2 + sqrt(4×3))(5 - sqrt(4×3))

2×4×sqrt(3) - (2 + 2×sqrt(3))(5 - 2×sqrt(3))

8×sqrt(3) - (10 - 4×sqrt(3) + 10×sqrt(3) - 4×3)

8×sqrt(3) - 10 - 6×sqrt(3) + 12

2×sqrt(3) + 2

Answer:

n = ±0.13363

Step-by-step explanation:

2/8 - (14*n*(n))=0                                              • Use this formula for proof

2/8 = 1/4                                                            A^2 - AB + BA - B^2 =

1/4 - 14n^2 = 0                                                   A^2 - AB + AB - B^2 =

14n^2 = 14n^2 ÷ 1 = 14n^2 • 4 ÷ 4                      A^2 - B^2

1 - (14n^2 • 4) ÷ 4 = 1 - 56n^2 ÷ 4

1 - 56n^2 ÷ 4 = 0

1-56n2 ÷ 4 • 4 = 0 • 4

1-56n^2  = 0

56n^2 = 1

n^2 = 1/56 = 0.018

n ≈ ±0.13363

Using translation concepts, it is found that the necessary transformations are given as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The original function f(x) is given by:

[tex]f(x) = \sqrt{x}[/tex]

The transformations are as follows:

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Answer:

Step-by-step explanation:

3x + 8 = 4x + 4

-x + 8 = 4

x = 4

answer is A

Answer:

[tex]f'(x)=\displaystyle -\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]

Step-by-step explanation:

Recall the power series [tex]\sin(x)=\displaystyle \sum\limits^\infty_{n=0}(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex].

In this case, [tex]x[/tex] is replaced with [tex]\displaystyle \frac{1}{1+e^x}[/tex], so our power series actually works out to be [tex]\displaystyle \sin\biggr(\frac{1}{1+e^x}\biggr) =\sum\limits^\infty_{n=0}(-1)^n\frac{\bigr(\frac{1}{1+e^x}\bigr)^{2n+1}}{(2n+1)!}[/tex]! Amazing, huh?

Now, we find the derivative of the function by using the chain rule:

[tex]\displaystyle \frac{d}{dx}\sin\biggr(\frac{1}{1+e^x}\biggr)=\frac{d}{dx}\biggr(\frac{1}{1+e^x}\biggr)*\cos\biggr(\frac{1}{1+e^x}\biggr)=-\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]

You didn't specify if you just wanted the derivative of the series to be a function or a series, so I'm going to assume you want the function. Let me know if there's more to your problem.

Answer:

The set of points equidistant from a given point (the center). Radius : A segment with endpoints at the center and on the circle.

Step-by-step explanation:

The probability of drawing a number card and then number card without replacement is 105/221 option first is correct.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The total number of cards = 52

Total number of cards printed number on it = 36

The probability of drawing a number card and then number card without replacement:

[tex]= \rm \dfrac{36}{52}\times \dfrac{35}{51}[/tex]

= 1260/2652

= 105/221

Thus, the probability of drawing a number card and then number card without replacement is 105/221 option first is correct.

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To find the perimeter of a shape you add all the side lengths together.

Perimeter of A is 20cm because 7+7+3+3=20

Perimeter of B is 27cm because 9+8+10=27

Perimeter of C is 17cm because 6+6+5=17

Perimeter of D is 34cm because 10+10+4+4+3+3=34

On shape E there is one side length that we do not know. To find that do 8-3=5 because 5+3 would be the opposite side of the 8. Now do 5+8+8+4+12+3=40 cm which is the perimeter of shape E.

I hope this helps you have a good day

Answer:

[tex]f(x)=(x-\frac{5}{2})^2+\frac{7}{4}[/tex]

Step-by-step explanation:

Complete the square

[tex]f(x)=x^2-5x+8\\\\f(x)-1.75=x^2-5x+8-1.75\\\\f(x)-1.75=x^2-5x+6.25\\\\f(x)-1.75=(x-2.5)^2\\\\f(x)=(x-2.5)^2+1.75\\\\f(x)=(x-\frac{5}{2})^2+\frac{7}{4}[/tex]

Answer:

g(p + 4) = [p² + 8p + 21 / 3p + 12]

Step-by-step explanation:

Function :

g(x) = (x² + 5) / 3x

Substitute x = p + 4 :

⇒ g(p + 4) = [(p + 4)² + 5] / 3(p + 4)

⇒ g(p + 4) = [p² + 8p + 16 + 5 / 3p + 12]

⇒ g(p + 4) = [p² + 8p + 21 / 3p + 12]

We will see that the vertex of the quadratic equation is at (1, 14)

For a general quadratic:

[tex]y = a*x^2 + b*x + c[/tex]

The x-component of the vertex is at:

[tex]x = -b/2a[/tex]

In this case, we have:

[tex]y = -2x^2 + 4x + 12[/tex]

Then the vertex is at:

[tex]x = -4/(2*-2) = 1[/tex]

To get the y-component of the vertex, we need to evaluate in x = 1.

[tex]y = -2*1^2 + 4*1 + 12 = -2 + 4 + 12 = 14[/tex]

Then we conclude that the vertex is at (1, 14), so the correct option is d.

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The total amount of the fuel needed for the trip is 42.5 gallons if the distance from their old house to their new house is 1003 miles.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have total distance between from their old house to their new house:

d = 1003 miles

The car travel 23.6 miles per gallon

So the total amount of the fuel needed = 1003/23.6 = 42.5 gallons

42.5 gallons fuel will be required to travel 1003 miles

For the return trip (considering 23.6 miles per gallon) the same amount of fuel will be needed.

So the total fuel needed including roundtrip = 42.5×2 = 85 gallons

Thus, the total amount of the fuel needed for the trip is 42.5 gallons if the distance from their old house to their new house is 1003 miles.

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Answer:

d = 2

Step-by-step explanation:

3(d + 2) = 12 ( divide both sides by 3 )

d + 2 = 4 ( subtract 2 from both sides )

d = 2

Answer:

d=2

Step-by-step explanation:

3(d+2)=12

divide both side by 3

d+2 =4

substract 2 from both side

d=2

Factorising the polynomial 5x³ + 35x² + 6x + 42, the value of A is 6.

Factorising a polynomial simply means to decompose the polynomial into a product of two or more polynomials.

Therefore, let's factorise 5x³ + 35x² + 6x + 42 and find the value of A

(5x² + A)(x + B)

Therefore,

5x³ + 35x² + 6x + 42

5x³ + 6x  + 35x² + 42

x(5x² + 6) + 7(5x² + 6)

Therefore,

(5x² + 6)(x + 7)

Therefore, the value of A is 6

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Answer:

Step-by-step explanation:

(4x^4 - 1)(4x^4 + 1)

(2x^2 - 1)(2x^2 + 1)(4x^4 + 1)

Answer:

56

Step-by-step explanation:

If each child gets 2 sweets then we have to multiply the number of children by 2.

[tex]28 \times 2 = 56[/tex]

Answer:

30 sweets.

Add 28 and 2.

Answer:answer to 9:$1,025.00 answer to 10:$243.90 answer to 11:$1,025.15

Step-by-step explanation:

explanation to 9:First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year.

Solving our equation:

A = 500(1 + (0.07 × 15)) = 1025

A = $1,025.00

The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 7% per year for 15 years is $1,025.00.explanation to 10:First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year.

Solving our equation:

P = 500 / ( 1 + (0.07 × 15)) = 243.90243902439

P = $243.90

The principal investment required to get a total amount, principal plus interest, of $500.00 from simple interest at a rate of 7% per year for 15 years is $243.90. explantion to 11:First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year.

Solving our equation:

A = 500(1 + (0.07 × 15)) = 1025

A = $1,025.00

The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 7% per year for 15 years is $1,025.25.

The probability that if you sell 160 tickets for your flight, more passengers will show up than there are seats available is 0.02

The scenario meets the following requirements

The given parameters are:

n = 160

p = 0.91 i.e. 91%

x = 152

The distribution is a binomial distribution, and it is calculated using:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n -x}[/tex]

The probability is represented as:

P(x > 152) = P(153) + ..... P(160)

Using a technology tool, we have:

P(x ≤ 152) = 0.02

Probability values less than 0.25 are unlikely probabilities.

Because the probability value 0.02 is less than 0.25, then we can conclude that it is a wise business practice to oversell your flight in this manner.

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Answer:

7.1

Step-by-step explanation:

To round 7.09 to the nearest tenth, you must use the hundredths' place value of 7.09, which is 9 and equal or more than 5. Therefore, the tenths value of 7.09 increases by 1 to 7.1.

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

-2x   -2x

6=-x-4

+4    +4

10=-x

-1    -1

-10=x

[tex] \Large{\boxed{\sf x = 10}} [/tex]

[tex] \\ [/tex]

Given equation:

[tex] \sf 2(x + 3) = x - 4 [/tex]

[tex] \\ [/tex]

Expand the left side using the following distributive property:

A(B + C) = AB + AC

[tex] \\ [/tex]

Here, A = 2, B = x, and C = 3.

We get:

[tex] \sf 2(x) + 2(3) = x - 4 \\ \\ \sf 2x + 6 = x - 4 [/tex]

[tex] \\ [/tex]

Now, subtract 6 from both sides:

[tex] \sf 2x + 6 - 6 = x - 4 - 6 \\ \\ \sf 2x = x - 10 [/tex]

[tex] \\ [/tex]

Subtract x from both sides :

[tex] \sf 2x - x = x - 10 - x \\ \\ \\ \boxed{\boxed{\sf x = -10}} [/tex]

[tex] \\ \\ [/tex]

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Based on the graph given, the two points that need to be plotted are (9, 4) and (7, 3).

The points that are already plotted on the graph represent the results of the hours of television watched by children.

For instance, children of 6 years watched 2 hours of television. For that reason, the point where 6 (x axis) and 2 (y axis) meet on the graph is marked with an x.

The last two points would therefore be (9, 4) and (7, 3) to show that 9 year olds watch 4 hours of television and 7 year olds watch 3 hours of television.

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