express the standard form53630000​

Answer:

[tex]x = 97[/tex]

Step-by-step explanation:

Given

[tex]t = 20[/tex] --- time (years)

[tex]A =1000[/tex] --- amount

[tex]r = 10\%[/tex] --- rate of interest

Required

The last 10 payments (x)

First, calculate the end of year 1 payment

[tex]y_1(end) = 10\% * 1000 * 150\%[/tex]

[tex]y_1(end) = 150[/tex]

Amount at end of year 1

[tex]A_1=A - y_1(end) - r * A[/tex]

[tex]A_1=1000 - (150 - 10\% * 1000)[/tex]

[tex]A_1 =1000 - (150- 100)[/tex]

[tex]A_1 =950[/tex]

Rewrite as:

[tex]A_1 = 0.95 * 1000^1[/tex]

Next, calculate the end of year 1 payment

[tex]y_2(end) = 10\% * 950 * 150\%[/tex]

[tex]y_2(end) = 142.5[/tex]

Amount at end of year 2

[tex]A_2=A_1 - (y_2(end) - r * A_1)[/tex]

[tex]A_2=950 - (142.5 - 10\%*950)[/tex]

[tex]A_2 = 902.5[/tex]

Rewrite as:

[tex]A_2 = 0.95 * 1000^2[/tex]

We have been able to create a pattern:

[tex]A_1 = 1000 * 0.95^1 = 950[/tex]

[tex]A_2 = 1000 * 0.95^2 = 902.5[/tex]

So, the payment till the end of the 10th year is:

[tex]A_{10} = 1000*0.95^{10}[/tex]

[tex]A_{10} = 598.74[/tex]

To calculate X (the last 10 payments), we make use of the following geometric series:

[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + r)^n[/tex]

[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 10\%)^n[/tex]

[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 0.10)^n[/tex]

[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

The amount to be paid is:

[tex]Amount = A_{10}*(1 + r)^{10}[/tex] --- i.e. amount at the end of the 10th year * rate of 10 years

[tex]Amount = 1000 * 0.95^{10} * (1+r)^{10}[/tex]

So, we have:

[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+r)^{10}[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+10\%)^{10}[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+0.10)^{10}[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1.10)^{10}[/tex]

The geometric sum can be rewritten using the following formula:

[tex]S_n = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]S_n =\frac{a(r^n - 1)}{r -1}[/tex]

In this case:

[tex]a = x[/tex]

[tex]r = 1.10[/tex]

[tex]n =10[/tex]

So, we have:

[tex]\frac{x(r^{10} - 1)}{r -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]\frac{x((1.10)^{10} - 1)}{1.10 -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]\frac{x((1.10)^{10} - 1)}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]x * \frac{1.10^{10} - 1}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

So, the equation becomes:

[tex]x * \frac{1.10^{10} - 1}{0.10} = 1000 * 0.95^{10} * (1.10)^{10}[/tex]

Solve for x

[tex]x = \frac{1000 * 0.95^{10} * 1.10^{10} * 0.10}{1.10^{10} - 1}[/tex]

[tex]x = 97.44[/tex]

Approximate

[tex]x = 97[/tex]

Answer:

The probability mass function is:

[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]

Step-by-step explanation:

The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability mass of the hypergeometric probability distribution is given by:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

22 + 25 = 47 jurors, so [tex]N = 47[/tex]

22 are women, which means that [tex]k = 22[/tex]

Jury of 12, which means that [tex]n = 12[/tex].

Thus

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]

Which is the probability mass function.

Answer:

Base

Step-by-step explanation:

Every solid shape has to have a base that they sit/stand on. Because the base  is the bottom of the shape and lies on the table. Hence, answering your question.

Hope this helps!

This one was difficult but if your work through it, you will get it.

Keep trying!

Answer:

16 orang

Step-by-step explanation:

jumlah siswa pria = 45-25 = 20 orang

jumlah siswa pria yang berkacamata =

7-3 = 4 orang.

maka jumlah siswa pria yang tidak berkacamata =

20-4 = 16 orang

semoga membantu

Answer:

x=161

Step-by-step explanation:

Answer:

Rectangle

Step-by-step explanation:

Given the points :

(0, 8), (5,2), (0, 2), and (5, 8).

Based on the vertices given :

If we mark the points on a graph and then join the points, we'll Obtain a rectangle ; this is because the length and with are not equal, with a length of 6 unit and width of 5 unit

Attached below is a rough sketch if the plot created in a notebook.

Answer:

21; the age of the teacher

Step-by-step explanation:

15+x/2=18

Estimate - I estimated in the 20's because it only averaged up a little bit

Started with 23 and kept going until i got to my answer

21

15+21/2

36/2

18

Please mark brainliest :)

Answer:

The answer is 939

Step-by-step explanation:

If you divide 939 by 9 it equals 104 R3.

If you divided 939 by 2 it equals 469 R1

And if you divide 939 by 5 it equals 187 R4

  Hope this helps!

Answer

19.013.153,42629466 giây

Step-by-step explanati

van toc ánh sán  =299.792.458 m/s

s= v*t

t=s/v

t= 5.699.999.999.999.999/299.792.458= 19.013.153,42629466 giây

The formula for perimeter is 2(Length) + 2(width)

Fill in the known information:

22 = 2(6.5)+ 2(width)

Simplify:

22 = 13 + 2(width)

Subtract 13 from both sides:

9 = 2(width)

Divide both sides by 2:

Width = 4.5m

Answer:

Number of 10 cents = 18

Number of  20 cents = 10

Step-by-step explanation:

Let number of 10 cents be = x

Let number 20 cents be = y

Total number of coins = x + y = 28  -------- ( 1 )

Total amount in the box = 0.10 x + 0.20y = 3.80 ---------- ( 2 )

Solve the equations to find x and y

( 1 ) => x + y = 28

         x = 28 - y

Substitute x in ( 2 )

( 2 ) => 0.10(28 - y) + 0.20y = 3.80

          2.80 - 0.10y + 0.20y = 3.80

            0.10 y = 3.80 - 2.80

            0.10 y = 1.00

                [tex]y = \frac{1}{0.10} = 10[/tex]

                y = 10

Substitute y in ( 1 ) => x + y = 28

                                x + 10 = 28

                                x = 28 - 10

                                x = 18

Answer:

C(min)  =  277.95 $

Container dimensions:

x = 2.822 m

y = 1.411 m

h = 3.52 m

Step-by-step explanation:

Let´s call x  and  y the sides of the rectangular base.

The surface area for  a rectangular container is:

S = Area of the base (A₁) +  2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)

Area of the base is :

A₁ =  x*y       we assume, according to problem statement that

x  =  2*y      y  = x/2

A₁  =  x²/2

Area lateral on side x

A₂  = x*h           ( h  is the height of the box )

Area lateral on side y

A₃ = y*h        ( h  is the height of the box )

s = x²/2  + 2*x*h + 2*y*h

Cost  =  Cost of the base + cost of area lateral on x + cost of area lateral on y

C = 10*x²/2  + 8* 2*x*h  + 8*2*y*h

C as function of x is:

The volume of the box is:

V(b) = 14 m³  = (x²/2)*h       28 = x²h      h = 28/x²

C(x) = 10*x²/2  + 16*x*28/x² + 16*(x/2)*28/x²

C(x)  =  5*x²  +  448/x  + 224/x

Taking derivatives on both sides of the equation we get:

C´(x)  =  10*x  -  448/x² - 224/x²

C´(x)  =  0             10x  -  448/x² - 224/x² = 0     ( 10*x³ - 448 - 224 )/x² = 0

10*x³ - 448 - 224 = 0       10*x³ = 224

x³  =22.4

x = ∛ 22.4

x = 2.822 m

y = x/2  =  1.411 m

h = 28/x²  =  28 /7.96

h =  3.52 m

To find out if the container of such dimension is the cheapest container we look to the second derivative of C

C´´(x) = 10 + 224*2*x/x⁴

C´´(x)  =  10 + 448/x³    is positive then C has a minimum for x = 2.82

And the cost of the container is:

C = 10*(x²/2) +  16*x*h + 16*y*h

C = 39.82 +  158.75  + 79.38

C =  277.95 $

Answer:

19 boys

Step-by-step explanation:

38 kids on the bus

1/2 are girls, that means 1/2 are boys

1/2 * 38 = 19

There are 19 girls and 19 boys

9514 1404 393

Answer:

  x = -7, 5

Step-by-step explanation:

The equation is written as a product equal to zero. The "zero product rule" tells us that a product is zero if and only if one or more factors are zero. Each factor will be zero when x takes on a value equal to the opposite of the constant in that factor.

  x -5 = 0   ⇒   x = 5

  x +7 = 0   ⇒   x = -7

The solutions to the equation are x = -7, 5.

=======================================================

Explanation:

The triangular face has area of base*height/2 = 8*2/2 = 16/2 = 8 square feet.

Multiply this with the depth of the prism to get 8*12 = 96 cubic feet

----------

For any prism, the volume formula is

V = (area of base)*(depth of prism)

The term "depth" can be replaced with "height" and it's the same idea.

In this problem, we have a triangular prism because the parallel sides are triangles.

Answer:

The answer would be [tex]-a(-a)^{n-1}[/tex].

Step-by-step explanation:

We can simply substitute the terms into this equation. Checking the 1st term, [tex]-a(-a)^{1-1} = -a(-a)^{0} = -a(1) = -a[/tex]. Moving on to the second term, we see [tex]-a(-a)^{2-1} = -a(-a)^{1} = -a(-a) = a^{2}[/tex]. And so on and so forth. We can see how the answer fluctuates between negative and positive, while gaining one more exponent every term, which fits with the sequence given. Therefore, the answer would be [tex]-a(-a)^{n-1}[/tex].

Hope this helped!

Answer:

ok so this is what we have to do

250*0.95*0.95*0.95

ok so

214.34375

so about 214.3

Hope This Helps!!!

Answer:

b = -4 and 0

Step-by-step explanation:

Using the distance formula

D = √(x2-x1)² + (y2-y1)²

√8 = √(b-2)² + (3-1)²

√8 = √(b-2)² + 2²

Square both sides

8 = (b-2)² + 2²

8 = (b-2)² + 4

8 - 4 = (b-2)²

4 = (b-2)²

Square root both sides

±√4 = b- 2

±2 = b - 2

b = -2 - 2 and b = -2 + 2

b = -4 and 0

This gives the values of b

Answer:

x = 2 degree and unknown angle = 31 degree

Step-by-step explanation:

149 + 13x + 5 =180 degree (being linear pair)

154 + 13x = 180

13x = 180 - 154

x = 26/13

x = 2 degree

unknown angle = 13x + 5

=13*2 + 5

=26 + 5

=31 degree

The value of the variable x is 2°. Then the value of the unknown angle is 31°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Both angles are supplementary angles. Then the equation is given as,

13x + 5° + 149° = 180°

13x + 154° = 180°

13x = 180° - 154°

13x = 26°

x = 26° / 13

x = 2°

The value of the variable x is 2°. Then the value of the unknown angle is given as,

13x + 5° = 13(2°) + 5°

13x + 5° = 26° + 5

13x + 5° = 31°

The value of the variable x is 2°. Then the value of the unknown angle is 31°.

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Answer:

His practice is 55 minutes long

you can look at it this way

from 5:20pm to 6:pm, is only 40 minutes

then from 6:00pm to 6:15pm is only 15 minutes

40 + 15 = 55

Answer:

x=2

Step-by-step explanation:

the sides are proportional due the angles being equal

since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference

so 4÷2=x

x=2

Answer:

The solution of the graph is at (-3,-8).

Step-by-step explanation:

The given equations are :

-4x+3y=-12

and

-2x+3y=-18

These are the system of equations in two variables.

The graphs for the equations are :

The solution of the graph is at (-3,-8).

Answer:

x = 1.7

Step-by-step explanation:

Answer:

d = 4.5 cm

A = 1/4 (p x d²)

= 1/4 (3.14 x d x d)

= 1/4 (3.14 x 4.5 cm x 4.5 cm)

= 15.9 cm2

The area of the plate nearest square centimeters is 12cm².

A scalene triangle has three different sides and corresponding to that three different interior angles.

According to the given question we have  triangle with sides  4.5cm,6cm and 7.5cm.

We know for a scalene triangle given 3 sides.

area(A) = [tex]\sqrt{s(s-a)(s-b)(s-c)[/tex].

Where S is semi perimeter and a,b,c are the three sides.

= (a+b+c)/2.

= (4.5+6+7.5)/2 cm.

= 18/2 cm.

= 9 cm.

∴ The area of the triangle is

= [tex]\sqrt{9(9-4.5)(9-6)(9-7.5)[/tex]cm².

= [tex]\sqrt{9(4.5)(3)(1.5)}[/tex] cm².

= [tex]\sqrt{182.5}[/tex] cm² this is in between 13 square and 14 square approx 13.5 cm².

Now it has three small circles of radius of 4 mm or 0.4 cm.

We know area of a circle is πr² and area of 3 circles having same radius is 3(πr²) cm².

= 3{π(0.4)²}

= 3{3.14(0.16)} cm².

= 3(0.5024) cm².

= 1.5072 cm².

Now to obtain the area of the scalene triangle with those three holes of 0.4 cm we have subtract the area of the three circles from the triangle which is

= (13.5 - 1.5) cm².

= 12 cm².

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9514 1404 393

Answer:

  h = 7

Step-by-step explanation:

Perhaps you want the solution to ...

  1/(h -5) +2/(h +5) = 16/(h^2 -25)

Parentheses are required around denominators that have math operations.

Multiply by (h^2-25) and solve the linear equation.

  [tex]\displaystyle\frac{1}{h-5}+\frac{2}{h+5}=\frac{16}{h^2-25}\qquad\text{given}\\\\(h+5)+2(h-5)=16\qquad\text{multiply by $h^2-25$}\\\\3h-5=16\qquad\text{simplify}\\\\3h=21\qquad\text{add 5}\\\\\boxed{h=7}\qquad\text{divide by 3}[/tex]

Answer:

$1

max rev = 80(4) = $320

Step-by-step explanation:

let us do this in pennies  

R = (100 - x/5)(300 + x)

d/dr = -2x - 200

               5

(-2x-200)/5 = 0  

-2x = 200

x = 100

An amount of $320 is the admission price that should be charged in order to maximize revenue.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, Let x represent the revenue function.

Hence, We can formulate;

x = (3 + 0.1(x))(100 - 2x)

x = 300 - 6x + 10x - 0.2x²

x = 300 + 4x- 0.2x²

x' = 4 - 0.4x

Generally, a maximum revenue occurs when x' = 0:

x' = 4 - 0.4x = 0

4 = 0.4x

x = 4 / 0.4

x = 10

Hence, The admission price,

= 3 + 0.1x

= 3 + 0.1 x 10

= 3 + 1

= $4

Thus, The Maximum revenue is,

= $4 (100 - (10 x 2)

= $4 (100 - 20)

= $4 x 80

= $320

In conclusion, the amount of $320 is the admission price that should be charged in order to maximize revenue.

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