Bonds with a face value of $744000 and a quoted price of 98.5 have a selling price of

Step (1)

We know that the sum of all the terms in an infinite geometric sequence finding from following equation whenever |q| < 1 .

q = magnitude

[tex]s( \infty ) = \frac{t(1)}{1 - q} \\ [/tex]

So :

[tex]s( \infty ) = \frac{t(1)}{1 - q} \\ [/tex]

[tex]81 = \frac{t(1)}{1 - q} \\ [/tex]

[tex]81(1 - q) = t(1)[/tex]

Remember it I'll use it again.

_________________________________

Step (2)

We know that the sum of the n first terms of a geometric sequence finding from following equation.

[tex]s(n) = \frac{t(1) \times (1 - {q})^{n} }{1 - q} \\ [/tex]

_________________________________

Sum of all terms starting from the third is 9.

So :

[tex]s(2) + s(3 - \infty ) = 81[/tex]

[tex]s(2) + 9 = 81[/tex]

Sides minus 9

[tex]s(2) = 81 - 9[/tex]

[tex]s(2) = 72[/tex]

So :

[tex]t(1) + t(2) = 72[/tex]

[tex]t(1) + t(1) \times q = 72[/tex]

Factoring t(1)

[tex]t(1) \times (1 + q) = 72[/tex]

We have found t(1) = 81 ( 1 - q ) in step (1).

So :

[tex]81(1 - q)(1 + q) = 72[/tex]

Divided sides by 81

[tex](1 - q)(1 + q) = \frac{72}{81} \\ [/tex]

[tex](1 - q)( 1 + q) = \frac{8}{9} \\ [/tex]

[tex]1 - {q}^{2} = \frac{8}{9} \\ [/tex]

Subtract sides minus -1

[tex] - {q}^{2} = \frac{8}{9} - 1 \\ [/tex]

[tex] - {q}^{2} = \frac{8}{9} - \frac{9}{9} \\ [/tex]

[tex] - {q}^{2} = - \frac{1}{9} \\ [/tex]

Negatives simplifies

[tex] {q}^{2} = \frac{1}{9} \\ [/tex]

Radical sides

[tex]q = + \frac{1}{3} \\ q = - \frac{1}{3} [/tex]

_________________________________

Step (4)

If q = 1/3 :

[tex]81(1 - q) = t(1)[/tex]

[tex]81(1 - \frac{1}{3}) = t(1) \\ [/tex]

[tex]81( \frac{2}{3}) = t(1) \\ [/tex]

[tex]t(1) = 27 \times 2[/tex]

[tex]t(1) = 54[/tex]

So :

[tex]t(2) = t(1) \times q[/tex]

[tex]t(2) = 54 \times \frac{1}{3} \\ [/tex]

[tex]t(2) = 18[/tex]

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

If q = - 1/3 :

[tex]81(1 - q) = t(1)[/tex]

[tex]81(1 - ( - \frac{1}{3})) = t(1) \\ [/tex]

[tex]81(1 + \frac{1}{3}) = t(1) \\ [/tex]

[tex]81( \frac{4}{3}) = t(1) \\ [/tex]

[tex]t(1) = 27 \times 4[/tex]

[tex]t(1) = 108[/tex]

So :

[tex]t(2) = t(1) \times q[/tex]

[tex]t(2) = 108 \times - \frac{1}{3} \\ [/tex]

[tex]t(2) = - 36[/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Step-by-step explanation:

use -4y for x in the second equation

-4 y + 5 y = 2

so

y = 2

then x = -4(2) = -8

(-8 , 2)

Hope it helps you

:DD

Answer:

bjc hnfj yn yt NV ubf. giving! y NV,

Answer:

x= 45°

x+10=55°

2x-10=80°

Step-by-step explanation:

According to ASP,

x+x+10+2x-10=180°

4x=180°

Therefore, x=180/4

                    =45°

x+10=45+10

        =55°

2x-10=90-10

         =80°

Mark me Brainliest!!!

Answer:

-12

Step-by-step explanation:

y = mx + b

the one being multiplied  to x is the slope

Answer:

slope: -12

y-intercept: 7

Step-by-step explanation:

The slope-intercept form of the equation of a line is

y = mx + b

where m = slope, and b = y-intercept.

Your equation is

y = -12x + 7

Your equation is already in the slope-intercept form.

m = -12

b = 7

slope: -12

y-intercept: 7

Answer:

40

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent, so the other base angle is also 70 degrees.

This means that the interior angles are 70, 70, and x

Since the sum of the measures of the angles of a triangle is 180 degrees,

70+70+x=180

140+x=180

x=40

Answer:

Step-by-step explanation:

[tex] {x}^{o} + {115}^{o} + {95}^{o} + {70}^{o} = {360}^{o} \\ [/tex]

(The measure of the interior angle of a square is 90°)

[tex]{x}^{o} + {115}^{o} + {95}^{o} + {70}^{o} = {360}^{o} \\ {x}^{o} + {280}^{o} = {360}^{o} \\ {x}^{o} = {360}^{o} - {280}^{o} \\ {x}^{o} = {80}^{o} \\ [/tex]

The graph of both plots would be the one graph in option C.

Combined area = 2(area of one rectangular plot) = 720 sq. yds.

Area of a rectangular shape = length × width

From the graph given, 1 unit represents 20 yards. Therefore:

Therefore, the graph of both plots would be the one given in option C.

The plot is rectangular in shape having 60 yards × 60 yards. Therefore:

Area of 1 plot = length × width = 60 × 60 = 360 square yards.

Combined area = 2(area of one rectangular plot) = 2(360) = 720 sq. yds.

Learn more about area of rectangular shapes on:

https://brainly.com/question/6843877

Answer:

Answer:

125 and 55

Step-by-step explanation:

180=8x+20

160=8x

x=20

6(20)+5                            2(20)+15=

120+5=125 degrees           40+15=55 degrees

answer:

a is not true but C and b is true

Answer:

36π

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

2x - 3(0) = - 12

2x  - 0 = - 12

2x = - 12 ( divide both sides by 2 )

x = - 6 ← x- intercept

To find the y- intercept let x = 0 in the equation and solve for y

2(0) - 3y = - 12

0 - 3y = - 12

- 3y = - 12 ( divide both sides by - 3 )

y = 4 ← y- intercept

Answer:

7L

Step-by-step explanation:

8-1

Minus 8-1=7

I hope it is the right answer

[tex]f(x) = \sqrt{7 + x} [/tex]

[tex]7 + x \geqslant 0[/tex]

[tex]x \geqslant - 7[/tex]

[tex]domain \: - 7 \leqslant x \leqslant \infty [/tex]

[tex]range \: \: 0 \leqslant f(x) \leqslant \infty [/tex]

Answer:

1:4

Step-by-step explanation:

To represent 14:56 as a simplified ratio, we need to reduce it by finding the GCF (greatest common factor) and dividing it by both terms.

The GCF of 14 & 56 is 14.

14 / 14 = 1

56 / 14 = 4

Thus we are left with our new simplified ratio, 1:4.

Answer:

65

Step-by-step explanation:

1*5*2 + -1*0*-3 + 3*2*1 - -3*5*3 - 1*0*1 - 2*2*-1 =

10 + 0 + 6 + 45 - 0 + 4 =

65

see attached picture, that shows the recipe to do the other one.

To show that the equations are the same, we need to rewrite one of the equations as an equivalent equation of the second

Damita's claim is true

The equations are given as:

0.8x - 0.8 = 1.6

4/5 ( x - 1 ) = 1 (3/5)

We need to rewrite one of the equations, as follows:

4/5 ( x - 1 ) = 1 (3/5)

Express as decimal

0.8 ( x - 1 ) = 1 + 0.6

Open the brackets

0.8x - 0.8 = 1.6

Now we have:

0.8x - 0.8 = 1.6 (the first equation) and 0.8x - 0.8 = 1.6 (the equivalent of the second equation)

The above shows that both equations are the same

Read more about equivalent equations at:

https://brainly.com/question/2972832

The constant terms are 12, -16, -10.

Look at the attached image for an example of how to identify constants!

Hope that helped!

Answer:

[tex]\huge\boxed{\sf{12, -16, -10}}[/tex]

Step-by-step explanation:

Hello.

Please remember that a constant is a number without any variables next to it.

Let's search for constants in this expression.

The first term is 12. It has no variables, thus, it's a constant.

The second term is 15x. It does have a variable, thus, it's not a constant.

The third term is -16. It has no variables, thus, it's also a constant.

The 4th term is -4x (not a constant)

The last term is -10 (a constant)

I hope it helps & have an outstanding day.

[tex]\boxed{imperturbability}[/tex]

Answer:

[tex]y=\frac{6}{1} x[/tex]

Step-by-step explanation:

slope is [tex]\frac{6}{1}[/tex]

y=mx+b

replace m with slope

[tex]y=\frac{6}{1} x[/tex]

Slope:-

Equation in point slope form

Answer:

43/9

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

9 × 4 = 36

Step 2

Add the answer from Step 1 to the numerator

36 + 7 = 43

Step 3

Write answer from Step 2 over the denominator

43/9

=439

Answer:

a

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

Here  k is the random number of number of pairs of shoes that will be returned for refund, which can be  k = 0,1 ,2,3,4 ..., 120

b

The mean is   [tex]E(K) =  np =  13.2[/tex]  

The  standard deviation is  [tex]\sigma =  3.43[/tex]

c

The mean is  [tex]E(C) =   E(105 K) =  1386[/tex]

The standard deviation is   [tex]\sigma  =  381.48 [/tex]  

Step-by-step explanation:

From the question we are told that

   The  cost to dealer for each refund is  [tex]C =  \$105[/tex]

   The  probability  that a shoe will refunded is  [tex]P(x) =  0.11[/tex]

   The number of shoes purchased is  n  =  120 pairs

Generally the probability distribution of the number of pairs of shoes that will be returned for refunds is

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

Here  k is the random number of number of pairs of shoes that will be returned for refund, which can be  k = 0,1 ,2,3,4 ..., 120

Generally the mean is mathematically represented as

     [tex]E(K) =  np =  120 * 0.11[/tex]

=>    [tex]E(K) =  np =  13.2[/tex]  

Generally the  standard deviation is mathematically represented as

     [tex]\sigma  =  \sqrt{ n*  p  (1-p)}[/tex]

=>    [tex]\sigma  =  \sqrt{ 120* 0.11  (1-0.11)}[/tex]

=>    [tex]\sigma =  3.43[/tex]

Generally the total refund cost is mathematically represented as

     [tex]C =  105 K[/tex]

Here K denotes the number of shoes returned

Generally the mean of the total refund cost is mathematically represented as

           [tex]E(C) =   E(105 K) =  105 E(K)[/tex]

=>         [tex]E(C) =   E(105 K) =  105 * 13.2[/tex]

=>         [tex]E(C) =   E(105 K) =  1386[/tex]

Generally the variance of the total refund cost is mathematically represented as

       [tex]Var(K) =  105^2 *  E(K)[/tex]

=>     [tex]Var(K) =  105^2 *  13.2[/tex]

=>    [tex]Var(K) =  145530[/tex]  

=>      [tex]\sigma =  \sqrt{145530 }[/tex]

=>    [tex]\sigma  =  381.48 [/tex]  

Answer:

y(x) = c_1 e^(-1/(2 x^2))

Step-by-step explanation:

Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:

Solve for (dy(x))/(dx):

(dy(x))/(dx) = y(x)/x^3

Divide both sides by y(x):

((dy(x))/(dx))/y(x) = 1/x^3

Integrate both sides with respect to x:

integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx

Evaluate the integrals:

log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.

Solve for y(x):

y(x) = e^(-1/(2 x^2) + c_1)

Simplify the arbitrary constants:

Answer:  y(x) = c_1 e^(-1/(2 x^2))

Answer:

6 quarts because 2/3 of 9 is 6 :)

The container holds 9 quarts and she wants only 2/3 of the way. 2/3 of the way is the same thing as 2/3 of 9.

  [tex]\frac{2}{3} *9=6[/tex]

Thus Lauren needs to fill 6 quarts of the 9 quarts to get to the 2/3 of the way.

Hope that helps!

Answer:

I think it is x is equals to 5/6.

Step-by-step explanation:

5/x = 25/6

x/5 * 5/x = 25/6 * x/5

x = 5/6

▪ Answer:

x = 5/6

▪ Step-by-step explanation:

Hi there !

5/x = 25/6

x = 5×6/25

x = 30/25

simplist 5

x = 6/5

Good luck !

common denominator = 7x11 = 77

5/7 = (5x11) / (7x11) = 55/77

and

8/11 = (8x7) / (11x7) = 56/77

5/7 and 8/11 can be rewritten as 55/77 and 56/77, respectively, so that they have a common denominator of 77.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To rewrite 5/7 and 8/11 with a common denominator:

We can find the least common multiple (LCM) of the denominators 7 and 11, which is 77.

Then, we can multiply each fraction by the appropriate form of 1 so that the denominators are equal to 77.

Here are the steps:

5/7 = (5/7) x (11/11) = 55/77 (multiply the numerator and denominator of the first fraction by 11)

8/11 = (8/11) x (7/7) = 56/77 (multiply the numerator and denominator of the second fraction by 7)

Therefore, 55/77 and 56/77 are the required fractions.

To learn more about fractions;

https://brainly.com/question/10354322

#SPJ2

You circled b and i would agree. Because Francesca is doing a living room, it would natuarly start at $25. So it cant be c. And Because x represents the walls, the graph would be a possitive corrolotion so i would say it is b

The graph b shows the adequate information for painting cost of living room. Option b is correct.

Graph that shows adequate information for cost of painting for living room to be determine.

The graph is a demonstration of curves  which gives the relationship between x and y axis.

Here, equation for the painting of living room can be given as y = 1x+25.
This relation ship clearly seen in graph b.

Thus, the graph b shows the adequate information for painting cost of living room.

Learn more about graphs here:

brainly.com/question/16608196

#SPJ2

Answer:

the slope is −12

Step-by-step explanation:

The equation of a perpendicular line to y=−x2+5 y = - x 2 + 5 must have a slope that is the negative reciprocal of the original slope.

-1/2

That would be the answer