The Knutson Corporation needs to save ​$15 million to retire​ a(n) ​$15 million mortgage that matures in 10 years. To retire this​ mortgage, the company plans to put a fixed amount into an account at the end of each year for 10 years. The Knutson Corporation expects to earn 10 percent annually on the money in this account. What equal annual contribution must the firm make to this account to accumulate the ​$15 million by the end of 10 ​years?

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06[/tex]

2:3=5

Ali=2÷5×£68000

Ali=£40800

Hassan=3÷5×£68000

Hassan=£27200

Answer:

C. ME ZH

B. IG LM

F. TH= NM

Step-by-step explanation:

The correct congruence statements are A, B, and C such that ∠N = ∠I, GH = LM, and ∠M= ∠H are true for similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

To determine which congruence statements are correct, we need to identify the corresponding sides and angles of the triangles.

The corresponding sides and angles are those that are in the same position in each triangle.

Using this information, we can check each statement:

A. ∠N = ∠I: This statement is true because ∠N and ∠I are corresponding angles in the congruent triangles.

B. GH = LM: This statement is true because GH and LM are corresponding sides in the congruent triangles.

C. ∠M= ∠H: This statement is true because ∠M and ∠H are corresponding angles in the congruent triangles.

D. IG = LM: This statement is false because IG and LM are not corresponding sides in the congruent triangles.

E. IH = NM: This statement is false because IH and NM are not corresponding sides in the congruent triangles.

F. ∠L = ∠I: This statement is false because ∠L and ∠I are not corresponding angles in the congruent triangles.

Therefore, the correct congruence statements are A, B, and C.

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Answer:

$560.33

Step-by-step explanation:

Hotel: 79.95*2*2=$319.8

Dinner: 182-50=$132

Breakfast:

Rental:

Hotel+dinner+breakfast+rental: 319.8+132+35.09+73.44=$560.33

A--->A'=(-2,6)

B--->B'=(7,3)

Solution:

Substitute the value of the variable into the expression, then simplify.

             Answer: -8

_________________________________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer:

2x/y = -8

Step-by-step explanation:

The values are,

→ x = 12

→ y = -3

Given expression,

→ 2x/y

Simplifying the expression,

→ 2x/y

→ (2 × 12)/(-3)

→ (24)/(-3)

→ -(24/3) = -8

Hence, the answer is -8.

Answer:

the answer is 3.456 × 108

The mass of the tow chain will be equal to 12.96 kg.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m.

The mass of 1 m chain = 2.16 kg

Mass of 6-meter chain = 2.16 x 6

Mass of 6-meter chain = 12.96 kg

Therefore, the mass of the tow chain will be equal to 12.96 kg.

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Answer:

me not soluesan match huiudresst

Number of bags of sand needed to cover the area of circular pool is 51 bags.

A circle is a round-shaped figure that has no corners or edges.

Now it is given that,

Diameter of pool, D = 14 feet

So, Area of pool = π(D/2)²

⇒  Area of pool = π(14/2)²

⇒  Area of pool = π(7)²

⇒  Area of pool = 153.86 square feet

Now given Area of 1 bag = 3 square feet

So, number of bags required = Area of pool / Area of 1 bag

⇒ number of bags required = 153.86/ 3

⇒ number of bags required = 51.28

⇒ number of bags required ≈ 51

Thus, Number of bags of sand needed to cover the area of circular pool is 51 bags.

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Answer:

[tex]a_{14}=\dfrac{52}{3}[/tex]

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

where:

Given terms of an arithmetic sequence:

Substitute the values into the general formula to create two equations:

[tex]\sf\underline{Equation \:1}\\\begin{aligned}a_4 & = 14\\\implies a+(4-1)d & = 14\\a + 3d & = 14\end{aligned}[/tex]

[tex]\sf\underline{Equation \:2}\\\begin{aligned}a_{10} & = 16\\\implies a+(10-1)d & = 16\\a + 9d & = 16\end{aligned}[/tex]

Subtract Equation 1 from Equation 2 to eliminate a:

[tex]\begin{array}{l r l}& a+9d & = 16\\- & a+3d & = 14\\\cline{2-3}&6d & = \:\:2\end{array}[/tex]

Solve for d:

[tex]\begin{aligned}\implies 6d & = 2\\\dfrac{6d}{6} & = \dfrac{2}{6}\\d & = \dfrac{1}{3} \end{aligned}[/tex]

Substitute the found value of d into one of the equations and solve for a:

[tex]\begin{aligned}a + 3d & = 14\\ \implies a+3 \left(\dfrac{1}{3}\right)&=14\\a+1&=14\\a+1-1&=14-1\\a&=13\end{aligned}[/tex]

Substitute the found values of a and d into the general formula to create an equation for the nth term of the arithmetic sequence.

[tex]\implies a_n=13+(n-1)\dfrac{1}{3}[/tex]

[tex]\implies a_n=13+\dfrac{1}{3}(n-1)[/tex]

To find the 14th term, simply substitute n = 14 into the equation:

[tex]\begin{aligned}a_n & = 13+\dfrac{1}{3}(n-1)\\\implies a_{14}& = 13+\dfrac{1}{3}(14-1)\\&=13+\dfrac{1}{3}(13)\\ & = \dfrac{39}{3}+\dfrac{13}{3}\\&=\dfrac{52}{3}\end{aligned}[/tex]

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Answer: 8 = g

Step-by-step explanation:

56 divided by 7 = g

8 = g

Answer:

  31/45 lb

Step-by-step explanation:

You want to know the weight of a 5/9 lb bag after 2/15 lb of fruit are added to it.

Fractions can be added when they have a common denominator. Here, the denominator will need to have factors of 3² = 9 and 3·5 = 15. It can be ...

   3·3·9 = 45

Using this denominator, the fractions are ...

  bag weight = 5/9 lb = 25/45 lb

  fruit weight = 2/15 lb = 6/45 lb

The total weight of the fruit and the bag is ...

  total weight = 25/45 lb + 6/45 lb = 31/45 lb

With the fruit, the bag weighs 31/45 pounds.

The interval where the function is negative is:

(-5 - √19 , -5 + √19)

That is the solution set of the inequality.

Here we have the following inequality:

x^2 + 10x + 5 < 0

So we want to find the values of x for which the quadratic function is negative.

To do so, we can solve:

x^2 + 10x + 5 = 0

The solutions are given by the quadratic formula:

x = (-10 ± √(10^2 - 4*6))/(2*1)

x = (-5 ± √19)

notice that the quadratic has positive leading coefficient, so it open upwards, then the function is below zero between the two roots, on the interval:

-5 - √19 < x < -5 + √19

Then the correct option is D.

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Answer:

d

Step-by-step explanation:

Let the number be 'x'.

First find x and then find 130% of x.

30% of  x = 25

   [tex]\sf \dfrac{30}{100}*x = 25[/tex]

            [tex]\sf x = 25*\dfrac{100}{30}\\\\ x = \dfrac{250}{3}\\\\[/tex]

Now, find 130% of x

   130% of x = [tex]\sf \dfrac{130}{100}*\dfrac{250}{3}\\\\[/tex]

                    [tex]\sf = \dfrac{325}{3}\\\\ = 108.3[/tex]

Answer:

5y + 3 is the sum of the three ages

Step-by-step explanation:

Let y=Mark, d=Daniel j=Jack, and s=The sum

Mark is y years old. In five years jack will be twice as old as Mark

j + 5 = 2(y+5)

j + 5 = 2y + 10

j = 2y + 10 - 5

j = 2y + 5

Daniel will be two years younger than jack is now

d + 5 = j - 2

d = j - 2 - 5

d = j - 7

Replace j with (2y+5)

d = (2y+5) - 7

d = 2y - 2

Expression in terms of y for the sum of the 3 ages now

s = y + j + d

replace j and d with expressions we came up with above

s = y + (2y+5) + (2y-2)

s = y + 4y + 3

s = 5y + 3 is the sum of the three ages

From the given table, we can see that the value of f(2) is 4

The input values in a function table are the dependent variables while the output values in a function table are the dependent variables.

Let the function of the table be represented as y = f(x), this shows that the variable x is independent while f(x) is dependent.

In order to determine the value of f(2), we need the output value, when the input value is 2. From the given table, we can see that the value of f(2) is 4

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Answer:

x<0; x>0

Step-by-step explanation:

Basically, anything but zero, depending on what a is.

Answer:

x = ± [tex]\sqrt{a}[/tex]

Step-by-step explanation:

x² = a ( take square root of both sides )

x = ± [tex]\sqrt{a}[/tex]

Answer: 24.33 units

Step-by-step explanation: If we appropriately measure the distance between the points we can depict a parallelogram with 2 sides measuring 6.083 units and 2 others measuring 4 units. We multiply 4 x 6.083 and get the area: 24.33 units

Answer: 24

Step-by-step explanation: As the formula to solve this equation is A= 1/2 | [(x1y2) - (x2y1)] + [(x2y3) - (x3y2)] + [(x3y4) - (x4y3)] + [(x4y1) - (x1y4)]

Which would be (with the numbers)

[(-3 x 4) - 1 x 4)] + [(1 x -2) - (0 x 4)] + [(10 x 2) - (-4 x -2)] + [(-4 x 4) - (-3 x -2)]

which lowers down too

(-12 - 4) + (-2 - 0) + (0 - -8) + (-16 - 6)

Then that gets us (absolute values) of

|-16| + |-2| + |8| + |-22|

using absolute values that gets us to

16 + 2 + 8 + 22

Which is equal to 48.

Don't forget to divide by 2 because we need half of it as it says in the beginning of the formula (A = 1/2)

So that gives us the answer of 24.

Hope this helped :)

Also, this could help by labeling each coordinate as a (X, Y) Number

[-3(x1) , 4(y1)}  (you could write the x and y part above it)

And then you go down the list and label each as either x1 , x2 , x3 , x4 (for the left side of comma) and then y1 , y2, y3 , y4 (for the right side of the comma)

the correct option is the second one:

"No, because she should have rounded 63 down to 60"

In that case, her estimation would have been 24.

First, we need to understand how rounding works. When we want to round to a given digit, we need to look at the digit that its located at its right.

In this case, LaVonne estimated 38% of 63, and the roundings that she did are:

38% up to 40%. This is correct, because the second digit is 8, so we round up here.

63 to 70. This is incorrect, because the second digit is 3 (smaller than 4) then here she should have round down to 60 instead of up to 70.

So what she should have gotten is:

0.4*60 = 24

That is a better estimation, were the actual value of the 38% of 63 is:

0.38*63 = 23.94

You can see that when rounding down, the estimation is much closer to the actual value.

So, the correct option is the second one:

"No, because she should have rounded 63 down to 60"

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a) The minimum 75% of commuters in Boston has a commute time within 2 standard deviation of the mean.

b) The minimum 60.93% of commuters in Boston has a commute time within 1.6 standard deviation of the mean.

c) Commute times within 1.4 standard deviation are lie between 15.48 to 38.72.

Explanation:

Given that

To find

So, according to the question

We know that

                            = (1- [tex]\frac{1}{k^2}[/tex] )×100

a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?

                            = (1- [tex]\frac{1}{2^2}[/tex] )×100

                            = (1- [tex]\frac{1}{4}[/tex] )×100

                            = ( [tex]\frac{4-1}{4}[/tex] )×100

                            =  [tex]\frac{3}{4}[/tex] ×100

                            = 3 × 25

                            = 75%

b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?

                            = (1- [tex]\frac{1}{1.6^2}[/tex] )×100

                            = (1- [tex]\frac{1}{2.56}[/tex] )×100

                            = ( [tex]\frac{2.56-1}{2.56}[/tex] )×100

                            =  [tex]\frac{1.56}{2.56}[/tex] ×100

                            = 1.56 × 39.06

                           = 60.93%

c) What are the commute times within 1.4 standard deviation?

     commute times  = 27.1 ± (1.4×8.3)

                                 = 27.1 ± 11.62

      for + sign,

                                 = 27.1 + 11.62

                                 = 38.72

      for - sign,

                                 = 27.1 - 11.62

                                 = 15.48

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Answer:

[tex]\frac{-10}{7}[/tex]

Step-by-step explanation:

Use the formula

m= [tex]\frac{y2-y1}{x2-x1}[/tex]

another way to say this is Δy divided by Δx

Δ means "change in"

m = slope

The y2 value is -7

The y1 value is 3

The x2 value is 5

The x1 value is -2

Plug those values in the formula

m = [tex]\frac{(-7)-3}{5-(-2)}[/tex]

Simplify

m = [tex]\frac{-10}{7}[/tex]

The slope is [tex]\frac{-10}{7}[/tex]

The distance covered by the falling freely body from rest will be 48 feet.

The study of motion without considering the mass and the cause of the motion.

When a body falls freely from rest, the distance it travels straight changes as the square of the time (air resistance excluded). If something is dropped 192 feet from the summit of a tower, it lands on the ground in 8 seconds.

We know that the acceleration is due to gravity (g = 32 ft/s²).

d ∝ t²

d/t² = constant

Then the distance covered by the falling freely body from rest will be given as,

d / 4² = 192 / 8²

d / 16 = 192 / 64

d = 16 x 192 / 64

d = 48 feet

The distance covered by the falling freely body from rest will be 48 feet.

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Answer:

x=18

Step-by-step explanation:

m(<BCD) = 2x alternative Z

c=2x d=8x

m(<CD) =180 U

180/10x

x=18