actuarial math, see attached

A set-to-set function f is a relation that assigns one element of the set A to each element of the other set B. The set A is the domain of the function (also called the set of inputs) and the set B contains the range (also called the set of outputs).

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

1. Not an exponential function:

We have the following equation:

[tex]y = 100 (1 - 12)^{t}[/tex]

We can write the equation as:

[tex]y = 100 (-11)^{t}[/tex]

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

Therefore: a must be more than 01.

In this problem, a = -11, therefore this is not an exponential function.

2. Growth.:

The function:

[tex]y= 0.1(1.25)^{t}[/tex]

The above equation is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

Therefore, k = 0.1 and  a = 1.25 . So, a is greater than 1.

3. Growth:

The function:

[tex]y = {(1 - 0.03)12}^2t[/tex]

The above equation can be written as:

[tex]y = 11.64^{2t}[/tex]

which  is an exponential function because is a function of the form

[tex]f(t) = a^{bt}[/tex]

where, a > 0 and b is constant.

So, a = 11.64 and b = 4 . Since a is greater than 1.

4. Decay:

The function:

[tex]y = 426(0.98)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

So, k = 426 and a = 0.98. Since, a is less than 1.  

5. Growth:

The function:

[tex]y = 2050(12)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant.

So, k = 2050 and a = 12  . Since, a is greater than 01.  

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Answer:

$6.35

Step-by-step explanation:

25.40/4 = 6.35

F0.05 (4,5)=5.19>f according to the F-distribution table. Following that, P(F>1.442)>P(F>f0.05 (94.5))=0.05. This leads us to conclude that the sample has a higher than 5% chance of producing such data under the premise that σx=σy.

We cannot conclude that the variances of the two populations are not equal based on the standards of a 95% confidence interval.

Step 1 : the mines' 1 and 2 standard deviations should be calculated. [tex]n_{x}[/tex] =5&[tex]n_{y}[/tex]=6.

To determine the sample means, use the formulas

x bar = 8260 + 8130 + 8350 + 8070 + 8340/ [tex]n_{x}[/tex]

x bar = 41150/ 5

x bar = 8230 and y bar = 7950 + 7890 + 7900 + 8140 + 7920 + 7840/ [tex]n_{y}[/tex]

y bar = 47640/6

y bar = 7940.

step 2: Now,  [tex]s_{x}[/tex]provides the standard deviations.

[tex]s_{x}^{2}[/tex] =1/4i=1∑^5i=1(xi−x)^2

=1/ 4 ⋅63000

=15750

for [tex]s^{2}_{y}[/tex]

[tex]s^{2}_{y}[/tex]^2=1/5∑i=1^6(yi−y)^2

=1/5⋅54600

=10920

If we assume that the variances of the two populations are equal—

that is,  σx=σy and

 [tex]s_{x}^{2}[/tex] and[tex]s^{2}_{y}[/tex] are the variances of independent random samples with sizes of [tex]n_{x}[/tex]=5 and[tex]n_{y}[/tex] =6 drawn from normal populations—then we can say that the random variable exists.

The formula F is

=[tex]s_{x}^{2}[/tex]/ [tex]s^{2}_{y}[/tex]has an F distribution with

v1=nx- 1

=5- 1

=4 and

v2=ny-1

=6- 1

=5

The observed samples' f-value is f=[tex]s_{x}^{2}[/tex] / [tex]s^{2}_{y}[/tex]

=15750/10920

=1.442.

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The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.

The price of a bond is its present value.

The present value can be computed by setting the following parameters:

This can be done using an online finance calculator with the results as follows:

N (# of periods) = 20 semiannual periods (10 years x 2)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)

FV (Future Value) = $105

Results:

Present Value (PV) = $115.87

Sum of all periodic payments = $100 ($5 x 20)

Total Interest = $89.13

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Answer: 115.87 (If you don't get this answer then the solution is incorrect.)

The scientific terms for peaks and valleys is B. Crests and troughs.

The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.

The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.

The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.

Therefore, based on the information given, the correct option is B.

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The graph that shows the linear relationship of the table is attached below.

To determine the graph of a linear relationship, do the following:

Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:

Slope = change in y / change in x = (1 - 0) / (2 - 0)

Slope = 1/2.

The y-intercept (b) = 0.

Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.

Thus, the graph is shown below.

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The total income from the machines over the first 5 years is $185.89

From the question, we have the following parameters that can be used in our computation:

f(t) = 160e0.03t

Where

Rewrite the function properly

so, we have the following representation

f(t) = 160e⁰.⁰³ⁿ

The above function is an exponential function

So: In the first 5 years, we have the value of t to be 5

This is represented as follows

t = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 160e⁰.⁰³ ˣ ⁵

Evaluate the product of the exponents

f(5) = 160e⁰.¹⁵

The products above give

f(5) = 185.89

Hence, the total income is $185.89

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Step-by-step explanation:

similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).

so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.

some correct answer options are not listed, so we need to adjust to the existing ones.

remember, the sum of all angles in a triangle is always 180°.

so,

angle A + angle B + angle C = 180

40 + angle B + 60 = 180

angle B = 80°

so, angle E = 80° for the triangles to be similar.

AC × c = DF

12 × c = 16

3 × c = 4

c = 4/3

so,

AB × c = DE

9 × 4/3 = DE

36/3 = DE

DE = 12

so, either angle E = 80° or DE = 12.

The degree to turn before walking 673 paces is 59 degrees

From the question, we have the following parameters that can be used in our computation:

Lengths = 989 paces, 673 paces and 861 paces

These paces can be represented as

x = 989

y = 673

z = 861

The measure of the required angle (angle Z) i.e.  the degree to walk can be calculated using the following cosine rule

z² = x² + y² - 2xy * cos(Z)

Substitute the known values in the above equation, so, we have the following representation

861² = 989² + 673² - 2 * 989 * 673 * cos(Z)

Evaluate the exponents, the products and the summation

So, we have the following representation

741321 = 1431050 - 1331194 * cos(Z)

Evaluate the like terms

- 1331194 * cos(Z) = -689729

Divide both sides by  - 1331194

cos(Z) = 0.51812808651

Take the arc-cos of both sides

Z = 58.7

Approximate

Z= 59 degrees

Hence, the measure of the angle is 59 degrees

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Answer:

The length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.

Step-by-step explanation:

Since angle A and angle R are both congruent to angle B, we know that angle A = angle R = y + 7°. We can use this information, along with the angles and sides of the triangles, to find the value of y and the lengths of the sides of the triangles.

From the given information, we know that the angles of triangle ABC add up to 180°, so we can use that to find the value of y:

4y - 71° + y + 7° + 106 - 2y° = 180°

6y - 64° = 180°

6y = 244°

y = 40.67°

We can use the value of y to find the measure of angle C:

C = 106 - 2y° = 106 - 2(40.67°) = 106 - 81.34° = 24.66°

Now that we know the measure of angle C, we can use the Law of Sines to find the length of side BC:

BC / sin C = AC / sin A

BC = (AC * sin C) / sin A

BC = (13 cm * sin 24.66°) / sin (4y - 71°)

BC = (13 cm * 0.4237) / sin (4(40.67°) - 71°)

BC = 5.525 cm

We can use the same method to find the length of side ST in triangle RST:

ST = (RT * sin C) / sin A

ST = ((2x + 5 cm) * sin 24.66°) / sin (4y - 71°)

ST = ((2x + 5 cm) * 0.4237) / sin (4(40.67°) - 71°)

ST = (2x + 5 cm) * 0.4237 * 0.4514

ST = (2x + 5 cm) * 0.1901

ST = 0.3802x + 0.9505 cm

Therefore, the length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.

(a) Using y the manufacture can find the required diameter of the hole.

(b) The mean of the random variable y is 0.003.

(c) The standard deviation of the y is 0.0063.

(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

(e)  We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.

a) y=x2-x1 denote the difference between hole and peg diameter

if y<0 , the peg won’t go inside the hole and

if y>0 ,the peg be loose to the hole

So using y the manufacture can find the required diameter of the hole.

b)Now, we have to find the mean of the random variable y

μ(y) = μ(x2) - μ(x1)

μ(y) = 0.253-0.25

μ(y) = 0.003

c) Now we have to find the standard deviation of the y

σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)

σ(y) = √0.000036+0.000004

σ(y) = √0.00004

σ(y) = 0.0063

d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

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We had written an algorithm, using pseudo code.

//Define the required variables.

total_number_of_steps = 0

number_of_steps = 0

//robot stands up to walk.

stand

//the robot moves forward till the wall is not reached.

while (wall is not reached)

//the robot senses the wall with the help of arms.

raise arms

sense_the_wall

if (wall is not there)

//if the wall is not found, the robot lowers the arms

lower arms

//if wall is not detected, the robot moves forward.

step_forward

//increment the number of steps forward.

number_of_steps=number_of_steps+1

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

else

exit

end if

end while

//else if the wall is found, lower the arms

lower arms

//the robot turns 90 degrees right once.

turn_right_90

//the robot turns 90 degrees right again.

turn_right_90

//till the number of steps does not reach 0, move

for (number_of_steps! = 0)

step

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

//the robot moves backwards on detecting the wall, so

//decrement the number of steps.

number_of_steps = number_of_steps-1

//end the for loop.

end for

//the robot turns 90 degrees left once.

turn

//the robot turns 90 degrees left again.

turn

//the robot sits down.

sit

//display the total number of steps taken by robot

display total_number_of_steps

The last line ends the pseudocode

Stop

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Answer: 160 inches

Step-by-step explanation:

To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.

The correct matching regarding the linear functions are given as follows:

i. A set of points where the coordinates of each point has a sum of 2: Line n.

ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.

b - i) Two numbers with a sum of 2: A and C.

b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.

b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.

The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function

x + y = 2.

In slope-intercept form, it is of:

y = 2 - x.

Which is the decreasing line n, with an intercept of 2.

A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function

y = x - 10.

Which is the increasing line m, which an intercept of m.

The coordinates of each point are given as follows:

These points are then used to match the sentences in item b.

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The value of down payment will be;

⇒ $705

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Now,

Since, Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Hence, The value of down payment = 15% of $4700

                                                        = 15/100 × 4700

                                                        = 15 × 47

                                                        = 705

Thus, The value of down payment = $705

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Answer:0.1875

Step-by-step explanation: you would take the miles and divide it my the minutes which would be 3 divided by 16 which equals 0.1875

Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.

Step-by-step explanation:

==> 30 = 3.75 + 12.35 + x

Take 16.1 from both sides:

==> 30 = 16.1 + x

==> 30 = 13.9km

Answer:

Step-by-step explanation:

The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30

A solid figure is a three-dimensional object. That is, it has length, width, and height. Because they are three-dimensional, they have depth and occupy space in our universe. Body types are identified according to characteristics specific to each body type. In particular, we can observe the number of faces, edges, vertices, and the shape of the base.

A flat face of a solid is its face or side, as it is commonly called. The base is the surface on which the figure rests. A solid edge is a line segment where two faces meet. A vertex  is an angle formed where the endpoints of two or more face segments meet.

A sphere is a solid figure that has no faces, edges, or vertices. This is because it is perfectly round. No flat sides or corners.

A cone has faces but no edges or vertices. His face is circular. A circle is a plane because it is a flat planar shape. However, since it is rounded on the outside, it does not form edges or corners.

Cylinder that has two circular faces but no edges or corners:

A pyramid has a base and at least three triangular faces. There are edges where faces meet each other or meet the bottom, vertices where two faces meet the bottom, and top vertices where all the triangle faces meet. Pyramids are named for the shape of their base.

A triangular pyramid has a triangular base and his other three triangular faces, or four triangles in total.

A pyramid has a rectangular base and a pyramid has a square base. Both have four triangular faces, for a total of five faces.

Prism:

A prism is a solid with two congruent parallel faces and any number of sides. That is, it can have any number of faces, but at least two faces must be parallel. The shape of the two parallel faces can be triangles, squares, rectangles, pentagons, hexagons, or other types of polygons. Prisms are named after the shape of the base.

Sphere:

A sphere is a geometric object that is the three-dimensional analogue of the two-dimensional circle. A sphere is a set of points that are all the same distance r from a given point in 3D space. This given point is the center of the sphere and r is the radius of the sphere. Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy.

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Step-by-step explanation:

Add the values

x - y = 6

x + y = 2

-------------

2x = 8

--------------

Substitute for x

2x = 8

x = 8/2

x = 4

insert x = 4 into equation x - y = 6

x - y = 6

4 - y = 6

-y = 6 - 4

-y = 2

-y/-1 = 2/-1

y = -2

∴ y = -2 , x = 4

Solved by elimination

Solved by elimination Through chibabykalu16

The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²

An expression is combination of variables, numbers and operators.

(4c − 3d)(3c + d) is the given expression.

Four times c minus three times d into three times f c plus d.

In the given expression c and d are variables.

Plus and minus are operators.

We need to find the equivalent expression of (4c − 3d)(3c + d).

(4c − 3d)(3c + d)

4c(3c+d)-3d(3c + d)

Apply the distributive property.

12c² + 4cd - 9cd - 3d²

Add the like terms

12c² - 5cd - 3d²

Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).

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Sandra needs 8 bowls to divide the trail mix equally.

To determine the number of bowls Sandra needs, we need to divide the total weight of the trail mix by the weight of each bowl.

First, we need to convert the weight of the trail mix from pounds to ounces. There are 16 ounces in a pound, so 5.2 pounds is equal to 5.2 x 16 = 83.2 ounces.

Next, we need to convert the weight of each bowl from pounds to ounces. There are 16 ounces in a pound, so 0.65 pounds is equal to 0.65 x 16 = 10.4 ounces.

Now that we have both weights in the same units, we can divide the total weight of the trail mix by the weight of each bowl to find the number of bowls needed.

⇒ 83.2 ounces / 10.4 ounces per bowl

Apply the division operation,

⇒ 8 bowls.

Therefore, she needs 8 bowls to divide the trail mix equally.

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Answer:

Below

Step-by-step explanation:

1/3 x   = - 2/5      <=====multiply both sides of the equation by 3 to get

x = -6/5   = - 1  1/5

The population standard deviation [tex]\sigma[/tex] is 6.697.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.

Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.

Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.

We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].

= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².

= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.

= 44.85

And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697

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The maximum no. of fish tacos they can order is 8.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

let, The no. of fish taco be 'F'.

Therefore, 2F + 3.75 ≤ 20.  

So, The no. of fish tacos they order is,

2F ≤ 20 - 3.75.

2F ≤ 16.25.

F ≤ 16.25/2.

F ≤ 8.125 Or 8 as the no. of fish tacos must be in integers.

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By solving a linear equation, it can be calculated that-

First fourth and fifth option are correct

What is a linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Length of two sides of a right angled triangle = x, x+2

Area = [tex]\frac{1}{2}\times x \times (x + 2)[/tex]

By the problem,

The linear equation is

[tex]\frac{1}{2}\times x \times (x + 2) = 24\\[/tex]

0.5x(x + 2) = 24

First option is correct

x(x + 2) = 48

[tex]x^2 + 2x - 48 = 0[/tex]

Fourth option is correct

For the sixth option,

[tex]x^2 + (x + 2)^2 = 100\\x^2 + x^2 + 4x + 4 - 100 = 0\\2x^2 + 4x - 96 = 0\\2(x^2 + 2x - 48) = 0\\x^2 + 2x - 48 = 0[/tex]

Which is the third option.

First fourth and fifth option are correct

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The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.

A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.

The expression for the volume of a regular pentagon is given as V =  5/2 × abh

Where h is the height and a and b are the length of the sides.

Now, the value of a, b and h as per the question is given as,

a = b = h = 1.

Then, the volume can be calculated as,

V = 5/2 × 1 ×1 × 1
   = 2.5

Hence, the volume of the regular pentagonal prism  is given as 2.5 cm³.

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Answer:

[tex] \sqrt{176} [/tex]

[tex] \sqrt{16 + 11} [/tex]

[tex]4 \sqrt{11} [/tex]

Step-by-step explanation:

The answer is

[tex]4 \sqrt{11} [/tex]

We

need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.

i hope this helped

Answer:B

Step-by-step explanation:

I took the test

The simplified equation is y = 3x -40.

What do you mean by translation of graph?

Translating a graph means that moving the graph of a parent operate either vertically or horizontally. To translate a graph vertically means that to shift the graph k units upward or downward looking on the sign of k. If k is positive, shift the graph upward however if k is negative, shift the graph downward. On the opposite hand, translating a graph horizontally means that shifting the graph side wards by h units to the left or to the correct. If h>0, shift the graph to the correct however if h<0, shift the graph to the left.

Main body:

According to question:

Y = √9x-36-4

√9 can be written as 3.

y = 3x -40

Hence , the simplified equation is y = 3x -40.

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