A sofa is on sale for 66% off. The sale price is $231.20.

1. Her age is 41 years and her annual premium is $732.

2. His age for insurance purposes is 27 years.

Her annual premium is $556.

3. His semiannually premiums = $577

And, His quarterly premiums = $288.5

And, His monthly premiums = $96

4. His semiannually premiums = $312.5

His quarterly premiums = $156.25

His monthly premiums = $52

5. His semiannually premiums  = $463

The difference between these payment options = $463

6. His quarterly premium is = $56.5

The difference between the two options is = $170

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

1. Carla Sanborn was born on July 12, 1936.

On October 25, 1977, She bought $30,000 worth of ordinary  life insurance on August 25, 2020.

Now, firstly we have to find her age for insurance purpose and secondly her annual premium.

Since, The age for her insurance purposes will be calculated by the nearest birthday year.

So,

July 12 ,1989 - October 25, 2020 = 31 years.

Hence, She is 31 years of age.

Now, For Her annual premium we divide what she purchased with her age as,

$30,000/31 = $ 967.74

Which is approximately be $968.

2. Bruce Lovegren was born on September 27, 1950.

On April 27, 1977, he purchased a $15,000 ten-year term life insurance     policy.

Now, firstly we have to find her age for insurance purpose and secondly her annual premium.

Since, The age for her insurance purposes will be calculated by the nearest birthday year.

So, September 27, 1950 - April 27, 1977 = 27 years

Now, For Her annual premium we divide what she purchased with her age as,

$15,000/ 27 = $555.55

Which is approximately be $556.

3. Edward Anderson has $30,000 of twenty-payment life.

He is twenty-six years old.

For His annual premium we divide what he purchased with his age as,

$30,000/ 26 = 1,153.84

Which is approximately be $1,154

Hence, His semiannually premiums = $1,154/2 = $577

And, His quarterly premiums =  $1,154/4 = $288.5

And, His monthly premiums = $1,154/12 = $96

4. Tom Harris is twenty-four.

He purchases $15,000 of ten-year term insurance.

For His annual premium we divide what he purchased with his age as,

$15,000/ 24 = $625

His semiannually premiums = $625/2 = $312.5

His quarterly premiums = $625/4 = $156.25

His monthly premiums = $625/12 = $52

5.  Emily Webster purchased a twenty-year endowment policy at age 27 with a face value of $25,000.

For His annual premium we divide what he purchased with his age as,

$25,000/27 = $926

His semiannually premiums =  $926/2 = $463

The difference between these payment options = $926 - $463 = $463

6. Tom Hornet purchases $7,000 of ten year term life. He is 31 years old.

For His annual premium we divide what he purchased with his age as,

$7,000/31 = $225.8

His quarterly premium is $226/4 = $56.5

The difference between the two options is $226 -  $56.5 = $170

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Answer: (Looking back, I may have gotten this question wrong, but if I haven't then nice.)

a) 13 degrees

b) acute angle

Step-by-step explanation:

Given that we know a triangle is 180 degrees. Lets recall what an obtuse, acute, right and reflex angle are.

Obtuse: An angle greater than 90 degrees

Acute: An angle less than 90 degrees

Right: An angle that is 90 degrees

Reflex: An angle in between 180-360 degrees

Since we know that two of the three angles are 54 and 113 degrees, we can say that 54+113+x=180. That means that the missing angle, x, is 13 degrees.

Knowing that 13 is less than 90, we can also say that the third angle is an acute angle.

The number of hours in which Jim will make $126 is equal to 9 hours.

What is the unit rate ?

An unit rate is a ratio that is used for comparing two different kinds of quantities which have different units.

It is given that Jim has made $238 after working for 17 hours.

If we try to find out the unit rate that how much he earn in 1 hour then it can be find out by dividing money earned by no. of hours he has worked.

So , the in 1 hour Jim will make money :

= 238 / 17

= $14

Now , we have to find out that how many hours he has to work to make 126. So , for this we need to divide it by 14 which is the unit rate.

The no. of hours in which Jim will make $126 will be :

= 126 / 14

= 9 hours

Therefore , the number of hours in which Jim will make $126 is equal to 9 hours.

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Using scientific notation, the number of significant digits that the product should have is:

B. 3.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

When two numbers in scientific notation are multiplied, we have that:

For this problem, the product is given by:

[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3[/tex]

Multiplying the bases and adding the exponents, we have that:

[tex]5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^{7}[/tex]

42.8 has to be divided by 10 to assume for the base have only one digit, hence:

[tex]42.8 \times 10^{7} = 4.28 \times 10^6[/tex]

Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.

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The greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] .

The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.

In the given expression

[tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]

Applying Prime Factorization and Writing all the terms in the above expression as

[tex]20x^{6} y=10x^{4}y *2x^{2}[/tex]

[tex]40x^{4} y^{2} =10x^{4} y*4y[/tex]

[tex]10x^{5} y^{5} =10x^{4}y*xy^{4}[/tex]

As we can see that [tex]10x^{4} y[/tex] is common and greatest in all the terms .

Hence [tex]10x^{4} y[/tex] is the Greatest common factor.

Therefore , the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] , the correct option is (a)[tex]10x^{4} y[/tex].

The given question is incomplete , the complete question is

What is the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]

(a)[tex]10x^{4} y[/tex]

(b)[tex]5x^{2} y^{5}[/tex]

(c)[tex]5x^{4} y[/tex]

(d)[tex]20x^{6} y[/tex]

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The given expression (4 × 10) + (7 × 1/100)  expressed in decimal form is written as; 40.07

We want to find the decimal that is equivalent to;

(4 × 10) + (7 × 1/100)

Now expanding the brackets contents, we have;

40 + 7/100

Now, 7/100 when written in decimal form gives;

7/100 = 0.07

Thus, the given expression (4 × 10) + (7 × 1/100)  expressed in decimal form is written as;

(4 × 10) + (7 × 1/100)  

40 + 0.07 = 40.07

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The coordinates of endpoint B are (-7, 11)

From the question, we are to determine the coordinates of the endpoint B

If the coordinates of the endpoints of a line, AB, are A(x₁, y₁) and B(x₂, y₂), then the coordinates of the midpoint is given by

((x₁+x₂)/2, (y₁+y₂)/2)

From the given information,

The coordinates of A are (3, 7) and the coordinates of the midpoint are (-2, 9)

Let the coordinates of endpoint B be (x, y)

Then,

(3+x)/2 = -2

3 +x =-4

x = -4 -3

x =  -7

and

(7 + y)/2 = 9

7 + y = 18

y = 18 - 7

y = 11

Hence, the coordinates are (-7, 11)

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The factoring of the expression 2 x²+x=3 is (x-1) (2x+3)

By ordering the values, we get:

2x² + x - 3 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Factor 1 from 1x:

2x² + x - 3 = 0

2x²  + (-2 + 3) x -3 = 0

2. Apply the distributive property:

2x² - 2x + 3x - 3 = 0

3. Groups the first two terms and the last two terms:

(2x² - 2x) + 3x - 3 = 0

4. Factorize the greatest common denominator (GCM) of each group:

2x(x - 1) + 3(x - 1) = 0

5. Simplify the common term (x - 1) with the distributive property:

(x-1) (2x+3)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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ln(e²) = 2, by properties of logarithm.

Now, as we know by properties of logarithm, [tex]log_b(a)^m = m(log_b(a))[/tex],

ln (e²) = 2 ( ln(e))

Also, as ln (e) = 1, ln (e²)  = 2 (1) = 2.

Hence, ln(e²) = 2, by properties of logarithm.

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Answer:

A

Step-by-step explanation:

The opposite of cubing is cube root

cube rooting both sides would leave you with h = Sqr^3 of 343

Answer:

1.5 more games to win 90% which would mean a total of 13.5 games.

80% of 15 = 12

10% of 15 = 1.5

12+1.5=13.5

Based on the formulas given for PR and QR, the length of PR is 19.8 units.

The shape that is given is an equilateral triangle. This allows us to know that all the sides of the shape are equal.

This means that PR and QR are the same:

PR = QR

Equate both formulas as:

2n + 9 = 7n - 18

You can then solve for the value of n:

7n - 2n = 18 + 9

5n = 27

n = 5.4

The length of PR can then be solved by using substitution:

= 2n + 9

= 2 (5.4) + 9

= 19.8 units

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Answer:

25

Step-by-step explanation:

If youre going by 5's youd get 30 but then you gotta take away -5 so it comes out to 25

Answer:

25

Step-by-step explanation:

There are 10000 different possible codes to guess the correct code on the first try..

A percentage, or a figure between 0 and 100 percent, can also be used to express probability. The likelihood of an event occurring increases with its probability value or percentage. How many potential outcomes an event has will determine how likely it is to occur.

1)There are 5040 possible codes if the digits are not repeated.

2)Probability of guessing correct code on first try p = 1/5040.

3)There are 10000 different codes, if the digits are repeated.

Given,

Total digits = 10.

{0,1,2,3,4,5,6,7,8,9}

4 digit code must be formed.

1. Code without repeating digits

 → 4 digit code

Therefore possible ways = 10×9×8×7

= 5040

2. Probability of guessing correct code on first try.

n(A)→ event which has correct code=1

n(S)→total possible ways=5040.

P(A) = n(A)/n(S) = 1/5040

3. If the digits are repeated

→ 4 digit repeated

Therefore possible ways = 10×10×10×10

= 104

= 10000 ways

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a. The slope of a line that is parallel to y = 3/5x + 7 is: 3/5.

b. The slope of a line that is perpendicular to y = 3/5x + 7 is: -5/3.

Given a line is represented by the equation, y = 3/5x + 7, the slope (m) of the line is 3/5.

Any line that is parallel to y = 3/5x + 7 will have a slope (m) = 3/5 [same slope value].

On the other hand, any line that is perpendicular to y = 3/5x + 7 will have a slope of -5/3 [negative reciprocal].

Therefore:

a. The slope of a line that is parallel to y = 3/5x + 7 would be: 3/5.

b. The slope of a line that is perpendicular to y = 3/5x + 7 would be the negative reciprocal of 3/5, which is: -5/3.

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Answer:

x=1 y=3

Step-by-step explanation:

Hello!

So, this says to use the substitution method. The substitution method is where you set one equation equal to one of the letters, and then put that whole equation in the other equation.

So->

3x-y=0

if we move the y to the other side we have:

3x=y

then we have our second equation:

2x+y=5

Now, we don't know what NUMBER y is yet, but we do know that it is equal to 3x. Thus, we can put it into the equation like this.

2x+(3x)=5

Then, we can add like terms and get:

5x=5

Dividing each term by five, we get

x=1

We could have also done this be solving for x in the equations and then substituting that in instead of y.

Now that we have x, we can easily put it into the equations and solve for y.

3x-y=0

3(1)-y=0

3=y

So now we know that x is equal to 1 and y is equal to 3.

The function's formula is given by c=150-8s .

It is given in the question that

number of candies taken by tyrone in each snack  = 8

number of times tyrone snacks = 18

Total candies= (number of times tyrone snacks)x(number of candies taken in each snack )

Total candies=18x8=144.

There are 6 candies left in the bag .

So total candies = 144+6=150.

It is also given that "s" is the number of snacks tyrone eats .

and "c" is the number of candies remaining.

number of candies tyrone eats in each snack = 8

number of candies tyrone eats in s each snack =8s

the number of candies remaining = (total candies) - (number of candies tyrone eats in s each snack ).

Substituting the values we get

c=150-8s.

Therefore , the function's formula is given by c=150-8s .

The given question is incomplete , the complete question is

Tyrone likes to snack on his big bag of candy. he takes 8 pieces of candy from the bag each time he snacks. after he has snacked 18 times, there are only 6 pieces of candy remaining in the bag. the number "c" of pieces of candy remaining in the bag is a function of s, the number of snacks Tyrone eats. Write the function's formula.

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The required measure of the alternate opposite angle is 25°

Given that,
The figure has been shown in which measure of the angle is to be dtermined.

The angle can be defined as the one line inclined over other line. the measure of an angle is measured in two units of degrees and in radiants.

Here,
2x - 1 = 5x - 40
5x - 2x = 40 - 1
3x = 39
x = 13

Now,
measures of the angle,
= 2x - 1 = 2 * 13 - 1
= 25°
and
5x - 40 = 5*13 - 40
= 65 - 40
= 25°

Thus, the required measure of the alternate opposite angle is 25°.

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Answer:

y=x+6

Step-by-step explanation:

The gradient of the line is change in y/ change in x

Thus meaning the gradient is 1. (defined as x)

The line crosses through the y-axis on the point (0,6)

So your euqation will be y = (1 - the gradient) x + (interception of y-axis) 6

Answer:

y = x + 6

Step-by-step explanation:

The general form of an equation of a line is

y= mx+b

y = slope ·x + y-intercept

Find the slope of the line, m:

-Pick any 2 points on the line, for example lets pick the points (0, 6) and (3, 10)

-Start at any of the points and go towards the other while note the path

start at (0, 6) and to go to (4, 10) we have to

go up (rise) 4 units  from 6 to 10 and

go to the right (run) 4 from 0 to 4.

Slope = m = rise/run = 4/4 = 1

m = 1

Find the y-intercept, b:

The y-intercept is where the line intersects the y-axis. By looking at the given graph we can see y-intercept is 6.

b = 6

The equation of our line is

y = x + 6

Answer:

I don't think it is proportional

Step-by-step explanation:

i can't explain it bc it's like hard to explain so u gotta do that on ur own

The coordinates of K' are (-2, 3) and the coordinates of M' are (-4, 1)

What are the coordinates of K'?

The graph represents the given parameter

On the graph, we have the following coordinates for point K

K = (4, 1)

The transformation vector is given as

[-6]

[2]

The transformation vector implies that

(x, y) = (x - 6, y + 2)

So, we have

K' = (4 - 6, 1 + 2)

Evaluate

K' = (-2, 3)

Hence, the coordinates of K' are (-2, 3)

What are the coordinates of M'?

The graph represents the given parameter

On the graph, we have the following coordinates for point M

M = (2, -1)

The transformation vector is given as

[-6]

[2]

The transformation vector implies that

(x, y) = (x - 6, y + 2)

So, we have

M' = (2 - 6, -1 + 2)

Evaluate

M' = (-4, 1)

Hence, the coordinates of M' are (-4, 1)

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The length of the line AB is 10

The length of the line CD is 5

A line segment is bounded by two distinct points on a line.

We have,

AB formed by A(2, -7) and B(2, 3)

CD formed by C(-4, 0) and D(-4, -5)

The distance between two points (a, b) and (c, d) is given by:

= √(c - a)² + (d - b)²

The length between A and B:

= √(2 - 2)² + (3 +7)²

= √100

= 10

The length of C and D:

= √(-4 + 4)² + (-5 - 0)²

= √25

= 5

Thus,

The length of the line AB is 10

The length of the line CD is 5

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[tex]y = \begin{cases}- 2x + 1& x > 1 \\- x + 2&x\leqslant1\end{cases}[/tex]

from the figure

[tex](x_1,y_1) \: (x_2,y_2) = >y = \frac{y_2 - y_1}{x_2 - x_1} \: x + a \\ a = y_1 - \frac{y_2 - y_1}{x_2 - x_1} \: x_1[/tex]

Answer:4
7
82
83

Step-by-step explanation:

REALLY EASY

If the equation is log x=5 then the value of 1/x is equal to 0.00001.

Given that the equation is log x=5.

We are required to find the value of 1/x.

Equation is basically the relationship between two or more variables that are represented in equal to form. It may be linear equation,quadratic equation and cubic equation and many more depending on the power of variables present in the equation. The given equation contains logarithm.

The equation is log x=5.

Take the base of the log and raise it to both the sides of the equation:

[tex]10^{log x}[/tex]=[tex]10^{5}[/tex]

x=100000     (log 100000=5)

1/x=1/100000

1/x=0.00001

Hence if the equation is log x=5 then the value of 1/x is 0.00001.

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Answer: 5/12

Step-by-step explanation:

6x6=36

36 is all possible values.

1+2+3+4+5=15

The higher the number betty rolls there will be one less possible value that will be bigger than hers.

15/36=5/12

Answer:88888880.8

Step-by-step explanation:

0.9

Answer:

  A.) P(t) = 130t +3330

  B.) P(16) = 5410

Step-by-step explanation:

Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).

We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:

  m = (P2 -P1)/(t2 -t1)

  m = (4500 -3590)/(9 -2) = 910/7 = 130

The point-slope equation will be ...

  P -P1 = m(t -t1)

  P -3590 = 130(t -2)

Solving for P, we find ...

  P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590

  P(t) = 130t +3330

The value of P(16) will be ...

  P(16) = 130(16) +3330 = 2080 +3330 = 5410

The moose population is predicted to be 5410 in 2006.

__

Additional comment

The value of t is years since 1990, so the relevant values are ...

  1992: t = 1992 -1990 = 2

  1999: t = 1999 -1990 = 9

  2006: t = 2006 -1990 = 16

Values of moose population by  linear model A.) P(t) = 130t +3330  B.) P(16) = 5410

What does the term "linear model" mean?

Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).

A.) Linear model

We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:

 m = (P2 -P1)/(t2 -t1)

 m = (4500 -3590)/(9 -2) = 910/7 = 130

The point-slope equation will be

 P -P1 = m(t -t1)

 P -3590 = 130(t -2)

Solving for P, we find

 P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590

 P(t) = 130t +3330

B.) Prediction

The value of P(16) will be

 P(16) = 130(16) +3330 = 2080 +3330 = 5410

The moose population is predicted to be 5410 in 2006.

(B) The value of t is years since 1990, so the relevant values are

 1992: t = 1992 -1990 = 2

 1999: t = 1999 -1990 = 9

2006: t = 2006 -1990 = 16

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Answer:

[tex]19\%[/tex]

Percentages are evaluated values that say how much of a whole is occupied by that value. For example, if we were to say 75% of a strawberry pie remained, we could also see this as 3/4, or three-fourths.

To solve this particular problem, we will need to divide two values and convert a decimal to a percentage.

First, set up the fraction of economics majors that are freshman students to the total number of freshman students.

[tex]\displaystyle \frac{1634}{8600}[/tex]

Then, divide the two using a calculator or long division.

[tex]\displaystyle \frac{19}{100}[/tex]

Finally, to convert this to a decimal, use a calculator.

[tex]0.19[/tex]

To convert a decimal to a percentage, multiply the decimal by 100.

[tex]0.19 \times 100 = 19\%[/tex]

The final answer is [tex]19\%[/tex].

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Answer:

19%

Key Points:

In order to find the percentage of freshman majoring in economics, we must divide the econ major students by the overall size of the freshman class.

[tex]\frac{1634}{8600}[/tex]

Our next step is to grab a calculator and input 1634 ÷ 8600. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.19

Now, you need to multiply it by 100 so that you can create a percentage.

0.19 × 100 = 19%

Therefore, 19% of the freshman class are economics majors.

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