Nikolai Bell was recently hired at a new company. The Bells need to choose between two different health plans for their family’s primary insurance: Option 1: the Deluxe Plan or Option 2: the Basic Plan.



Step 2: Identify Variables and Assumptions

Identify the key variables in the Bell’s situation. (Select all that apply)



The cost of each plan.


The benefits paid by each plan.


The health of the Bell family.


The location of the nearest fast food restaurant.


The number of hours that Nikolai works each week.


The Bell’s monthly income.



To help make a decision Nikolai looked at all of the family’s medical expenses from the last year. He used mathematical tools to calculate what the total costs would have been if they had Option 1: the Deluxe Plan and what the total costs would have been if they had Option 2: the Basic Plan.

Identify the assumptions that Nikolai is using to make his decision.



The Bell’s medical costs will remain about the same as last year.


If Nikolai works hard, he can get a raise.


If the Bells are careful, they will not need any medical insurance.


If the Bell’s have health insurance they do not need to have an emergency savings account.



Step 3: Apply Quantitative Tools

Use computational and algebraic tools to quantify the total costs for each plan using last year’s medical expenses as an estimate.

Option 1: The Deluxe Plan
(You pay . . .)

Option 2: The Basic Plan
(You pay . . .)

Co-payment for Office Visit = $
20

Co-payment for Office Visit = $
30

Prescription Drugs at 30%

Prescription Drugs at 50%

Emergency Room Visit = first $
75 plus 10% of remaining charge

Emergency Room visit = first $
75 plus 30% of remaining charge

Hospital stay or procedures at 10%

Hospital stay or procedures at 30%

Other approved expenses at 10%

Other approved expenses at 30%

Monthly premium = $
425

Monthly premium = $
150


The Bell Family’s medical expenses from last year are summarized in the table below:


Month

The Bell Family’s Medical Expenses

January

1 office visit(s) & $
95 prescription

February

1 Emergency room visit (charged $
400)

March

2 office visit(s)

July

1 office visit(s)

August

Hospital stay for surgery (hospital/doctor charged $
9,000) and $
85 prescription

September

2 office visit(s)

A regression through the origin is a linear regression model where the intercept time period is assumed to be 0, meaning the regression line passes through the starting place.

This version is also referred to as zero-intercept regression or homogeneous regression.

It's far frequently used whilst there's a theoretical foundation to agree with that the relationship among the dependent and unbiased variable passes via the foundation or whilst the information propose that the intercept ought to be 0.

The slope coefficient represents the change within the structured variable for a one-unit increase inside the unbiased variable.

However, this kind of regression may not be appropriate in all cases, and a general linear regression version with an intercept term can be greater suitable.

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Answer:

The set of ordered pairs that represents g¹(x) can be found by reversing the order of each pair in the original function g(x) and then solving for x. Therefore, g¹(x) would be:

{(-14, -9), (40, 18), (10, 3), (-26, -15)} with the x-coordinates being -9, 18, 3, and -15 respectively.

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

Arranging the numbers

-4 (n+8) = -12

n+8 = -12/-4

n+8 = 3

n = 3-8

n = -5

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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The solution to the system is 6 and 11.

We have,

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation.

Given equation:

y=2x-1 .....(1)

y=x+5....(2)

Now solving equation 1 and 2, we get

2x -1 = x + 5

2x - x= 5 +1

x = 6

and, y= 2x-1

y= 2(6)-1

y= 12 -1

y= 11

Hence, the value of x is 6 and y is 11.

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complete question:

On a piece of paper, graph the system of equations. Find the solution to the system. y=2x-1 y=x+5

Answer:

  8 m

Step-by-step explanation:

You want the length x that gives a triangle area of 26 m² when the angle between side x and side 13 m is 30°.

The area formula is ...

  A = 1/2ab·sin(C)

  26 = 1/2(13)(x)·sin(30°) = 13/4x . . . . . use given values

  x = (4/13)(26) = 8 . . . . . . divide by the coefficient of x

The length x in the triangle is 8 m.

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The absolute value equation that has these minimum and maximum heights as its solutions is 9=|x−45|

We have,

"The min is simply the lowest observation, while the max is the highest observation. Obviously, it is easiest to determine the min and max if the data are ordered from lowest to highest."

First, find the difference of both solutions.

54 - 36 = 18

Than, divide it by 2

18/2 = 9

9 = | x − 54+9 |

Either way:       9 =|x−45|

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compplete question:

For the Pony Ride, the minimum height is 36 inches and the maximum height is 54 inches. Write and solve an absolute value equation that has these minimum and maximum heights as its solutions.​

The perimeters and areas of the rectangles are listed below:

Case 1: p = 54 yd, A = 170 yd²

Case 2: p = 46 m, A = 120 m²

Case 3: p = 44 mm, A = 72 mm²

Case 4: p = 60 in, A = 209 in²

Cases 5 / 6: p = 32 mi, A = 55 mi

Case 7: p = 66 m, A = 242 m²

Case 8: p = 94 yd, A = 550 yd²

Case 9: p = 72 km, A = 320 km²

In this problem we must determine the perimeter and the area of eight rectangles, whose formulae are introduced below:

Perimeter

p = 2 · (w + h)

Area

A = w · h

Where:

Now we determine the perimeter and the area for each case:

Case 1

p = 2 · (17 yd + 10 yd)

p = 54 yd

A = (17 yd) · (10 yd)

A = 170 yd²

Case 2

p = 2 · (15 m + 8 m)

p = 46 m

A = (15 m) · (8 m)

A = 120 m²

Case 3

p = 2 · (18 mm + 4 mm)

p = 44 mm

A = (18 mm) · (4 mm)

A = 72 mm²

Case 4

p = 2 · (11 in + 19 in)

p = 60 in

A = (11 in) · (19 in)

A = 209 in²

Cases 5 and 6

p = 2 · (5 mi + 11 mi)

p = 32 mi

A = (5 mi) · (11 mi)

A = 55 mi

Case 7

p = 2 · (22 m + 11 m)

p = 66 m

A = (22 m) · (11 m)

A = 242 m²

Case 8

p = 2 · (22 yd + 25 yd)

p = 94 yd

A = (22 yd) · (25 yd)

A = 550 yd²

Case 9

p = 2 · (16 km + 20 km)

p = 72 km

A = (16 km) · (20 km)

A = 320 km²

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The volume of this rectangular prism given the base area and height is 385 cubic inches.

Volume of the rectangular prism = Base area × height

Base area = 35 square inches

h = 11 inches

Volume of the rectangular prism = Bh

= 35 square inches × 11 inches

= 385 cubic inches

Hence, 385 cubic inches is the volume of the rectangular prism.

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The expression a² - 16a - 12 when factored is a(a - 16) - 12

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

a² - 16a - 12

The above expression is a quadratic expression

It cannot be completely factored

This is because the roots of the expressions are irrational numbers

To partially factor the expression, we have

a² - 16a - 12 = a(a - 16) - 12

Hence, the expression a² - 16a - 12 when factored is a(a - 16) - 12

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The first statement, "if 1 + 1 = 2, then 2 + 2 = 1 + 1," is true due to the associative property of addition, which allows us to group the numbers in any order we want.

The first statement, "if 1 + 1 = 2, then 2 + 2 = 1 + 1," is true due to the associative property of addition, which allows us to group the numbers in any order we want.

The second statement, "If 2 + 1 = 21, then everything else must equal 21," is false. If we assume that 2 + 1 = 21, we must know the specific mathematical system being used to determine if everything else equals 21.

Without additional information or constraints, the equation "[tex]3 + y^3 + z^3 = k[/tex] cannot be solved. It is a three-variable equation with only one equation, which means there are an infinite number of solutions depending on the values of y, z, and k.

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The sentence that uses active voice is: "My friend invited his whole class to Saturday's soccer championship."

Now, let's examine the sentences you provided:

Passive voice: The subject ("the winning homerun") is being acted upon by the action (hit by the worst player).

Active voice: The subject ("my friend") is performing the action (inviting his whole class).

Passive voice: The subject ("the children") is being acted upon by the action (taken to the circus by their doting grandfather).

Passive voice: The subject ("some cookies") is being acted upon by the action (baked by the baker).

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Step-by-step explanation:

All of the sides are equal so find 'x'

6x -10 =  4x + 5

2x = 15

x = 7.5

as a check : the the sides are     6(7.5) - 10 = 35 cm

                                                      4 ( 7.5) + 5 = 35

                                                      10 ( 7.5 - 4 = 35 cm

three sides of 35 cm =   3 x 35 = 105 cm = 1.05 m

    so YES the perimeter is greater than one meter

Step-by-step explanation:

14 10 is 90 less than the mean 1500

   z score =  - 90 / 75 =  -  1.200

    from a z-score table this represents  .1151  

       or  11.51 % will last LESS than 1410 hrs

Answer:

1.a.SAS axiom

b. ASA axiom

Step-by-step explanation:

There are five basic conditions for triangles to be congruent:

For Question:

1.

a. InΔABC and ΔBCD

AB=CD opposite sides of the parallel line are equal Side

∡BAC=∡BDA Given Angle

BC=BC Same side Side

It fulfills the condition of the SAS axiom,

InΔABC ≅ ΔBCD by SAS axiom

b. InΔABC and ΔCDE

∡ACB=∡DCE Vertically opposite angle Angle

BC=CD given Side

∡ABC=∡CDE right angle Angle

It fulfills the condition of the ASA axiom,

InΔABC ≅ ΔCDE by ASA axiom It may be R.H.S. axiom too.

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

The probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.

We have,

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

The conditional probability is the happening of an event, when the probability of occurring of other event is given. The probability of event A, given that the event B is occurred.

Students of high school who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. In this,

74% likely to tryout for softball;

27% likely to tryout for volleyball;

42% likely to tryout for tennis;  

88% likely to tryout for swimming.

Let the tryout for volleyball is event A and tryout for swimming is event B. Thus,

P(A)=0.27

P(B)=0.88

Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

Thus, probability of the union of trying out for either volleyball or swimming

P(A or B)=P(A)+P(B)-P(A and B)

P(A or B)=0.27+0.88-P(A)*P(B)

P(A or B)=0.27+0.88-0.27×0.88

P(A or B)=0.9

Hence, the probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.

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complete question:

The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the union of trying out for either volleyball or swimming?

a. 1. 15

b. 0. 61

c. 0. 91

d. 0. 24

The option that makes the function, f(x) = P·(a)ˣ, an exponential growth function is the option B

B. P = 1/9; a = 12

An exponential function is a function of the form; Y = a·bˣ

Where;

a = The y-intercept, (a, 0)

b = The growth or decay factor

x = The exponent

The function can be expressed as follows;

f(x) = P·(a)ˣ

An exponential growth function is one that increases in value as the value of the input variable increases, in which the growth or decay factor is a > 1

The option that therefore yields an exponential growth is one in which the value of the variable a is larger than 1.

The correct option is therefore, option B.

B. P = 1/9; a = 12

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The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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it is 19 because maths says that 9+10 is 19

Answer:

the answer is 19......

Step-by-step explanation:

Hello!

the equation of the blue line is 3y + 0.5x

We can say that a chip can hold 1 billion transistors in the year 2007.

To solve for the year when a chip can hold 1 billion transistors, we need to set the function f(x) equal to 1000 (since 1 billion is 1000 million).

So,[tex]42(1.41)^x = 1000[/tex]

Divide both sides by 42:

[tex](1.41)^x = 23.81[/tex]

Take the logarithm of both sides (with base 1.41):

x = log(23.81)

Using a calculator, we find that x is approximately 5.98.

Since X represents the number of years since 2000, we add 5.98 to 2000 to get the year when a chip can hold 1 billion transistors:

2000 + 5.98 = 2006.98

Rounding to the nearest year, we can say that a chip can hold 1 billion transistors in the year 2007.

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5/2 pounds is equal to 40 ounces.

We have to find the 5/2 pounds to ounces

1 pound is equal to 16 ounces.

To convert 5/2 pounds to ounces, we can multiply by 16:

5/2 pounds × 16 ounces/pound = 40 ounces

Therefore, 5/2 pounds is equal to 40 ounces.

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Step-by-step explanation:

Volume = length X width X height =  8 x 2 x 6 = 96 m^3

The solution is, the solution is x > −1.

This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1.

This means that any value of x greater than −1 satisfies x + 3 > 2.

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Answer:

r = 4

Step-by-step explanation:

The general form of the equation is y=mx + b where m is the slope and b is the intercept. The problem tells us that the slope is -3. So we know that y=-3x+b

Let's use the known coordinate (-5,13) to solve for b.

y=-3x+b

13 = -3(-5) + b

13 = 15 + b

b = -2

So now we have the equation:

y=-3x-2

Let's use the other coordinate (-2,r) and solve for the unknown "r" (which is y):

y = -3*-2 - 2

y = 6 - 2

y = 4

So the answer is 4.

The quadratic equation with roots a - 2 and b - 2 is x² + 9x + 22 = 0

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 5x + 8 = 0

On simplifying , we get

From the given quadratic equation x² + 5x + 8 = 0, we can identify that a = 1, b = 5, and c = 8.

So, the sum of the roots a and ß is -b/a = -5/1 = -5, and the product of the roots is a x b = c/a = 8/1 = 8.

Now, we need to find the quadratic equation with roots a - 2 and ß - 2.

By using the sum and product of the roots, we can write:

Sum of roots = (a - 2) + (b - 2) = a + b - 4

Product of roots = (a - 2) x (b - 2) = ab - 2a - 2ß + 4

From the given quadratic equation x² + 5x + 8 = 0, we know that:

a + b = -5

ab = 8

Substituting these values in the above equations, we get:

Sum of roots = -5 - 4 = -9

Product of roots = 8 - 2a - 2b + 4 = 12 - 2(a + b) = 22

So , the quadratic equation is given as x² + 9x + 22 = 0

Hence , the equation is x² + 9x + 22 = 0

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Answer:

D

Step-by-step explanation:

To find the center and radius of a circle given its equation, we need to rewrite the equation in the standard form (x - a)^2 + (y - b)^2 = r^2, where (a,b) are the coordinates of the center and r is the radius.

So, let's complete square for x and y terms:

x^2 + 14x + y^2 + 2y + 14 = 0

x^2 + 14x + 49 - 49 + y^2 + 2y + 1 - 1 + 14 = 0

(x + 7)^2 + (y + 1)^2 = 36

Comparing this equation with the standard equation, we get the center at (-7, -1) and radius as sqrt(36) = 6 units.

So, the correct answer is option D: (-7, -1), 6 units.

Bernie drove 1.125 times as fast as Janelle.

To determine who drove faster, we can calculate the average speed (in km/h) of each driver using the formula:

average speed = distance / time

For Janelle:

average speed = 60 km / (5/6 hours) = (60 km) x (6/5 hours) = 72 km/h

For Bernie:

average speed = 54 km / (2/3 hours) = (54 km) x (3/2 hours) = 81 km/h

Therefore, Bernie drove faster than Janelle. To determine how many times as fast, we can divide Bernie's average speed by Janelle's average speed:

81 km/h / 72 km/h = 1.125

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