enter the expression that is equivalent to: -1/2(6x - 10)​

a. The value corresponding to surviving the year is $0, and the value corresponding to not surviving the year is -$90,000.

b. The expected value for the 33-year-old male purchasing the policy is -$579.06.

c. Yes, the insurance company can expect to make a profit from many such policies because the expected profit per 33-year-old male insured for 1 year is $408.06.

a. The monetary value corresponding to surviving the year is $0 because the individual would not receive any payout from the insurance policy if he survives. The monetary value corresponding to not surviving the year is -$90,000 because in the event of the individual's death, the policy pays out a death benefit of $90,000.

b. To calculate the expected value for the 33-year-old male purchasing the policy, we need to multiply the probability of each event by its corresponding monetary value and sum them up. The probability of surviving the year is 0.9988, and the value corresponding to surviving is $0. The probability of not surviving the year is (1 - 0.9988) = 0.0012, and the value corresponding to not surviving is -$90,000.

Expected value = (Probability of surviving * Value of surviving) + (Probability of not surviving * Value of not surviving)

Expected value = (0.9988 * $0) + (0.0012 * -$90,000)

Expected value = -$108 + -$471.06

Expected value = -$579.06 (rounded to the nearest cent)

c. The insurance company can expect to make a profit from many such policies because the expected value for the 33-year-old male purchasing the policy is negative (-$579.06). This means, on average, the insurance company would pay out $579.06 more in claims than it collects in premiums for each 33-year-old male insured for 1 year. Therefore, the insurance company expects to make an average profit of $579.06 on every 33-year-old male it insures for 1 year.

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For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.

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Answer:

50

Step-by-step explanation:

35/7= 5

5*10=50

Answer:

50 people in the choir

Step-by-step explanation:

we can solve for x, assuming x is the value in which 1 is on the ratio. 7x=35, so the value of x would be 5. Next, we must multiply x by 3 since that is what the ratio states. If we do this, we will get 5*3, or 15. Therefore, there are 15 boys in the choir. Last, we have to add 15+35 to get the total number of people in the choir. There are 50 people in the choir.

Hope this helps! :)

(Also i know my explanation is rly bad just ignore it)

The total distance traveled by bus is 420 miles.

Let's denote the distance traveled by car as "x" miles.

The time taken for the car journey can be calculated by dividing the distance by the speed:

Time taken by car = x miles / 30 mph = x/30 hours.

The remaining distance, which was traveled by bus, would be the total distance of 630 miles minus the distance traveled by car:

Distance traveled by bus = 630 miles - x miles = (630 - x) miles.

The time taken for the bus journey can be calculated by dividing the distance by the speed:

Time taken by bus = (630 - x) miles / 60 mph = (630 - x)/60 hours.

Given that the total time was 14 hours, we can write the equation:

Time taken by car + Time taken by bus = Total time

x/30 + (630 - x)/60 = 14.

To solve this equation and find the value of x, we can multiply all terms by 60 to eliminate the denominators:

2x + 630 - x = 840,

x + 630 = 840,

x = 840 - 630,

x = 210.

Therefore, the distance traveled by bus is:

Distance traveled by bus = 630 miles - x miles = 630 miles - 210 miles = 420 miles.

So, the total distance traveled by bus is 420 miles.

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Answer: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

The statement that is true is (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1].

A function that is strictly increasing on an open interval is not bounded above or below, meaning that it does not attain a maximum or minimum value within that interval.

Since f is defined on the closed interval [0, 1], which includes the endpoints 0 and 1, it also does not attain a maximum or minimum value on the entire closed interval.

For the function f to attain a minimum value, the function must be defined for all x in the closed interval and all x in the domain and at least one point x in the domain must be a global minimum.

For the function to attain a maximum value, at least one point x in the domain must be a global maximum, in this case, the function is continuous and strictly increasing on the open interval (0, 1) which means that the function doesn't have a minimum or a maximum.

In conclusion, the statement that is true is (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1] because a function that is strictly increasing on an open interval is not bounded above or below, meaning that it does not attain a maximum or minimum value within that interval.

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Answer:

Read below for full answer :)

Step-by-step explanation:

We can conclude that the total cost of all meals was $205.

There were a total of 8 kids meals and 5 adult meals.

You'd have to divide 205 by 8, and you'd get 25.625.

Then, divide 205 by 5, and you'd get 41.

For example, we could say that each childrens meal was $15 ($120 total in kid's meals), and each adult was $17 ($85 total in adult meals).

When you total $85 and $120, it then given you a sum of $205.

There are many ways to complete this equation, but i feel that this is the easiest way.

Hope this helps! :)

Answer:

33

Step-by-step explanation:

The original price is $44

As if she bought it at Sales time

- 75% off the original price

Method

75 x 44/100

would equal to 33

Hope this helped you

:-)

Answer:

d

Step-by-step explanation:

it is opened up because the voeff of X^2 tetm is positive

Answer:

x = 0

Step-by-step explanation:

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

3x - 3 = 2x - 3 + 3x

0 - 3 = 2x - 3

0 = 2x

2x = 0

x = 0 ÷ 2

x = 0

Answer:

25

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. 66.8 58.2 83.3 83.3 44.2 83.3 76.4 54.3 65.2 62.9

Range = highest value - lowest

= 83.3 - 44.2 = 39.1.

b. Mean m = 677.9 / 10

= 67.8

Differences from the mean

= 66.8 - 67.8 = -1.0

-9.6

15.5

-23.6

15.5

15.5

8.6

-13.5

-2.6

-4.9

Now we sqare the above vales:

= 1 , 92.16, 240.25, 240.25, 240.25, 556.96, 73.96, 182.25, 6.76, 24.01

Now the sm of these is 1657.85

Now we divide this by 10 and find the sqare root

= √(165.785)

= 12.86.

Standrad deviation is 12.86.

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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Answer:

x = 5/8, y = -7/8

Step-by-step explanation:

The value of x in the ratio 5x : 9 = 7 : 3 is x = 21/5

From the question, the ratio is given as

5x : 9 = 7 : 3

Express the ratio, as a fraction

So, we have the following representation

5x / 9 = 7 / 3

Cross multiply the following expression

So, we have the following representation

3 * 5x = 9 * 7

Evaluate the products

15x = 63

Divide both sides by 15

So, we have

x = 63/15

Simplify the fraction

x = 21/5

Hence, the solution to the ratio is x = 21/5

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Answer:

About 66 Lb

Step-by-step explanation:

The numerical value "62" is a statistic because it is based on the sample of passengers aboard the Hindenburg airship.

In the given scenario, the numerical value is "62." We are told that there were 97 passengers aboard the Hindenburg airship and that 62 of them survived its explosion.

Since the numerical value is based on the sample (i.e., the passengers aboard the Hindenburg airship), it is a statistic. It describes the proportion of passengers who survived the explosion in the sample.

If we wanted to know the proportion of passengers who survived the explosion in the entire population (i.e., all passengers who have ever traveled on the Hindenburg airship), we would need to determine the parameter.

However, since we do not have data on the entire population, we cannot determine the parameter.

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The answer is , the correct option is (d), the intersection of three planes is in plane, which can be described by equations that are linear combinations of original equations.

Geometrically, the solution to the linear system x+3y+2z=31, x+4y+3z=26 and 5x+2y+z=19 is the intersection of 3 planes in the three-dimensional space.

The intersection of three planes can be described in 5 ways:

(a) The planes have no point in common, so there is no solution. (The planes are parallel but not identical.)

(b) The planes have a line in common and a unique solution exists. (The planes intersect in a line.)

(c) The planes have a point in common and a unique solution exists. (The planes intersect in a point.)

(d) The planes intersect in a plane, which can be described by equations that are linear combinations of the original equations. This plane has infinitely many solutions.

(e) The planes intersect in a line segment, or they are all identical. The system has infinitely many solutions.

The correct option is (d), the intersection of three planes is in a plane, which can be described by equations that are linear combinations of the original equations.

This plane has infinitely many solutions.

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There is a unique solution for this system of linear equations. The correct answer is B) One Solution.

Given system of linear equations is:

x + 3y + 2z = 31

x + 4y + 3z = 265

x + 2y + z = 19

In general, an intersection of this kind may include (A) zero solutions (B) one solution (C) two solutions (D) three solutions (E) infinitely many solutions.

The solution of the linear system of equations is the intersection of three planes, and it can have:

A single solution (one point of intersection) if the three planes intersect at one point in space.

Infinite solutions (one line of intersection) if the three planes have a common line of intersection.

No solutions if the planes do not have a common intersection point.

The planes are given by the following equations:

x + 3y + 2z = 31, x + 4y + 3z = 26, and 5x + 2y + z = 19.

To solve this system of equations, we can use any of the methods of solving linear systems of equations, such as: Gauss elimination, inverse matrix, determinants, or Cramer's rule.

Gauss Elimination Methodx + 3y + 2z = 31x + 4y + 3z = 265x + 2y + z = 19

Use row operation 2 * row 1 - row 2

-> row 2 to eliminate x in the second equation.

x + 3y + 2z = 31x + 4y + 3z = 26 - 2 * (x + 3y + 2z)5x + 2y + z = 19

Simplify and solve for z:

x + 3y + 2z = 31

x + 4y + 3z = 26 - 2

x - 6y - 4z5x + 2y + z = 19

2x + y - z = -6

Solve for y:

x + 3y + 2z = 31

x + 4y + 3z = 26 - 2x - 6y - 4

z5x + 2y + z = 192x + y - z = -6

Use row operation -2 * row 1 + row 2

-> row 2 to eliminate x in the second equation.

x + 3y + 2z = 31

x + 4y + 3z = 26 - 2

x - 6y - 4z5x + 2y + z = 192

x + y - z = -6-2

x - 6y - 4z + x + 4y + 3z = 26-3y - z = -5

Solve for y:

x + 3y + 2z = 31

x + 4y + 3z = 26 - 2

x - 6y - 4z5

x + 2y + z = 192

x + y - z = -6-2

x - 6y - 4z + x + 4y + 3z = 26-3y - z = -5

Use row operation -5 * row 1 + row 3

-> row 3 to eliminate x in the third equation.

x + 3y + 2z = 31

x + 4y + 3z = 26 - 2

x - 6y - 4z5x + 2y + z = 192

x + y - z = -6-2

x - 6y - 4z + x + 4y + 3z = 26-3y - z = -5-5

x - 15y - 10z + 5x + 15y + 10z = -155

x = -15

x =  -3

Substitute x = -3 into equation 2:

x + 3y + 2z = 31-3 + 3y + 2z = 31 y = 2z = 9

Therefore, there is a unique solution for this system of linear equations. The correct answer is B) One Solution.

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If the stream narrows from 30 feet to 20 feet, the width of the stream has narrowed, and the velocity should increase. The correct answer is b.

According to the principle of conservation of mass, when the width of a stream narrows, the volume flow rate (the amount of water passing through a given point per unit time) must remain constant if there are no other factors involved.

The volume flow rate (Q) can be calculated as the product of the cross-sectional area (A) and the velocity (v): Q = A * v.

When the width of the stream narrows from 30 feet to 20 feet while the volume flow rate remains constant, the cross-sectional area decreases. To maintain a constant volume flow rate, the velocity must increase.

This is because the same amount of water is passing through a smaller cross-sectional area, requiring an increase in velocity to compensate for the reduced width.

Therefore, the correct statement is that the width of the stream has narrowed, and the velocity should increase.

The correct answer is b.

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The equation x=1-2y/3y+5,  can be expressed as 3xy+2y=1-5x below:

The concept that will be used in the expression is simplification and expansion.

Given x=1-2y/3y+5

then we can cross multiply as

x(3y+5) = 1-2y

Then we can expand the equation as

3xy + 5x = 1-2y

then we can rearrange the equation as:

3xy+2y=1-5x

Therefore, the fact that  x=1-2y/3y+5,  can be simplified to  3xy+2y=1-5x has been shown.

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The equation for the line of best fit that predicts how much money travelers will spend in 2008 is y = 20x + 320.

What is the equation of the line?

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y-intercept (the point at which the line crosses the y -axis).

This is a linear function,

let's say the equation is y =ax + b,

the points (1.5, 350) and (4, 400)

a = (400-350) /(4 - 1.5)

= 50/2.5

= 20

y = 20x + b,

350 = 20(1.5) + b

350 = 30 + b

350 -30 = b

b = 320

y = 20x + 320

so, in 2008,

x =15,

y = 20(15) + 320 = 300 + 320 = 620

Hence, the equation for the line of best fit that predicts how much money travelers will spend in 2008 is y = 20x + 320.

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Step-by-step explanation:

Lets solve each simultaneous equation

1.)

2x – y = 1. ----------(1)

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

x = 5 – y -------------(3)

just substitute for x in equation (1)

2(5–y) – y = 1

10 – 2y – y = 1

10 – 3y = 1

–3y = 1 – 10

–3y = – 9

divide both sides by (–3)

y = 3

since y= 3 just substitute for equation (3)

x = 5–y

x = 5–3

x = 2

for the first simultaneous equation x=2,y=3

2.)

x – y = 3 ---------(1)

2x + 4y = 12------(2)

x = y + 3 --------(3)

just substitute for x in equation (2)

2(y+3) + 4y = 12

2y + 6 + 4y = 12

6y + 6 = 12

6y = 12– 6

6y = 6

divide both sides by (6)

y = 1

since y=1 just substitute for y in eqn (3)

x = y + 3

x = 1 + 3

x = 4

for the second simultaneous equation x = 4, y = 1

3.) x + y = 4 -----------(1)

2x – y = 3 -------------(2)

x = 4 – y ---------------(3)

just substitute for x in equation 2

2(4–y) – y = 3

8 – 2y – y = 3

8 –3y = 3

–3y = 3 – 8

–3y = –5

divide both sides by (-3)

y = 5/3

substitute for y in equation (3)

x = 4– y

x = 4 – 5/3

multiply both sides by (3)

3x = 12 – 5

3x = 7

divide both sides by (3)

x = 7/3

for the third simultaneous equation x = 7/3 ,y = 5/3

4.) x– 2y = 10 ------------(1)

4x – 4y = 4. -------------(2)

x = 2y + 10. ----------(3)

The most appropriate domain of the function /(x) - 2.5x models is (A) OS XS 55.The function / (x) - 2.5x models the distance Alex has to go to the store. To find the most appropriate domain of the function, we need to consider the given problem carefully. Alex takes 22 minutes to walk from his home to the store.

Therefore, it is evident that he cannot walk for more than 22 minutes to reach the store. It is also true that he cannot cover a distance of more than 22 minutes. Hence, the most appropriate domain of the function would be (A) OS XS 55. Therefore, the most appropriate domain of the function /(x) - 2.5x models is (A) OS XS 55.

This is because Alex cannot walk for more than 22 minutes to reach the store, and he cannot cover a distance of more than 22 minutes.

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The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

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Answer:

Step-by-step explanation:

A real-world relationship that could be considered a function is the height of a function after x days, hence:

The input is the number of days.

The output is the height of the tree.

Following the function given by the table at the end of the answer, the input that produces an output of 11 is:

y = 0.5.

credits to joaobezerra

Answer:

Area: 531 in²

Circumference: 82 in

Step-by-step explanation:

Given:

To find:

Area of Circle:

\(\displaystyle \large{A=\pi r^2}\)

Therefore:

\(\displaystyle \large{A=3.14 \cdot 13^2}\\\displaystyle \large{A=530.66 }\)

Round to nearest whole number:

Therefore, the area is 531 inches squared

Circumference of Circle:

\(\displaystyle \large{C=2\pi r}\)

Therefore:

\(\displaystyle \large{C=2\cdot 3.14 \cdot 13}\\\displaystyle \large{C=81.64}\)

Round to nearest whole number:

Hence, the circumference is 82 inches

No, an isosceles triangle is not always a right triangle.

An isosceles triangle is a triangle that has two sides of equal length and two angles of equal measure. The two equal sides are known as the legs, and the angle opposite the base is known as the vertex angle.

A right triangle, on the other hand, is a triangle that has one right angle (an angle measuring 90 degrees). In a right triangle, the side opposite the right angle is the longest side and is called the hypotenuse.

While it is possible for an isosceles triangle to be a right triangle, it is not a requirement. In an isosceles triangle, the vertex angle can be acute (less than 90 degrees) or obtuse (greater than 90 degrees). Only if the vertex angle of an isosceles triangle measures 90 degrees, then it becomes a right isosceles triangle.

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