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the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare  is [$12,000, $14,000].

The estimated average cost of providing healthcare for a senior citizen receiving Medicare is $13,000 per year, and the margin of error for this estimate is $1,000 with a 90% confidence level.

To find the confidence interval, we need to add and subtract the margin of error from the estimated mean.

Lower Limit = Estimated Mean - Margin of Error

Lower Limit = 13,000 - 1,000

Lower Limit = 12,000

Upper Limit = Estimated Mean + Margin of Error

Upper Limit = 13,000 + 1,000

Upper Limit = 14,000

Therefore, the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is [$12,000, $14,000]. This means we are 90% confident that the true mean cost of providing healthcare for a senior citizen receiving Medicare is between $12,000 and $14,000 per year.

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The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".

The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100

Simplifying the expression, we get:

5a + 10d = 100

Dividing both sides by 5, we get:

a + 2d = 20

Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:

1 + 2 * 1 = 3

Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.

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The value of p in the equation m = 4 / (p - d) on solving is p =  (4 + md) / m.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

m = 4 / (p - d)

Multiply the denominator of the right side by the left term as shown below,

m (p - d) = 4

mp - md = 4

Add md to both sides,

mp - md + md = 4 + md

mp = 4 + md

p =  (4 + md) / m

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Answer:

The answer to this is Kristin is 18 years old..

Step-by-step explanation:

The translation of the polygon is ABCD by 5 units to the right;

A(-1, -1) → A'(4, -1)

B(1, -5) → B'(6, -5)

C(5, -5) → C'(10, -5)

D(3, -1) → D'(8, -1)

A shape can be moved up, down, or side to side by translation, but it has no effect on how it looks.

Every point on a figure is moved in a certain direction by a translation in the coordinate plane. Any point on the figure that is (x, y) moves to (x + a, y + b), where a and b are real numbers.

The first polygon, ABCD, has vertices at (-1, -1), (1, -5), (5, -5), and (3, -1).
The vertices of the second polygon, A'B'C'D', are located at (-6, -1), (-4, -5), (0, -5), and (-2, -1).

To translate polygon ABCD by 5 units to the right, we add 5 to the x-coordinate of each vertex:

A(-1, -1) → A'(4, -1)

B(1, -5) → B'(6, -5)

C(5, -5) → C'(10, -5)

D(3, -1) → D'(8, -1)

To translate polygon ABCD by 1 unit to the right, we add 1 to the x-coordinate of each vertex:

A(-1, -1) → A'(0, -1)

B(1, -5) → B'(2, -5)

C(5, -5) → C'(6, -5)

D(3, -1) → D'(4, -1)

To translate polygon ABCD by 5 units to the left, we subtract 5 from the x-coordinate of each vertex:

A(-1, -1) → A'(-6, -1)

B(1, -5) → B'(-4, -5)

C(5, -5) → C'(0, -5)

D(3, -1) → D'(-2, -1)

To translate polygon ABCD by 1 unit to the left, we subtract 1 from the x-coordinate of each vertex:

A(-1, -1) → A'(-2, -1)

B(1, -5) → B'(0, -5)

C(5, -5) → C'(4, -5)

D(3, -1) → D'(2, -1)

So, the vertices of the translated polygon A'B'C'D' are (-2, -1), (0, -5), (4, -5), and (2, -1).

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Answer:

A

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Divide second triangle measurements by first to see what was used to multiply

6/4 = 3/2

7.5/5 = 3/2

12/8 = 3/2

The y-coordinate for the solution to the system of equations is -3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations. The intersection of two lines represents the system of equations' solution.

Given system of equations are,

6x + 11y = -3

4x + y = 17

To solve these equations, we must first remove x or y terms.

To do this we must make the removing term's coefficients the same.

In this case, let's remove y.

We are multiplying the second equation by 11. Then,

6x + 11y = -3

44x + 11y = 187

Now we will subtract the second equation from the first.

- 38x  = -190

x = 5

Now to find y, substitute x in any one of the equations.

6 * 5 + 11y = -3

11y = -33

y = -3

Hence the y-coordinate for the solution to the system of equations is -3.

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Answer:

2 solutions so it can be inferred that it might be a quadratic

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

y = 0 and y = - 7 are horizontal parallel lines.

Since they are parallel, they never intersect and so have no solutions.

=======================================================

Explanation:

From the table, we see that g(1) = 0

Locate x = 1 in the first row. Then look straight down to see 0 in the g(x) row. That's why g(1) = 0.

This means f( g(1) ) = f( 0 ). I simply replaced g(1) with 0.

The last step is to evaluate f(0).

Locate 0 in the x row. Then look down to see 5 below it. Therefore, f(0) = 5.

Ultimately, f( g(1) ) = f(0) = 5

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

In short: the input x = 1 leads to g(x) = 0. Then x = 0 is the input for f(x) which leads to 5.

Answer:

k = 2.5

Step-by-step explanation:

So we start off with: 2.5(4k+2) = 12k

Let's first distribute.

10k + 5 = 12k

Now let's subtract 10k from both sides.

5 = 2k

Now let's divide both sides by 2.

2.5 = k

The domain of the function is defined as 0 ≤  x ≤ 4.

option A is the correct answer.

A domain of a function refers to "all the values" that can go into a function without resulting in undefined values.

So the domain of a function is the set of x values, while the range of a function is the set of y values.

From the given statement, the range of the function is defined as;

y = vt

where;

y = 60 mph x 4 hr

y = 240 miles

From the given statement, the domain of the function is defined as;

0 ≤  x ≤ 4

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Answer:

9. Let's simplify step-by-step.

Ans. 5x + 24 + 147

Combine Like Terms:

= 5x + 24 + 147

= ( 5x ) + ( 24 + 147 )

= 5x + 171

10.  Let's simplify step-by-step.

Ans. 3x + ( 7x + 10 )

Combine Like Terms:

( 3x + 7x ) + 10

10x +10

11.  Let's simplify step-by-step.

Ans. 5x + ( 2 + 3 )

5x + 5

12. 4 * 10

Ans. 40

13. 3 ( 12x )

Ans. 36x

14. 14r + 9y + 6x

Ans. 14r + 6x + 9y

Hope it helps

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Thank you

Answer:

You did! well done

Step-by-step explanation:

Each person can spend up to 34 at the park.

To maximize their budget and make the most of their day, the Livingston family could consider packing a picnic lunch instead of buying food at the park, looking for free or low-cost activities to do, and taking advantage of any discounts or coupons that may be available. By being mindful of their spending and making smart choices, they can have a fun and memorable day without breaking the bank.

170 ÷ 5 = 34

However, it's important to keep in mind that this is the maximum amount they can spend and they should aim to spend less than that to ensure they have enough money for other activities and unforeseen expenses.

It's also worth noting that there may be additional expenses associated with visiting the park, such as admission fees or the cost of food and drinks. The family should factor in these expenses when determining how much money each person can spend.

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The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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Answer:i think its 115 degres

Step-by-step explanation:

Answer:

  x = log(33)/(3·log(2))

Step-by-step explanation:

The relevant logarithm relation is ...

  log(a^b) = b·log(a)

__

Taking the logarithm of both sides of your equation gives ...

  2^(3x) = 33

  log(2^(3x)) = log(33)

  (3x)·log(2) = log(33)

The coefficient of x is 3·log(2). Dividing by that gives the value of x:

  x = log(33)/(3·log(2))

  x ≈ 1.51851/(3·0.301030) ≈ 1.6814647

Answer:

2/6

Step-by-step explanation:

The LCD of 18 and 6, so when you multiply 2/6, it will be 5/18. So 5/18 is greater than 3/18

Answer:

3/18  is smaller than 2/6

Step-by-step explanation:

Simplifying the equation, we have: z = √√√81 - x²

(i) To determine the domain and range of f(x, y), we need to consider the restrictions on the variables x and y that would make the expression inside the square root function valid.

For the expression inside the square root to be valid, we must have:

81 - x² - 9y² ≥ 0

Simplifying the inequality, we get:

81 ≥ x² + 9y²

This represents an ellipse centered at the origin with major axis length 9 in the x-direction and minor axis length √81 = 9 in the y-direction.

Therefore, the domain of f(x, y) is the region inside or on the boundary of this ellipse.

As for the range, since we are taking the square root of the expression, the range will be all non-negative real numbers (z ≥ 0).

(ii) To sketch the contour of f for different values of z, we can set the function equal to the given values of z and solve for the corresponding curves in the xy-plane.

For z = 0:

0 = √√√81 - x² - 9y²

Simplifying the equation, we have:

x² + 9y² = 81

This represents the boundary of the ellipse mentioned in part (i).

For z = √17:

√17 = √√√81 - x² - 9y²

Simplifying the equation, we have:

x² + 9y² = 64

This represents another ellipse with a smaller major axis length.

For z = 9:

9 = √√√81 - x² - 9y²

Simplifying the equation, we have:

x² + 9y² = 0

This represents a single point (0,0).

(iii) To sketch the traces of f for x = 0 and y = 0, we substitute the corresponding values and solve for the remaining variable.

For x = 0:

z = √√√81 - 0 - 9y²

Simplifying the equation, we have:

z = √√√81 - 9y²

This represents a curve in the yz-plane.

For y = 0:

z = √√√81 - x² - 0

Simplifying the equation, we have:

z = √√√81 - x²

This represents a curve in the xz-plane.

(iv) To sketch the surface of f in three dimensions, we plot the points (x, y, z) that satisfy the equation z = √√√81 - x² - 9y². The surface will resemble a curved shape, similar to an elliptical paraboloid.

Please note that the sketches provided in parts (ii), (iii), and (iv) are best visualized with the help of a graphing software or tool.

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Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:

Volume = Area of Base × Height

Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.

When d = 1:

The area of the base is 2d × 2d = 4 square units

The height is d = 1 unit

Therefore, the volume is:

Volume = Area of Base × Height = 4 × 1 = 4 cubic units

When d = 2:

The area of the base is 2d × 2d = 8 square units

The height is d = 2 units

Therefore, the volume is:

Volume = Area of Base × Height = 8 × 2 = 16 cubic units

When d = 1/2:

The area of the base is 2d × 2d = 1 square unit

The height is d = 1/2 unit

Therefore, the volume is:

Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units

So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

If I am correct I'm pretty sure its about 24 sorry is I am wrong

Answer:

about 24

Step-by-step explanation:

the length is like 6 ½

and the the width is almost 4

Answer:

\( \sf \: 19c + 30 \)

Step-by-step explanation:

Given expression,

→ 1(19c + 30)

Let's simplify the expression,

→ 1(19c + 30)

→ 1(19c) + 1(30)

→ (1 × 19)c + (1 × 30)

→ (19)c + (30)

→ 19c + 30

Hence, answer is 19c + 30.

Answer:

-25

Step-by-step explanation:

\(-5^2=-25\)

Answer:

m=9/2

Step-by-step explanation:

Answer:

-9/-2

Step-by-step explanation:

Use the slope formula... M = Rise/Run = Y2-Y1 all over X2 - X1

Answer:

C ; 20 weeks

Step-by-step explanation:

\(y=0.25x+18\\23=0.25x+18\\23-18=0.25x+18-18\\5=0.25x\\\frac{5}{0.25}=\frac{0.25x}{0.25} \\20=x\)

Answer:

130°

Step-by-step explanation:

22x -2 = 21x +4 ; because alternate interior angles are congruent

22x -21x = 4 +2; subtract 21x and add 2 to both sides

x= 6

the angle measure is

22*6 -2 = 130°

The side lengths of the real object will be 50 inches and 60 inches.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

The given scale factor is 5:1, which means that the dimensions of the scale drawing are 1/5 of the dimensions of the real object.

To find the side lengths of the real object, we can use the ratio of the dimensions in the scale drawing and the real object.

For example, the length of the real object can be found by multiplying the length of the scale drawing by the scale factor:

Real object length = Scale drawing length x Scale factor

Real object length = 10 in x 5

Real object length = 50 in

Similarly, the width of the real object can be found using the same method:

Real object width = Scale drawing width x Scale factor

Real object width = 12 in x 5

Real object width = 60 in

Therefore, the side lengths of the real object are 50 inches and 60 inches.

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The inequality representing the given statement is 3s + 4d ≥ 320, so option B is correct, and the number the minimum number of deluxe flashlights they would need to sell in order to make a profit of $320 is 43.

Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal

Given:

The profit company makes on a standard flashlight = $3,

The profit company makes on a deluxe flashlight = $4,

The company wants to make at least a profit of $320 dollars,

Assume the number of the standard flashlights is s and the number of the deluxe flashlights is d,

The inequality can be written as shown below,

The profit company makes on a standard flashlight × the number of the standard flashlights + The profit company makes on a deluxe flashlight × the number of the deluxe flashlights ≥ 320

3s + 4d ≥ 320

Solve the inequality by putting value, s = 50

50 × 3 + 4d ≥ 320

4d ≥ 320 - 150

d ≥ 170 / 4

d ≥ 42.5 or 43

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