Consider an annuity-immediate with monthly payments for twenty years. The
payments are level in the course of each year, then increase by 2% for the next year. Find the present value of this annuity if the initial payment is $1,000 and
i=4%

Using a standard normal distribution table, the value of z₀ is -0.64

To find z₀, we need to use the standard normal distribution table or calculator. We know that the area under the standard normal curve between z₀ and 2.2 is 0.7258.

Using a standard normal distribution table or calculator, we can find the z-score corresponding to 0.7258.

From the table, we can find that the closest value to 0.7258 is 0.7257, and the corresponding z-score is approximately 0.61.

Therefore, we have:

P(z₀ < z < 2.2) = 0.7258

P(z < 2.2) - P(z < z₀) = 0.7258

Using the z-score table again, we can find that P(z < 2.2) is approximately 0.9861.

So we have:

0.9861 - P(z < z₀) = 0.7258

P(z < z₀) = 0.2603

Using the z-score table again, we can find that the z-score corresponding to 0.2603 is approximately -0.64.

Therefore, we have:

z₀ = -0.64

Rounding to at least four decimal places, we get:

z₀ = -0.6400

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The sample suggests that the true mean is likely to be between 98.0°F and 98.2°F, which is lower than 98.6°F.  98.6°F overestimates the mean body temperature of all healthy humans.

Standard deviation is defined as the measure of how spread out numbers are. It measures the average distance between each number in a set of data and the mean. It is used to measure the variation and dispersion of a set of data from its mean.

A 99% confidence interval estimate of the mean body temperature for all healthy humans can be calculated using the following formula: mean ± 2*standard deviation/square root of the sample size. In this case, the confidence interval is 98.1°F ± 0.12°F. This means that the mean body temperature of all healthy humans is likely to be between 98.0°F and 98.2°F.

This sample suggests that 98.6°F is not an accurate representation of the mean body temperature of all healthy humans.

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Answer:

I do not have access to drawing tools to create a graph. However, I can explain how to plot the function h on the graph based on the given information.

The function h(x) has two parts:

For x < -3, the value of h(x) is J-4.

For x >= -3, the value of h(x) is x-3.

To plot this on a graph, you would need to draw a vertical line at x = -3 to separate the two parts of the function. Then, for x < -3, you would plot a horizontal line at a height of J-4 to represent the constant value of h(x) in that region. For x >= -3, you would plot the line y = x-3.

I hope this explanation helps you to plot the function h on the graph!

Step-by-step explanation:

Given - The expression as

[tex]\frac{3.07+2^4}{5.03-1.79}[/tex]

To find - the solution of the expression

Explanation To simplify the expression, we will simply the terms in the expression

[tex]\frac{3.07+2^4}{5.03-1.79} =\frac{3.07+16}{3.24} =5.885[/tex]

Hence the value of the expression is 5.885

Final answer- The value is 5.885

Answer:

11, 20.

Step-by-step explanation:

5,6,8, 11 ,15, 20.

Answer:

below

Step-by-step explanation:

Given cos, you will have to use this to calculate sin because csc is  1/ sin

Remember    cos^2 + sin^2 = 1

                        (2/5)^2 + sin^2 = 1

                                  sin^2 = 21/25  

                                    sin = sqrt (21) / 5     (ignoring negative root)

csc = 1/sin = 5 / sqrt(21)

Answer:

Tahlia was correct in remembering that you can find the slope of a line using the slope formula.

She was also correct that the slope is 0.5.

However, if you use the slope-intercept formula y = mx + b, you still have to find b (the y-intercept) by plugging in one of the two points and the slope.

So, if we plug in the first point and the slope into the line, we can find b and thus the full equation of the line:

[tex]-7.5=0.5(-3)+b\\-7.5=-1.5+b\\b=-6\\\\y=0.5x-6[/tex]

Answer: 5/18.  or 5 over 18

Step-by-step explanation:

5 is the number of kids that want pancakes

13 is the number of kids that want waffles

18 is the total number of students

The question is asking what is the ratio of the number of students who want pancakes to the total number of students?

So you just do

5 kids that want pancakes over 18 kids total or 5/18

Subtract 4x 4 x from 6x 6 x . Divide each term in 2x=−12 2 x = - 12 by 2 2 and simplify. Divide each term in 2x=−12 2 x = - 12 by 2 2 . Simplify the left side.

Answer:

8x^11

Step-by-step explanation:

x^8 * (2x)^3

x^8 * (8x^3)

8x^11

The variability of the mean is 0.154

The total of all values divided by all of the values constitutes the result of a set, also called as the arithmetic mean. It is considered to be the most popular central trend indicator, and the word "mean" is commonly used to describe it. The average of a figure is known to as the average.

We are Given a normal distribution, the MAD and standard deviation (SD) are roughly inversely proportional to one another as follows:

=> MAD = 1.4826 × SD

Here we can calculate the standard deviation as follows:

=> SD = MAD / 1.4826

Since the MAD in this instance is provided as 3.2,

=> SD ≈ 3.2 / 1.4826 ≈ 2.16

The standard error of the mean (SEM), can be determined as follows, then gives the variability of the mean.

=> SEM ≈ SD / sqrt(n)

=> CV Equals SD/mean

2.16 / 14 ≈ 0.154

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Answer:

1. 6/18 = 1/3

   9/21 = 3/7

2. 4/6 = 2/3

   2/4 = 1/2

3. 6/12 = 1/2

   8/12 = 2/3

4. 2/8 = 1/4

   3/6 = 1/2

5. 7/21 = 1/3

   8/10 = 4/5

6. 9/12 = 3/4

   12/20 = 3/5

7. 8/16 = 1/2

   10/25 = 2/5

Answer:

15 + t = greather than 180

Step-by-step explanation:

Answer:

The interest earned would be $600.

To calculate this, you would subtract the initial investment from the final amount:

$5,600 - $5,000 = $600.

Therefore, the interest earned is $600.

Answer:

d = |c1-c2|/√(a2 + b2).

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

This is because angles A, B, C, and D are all 40° and angle o looks to be bigger than 40° but is still an acute angle so forth being 80°

Let's say the cost to rent each chair is "x" and the cost to rent each table is "y". Then we can set up two equations based on the given information:

3x + 2y = 21 (for the first rental)

8x + 4y = 45 (for the second rental)

We can simplify the second equation by dividing both sides by 4:

2x + y = 11.25

Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:

3x + 2y = 21

2x + y = 11.25

From the second equation, we can solve for y in terms of x:

y = 11.25 - 2x

Then we can substitute this expression for y in the first equation:

3x + 2(11.25 - 2x) = 21

Simplifying and solving for x, we get:

3x + 22.5 - 4x = 21

-x + 22.5 = 21

-x = -1.5

x = 1.5

So the cost to rent each chair is $1.50. We can substitute this value back into either of the original equations to solve for y:

3(1.5) + 2y = 21

4.5 + 2y = 21

2y = 16.5

y = 8.25

So the cost to rent each table is $8.25. Therefore, the answer is $1.50 for each chair and $8.25 for each table.

Answer:

Below

Step-by-step explanation:

x = original amount of fabric

2/9 * x = amount of cut fabric

8/9 * ( 2/9 * x) = amount of fabric used

8/9 * 2/9 * x =   ( 8 *2) / ( 9 * 9) * x = 16 / 81  x

 she used 16/81  of her fabric

Answer: 2/3

Step-by-step explanation:   y1-y2    3-(-1) = 4       simplify  4/6=2/3

                                               x1-x2     4-(-2)= 6

Slope is described as "the rise over the run," meaning that it's the fraction of "the change in the y-values compared to the change in the x-values."

In this situation
    - the change in the y-values is 3 - (-1) = 4.
    - the change in the x-values is 4 - (-2) = 6.
so the fraction is 4/6 or 2/3.

As a general formula, the formula for slope is [tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex].

      [tex]m = \dfrac{3-(-1)}{4-(-2)}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

The response to the given question would be that Because it has a interest higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The interest rate of the loan is defined as this ratio.

The following would be the order of 2000 simple interest generated on an investment, from least to most:

2000 invested for 20 years at 3% simple interest

2000 invested for three years at 10% simple interest

2000 invested at 10% simple interest for nine years

Because of its longer length and lower interest rate than the other two alternatives, Option 2 would yield the least amount of interest.

Due to its higher interest rate and longer period, option 3 would generate more interest than option 2.

Because it has a higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.

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Answer:

Step-by-step explanation:

If you know how to subtract which you should the answer is 2.

How many more means subtraction.

Hope that is helpful!

The key features of the parabola include the following:

A) opens down

C) directrix at y = 1/8

D) vertex at (-1/2, 0).

Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:

y = a(x - h)² + k.

Where:

Based on the information provided about the parabola, we have:

4x^2 + 4x + 2y + 1 = 0

2(y + 1/2) = -4(x + 1/2)^2 + 1

(y + 1/2) = -2(x + 1/2)^2 + 1/2

By comparing to the standard form, we have:

Vertex, (h, k) = (-1/2, 0).

Additionally, the distance between the vertex and the directrix is given by:

y = |1/(4a)|

y = |1/(4 × -2)|

y = |-1/8|

y = 1/8.

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Therefore , the solution of the given problem of rational comes out to be  53.00 for the given rational number after rounding off.

The percentage (not the percentage) of two integers can be used to represent rational numbers. A reasonable fraction is one with a non-zero denominator. Rational values are including 1/2, 1/5, but they also include 3/4. Additionally, "0" could be expression as a real purpose in a variety of forms, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, along with others. Seven is a reasonable amount. A rational number can be obtained by dividing two factors.

Here,

Given :

rational number or integer is 53.121

To round it to the nearest half so ,

According to rounding off the integer , we can round off to 54 when it is 53.5 or above .

But since it is below than that

We get answer as 53.00 for the given rational number after rounding off.

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The vertex of the function is,

⇒ Vertex = (1, - 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = -x² + 2x - 5

Now,

We can change the quadratic function in the form,

⇒ f (x) = a (x - h)² + k

Hence, We get;

⇒ f (x) = - x² + 2x - 5

⇒ f (x) = - (x² - 2x + 1 - 1) - 5

⇒ f (x) = - (x - 1)² + 1 - 5

⇒ f (x) = - (x - 1)² - 4

Thus, The vertex of the function is,

⇒ Vertex = (1, - 4)

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We simplify the summation to get:

S₄ = 8*(3ⁿ⁻¹)

Remember that the large sigma means that we need to add from the lower number to the larger number.

The particular problem here is that "n" is not the index in the summation, so we can't evaluate that variable, we will just have 4 terms (for k = 1 to k = 4) but the variable k does not appear, so we will  have 4 times the same term:

S₄ = 2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹)

S₄ = 4*2*(3ⁿ⁻¹)

S₄ = 8*(3ⁿ⁻¹)

That is the simplification we can do.

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Answer:

3,418.32yd³

Step-by-step explanation:

For volume you do the area (8)² multiplied by the height (17). 8 x 8 = 64. 64 x 17 = 1,088. you then multiply 1,088 by 3.14, the π, which is 3,416.32. We are using yards so the end result is 3,418.32yd³.

Don't understand? Yeah, I didn't at first either, I had to refresh my memory. If you don't understand, https://youtu.be/fGVlL47TKAw helped me. Have a wonderful day!

∠1 = 68°

∠2 = 22°

side 3 = 5 cm

side 4 = 19.5 cm

5: perimeter of ΔABC = 45 cm

6: perimeter of ΔPQR = 30 cm

7: Area of ΔPQR = 30 cm²

Similar triangles are triangles that have the same shape but may have different sizes. This means that corresponding angles of similar triangles are equal, and corresponding sides are in proportion.

The hotspots can be completed as follow:

∠1 = 180° - 22° - 90° = 68°  (angle sum in a triangle)

∠2 = 22° (similar triangle)

side 3 = √(13²-12²) = 5 cm (Pythagoras)

side 4 = √(18²+7.5²) = 19.5 cm (Pythagoras)

5: perimeter of ΔABC = AB + BC + AC = 7.5 + 19.5 + 18 = 45 cm

6: perimeter of ΔPQR = PQ + QR + PR = 5 + 13 + 12 = 30 cm

7: Area of ΔPQR = 1/2 * base * height = 1/2 * 12 * 5 = 30 cm²

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Using the Pythagorean theorem we know that the rest 2 sides of the given right triangle are 27 inches long.

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry.

The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.

So, we know the Pythagorean theorem which is:

H² = a² + b²

We know that:

H² = a² + b²

54² = a² + b²

Suppose that the given right triangle is also an isosceles triangle with the rest of the sides being of the same length. Then,

54/2 = 27

Similarly,

54² = a² + b²

54² = 27² + 27²

Therefore, using the Pythagorean theorem we know that the rest 2 sides of the given right triangle are 27 inches long.

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If the woman receives $24 per day, the amount of the man's daily wage will be $42.

In mathematics, a ratio shows how many times one number contains another. Its says how much of one thing there is compared to another thing.

Let m be the man's hourly wage

Let w be the woman's hourly wage

We are told that the woman's daily wage is $24, which we can express in terms of her hourly wage as: w * 8 = $24

Solving for w, we get:

w = $24 / 8

w = $3

We are also told that the ratio of the man's hourly wage to the woman's hourly wage is 7:5, which we can express as: m / w = 7 / 5

Substituting w = $3, we get:

m / 3 = 7 / 5

Solving for m, we get:

m = (7 / 5) * 3

m = $4.20

Therefore, the man's daily wage is:

m * 10 = $4.20 * 10

m = $42

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Answer:

Using the slope-intercept form, the slope is −2 .

Step-by-step explanation:

Step-by-step explanation:

solution

Equation of line,

y=-2x-2

2x+y=2 - - - - - - -1

Now,

slope of line,

m= -x coefficient/ y coefficient

= -2/1

= -2

Slope of required line which is perpendicular to the line

m.m = -1

-2.m = -1

m = -1/-2

m =1/2