You are working as a financial planner. a couple has asked you to put together an investment plan for the education of their daughter. she is a bright seven-year-old (her birthday is today), and everyone hopes she will go to university after high school in 10 years, on her 17th birthday. you estimate that today the cost of a year of university is $17,500, including the cost of tuition, books, accommodation, food, and clothing. you forecast that the annual inflation rate will be 5. 6%. you may assume that these costs are incurred at the start of each university year. a typical university program lasts 4 years. the effective annual interest rate is 6. 75% and is nominal. a. suppose the couple invests money on her birthday, starting today and ending one year before she starts university. how much must they invest each year to have money to send their daughter to university? (do not round intermediate calculations. round your answer to 2 decimal places. )

investment per year $



b. if the couple waits 1 year, until their daughter’s 8th birthday, how much more do they need to invest annually? (do not round intermediate calculations. round your answer to 2 decimal places. )

additional yearly payments $

-19

1) Let's evaluate that

-9-16-12+18 Add the negative ones

-25 -12+18

-25+6

-19

2) Hence, the answer is -19

Answer:

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

Step-by-step explanation:

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

y+1 = 1/4x-1

y = 1/4x -2 -which is the equation of the line

Answer:

The bond yield is 6.80%.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

You purchase a bond with a coupon rate of 8.5% and par value of $2,000. The value of the bond rose to $2,500. What is the bond yield?

The bond can now be calculated as follows:

Coupon payment = Coupon rate * Bond per value = 8.5% * $2,000 = $170

Bond yield = Coupon payment / Current value of the bond = $170 / $2,500 = 0.068, or 6.80%

Therefore, the bond yield is 6.80%.

The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

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Answer:

It is the last one: (4x-9)(x+8)

Step-by-step explanation:

You have to split the "b", or split the 23x so that you can perform grouping, and then combine.

Answer:

(4x-9)(x+8)is the correct answer

To calculate the 90% confidence interval for the average EPS of all industrials listed on the DJIA, we will use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / √sample size)

Step 1: Find the critical value.
Since we want a 90% confidence interval, the corresponding critical value can be obtained from the z-table. The critical value for a 90% confidence level is 1.645.

Step 2: Calculate the margin of error.
The margin of error is given by (critical value * standard deviation / √sample size).
Substituting the values, we get: 1.645 * 0.395 / √9 = 0.29175.

Step 3: Calculate the confidence interval.
The confidence interval is given by the sample mean ± margin of error.
Substituting the values, we get: 1.85 ± 0.29175.

The 90% confidence interval for the average EPS of all industrials listed on the DJIA is (1.55825, 2.14175).

We can be 90% confident that the true average EPS of all industrials listed on the DJIA falls within the range of 1.55825 to 2.14175.

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0 degrees Celsius + 0 degrees Celsius = 0 degrees Celsius = 32 degrees Fahrenheit.

To convert Celsius to Fahrenheit, we use the formula:

°F = (°C × 9/5) + 32

Let's calculate the conversion for 0 degrees Celsius:

°F = (0 × 9/5) + 32

°F = 0 + 32

°F = 32

Therefore, 0 degrees Celsius is equal to 32 degrees Fahrenheit.

Now, let's consider the addition of 0 degrees Celsius and 0 degrees Celsius:

0 degrees Celsius + 0 degrees Celsius = 0 + 0 = 0

Since 0 degrees Celsius is equivalent to 32 degrees Fahrenheit, the sum of 0 degrees Celsius and 0 degrees Celsius is 0, not 64 degrees Fahrenheit.

So, 0 degrees Celsius + 0 degrees Celsius = 0 degrees Celsius = 32 degrees Fahrenheit.

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\(\Large{\red{\underline{\underline{\mathrm{ SOLUTION :- }}}}}\)

Here it is given that , a postal service charges a flat rate of 11.10 and a additional rate of 3 / kg .We need to write the equation in slope intercept form . And let ,

\(\sf\qquad\longrightarrow Total \ cost \ = \ y\\\)

\(\sf\qquad\longrightarrow Total\ weight\ = \ x \)

So the total cost would be the sum of flat rate plus the cost of the total weight . Therefore,

\(\sf\qquad\longrightarrow Cost_{weight}= \$3 \times x =\pink{\$3x}\)

Therefore the total cost would be,

\(\sf\qquad\longrightarrow Cost_{total}= Cost_{flat}+Cost_{weight}\\\)

\(\sf\qquad\longrightarrow y = \$11 + \$ 3x \)

Rearrange in slope intercept form , which is y = mx + c , as ;

\(\sf\qquad\longrightarrow \boxed{\pink{\sf y = \$3x + \$11}}\)

Answer:

y = -7x + 10

Step-by-step explanation:

As the y's are decreasing by 7, the x are increasing by 1.  This gives us a slope of -7.  When x is 0, y is 10 that is our y intercept.

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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When measuring the effects of a new diuretic medication, hourly urine output represents the ratio level of measurement.

What is ratio level of measurement?

Ratio level of measurement is a type of measurement that features a true zero point, meaning that the value 0 represents the absence of the characteristic being measured.

Some examples of ratio level measurements include weight, height, length, distance, speed, and many others. In this case, the hourly urine output of subjects is measured to determine the effects of a new diuretic medication.

The hourly urine output is a ratio measurement because it has a true zero point, which is the absence of urine output. In other words, if there is no urine output, the value would be 0, which represents the absence of the characteristic being measured.

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Volume of pyramid/ volume of prism=1. Option A

From the information given, we have that;

The pyramid height is three times the height of the prism.

But note that;

The formula of the volume of pyramid = 1/3 × base × height

The volume of prism= base × height

We should know that the  height of pyramid is 3 times more than the height of prism so that if the height of prism is a = the volume of prism is a*base

Substitute the values, we get;

Height of prism is 3a so that =  the volume of pyramid is =

=  1 /3  × 3a × base =a × base

Divide the values, we get;

Ratio is 1/1

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Answer:

n = log(\(\frac{100}{x^2}\))

Step-by-step explanation:

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Answer:

Step-by-step explanation:

Let the height be h units

then the base is h+3 units

Area = (1/2)(base)(height)

= (1/2)(h)(h+3) or (1/2)(h^2 + 3h)

The value of x and y is 19 and 132.

What is equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables. More than one variable may be present in a linear equation. An equation is said to be linear if the highest power of a variable is consistently 1. Another name for it is a one-degree equation.

Sol- as per the given question y= 8x -20

We have to add the equations

(2x+10)° + (8x-20)°= 180°

= (10x-10)° = 180°

= (10x)° = 190°

= X= 19

= Y = 8.19-20 = 132

Thus,

X = 19 and Y = 132.

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The yield of the 20-year 7% annual interest bond selling for $1,084 is approximately 3.12%(d).

To calculate the yield of a bond, we can use the formula:

Yield = (Annual Interest / Bond Price) × 100

We are given the information with Annual Interest = 7% of the face value = 0.07 × $1,000 = $70

Bond Price = $1,084

Yield = (70 / 1084) × 100 ≈ 3.12%

Therefore, the yield of the bond is approximately 3.12%. So the correct option is d which means that the yield of the bond is approximately 3.12%.

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(a) The 95% confidence interval for proportion of residents in Muscat who consider television news as their major source of news is (0.485, 0.615).

(b) The sample-size of approximately 384 would be necessary to estimate the population proportion with a maximum error of 0.05 at a 95% confidence level.

To construct a confidence-interval for proportion of residents in Muscat who consider television news as their "major-source" of news, we use the  formula;

The Confidence-Interval = Sample Proportion ± Margin of Error

Part (a) : To calculate confidence-interval, we first find the sample proportion (p') and margin-of-error.

The Sample-Proportion (p') = Number of successes / Sample size

p' = 110 / 200 = 0.55,

The Margin-of-Error (ME) = Critical value × Standard Error

The "critical-value" depends on desired confidence-level. For 95% confidence-level, the "critical-value" corresponds to a z-score of 1.96.

The Standard-Error (SE) = √((p' × (1 - p')) / n)

Where n = sample size,

SE = √((0.55 × (1 - 0.55)) / 200) ≈ 0.033

Now we calculate the margin-of-error as :

ME = 1.96 × 0.033 ≈ 0.065,

Now, we construct the confidence interval:

Confidence Interval = 0.55 ± 0.065

Confidence Interval ≈ (0.485, 0.615)

So, the required confidence-interval is (0.485, 0.615).

Part (b) : To determine the sample size required to estimate the population proportion with "maximum-error" of 0.05 at a 95% confidence level, we use the formula:

Sample Size (n) = (Z² × p' × (1 - p'))/E²,

Where Z = critical value corresponding to desired confidence level,

p' = estimated proportion, and E = maximum error,

Using a Z-score of 1.96, and p' = 0.5 and E = 0.05, we calculate the sample size as :

n = (1.96 × 0.5 × (1 - 0.5)) / 0.05²

n ≈ 384.16

Therefore, the required sample-size is 384.

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Solution

Step 1

A)The domain refers to all values of x for which the function remains defined. Any value of x that makes the function undefined is out of the domain. This can be achieved by factorizing the denominator of the known function to get the values of x that make the function undefined. All other values of x that make the function defined are part of the domain.

Step 2

B)Factorize the denominator

Hence factorizing further we will have

Hence, the domain of the function given is all real values of x except -3 and 5/6

The reasonable estimate for the limit of f(x) as x approaches π/4 is √2.

To find the limit, we need to evaluate the function f(x) as x approaches π/4. The function f(x) is not explicitly defined, so we'll need to use some known mathematical properties. One property is that the limit of the square root of x as x approaches a is equal to the square root of the limit of x as x approaches a (provided the limit exists).

Applying this property, we can rewrite the limit as the square root of the limit of x as x approaches π/4. Since x is approaching π/4, the value of x itself will be very close to π/4.

The limit of x as x approaches π/4 is simply π/4. Taking the square root of π/4 gives us the final answer, which is √2. Therefore, the reasonable estimate for the limit of f(x) as x approaches π/4 is √2.

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Answer:

a) i) y = - 5/3

  ii) y = 4/3

b) i) x = 1

   ii) x = -3/4

Step-by-step explanation:

\(y=\dfrac23x +\dfrac13\)

a) i) \(x=-3\)

\(\implies y=\dfrac23(-3) +\dfrac13\\\\\\\implies y=\dfrac{-6}{3} +\dfrac13\\\\\\\implies y=\dfrac{1-6}{3} \\\\\\\implies y=-\dfrac53\)

ii) \(x=1\frac12=\dfrac32\)

\(\implies y=\dfrac23\left(\dfrac32\right) +\dfrac13\\\\\\\implies y=\dfrac{6}{6}+\dfrac13\\\\\\\implies y=\dfrac{3}{3}+\dfrac13\\\\\\\implies y=\dfrac{3+1}{3}\\\\\\\implies y=\dfrac43\)

b) i) \(y=1\)

\(\implies \dfrac23x +\dfrac13=1\\\\\\\implies \dfrac23x =1-\dfrac13\\\\\\\implies \dfrac23x =\dfrac23\\\\\\\implies x =1\)

ii) \(y=-\dfrac16\)

\(\implies \dfrac23x +\dfrac13=-\dfrac16\\\\\\\implies \dfrac23x =-\dfrac12\\\\\\\implies x =-\dfrac12 \div \dfrac23=-\dfrac12 \times\dfrac32=-\dfrac34\)

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The A. height of the flag pole in the larger triangle corresponds to the height of the person in the smaller triangle.

The vertical side of the large triangle corresponds to the C. vertical side of the small triangle.

Corresponding sides are sides of two or more geometric figures that are in the same relative position and have the same length. Corresponding sides are often compared when working with similar figures, which are figures that have the same shape but may have different sizes.

The flag pole in the larger triangle of the supplied triangles is the same height as the person in the smaller triangle. Thus, the vertical side of the little triangle matches the vertical side of the huge triangle.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

Answers

Selecting a green marble on the second

draw if the first marble is blue.

Answer:

Selecting a white marble on the first

draw and red marble on the second

draw.

Answer:

Selecting a red marbles on both draws.

Answer:

Selecting a red or white on the first

draw and green or blue on the second

draw.

Answer:  

Selecting a white marble on the first

draw and a white or blue on the second

draw.

Step-by-step explanation:

(a) There are 81 possible answer sequences for the four questions.

(b) The probability of getting all four answers correct when guessing is approximately 0.01235 when rounded to five decimal places.

(c) The probability of answering at least one question correctly when guessing is approximately 0.51775 when rounded to five decimal places.

(a) Since there are three possible answers for each of the four questions, there are a total of 3^4 = 81 possible answer sequences for the four questions.

(b) If you are guessing on each question, the probability of getting one question correct is 1/3. Since there are four questions, the probability of getting all four correct is (1/3)^4 = 1/81, which is approximately 0.01235 when rounded to five decimal places.

(c) The probability of not getting any question correct is (2/3)^4, since there are two incorrect answers for each question and we are guessing on all four questions. Therefore, the probability of getting at least one question correct is 1 - (2/3)^4, which is approximately 0.51775 when rounded to five decimal places.

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The exponential equation representing the given table is -

y = 2.84(1.072)ˣ.

Given is a function table as shown in below -

{X}   0     5        10       15       20

{Y}   0  4.02   5.69   6.97    8.05

Let the expression be -

y = A(B)ˣ

At {x} = 5, y = 4.02.

We can write -

4.02 = A(B)⁵                                               ... Eq { 1 }

At {x} = 10, {y} = 5.69

We can write -

5.69 = A(B)¹⁰                                            ... Eq { 2 }

Refer to the graph. The point of intersection represents -

A = 2.84
B = 1.072

The equation would be -

y = 2.84(1.072)ˣ                                      ... Eq { 3 }

Therefore, the exponential equation representing the given table is -

y = 2.84(1.072)ˣ.

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The sample size should be 24.

What is the sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Here, we have

Given

Margin of error = 300

confidence level = 0.9

standard deviation = 900

Assuming the standard deviation to be of population

ME = Z(0.1/2) × σ/√n

300 = 1.645 × 900/√n

n =  {(1.645 × 900)300}²

n = 24

Hence, the sample size should be 24.

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Answer:

Equation of circle in standard form with centre (0, – 10) and radius 6. \(\mathbf{x^2+(y+10)^2=36}\)

Step-by-step explanation:

We need to write equation of circle in standard form with centre (0, – 10) and radius 6.

The equation of circle is: \((x-h)^2+(y-k)^2=r^2\)

where (h,k) is centre of circle and r is radius

We are given centre (0,-10) so, h=0, k=-10 and radius r = 6

Putting values and finding equation:

\((x-h)^2+(y-k)^2=r^2\\(x-0)^2+(y-(-10))^2=(6)^2\\x^2+(y+10)^2=36\)

So, equation of circle in standard form with centre (0, – 10) and radius 6. \(\mathbf{x^2+(y+10)^2=36}\)

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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