Your goal is to create a college fund for your child. Suppose
you find a fund that offers an APR of 5% How much should
you deposit monthly to accumulate $170,000 in 15 years?

The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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Answer:

The circle's circumference is approximately 106.81 centimeters.

Explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

Therefore, the circumference of the circle is approximately 106.81 centimeters.

The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.

To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.

It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.

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The percentage of the data values that are greater than 130 is 25%

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

The box plot

From the box plot, the five-number summary are

40, 70, 110, 130, and 150

In the above five-number summary, we have

Third quartile = 130

This means that the percentage of the data values that are greater than 130 is 25%

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It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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If the point you end up at is coordinate (0.25, 0) then you would have ran one full lap around the track.

1. The given track is a circular track with a radius of 0.25 miles, and the center of the track is at (0, 0).

2. If you end up at the point (0.25, 0), then you would have ran one full lap around the track. This is because the coordinates of the point you end up at, (0.25, 0), are the same as the coordinates of the circumference of the track, which is located 0.25 miles from the center of the track.

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

first blank: 22

second blank: 1

third blank: 7

fourth blank: 18

Step-by-step explanation:

edge 2020

Answer: 22, 1, 7, 18

The results of a survey of common allergies was organized into a Venn diagram.

Circles D, C, and P overlap. Circle D contains 15. Circle C contains 18. Circle P contains 9. The overlap of circles C and D contains 7. The overlap of circles D and P contains 12. The overlap of C and P contains 10. The overlap of all 3 circles contains 1.

Answer the questions about the following sets:

D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen}

How many people are not allergic to any of the three choices?

✔ 22

How many people are allergic to all three choices?

✔ 1

How many people are allergic to both dogs and cats but not allergic to pollen?

✔ 7

How many people are allergic to cats only?

✔ 18

The graph of the system of equations:

y = 5 - 3x

y = -3x + 4

Can be seen on the image at the end, there we can see that the lines are parallel, and thus, the system has no solutions.

Here we want to solve a system of equations graphically, let's do the first one.

y = 5 - 3x

y = -3x + 4

To solve it graphically, you need to graph both of these lines on the same coordinate axis.

Remember that to graph a line you need to find two points on the line, to get that, you need to evaluate the line.

For example with the first one:

if x = 0

y = 5 - 3*0 = 5

if x = 1

y = 5 - 3*1 = 5 - 3  =2

So we have the points (0, 5)and (1, 2). Now you can graph these points and connect them with a line, that will be the graph of the line.

Once you have both graphs on the coordinate axis, you need to find the point where the graphs intercept. That point will be the solution.

The graph of the system can be seen on the image below, there, we can see that the two lines are parallel lines, thus they never do intercept, then this system of equations has no solutions.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.

In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.

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(81 + 36)

The GCF is 9.

We write 9(9 + 4).

9514 1404 393

Answer:

  $708.87

Step-by-step explanation:

The price with tax included is ...

  660.95 + 0.0725×660.95 = 660.95(1 +0.0725) = 708.87

The total cost of the bicycle with tax is $708.87.

Answer:

$ 708.87

Step-by-step explanation:

Think that, a bicycle has listed price of $ 100,

Listed price              Tax rate            Total cost of the bicycle with sales tax

$ 100                           7.25                       107.25

$ 660.95                                                     x

Let the Total price of the bicycle be x

Now you can create a equation like this,

\(\frac{100}{660.95}=\frac{107.25}{x}\)

Use cross multiplication, and find out the total cost of the bicycle with sales tax.

\(100x=660.95*107.25\)

\(100x=70886.8875\)

\(\frac{100x}{100} =\frac{70886.8875}{100} \\\)

\(x=708.8688\)

Therefore, the total cost of the bicycle with sales tax is,

≈ $ 708.87

Hope this helps you.

Let me know if you have any other questions :-)

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

A. 7√3 in

Step-by-step explanation:

We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:

tan60° = x/7

x = 7tan60°

x = 7√3

Answer:

It's A

Step-by-step explanation:

Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer:

1) Option (b) 32km

2) Option (c) 17

Step-by-step explanation:

According to Pythagoras Theorem,

Hypotenuse²=Perpendicular²+Base²

H²=P²+B²

1) Perpendicular=?

Base=24km

Hypotenuse=40km

40²=P²+24²

1600=P²+576

1600-576=P²

1024=P²

√1024=P

32=P

2) Perpendicular=15

Base=8

Hypotenuse=?

H²=15²+8²

H²=225+64

H²=289

H=√289

H=17

The number of farmers who grew at least one of the three crops is 921

Let's analyze the given information step by step to determine the number of farmers who grew at least one of the three crops, the number of farmers who did not grow any of the three crops, and the number of farmers who grew exactly two of the three crops.

According to the survey results:

125 farmers grow only beans.

107 farmers grow only corn.

87 farmers grow only old.

200 farmers grow wheat and corn.

50 farmers grow wheat and old.

176 farmers grow corn.

To find the number of farmers who grew at least one of the three crops, we need to sum up the number of farmers who grew each crop individually and subtract the number of farmers who grew both combinations of crops:

Number of farmers who grew beans = 125

Number of farmers who grew corn = 107 + 200 + 176 = 483

Number of farmers who grew old = 87 + 50 + 176 = 313

Adding these numbers, we get:

125 + 483 + 313 = 921

Therefore, 921 farmers grew at least one of the three crops.

To find the number of farmers who did not grow any of the three crops, we subtract the total number of farmers in the survey from the number of farmers who grew at least one of the three crops:

500 - 921 = -421

Since we can't have a negative number of farmers, we can conclude that there is an error in the given information.

As for the number of farmers who grew exactly two of the three crops (beans, corn, or old), we don't have enough information to determine this value based on the given data.

In conclusion, the number of farmers who grew at least one of the three crops is 921 (assuming there was an error in the given information). The number of farmers who did not grow any of the three crops cannot be determined with the information provided, and the number of farmers who grew exactly two of the three crops cannot be determined.

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The mid segment would be 1/2 the length of the longest side which is YZ

YZ = 2 x VX

U + 9 = 2u

Subtract 1u from both sides:

U = 9

now you have the value for u, replace in the equation for YZ and solve.

YZ = 9 + 9 = 18

answer: 18

Answer:

Step-by-step explanation:

The equation is poorly written and I cannot unfortunately solve it.

The value of √7 to the nearest hundredth is 2.65.

A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

Here, given number;

     y = \(\sqrt{7}\)

    y = 2.64575....

    y = 2.65

Thus, the value of √7 to the nearest hundredth is 2.65.

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The student's grade point average is 2.32.

The student will not be admitted to the business college.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

(a)

Total grade points earned

= (6 x 4) + (15 x 3) + (31 x 2) + (8 x 1)

= 24 + 45 + 62 + 8

= 139

Total credit hours.

= 6 + 15 + 31 + 8

= 60

Now,

The student's grade point average:

= Total grade points earned / Total credit hours taken

= 139 / 60

= 2.32

(b)

2.32 < 2.5

This means,

The student's grade point average is lower than the required 2.5 GPA for admission to the business college.

Thus,

The student's grade point average is 2.32.

The student will not be admitted to the business college.

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

A. 7

Step-by-step explanation:

No.of unique roots are possible in a seventh-degree polynomial is 7

f(p) = 0.

Since seventh degree polynomial has degree 7, number of roots in a seventh-degree polynomial is 7.

Therefore, the number of unique roots are possible in a seventh-degree polynomial is 7.

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The algebraic expression is x + y = -17

Given,

The sum of two numbers = -17

One number = x

We have to write an algebraic expression for the above condition:

Algebraic expression

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

So, let’s find the algebraic expression:

Given that one number is x. We can take other number as y.

So, the expression will be like:

x + y = -17

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Answer:

no rocky

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

I think it's C and I am always right so it is C! You're welcome!

Answer:

Ddkdkdckkpooooooopppppp

Step-by-step explanation:

Answer:

Here we have:

IxI < 7

This also can be written as:

-7 < x < 7

and:

IyI < 2.

As above, we can write this as:

-2 < y < 2.

Then the graph of this region will be a rectangular area, where the perimeter is a dashed line (because here we use the strictly smaller or strictly larger symbols)

Such that the vertical component goes from -2 to 2, and the horizontal component goes from -7 to 7.

The area would be the area inside that rectangle, where i did not shade it so it is easier to read.