Find the final value of $2000 investment at an interest rate of 2%compounded quarterly (4 times a year) for 8 years

Answer:

missing length= 2.8

Step-by-step explanation:

a^2+b^2=c^2

a^2+1^2=3^2

a^2=3^2-1^2

a^2=8

a=2.8284271247461

a=2.8

Check the picture below.

let's firstly find side "t"

[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ t = \sqrt{18^2+46^2~-~2(18)(46)\cos(158^o)} \implies t = \sqrt{ 2440 - 1371168 \cos(158^o) } \\\\\\ t \approx \sqrt{ 2440 - (-1535.42) } \implies t \approx \sqrt{ 3975.42 } \implies t \approx 63.05 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin( R )}{18}\approx\cfrac{\sin( 158^o )}{63.05}\implies 63.05\sin(R)\approx18\sin(158^o) \\\\\\ \sin(R)\approx\cfrac{18\sin(158^o)}{63.05} \implies R\approx\sin^{-1}\left( ~~ \cfrac{18\sin( 158^o)}{63.05} ~~\right)\implies \boxed{R\approx 6.14^o}[/tex]

Make sure your calculator is in Degree mode.

part A.

The equation of the ellipse is:

x² / 280900 + y² / 198025 = 1

part B.

The area of the ellipse at the White House is found to be  741,022.16 square feet.

The standard form equation for an ellipse is given as :

(x² / a²) + (y² / b²) = 1

Where "a" =  half the length of the major axis

b =   half the length of the minor axis.

length of the major axis = 1060 feet,

a = 1060 / 2 = 530 feet.

The length of the minor axis is 890 feet,

b = 890 / 2

b= 445 feet.

x² / 530² + y² / 445² = 1

x² / 280900 + y² / 198025 = 1

B.

a = 530 feet and b = 445 feet.

Area = π * 530 * 445

A = 741,022.16 square feet

Learn more about ellipse at:

https://brainly.com/question/16904744

#SPJ1

Answer: $34.20

Step-by-step explanation:

$3.80 is for 1 book.

Since she would buy 9 books, you would do the equation of 3.80 x 9.

You'll get the answer of 34.2, but then by making that a dollar amount it would be 34.20. Add the dollar sign, $34.20, and wahlah!

The company will use approximately 7 trucks.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To calculate the number of trucks needed, divide the total number of bicycles by the number of bicycles that can fit in each truck:

328 bicycles / 50 bicycles per truck = 6.56 trucks.

Since you can't have a fraction of a truck, the company will need to round up to the nearest whole number. Therefore, the company will use 7 trucks to ship the 328 bicycles across the country.

Know more about divide here;

https://brainly.com/question/15381501

#SPJ11

Answer: it would be 13 beeps

Step-by-step explanation:

it's the second answer 2 and 3 are same side interior angles

Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

The statement is False" Some seventh graders" isn't a set.

we know, set is a well- defined collection of distinct objects, which are appertained to as rudiments or members of the set.

For illustration, consider the set A = { 1, 2, 3}. This set contains the rudiments 1, 2, and 3.

It's a expression that describes a group of individualities without furnishing a well- defined collection of rudiments.

A set is a well- defined collection of distinct objects.

To represent a set, we generally use curled braces and list the rudiments within the set.

For illustration,{ 1, 2, 3} is a set containing the rudiments 1, 2, and 3.

Learn more about Set here:

https://brainly.com/question/8053622

#SPJ1

The HCF of each of the pair of numbers are 2, 6 and 4

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

The HCF of each of the pair of numbers is calculated as follows

Pair 1

2 = 2

36 = 2 * 2 * 3 * 3

The highest common factor above is

HCF = 2

Pair 2

42 = 2 * 3 * 7

24 = 2 * 2 * 2 * 3

The highest common factor above is

HCF = 2 * 3

Evaluate

HCF = 6

Pair 3

8 = 2 * 2 * 2

12 = 2 * 2 * 3

The highest common factor above is

HCF = 2 * 2

Evaluate

HCF = 4

Hence, the HCF of each of the pair of numbers are 2, 6 and 4

The venn diagrams are also attached

Read more about HCF at

https://brainly.com/question/26569165

#SPJ1

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer:

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

Given data:

Put the data in the ascending order:

The mode, the most repeated term, is 11.

The median is the middle term, also 11.

The mean is the average:

Answer & step-by-step explanation:

Let us find the median of the data set

First, you should arrange the data in ascending to descending to find the median.

4, 7, 10, 11, 11, 12, 16

Now let us use the given formula to find the median.

[tex]\sf \dfrac{n+1}{2} =--^t^h data[/tex]

Here,

n → the number of elements

Let us find it now.

[tex]\sf Median= \dfrac{n+1}{2}\\\\\sf Median=\dfrac{7+1}{2} =4^t^h data\\\\Median=11[/tex]

Let us find the mode of the data set.

Mode is the most frequent number in the data set.

∴ mode → 11

Let us find the mean of the data set

Mean is the average of a data set.

To find that, you have to add all the data together and divide it by number of elements.

Mean = Σx ÷ n

Mean = ( 10 + 11 + 4 + 7 + 12 + 11 + 16 ) ÷ 7

Mean =  71 ÷ 7

Mean =  10.14

The equation of the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d

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

T(d) = d² + 20d

A(d) = 12d

The function B(d) is the difference between the functions A(d) and T(d)

Using the above as a guide, we have the following:

B(d) = T(d) - A(d)

In terms of d, we have

B(d) = d² + 20d - 12d

Evaluate the difference

B(d) = d² + 8d

Hence, the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

Answer: t = 7°

Step-by-step explanation:

        We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. Using this information we can create an equation to solve for t.

   Given:

180° = 90° + 6t° + 6° + 7t° - 7°

   Combine like terms:

180° = 89° + 13t°

   Subtract 89 from both sides of the equation:

91° = 13t°

   Divide both sides of the equation by 13:

t = 7°

Answer:

x = 3 , y = 1

Step-by-step explanation:

[tex]2^{x+y} = 16\\2^{x+y} = 2^4\\x + y = 4 ---- (1)\\\\3^{x-y} = 9\\3^{x-y} = 3^2\\x-y = 2 ----- (2)\\\\Adding 1 and 2 , we get ,\\ 2x = 6\\x = 3\\y = 1[/tex]

Answer:

y = 1, x = 3

Step-by-step explanation:

1.) Based on the given, we have [tex]2^{x+y}[/tex] = 16, and [tex]3^{x-y}[/tex]=9. Since [tex]2^4[/tex] is equal to 16, that means that x + y = 4. Since [tex]3^2[/tex] is equal to 9, that means that x - y = 2

2.) Now, we have a system of equations. By using elimination (adding the two together), you get x + x + y - y = 2 + 4. By simplifying, the y cancels out and you get 2x = 6. Finally, you get x = 3.

3.) To end, you need to find y. Since we have x - y = 2, and x = 3, that means that 3 - y = 2, meaning y = 1.

Answer:

$38.80

Step-by-step explanation:

Answer:

  (c)  379.2 in²

Step-by-step explanation:

You want to know the total surface area of 6 cylinders of diameter 3.5 inches and height 4 inches.

The area of a cylinder in terms of diameter and height can be found by ...

  A = πd(d/2 +h)

The area of 6 cylinders with d=3.5 and h=4 is ...

  6A = 6π(3.5 in)(3.5 in/2 +4 in) ≈ 379.2 in²

The minimum wrap needed is 379.2 square inches.

<95141404393>

The complement set of S is {1, 3, 5, 8, 9, 10}.

To find the complement set of S, we need to identify all the elements in the universal set U that are not present in set S.

Given:

Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Set S = {2, 4, 6, 7}

The complement set of S, denoted as S', consists of all the elements in U that are not in S.

Complement set of S (S') = U - S

To find S', we subtract the elements of S from U:

S' = {1, 3, 5, 8, 9, 10}

Know more about complement set here:

https://brainly.com/question/24341632

#SPJ11

To determine which ordered pairs satisfy the equation 3x - 4y = 21, we can substitute the given x and y values into the equation and check if the equation holds true.

Let's check each ordered pair:

1. (-1, -6):

  Substituting x = -1 and y = -6 into the equation: 3(-1) - 4(-6) = 3 + 24 = 27, which is not equal to 21. Therefore, (-1, -6) is not a solution.

2. (7, 0):

  Substituting x = 7 and y = 0 into the equation: 3(7) - 4(0) = 21, which is equal to 21. Therefore, (7, 0) is a solution.

3. (-3, 3):

  Substituting x = -3 and y = 3 into the equation: 3(-3) - 4(3) = -9 - 12 = -21, which is not equal to 21. Therefore, (-3, 3) is not a solution.

4. (11, 3):

  Substituting x = 11 and y = 3 into the equation: 3(11) - 4(3) = 33 - 12 = 21, which is equal to 21. Therefore, (11, 3) is a solution.

Based on the calculations, the ordered pairs that are solutions to the equation 3x - 4y = 21 are (7, 0) and (11, 3).

Learn more about  equation here: brainly.com/question/29326605

#SPJ11

The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

Learn more about APR here:

https://brainly.com/question/14184570

#SPJ1

Therefore, the value of fy at (4, 1) is (sin⁻¹(4) + 4/√(-60)) / 8, or approximately -0.105 for given partial derivatives.

To find fy, we need to take the partial derivative of f with respect to y, treating x as a constant. Using the chain rule, we get:

f(x, y) = y sin⁻¹(xy)

∂f/∂y = sin⁻¹(xy) + y(1/√(1 - x²y²))(x)

Now we can substitute the given values of x and y to get:

∂f/∂y (4, 1) = sin⁻¹(4) + 1(1/√(1 - 16))(4)

= sin⁻¹(4) + 4/√(-60)

To know more about partial derivative,

https://brainly.com/question/30904314

#SPJ11

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

To know more about regression model:

https://brainly.com/question/31969332

#SPJ4

To use the normal approximation for a test of two proportions, n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2) must all be greater than or equal to 5.

This is because the normal distribution assumes that the sample size is large enough to approximate the binomial distribution, and the rule of thumb is that each cell (n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2)) should have at least 5 expected counts. If any of these cells have fewer than 5 expected counts, then the normal approximation is not reliable and a more appropriate test should be used. It is important to note that this is just a rule of thumb, and other factors such as the size of the effect and the desired level of significance should also be considered when deciding on a statistical test.

To know more about proportions visit :

https://brainly.com/question/14172488

#SPJ11

Answer: 9 + 3r

Step-by-step explanation:

To reduce the number of terms we need to combine like terms

15 - (6-3r)

Distributive property (distribute the -1)

15 - 6 + 3r

9 + 3r

Obtuse-angled: This term refers to triangles with one angle greater than 90 degrees. The triangle in question has an angle of 100º, so it is obtuse-angled.

To calculate the incidence of breast cancer in the unexposed group (i0) per 1,000, we need to first calculate the total number of mothers in the unexposed group. The total number of mothers in the study is 1,628 + 4,450 = 6,078.
We know that among the 4,450 mothers who first gave birth before the age of 30, 65 subsequently developed breast cancer.

Therefore, the incidence of breast cancer in this group is 65/4,450 = 0.0146.

To convert this incidence rate to a per 1,000 basis, we multiply by 1,000: 0.0146 x 1,000 = 14.6.

Therefore, the incidence of breast cancer in the unexposed group (i0) per 1,000 is 14.6.

It's important to note that we cannot directly calculate the incidence rate of breast cancer in the exposed group since we do not have information on the total number of mothers in that group who did not develop breast cancer. However, we can still compare the incidence rates between the exposed and unexposed groups to see if there is a significant difference.

To know more about Age visit :

https://brainly.com/question/28686134

#SPJ11

Answer:The given expression is 6 - 8x + 3.

Combining like terms, we have:

6 - 8x + 3 = 9 - 8x

Therefore, the simplified expression is 9 - 8x.

Step-by-step explanation:

THANKS