$2000 should be invested into checking with interest rate 3% and savings account with interest rate 5% so that the total interest will be $84. How much should be invested into each account?

[tex]\displaystyle \int \dfrac{dx}{5x^2 -10x +15}\\\\\\=\displaystyle \int \dfrac{dx}{5(x^2-2x+3)}\\\\\\=\dfrac 1 5 \displaystyle \int \dfrac{dx}{x^2-2x+3}\\\\\\=\dfrac 15 \displaystyle \int \dfrac{dx}{x^2 -2x +1^2 -1 +3}\\\\\\=\dfrac 15 \displaystyle \int \dfrac{dx}{(x-1)^2+2}\\\\\\=\dfrac 15 \displaystyle \int \dfrac{du}{u^2 +\left(\sqrt 2 \right)^2}~~~~~~~~~;[x-1 =u \implies dx = du]\\\\\\\\[/tex]

[tex]=\dfrac 1 {5\sqrt 2} \tan^{-1} \left( \dfrac u{\sqrt 2}\right)+C~~~~~~;\left[\displaystyle \int \dfrac{dx}{a^2 +x^2} = \dfrac 1a \tan^{-1} \left( \dfrac xa \right) +C\right]\\\\\\=\dfrac{1}{5\sqrt 2} \tan^{-1} \left( \dfrac{x-1}{\sqrt 2}\right)+C[/tex]

Answer:

255cm²

Explanation:

To find the area of the triangle we must us a formula which is base x height ÷ 2 divide. So on the left side it is 17 cm and on the right without the triangle it is 10 so the triangle is 7cm tall. Next on the bottom without the triangle it is 22 and with it is 12 so the base is 10 now we multiply them which will be 70 then divide it by 2 which is 35cm².

And dont forget the squared!!

Answer:

C Cos32

Step-by-step explanation:

Fraction are ratio of two integers. It will take Amen 20 days to do the task alone

From the given question, we have the following information

Let the number of days Amen can take to complete a task be x

If Payson is thrice as fast as Amen at completing a task, then the number of das Payson takes will be 3x

If they both pick up a task together, and complete it in 5 days, then;

1/x + 1/3x = 1/5

Find the LCM
3+1/3x = 1/5

4/3x = 1/5

Cross multiply

3x = 20

Determine the time taken by Amen:

x =20/3

This shows that it will take Amen 20 days to do the task alone

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Answer:

He generates a random whole number from 1 to 3.

Step-by-step explanation:

Each winner has 3 possibilities, gets cotton candy, gets a shirt, or gets a keychain. We can asign each of this possibiltiies a number, 1 for cotton candy, 2 for the shirt and 3 for a keychain. So, for a simulation, its enough to take one of this whole numbers for each winner.

Answer:

8

Step-by-step explanation:

P=2(l+w)=2·(1+3)=8 The length was 1 and the width was 3.

Answer:

1. you will multiply base times height:

16m * 12m = 192 sq m

2. same steps but just multiply it by two because its "twice as long"

18 cm * 6 cm = 108 * 2= 216

3. now for this one sice we are finding the base we will have to divide the 432 by 18 = 24

4. same steps like in question 1:  

12 * 5 = 60

5. same steps like in question 1:

7 * 10 = 70

Step-by-step explanation:

hope this helps and have a great day!! :)

Answer: Okay, so you probably already know this but,

The mean - is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.

Add up all of the numbers and divide by the number of numbers in the data set. The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number.

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

Step-by-step explanation:

In a perfectly symmetrical distribution, the mean and the median are the same. This example has one mode (unimodal), and the mode is the same as the mean and median. In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median.

hope this helps you!!

Answer:

One of the many examples is {0, 0, 0, 0, 0}

Step-by-step explanation:

The mean is the average of a data set.
The median is the number in the middle (or between the 2 middle numbers) of a data set that is placed from least to greatest.
The mode is the value that shows up the most times in the data set.

A few examples of a set with the same mean, median, and mode could be any number repeated in a data set:
{0, 0, 0, 0, 0}
This would work because the mean is 0, the median is 0, and the mode is 0.

Answer:

so what should we do?!?!?!?!¡!?!

Answer:

[tex]\displaystyle 21 \approx c[/tex]

Explanation:

Solving for Angles

[tex]\displaystyle \frac{a^2 + b^2 - c^2}{2ab} = cos\angle{C} \\ \frac{a^2 - b^2 + c^2}{2ac} = cos\angle{B} \\ \frac{-a^2 + b^2 + c^2}{2bc} = cos\angle{A}[/tex]

Do not forget to use [tex]\displaystyle arccos[/tex] or [tex]\displaystyle cos^{-1}[/tex]towards the end, or the result will be thrown off.

Solving for Edges

[tex]\displaystyle b^2 + a^2 - 2ba\:cos\angle{C} = c^2 \\ c^2 + a^2 - 2ca\:cos\angle{B} = b^2 \\ c^2 + b^2 - 2cb\:cos\angle{A} = a^2[/tex]

Take the square root of the result in the end, or you will throw yourself off.

Well, let us get to work:

[tex]\displaystyle 13^2 + 29^2 - 2[13][29]cos\:41 = c^2 \\ 169 + 841 - 754cos\:41 = c^2 \\ 1010 - 754cos\:41 = c^2 \\ \\ \sqrt{440,94897651...} = \sqrt{c^2} \\ 20,99878512... = c \\ \\ \boxed{21 \approx c}[/tex]

I am joyous to assist you at any time.

Answer:

Total periodic pension costs (TPPC) is equal to the contributions plus change in the pension liability during the year. Each period, the periodic pension cost is recognized in profit or loss (P&L) and/or in other comprehensive income (OCI).

Answer:

947393

Step-by-step explanation:

Answer:

T = 2

Step-by-step explanation:

Take the given formulaer

I = PRT

And plug in the variables you know (I, P, R)

387.50 = 1,550(.125)T

(12.5% becomes .125 after you divide it by 100, because precents are really just fractions out of 100)

387.50 = 193.75T

T = 2

Answer:

[tex](x+2)^2+(y-9)^2=[/tex] 90

Step-by-step explanation:

The centre is (-2,9) so the first part of the equation will be (x+2)^2 + (y-9)^2 and to get the second half, you know the point on the circle which you can use to find the radius. So the triangle formed would be 3 long, 9 high and using Pythagoras you can do:

[tex]3^2+9^2=r^2[/tex]

9+81= [tex]r^2\\[/tex]

90 = [tex]r^2[/tex]

and this equation ends with r^2 so you can substitute that back into the equation so together it will be

[tex](x+2)^2+(y-9)^2=[/tex] 90

The value of x in the triangle ABC is 25.

The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.

The exterior angle of the triangle is given as m∠ACD = 5x.  

The sum of angle in a triangle is equals to 180 degrees. Therefore,

3x + 50 + (180 - 5x)  = 180

3x + 50 - 5x + 180 = 180

3x - 5x + 50 + 180 = 180

-2x + 230 = 180

subtract 230 from both sides

-2x + 230 - 230 = 180 - 230

-2x = -50

divide both sidesby -2

-2x / -2 = -50 / -2

x = 25

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Answer: 3/20

Step-by-step explanation:

Inital Equation:

[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{6}{1}[/tex]

Find the Recipricol of 6/1:

It's: 1/6

Multiply the Recipricol of 6/1 (1/6) by 9/10

9/10 x 1/6 = 9/60

Simplify

9/60 = 3/20

Answer: 3/20

Beth salary in 14 years would be $62900.

Simple interest is the borrowing amount added only to the principal amount.

Given, Beth currently brings in an annual salary of $37,000 and anticipates a raise of 5% every year.

To find the interest rate:

The formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100 ,

Where S.I. is simple interest , P is principal amount, T is time period and R is interest rate in a year.

And according to the question,

P = 37000, T = 14 years and R = 5%

Substituting all the values to the formula,

S.I. = P x T x R / 100

S.I. = 37000 x 14 x 5 / 100

      = 25900

Beth final salary = principal amount + interest rate

                           = 37000 + 25900

                          = 62900

Therefore, Beth salary after 14 years is $62900.

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#SPJ2

Answer:

Step 1 The two sides we know are Opposite (300) and Adjacent (400).

Step 2 SOHCAHTOA tells us we must use Tangent.

Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.

Step 4 Find the angle from your calculator using tan-1

Answer:

negative

Step-by-step explanation:

A positive times a negative is a negative

Answer:

0.5

Step-by-step explanation:

An equation is written as :

Taking the first row data (x = 2, y = 1),

Answer:

Option A, 0.5

Step-by-step explanation:

Step 1:  Determine the slope/proportionality

[tex]Slope = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]Slope = \frac{1.5-1}{3-2}[/tex]

[tex]Slope = \frac{0.5}{1}[/tex]

[tex]Slope =0.5[/tex]

Answer:  Option A, 0.5

Answer:

A) 5

Step-by-step explanation:

distance = √(distance between x coordinates² + distance between y coordinates²)

the horizontal distance between the two points is 4

the vertical distance between the two points is 3

to prove this, if you started at Q and went 4 points right and then 3 points up, you would get to P

distance = √(4²+3²) = √25 = 5

Answer:

Area = 48.6 in²

Explanation:

The area of the triangle can be calculated using the side-angle-side method as follows:

Area = 0.5 * first side * second side * sin(angle included between the two sides)

This rule is illustrated in the attached image.

Now, we have:

first side = 13 in

second side = 7.5 in

The angle included between the two sides = 94 degrees

The given angle is included between the two given sides, therefore, we can apply the above rule to get the area.

Area of triangle = 0.5 * 13 * 7.5 * sin(94)

Area of triangle = 48.63 which is approximately 48.6 in²

Hope this helps :)

Step by step explanation: The last answer i wrote was wrong, so i retook the quiz and got 100% and this was right.

Answer:

.C ,375

I HOPE THIS helps  i just know i got connect shons

Based on characteristics of regular polygons, the area of the regular octagon with an apothema of 17 units is approximately 239.415 square units. #SPJ1

A polygon is regular when all sides and central angles have the same length.The area of a regular polygon (A) can be found in terms of the number of sides (n) and the apothema (a), whose length is 17, by using the following formula:

A = 0.25 · n · a² · tan (180/n)     (1)

If we know that n = 8 and a = 17, then the area of the regular octagon is:

A ≈ 239.415

Based on characteristics of regular polygons, the area of the regular octagon with an apothema of 17 units is approximately 239.415 square units. #SPJ1

To learn more on regular polygons, we kindly invite to check this: https://brainly.com/question/11810316  #SPJ1

Answer:  The vector is < 2, 5 >

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

Explanation:

Label the initial point (1,-7) as point P and (3,-2) as point Q.

This is a change of +2, meaning we move 2 units to the right.

Therefore, the x component of the vector is +2 or simply 2.

This is a change of +5 when moving from P to Q. We have moved 5 units up. The y coordinate of the vector is +5 or simply 5.

Overall, the vector is < 2, 5 > which tells the reader "move 2 units to the right and 5 units up.

Refer to the diagram below.

Answer:

C

Step-by-step explanation:

[tex]\text{All other options contain rational numbers, such as} ~\sqrt{36} , \sqrt{25}, \sqrt{16}[/tex]

Answer:

1.33

Step-by-step explanation:

2.87349 rounded to the nearest thousandth is 2.873 because the number next to it (4) is less than 5.

1.54324 rounded to the nearest thousandth is 1.54324 is 1.543 because the number next to it (2) is less than 5.

Then you do 2.873 - 1.543 and that = 1.33. So 1.33 is your final answer :)

Answer:

3.31662479... is irrational

Step-by-step explanation:

The number 3.31662479... is written in a decimal form:

It is a nonterminating decimal (look at the three dots at the end)

and a nonrepeating decimal (no repeating pattern)

So it is irrational.

Answer:

Step-by-step explanation:

The given number is :

The three dots at the end of the number indicates that it is non-terminating

Also you see that the digits do not repeat, hence it is also non-repeating

Definition of An Irrational Number

⇒  The decimal expansion of an irrational number is neither terminating nor recurring.

As it satisfies the criteria, the given number is irrational