Jack has $15,000 to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of 8%, compound continuously, and the other third in a regular savings account at 6% simple interest, how much does Jack earn after one year?

Answer:

Step-by-step explanation:

Use the formulas supplied in the picture attached. There's nothing to really learn here, it is just a plug-and-chug formula:

[tex]sin(3x)sin(2x)=\frac{1}{2} [cos(3x-2x)-cos(3x+2x)][/tex]

[tex]sin(3x)sin(2x)=\frac{1}{2} [cos(x)-cos(5x)][/tex]

Moving on to the second problem:

[tex]cos(a)sin(b)=\frac{1}{2}[ sin(a+b)-sin(a-b)][/tex]

Therefore:

[tex]2cos(a)sin(b)=sin(a+b)-sin(a-b)[/tex]

Where:

[tex]a+b=5x[/tex]

[tex]a-b=3x[/tex]

Solve for 'a' using the second equation to get:

[tex]a=3x+b[/tex]

Plug this into the first equation to get:

[tex]3x+b+b=5x[/tex]

[tex]3x+2b=5x[/tex]

[tex]2b=2x[/tex]

[tex]b=x[/tex]

Therefore:

[tex]a+x=5x[/tex]

[tex]a=4x[/tex]

Finally:

[tex]sin(a+b)-sin(a-b)=2cos(4x)sin(x)[/tex]

Answer:

y=2x+1

Step-by-step explanation:

You use the equation y=mx+b and substitute m for the slope/gradient. Then you use (2,5) to subtitue for y and x. Solve the equation for b. Then you have your slope and b, and you can make your equation from this.

Answer:

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact Form:

24/5

Decimal Form:

4.8

Mixed Number Form:

4 4/5

Answer:

b

Step-by-step explanation:

the x has been cubed meaning

X * X *X = x^3

X^3 has been added to 5

C is saying they multiplied three to x therefore being

B

Answer:

$2000 with payments of $320 a month

Step-by-step explanation:

360 x 6 = 2160

2160 + 2400 = 4560

320 x 6 = 1920

1920 + 2000 = 3920

Answer:

dealer A

Step-by-step explanation:

A: 360×6=2160

2400-2160=240

they save $240

B: 320×6=1920

2000-1920=80

they save $80

have a government

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Step-by-step explanation:

yan napo lahat answer

Answer:

I think 50 yrs old

Step-by-step explanation:

I'm not good at percentages, but if you have 100% hair, and lose 5% every year, 5x10= 50 which can be written as 50%, meaning half of 100%

The  two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Let the two unknown numbers be x and y

If the sum of the numbers is 21, hence;

x + y = 21

x = 21 - y

If the product is 104, then;

xy = 104
(21-y)y = 104

21y - y^2 = 104
y^2-21y + 104 = 0

Factorize the result

y^2-8y - 13y+ 104 = 0
y(y-8) - 13()y-8) = 0
y = 13 and 8

Hence the two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Learn more on system of equation here:  https://brainly.com/question/847634

Answer:

14.3

Step-by-step explanation:

Formula: a^2 + b^2 = c^2

9+196= 205 then find the square root of 205, approximate then use tenths.

Answer:

14.3

Step-by-step explanation:

Use the following equation:

a² + b² = c² , in which the variable c = hypotenuse, and a & b are the other legs.

It is given that the legs measure 3 and 14 respectively. Plug in the given numbers to the given leg variables:

a² + b² = c²

3² + 14² = c²

Simplify. First, solve the powers, and then combine like terms:

(3 * 3) + (14 * 14) = c²

9 + 196 = c²

c² = 205

Next, root both sides of the equation:

√c² = √205

c = √205 = 14.3178

c = 14.3 (Rounded to the nearest tenth).

14.3 is your answer.

~

Answer:

please the question is not clear

Answer:

318

Step-by-step explanation:

find area of the big triangle then split the remaining shape into a large rectangle and a smaller rectangle

Answer:

318 mi²

Step-by-step explanation:

Formulae

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Divide the figure into 1 triangle and 2 rectangles (see attachment).

Area of Triangle 1 = 1/2 x (10 + 6 + (11 - 8)) x 22

                             = 1/2 x 19 x 22

                             = 209 mi²

Area of Rectangle 2 = 5 x (11 + 6)

                                  = 85 mi²

Area of Rectangle 3 = 4 x 6

                                  = 24 mi²

Total area = 209 + 85 + 24 = 318 mi²

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The general strategy for solving the equation in form of :

[tex]\qquad \tt \dashrightarrow \: \dfrac{x}{a} = b[/tex]

is to multiply both sides by a, because if we multiply both sides by a, then a on left side get cancel out and we get the value of x in terms of a and b.

so, correct choice is C. multiply both sides by a

Best way is multiply with a

By which x gets isolated

Let's check how?

Answer:

B

Step-by-step explanation:

center (1/2,-5/2)

radius=1/2

Answer:

8 inches

Step-by-step explanation:

Nacho cheese

v= Pi×radius×2×height

v = 3.14×8×2×4 = 200.96

jalapeño

3.14×4×2=25.12

200.96÷25.12=8

the height is 8

to check your work you can do

(multiply by 8 and see if it equals 200.96)

3.14×4×2×8 = 200.96

since the volume is the same as the volume for nacho cheese we can say that 8 inches for height is correct

Answer: are congruent, rotation

Step-by-step explanation:

Answer:

20-x

Step-by-step explanation:

you need the value of x to answer

Answer:

$469887

Step-by-step explanation:

you should use compound interest formula which is

A=P(1+r/100) ^t

A = 242800 ( 1 + 0.045 ) ^ 15

when you punch this into a calculator you will get 469886.5771.....

when you round it off to a whole number the answer is $469887

Answer:

i don't know how much will l loose

The correct location is between the two and three for the first digit and the three and six for the second number.

Answer:

2×5÷4=2.5

Step-by-step explanation:

2 boxes × 5 cards ÷ white cards

Answer:

its logx=logy

Answer:

its logx=logy

The equivalent expression of 3 to the power of 4. is 9 to the power of 2.

The expression is given as:

3 to the power of 4.

Mathematically the expression is

[tex]3^4[/tex]

Express 4 as 2 * 2

[tex]3^{2*2}[/tex]

Evaluate 3^2

[tex]9^2[/tex]

This means that:

9 to the power of 2.

Hence, the equivalent expression of 3 to the power of 4. is 9 to the power of 2.

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ2

Answer:

y = 3x - 5

Step-by-step explanation:

To find the equation of the line, you can use y = m x + c.

Here,

m ⇒ slope

c ⇒ y-intercept

Given that,

slope = 3

y-intercept = -5

So, to find the equation of the line you have to simply replace m and c in the formula, (y = m x + c )with the given slope and y-intercept.

Let us solve it now.

y = m x + c

y = 3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

Slope-intercept form of an equation

Given that m = 3 and b = -5

Answer:

-8x

Step-by-step explanation:

[tex]-3(x+2)^{2}+4\\-3(2x)^{2}+4\\-12+4\\\ y=-8x[/tex]

Answer: 12

Step-by-step explanation:  2 times of 8 is 16, but it says 4 less, so you subtract 4 and that equals 12.

Answer:

Graph Passing through origin with Gradient ⅓

Step-by-step Solution:

1. Aquire x and y Intercepts by substituting 0 to corresponding value.

When x=0,

[tex]y = \frac{1}{3} (0) \\ y = 0[/tex]

When y=0,

[tex]0 = \frac{1}{3} x \\ x = 0[/tex]

i.e. passing through Origin

do the same for any other 2 points and connect the dots/coordinates and extend the line

Answer:

9 3/10

Step-by-step explanation:

5 4/5 = 5 8/10

3 1/2 = 3 5/10

3 5/10 + 5 8/10 = 9 3/10

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Here we go ~

[tex]\qquad \tt \dashrightarrow \:5 \frac{4}{5} + 3 \frac{1}{2} [/tex]

[tex]\qquad \tt \dashrightarrow \:\frac{29}{5} + \frac{7}{2} [/tex]

[tex]\qquad \tt \dashrightarrow \:\frac{58 + 35}{10} [/tex]

[tex]\qquad \tt \dashrightarrow \:\frac{93}{10} [/tex]

[tex]\qquad \tt \dashrightarrow \:9\frac{3}{10} [/tex]

Answer:

$15.49

Step-by-step explanation:

0.75 x 2 = 1.5

1.50 + 13.99 = 15.49

The clerk is correct; Anna only gave 20 dollars (10x2). 20 - 15.49 = 4.51, which then would be the correct change.  

[tex]v = \frac{4}{3} \times \pi \times ({ \frac{8}{2} })^{3} \\ [/tex]

[tex]v = \frac{4}{3} \times 3 \times {4}^{3} \\ [/tex]

[tex]v = {4}^{4} [/tex]

[tex]v = {2}^{8} [/tex]

[tex]v = 256 \: \: {cm}^{3} [/tex]

8 times

I hope this helps you

:)