Noah invested $8,600 in an account paying an interest rate of 2.4% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $10,900?

Answer:

[tex]y\ge \:-1+x,\:y<\frac{4-x}{2}\quad :\quad \begin{bmatrix}y\ge \:-1+x\\ y<\frac{4-x}{2}\end{bmatrix}\quad \mathrm{Unbounded}[/tex]

The graph is attached below.

Step-by-step explanation:

Given the system of inequalities.

[tex]\begin{bmatrix}x-y\le \:1\\ x+2y<4\end{bmatrix}[/tex]

Isolate y for [tex]x-y\le \:1[/tex]

[tex]x-y\le \:1[/tex]

subtract x from both sides

[tex]x-y-x\le \:1-x[/tex]

simplify

[tex]-y\le \:1-x[/tex]

Multiply both sides by -1 (reverse the inequality)

[tex]\left(-y\right)\left(-1\right)\ge \:1\cdot \left(-1\right)-x\left(-1\right)[/tex]

simplify

[tex]y\ge \:-1+x[/tex]

now solving

[tex]x+2y < 4[/tex]

isolate y for [tex]x+2y < 4[/tex]

[tex]x+2y < 4[/tex]

subtract x from both sides

[tex]x+2y-x<4-x[/tex]

simplify

[tex]2y<4-x[/tex]

Divide both sides by 2

[tex]\frac{2y}{2}<\frac{4}{2}-\frac{x}{2}[/tex]

Simplify

[tex]y<\frac{4-x}{2}[/tex]

Graphing Method:

1. Graph each inequality separately

2. Choose a test point to determine which side of the line needs to be shaded

3. The solution to the system will be the area where the shadings from each inequality overlap one another.

Thus,

[tex]y\ge \:-1+x,\:y<\frac{4-x}{2}\quad :\quad \begin{bmatrix}y\ge \:-1+x\\ y<\frac{4-x}{2}\end{bmatrix}\quad \mathrm{Unbounded}[/tex]

The graph is attached below.

Answer:

hakdog keep it up po11828282882827272++--yyyxxxxxx

Answer:

150

Step-by-step explanation:

The question is unclear. Do they want an angle that is under 180 (to your left) or over 180 (to your right)? I'm guessing that it is just under 180.

Each hour on a clock takes up 30 degrees. Each 5 minutes hand sweep out out 5/60 * 360 = 30 degrees as well. This angle looks like it is 5 minutes to seven if it was on a clock.

So the large angle from 12 oclock would sweep out 210 degrees and that would mean that the left angle would be 150. But the time is not quite 7 o,clock.

My guess would be 150. Remember, this is an estimate. You can't use a protractor on the question.

Answer

The slope-intercept form of the equation of the line with a slope of 1/4 and y-intercept at the origin:

[tex]y=\frac{1}{4}x[/tex]

Step-by-step explanation:

Given

We know that the slope-intercept form of the line equation is

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept.

substituting the values m=1/4 and the y-intercept b=0 to determine the equation in slope-intercept form

[tex]y=mx+b[/tex]

[tex]y=\frac{1}{4}x+0[/tex]

[tex]y=\frac{1}{4}x[/tex]

Thus, the slope-intercept form of the equation of the line with a slope of 1/4 and y-intercept at the origin:

[tex]y=\frac{1}{4}x[/tex]

^starigjt line equation (SLE)^

how to find slope of line (m)

=y2 - y1/x2 - x1

7. there, (16,2) occupies the x1 (16) and y1 (2) positions.

and, (32,4) occupies the x2 (32) and y2 (4) positions.

ok, enter:

m = y2 - y1/ x2 - x1

=4 - 2 / 32 - 16

=2/16

8. there, (-2,17) occupies the x1 (-2) and y1 (17) positions.

and, (-1,5) occupies the x2 (-1) and y2 (5) positions.

ok, enter:

m= y2 - y1/ x2 - x1

=5 - 17/ -1 - (-2)

=5 - 17 / -1 + 2

= -12 / 1

Answer:

6

Step-by-step explanation:

sqrt(36) = 6

Answer:

1296

Step-by-step explanation:

36 x 36 = 1296

Answer:

D

Step-by-step explanation:

The Triangle Sum theorem states the angles of all triangles will add up to 180.

70 + 50 + 70 = 190. Therefore, this cannot be a triangle.

Answer:

Step-by-step explanation:

100/30=3  1/3hrs to go

3  1/3*3/4=  

10/3*3/4=30

30/12=2  1/5hrs return

100/2  1/2=

100/(5/2)=

100*2/5=200/5=40

100/2.5=40mph return

Answer:

[tex]\frac{7}{3}-\frac{2}{3}+\sqrt{3}-3\sqrt{3}=\frac{5}{3}-2\sqrt{3}[/tex]    

Step-by-step explanation:

Given the expression

[tex]\frac{7}{3}\:-\:\frac{2}{3}\:+\:v^3\:-\:3v^3[/tex]

solving the expression

[tex]\frac{7}{3}\:-\:\frac{2}{3}\:+\:\sqrt{3}-3\sqrt{3}[/tex]

combine the fractions i.e [tex]\frac{7}{3}-\frac{2}{3}=\frac{5}{3}[/tex]

[tex]\frac{7}{3}\:-\:\frac{2}{3}\:+\:\sqrt{3}-3\sqrt{3}=\frac{5}{3}+\sqrt{3}-3\sqrt{3}[/tex]

add similar elements  i.e [tex]\sqrt{3}-3\sqrt{3}=-2\sqrt{3}[/tex]

                                 [tex]=\frac{5}{3}-2\sqrt{3}[/tex]      

Thus,

[tex]\frac{7}{3}-\frac{2}{3}+\sqrt{3}-3\sqrt{3}=\frac{5}{3}-2\sqrt{3}[/tex]                        

The name of the ray shown would be: C. ray AG.

A ray can be defined as a part of a line which has a fixed starting point that is called an endpoint and extends to infinity towards the opposite direction of the fixed point, called the endpoint.

The first letter to use when naming a ray is the letter of the endpoint, which is the starting point of the ray, then use another letter that the ray passes through to infinity.  There would be only one arrow head facing the right, drawn on top of the letters used in naming the ray.

The image shows an endpoint of A, which marks the starting point. The line extends from G to infinity as well.

Therefore, the name of the ray shown would be: C. ray AG.

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Answer:

C

Step-by-step explanation:

Answer:

SSS

Step-by-step explanation:

right on acellus

The area of the geometric figure which is the square will be 42.25.

It should be noted that a square simply means a shape that has all its sides equal. It should be noted that the area of a square will be calculated as:

= Side × Side

In this case, the side is given as 6.5. Therefore, it should be noted that the area will be:

Area of a square = Side × Side

= 6.5 × 6.5

= 42.25

Therefore, the area of the geometric figure which is the square will be 42.25.

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Answer:

you can calculate it like two rectangle volume

Answer:

1st. false

2nd. true

Step-by-step explanation:

Itll only be considered a function when it passed the vertical line test.

The equation y=2x+1 is a linear function

Answer:

15

Step-by-step explanation:

15 seventh graders play in the jazz band as per the given ratio.

One quantity can be expressed as a fraction of other quantities using a ratio, which is a number. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given At Charles School, 1/5 of the 75 students in seventh-grade play in the jazz band.

In the form of a ratio

1/5 the students out of 75 play in the jazz band

Total students play in the jazz band = 75* 1/5

Total students play in the jazz band = 15

Therefore, The jazz band has 15 seventh graders playing according to the ratio.

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Answer:

Tobias repayed a total of $7,200.

Step-by-step explanation:

If Tobias borrowed $20,000, and the annual interest rate is 9% of this per year, then we need to find 9% of 20,000.

20,000 x 0.09 = 1,800

Therefore, the yearly interest rate is $1,800. Now, we need to multiply this by 4.

1,800 x 4 = 7,200

Therefore, Tobias repayed a total of $7,200.

Hope this helps! :D

The value of the logarithmic expression log(10³ x) is 3 + log(x).

The opposite of exponential functions is logarithmic functions. The exponential function y = aˣ has the inverse, [tex]x=a^{y}[/tex]. The exponential equation [tex]x=a^{y}[/tex] is defined as being identical to the logarithmic function y = logₐ x.

The properties of logarithm are:

Product rule: logₐ (mn) = logₐ m + logₐ n

Quotient rule: logₐ (m/n) = logₐ m – logₐ n

Power rule: logₐ (mn) = n( logₐ m )

Consider the logarithmic expression,

a = log ( 10³ x )

Using the property of logarithm:

logₐ ( mn ) = logₐ m + logₐ n

Then,

a = log( 10³ x )

a = log( 10³ × x)

a = log( 10³ ) + log( x )

By using the property of logarithm:

logₐ mⁿ = n(  logₐ m )

So,

a = 3( log 10 ) + log( x )

a = 3 + log ( x )

Therefore, log( 10³ x ) = 3 + log ( x ).

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[tex] \tt cotA = \sqrt{ \dfrac{1}{3}}[/tex]

[tex] \tt \implies cotA = \dfrac{1}{\sqrt{3}}[/tex]

All other trigonometric ratios, which are :

Let's make a diagram of right angled triangle ABC.

Now, From point A,

AC = Hypotenuse

BC = Perpendicular

AB = Base

[tex] \tt We \: are \: given, \: cotA = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt We \: know \: that \: cot \theta = \dfrac{base}{perpendicular}[/tex]

[tex] \tt \implies \dfrac{base}{perpendicular} = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt \implies \dfrac{AB}{BC} = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt \implies AB = 1x \: ; \: BC = \sqrt{3}x \: (x \: is \: positive)[/tex]

Now, by Pythagoras' theorem, we have

AC² = AB² + BC²

[tex] \tt \implies AC^{2} = (1x)^{2} + (\sqrt{3}x)^{2}[/tex]

[tex] \tt \implies AC^{2} = 1x^{2} + 3x^{2}[/tex]

[tex] \tt \implies AC^{2} = 4x^{2}[/tex]

[tex] \tt \implies AC = \sqrt{4x^{2}}[/tex]

[tex] \tt \implies AC = 2x[/tex]

Now,

[tex] \tt sin \theta = \dfrac{perpendicular}{hypotenuse}[/tex]

[tex] \tt \implies sinA = \dfrac{BC}{AC} [/tex]

[tex] \tt \implies sinA = \dfrac{\sqrt{3}x}{2x} [/tex]

[tex] \tt \implies sinA = \dfrac{\sqrt{3}}{2} [/tex]

[tex] \Large \boxed{\tt sinA = \dfrac{\sqrt{3}}{2}} [/tex]

[tex] \tt cos \theta = \dfrac{base}{hypotenuse}[/tex]

[tex] \tt \implies cosA = \dfrac{AB}{AC} [/tex]

[tex] \tt \implies cosA = \dfrac{1x}{2x} [/tex]

[tex] \tt \implies cosA = \dfrac{1}{2} [/tex]

[tex] \Large \boxed{\tt cosA = \dfrac{1}{2}} [/tex]

[tex] \tt tan \theta = \dfrac{perpendicular}{base}[/tex]

[tex] \tt \implies tanA = \dfrac{BC}{AB} [/tex]

[tex] \tt \implies tanA = \dfrac{\sqrt{3}x}{1x} [/tex]

[tex] \tt \implies tanA = \sqrt{3}[/tex]

[tex] \Large \boxed{\tt tanA = \sqrt{3}}[/tex]

[tex] \tt cosec \theta = \dfrac{hypotenuse}{perpendicular}[/tex]

[tex] \tt \implies cosecA = \dfrac{AC}{BC} [/tex]

[tex] \tt \implies cosecA = \dfrac{2x}{\sqrt{3}x} [/tex]

[tex] \tt \implies cosecA = \dfrac{2}{\sqrt{3}}[/tex]

[tex] \Large \boxed{\tt cosecA = \dfrac{2}{\sqrt{3}}}[/tex]

[tex] \tt sec \theta = \dfrac{hypotenuse}{base}[/tex]

[tex] \tt \implies secA = \dfrac{AC}{AB} [/tex]

[tex] \tt \implies secA = \dfrac{2x}{1x} [/tex]

[tex] \tt \implies secA = 2[/tex]

[tex] \Large \boxed{\tt secA = 2}[/tex]

[tex]\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(0,0){\line(3,0){2.5cm}}\put(0,0){\line(0,3){2.5cm}}\qbezier(12.4,0)(6.6,5)(0,12.4)\put(-2,13){\sf A}\put(13,-2){\sf C}\put(-2,-2){\sf B}\put(-3,6){\sf 1}\put(6,-3){\sf \sqrt3$}\put(7,7){\sf 2}\end{picture}[/tex]

Given ,

We need to find ,

First finding the other side of the triangle using Pythagoras theorem .

Hypotenuse² = Base² + Height²

[tex]\to\sf Hypotenuse^2 = (1)^2 + (\sqrt3)^2[/tex]

[tex]\to\sf Hypotenuse^2 = 1 + 3 [/tex]

[tex]\to \sf Hypotenuse = \sqrt4[/tex]

[tex]\to\bf Hypotenuse = 2[/tex]

Now ,

The correct option is B) 5 minutes.

The width of each class /(class width) is 5 minutes.

The term "class interval" refers to the numerical width of a class in such a frequency distribution.

Some key features regarding the class width/class interval are-

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The complete question is -

The following are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

RelativeTime (in Minutes)/

Frequency

0 but less than 5/0.37

5 but less than 10/0.22

10 but less than 15/0.15

15 but less than 20/0.10

20 but less than 25/0.07

25 but less than 30/0.07

30 or more/0.02

What is the width of each class?

A) 1 minute

B) 5 minutes

c) 2%

d) 100%

Probability that [tex]x^2+y^2+z^2\leq 1[/tex] is 0.523

Given that a point (x, y, z) is in space which is randomly selected as

[tex]-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$[/tex]

These three equations represents a cube in space.

Length of each side of the cube = 1 - -1 = 2

Now  [tex]x^2+y^2+z^2\leq 1[/tex]  represents a sphere with center (0, 0, 0) and of radius less than or equal to 1.

So we can imagine that this sphere is inside the cube.

So the probability that   [tex]x^2+y^2+z^2\leq 1[/tex]  = Volume of the sphere/Volume of the cube

Volume of sphere with radius 1 = [tex]\frac{4}{3} \pi r^3=\frac{4}{3} \pi \times 1 = \frac{4}{3}\times 3.14 = 4.186[/tex] cubic unit

Volume of the cube of length 2 = [tex]2^3 = 8[/tex] cubic units

So the probability that  [tex]x^2+y^2+z^2\leq 1[/tex]  = 4.186/8 = 0.523

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Answer:

trapezoid

Step-by-step explanation:

Answer: = a^2 + 2ab + 2(ac+ b^2 + 2bc)

Step-by-step explanation:

Answer: 0.03

Step-by-step explanation:

Answer:

0.03

Step-by-step explanation:

[tex]\frac{25}{10}[/tex]×[tex]\frac{12}{1000}[/tex]=

[tex]\frac{300}{10000}[/tex]=0.03

Answer:

I cant answer, but I can help, divide 100 by 16, than multiply what you get from that with 24, it'll look like this:

(100÷16)x24=A

Answer: 550t + 150c ≥ 8500

Step-by-step explanation: the store makes 550 for each table sold, so for t tables, the store will make 550t dollars. The store makes 150 for each chair sold, so for c chairs, the store will make 150c dollars. Therefore, the total revenue 550t + 150c must be greater than or equal to 8500

Answer:

Tomatoes = 11.5

Onions = 2

Step-by-step explanation:

Andre wants to purchase some onions and tomatoes to make tomato soup. The recipe states that four times the number of tomatoes, , plus five times the number of onions, x, should produce 56 bowls of tomato soup. A different recipe states that two times the number of tomatoes used minus the number of onions used should produce 21 bowls of tomato soup. What is the resulting recipe for the number or tomatoes and onions used in the soup when Andre adds the two recipes together?

Let

Tomatoes = x

Onions = y

Recipe 1:

4x + 5y = 56

Recipe 2:

2x - y = 21

4x + 5y = 56 (1)

2x - y = 21 (2)

Multiply (2) by 5

4x + 5y = 56 (1)

10x - 5y = 105 (3)

Add

10x + 4x = 105 + 56

14x = 161

x = 161 / 14

= 11.5

Substitute x =11.5 into

2x - y = 21

2(11.5) - y = 21

23 - y = 21

-y = 21 - 23

-y = -2

y = 2

Tomatoes = 11.5

Onions = 2