If $600 is put in the bank and each year the account earns 7% simple interest, then how much interest will be earned in two years?

Answer:

a. 3⁄10 + 6⁄10 = 9/10

b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4

c. 5⁄6 – 3⁄6 = 1/3

d. 2⁄3 – 6⁄10 = 1/15

e. 4⁄10 × 3⁄7 = 6/35

f. 1⁄6 × 6⁄15 = 1/15

g. 1⁄8 ÷ 4⁄9 = 9/32

h. 1⁄5 ÷ 3⁄4 = 4/15

Step-by-step explanation:

a. 3⁄10 + 6⁄10

= 3*1 + 6*1 / 10

= 3+6/10

= 9/10

b. 1⁄3 + 1⁄4 + 1⁄6

since denominators are different we take LCM of 3,4,6 which is 12

= 1*4 + 1*3 + 1*2 / 12

= 4+3+2/12

= 9 ÷ 3 / 12 ÷ 3

= 3 / 4

c. 5⁄6 – 3⁄6

= 5 - 3 / 6

= 2 ÷ 2 / 6 ÷ 2 = 1/3

d. 2⁄3 – 6⁄10

LCM of 3 and 10 is 30

= 2 * 10 - 6 * 3 / 30

= 20 - 18 / 30

= 2 ÷ 2 / 30 ÷ 2 = 1/15

e. 4⁄10 × 3⁄7

= 12 ÷ 2 / 70 ÷ 2 = 6/35

f. 1⁄6 × 6⁄15

= 6 ÷ 6/90 ÷ 6 = 1/15

g. 1⁄8 ÷ 4⁄9

= 1/ 8 * 9/4

=9/32

h. 1⁄5 ÷ 3⁄4

=1/5 * 4/3

= 4/15

a)

[tex]\dfrac{9}{10}[/tex]

b)

[tex]\dfrac{3}{4}[/tex]

c)

[tex]\dfrac{1}{3}[/tex]

d)

[tex]\dfrac{1}{15}[/tex]

e)

[tex]\dfrac{6}{35}[/tex]

f)

[tex]\dfrac{1}{15}[/tex]

g)

[tex]\dfrac{9}{32}[/tex]

h)

[tex]\dfrac{4}{15}[/tex]

a)

[tex]\dfrac{3}{10}+\dfrac{6}{10}[/tex]

Now, this expression could also be given by:

[tex]=\dfrac{6+3}{10}\\\\=\dfrac{9}{10}[/tex]

b)

[tex]\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6}[/tex]

On taking the least common multiple of the denominator we have:

[tex]L.C.M\{3,4,6\}=12[/tex]

Hence, we have:

[tex]=\dfrac{1\times 4+1\times 3+1\times 2}{12}\\\\=\dfrac{4+3+2}{12}\\\\=\dfrac{9}{12}\\\\=\dfrac{3\times 3}{3\times 4}\\\\=\dfrac{3}{4}[/tex]

c)

[tex]\dfrac{5}{6}-\dfrac{3}{6}[/tex]

Now, this expression could also be given by:

[tex]=\dfrac{5-3}{6}\\\\=\dfrac{2}{6}[/tex]

which on reducing to the lowest terms is given by:

[tex]=\dfrac{1}{3}[/tex]

d)

[tex]\dfrac{2}{3}-\dfrac{6}{10}[/tex]

on reducing the second term we have:

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

Now on simplifying the expression we have:

[tex]=\dfrac{2\times 5-3\times 3}{15}\\\\=\dfrac{10-9}{15}\\\\=\dfrac{1}{15}[/tex]

e)

[tex]\dfrac{4}{10}\times \dfrac{3}{7}[/tex]

We know that:

[tex]\dfrac{4}{10}=\dfrac{2}{5}[/tex]

Hence, we have:

[tex]=\dfrac{2}{5}\times \dfrac{3}{7}\\\\=\dfrac{6}{35}[/tex]

f)

[tex]\dfrac{1}{6}\times \dfrac{6}{15}[/tex]

which on simplifying gives:

[tex]=\dfrac{1}{15}[/tex]

g)

[tex]\dfrac{\dfrac{1}{8}}{\dfrac{4}{9}}[/tex]

which is further written as:

[tex]=\dfrac{1\times 9}{4\times 8}\\\\=\dfrac{9}{32}[/tex]

h)

[tex]\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}[/tex]

which is given by:

[tex]=\dfrac{1\times 4}{3\times 5}\\\\=\dfrac{4}{15}[/tex]

Answer:

Step-by-step explanation:                         1

Note that y = sec x is equivalent to y = ----------

                                                                  cos x

Also note that the range of the cos x function is [-1, 1], which means that there is no x value for which sec x has a zero.  

no, if the each item only occurs once the set will not have a mode. Mode is an item that occurs more number of times in a distribution.

Answer: No

Step-by-step explanation: Unlike the mean and median of a data set, it's completely possible for a data set to have no mode. Remember, the mode is the number that appears most frequently in a data set.

I'll show you an example of a data set that has no mode.

In the image provided, you will see that each of the numbers appear only once. In this situation, we would just write no mode.

Answer:

10

Step-by-step explanation:

1 gallon = 4 quarts

1.5 gallon = 1.5 * 4 quarts = 6 quarts

2 quarts + 2 quarts + 6 quarts = 10 quarts

Answer:

The correct answer option is a) y =2.

Step-by-step explanation:

We are given the following equation and we are to find the solution of this equation:

[tex] | 1 0 - 5 y | = 2 0 [/tex]

Here, the expression [tex]10-5y[/tex] is given in a modulus, which means that its value cannot be negative.

[tex] 1 0 - 5 y = 2 0 [/tex]

[tex] -5 y = 2 0 - 1 0 [/tex]

[tex] -5 y = 1 0 [/tex]

Ignoring the negative sign because of mod.

[tex]y=\frac{10}{5}[/tex]

y = 2

The equation |10-5y| = 20 has two solutions, which are y = -2 and y = 6. These solutions are obtained by considering the two possible scenarios due to the absolute value.

The equation provided is |10-5y| = 20. To solve the equation, we need to consider the absolute value conditions separately. Since absolute value represents distance, it can be equal to the positive or negative of the number within the absolute value. Therefore, we have two cases to solve:

10 - 5y = 20

10 - 5y = -20

Solving the first case:

-5y = 20 - 10
-5y = 10
y = -2

Solving the second case:

-5y = -30
y = 6

Thus, the solutions to the equation are y = -2 and y = 6.

Answer: (-6, 4)

Step-by-step explanation:

You can use the Elimination method:

- Multiply the the first equation by -3 and the second one by 5.

- Add both equations.

- Solve for y:

[tex]\left \{ {{(-3)(5x+4y=-14(-3)} \atop {5(3x+6y)=6(5)}} \right.\\\\\left \{ {{-15x-12y=42} \atop {15x+30y=30}} \right.\\-------\\18y=72\\y=4[/tex]

- Susbtittute y=4 into any of the original equations and solve for x:

[tex]3x+6(4)=6\\3x=6-24\\3x=-18\\x=-6[/tex]

Then the ordered pair is:

(-6, 4)

Answer:

(-6, 4)

Step-by-step explanation:

We are given the following two equations and we are to solve them:

[tex]5x+4y=-14[/tex] --- (1)

[tex]3x+6y=6[/tex] --- (2)

Using the substitution method:

From equation (2):

[tex] 3 x = 6 - 6 y \\\\ x = \frac { 6 - 6 y } { 3 } \\ \\ x = 2 - 2 y [/tex]

Substituting this value of x in equation (1) to get:

[tex] 5 ( 2 - 2 y ) + 4 y = -14 \\\\ 10 - 10 y + 4 y = -14 \\\\ 1 0 + 14 = 6 y \\\\ y = \frac { 24 } { 6 } \\ \\ y = 4 [/tex]

Putting this value of y in equation (2) to find the value of x:

[tex] 3 x + 6 ( 4 ) = 6 \\\\ 3x + 24 = 6 \\\\ 3x = 6 - 24 \\\\ x = \frac { -18 } { 3 } \\\\ x = -6 [/tex]

Therefore, (-6, 4) is the solution to the given system of equations.

Answer:

[tex]\large\boxed{C.\ 9x^3+11x^2}[/tex]

Step-by-step explanation:

[tex]9x^3+8x^2+3x^2\qquad\text{combine like terms}\\\\=9x^3+(8x^2+3x^2)\\\\=9x^3+11x^2[/tex]

Answer:

x=  nπ/3

Step-by-step explanation:

We are given that: [tex]\sqrt{3}*tan(3x) = 0[/tex]

Divide both sides by [tex]\sqrt{3}[/tex]

=> [tex]\frac{\sqrt{3}*tan(3x)}{\sqrt{3}} = \frac{0}{\sqrt{3}}[/tex]

=> tan(3x) = 0

we know that arctan(0) = nπ

Therefore,

3x = nπ

or

x=  nπ/3 (where n belongs to positive and negative integers)

Answer:

The graphs of the equations are parallel lines.

Step-by-step explanation:

Parallel lines have no solution, not infinitely many solutions. When graphed, infinitely many solutions will appear as the same line.

Answer:

The graphs of the equations are parallel lines.

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

Any rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a, b are integers

- 16 can be expressed as

[tex]\frac{-16}{1}[/tex] ← - 16 and 1 are integers

Hence - 16 is rational

Answer:

The axis of symmetry is [tex]x=1[/tex]

Step-by-step explanation:

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

In this problem we have a vertical parabola open upward

The x-coordinate of the vertex is equal to the midpoint between the zeros of the parabola

so

[tex]x=\frac{5-3}{2}=1[/tex]

therefore

The axis of symmetry is [tex]x=1[/tex]

Answer:

Option B. The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=-2x-5[/tex] ----> equation A

[tex]-2x+4y=12[/tex] -----> equation B

we know that

To graph the lines, find the intercepts

Remember that

The y-intercept is the value of y when the value of x is equal to zero

The x-intercept is the value of x when the value of y is equal to zero

Equation A

[tex]y=-2x-5[/tex]

For [tex]x=0, y=-5[/tex] ----> y-intercept

For [tex]y=0, x=-2.5[/tex] ----> x-intercept

Equation B

[tex]-2x+4y=12[/tex]

For [tex]x=0, y=3[/tex] ----> y-intercept

For [tex]y=0, x=-6[/tex] ----> x-intercept

Plot the intercepts to graphs the lines

see the attached figure

Answer:

amplitude:  3; midline is y = 2

Step-by-step explanation:

Note that the range of this function is [-1, 5], values that are 6 units apart.  The amplitude is half that, or 3 units.

The midline is the horiz. line halfway between -1 and +5.:  y = 3.

These values correspond to the last (fourth) answer choice.

The amplitude and midline of a periodic function can be determined from the function's equation. The amplitude is the absolute value of the coefficient attached to the sine or cosine, and the midline (or vertical shift) is the constant added or subtracted in the function.

From the equation of a periodic function, we can determine the amplitude and midline. The amplitude is the absolute value of the coefficient of the function while the midline (or the vertical shift) can be found as the constant added or subtracted in the equation.

Let's consider your periodic function as y = A sin(kx) + D. Here, |A| is the amplitude and D is the midline of the function. However, the function itself is not provided in your question.

For instance, in the function y=0.2 m sin(6.28 m¯¹x − 1.57 s¯¹t), the amplitude, wave number, and angular frequency can be read directly. The amplitude here is 0.2 m (the multiplier of the sine term). It and doesn't seem to be any shifts up or down, so the midline is y = 0 (the x-axis).

So, you can find the amplitude and midline of a periodic function from the equation itself, however, you need the specific equation of your function to do that.

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I would say the answer is A

To find the portion of the beaker filled, consider the total volume of the beaker and the volume up to which it is filled. Perform division and multiply by 100 to get the percentage filled.

To determine the portion of the beaker filled, one must first understand the metrics of a beaker. A beaker is a cylindrical container with a flat bottom used to measure liquids. The scale etched on the side of the beaker represents the volume it contains. Suppose the total volume from the bottom up to the line of liquid is 300 mL and the total capacity of the beaker is 500 mL. By performing a simple division, 300 mL divided by 500 mL=0.6. Therefore, approximately 60% of the beaker would be filled. This is an approximate measure and for more accuracy, one should use a graduated cylinder.

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Answer:

39 feet

Step-by-step explanation:

From the question;

let length of ladder =x feet

height of ladder will be=x-3 feet

ground distance of ladder bottom to building=15 feet

Applying Pythagorean relation

a²+b²=c²

where a=15 feet b=x-3 feet and c=x feet thus

x²-15²=(x-3)²

x²-225=x²-6x+9

collect like term

x²-x²-225-9=-6x

-234= -6x

x= 39 feet length of ladder

distance from ground to top of ladder= 39-3=36 feet

The length of the ladder is 39 feet.

Let's denote the length of the ladder as x. According to the problem, the distance from the ground to the top of the ladder is 3 feetless than the length of the ladder. So, the height from the ground to the top of the ladder is x - 3 feet. The distance from the bottom of the ladder to the building is given as 15 feet. We can set up a right triangle where the ladder is the hypotenuse and solve for x using the Pythagorean Theorem:

x^2 = (x - 3)^2 + 15^2

Expanding and simplifying, we get:

x^2 = x^2 - 6x + 9 + 225

Combining like terms, we have:

0 = -6x + 234

Now, let's solve for x:

6x = 234

x = 39

Therefore, the length of the ladder is 39 feet.

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Answer:

x > -1

Step-by-step explanation:

Simplify x – 3 > -4 by adding 3 to both sides:

x > -1

This matches the 2nd answer choice.

The solution of the given expression x - 3 > -4 will be x > -1 thus, option (A) is correct.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given,

x - 3 > -4

Add 3 on both sides of the above inequality,

x - 3 + 3 > -4 + 3

x > -1

Hence "The solution of the given expression x - 3 > -4 will be x > -1".

For more about inequality,

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Answer:

15x

Step-by-step explanation:

9x+5x-1÷(x+1)

9x+5x-1÷1x

15x

Answer:

YESSSSSS

Step-by-step explanation:

i myself skipped pre-algebra and let me tell you it was the best decision ever. pre-algebra is by far the easiest and probably the most useless math course followed by geometry/trigonometry.

Yes

I would because it is a great opportunity to be ahead for when you get in 9th grade

Trig ratios can only be used on right triangles with acute measures.

If given an angle and there are adjacent and opposite sides, then use tan(opposite/adjacent)

If given an angle and there is an adjacent side and a hypotenuse, then use cosine(adjacent/hypotenuse)

If given an angle and there is an opposite and adjacent side, then use sin(opposite/hypotenuse)

A common mnemonic device used to memorize the trig rules is SOH-CAH-TOA

Trig ratios refer to the ratios of sides of a right triangle expressed about an angle. These include sine (sin), cosine (cos), and tangent (tan), as well as their reciprocals cosecant (csc), secant (sec), and cotangent (cot). They are fundamental in many real-world applications, including engineering, navigation, and physics.

The trigonometric ratios are ratios of sides of a right triangle. Specifically, we have the following respected relations between angles and sides: Sine (sin) is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Tangent (tan) is the ratio of the opposite side's length to the adjacent side's length. This is also equivalent to sin/cos. Respective reciprocal ratios are: cosecant (csc), secant (sec), and cotangent (cot).

These trig ratios allow us to determine distances, angles, and other aspects within a right triangle or representation of a circle.

For example, suppose we have a right triangle where the angle A is 30°, and the hypotenuse (the side opposite the right angle) is 10. In that case, we can determine the length of the opposite side by using the sin ratio, which is sin(30°) = Opposite/Hypotenuse. Solving, we get Opposite = sin(30°) * 10.

How do these trig ratios apply to real-world examples? Consider a ladder leaning against a wall, creating a right triangle with the ground. With the angle made at the ground and the length of the ladder, we can figure out how high up the ladder reaches on the wall using sin or how far from the base of the ladder's base should be placed using cos.

In conclusion, understanding trig ratios is an essential part of trigonometry and has numerous practical applications in real life, from construction and engineering to navigation and physics.

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Answer:

Part A: Up 9

Part B: Up 6

Step-by-step explanation:

Part A: The graph appears to be a cosine graph since it starts at a peak on the y-axis. Normally a cosine graph starts at (0,1). This graph begins at (0,10). It has been shifted up y a translation by 9.

Part B: Each trig equation has a basic structure f(x) = a sin (x+b) + k where:

A vertical translation is a vertical shift and is represented by the value in k added outside of the function. In the equation f(x) = 2sin(θ + 120°) + 6, k = 6. The vertical translation is 6.

47. 12388980384689 would be the exact circumference of a circle witha  diameter of 15 inches :)

Answer: Charles Darwin : the father of modern biology. AFP. Charles Darwin , born 200 years ago, put man in his place by including him in the long history of the evolution of species, denying the belief of a divine creation and founding modern biology.

Step-by-step explanation:

Answer:

The answer is (-7/2,0).

Answer:  [tex]\bold{x=\{0,-\dfrac{7}{2}\}}[/tex]

Step-by-step explanation:

[tex](x+2)(2x+3)=6\\\\\text{Expand:}\\2x^2+3x+4x+6=6\\\\\text{Simplify (add like terms):}\\2x^2+7x+6=0\\\\\text{Subtract 6 from both sides:}\\2x^2+7x=0\\\\\text{Factor out the common term:}\\x(2x+7)=0\\\\\text{Apply the Zero Product Property:}\\\boxed{x=0}\qquad 2x+7=0\\\\.\qquad \qquad 2x=-7\\\\.\qquad \qquad \boxed{x=-\dfrac{7}{2}}[/tex]

Answer:

[tex]y = x^2 + 6x + 8[/tex]

Step-by-step explanation:

The equation can be written using information from the graph. The vertex of the parabola is (-3,-1). Use the vertex form [tex]y = a(x-h)^2 + k[/tex] by substituting h = -3 and k = -1. The equation becomes [tex]y = a(x--3)^2 + -1[/tex]. It simplifies to [tex]y = a(x+3)^2 - 1[/tex]. To find a, substitute the point (x,y) on the graph into the equation and solve for a. Substitute x = -2 and y = 0.

[tex]0 = a(-2+3)^2 - 1[/tex]

[tex]0 = a(1)^2 - 1[/tex]

[tex]0 = a - 1[/tex]

[tex]1 = a[/tex]

So the equation is [tex]y = (x+ 3)^2 - 1[/tex]. Convert to standard form by distributing the parenthesis and combining like terms.

[tex]y = (x+ 3)^2 - 1\\y = x^2 + 3x + 3x + 9 - 1\\y = x^2 + 6x + 8[/tex]

Answer:

A=672 m²

Step-by-step explanation:

a²+b²=c² (to find h)

14²+b²=50²

196+b²=2,500

b²=2,304

√b²=√2,304

b=48

h=48

(base×height)÷2

(28×48)÷2

1,344÷2

A=672 m²

[tex]\[ n = 12 + 24 \][/tex] equation represents the total number of cookies Jesse.

Let's denote the total number of cookies Jesse bakes as [tex]\(n\)[/tex].

From the given information:

The total number of cookies he bakes is the sum of the cookies he leaves at home and the cookies he brings to school. We can represent this situation using an equation:

Total number of cookies baked [tex](\(n\))[/tex] = Cookies left at home + Cookies brought to school

[tex]\[ n = 12 + 24 \][/tex]

This equation represents the total number of cookies Jesse bakes [tex](\(n\))[/tex] as the sum of the cookies left at home (12 cookies) and the cookies brought to school (24 cookies).

Answer:

900

Step-by-step explanation:

If 40% per month = 300. Multiply 300 by 3.

Answer:

823 pounds of trash. ( approx )

Step-by-step explanation:

Since, the exponential growth function is,

[tex]A=P(1+r)^t[/tex]

Where,

P = initial value,

r = growth rate per period,

t = number of periods,

Here, P = 300 pounds, r = 40% = 0.4, t = 3 months,

Thus, the quantity of trash after 3 months,

[tex]A=300(1+0.4)^3=300(1.4)^3 = 823.2\approx 823\text{ pounds}[/tex]

Answer:

[tex]\boxed{\bold{3x+8}}[/tex]

Step By Step Explanation:

Remove Parenthesis: (a) = a

[tex]\bold{x+5+2x+3}[/tex]

Group Like Terms

[tex]\bold{x+2x+5+3}[/tex]

Combine Similar Elements: [tex]\bold{x+2x=3x}[/tex]

[tex]\bold{3x+5+3}[/tex]

Add: [tex]\bold{5+3=8}[/tex]

[tex]\bold{3x+8}[/tex]

➤ [tex]\boxed{\bold{Mordancy}}[/tex]

Answer:

3x + 8

Step-by-step explanation:

x + 5 + 2x + 3

You have to add like terms. You can't add x and 5 or 2x and 3.

x + 2x is like 2x + 2x, so 3x

5 + 3 is 8, so 3x + 8 is the answer.