Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.

a. How much will be in the account after 3 years?

The given expression contains a fractional exponent and would be simplified through solving for it.

The reciprocal of power associated with the base is the degree of the radical signs.

For example: ∜7=7^1/4

In the given expression, there are two considerations. The number 243 has a power of 1/5, and the negative sign or say -1 also has a power of 1/5.

As a general rule, if the denominator of the fractional exponent is an odd number, as 5 in this case, the negative sign is extracted from the radical. Another way to look at it is -1 raised to any odd power would be -1.

Hence, (-243)^¹/₅ =-(243)^¹/₅

Factorizing the term,

243=3*3*3*3*3

Which can be expressed as 3^5

Hence,

-(243)^1/5=-(35)^1/5

As we know that (a^b)^c=a^bc, thus,

-(3^5^)1/5=-(3^5*1/5)= -(3^1)=-3

(-243)^¹/₅is simplified to -3

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Answer:

244Y

1E

Step-by-step explanation:

Answer:

The answer is D. 20,000

Step-by-step explanation:

Hope this helps!!!

Sorry if I'm wrong

The kilograms of apples and pears that the store rreceiv is 120kg and 108kg.

It should be noted that 40% of them are apples, 36% are pears. The percentage for peaches will be:

= 100 - (40% + 36%)

= 24%

The total fruit will be x. This will be:

24% of x = 72

0.24x = 72

x = 72/0.24

x = 300

Apples will be:

= 40% × 300

= 120kg

Pears = 36% × 300

= 108kg

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Using the graph, the value of f(-3) is 2

From the question, we are to determine the value of the given function

The given function is f(-3)

To determine the value of f(-3) on the graph, we will trace from the point where x = -3 on the x-axis to the line of the function and then trace from the line to the y-axis. The value on the y-axis is the value of f(-3)

From the graph,

Tracing from the point where x = -3 to the line and then to the y-axis, we get y = 2

∴ f(-3) = 2

Hence, the value of f(-3) is 2

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The drawing's scale factor that Shannon used to measure a neighborhood park is 1:72.

It should be noted that 36 inches equals to 1 yards. Therefore, the value of 2 yards will be:

= 2 × 36

= 72 inches.

Therefore, the drawing's scale factor that Shannon used to measure a neighborhood park is 1:72.

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The relation that is not a function, but whose inverse is a function are:

for every x in the domain of f, f -1[f(x)] = x, and

for every x in the domain of f -1, f[f -1(x)] = x

An inverse function is a characteristic that undoes the movement of another characteristic. A feature g is the inverse of a characteristic f if whenever y=f(x) then x=g(y). In different words, applying f and then g is the equal aspect as doing not anything. we are able to write this in terms of the composition of f and g as g(f(x))=x.

A few capabilities do not have inverse functions. for instance, remember f(x) = x2. There are numbers that f takes to four, f(2) = 4 and f(-2) = four. If f had an inverse, then the fact that f(2) = 4 might mean that the inverse of f takes four again to 2.

To discover the inverse function of an algebraic relation in terms of x and y, simply interchange the variables x and y, and resolve the equation for y. as an example, to discover the inverse of a relation y = x3, interchange x, and y after which clear up it for y. Then we get x = y3 ⇒ y = x1/3.

An inverse version can be represented by means of the equation xy=k or y=kx. this is, y varies inversely as x if there are a few nonzero steady k such that, xy=k or y=kx in which x≠0,y≠0 . assume y varies inversely as x such that xy=3 or y=3x.

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Answer:

2/3

Step-by-step explanation:

btw was it -11/3 or -1 & 1/3 cuz I did -2/3 - (-1 &1/3)​

The model equation to find the number of hours she should work to earn $728 per week is given as 16a +56b = 728

It is given that,

Elena is earning as a swimming instructor = $16.00 an hour

Also, she is earning as an intern in a genetics = $56.00 per hour

The condition which is given is that, Elena needs to earn at least $728

per week in order par her college fees

We need to find the, equation which can resolve this situation to find the number of hours she should work to earn $728 per week

Let the number of hours she works teaching swimming = a

And, let number of hours she works as an intern in genetics = b

Then, the equation can be made as = 16a +56b = 728

Hence, the model equation to find the number of hours she should work to earn $728 per week is given as 16a +56b = 728  

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The surface area of a rectangular cuboid cake which covered by a cookie crumble is approximately 35.1 m²

The cake can be depicted as in the attached picture with

length (l) = 4.45 meters

wide (w) = 4.06 meters

height (h) = 1 meter

It is a rectangular cuboid, or a right rectangular prism, which has 6 rectangular faces. Since all surfaces were covered by a cookie crumble except the bottom, hence, the surface areas are:

top face = l x w = 4.45 x 4.06 = 18.067 m²

left/right faces = 2 x w x h = 2 x 4.06 x 1 = 8.12 m²

front/back faces = 2 x l x h = 2 x 4.45 x 1 = 8.90 m²

Therefore, total surface area covered by the sprinkle is:

Total surface = 18.067 + 8.12 + 8.90  ≈ 35.1 m² ( to the nearest tenth)

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Answer:

The answer is C: y=3x+6

Step-by-step explanation:

Answer: n = 15/2

Step-by-step explanation:

Divide both sides n/10 = 3/34

Calculate n = 3/4 x 10

Answer is n = 15/2

Answer:

Given: two sides and a non-included angle

Step-by-step explanation:

This can sometimes result in 2 possible values when using the Law of Sines, since sin(180°-x)=sin(x)

A uniform distribution has the data values evenly distributed throughout the range of the data. A bimodal distribution has two very common data values seen in a dot plot or histogram as distinct peaks.

A Dot Plot, also called a dot chart or strip plot, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins (categories). A dot plot is similar to a bar graph because the height of each “bar” of dots is equal to the number of items in a particular category.

A dot plot is a graphical display of data using dots: Dot Plot is a graph for displaying the distribution of quantitative variable where each dot represents a value. For whole numbers, if a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value.

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After expanding logarithm equation is : [tex]\frac{5.log_4(\sqrt{x} )y^7}{zu^4}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_4((\sqrt{x})^5 )y^7}{zu^4} \\[/tex]

apply formulas log a^x = x log a

[tex]log_4\sqrt{x}^5 = 5 log_4\sqrt{x}[/tex]

=> [tex]\frac{5.log_4(\sqrt{x} )y^7}{zu^4}[/tex]

Thus, after expanding the logarithm equation is : [tex]\frac{5.log_4(\sqrt{x} )y^7}{zu^4}[/tex]

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After solving the given equation 7x-2=252, the value of x = 36.9.

So,

Then,

7x-2=252

Therefore, after solving the given equation 7x-2=252, the value of x = 36.9.

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The amount that Carl will receive after 3 years is $ 27,146.49 when he invested $ 1220 at 9 % compound interest monthly.

We are given that:

Principal amount = P = $ 1,220

Compound interest rate = r = 9 % monthly

Time = 3 years = 3 × 12 months = 36 months.

The amount after 3 years will be given by:

Amount = 1,220 ( 1 + 0.09)³⁶

Amount = 1,220 ( 1.09 )³⁶

Amount = 1220 ( 22.25 )

Amount = $ 27,146.49

Therefore, we get that, the amount that Carl will receive after 3 years is $ 27,146.49 when he invested $ 1220 at 9 % compound interest monthly.

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The midpoint of diagonal AC is (5,-3).

Given A(3,-1) and C(7,-5)

Let the midpoint of diagonal AC be represented by P (say). Then the coordinate of P can be calculated by using the formula listed below:

let us suppose the coordinates of A be (a, b) and B be (c, d) and P is the midpoint of AC then the coordinate of P will be (a+c/2, b+d/2).

Now, by using the above formula, we get

x-coordinate of P be (3+7)/2 = 10/2 = 5

y-coordinate of P be (-1+(-5))/2 = -6/2 = -3

∴ The coordinate of midpoint of AC i.e., P be (5, -3).

Hence, the midpoint of diagonal AC is (5,-3).

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The solution of the given expression 3x⁻¹=24 is x = 1/8.

An exponent (also known as a power or degree) indicates the number of times the base is multiplied by itself. For example,'has an exponent of 5 and a base of. This means that variable would be multiplied 5 times by itself. This can also be thought of as to a fifth power.

Some properties of the exponents are given as-

Now, for the stated question;

The given expression is;

=> 3x⁻¹ = 24

Divide both sides by 3.

=> x⁻¹ = 8

Taking the reciprocal on both sides.

=> 1/x⁻¹ = 1/8

This 1/x⁻¹ can be written as x.

=> x = 1/8

Therefore, the value of the x for the given expression 3x⁻¹=24 is 1/8.

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Answer: x∈[0;+∞)

Step-by-step explanation:

[tex]|x|-6 > -16\\|x|-6+6 > -16+6\\|x| > -10\\[/tex]

As |x|≥0, hence: x≥0

Answer: I just did the ones that did not already have an answer

Section A:

7. 1.5 hours

9. 480 meters

10. 10 km

Section B:

1. 40 mph

2. 160 miles

3. 168 miles

4. 5.2 mph

5. 26.25 km/h

Answer:

J.o.i.n p.l.z pqp-yuth-ygd

From the information given, the value of b if YH = 12b - 4.5, MV = 17b +0.75, and MW-WH = 13.25 is 0. 59

Algebraic expressions are simplify defined as expressions that are composed of terms, variable, coefficients, factors and also constants.

They also seen as expressions involving arithmetic operations such as;

From the information given, we have that;

MW-WH = 13.25.

Where;

Now, to determine the value of b, substitute the values into the equation

17b +0.75 + 12b - 4.5 = 13. 25

collect like terms

17b + 12b = 13.25 + 4. 5 - 0. 75

add or subtract like terms

29b = 17

Make 'b' the subject of formula by dividing both sides by 29, we have;

29b/29 = 17/29

Divide through

b = 0. 59

Thus, the value of b is 0. 59

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Based on the dimensions of the rectangle and the dimensions of the sod, Jim will need to buy 87 pieces of sod to cover his backyard with sod.

First, find the area of the backyard which is shaped like a rectangle:

= 14⁵/₆ x 10²/₅

= 154.27 yards²

The area of a single sod is:

= 1¹/₃ x 1¹/₃

= 1.78 yards²

The number of sods needed is:

= 154.27 / 1.78

= 86.775

= 87 sods

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C.It is zero.

The net force is the sum of all of the forces exerted on an object.

Identifying Forces

Force is measured in newtons, which is shortened to N. Additionally, force will always have a direction, like 5N up or 3N to the left.

Sometimes force will be negative to represent direction. A force moving down or to the left might be negative because moving down or to the left on an axis moves towards negative numbers.

Net Force

As stated above, the net force is the sum of all of the forces acting on an object. For example, if one object is being moved 5N to the left and 4N to the right, the net force will be 1N to the left.

On the other hand, if the forces are balanced, like 5N on both the left and right, then the forces cancel out. This leaves a net force of 0.

The solution to start fraction x over negative 6 end fraction = 10 is -60.

Here the equation will be

x/-6 = 10

We have to solve for the value of x. So, in order to solve for the value of x we simply have to multiply -6 by the RHS of the equation i.e., 10.

⇒x = -6x10

⇒x = -60

Therefore, the solution to start fraction x over negative 6 end fraction = 10 is -60.

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The measure of angles 1, 2 and 3 for fig in 11. are 100°, 80° and 100°. And for part 12. are 80°, 80° and 100° respectively.

For 11. part:

Considering two parallel lines l and m cut by a transversal p,

If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.

m∠1 + 80° = 180°

m∠1 = 180° - 80°

m∠1 = 100°

Similarly, m∠1 + m∠2 = 180°

⇒ 100° + m∠2 = 180°

⇒m∠2 = 180° - 100°

⇒m∠2 = 80°

and also, m∠2 + m∠3 = 180°

⇒ 80° + m∠3 = 180°

⇒m∠3 = 180° - 80°

⇒m∠3 = 100°

Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.

For 13. part:

m∠3 = 100° (vertically opposite angle)

Now, let us suppose the angle adjacent to ∠3 be x then, m∠x will be simply equal to

m∠3 + m ∠x = 180° (Linear pair property.)

100° + m ∠x = 180°

m ∠x = 180° - 100°

m ∠x = 80°

Now, from the figure we can clearly see that,

m∠1 = m∠2 = m ∠x  = 80°(Corresponding angles are equal.)

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Answer:

Dad: 312 miles

Mom: 62.4 miles

Sister: 105.6 miles

Step-by-step explanation:

Dad: 480 x .65 = 312

Mom: 312 x .2 = 62.4

Sister: 480 - 312 -62.4 = 105.6

The equation 18/6 = 3 shows that 6 is a factor of the number 18.

An equation is an expression that shows the relationship between two or more numbers and variables.

A factor is a number that divides the given number without having any remainder.

Given that 6 is a factor of 18, hence:

18/6 = 3

The equation 18/6 = 3 shows that 6 is a factor of the number 18.

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