Exponents Properties Practice

Write an equation to model the situation and answer the question. Include units when applicable.

In a much happier economy, Mr. Demo earns 5% monthly interest on his savings. After a $300 withdrawal, he notices he has $2021 in his account. He has collected interest for 3 months. What amount did he start with?

Answer:

what are the answers

Step-by-step explanation:

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Explanation:

The given function is f(x) = x^2 - 2x

Let's apply function composition like so

[tex]f(x) = x^2 - 2x\\\\f(f(x)) = (f(x))^2 - 2(f(x))\\\\f(f(x)) = (x^2-2x)^2 - 2(x^2-2x)\\\\[/tex]

In the second step, I replaced every x with f(x). Then in the third step, I replaced f(x) with x^2-2x on the right side.

Setting this equal to f(x) gets us

[tex]f(f(x)) = f(x)\\\\(x^2-2x)^2 - 2(x^2-2x) = x^2-2x\\\\[/tex]

which is a bit cluttered. However, we have "x^2-2x" show up three times. Let's say w = x^2-2x

If we replaced all those "x^2-2x" expressions with w, then we get,

[tex](x^2-2x)^2 - 2(x^2-2x) = x^2-2x\\\\w^2 - 2w = w\\\\[/tex]

Which looks more manageable

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Let's solve for w

w^2 - 2w = w

w^2 - 2w-w = 0

w^2 - 3w = 0

w(w - 3) = 0

w = 0 or w-3 = 0

w = 0 or w = 3

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If w = 0, then,

w = x^2 - 2x

x^2 - 2x = w

x^2 - 2x = 0

x(x - 2) = 0

x = 0 or x-2 = 0

x = 0 or x = 2 are two solutions (out of four total)

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Or, if w = 3, then,

w = x^2 - 2x

x^2 - 2x = w

x^2 - 2x = 3

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x-3 = 0 or x+1 = 0

x = 3 or x = -1 are the other two solutions

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To summarize, the four solutions are:  x = -1, x = 0, x = 2, x = 3

Answer:

217 is the perfect swuare i think

Answer:

[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]

Answer:

(y, -x)

Step-by-step explanation:

Rotation of 90°

(Clockwise)

(x, y)  ---> (y, -x)

Rotation of 90°

(CounterClockwise)

(x, y) --> (-y, x)

Rotation of 180°

(Both Clockwise and Counterclockwise)

(x, y) ---> (-x, -y)

Rotation of 270°

(Clockwise)

(x, y) ---> (-y, x)

Rotation of 270°

(CounterClockwise)

(x, y) ---> (y, -x)

Answer:

0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

For the pair of dice:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

So 36 total outcomes.

Desired outcomes:

Sum being multiplies of 3 or multiples of 4, so:

(1,2), (1,3), (1,5)

(2,1), (2,2), (2,4), (2,6)

(3,1), (3,3), (3,5), (3,6)

(4,2), (4,4), (4,5)

(5,1), (5,3), (5,4)

(6,2), (6,3), (6,6)

3 + 4 + 4 + 3 + 3 + 3 = 20

Probability:

[tex]p = \frac{20}{36} = 0.5555[/tex]

0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.

By taking the addition of the values in the table and overestimating a little bit, the correct option is B: $60.00

Here we have the following table of average costs:

Assuming you eat these 3 per day, the total cost in food per day is the sum of all the values in the table.

It gives:

Total cost: $12.98 + $18.95 + $26.58 = $48.51

Notice that these are average costs, so you should budget a little bit over that just in case, then the correct option is $60, which is the first option over the average total cost.

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Answer:

45

Step-by-step explanation:

Answer:

i cant see it good

Step-by-step explanation:

prob its me

Answer:

B. √3 inches

Step-by-step explanation:

Apply trigonometry ratio to solve for AB

AB = DC (opposite sides of a rectangle are equal)

Given,

reference angle (θ) = 30°

Hypotenuse = BD = 2

Adjacent = DC = ?

Apply CAH, which is:

Cos θ = Adj/Hyp

Substitute

Cos 30° = DC/2

2*Cos 30° = DC

2*√3/2 = DC (Cos 30° = √3/2)

DC = √3 in.

AB = DC. Therefore,

AB = √3 inches

9514 1404 393

Answer:

  (b)  x = -2

Step-by-step explanation:

The graph shows the lines intersect at (x, y) = (-2, 3).

The x-coordinate of the solution is x = -2.

Answer:

{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}

Step-by-step explanation:

We have:

Weight as a function of height.

Give the points for these students that represent height as a function of weight:

Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:

{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}

9514 1404 393

Answer:

  382 cm²

Step-by-step explanation:

The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(8 +14)(7) = 77 . . . . cm²

The perimeter of the face is ...

  7 cm + 8 cm + 9 cm + 14 cm = 38 cm

The total surface area is the sum of the lateral area and the base area.

  SA = LA + BA

  SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²

  SA = 382 cm²

The surface area of the composite figure is 382 square centimeters.

_____

Additional comment

The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).

There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.

Answer:

The point is a solution

Step-by-step explanation:

y = x^2

Substitute the point into the equation and see if it is true

0 = 0^2

0=0

True

15,068 mi/hr

Step-by-step explanation:

[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]

[tex]=15,068\:\text{mi/hr}[/tex]

The speed of 22100 feet per second will be 15068.18 miles per hour.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.

Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,

22100 ft /s = ( 22100 x 3600 ) / 5280

22100 ft/s = 79560000 / 5280

22100 ft/s = 15068.18 miles per hour

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Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

Answer:

E

Step-by-step explanation:

Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by

[tex]10 {}^{2} [/tex]

So our new equation is

[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]

Solve by AC method

[tex]ac = - 462[/tex]

[tex]b = 71[/tex]

We must think of two numbers that

Multiply to -462 and Add to 71. Set up equation

The numbers are 77 and -6.

So our new equation is

[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]

Solve by factoring by grouping

[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]

Factor out 11 for the first equation

[tex]11x(3x + 7) - 2(3x + 7)[/tex]

So our factors are

[tex](11x - 2)(3x + 7)[/tex]

Set each equal to zero

[tex]11x - 2 = 0[/tex]

[tex]11x = 2[/tex]

[tex]x = \frac{2}{11} [/tex]

[tex]3x + 7 = [/tex]

[tex]3x = - 7[/tex]

[tex]x = \frac{ - 7}{3} [/tex]

Answer:

I'm sorry but I don't know this one

Answer:

8 x 9

Have a nice day!

Answer:

50 ft

Step-by-step explanation:

For this problem we will use the Pythagorean theorem which is: a^2+b^2= c^2

I found the length for both of the legs on this triangle which are: 30 ft (for the side on the far left) and 40ft (for the other leg of the triangle whose hypotenuse is the walkway).

Now that we know the two legs we can use the Pythagorean theorem:

40^2 + 30^2 = 2500

then take the square root of 2500 in order to find the hypotenuse length:

Square root of 2500= 50ft

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Answer:

50ft

Step-by-step explanation:

trust me on this answer

Answer:

F. Obtuse isosceles

Step-by-step explanation:

Since we have an angle that is 100 degrees, we have an obtuse angle

We have two angles that are 40, which means we have two sides that are equal length, because two angles have the same measure.  That means it is isosceles

The triangle is an obtuse isosceles

The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,

[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]

Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.

So you have

• upper estimate:

(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)

= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)

= 70.2 L

• lower estimate:

(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)

= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)

= 63.2 L

Answer:

-3<x≤4

Step-by-step explanation:

Answer:

4 [tex]\geq[/tex] x > -3

Step-by-step explanation:

I just put the written form into inequality form.

Answer:

5

Step-by-step explanation:

trust

Answer:

24

Step-by-step explanation:

The sample space is the total possible values of an experiment or research. Since the total number of hours is 24, then the total possible number (or the limit she can use have) is 24. This she cannot exceed this 24 hour limit. Then we call this the total possible outcome and thus the sample space.

Answer:

2 Gallons of Soda

Step-by-step explanation:

that is the answer above

Answer:

5.503484≤x≤9.116516

Step-by-step explanation:

The formula for calculating the CI is expressed as;

CI = x±z*s/√n

x is the mean= 7.31

z is the 99% z-score = 2.58

s is the standard deviation = 6.26

n is the sample size = 80

Substitute into the formula

CI = 7.31± 2.58*6.26/√80

CI = 7.31± 2.58*6.26/8.94

CI = 7.31± (2.58*0.7002)

CI = 7.31±1.806516

CI = (7.31-1.806516, 7.31+1.806516)

CI = (5.503484, 9.116516)

Hence the 99% confidence interval for the population mean is

5.503484≤x≤9.116516

Answer:

Pick only one of these values. So if the first one doesn't work, then try the other one. Unfortunately, your teacher isn't clear on which value to go with.

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Explanation:

Nice work on getting the mean so far.

To get the standard deviation, we'll use the value 236 in the table. This value is the sum of everything above it. So it's the sum of the [tex](x-\overline{x})^2[/tex] values. We call this the sum of the squared errors. The errors themselves being [tex]x-\overline{x}[/tex]

So we'll divide 236 over n = 4 to get 236/4 = 59

This will get us the population variance. Apply the square root to get [tex]\sqrt{59} \approx 7.68[/tex] which is the population standard deviation.

So if your teacher wants the population standard deviation, then the answer is 7.68

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If that answer doesn't work, then try this section.

Unfortunately, there are two flavors of standard deviation. The good news is that we don't have to do much work to find the sample standard deviation.

Instead of dividing by n = 4, we'll divide by n-1 = 4-1 = 3.

So 236/3 = 78.667

Since the value is approximate, I'll leave it as a fraction.

This represents the sample variance.

Apply the square root to get the sample standard deviation

[tex]\sqrt{\frac{236}{3}} \approx 8.87[/tex]

and that value is the sample standard deviation.

If the answer in the previous section doesn't work, then the answer must be 8.87

b(8b+7)

Answer:

Solution given;

8b²+7b

let look what is common there;

8*b*b+7*b

over here b is common

take common and keep other remaining on bracket

b(8b+7)

In a simple way b(8b+7) is a factorise form of

8b²+7b

Answer:

Step-by-step explanation:

2.5 = 5 * .5

1 = 1

70 = 2 * 5 *  7

LCM = 2 * 5 * 7

If you include the 1/2, you will reduce the LCM to 35, but 70 will be left out of the LCM.