How do you write 3 exponents?

The expansion of the series is 16 + 64 + 256 + 1024

The series is given as:

[tex]\sum\limits^4_{n=1} 4^{n+1}[/tex]

When n = 1, we have:

[tex]4^{n+1} = 4^{1+1} = 16[/tex]

[tex]4^{n+1} = 4^{2+1} = 64[/tex]

[tex]4^{n+1} = 4^{3+1} = 256[/tex]

[tex]4^{n+1} = 4^{4+1} = 1024[/tex]

Hence, the expansion of the series is 16 + 64 + 256 + 1024

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Answer:

C). 16 + 64 + 256 + 1,024

Step-by-step explanation:

I took the test and got it right :)

Answer:

b

Step-by-step explanation:

I'm quite positive its b hopefully:)!

Answer:

B.b if you follow the formula and chances are very high for it to be b

Total amount paid over the next year including the initial down payment and finance charge = $856

The difference between paying in cash for the laptop and this financial arrangement = $106

Cost of laptop=$750

Down payment=$150

Finance charges = $25

Remaining amount =$600

Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12

                                                                       =$56.75

Total amount paid over the next year including the initial down payment and finance charge =  56.75*12+150+25 = $ 856

The difference between paying in cash for the laptop and this financial arrangement = $106

Benefits of financing laptop:

A costly laptop can be yours without having to pay in full.

Bank loans and conventional credit card services are not required.

Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.

Downsides of financing laptop:

It's dangerous to borrow money because late payments might result in fees and excessive interest rates.

A credit score may suffer if there is no interest charged.

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Answer:

Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)

Step-by-step explanation:

The question doesn't specify which leg is under question.  Is it the adacent leg or the opposite leg?  I'll assume adjacent.

We can use the acronym

SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions.  For an angle other than the right angle, the following relationships are defined.

SOH:  S is sine = Opposite/Hypotenuse

CAH:  C is cosine = Adjacent/Hypotenuse

TOA:  T is tangent = Opposite/Adjacent

For a side adjacent (A) to the 36° angle, we can use

Cosine = Adjacent/Hypotenuse

Since we know the hypotenuse (12) we can find A:

Cosine(36) = A/12

A = Cosine(36)*12

A = (0.809)*12

Adjacent = 9.71

====================

If the opposite leg is calculated, we would use

Sine= Opposite/Hypotenuse

Sine(36) = Opposite/12

O = (0.5877)*12

Opposite = 7.053

Answer:

Step-by-step explanation:

The displacement is 90.7 meter from initial point.

According to the statement

Aster first walks 70m in the direction of 37 degree north of east

Aster walks 82m 20 degree south of east

Aster finally walks 28m in the direction of 30 degree west of north

We use

β= 37 degree +(30 degree −20 degree) = 47 degree

We can use cosine law to solve for R.

R = ((A)^2 + (B)^2 + 2ABcosβ)^1/2

R = ((70)^2 + (28)^2 + 2*70*28cos47)^1/2

R = (4900 + 784 + 3920*0.682)^1/2

R = (4900 + 784 + 2673.5)^1/2

R = (8357.5)^1/2

R = 90.7 m

So, The displacement is 90.7 meter from initial point.

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Answer: The percentile is 89

Step-by-step explanation:

This question can be solved using concept for t tables

In a normal distribution the curve. [tex]\mu= 1470 , \sigma = 230, x=1750[/tex]

The relationship between z score, mean and standard deviation is given by

[tex]x = \mu+z\sigma[/tex]

So the z value according to this is given by the formula

[tex]1750=1470+z(230)\\ z=\frac{280}{230} \\\\z = 1.217[/tex]

From the z table we can infer that p value for z=+1.217 is 88.82

So 1750 is 89th percentile

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Answer:

3.959797975

Step-by-step explanation:

1. Find the square root of 98 which is 9.899494937

2. Divide 9.899494937 by 2.5 which is 3.959797975

(sorry if it's wrong, but I think it's correct)

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Step-by-step explanation:

[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)

Take the expression

[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]

We can also write it as:

[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]

According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,

b² will be:

[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]

So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)

For STEP 4, the equation will become:

[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The next step is to divide b/a by 2 then square it and add to both sides.

This creates a perfect square quadratic on left side.

So the answer is :

x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared

Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm

Answer:

  (a)  6√3, 6√7

Step-by-step explanation:

The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.

Using P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...

  PF/FH = FL/PF   ⇒   PF = √(FH·FL)

  PL/FL = HL/PL   ⇒   PL = √(FL·HL)

  PH/HL = HF/PH   ⇒   PH = √(HL·HF)

(a) The distance from the park to the library is ...

  PL = √(FL·HL) = √(12·9) = 6√3 . . . miles

(b) The distance from the football field to the park is ...

  PF = √(FH·FL) = √(21·12) = 6√7 . . . miles

Answer: 17/y-5

Step-by-step explanation:

The expression that gives the product of the polynomials x³ + 2x + 1 and 4x³ + 3 is:

[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]

We multiply them applying the distributive property, multiplying all the terms and then combining the like terms.

In this problem, the factors are given as follows:

Hence the multiplication will be given by:

[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]

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The item which yield the greatest level of accuracy to the true weight of rock with the least error is bricks.

A rock refers to a solid substance formed from the fusion of organic minerals.

Therefore, bricks is the item which yield the greatest level of accuracy to the true weight of rock with the least error.

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The value of n is 99

Integers are the set of numbers including all natural numbers and 0. They are part of the real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered whole numbers.

Natural numbers together with zero (0) are referred to as whole numbers. We know that natural numbers refer to the set of counting numbers starting from 1, 2, 3, 4 and so on. Simply put, integers are a set of numbers without fractions, decimals, or even negative integers. It is a collection of positive integers and zero. Or we can say that integers are the set of non-negative integers.

Integers are the set of natural numbers togethe with the number 0. In mathematics, the set of integers is given as {0, 1, 2, 3, ...}, denoted by the symbol W.

W = {0, 1, 2, 3, 4, …}

All natural numbers are integers.

All integers are real numbers.

It is given that If n a whole number, and 0.01 is between 1/n and 1/n+2, then we need to find the value of n.

1/n+2 < 0.01 < 1/n

1/n+2 < 1/100 < 1/n

n< 100 < n +2

Put n = 99, then we get

99 < 100 < 101

Hence the value of n is 99.

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By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Given the following system of inequalities:

y ≤ 1/3x  ⇒ y - 1/3x ≤ 0

y - 2x < 4

By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

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Complete Question:

Graph the following system of inequalities.

y ≤ 1/3x and y - 2x < 4

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

The first quartile is the median of the first half, composed by 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of the second half, composed by 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

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The ratio of the tapestries' height to breadth is 3:2 when using full integers.

The ratio of two numbers is used to indicate proportions.

A/b, for example, is the ratio of a to b.

Given the subsequent sides, it is a tapestry.

Height = 1.5 m

Width = 1 m

So, height : width= 1.5:1

or, the fraction = 1.5/1=15/10= 3/2

or, it can be said 3:2

Since entire numbers are used, the ratio of the tapestries' height to breadth is 3:2.

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128000.

Let the three frithe ends x, y, z x is the first friend y is secmy ond friend

z is third friend

X+y+z=128000  

x=4z    

z=3y    

x=4(3y)=12y   put values of x and z in the first equation we got

12y+y+3y=128000

16y=128000

= 128000 - = 8000 16

Put the y value in equation 3 wee got

z=3*8000=24000

Put the z value in equation 2 we got

x=4*24000=96000

8000+24000+96000=128000.

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Answer:

The answer is A

Step-by-step explanation:

Answer:

, a ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction.

Then the answer will the first

Answer:

The powers are 3 and 5.

Step-by-step explanation:

When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:

11^a * 11^b = 11^(a+b)

11^a/ 11^b = 11^(a-b)

So, from the information given:

      a + b = 8

      a -  b = 2       Adding:-

    2a = 10

     a = 5.

and substituting in the second equation

   5 - b = 2

         b = 3.

Answer:

1. D) Both b) and c)

2. B) Cosine Law

3. B) Find the measures of angles and sides that we can't physically measure.

Step-by-step explanation:

1. To solve non-right triangles we use Sine Law and Cosine Law.

2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.

3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.

Answer:

Step-by-step explanation:

The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.

The domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).

The range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).

Answer:

Improper fraction

Step-by-step explanation:

-36/12 is indeed an improper fraction. An improper fraction is usually a fraction where the numerator is larger than the denominator. Which in order for the fraction to be a "proper" fraction, the fraction has to have a numerator that is smaller than the denominator. Not only is this fraction an improper one, but it can also be heavily reduced (or simplified) by dividing the numerator/denominator by a common factor, which you would still have an improper fraction speaking how the numerator will still be greater than the denominator.

Hope this helps.

Answer:

Proper Fraction

Step-by-step explanation:

Answer:

or in interval notation [-2,∞)

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

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

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The height (h) is represented by:

h(t) = -4.9t² + 40t + 20

The maximum height is at h'(t) = 0, hence:

h'(t) = -9,8t + 40

-9.8t + 40 = 0

t =  4.082

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

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

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt[4]{x - 4} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4 = (3) {}^{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4 = 81[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 81 + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 85[/tex]

So, the correct choice is 85

Answer:

Step-by-step explanation:

4√(x-4) = 3

√(x-4) = 3/4

Square both sides:

x - 4  = 9/16

x = 4 + 9/16

x = 4 9/16.

Option 2. The equation of the parabola is given as y = one eighthx² + 5

We have the coordinate plane to be passing through the graph at point C on the y axis. This is used to represent the slope.

Hence the slope is 5

The equation of the line is given as  y=x²+C

Hence we can see that there is a rising slope. So the answer is Option 2.

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Applying the commutative law to our question, we have; 14 + ab = ab + 14

The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;

ab + cd = cd + ab

similarly, fg * jk = jk * fg

Applying the above commutative law to our question, we have;

14 + ab = ab + 14

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Answer:

7k - 7

Step-by-step explanation:

- k - (- 8k + 7) ← distribute parenthesis by - 1

= - k + 8k - 7 ← collect like terms

= 7k - 7