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The length of a bacterial cell is about 3 x 10−6 m, and the length of an amoeba cell is about 4.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.

2 x 102
2 x 103
0.7 x 101
6.67 x 102

Answer:

  no, no, yes, yes

Step-by-step explanation:

You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.

The attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.

  (4, -5) . . . not a solution

  (-1, 8) . . . not a solution

  (7, 11) is a solution

  (0, -3) is a solution

1. The table of values for Dianely's salary can be represented for 4 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.

For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.

Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.

Initial salary = $40,000

Salary raise per year = $2,500

Disney's salary after n years in equation form, S = 40,000 + 2,500n.

Table of Values for Dianely's Salary:

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

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The value of a, and c is 1, -3, and 0;, using the factorization of factors.

What is factorization of expressions?

To factorize an algebraic statement, we first identify the terms' greatest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic statement gets expanded in the opposite direction.

Not every term may share a factor in some algebraic formulas. For instance, have a look at the algebraic formula 12a + n -na - 12. There is no specific factor that unites the terms in this statement, yet the first and last terms share a factor of 12. The common factor between the second and third terms is n. Consequently, the terms can be rearranged as follows:

12a + n - na - 12= 12a - 12 + n - an

12a - 12 - a plus n = 12(a - 1) -n (a -1)

Following regrouping, each term's common component may be shown to be (a-1): 12a + n -na - 12=(a-1) (12 – n)

In the given question,

The expression is:

[tex]\frac{31x^{2}y}{x^{5}y}[/tex]

and after simplifying the expression, we get:

[tex]\frac{31}{x^{3}}[/tex]

So, Now comparing the equation, with a[tex]x^{b}[/tex]×[tex]y^{c}[/tex], we get;

b = -3;

c = 0;

a = 1;

Hence, The value of a, and c is 1, -3, and 0;

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Answer: v=2.33333333333333.........

Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......

Answer: [tex]x=\pm \sqrt{22}[/tex]

Step-by-step explanation:

[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]

Answer:

sqrt(22) = [tex]\sqrt{22}[/tex]

Step-by-step explanation:

we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem

log(x-1) + log(x+1) =  = [tex]log((x-1)(x+1))[/tex] = log(21)

this means that x^2 - 1 equals 21

xx-1 = 21

xx=22

x=sqrt(22)

Step-by-step explanation:

To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.

(a) What was the total amount Linda ended up paying for the equipment

(including the down payment and monthly payments)?

How much on loan:

12,200 - 1,600 = $10,600 loan amount

How much paid on loan:

$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan

Total paid:

= loan amount + amount paid on loan

$10,600 + $$11,608.28

= $22,208.28 paid overall

________________________________________

(b) How much interest did Linda pay on the loan?

= loan amount - amount  paid on loan

= $11,608.28 - $10,600

= $1,009.28 paid in interest

Answer:

120 free throw attempts

Step-by-step explanation:

[tex]95\%=0.95[/tex]

[tex]0.95x=114[/tex]

[tex]x=\frac{114}{0.95}[/tex]

[tex]x=120[/tex]

The solution of the geometric equation is x = 1/2 or x = 1

An equation is a mathematical expression that shows the relationship between variables.

A geometric series is the sum of a geometric sequence.

Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p

So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).

0 = (1 - [X + X²+...) (2 - [X + X²+...).

Substitute x + x² + ... = p. So,

0 = (1 - [X + X²+...) (2 - [X + X²+...).

0 = (1 - p)(2 - p).

So, (1 - p) = 0 or (2 - p) = 0

p = 1 or p = 2

Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.

The sum to infinity of the geometric series is given by

S = a/(1 - r) where

For the given series,

So, S = a/(1 - r)

= x/(1 - x)

Since S = p, we have that

x/(1 - x) = 1 or x/(1 - x) = 2

So, x = 1 - x or x = 2 - x

x + x = 1 or x + x = 2

2x = 1 or 2x = 2

x = 1/2 or x = 2/2

x = 1/2 or x = 1

So, the solution is x = 1/2 or x = 1

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The critical number are 0, 7 , -7.

Given function:

g(x) = [tex]\sqrt{49-x^{2} }[/tex]

first derivative is,

= -x/([tex]\sqrt{49-x^{2} }[/tex] )

-x = 0 or x = 0

[tex]\sqrt{49-x^{2} }[/tex] = 0

49 - [tex]x^{2} =0[/tex]

49 = [tex]x^{2}[/tex]

x = 7 , -7.

Therefore the critical number are 0, 7 , -7.

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The numbers are plotted in the attached graph.

A number line is a representation of real numbers in the form of a graded straight line.

Note that 5/3 is approximately equal to 1.7.

Similarly, -5/3 is approximately equal to -1.7.

Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.

The numbers are plotted in the attached graph.

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Answer: 1/6

Step-by-step explanation: Make all of the denominators the same. The least common multiple of 6 and 12 is 12. 1/6 gets multiplied by 2/2 to the equivalent fraction 2/12. 11/12 stays the same. 5/6 is multiplied by 2/2 to get 10/12. 10/12 stays the same. 1/6 is the smallest fraction so it is the closest to 0.

Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.

An equation is an algebraic equality in which letters appear with unknown value.

In an equation appears:

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:

Being "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:

y + (-3)= -8

Solving:

y -3= -8

y= -8 +3

y= -5

Finally, the number "y" is -5.

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Answer:

Step-by-step explanation:

step 1 of 2:  

We got pairs: (-3, y) and (x, 2), to compute the missing x and y values, we plugin the number into the equation.

(-3, y)

y = -3x - 1

y = -3(-3) - 1

y = 9 - 1

y = 8

So we solve this pair as (-3, 8).

(x, 2)

y = -3x - 1

2 = -3x - 1

3 = -3x

x = -1

So we solve this pair as (-1, 2).

Sorry that I cannot see the following questions.

The values of the variables as represented in the right triangle are; (8√15)/3 and s = (4√15)/3.

It follows from the task content that the values of the variables in the right triangle are to be determined.

It follows from trigonometric ratios that;

Sin (∆) = opposite / hypothenuse

Cos (∆) = adjacent / hypothenuse

Tan (∆) = opposite / adjacent

It therefore follows from the attached image that;

Sin (60) = 4√5 ÷ p

p = 4√5 ÷ √3/2

p = (8√15)/3.

Also;

Tan (60) = 4√5 ÷ s

s = 4√5 ÷ √3

s = (4√15)/3

Therefore, the value of the variables are; p = (8√15)/3 and s = (4√15)/3.

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The revolution per minute done by the wheel of a bicycle is 16.9 rev/min.

Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.

In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.

As per the given information in the question,

Diameter of wheel = 20 inch

Radius, r = 10 inch

The velocity of the bicycle, v = 13 mi/h.

Revolution, R = v²/r

R = 13²/10

R = 16.9 rev/min

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The fraction of page in the photograph is 3/32.

So, the fraction of the page in the photograph:

We know that,

Now, calculate as follows:

Therefore, the fraction of page in the photograph is 3/32.

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Answer:

=3/32

Step-by-step explanation:

(1/2÷4)*3/4

1/2*1/4*3/4

1/8*3/4

There-For The Answer Is:

=3/32

Step-by-step explanation:

5.

xnew = 205 = 2×xold + 5

200 = 2×xold

xold = 100

the old city machine can produce 100 copies per hour.

6.

2 cups of milk relate to 6 1/4 cups of flour.

such recipes represent a direct dependency of one variable on the other. one variable is always the other variable multiplied by a constant factor.

m = cups of milk

f = cups of flour

m = n×f

2 = n×(6 1/4) = n×(6×4 + 1)/4 = n×25/4

8 = 25n

n = 8/25

now, f = 43 3/4 = (43×4 + 3)/4 = 175/4

so,

m = 8/25 × 175/4 = (8×175)/(25×4) = 2×7 = 14

you will need 14 cups of milk.

A set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers.

What are Real numbers?

The set of real numbers is represented by the letter R.

Every number (except complex numbers) is contained in the set of real numbers. For example: 2, -8, 33/5, -1/5, 0, etc.

What are Integers?

The set of integers is represented by the letter Z.

An integer is any number in the infinite set, Z = (..., -3, -2, -1, 0, 1, 2, 3, ...}

Integers can further be divided into

What are Natural numbers?

The set of natural numbers is represented by the letter N.

A natural number is a positive integer.

N = { 1, 2, 3, 4, ... }

According to the given question:-

Set of real numbers comprises of Rational numbers, irrational numbers, integers, whole numbers, etc.

Hence a set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers i.e.

N = { 1, 2, 3, 4, ... }

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Step-by-step explanation:

that means that

$37.45 = 107%

as the price was 100% base price + 7% tax.

1% = 107%/107

100% = 1% × 100 = 107% × 100 / 107

so, the basic price (the "original cost") is

37.45 × 100/107 = $35.00

The value of y is,  [tex]y = \frac{tan^-^1(-x) + \pi n}{x}[/tex].

What is tangent function?

One of the primary six trigonometric functions, the tangent function is typically expressed as tan x. When considering the angle in a right-angled triangle, it is the ratio of the opposite side to the adjacent side.

Consider, the given function

x + tan(xy) = 0

Subtract x from both sides,

x + tan(xy) - x = -x

          tan(xy) = -x

Apply tan inverse on both sides,

[tex]xy = tan^-^1(-x) + n\pi[/tex]                      (Tangent function is a periodic function)

Divide both sides by x,

[tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex],         x ≠ 0

Hence, the value of y is, y = [tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex].

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Answer:

-2/5

Step-by-step explanation:

the slope is change in y over change in x

formula for slope is

(y2-y1)/(x2-x1), so if you input the coordinates, (10-(-2))/(-11-19) = 12/30 = 2/5

[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]

The statement that accurately describes the difference between short-term and long-term capital gains in terms of taxes is A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains.

A capital gains tax is a tax levied on profits made from the sale of a non-inventory asset. Capital gains from the sale of stocks, bonds, precious metals, real estate, and property are the most common.

Short-term capital gains are profits made from selling assets held for a year or less. Long-term capital gains, on the other hand, are gains from assets held for more than a year.

In conclusion, based on the information illustrated, the correct option is A.

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Answer:

25+10(4)= 65

Step-by-step explanation:

think of it as she makes 10 dollars an hour plus then she gets a 25 dollar bonus so you multiply the number of hours by 10 then and the bonus

Answer: $65

Step-by-step explanation:

25+10h h=4

25+10x4=

25+40=

65

Answer:

the answer is down there