16. Use the number line to help you decide which statement is true. ​

The picoseconds that are there in 6 minutes is 3.6 × 10^14.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12

The seconds in 6 minutes will be:

= 60 × 6

= 360 seconds

= 3.6 × 10^2

The picoseconds in 6 minutes will be:

= 1 × 10^12 × 3.6 × 10^2

= 3.6 × 10^14

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The slope is 5 and the y-intercept is -2000.

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.

(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.

In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b).  y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.

(a) Consider two points

(x₁, y₁) = (400, 0)

(x₂, y₂) = (500, 500)

The slope is given as

m = (y₂ - y₁)/ (x₂ - x₁)

= (500-0)/(500-400)

= 500/100

= 5

To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)

0 = 5(400)+b

0 = 2000 + b

b= - 2000

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) Let the number of customers per week = x

And the profit per week = y

Then, the situation can be modeled using slope-intercept form as

y = 5x -200

(d) Put x= 2500 in y = 5x -200

y = 5(2500)-2000

= 12,500-2000

= 10,500

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The volume of the crate if there is no extra space in the crate is 36m³.

From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.

In this case, the volume will be:

= Length × Width × Height

= 2 × 1 × 1

= 2m³

Since there are 18 crates, the total volume will be:

= 2m³ × 18

= 36m³

The volume is 36m³.

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Complete question

A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?

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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The reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The reflection of the point (2,3) over the x-axis is calculated as,

(2,3) ⇒  (2,-3)

The reflection of the point (7,-2) over the y-axis is calculated as,

(7,-2) ⇒ (-7,-2)

Therefore, the reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).

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Answer:

A the scale factor is 2 from LMN to CDF (or 1/2 from CDF to LMN).

Step-by-step explanation:

shadows are similar, when they have the same angles, abd if there is one scale factor for all sides and other lengths from one shape to the other.

8×2 = 17

15×2 = 30

17×2 = 34

The simple interest on $1,200, 3.9%, 8 months is $31.356.

From the informationm, we want to calculate the simple interest of the amount that is given.

The simple interest is calculated thus:

Simple interest = PRT / 100

where

P = Principal = $1200

R = Rate = 3.9%

T = Time = 8 months = 8/12 = 0.67 years

The interest will be:

Simple interest = PRT / 100

Simple interest = (1200 × 3.9 × 0.67) / 100

Simple interest = 31.356

The interest is $31.356.

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Complete question

Calculate the simple interest on $1,200, 3.9%, 8 months

If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

What do you mean by traversal line?

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

What do you mean by angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

From the figure,

x + 1 = 180°

y + 2 = 180°

Adding above equations,

x + y + 1 + 2 = 360°

Given ,

x + y = 1 +2

x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Angles made on same side of transversal is supplementary . So the lines are parallel.

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Step-by-step explanation:

first order them from least to greatest

13,14,18,21,22,26,32,39,39,42

then just look for the term in the middle

sunset there are 2 numbers in the middle you will add them both and subtract them by 2

42+39 then / 2 =40.5

The marginal cost is the labor utilized in order to provide an additional cost of a haircut.

The marginal cost is the extra cost of generating one additional unit of output.

The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.

Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.

Change in cost / Change in quantity Equals Marginal cost.

The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.

Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.

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Step-by-step explanation:

Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15

packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about

the purchase is correct.

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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Answer:

j=24

Step-by-step explanation:

j/8 - 2 = 1

j/8 - 2 + 2 = 1 + 2

j/8 = 3

8 * j/8 = 8 * 3

j=24

With the help of subtraction we can say that the answer is =21/15

Acc to the question-

Hence,The answer is = 21/15

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Answer:

21/15

Step-by-step explanation:

Given problem,

→ (32/15) - (11/15)

Let's solve the given problem,

→ (32/15) - (11/15)

→ (32 - 11)/15

→ 21/15

Hence, the answer is 21/15.

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:

Karen is waiting for a pot of soup to cool off before serving it. After 4 min the soup has cooled from 100°C to 78°C. What was the average change in temperature each minute?

✓ Answer:It went down 5.5°C a minute.Step-by-step explanation:You have to look for the difference of 100 and 78, which is …

The percentage of computers not working is 10%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that there are three of the 30 computers are out of service.

The percentage of the computers which are out of service will be calculated as,

P = 3 / 30

P = 0.1

P = 0.1x 100

P = 10%

Therefore, the percentage of computers not working is 10%.

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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 measure of the angle 1, angle 2, angle 3 is 68°, 94°, 25° respectively.

What is angle?

An angle is created where two straight lines or rays meet at a single point. The point from where two lines converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which meaning "corner."

Let's firstly find angle 1,

We  know that, the sum of the all three angles of a triangle is 180°.

So,

18° + 94° + angle 1 = 180°

112° + angle 1 = 180°

angle 1 = 180° - 112°

angle 1 = 68°

Now, we know that, opposite angle are always equal

Therefore,

angle 2 = 94°

Now, again applying the property of triangle that sum of all three angles are equal:

Therefore,

angle 3 + angle 2 + 61° = 180°

angle 3 + 94° + 61° = 180°

angle 3 = 25°

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Answer:

0

Step-by-step explanation:

to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.

Answer: 78

Step-by-step explanation:

3z2-6z for z=5

12 ounces of water.

Total mass of the solution: 30 ounces.

Total mass of salt (solute): (30*0.07)= 2.1 ounces.

Total mass of water (solvent): (30*0.93) 27.9 ounces.

2. Find an equation that relates amount of water and percentage of salt.

Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:

[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.

Side note: The number "0.05" is 5% converted into a decimal.

[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]

42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.

12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.

The percentage of the tip will be equal to 24.81%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24.

The percentage tip will be calculated as,

P = ( (37.24 - 28 ) / 37.24

P = 9.24 / 37.24

P = 0.2481 x 100

P = 24.81%

Therefore, the percentage of the tip will be equal to 24.81%.

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Answer:

y=3x+2

Step-by-step explanation:

Divide by 5 on all sides.

3x-y=-2

Step-by-step explanation:

If the value of R² in the regression equation is 0.810, the value of R is 0.9

From the question, we have the following parameters that can be used in our computation:

Regression equation: y = -2.6x + 10

Value of R2 = 0.810

Rewrite the above parameters properly

So, we have the following representation

y = -2.6x + 10

R² = 0.810

The variable r² represents the coefficient of determination

Recall that

R² = 0.810

This gives

r² = 0.810

Take the square roots of both sides

r = 0.9

Hence, the value of r is 0.9

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As per the given interest rate and types of annual interest , investor should choose compounded monthly as it gives interest more frequently .

As given in the question,

Time period to calculate the compound interest  = 3years

Interest rate compounded monthly = 5.50%

Each month interest output is 5.64079

Rate of interest compounded semi- annually = 5.70%

Each month interest output is 5.78123

Compounded monthly gives interest every month and semi-annually gives twice a year.

Monthly is more frequent  compare to semi-annually.

Investor should choose monthly.

Therefore, as per the given interest rate and types of annual interest , investor should choose compounded monthly as it is more frequent .

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Answer:

the answer is down there