(Scientific Notation in the Real World MC)


The mass of a paper clip is 7.0 x 10−4 mg. If a box of paper clips has 3.18 x 104 paper clips, determine the total mass of the paper clips in the box. Write the final answer in scientific notation with the correct number of significant digits.


2.2 x 101 mg

2 x 101 mg

2.226 x 101 mg

2.23 x 100 mg

Answer:

121°

Step-by-step explanation:

x + 6 + 3x -15 + 5x + 36 = 180

9x + 27= 180

9x = 180 - 27

9x = 153

9/9 x = 153/9

x = 17

mC = 5·17 + 36

85 + 36

121°

Answer:Use it as it is or fit non-normal distribution

Step-by-step explanation:

Answer:

0.44

Step-by-step explanation:

Answer:

A split infinitive is a common grammatical mistake that can be hard for writers to spot. Many people think they are not a big deal, but they can often have a major impact on your writing and make it hard for a reader to understand what you have to say.

Step-by-step explanation:

Take, for example, this sentence:

I like to on a hot day eat a lot of ice cream.

Did you have to read it twice to be clear what it was saying? I know I did. But let's make just a little adjustment:

On a hot day, I like to eat a lot of ice cream.

Answer:

a value that is not yet known

888030 ways are there for teachers to select the students.

What is the combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we have

A teacher selects 7 students from her class of 27 students.

We have to find how many ways are there for her to select the students of the chosen students.

The order of selecting the students does not matter here so the number of ways to select 7 students from the class of 27 to work together on a project is:

C(27,7) = 27!/(7!*(27-2)! = 888030

Hence, 888030 ways are there for teachers to select the students.

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The length L of an edge of each small cube if adjacent cubes touch but don't overlap is 3.45 nm.

The formula to be used for calculation is -

PV = Nkt, where P is pressure, V is volume, N is number of molecules, k is Boltzmann constant and T is temperature in Kelvin.

T = 273 + 27

Performing addition on Right Hand Side of the equation

T = 300 K

P = 101325 Pa

k = 1.38 × [tex] {10}^{-23} [/tex] J/K

Now finding the volume

V = (1 × 1.38 × [tex] {10}^{-23} [/tex] × 300)/101325

Performing multiplication and division on Right Hand Side of the equation

V = 4.09 × [tex] {10}^{-3} [/tex] m³

As we know, V = L³

So, L = [tex] {V}^{1/3} [/tex]

Keep the value of volume

L = [tex] { (4.09/1000) }^{1/3} [/tex]

Performing calculations

L = 3.45 × [tex] {10}^{-9} [/tex] m

Hence, length is 3.45 nm.

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The domain for the given function is {-1, 2, 33, 32}.

A function's or relation's domain is the set of all possible independent values that the relation can take. It is the sum of all possible inputs.

A function's or relation's range is the set of all possible dependent values that the relation can produce from the domain values. It is the sum of all possible outputs.

When dealing with sets of ordered pairs, we simply divide the pairs into x- and y-coordinates. The domain is formed by the x-coordinates, which are independent values. The y-coordinates are the dependent values, i.e. they define the range.The domain in the set of ordered pairs {(a,b); (c,d); (e,f); (g,h)} is the set of the first number in each pair (those are the x-coordinates): {a,c,e,g}. The range is the set of all the pairs with the second number (the y-coordinates): {b,d,f,h}.

Given,

The set of ordered pair =   {(-1,5) , (2,3), (33,6), (32,7)}

then,

the Domain = {-1, 2, 33, 32}

Range = {5, 3, 6, 7}

Thus, the domain for the given function is {-1, 2, 33, 32}

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The total amount they will pay would be $95.557

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Given that the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal.

Cost of meal = $75.99

The tax amount = 6.75% of 75.99

                  = ( 6.75/100 ) x 75.99

                  = $5.129

Tip amount = 19% of 75.99

                  = (19/100) x 75.99

                  =  $14.438

Thus, the Total amount they will pay

= $75.99 + $5.129 + $14.438 = $95.557

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Answer: 12.5 meters!

Step-by-step explanation:

1km = 1000 meters

So 5km = 5000 meters

So take 5000 divided by 400 = 12.5 meters

Answer:

12.5 is the answer for this question

The reasoning above makes it very evident that the hyperbola's coordinate is (8, -1)

The hyperbola is open upward and downward because the expression 'y' has a positive leading coefficient. In comparison to the usual equation, the hyperbola's center is found to be at (2, -1) and its 'a' point, 6, and 'b' point is 8. A smooth curve that lies in a plane and is classified as a hyperbola in mathematics by either its geometric characteristics or by equations for which it is the solution set. Two parts of a hyperbola, referred to as connected components or branches, are mirror reflections of one another and resemble two infinite bows.

Given,

((x-2)²/36)-((y+1)²/64)=1

We know that the standard form of a parabola is:

((x-k)²/a²)-((y-h)²/b²)=1

Center for the given hyperbola is (2, -1)

And a=6, b=8

And the coordinates for the center of the hyperbola are x=8, y= -1

Therefore, (x, y)=(8, -1)

The reasoning above makes it very evident that the hyperbola's coordinate is

(8, -1)

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10x-61/12 is the difference of  (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).

An expression is combination of variables, numbers and operators.

The given expression is (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex])

7x-[tex]6\frac{2}{3}[/tex]+3x- [tex]4\frac{3}{4}[/tex]

7x-20/3+3x-19/4

Add the variable terms and constant terms.

10x-20/3-19/4

The LCM of 3 and 4 is 12/

10x-4-57/12

10x-61/12

Hence, 10x-61/12 is the difference of  (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).

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The coefficient of determination resulting from a particular regression analysis was 0.85. Then, the correlation coefficient, assuming a positive linear relationship is 0.922.

The coefficient of determination, denoted R2 or r2 and pronounced "R-squared," is the proportion of predictable variation in the dependent variable from the independent variables.

R2 has several definitions, sometimes the same. One class of such cases involves simple linear regression where r2 is used instead of R2. If only one bin is included, r2 is simply the square of the sample correlation coefficient (that is, r) between the observed outcome and the observed prediction. If additional regressors are included, R2 is the square of the multiple correlation coefficient. In both cases, the coefficient of determination is usually between 0 and 1.

Regression analysis consists of a dependent variable (often called the "outcome" or "response" variable, or "label" in machine learning parlance) and one or more independent variables (often called "predictors"). ). ', 'covariate', 'explanatory variable' or 'feature'). The most common form of regression analysis is linear regression, which finds the best fit line (or more complex linear combination) to the data according to mathematical criteria. For example, the ordinary least-squares method computes a unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For certain mathematical reasons (see linear regression), researchers can estimate the conditional expected value (or population mean) of the dependent variable given that the independent variable takes on a particular set of values . Less common forms of regression use slightly different techniques to estimate alternative site parameters (such as quantile regression and requirement analysis, or conditional expectations on a broader collection of nonlinear models. estimating values ​​(such as nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes.

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Answer:

Below

Step-by-step explanation:

y = 19/x^3       <===== solve for 'x'

x = cube rt (19/y)     < ====now switch the x and y's

y = cube rt ( 19/x)

Answer: f^-1(x) = 19^3/x

Step-by-step explanation:

Given that : f(x) = y = 19/x^3

x^3 = 19/y

y = (19)^3/x = f^-1(x)

think sometimes prob 4x5 i don't know

( x - 1 ) is the factor of f(x) as remainder is 0

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

According to the given information

The given polynomial is

f(x) = [tex]x^{3} + 4x^{2} +x -6[/tex]

According to the remainder theorem

( x - 1 ) will be the factor of f(x) , if f(1) is zero

So

= [tex]1^{3} + 4(1)^{2} + 1 -6[/tex]

= 1+4+1-6

= 6-6

= 0

So

( x - 1 ) is the factor of f(x) as remainder is 0

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Answer: y = 8 , x = 4

Step-by-step explanation:

gosh darn i haven done this since algebra 1 !!

since both equations equal y, we can make them equal to each other since y = y

-2x +16 = 2x (im just gonna simplify without all the extra steps sorry)

x = 4 (this is the first answer)

now we can plug in x to find y

y = 2(4)

y = 8 (second answer)

im sorry if the grammar is horrid its 3 am

The constant of proportionality that relates the number of servings to cups of cheese is  0.25.

According to the question,

Sarah used 2.5 cups of cheese in a dish that serves 10 people, this can be written as :

let the c be the cups of cheese : c = 2.5 cups of cheese

let n be the number of the people that is been served

Then the equation can be written as :

c ∝ n

then we can bring in the proportionality constant sign as ;

then c = kn

then we can introduce the given figures into the equation as ;

=> 2.5=k (10)

the we can determine the value of the constant as :

=> k=2.5/10 = 0.25

Hence, constant of proportionality relates the number of servings to cups of cheese is 0.25

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Answer:

16

Step-by-step explanation:

The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.

Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.

The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

Considering that,

We need to find for the peripheral income capability, find the interest capability.

Recollect that the pay is zero assuming no things are sold:

R'(x) = 0.06x² - 0.05x + 138

p(x) is what.

That's what we know,

MR = dTR/dx = 0.06x² - 0.05x + 138

Incorporating the marginal revenue function , we get complete income capability,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x

= (0.06x³)/3 - (0.05x²)/2 + 138 x

TR = 0.02 x³ - 0.025 x² + 138 x

TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x

P = ( 0.02 x³ - 0.025 x² + 138 x)/x

P = 0.02x² - 0.025x + 138

In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

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The given equation after a translation by 2 units upwards is y = 3.5x + 2.

The rules for translating an equation in both vertical and horizontal directions are:

The given equation is y = 3.5x

The equation after translation by 2 units upward is obtained by using the rule we have y = f(x) + m.

⇒ y = 3.5x + 2

The graphs for the given equation and the translated equation are shown in the graph below.

For the pair that show translation in both equations, substituting x = 0, we get

y = 3.5x ⇒ y = 3.5(0) = 0; So, the point is (0,0)

and

y = 3.5x + 2 ⇒ y = 3.5(0) +2 = y = 2; So, the point (0,2)

Therefore, the required pair is (0,0) and (0,2).

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The radius of the circle having the equation x² + y² - 10x + 6y + 18 = 0 is 4  units , the correct option is (b) .

In the question ,

it is given that ,

the circle is having equation ⇒ x² + y² - 10x + 6y + 18 = 0 ,

we know that ,

general equation of circle is ⇒ x² + y² + 2fx + 2gy + c = 0 ;

So , radius of circle is calculated using the below formula ,

radius [tex]=[/tex] √(f² + g² - c)

On comparing,  given equation of circle with general equation of circle ,

we get , the values of f = -5 and g = 3 .

So after substituting values of f , g and c in radius formula ,

we get ,

radius = √(25 + 9 - 18)

= √(34 - 18)

= √16 = 4 .

Therefore , the given circle has radius = 4 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0 ?

(a) 2 units

(b) 4 units

(c) 8 units

(d) 16 units

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After dilation, the size of the image will change and the shape of the image will be same

Dilating an image means the changing the size of the image, but the shape of the image will be same

Dilation is the process of changing the size of the image without changing the shape of the image

The image after the dilation is called as the pre image.

The dilation can be done by using the scale factor or normally increase or decrease the size,

If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases

Therefore, size of the image will change after the dilation

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The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

What is continuous compounding?

There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.

We have,

9 years in an account with a 3.9% annual interest rate compounded continuously,

an investment is worth a total of $17,757.16.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

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Answer:

$12,500.75

Step-by-step explanation:

I got it right.

Therefore , Angela needs to fill this cup 6/7 times.

A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.

Here,

To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.

Thus, the number of times angela needs to fill  cup are = 12/14 times

thus ,

=> 12/14 =6/7

Therefore , Angela needs to fill this cup 6/7 times.

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The slope is the measure of the steepness and direction of a line. You can predict whether lines in a coordinate plane are parallel, perpendicular, or none by finding the slope of the lines.

There are two distinct points on any line that can be used to calculate its slope. Between two distinct points on a line, the slope formula calculates the ratio of vertical and horizontal changes. In mathematics, the slope is calculated as the ratio of the rise to the run, or as the rise divided by the run. The slope is a measure of how steep a line is in a coordinate plane.

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f(-2) = 254 , meaning if the company sells shirts -2 , they would make a profit of 254 dollars. This interpretation is true in the context of the problem.

f(12) = 266 , meaning if the company sells shirts 12 , they would make a profit of 266 dollars. This interpretation is true in the context of the problem.

f(17.5) = 270.25, meaning if the company sells shirts 17.5 , they would make a profit of 270.25 dollars. This interpretation is true in the context of the problem.

Based on the observations above, it is clear that an appropriate domain for the function is x ≥ - 2.

Functions and values given the function that represents elevation, in feet, of Jayden hikes expressed as:

f(x)=(x+2)²+250.

If the domain value of the function is -4, then;

f(-4)=(-4+2)²+250

f(-4) = 4 + 250

f(-4) = 254

f(-4) = 254 means If Jayden hikes 4 miles to the south, his elevation would be 254 feet. This interpretation is true in the context of the problem

If the domain value of the function is -4, then;

f(2)=(2+2)²+250

f(2) = 16 + 250

f(2) = 266

f(2) = 266 means If Jayden hikes 2 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem

If the domain value of the function is 2.5, then;

f(2.5)=(2.5+2)²+250

f(2.5) = 20.25 + 250

f(2.5) = 270.25

f(2.5) = 270.25 means If Jayden hikes 2.5 miles to the north, his elevation would be 270.25 feet. This interpretation is true in the context of the problem

Determining the domain

The domain exist for the value of (x+2)² ≥ 0

x + 2 ≥ 0

x ≥ - 2

Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2

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The measure of the perpendicular of the right-angle triangle will be 16.728 units.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The sine of the angle is the ratio of perpendicular to the hypotenuse.

sin θ = Perpendicular / Hypotenuse

The angle is 42° and the measure of Hypotenuse is 25. Then the measure of the side 'x' will be given as,

sin θ = Perpendicular / Hypotenuse

sin 42° = Perpendicular / 25

Perpendicular = 25 x sin 42°

Perpendicular = 16.728

The measure of the perpendicular of the right-angle triangle will be 16.728 units.

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Answer:

mode = 3

Step-by-step explanation:

the mode is the value that occurs most often in the data set

3, 7, 4, 6, 3, 5, 9, 40, 6, 3

the value 3 occurs most often , 3 times

then mode of data set = 3

The number of ways that we can remove the balls one at a time from the box is 1307674368000

Given,

The number of balls in a box;

5 red balls

6 blue balls

4 green balls

We have to find the number of ways the balls can removed from the box one at a time;

Here,

Order is indistinguishable, so combination can be followed;

Combination formula;

ⁿCr = n! / r1(n - r)!

Here,

Total number of balls in the box = 5 + 4 + 6 = 15 balls

Then.

¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000

That is,

We can remove the balls one at a time from the box in 1307674368000 ways.

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