Compare the volume and surface area of a sphere with radius 4 in. with that of a cube with sides measuring 6.45 in

The equations that match the tape diagram.

Thus, the correct equations are: A, B, D and F

A diagram that resembles a piece of tape that is used to show how numbers relate to one another. Also known as length model, fraction strip, bar model, and strip diagrams. to use whole numbers, fractions, and ratios to answer problems that include the four operations. Students can improve their problem-solving abilities and algebraic reasoning with the use of tape diagrams.

A visual tool known as a tape diagram represents the components of a ratio using equal-sized boxes. The reason it is named a tape diagram is because it resembles the lengthy strips of sticky tape used to bind documents or wrap gifts.

Thus, from the above given data it is clear that, x = 4.5

Correct option: A, B, D, and F

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Answer:

Step-by-step explanation:

To convert into a percent, multiply by 100

1)

a)0.543; = 0.543*100= 54.3%

b) 0.0098; = 0.0098*100=0.98%

c) 1.67; = 1.67*100=167%

To convert percentages into decimals, divide by 100

2)

a) 10%= 10÷100= 0.1

b) 0.010%= 0.010÷100= 0.0001

To convert mixed numbers into decimals, convert mixed numbers into improper fractions and divide

3)

a)2 1/3= 7/3= 2.333 =233.3%

b)5 3/5= 28/5= 5.6 =560%

To convert a fraction into a mixed number, divide the numerator by the denominator

4)

a) 11/4= 2+3/4= 2 3/4

b) 16/7= 2+2/7= 2 2/7

1. Convert decimals to percentages:

a) 0.543 can be converted to percentage by multiplying it by 100. So, 0.543 x 100 = 54.3%

b) 0.0098 can be converted to percentage by multiplying it by 100. So, 0.0098 x 100 = 0.98%

c) 1.67 can be converted to percentage by multiplying it by 100. So, 1.67 x 100 = 167%

2. Convert percentages to decimals:

a) 10% can be converted to a decimal by moving the decimal two places to the left. So, 10% = 0.10

b) 0.010% can be converted to a decimal by moving the decimal four places to the left. So, 0.010% = 0.0001

3. Convert mixed numbers to fractions and decimals:

a) 2 1/3 can be converted to a fraction by finding a common denominator of 3 and writing the whole number as a fraction. So, 2 1/3 = (2 x 3 + 1) / 3 = 7/3

It can also be converted to a decimal by dividing the numerator by the denominator. So, 7/3 = 2.333...

c) 5 3/5 can be converted to a fraction by finding a common denominator of 5 and writing the whole number as a fraction. So, 5 3/5 = (5 x 5 + 3) / 5 = 28/5

It can also be converted to a decimal by dividing the numerator by the denominator. So, 28/5 = 5.6

4. Convert fractions to mixed numbers:

a) 11/4 can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction. So, 11/4 = 2 3/4

b) 16/7 can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction. So, 16/7 = 2 2/7

There are (e) 125 positive integers that satisfy the n condition

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

(130n)^50 > n^100 > 2^200

[tex]\sqrt[50]{}[/tex][(130n)^50] > [tex]\sqrt[50]{}[/tex](n^100) > [tex]\sqrt[50]{}[/tex](2^200)

130n > n^2 > 2^4

130n > n^2 > 16

Solving each part, we get:

n^2 > 16

n > √16

n > 4

130n > n^2

130 > n^2/n

130 > n

130 > n > 4

Therefore the answer is the number of positive integers over 4 and 130 which is 129 - 5 + 1 = 125

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Correctly written question:

How many positive integers n satisfy the following condition (130n)⁵⁰ > n¹⁰⁰ > 2²⁰⁰ ? (a)0 (b)7 (c)12 (d)65 (e)125

Answer:

-5

Step-by-step explanation:

Let x be the number we are trying to find.

According to the problem statement, we know that:

3(x + 3) = x - 1

Expanding and solving for x, we get:

3x + 9 = x - 1

2x = -10

x = -5

So the number we were trying to find is -5.

Answer:

3 hours

Step-by-step explanation:

The matrix representation of the problem can be written as: ε = [ε1 ε2 ε3]'

The matrix representation of the linear regression problem can be expressed as Y = Xβ + ε, where Y is the n x 1 vector of the dependent variable (Yi),

X is the n x k matrix of the independent variables (xi),

β is the k x 1 vector of coefficients, and

ε is the n x 1 vector of errors.

In this case, n = 3 (number of observations), k = 2 (number of independent variables) and the matrix representation of the problem can be written as:

Y = Xβ + ε

Y = [0.3 0.8 -0.3]

X = [1 1 1; 1 2 0.1]

β = [β0 β1]'

ε = [ε1 ε2 ε3]'

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Let's start by converting this word problem into math equations... This will make it much easier to choose an approach to the problem!

Write equations for both Dave and Angie. We will use the variables P for slices of pizza, and W for bottles of water bought.  

(1) Dave: [tex]3P+2B=12.75[/tex]

(2) Angie: [tex]1P+3B=7.75[/tex]

Now that we have these equations, it's much easier to tell that this is a system of two equations (two equations, two unknowns). To solve this system, we can use a variety of different methods. For this problem, let's use the Elimination method (removing one variable from the equation.

Start by multiplying (scaling) Angie's equation by a factor of -3, so that we will be able to remove Pizza slices from the equation:

(3) [tex]-3(1P+3B=7.75) \equiv -3P-9B=-23.25[/tex]

Now, let's add Angie's new equation to Dave's original:

[tex]-7B=-10.5[/tex]

Notice that we now only have one variable in this simple equation. This is very easy to solve!

Simplify:

[tex]B=1.5[/tex]

Now that we have the price for a bottle of water, we can substitute this value into either (1) Dave's or (2) Angie's original equation to find the price for a slice of Pizza (P). I will substitute into (1) Dave's equation:

Substitute:

[tex]3P+2(1.5)=12.75[/tex]

Simplify:

[tex]3P=9.75[/tex]

Divide:

[tex]P=3.25[/tex]

Finally, we have reached our conclusion... A slice of Pizza costs $3.25 and a bottle of water costs $1.5 at the concession stand! Let me know if you have any questions or want to learn other ways of solving this problem!

The height of the rectangular prism is 2x^3

The volume of a rectangular prism is given by the product of its length, width, and height.

We know that the volume is 48x^8, so we can write an equation:

48x^8 = (4x^2)(6x^3)(h)

We can simplify the left side:

48x^8 = 24x^5 * h

And divide both sides by 24x^5 to find the height:

h = 48x^8 / 24x^5 = 2x^3

So the height of the rectangular prism is 2x^3

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The distance between the two points is 13 units.

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)

point 1 (1, 4): x1 = 1 , y1 = 4

point 2 (6, 16): x2 = 6 , y2 = 16

Using the formula with the given values:

d=√((x2 – x1)² + (y2 – y1)²

d=√((6 – 1)² + (16 – 4)²)

d=√(5² + 12²)

d = √169

d = 13 units

Therefore, the distance is 13 units.

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To find a pattern in a sequence using differences, we can calculate the difference between consecutive terms and look for a pattern in the differences.

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Answer:

C

Step-by-step explanation:

So 28% of commission of each $55 game (I wish that was the real world)

Finding 28% of 55:

(.28)(55) = $15.40

Assuming she sells 20 games, we multiply $15.40 by 20

(15.40)(20) = $308

The total cost of the six fill-ups during winter is $4977.

Word problems are mathematical problems expressed with words that involve the interpretation of mathematical variables and the usage of the appropriate arithmetic operations to solve them.

From the given information;

If the price per gallon is $3.95 and a tank can hold 210 gallons. Then, the price for a single full tank is $3.95 × 210 = $829.5

In addition to that, if Tanis has six fill-ups tanks during the winter, his total cost would be:

= $829.5 × 6

= $4977

Therefore, we can conclude that the total cost of the six fill-ups during winter is $4977.

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The volume and radius of the ice cream and the ice cream cone are;

(a) Volume of the ice cream is about 6.3 cubic inches

(b) Radius of needed for the cone to contain 14.5 cubic inches per serving is about 1.422 inches

The volume of a solid is the space the solid occupies, which is the amount of cube units that fills the solid.

Rotation of a quarter circle to form an hemisphere, by integration is presented as follows;

[tex]\int\limits^1_0 \pi \times ({\sqrt{1-x^2} })^2 \, dx = \frac{2}{3} \cdot \pi[/tex]

The volume of the cone carrying the hemisphere = (1/3)×π×1²×4 = (4/3)·π

The volume of the ice cream = The volume of the cone + The volume of the hemisphere

Therefore;

Volume of the ice cream = (2/3)·π + (4/3)·π = (6/3)·π = 2·π  ≈ 6.3

(b) Volume of ice cream contained in the new ice cream cone, V = 14.5 cubic inches

The formula for the volume of the ice cream, V = (2/3)·π·r³ + (4/3)·π·r²

Therefore;

V = (2/3)·π·r³ + (4/3)·π·r² (substitution property)

V = (2/3)·π·r³ + (4/3)·π·r²

14.5 = (2/3)·π·r³ + (4/3)·π·r²

(2/3)·π·r³ + (4/3)·π·r² - 14.5 = 0

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The value of the given indefinite integral is[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]

An integral which is not having any upper and lower limit is known as an indefinite integral. Mathematically, if F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted, ∫f(x) dx = F(x) + C.

Given is an indefinite integral, [tex]\int \frac{x-6}{\left(x+3\right)^2+36}dx[/tex]

Solving,

Applying u-subsituition,

[tex]=\int \frac{u-9}{u^2+36}du[/tex]

Expanding,

[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex]

Since, [tex]\int \frac{u}{u^2+36}du = \frac{1}{2} ln|u^2+36|[/tex]

And,

[tex]\int \frac{9}{u^2+36}du = \frac{3}{2} tan^-^1(\frac{u}{6} )[/tex]

Therefore,

[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex] [tex]=\frac{1}{2}\ln \left|u^2+36\right|-\frac{3}{2}\arctan \left(\frac{u}{6}\right)[/tex]

Substitute u = x+3

[tex]=\frac{1}{2}\ln \left|\left(x+3\right)^2+36\right|-\frac{3}{2}\arctan \left(\frac{x+3}{6}\right)[/tex]

[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)[/tex]

Add constant c,

[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]

Hence, the value of the given indefinite integral is

[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]

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The correct Set-builder form for the following set written in Roster form       { -4,− 3 , − 2 , − 1 , 0 , 1 } is,

⇒ {x ∈ Z | - 4 ≤ x ≤ 1}

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The set is,

⇒ { -4,− 3 , − 2 , − 1 , 0 , 1 }

Now, The correct Set-builder form for the following set written in Roster form { -4,− 3 , − 2 , − 1 , 0 , 1 } is,

⇒ {x ∈ Z | - 4 ≤ x ≤ 1}

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Answer:

Greg borrowed $20,000.

Step-by-step explanation:

To calculate the principal (the amount borrowed), we can use the formula for simple interest:

I = Prt

where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.

Given that:

I = 1400

r = 7% (expressed as 0.07)

t = 4

P = I / (r * t) = 1400 / (0.07 * 4) = $20,000

Therefore, Greg borrowed $20,000.

Function F(X) is shifted 1 unit left and 1 unit up.

Identify The Parent Function.

Reflect Over X-Axis or Y-Axis.

Shift (Translate) Vertically or Horizontally.

Vertical and Horizontal Stretches/Compressions.

Plug in a couple of your coordinates into the parent function to double check your work.

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up.

There are different formulas for different rules of transformation. For vertically transformation the function f(x) is transformed to f(x) + a or f(x) - a. For horizontal transformation the function f(x) is transformed to f(x + a) or f(x - a). Further for stretched or compressed transformation is it f(cx) or cf(x).

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Answer:  9

Step-by-step explanation:

Y=x2=9

Using the definition of the derivative, the derivative of the function is f'(t) = 5t + 6. The domain of the function and its derivative are both the set of all real numbers.

The derivative is a concept in calculus that represents the rate of change or the slope of a function at a specific point. It is defined as the limit of the difference quotient of the function as the interval between the two points approaches zero. Mathematically, the derivative of a function f(x) at a point x is represented as f'(x) and can be expressed as:

f'(x) = lim h -> 0 [f(x + h) - f(x)]/h

where h is the interval between the two points.

The derivative is a fundamental tool for analyzing and understanding the behavior of functions, including their local maxima, minima, and inflection points, as well as for solving problems in physics and engineering.

The derivative of the function f(t) = 2.5t² + 6t can be found using the definition of the derivative:

f'(t) = limit as h -> 0 of [f(t + h) - f(t)]/h

= limit as h -> 0 of [2.5(t + h)² + 6(t + h) - (2.5t² + 6t)]/h

= limit as h -> 0 of [2.5t² + 5ht + 2.5h² + 6t + 6h - 2.5t² - 6t]/h

= limit as h -> 0 of [5ht + 2.5h² + 6h]/h

= limit as h -> 0 of [5t + 2.5h + 6]

= 5t + 6

The domain of the function f(t) = 2.5t^2 + 6t is all real numbers. The domain of its derivative f'(t) = 5t + 6 is also all real numbers.

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Answer:

=94

Step-by-step explanation:

Hope itvhelps you↑↑

Answer:

Do you still need help?

I can help with your geometry if it is not too late.

The correct option is (b)  Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.

According to the above evidence, it is concluded that Regression 2 is better fit as, in the regression 2, the graph represents to be nonlinear relationship between x and y.

Since all the other concluded ones are not best describe the residential plot of given evidence, Hence, based on the evidence Regression 2 is better than the Regression 1 as it includes the nonlinear relationship between x and y that is exactly shown in the above evidence.

Question:

Which of the following conclusions is best supported by the evidence above?

a) Regression 1 is a better fit because there appears to be a nonlinear relationship between x and y.

b) Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.

c) Regression 1 is a better fit because there appears to be a linear relationship between x and y.

d)Regression 2 is a better fit because there appears to be a linear relationship between x and y

e) There is a negative correlation between x and y.

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Answer: $72.93

Step-by-step explanation:

$72.93

A second-degree polynomial can be used to fit the three data points by finding the coefficients of the polynomial that pass through the three given points. The general form of a second-degree polynomial is:

p(x) = ax^2 + bx + c

We can use the three data points to solve for the coefficients a, b, and c. Let's use the year 2000 as the reference point and set x = 0. Then, we have:

p(0) = c = 287 million (at x = 0, the population is 287 million)

Next, let's use the data point for 1990, which is 244 million. The year 1990 is 10 years before 2000, so x = -10. Substituting these values into the polynomial, we have:

p(-10) = a * (-10)^2 + b * (-10) + c = 244 million

Solving for a and b using the two equations above, we have:

a = (244 - 287 + 10b) / 100

c = 287

Substituting these values back into the polynomial, we have:

p(x) = (244 - 287 + 10b) / 100 * x^2 + bx + 287

Finally, let's use the data point for 2010, which is 324 million. The year 2010 is 10 years after 2000, so x = 10. Substituting these values into the polynomial, we have:

p(10) = (244 - 287 + 10b) / 100 * 10^2 + b * 10 + 287 = 324 million

Solving for b, we have:

b = (324 - 244 + 287) / 10 - (244 - 287) / 100 * 10^2 = 37

Therefore, the final form of the second-degree polynomial that passes through the three data points is:

p(x) = (244 - 287 + 10 * 37) / 100 * x^2 + 37x + 287 = 7x^2 + 37x + 287

This polynomial can be used to estimate the population of the country for any year close to 1990, 2000, or 2010.

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Sarah consumes 12000 calories per day.

A calorie is a unit of energy.

Given is that Ben eats approximately 2,400 calories a day.

We can write the amount of calories eaten by Sarah as -

y = 5 x 2400

y = 12000

Therefore, Sarah consumes 12000 calories per day.

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{Question in english -

Ben eats approximately 2,400 calories a day. His wife Sarah eats 5 as much. How many calories does Sarah eat a day?}

Answer:

[tex]x = 1[/tex]

Step-by-step explanation:

In the rectangle, WU = 2NU, where WU = 13x - 1 and NU = 6

Replacing for the values in the equation: WU = 2NU, it becomes: 13x - 1 = 2 × 6

Going further:

[tex]13x - 1 = 12[/tex]

[tex]13x = 12 + 1 \\ 13x = 13[/tex]

[tex]x = \frac{13}{13} = 1[/tex]

Therefore, x = 1

Check the picture below.

r       = rate of the faster cyclist

r - 7 = rate of the slower cyclist

we know they both met 5 hours later, so the time each one has been cycling has been 5 hours for each.

let's say the faster cyclist on those 5 hours covered "k" kilometers, that means the slower one cover the slack, namely "255 - k" kilometers.

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{Km s}{distance}&\stackrel{km/h}{rate}&\stackrel{hour}{time}\\ \cline{2-4}&\\ \textit{faster cyclist}&k&r&5\\ \textit{slower cyclist}&255-k&r-7&5 \end{array}\hspace{5em} \begin{cases} k=(r)(5)\\\\ 255-k=(r-7)(5) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{k=5r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{255-(5r) = (r-7)(5)} \\\\\\ 255-5r=5r-35\implies 255=10r-35\implies 290=10r \\\\\\ \cfrac{290}{10}=r\implies 29=r\hspace{5em}\stackrel{\textit{faster cyclist}}{\text{\LARGE 29}~\frac{km}{h}}\hspace{5em}\stackrel{\textit{slower cyclist}}{\text{\LARGE 22}~\frac{km}{h}}[/tex]

The point C is equidistant to (b) CL = CM = CN

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

The triangle

From the triangle, we can see that the point C is the centroid of the triangle

As a general rule:

The centroid is the geometric centre of a triangle. It is equidistant from all the points present on the triangle.

This means that point C is equidistant from L, M and N

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