The question has already provided a formula to determine the width (W). The question also provides the thickness as well as the number of times (n) the paper would be folded. Hence, we have;
[tex]\begin{gathered} W=\pi\times T\times2\frac{3(n-1)}{2} \\ W=3.14\times0.004\times2\times\frac{3(13-1)}{2} \\ W=0.02512\times\frac{3(12)}{2} \\ W=0.02512\times18 \\ W=0.45216\text{ inches} \end{gathered}[/tex]The notebook paper would have to be 0.45216 inches wide
The formula has also been provided that would help in calculating the length of a long rectangular piece of paper. We've been given the thickness of the paper and the number of times it (n) it would be folded. Therefore, we now have;
[tex]\begin{gathered} L=\frac{\pi T}{6}(2^n+4)(2^n-1) \\ L=\frac{3.14\times0.002}{6}(2^{12}+4)(2^{12}-1) \\ L=0.00104667(4096+4)(4096-1) \\ L=0.00104667(4100)(4095) \\ L=17573.066\text{ inches} \end{gathered}[/tex]O is the center of the regular pentagon below. Find its perimeter. Round to the nearest tenth if necessary.
Answer:
To find the perimeter of the regular pentagon.
O is the center of the regular pentagon from the figure.
we know that, There are 360 degrees around a point, the angle formed over each side are equal that is eual to 360/5 =72
In the triangle made by the side and line joinging center, we get
[tex]72+x+x=180[/tex]whereb x is the angle made by the line joining to the center and one of the side.we get,
[tex]\begin{gathered} 72+2x=180 \\ 2x=108 \end{gathered}[/tex][tex]x=54[/tex]Consider the right angled triangle,
we know that,
[tex]\tan \theta=\frac{opposite\text{ side}}{Adjacent\text{ side}}[/tex]we get,
[tex]\tan 54\degree=\frac{10}{y}[/tex][tex]1.376=\frac{10}{y}[/tex][tex]y=\frac{10}{1.376}[/tex][tex]y=7.26[/tex]Side of a pentagon (s)= 2x7.26=14.52
Perimeter of a pentagon is,
[tex]=5s[/tex][tex]=5\times14.52[/tex][tex]=72.6[/tex]Perimeter of a pentagon is 72.6 units.
how to solve linear equations for example 7x-(x-3)=4x-2
7x-(x-3)=4x-2
We need to solve first the brackets
7x-x+3=4x-2
Next, we need to put all the terms with x on one side and all the terms without x on the other side, remember is you change the side of a term the sign will be the opposite that's why 4x change to -4x on the other side
7x-x-4x=-2-5
then we sum of the term
2x=-7
the term with x the 2 is multiplying x so on the other side change to divide the seven
x=-7/2
I have no clue pls help
The linear equation that passes through the point (4, -6) that is perpendicular to the line y = -3 is:
x = 4.
How to get the equation of the line?Im only answering the first question, like the guidelines say.
We want to find a line that passes through the point (4, -6) that is perpendicular to the line y = -3.
Now, line y = -3 is an horizontal line, so a line perpendicular to this one will be a vertical line of the form:
x = a.
Where a is a real number.
this line x = a must pass through (4, -6) where the x-value is 4, then the equation for the line will be:
x = 4.
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An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil) = 0.45
P(medium-quality oil) = 0.15
P(no oil) = 0.40
b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.
P(soil high-quality oil) = 0.20
P(soil medium-quality oil) = 0.75
P(soil no oil) 0.20
Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).
P(high-quality oil | soil)
P(medium-quality oil | soil)
P(no oil | soil)
What is the new probability of finding oil (to 4 decimals)?
Change the exponential expression to an equivalent expression involving a logarithm.
Since the exponential and natural logarithm are inverses each other, we can apply natural logarithm to both sides and get
[tex]x=\ln 8[/tex]or equivalently,
[tex]\ln 8=x[/tex]Threfore, the answer is the last option
The Mean age of swimmers for all of these teams is 10.
What does a large MAD tell you
I-ready
The MAD tells you that most of the data values are greater than the mean.
What is MAD?MAD is an abbreviation for mean absolute deviation. Mean absolute deviation measures the variation of a data set. It measures the spread of the dataset from the mean. The higher the value of the mean absolute deviation compared to the mean, the greater the spread or variation of the dataset.
MAD = (1 / n) ∑ l x - m(x) l
Mean is a measure of the center of a data set. It is the sum of the dataset divided by the total number in the dataset. Mean is also known as average.
Mean = sum of the data / total number in the dataset
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What is the explicit formula for the geometric sequence: 4, 20, 100, 500, ... .
aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾ is the explicit formula for the geometric sequence: 4, 20, 100, 500.
How to determine the geometric explicit formula of sequence?A geometric progression is simply a sequence of non-zero numbers, every term after the first can be determine by multiplying the previous number by a common ratio.
The nth term of a geometric sequence is expressed as;
aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾
Where a₁ is the first term, r is the common ratio and n is the number of terms.
Given the sequence in the question;
4, 20, 100, 500, ...
First determine the common ratio.
r = any term / previous term
r = 20/4
r = 5
Th first term in the sequence is 4.
Plug these into the geometric sequence formula and simply.
aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾
aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾
Therefore, the explicit formula for the sequence is aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾
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2. Solve: x/4.6 = 3.5 x/4.6 = 3.5 X M Check: Right Hand Side
Starting with the equation:
[tex]\frac{x}{4.6}=3.5[/tex]Multiply both sides by 4.6:
[tex]\frac{x}{4.6}\cdot4.6=3.5\cdot4.6[/tex]Simplify the left hand side:
[tex]x=3.5\cdot4.6[/tex]Simplify the right hand side:
[tex]x=16.1[/tex]The answer is: 16.1.
To check your answer, substitute x=16.1 into the first equaton to see if you obtain the same number in both sides:
[tex]\frac{16.1}{4.6}=3.5[/tex]Simplify the left hand side:
[tex]3.5=3.5[/tex]What ate the coordinates of A' and B' when AB is reflected in the x-axis?
The rule of reflection over the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]as shown in the figure:
The coordinates of point A = ( 2, 5 )
the coordinates of point B = (6, 3)
Apply the rule to the given points:
So,
A' = ( 2, -5)
B' = ( 6, -3)
So, the answer is option B
what is the simple interest earned on $8,350 principal deposited for 6 years at an interest rate of 2.28%
The simple interest earned on $8,350 principal deposited for 6 years at an interest rate of 2.28% is $ 1, 141. 28
How to determine the simple interestIt is of great importance to know the formula for calculating the simple interest. It is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal amount or the initial amountR is the interest rateT is the time takenNow, let's substitute the values into the formula, we have;
Simple interest, I = $8,350 × 2. 28 × 6/100
Multiply the denominators
Simple interest, I = 114228/100
Find the quotient
Simple interest, I = 1, 141. 28
Hence, the simple interest is $ 1, 141. 28
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Determine the value of x using a trigonometric ratio.Question options:A) 4.98B) 8.49C) 4.18D) 10.11
We know that the hypotenuse is 6.5 units long, and x is the opposite leg to angle 50.
To find the value of x, use the sine trigonometric reason.
[tex]\begin{gathered} \sin 50=\frac{x}{6.5} \\ x=6.5\cdot\sin 50 \\ x\approx4.98 \end{gathered}[/tex]Therefore, the answer is A) 4.98.Find the volume of this cylinder.Round to the nearest tenth.17ft8ft[ ? ] ft
The volume of the cylinder is 3418.1 cubic feet
Explanation:The volume of a cylinder is given by the formula:
[tex]v=\pi r^2h[/tex]Where r is the radius and h is the height.
The radius of the given cylinder is is 8 ft, the height is 17 ft
Volume is:
[tex]\begin{gathered} \pi(8^2)(17) \\ =1088\pi \\ =3418.1ft^3 \end{gathered}[/tex]Length = 2.4 yards; Height = 3.6 yards; Width = 4.2 yards. Find the surface area of a rectangular prism
Ok, so
Remember that the surface area of a rectangular prism can be found using:
[tex]SA=2lw+2wh+2lh[/tex]If we replace our values:
l = 2.4
h = 3.6
w = 4.2
We got that:
[tex]\begin{gathered} SA=2(2.4)(4.2)+2(4.2)(3.6)+2(2.4)(3.6) \\ SA=20,16+30,24+17,28 \\ SA=67,68 \end{gathered}[/tex]Then, the surface area of this rectangular prism is 67.68 yd2.
Explain how the following ordered pairs represent or doesn't represent a function - {(-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5). (2, 5)8 function a function a. For every x value there is one y value - not a c. For every y value, there is one x value - function b. For every x value, there is only one y value - d. . For every y value, there is one x value - not a function
The way in which the given ordered pairs represent a function is: b. For every x value, there is only one y value - a function.
What is a function?A function simply refers to a mathematical expression (equation) which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).
In this context, we can reasonably infer and logically deduce that these ordered pairs represent a function because it has different input variables (x-values) for different or the same output variables (y-values).
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Two students were competing to have the
highest amount of sales at a bake sale.
Together they made $132. If each
student had made $15 more in sales, one
student would have made twice as much
as the other student.
How much money did the winning
student make, in dollars?
Answer: The answer is either $83 or $70
The points (6, r) and (10, -3) lie on a line with slope 4. Find the missing coordinate r.
Answer: (6, -19)
Step-by-step explanation:
y = 4x + b
substitute ( 10, -3) to find b
b = -43
equation of line is:
y = 4x -43
substitute (6, r)
y = 4(6) - 43
solve for y to find r
y = -19
this means that the missing coordinate r is -19
the full coordinate is (6, -19)
Write an equation for a line perpendicular to 3y−12x=6 and passing through the point (-4,0)
Find −28+14 ? Hhhhhhhhhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeeellllllllllllllllllllpppppppppppppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!
MULTIPLE CHOICE QUESTION 2. Problem set: One jug of powdered plant teod treate an area of 138 aquare feet of flowers. How many Jugs would be needed to treat an area of 168 square yerde? what is your answer? 9 there are square feet there are 2.5 square feet wa 6 there are 12 square feet Belutien there are 3 square feet Newt 13
To answer how many Jugs would be needed to treat an are of 168 square feet, we can use proportional relationships:
[tex]\begin{gathered} \frac{138}{1}=\frac{168}{x} \\ 138x=168 \\ x=\frac{168}{138}=\frac{28}{23}=1.22\text{ jugs} \end{gathered}[/tex]Geena's hair grew 1 1/8 inches in 2 months. How many inches will her hair grow in 1 month?
Answer: 9/16 or 0.5625 or (3/4)^2 inches per month
Step-by-step explanation:
divide by two
(1 1/8) / 2
9/16 or 0.5625 or (3/4)^2
What is the equation for this graph?
Answer:
[tex]y=\frac{2}{3}x+4[/tex]
Step-by-step explanation:
Please answer: How do I find the points on the curve where the tangent is horizontal?
The points on the curve for the tangent is horizontal will be;
⇒ (1, -6) and (-2, 21)
What is mean by Tangent?
The tangent is defined by the line touching the ellipse and the circle at the only one point.
Given that;
The function is;
⇒ y = 2x³ + 3x² - 12x + 1
Now, Find the point on which the tangent is horizontal is find as;
The function is;
⇒ y = 2x³ + 3x² - 12x + 1
Differentiate it with respect to x as;
⇒ dy/dx = d/dx (2x³ + 3x² - 12x + 1)
⇒ dy/dx = 2 × 3x² + 3 × 2x - 12 × 1 + 0
⇒ dy/dx = 6x² + 6x - 12
Equate it to zero;
⇒ dy/dx = 0
⇒ 6x² + 6x - 12 = 0
Take common 6;
⇒ 6 (x² + x - 2) = 0
⇒ x² + x - 2 = 0
Solve for x, by the factorization as;
⇒ x² + 2x - x - 2 = 0
⇒ x (x + 2) - 1 (x + 2) = 0
⇒ (x - 1) (x + 2) = 0
We get two condition;
⇒ (x - 1) = 0 or (x + 2) = 0
⇒ x = 1 or x = -2
Substitute x = 1 in equation , we get;
y = 2x³ + 3x² - 12x + 1
y = 2 × 1 + 3 × 1 - 12 × 1 + 1
y = 2 + 3 - 12 + 1
y = - 6
Hence, The point = (1, -6)
Substitute x = -2 in equation , we get;
y = 2x³ + 3x² - 12x + 1
y = 2 × (-2)³ + 3 × (-2)² - 12 × -2 + 1
y = - 16 + 12 + 24 + 1
y = 21
Hence, The point = (-2, 21)
Therefore, The points on the curve for the tangent is horizontal will be;
⇒ (1, -6) and (-2, 21)
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Consider the following problem. A bicyclist is riding on a path modeled by the function f(x) = 0.03(8x − x^2), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 1. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
The rate of change of elevation is 0.18
Explanation:Given the function:
[tex]f(x)=0.03(8x-x^2)[/tex]To find the rate of change, we take the derivative of f(x)
[tex]f^{\prime}(x)=0.03(8-2x)[/tex]At the point x = 1, we have:
[tex]\begin{gathered} f^{\prime}(1)=0.03(8-2) \\ =0.03(6)=0.18 \end{gathered}[/tex]The rate of change of elevation is 0.18
VOn December 13, 2007, one U.S. dollar was worth 0.69 euro.(a) On that date, how many dollars was 71.33 euro worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many euro was 117.99 dollars worth?Round your answer to the nearest hundredth of a euro.I need help with both of these math problems.
Given
One US dollar was worth 0.69 euro.
To find:
a) How many dollars was 71.33 euro worth?
b) How many euro was 117.99 dollars worth?
Explanation:
It is given that,
One US dollar was worth 0.69 euro.
Then,
a) Let x be the number of dollars.
That implies,
Since 1 dollar=0.69euro.
Then,
[tex][/tex]
Given Point A, what is the coordinate for A' after the following transformation has occurred?(x, y) + (2 - 5, -y + 2)A (5,7)Al
In order to perform the given transformation, we just have to replace the x and y-coordinates into the transformation rule, like this:
A(5, 7), by replacing 5 for x and 7 for y into (x - 5, -y + 2), we get:
(5 - 5, -7 + 2) = (0, -5)
A(5, 7) -> A'(0, -5)
Then, the coordinates of the new point A' are (0, -5)
{-3,0,3} what is it closed under addition, multiplication,both or neither
{-3,0,3} is closed under multiplication.
What are functions of different types of brackets?Curly brackets are often used to denote sets in writing. For instance, a set of the integers 3, 4, 5, and 6 is denoted by "3, 4, 5, 6." In a calculus or physics lecture, angular brackets like 1,3> may denote an inner product, and square brackets may denote a matrix. Mathematicians often use brackets to group similar phrases or numbers together, which is a very important use of these symbols. An expression or thing encompassed by brackets is implied to be given precedence over other things by the presence of brackets. The most popular method for enclosing extra information from a third party is to use square brackets (someone other than the original author). In writing, a list of equal options is frequently denoted by curly brackets.
The set consist of numbers -3, 0 and 3 so if we use any combination of those 3 numbers under some operation and get as result one of those 3 numbers that means set is closed under that operation.
for multiplication you get:
0 × 3 = 0
0 × -3 = 0
-3 × 3 = -9
So all combinations used and answers are 0 and -9 which means set is closed under multiplication.
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Mrs. Valdez can type 438 words in 6 minutes. How many minutes does it take to type 512 words
Answer:
7 [tex]\frac{1}{73}[/tex]
Step-by-step explanation:
Set up a proportion
[tex]\frac{words}{minutes}[/tex] = [tex]\frac{words}{minutes}[/tex]
[tex]\frac{438}{6}[/tex] = [tex]\frac{512}{m}[/tex] Cross multiply
438m = 6(512)
438 m = 3072 Divide both sides by 438
m = 7 [tex]\frac{1}{73}[/tex]
assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute.if 1 adult female is randomly selected find the probability that her pulse rate is less than 81 beats per minute.
SOLUTION:
[tex]Z\text{ score = }\frac{\text{ Raw score - Mean Score}}{\text{Standard Deviation}}[/tex][tex]\begin{gathered} Z\text{ score = }\frac{81\text{ - 74}}{12.5} \\ \\ Z\text{ score = }\frac{7}{12.5} \\ \\ Z\text{ score = 0.56} \end{gathered}[/tex]From the Z-score probability table;
P < 81 = 0.7123
CONCLUSION:
If one adult female is randomly selected, the probability that her pulse rate is less than 81 beats per minute is 0.7123
Help me wolf this System of equations by the addition/elimination method
Given the system of equations
[tex]\begin{cases}x+y=-3 \\ 3x+4y=-7\end{cases}[/tex]Solve by elimination method as shown below.
Multiply the first equation by 3 and subtract it from the second equation,
[tex]\begin{gathered} 3(x+y)=3(-3) \\ \Rightarrow3x+3y=-9 \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow(3x+4y)-(3x+3y)=-7-(-9) \\ \Rightarrow y=-7+9=2 \\ \Rightarrow y=2 \end{gathered}[/tex]Use the value of y in the first equation,
[tex]\begin{gathered} y=2 \\ \Rightarrow x+2=-3 \\ \Rightarrow x=-5 \end{gathered}[/tex]Therefore, the answers are x=-5 and y=2, (x,y)=(-5,2)
Ethan surveyed the first 22 celebrities to arrive at the movie premiere.Is this sample of celebrities likely to be representative
No, the sample of celebrities is not likely to be representative
Here, we should understand if the sample collected is likely to be representative or not
We need to understand what is meant by a representative sample or representative sampling
When a sampling is representative, it means that the sample that we have obtained looks like the population in which we are taking the sample from
Now, from what we have selected as a sample, we only considered the early comers while we have left out the late comers
What this mean in this case is that whatever sample we have is in fact not representative of the total
So we conclude that the sample of celebrities is not likely to be representative
