Answer:
15.6 in² (nearest tenth)
Step-by-step explanation:
Circumference of a circle
[tex]\large\boxed{C=2\pi r}[/tex]
Where r is the radius of the circle.
Given:
C = 14 inSubstitute the given value into the equation for the circumference and solve for r:
[tex]\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = \dfrac{14}{2 \pi}\\\\ r & = \dfrac{7}{ \pi}\end{aligned}[/tex]
Area of a circle
[tex]\large\boxed{A=\pi r^2}[/tex]
Where r is the radius.
Substitute the found radius into the equation for area and solve for A:
[tex]\begin{aligned}\implies A&=\pi \left(\dfrac{7}{\pi}\right)^2\\\\ A&=\pi \cdot \dfrac{7^2}{\pi^2}\\\\ A&=\dfrac{49\pi}{\pi^2}\\\\ A&=\dfrac{49}{\pi}\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}[/tex]
Therefore, the area of the circle with a circumference of 14 in is 15.6 in².
FG is perpendicular to DM, if DF = 4R, FM = r + 21, and DF = FM, what is the value of R?
Answer:
(r+21 ) / 4
Step-by-step explanation:
as we can see DF = FM
and DF = 4R , FM =r+21
so,
4R = r+21
=> R= (r+21)/4
2.
If a train travels between two cities in 3 hours at an average speed of 65 miles per hour, how long
would it take at an average speed of 80 miles per hour?
Answer:
At 65mph the car traveled 195 miles in 3hrs.
So divide 195 miles by 80mph to get 2.4375 hrs
Given q = √(5p²-1)²-2 find p in terms of q.
Answer:
[tex]\sf p =\sqrt{\dfrac{q+3}{5}}[/tex]
Step-by-step explanation:
To find p in terms of q, we have to isolate p.
[tex]\sf \sqrt{(5p^2 - 1)^2}-2 = q\\\\[/tex]
5p² - 1 - 2 = q
5p² - 3 = q
Add 3 to both sides,
5p² = q + 3
Divide both sides by 5,
[tex]\sf p^2 = \dfrac{q+3}{5}\\\\\text{Take square root,}\\\\p =\sqrt{\dfrac{q+3}{5}}[/tex]
The cost to rent a storage unit is different for two storage companies. Stack n’ Store charges $150 per month, plus a non refundable deposit of $175. Smart Storage charges $185 each month with no deposit. Complete the table showing the total cost for each company during the first six months and use it to answer the questions.
Lee plans to store clothes for four months. Which company offers the better deal?
After how many months is the total cost the same at both storage companies?
Month Cost at Stack n’ Store Cost at Smart Storage
1 $325 $185
2 $475 $370
3 $625 $555
4 $775 $740
5 $925 $925
6 $1075 $1100
The company that offers the better deal is Smart Storage.
After 5 months the cost would be the same at both storage companies.
What are the total costs?The equation that represent the total cost of renting at Stack n’ Store is:
Total cost = non refundable deposit + charge per month
Total cost in the first month : $175 x ($150 x 1 ) = $325
Total cost in the second month : $175 x ($150 x 2 ) = $475
Total cost in the third month : $175 x ($150 x 3 ) = $625
Total cost in the fourth month : $175 x ($150 x 4) = $775
Total cost in the fifth month : $175 x ($150 x 5) = $925
Total cost in the sixth month : $175 x ($150 x 6) = $1075
The equation that represent the total cost of renting at Smart Storage is:
Total cost = cost per month x number of months
Total cost in the first month : $185 x 1 = $185
Total cost in the second month : $185 x 2 = $370
Total cost in the third month : $185 x 3 = $555
Total cost in the fourth month : $185 x 4 = $740
Total cost in the fifth month : $185 x 5 = $925
Total cost in the sixth month : $185 x 6 = $1,110
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Find the slope P=(-4,-1) Q=(-3,-3)
The slope of P=(-4,-1) Q=(-3,-3) is -2.
Given,
P=(-4,-1)
Q=(-3,-3)
The slope between two points P=(x₁, y₁)
Q=(x₂ ,y₂)
slope = (y₂-y₁)/(x₂-x₁)
So slope between P=(-4,-1) Q=(-3,-3) is
[(-3)-(-1) ]/ [(-3)-(-4)]
=-2/1
=-2
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
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change the subject. make x the subject
Answer:
X= 1/y
Step-by-step explanation:
[tex]y = 1 - \frac{1}{ \sqrt{1} - \frac{1}{1 - x} } \\ y = 1 - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{ \frac{1 - x - 1}{1 - x} } \\ y - 1 = - \frac{1 - x}{ - x} \\ y - 1 = \frac{1 - x}{x} \\ yx - x = 1 - x \\ yx = 1 \\ x = \frac{1}{y} [/tex]
a contractor purchases 3 dozen pairs of padded work gloves for $44.28. she incorrectly calculates the unit price as $14.76 per pair of the expense report. what is the correct unit price? what is the error?
The unit price of the pairs of padded will be $1.23 per pair. The error is the price of the pairs of pads should have been divided by 12.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
For $44.28 a contractor buys 3 dozen pairs of cushioned work gloves.
The unit price of the pairs of padded will be given as,
⇒ $44.28 / (12 x 3)
⇒ $1.23 per pair
The unit price of the pairs of padded will be $1.23 per pair.
The error is the price of the pairs of pads should have been divided by 12.
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Find all the solutions to the equation 4x3 + 16x2 + 28x = 0. 0, negative 4 + 2 i StartRoot 3 EndRoot, negative 4 negative 2 i StartRoot 3 EndRoot 0, 4 + 2 i StartRoot 3 EndRoot, 4 minus 2 i StartRoot 3 EndRoot 0, negative 2 + i StartRoot 3 EndRoot, negative 2 minus i StartRoot 3 EndRoot 0, 2 + StartRoot 3 EndRoot, 2 minus i StartRoot 3 EndRoot
The required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
4x^3 + 16x^2 + 28x = 0
Taking x common we get,
x(4x^2 + 16x + 28) = 0
So, we get
x = 0
And 4x^2 + 16x + 28 = 0
or, x^2 + 4x + 7 = 0
Thus from the above equation is of the form
ax^2 + bx + c = 0
where, a = 1, b = 4 and c = 7
Therefore solution of the above equation is given as,
x = [-b ± √(b^2 - 4ac)] / 2a
Putting the values we get,
x = [-4 ± √(4^2 - 4*1*7)] / 2*1
so, x = [-4 ± √(16 - 28)] / 2
x = [-4 ± √(- 12)] / 2
x = [-4 ± 2√(- 3)] / 2
or, x = [-2 ± √(- 3)]
Since √-1 = i
∴ √(- 3) = i√3
Thus,
x = -2 ± i√3
So, the required values of x are 0, -2 + i√3, -2 - i√3.
Thus, the required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3.
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The total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x. If the initial total attendance (that is, the total attendance when x=0) was measured January 1, 2013, what was the initial total attendance?
The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.
How to calculate the value?It should be noted that from the information, the total attendance at a science museum is modeled by the function
In this case, the total attendance when x=0 will be:
f(x) = 17,371(1.041)x.
f(x) = 17,371(1.041^0)
= 17371 × 1
= 17371
Therefore, the total attendance when x = 0 will be 17371.
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Which of the following statements are true?
a) 25:35 = 45:55
b) 105: 30 = 49: 14
c) 45:48 = 60:64
HELP 50 POINTS (see image attached)
5
1
2
8
-2
The value of the function f(3) is 1
How to determine the value of f(3)?The graph represents the given parameter
The value of f(3) implies that we calculate the value of the function when x = 3
From the graph, we have
f(x) = 1, when x = 3
This means that
f(3) = 1
The above is calculated by substituting 3 for x in the equation f(x) = 1
Hence, the value of f(3) is 1
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3. Jerry purchased two cans of paint. He used 6/4 of it. How much did Jerry have
used in decimal?
A. 6.40
B. 4.60
C. 1.50
D. 0.67
The amount used in decimal is 1.50
How to determine the amount used?The given parameters are
Cans = 2
Amount used = 6/4
The amount used in decimal is calculated as:
Amount used = 6/4
Divide 6 by 4
So, we have
Amount used = 1.50
Hence, the amount used in decimal is 1.50
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Jill has 4 one-dollar bills, 3 quarters, 4 dimes, and 3 pennies. Mark has 3 one-dollar bills, 4 dimes, and 2 pennies. What is the difference between the amount of money Jill has and the amount of money Mark has? A B C $1.01 $1.76 $7.85 D $8.60.
Answer: Answer choice 'B'
Step-by-step explanation:
4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.
3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.
To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)
if done correctly, your answer should be $1.76 (answer 'B')
If f(1)=6f(1)=6 and f(n)=f(n-1)-2f(n)=f(n−1)−2 then find the value of f(6)
The value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4
In this question,
we have been given a function f(n) = f(n - 1) - 2
Also, we have been given the value of function f(n) for n = 1
i.e., f(1) = 6
We need to find the value of f(6).
For n = 2,
f(2) = f(2 - 1) - 2
f(2) = f(1) - 2
f(2) = 6 - 2
f(2) = 4
For n = 3,
f(3) = f(3 - 1) - 2
f(3) = f(2) - 2
f(3) = 4 - 2
f(3) = 2
For n = 4,
f(4) = f(4 - 1) - 2
f(4) = f(3) - 2
f(4) = 2 - 2
f(4) = 0
For n = 5,
f(5) = f(5 - 1) - 2
f(5) = f(4) - 2
f(5) = 0 - 2
f(5) = -2
For n = 6,
f(6) = f(6 - 1) - 2
f(6) = f(5) - 2
f(6) = -2 - 2
f(6) = -4
Therefore, the value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4
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Mathematics in the modern world
Answer:
Mathematics shaping the modern world.
Find the vertex of the quadratic function f(x)=(x+3)2−4
The vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).
How to find the vertex of the parabola from the expression of a quadratic equation
Herein we find the expression of a quadratic equation in vertex form, whose definition is shown below:
4 · p · (y - k) = (x - h)² (1)
Where:
h, k - Coordinates of the vertex.
p - Distance from the vertex to the focus.
Then, the vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).
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There is a real number whose product with every real numbers equal zero
a. Some ___ has the property that is __.
b. There is a real number a such that the product of á __.
c. There is a real number á with the property that for every real number b __.
There is a real number whose product with every real number equals zero
a. Some real number has the property that its product with every real number equals 0.
b. There is a real number a such that the product of á and any real equals zero.
c. There is a real number á with the property that for every real number b, the product of a and b equals zero.
Find the area of the shaded region. Help please!
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =85 \end{cases}\implies \begin{array}{llll} A=\cfrac{(85)\pi (10)^2}{360} \\\\\\ A=\cfrac{425\pi }{18}\implies A\approx 74.18~cm^2 \end{array}[/tex]
100 POINTS PLEASE ANSWER QUICK
Use the box plot below to answer the questions.
Part A: Estimate the IQR for the male data.
Part B: Estimate the difference between the median values of each data set.
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each.
The median is a better measure of center for the male's data, while the mean is a better for the female's data.
What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
(a) The IQR of the male's data
From the given male's boxplot, we have the following data elements;
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
Then the IQR is calculated as:
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2
IQR = 12
Hence, the IQR for the given males' data is 12
(b) The difference between the median values can be calculated as;
Median of male's data = 14
Median of female's data = 9
The difference (d) between the median values is;
d = 14 - 9
d = 5
Hence, the difference between the median values of each data set is 5
(c) The distribution of data
It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.
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The median is a better measure of center for the male's data, while the mean is a better for the female's data.
What are quartiles?
When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
(a) The IQR of the male's data
From the given male's boxplot, we have the following data elements;
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
Then the IQR is calculated as:
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2
IQR = 12
Hence, the IQR for the given males' data is 12
(b) The difference between the median values can be calculated as;
Median of male's data = 14
Median of female's data = 9
The difference (d) between the median values is;
d = 14 - 9
d = 5
Hence, the difference between the median values of each data set is 5
(c) The distribution of data
It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.
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Help asap please!! I don’t understand
Answer: 2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3
Step-by-step explanation:
f(x)=2x^2-2
g(x)=x^2-3x
(f/g)(x)=
[tex]\frac{2x^2-2}{x^2-3x}[/tex]=
[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=
[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=
2+[tex]\frac{6x-2}{x^2-3x}[/tex]=2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3
14. Jennifer and Francine are running a race where Francine runs the race far faster than Jennifer.
It takes Jennifer just five seconds less than twice Francine's time to finish. If their combined
total time is 86 seconds and frepresents the amount of time it takes Francine to finish, then
which of the following equations models this situation?
(1) ƒ+2(ƒ-5)=86
(3) ƒ+2ƒ-5=86
(2) 2ƒ-5=86
(4) 2f-5=43
The answer is (2) 2f-5=86; I hope- :\
using associative property
(y+12)+28
Express the given function
Answer:
f(x) = [tex]{\displaystyle {\sqrt[8]{x}}}[/tex]
Step-by-step explanation:
If we let
[tex]g(x) = x^2 - 3\\\\\rm Then \;f(g(x) \;also \;written\; as\; (f\;\circ \rm \;g) \;is\; f(x^2 - 3)\\\\For\; this \;to \;be\; \sqrt[8]{x^2-3} , \\\\\rm f(x) \;has\;to\;be\;\sqrt[8]{x}[/tex]
Quantitative Reasoning :')
Answer:
Step-by-step explanation:
more taking a shower you use almost 3 gallons per a shower
Solve these questions
1) x +2x + x = 68
2) x+y+3y= 45
3) x+y-4z= -32
4) x+y+z= ?
5) -x + 8x= 63
6) 4x+3x-x=42
Same questions as the pic
Answer:
here is the answers
Step-by-step explanation:
sample:
1. 4x = 68
x = 68/4
x = 17
Solution :
1) x + 2x + x = 68
>> 4x = 68
>> x = 68 / 4
>> x = 17
2) x + y + 3y = 45
>> x + 4y = 45
>> 17 + 4y = 45
>> 4y = 45 - 17
>> 4y = 28
>> y = 28 / 4
>> y = 7
3) x + y - 4z = -32
>> 17 + 7 - 4z = -32
>> 24 - 4z = -32
>> -4z = -32 - 24
>> -4z = -56
>> z = 56 / 4
>> z = 14
4) x + y + z = ?
>> 17 + 7 + 14
>> 24 + 14
>> 38
5) -x + 8x = 63
>> 7x = 63
>> x = 63 / 7
>> x = 9
6) 4x + 3x - x = 42
>> 7x - x = 42
>> 6x = 42
>> x = 42 / 6
>> x = 7
K
Convert the angle to a decimal in degrees.
16°43'27"
The value of the angle 16°43'27"is approximately 16.724167 degrees.
A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.
The radian is the SI unit for measuring angles.1 degree = [tex]\frac{\pi}{180}[/tex] radiansA complete rotation around a circle is 180°.A degree is a narrow enough angle for many practical tasks where full degrees are enough for precision. In those instances when this is not the case, such as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be expressed in decimal degrees.To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.
1 degree=60 minutes.
1 minute = 60 seconds.
The given angle is 16°43'27"
27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree
43 minutes= 43 ÷ 60 degree = 0.71666666..
Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...
Therefore required angle ≈ 16.7241667 degrees.
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please help with this! i am stuck
The required simplification of the given expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex] is 1.
Given that,
To determine the simplified value of the expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex].
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
[tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex]
[tex]=\lim_{x \to \infty} \frac{x^2(1-4/x +4/x^2)}{x^2(1-4/x^2)}[/tex]
Now put limits, so 1 / x², 1 / x becomes zero so,
= 1
Thus, the required simplification of the given expression is 1.
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
In August 2006, a report was issued about an Internet poll conducted on behalf of the Oxygen Television Network. The survey included 1400 women and 700 men, aged 15 to 49. The following is part of a press release about the findings.
"Apparently if it's a gadget, women gotta have it, according to a survey done by Oxygen Media, an American cable network owned and operated by women. The Women's Watch: Girls Gone Wired survey released in August indicates that 77 per cent of women fancy a new plasma TV over a diamond solitaire necklace, 78 per cent would rather have a sleek new cell phone than shoes, and 86 per cent would prefer a new digital video camera over designer footwear."
What can be said about these poll results?
Answer:
Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.
PLEASE HELP in the figure below, what is the value of x? Show all work
Answer:
x=19
Step-by-step explanation:
All of the angles add up to 180 degrees since it is a straight angle. So, the equation is:
3x+7+90+x+7=180
You combine like terms:
4x+104=180
Then you subtract on both sides:
4x=76
Then you divide by 4 on both sides:
x=19