The area of a circle with radius r is given by the formula:
[tex]A=\pi r^2[/tex]If we change the value of r by a small amount Δr, the new value of the area will be:
[tex]\begin{gathered} A+\Delta A=\pi(r+\Delta r)^2 \\ =\pi(r^2+2r\Delta r+\Delta r^2) \end{gathered}[/tex]We can neglect the term Δr^2 since we are assuming that Δr is a very small quantity. Then:
[tex]A+\Delta A=\pi r^2+2\pi r\Delta r[/tex]Substitute A=πr^2 and isolate Δr from the equation:
[tex]\begin{gathered} \Rightarrow\pi r^2+\Delta A=\pi r^2+2\pi r\Delta r \\ \Rightarrow\Delta A=2\pi r\Delta r \\ \Rightarrow\Delta r=\frac{\Delta A}{2\pi r} \end{gathered}[/tex]Assuming that the ideal area of the disk is 1000in^2, calculate the ideal radius of the disk:
[tex]\begin{gathered} A=\pi r^2 \\ \Rightarrow r^2=\frac{A}{\pi} \\ \Rightarrow r=\sqrt[]{\frac{A}{\pi}} \\ \Rightarrow r=\sqrt[]{\frac{1000in^2}{\pi}} \\ \Rightarrow r=17.84124116\ldots in \end{gathered}[/tex]Substitute the value of r as well as the variation on the value of the area ΔA=4in^2 to find the variation in the value of the radius:
[tex]\begin{gathered} \Delta r=\frac{4in^2}{2\pi(17.84124116\ldots in)} \\ =0.03568248232\ldots in \end{gathered}[/tex]Up to 3 significant figures, the variation in the value of the radius must be less than:
[tex]0.0357in[/tex]Two cars leave an intersection. One car travels north; the other east.
When the car traveling north had gone 12 mi, the distance between
the cars was 4 mi more than the distance traveled by the car
heading east. How far had the east bound car traveled?
The distance travelled by the east bound car is 8 mi.
What is defined as the distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much floor an object has covered regardless of its starting as well as ending point.Distance and displacement have been two quantities that appear to mean the same thing but have very different definitions and meanings. Distance is defined as "how much earth an object has contained during its motion," whereas displacement is defined as how far of place an object is."The distance travelled by the north car is 12 mi.
Let the distance covered by south car is x.
The distance travelled by the north car is 4 mi more than the distance traveled by the car heading east.
Thus,
x + 4 = 12
x = 12 - 4
x = 8
Thus, the distance travelled by the east bound car is 8 mi.
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In Mr. Stowe's math class, Katherine earned an 88 in the 1st quarter and a 94 in the end quarter. What is the percentage of increase?
The percentage of increase in her score is 6.82%
What is the percentage of increase?Here we will define her first score, 88, as the 100%.
So we can write the relation:
88 = 100%.
Her next score is 94, this will be a percentage X, then we can write:
94 = X
Taking the quotient between the two equations:
94/88 = X/100%
Solving this for X we get:
(94/88)*100% = X = 106.82%
The difference between the percentages gives the increase:
106.82% - 100% = 6.82%
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18% of students use books
164 students use tablet
How many students are in sixth grade?
Total students in sixth grade 200students
What is Percentage?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no associated unit of measurement.
Given,
No. of students using Tablet = 164
No. of students using book = 18%
The students in sixth grade either use book or tablet
When 164 student use tablet then remaining use tablet, that is 18%
Then, the remaining percent would be the students using tablet:
100% - 18% = 82%
converting 82% into decimal we get,
82 /100
i.e, 0.82
Number of students in sixth grade = 164/0.82
= 200 students
Hence, 200 students are in sixth grade
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( Which table of values will generate this graph? 5 3 2 1 2 3 4 5 TT 1919 х 4 1 2
To identify the data corresponding to the points in the plane:
In x you count the units of distance from 0 to the point: from left (negative x) or right (positive x).
In y you count the units of distance from 0 to the point: down (negative y) or upwards (positive y)
Then, in coordinates (x,y) you have the next:
Corresponding to the table:
4. E is between D and F. If DE = 3x + 2, EF = 18, and DF = 5x, find the value of x.
The value of x is 10.
What are expressions in math?A mathematical expression consists of a statement, at least one arithmetic operation, and at least two integers or variables. With this mathematical operation, you can multiply, divide, add, or subtract.
Given:
E is between D and F.
DE = 3x + 2
EF = 18
DF = 5x
We need to determine the value of x which is a variable, whose value is unknown to us and can take any value.
So, DF = DE + EF
Substituting the given values, we get
5x = 3x + 2 + 18
5x - 3x = 20
2x = 20
x = 20/2
x = 10
Therefore, the value of x is 10.
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What would I set the scales to and where is the roots ,vertex and two other points
SOLUTION
Write out the equation
[tex]y=x^2+4x-12[/tex]The root of the equation is
[tex]\begin{gathered} x^2+4x-12=0 \\ x^2+6x-2x-12=0 \\ x(x+6)-2(x+6)=0 \\ (x+6)(x-2)=0 \end{gathered}[/tex]Equate the factors to zero
[tex]\begin{gathered} x+6=0,x-2=0 \\ x=-6,x=2 \end{gathered}[/tex]Hence, the root of the equation is
(-6,0) and (2,0)
The vertex of the equation will be obtained using
[tex]\begin{gathered} u\sin g\text{ the genera form of a quadractic equation } \\ ax^2+bx+c=0,\text{ tye vertex is given by } \\ \: x_v=-\frac{b}{2a} \\ \text{where } \\ a=1,b=4,c=-12\text{ from the given equation } \end{gathered}[/tex]Then
[tex]\begin{gathered} x=-\frac{4}{2\times1}=-\frac{4}{2}=-2 \\ \text{Then} \\ y=x^2+4x-12,\text{ where x=-2} \\ y=^{}(-2)^2+4(-2)-12=4-8-12=-16 \\ \text{Vertex (-2,-16)} \end{gathered}[/tex]Then
[tex]\begin{gathered} \text{The other two point could be } \\ x=0,y=0^2+4(0)-12=0+0-12=-12\text{ } \\ (0,-12) \\ x=2,y=2^2+4(2)-12=4+8-12=0 \\ (2,0) \end{gathered}[/tex]Plotting this point using the scale 2unit on both axes, the image of the graph will be
help meeee
11 Answer:
A box of rice is 19 centimeters long, 12 centimeters wide, and 3.5
centimeters deep. The volume of the box is the product of its length,
width, and height. What is the volume of the box?
20 Answer:
Write the verbal sentence as an equation or an inequality:
The sum of three and x is ten.
Answer:
798
Step-by-step explanation:
11. v = l x w x h
19 x 12 x 3.5 = 798
20. 3+x=10
Government agencies keep data about the income distribution of the population. The Moore family and Kelly family live in a county with 11,000 families.
Moore family's income is at the 24th percentile. The Kelly family's income is at the 77th percentile.
(If necessary, consult a list of formulas.)
(a) Which of the following must be true about the Moore family's and the Kelly
family's incomes?
The Kelly family earns more than the Moore family.
Both the Moore family and the Kelly family earn more than the median
income.
O The Kelly family earns $53,000 more than the Moore family.
The Moore family and the Kelly family both have incomes in the bottom half
of incomes in their county.
(b) Which of the following must be true about the Moore family's income?
O The Moore family earns more than about 76% of families in their county.
About 76% of the families in their county earn more than the Moore family.
O The Moore family earns about 24% of the highest income in their county.
The Moore family earns about 76% of the highest income in their county.
5
(a) (c) The Kelly family earns more than the Moore family.
(b) (a) The Kelly family earns more than the Moore family.
What is Percentile ?Each of the 100 equal groups into which a population can be divided according to the distribution of values of a particular variable is called percentile.
Percentile is computed using the following formula,
P = n/N X 100
Where, n =ordinal rank of a given value
N = number of values in the data set,
P = Percentile
In (a) part , Kelly family's percentile is 77th percentile and Moore family's percentile is 24th percentile.
therefore option (c) i.e. The Kelly family earns more than the Moore family is correct .
In (b) part , Moore family's income is less than Kelly's family income.
therefore option (a) i.e. The Kelly family earns more than the Moore family is correct.
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Given m || n, find the value of x and y.
45°
२०
yº
m
n
A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.
c. What is the probability that at least 12 sales will result from mailing to the 30 prospects?
Using the normal approximation to the binomial distribution, there is a 0.0060 = 0.60% probability that at least 12 sales will result from mailing to the 30 prospects.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in the context of this problem are given as follows:
n = 30, p = 0.2.
Hence the mean and the standard deviation for the approximation are given as follows:
[tex]\mu = np = 30 \times 0.2 = 6[/tex].[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{30 \times 0.2 \times 0.8} = 2.19[/tex]Using continuity correction, the probability that at least 12 sales will result from mailing to the 30 prospects is P(X > 11.5), which is one subtracted by the p-value of Z when X = 11.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11.5 - 6)/2.19
Z = 2.51
Z = 2.51 has a p-value of 0.9940.
1 - 0.9940 = 0.0060.
Hence the probability is of 0.0060 = 0.60%.
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Runners at a cross-country meet run 3 miles north and then 5 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line.
square root of 8 miles
4 miles
square root of 34 miles
8 miles
The shortest straight path they must run back to the starting line is the square root of 34 miles.
What is the shortest straight path?The distance run by the runners forms a right triangle. A right triangle is a polygon that has three sides. The length, base and the hypotenuse. The hypotenuse is the longest side of the right triangle.
The miles run north is the length, the miles run west is the base and the shortest straight path to the starting line is the hypotenuse.
In order to determine the hypotenuse, the Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
3² + 5²
= 9 + 25
= 34
c = √34
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Simplify the fraction
315
405
as much as possible.
7
9
35
45
3
4
Answer:
7/9
Hope this helps!
Have a good day :)
Answer:
7/9
Step-by-step explanation:
I took the quiz
Can you solve this please.
What's the answer to this equation? Please include steps
6(915 - x) = 100 + x
Answer:
x = 770
Step-by-step explanation:
You want the solution to the equation 6(915 - x) = 100 + x.
SolutionIt often works well to simplify the equation first. Here, that means eliminating parentheses using the distributive property:
6(915) -6(x) = 100 +x
5490 -6x = 100 +x . . . . . . . . carry out the multiplication
5490 -6x +6x = 100 +x +6x . . . . . add 6x to both sides
5490 = 100 +7x . . . . . . . . . . collect terms
5490 -100 = 100 +7x -100 . . . . . . subtract 100 from both sides
5390 = 7x . . . . . . . . . . . . . . collect terms
5390/7 = (7x)/7 . . . . . . . . . . . . . . . . divide both sides by 7
770 = x . . . . . . . . . . . . . . . . carry out the division
The solution to the equation is x = 770.
__
Check
6(915 -770) = 100 +770 . . . . use the value of x in the equation
6(145) = 870 . . . . true
__
Additional comment
After eliminating parentheses, this is a 3-step linear equation, so is solved in the usual way. First, the variable terms are collected on one side of the equal sign. Then the constant terms are collected on the other side of the equal sign. Finally, the equation is divided by the coefficient of the variable.
I
2. Which is the more economical purchase: a 20-ounce box of cereal for $4.23 or an 18-ounce box for
$3.75? Justify your answer
In the figure below, circle O has a central angle of 120°.
What is the area of the shaded sector of circle O in terms of r, the radius? Leave your answer in terms of pi.
The area of the shaded section, in terms of the radius R, is:
A = 0.67*R^2
How to get the area of the shaded part?
On the image we can see a circle where a section with an angle of 120° is not shaded and the rest is shaded.
Remember that the area of a circle of radius R is:
A = pi*R^2
Where pi = 3.14
Particularly, for a section defined by an angle x the area is:
A = (x/360°)*pi*R^2
In this case we have:
x = 360° - 120° = 240°
Then the area, in terms of the radius, is:
A = (240°/360°)*3.14*R^2 = 0.67*R^2
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The table represents a quadratic function. Write an equation of the function in standard form.
-9-7-5-3
0 8 8
X
y
y=0
Previous
1 2
0
30
4
32
5
6
7
10
Next
Answer:
Step-by-step explanation:
Given M(-2, 1) is the midpoint on AB and point A has coordinates (-8, -3), find:
Point B
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -8}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(-2~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -8}{2}=-2\implies x-8=-4\implies \boxed{x=4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3}{2}=1\implies y-3=2\implies \boxed{y=5}[/tex]
. Mandy and 6 of her teammates each sold an equal number of
shirts to raise money for their tennis team. If a total of 56 shirts
were sold, how many shirts did each person sell? Explain.
Answer:
8
Step-by-step explanation:
56 shirts were sold, and including Mandy, 7 people sold them.
7 * x = 56
(7x)/7=56/7 (canceling out the 7 to get x alone)
x=8
So basically just 56 divided by 7
Elzabeth brought a box of donuts to share There are two dozen (24) donuts in the box, all identical in size shape and color Two are jelly, 10 are lemon filled, and 12 are custard-filled. You randomly select one donut eat it and select another donut. Find the probability
of selecting a lemon-filled donut followed by a jelly-filled donut.
The probability of selecting a lemon-filled donut followed by a jelly-filled donut is [tex]\frac{5}{138}[/tex]
What is probability ?Probability is the potential for something to happen. In this area of mathematics, random events are studied. The range from 0 to 1 is used to express the value. To forecast the possibility of events, probability has been included into mathematics. The degree of likelihood that something will happen is basically how probability is defined. This fundamental theory of probability, which also applies to the probability distribution, can be used to estimate the likelihood of results in a random experiment.
The distribution of donuts is given as:
jelly = 2
lemon = 10
custard = 12
Total = 24
Eating a chosen donut without replacing it is an example of a selection.
So, the probability of selecting one lemon-filled donuts and one jelly filled donut is:
P = [tex]\frac{lemon}{Total}[/tex]×[tex]\frac{jelly}{total - 1}[/tex]
Substitute known values
P = [tex]\frac{10}{24}[/tex]×[tex]\frac{2}{23}[/tex]
Simplify
P = [tex]\frac{5}{138}[/tex]
Hence, the probability is [tex]\frac{5}{138}[/tex]
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An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)
R(x) =
The equation of the function of the agency revenus in terms of x is R(x) = (50 + x) * (100 - 3x)
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the agency's revenue R as a function of x?From the question, the given parameters are given as
Number of people = 50
Amount charged per person = $100
The above means that the total charges is
Total = Number of person * Amount charged per person
Rewrite as
Revenue = Number of person * Amount charged per person
From the question, we have
The charges for each traveller reduces by $3 for each additional person
Let the number of added person be x
So, we have
Revenue = (Number of person + x) * (Amount charged per person - 3x)
Substitute the known values in the above equation
So, we have
R(x) = (50 + x) * (100 - 3x)
Hence, the agency's revenue R as a function of x is R(x) = (50 + x) * (100 - 3x)
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An artist uses different types of paper to create her masterpieces. She has shiny metallic paper and pink glittery paper. The shiny paper comes in lengths of 24 inches and the glitter paper in lengths of 36 inches. She wants to make sure she can cut her paper into equal sizes but doesn’t want them to be too small. What’s the largest size she can cut them into without any waste?
An artist can cut the metallic paper and pink glittery paper of the largest size of 12 inches without any waste.
What is defined as the term highest common factor?The greatest common factor is the largest number that is a factor of two numbers or more (GCF). The largest number (factor) divides them, yielding a Natural number. Once all of the number's factors have been identified, there are a few that are shared by both.The length of the metallic paper is 24 inches.
The length of the pink glittery paper is 36 inches.
To find the largest size, find the HCF of both number.
First find the factors using prime factorisation;
24 = 2×2×2×3
36 = 2×2×3×3
Find the common term,
HCF (24, 36) = 2×2×3
HCF (24, 36) = 12
Thus, an artist can cut the metallic paper and pink glittery paper of the largest size of 12 inches without any waste.
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A state's recidivism rate is 22%. This means about 22% of released prisoners end up back in prison (within three years). Suppose two randomly selected prisoners who have been released are studied. What is the probability that both of them go back to prison?
The probability that both of them go back to prison is 4.48%.
What is probability?Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
The state recidivism rate is given by 22%.
So, the probability that both of the prisoners will go back to prison will be:
= 22% × 22%= 0.22 × 0.22= 4.84%Hence, the probability that both of them go back to prison is 4.48%.
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Select all the correct answers.
Which functions have a range of {ye R |-∞0 < y < ∞0}?
F(x)=x^2+7x-9
F(x)=-4x+11
F(x)=2/3X-8
F(x)=2^x+3
F(x)=-(x+1)^2-4
For all the given functions, the range lies between {y ∈ R |-∞ < y < ∞} as non of the function has imaginary number.
What is meant by the imaginary number?When imaginary numbers are squared, they produce a negative number. They can also be expressed as the square root of a negative number. An imaginary number is created by multiplying a non-zero real number by the imaginary unit I (also recognized as "iota"), where √(-1) = i (or) i² = -1. These are a type of complex number, which is the sum of a real number as well as an imaginary number. A complex number has the formula a + ib, where 'a' and 'b' are both real numbers and bi is just an imaginary number.For all the given functions;
F(x)=x^2+7x-9F(x)=-4x+11F(x)=2/3X-8F(x)=2^x+3F(x)=-(x+1)^2-4For any value of x ∈ R (real number), the value of y of f(x) will lie in the given range.
Thus, all the given function have the range of {y ∈ R |-∞ < y < ∞}.
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2x-3>7 i kinda need help can i get the answer
Answer:
x>5
Step-by-step explanation:
2x>10
x>5
I will give brainliest, like and rating if u solve this right
6) TRUE OR FALSE?
Answer: True
Step-by-step explanation:
Write 9⁴ as a power of 3.
Answer:
3^8
Step-by-step explanation:
9^4 = 9*9*9*9
9 = 3*3
9^4 = (3*3)*(3*3)*(3*3)*(3*3)
9^4 = 3*3*3*3*3*3*3*3 = 3^8
or, more simply
9 = 3^2
9^4 = (3^2)^4
we use (x^y)^z = x^(y*z)
(3^2)^4 = 3^(2*4) = 3^8
6 is added to the product of 7 and a number
The value of the expression will be equal to 55.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 6 is added to the product of 7 and a number 7. The expression will be written as,
E = 7 x 7 + 6
E = 49 + 6
E = 55
Therefore, the value of the expression will be equal to 55.
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Find the value of x
x=
112°
(3x + 11)°
Which ordered pair, when graphed, would be on the same line as (1, -2) and (-2, 4)?
OA) (-2, 6)
OB) (3, 6)
OC) (3,-6)
OD) (1, 2)
Ordered pair, when graphed, would be on the same line as (1, -2) and
(-2, 4) are (3,-6).
As given in the question,
Equation of the line passes through the point (1.-2) and (-2,4) when graphed is :
(y +2)/(x-1) = (4+2)/(-2-1)
⇒y +2 = -2(x -1)
⇒y =-2x
Ordered pair satisfied the equation of the line passes through the point (1.-2) and (-2,4) when graphed is :
A. (-2,6)
x=-2 ⇒y=4
Not satisfied.
B. (3,6)
x=3⇒y=-6
Not satisfied.
C.(3,-6)
x=3⇒y=-6
Satisfied.
D. (1,2)
x=1⇒y=-2
Not satisfied.
Therefore, ordered pair, when graphed, would be on the same line as (1, -2) and (-2, 4) are (3,-6).
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