A) The measure of the central angle is [tex]\frac{4}{3} \pi[/tex] .
B) The radius of the circle is 55.43 in.
A) We know,
The area of a sector is [tex]\frac{n}{2\pi } \pi R^{2}[/tex]
where n = the degree of the central angle of the sector
R = radius of the circle
Suppose, the measure of the central angle is x.
[tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]
⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]
⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]
⇒ [tex]x = \frac{4}{3} \pi[/tex]
So, the measure of the central angle is [tex]\frac{4}{3} \pi[/tex].
B) Suppose the radius of the circle is r in.
[tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]
⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]
⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]
⇒ [tex]r^{2} = 3072[/tex]
As r > 0
So, r = 55.43
Hence, The radius of the circle is 55.43 in.
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Question 32:
Write an equation in Slope-Intercept form for the
line that passes through (1,-3) and is parallel to
y+2 = 4(x-1)
The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.
For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.
To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)
So, using the point (1,-3) and the slope (4), we can write the equation as:
y - (-3) = 4(x - 1)
Simplifying this equation gives:
y + 3 = 4x - 4
Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:
y = 4x - 1
So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1
in how many different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another?
There are 384 ways to arrange these given letters as per the given situation.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another.
In this question, we have 2 ways where A and B (AB, BA) are next to each other and 2 ways where C and D (CD, DC) are next to each other. 2 ways where g and h (gh, hg) are next to each other and 2 ways where e and f (ef, fe) are next to each other.
The total number of arrangements is = 4! * 2 * 2 *2*2
The total number of arrangements is = 24 * 16
The total number of arrangements is = 384
Therefore, the Different ways to arrange these letters are 384.
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Given the following data, fill out the table for V* n and V/n
(give your answers to 3 sig figs).
The table for V* n and V/n shows the various answers as
What is multiplication and Division?Multiplication is when you take one number and add it together a number of times.
The table appears as follows
Volume(V) Moles(n) V*n V/n
3 0.145 0.435 20.7
4 0.193 0.773 20.7
5 0.242 1.210 20.7
6 0.290 1.740 20.7
These figures are gotten by the multiplication and division of the numbers in the tables as given by the formulae
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How much money would you need to deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years? Round to the nearest cent.
The account balance after five years will be $10355.
What is compound interest?The interest that is paid on the principal and interest at regular intervals is known as compound interest. The difference between compound interest and simple interest starts to show after the first year, though.
The formula to calculate the compound interest is given below;-
[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]
Given that deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years.
The account balance after five years will be:-
[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]
[tex]A = 10000 ( 1+\dfrac{0.07}{1})^{5}[/tex]
A = 10000 x ( 1.07)⁵
A = $10355
Hence, the amount will be $10355.
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 100 engines and the mean pressure was 5.5 lbs/square inch. assume the standard deviation is known to be 0.7 . if the valve was designed to produce a mean pressure of 5.3 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
There is sufficient evidence that the valve performs above the specifications.
Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch
Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch
To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.
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Things that have an equal an equal chance of happening are known as what?
Mutually exclusive events are events that have no overlap between them and the sum of the probabilities of all mutually exclusive events is equal to 1.
What is the probability theory?
Probability theory is a branch of mathematics that deals with the study of random phenomena. It provides a mathematical framework for analyzing the likelihood of different outcomes in a given situation, and for making predictions about future events based on past data.
Things that have an equal chance of happening are known as equally likely events or mutually exclusive events. In probability theory, mutually exclusive events are events that cannot happen at the same time; if one event occurs, the other cannot.
In general, mutually exclusive events are events that have no overlap between them and the sum of the probabilities of all mutually exclusive events is equal to 1.
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chris made 27 of the 45 putts while practicing golf. What percent of putts did he miss
Answer: The percent of putts that he missed is 60%.
Step-by-step explanation: You divide 27 by 45, and that equals 0.6. After that you multiply 0.6 by 100, which gets it to 60/60%.
Is 13,14,15 a pythagonrean triples
Answer:
milk
Step-by-step explanation:
milk store is where your dad went
help me please i need your help
Answer:
∞
Step-by-step explanation:
I don’t know just think it out. That is the explaination
Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101. Show your steps.
Please give answer immediately
Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.
What is the HCF?The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.
101 x 10 = 1010
101 x 11 = 1111
101 x 12 = 1212
101 x 13 = 1313
Now, from these numbers, there are two numbers whose difference is 303.
1313 - 1010 = 303
Based on this, the two numbers are 1010 and 1313
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The middle school has 24 students less than 3 times the number of students at one of
the elementary schools.
The required equation is y=3x-24, where x is the number of elementary school students and y is the number of middle school students.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
Let x be the number of students in elementary school and y be the number of students in middle school.
y=3x-24
The required equation is y=3x-24 where x be the number of students in elementary school and y be the number of students in middle school.
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Classify the sequence {1, 6, 11, 16, 21, …}.
Answer:
Classify the sequence {1, 6, 11, 16, 21, …}.
The pattern is +5:
1 + 5 = 6
6 + 5 = 11
11 + 5 = 16
16 + 5 = 21
21 + 5 = 26
And so on
Step-by-step explanation:
You're welcome
i dont understand this
The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77
How to find sin cos tan?In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.
Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).
We have, AB = 77 , BC = 36.and CA=85
When we consider the t-ratios of ∠A, we have
Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.
∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77
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peacock premium tv charges $5.00 per month plus a set-up fee. the total cost after 10 months was $65.00. write an equation in point-slope form to model this situation.
A point-slope form is an equation for a line, using a point and the slope of the line. So we have to find one x-coordinate and y-coordinate and write it in the form of (y-y₁) = m(x-x₁).
Here the total after 10 months is said to be 65 and number of months = 10. So we can calculate the set-up fee.
5 ×10 + x = 65
x = 65-50 = 15.
The only constant here is the set-up fee, 15.
Lets the number of months be x and total amount be y.
y- 5x = 15
Lets calculate the y intercept. x-term will be 0.
y+0 = 15
y = 15
Lets calculate the x-intercept. y term will be 0
-5x = 15
x = -3
Two points on the line are (-3,0) and (0,15)
slope = (15-0)/(0--3)
=15/3 = 5
So lets find out one point in the equation
If y=10,
10-5x = 15
-5x = 15-10
x = 5/-5 =-1
So a point on the line is (-1,10)
Point slope form,
(y-10) = 5 (x- ⁻1)
(y-10) = 5 (x+1)
So this is the point slope form.
y = 5x+15
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The two similar rectangles shown below have a scale factor of 3:10
If the perimeter of the larger rectangle is 90 centimeters, what is the perimeter of the smaller rectangle?
The perimeter of the smaller rectangle would be 27 cm.
What is scale factor? How it is used in Dilating sides?Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically : K = a/b.Rewriting, we get : a = KbIf a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].Given is that two similar rectangles shown below have a scale factor of
3 : 10.
Since the two rectangles are similar, then the ratio of their corresponding perimeters will be constant.
We can write -
P{1}/P{2} = 3/10
P{1}/90 = 3/10
P{1} = (3 x 90)/10
P{1} = 27
Therefore, the perimeter of the smaller rectangle would be 27 cm.
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What percent of 1 3/5 is 0.2? (im stu pid, sorry)
Answer: 12.5%
(Don't worry!)
After how many years will the loan be half-paid?
A. 15 years
B. 18 years
C. 21 years
D. 24 years
PLEASE HELPPP
You are the grade 10 representative on the student council and you have been assigned the
task of finding a location to host a dance for the students of CISE. You have narrowed it down
to three options which are outlined below:
Ancient Abyss is a location that charges a $200 flat fee and $4 per person.
Beautiful Babylon is a location that charges a $99 flat fee and $6 per person.
Crazy Cleopatra is a location that charges a $280 flat fee and $3 per person.
Task:
You will analyze the three options and put together a proposal to submit to the student
council outlining your recommendations.
Based on the information provided, I have analyzed the three options for hosting a dance for the students of CISE, and have come to the following recommendations:
Ancient Abyss: This location charges a flat fee of $200 and $4 per person. This option may be suitable for smaller events with less than 50 attendees, as the flat fee is relatively high. However, for larger events with more than 50 attendees, the per person cost will become more significant and may make this option less cost-effective.
Beautiful Babylon: This location charges a flat fee of $99 and $6 per person. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Ancient Abyss. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.
Crazy Cleopatra: This location charges a flat fee of $280 and $3 per person. This option has the highest flat fee but the lowest per person cost. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Beautiful Babylon. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.
Based on the above analysis, I recommend that the student council consider Beautiful Babylon as the most cost-effective option for hosting the dance. However, I also recommend that the council consider the number of attendees expected at the event and adjust their decision accordingly.
In summary, The council should consider the number of attendees expected, Beautiful Babylon is a good option for larger events, for smaller events, Crazy Cleopatra is the better option.
There's a 1/6 chance that a student will be in Miss Jones math class if there are 30 students in her class how many students are there at all
If there is a 1/6 chance that a student will be in Miss Jones's math class, if there are 30 students in her class, then 180 students will be there at all.
Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.
Total number of students present in the miss jones class = 30
The chance that a student will be in Miss Jones's math class = 1/6
Let x be the students are there at all
According to the question,
1/6 × x = 30
⇒x = 30 × 6
⇒x = 180
Hence, 180 students are there at all.
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Simplify this to help me out
When we simplify the expression (4x⁴y⁵ / 3xy²)⁵, the result obtained is 1024x¹⁵y¹⁵ / 243
How do I simplify (4x⁴y⁵ / 3xy²)⁵?To simplify the expression (4x⁴y⁵ / 3xy²)⁵, the laws of indices must be applied as illustrated below:
(4x⁴y⁵ / 3xy²)⁵
Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(4x⁴y⁵ / 3xy²)⁵ = 1024x²⁰y²⁵ / 243x⁵y¹⁰
Recall
Aᵐ / Aⁿ = Aᵐ⁻ⁿ
Thus,
1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x²⁰⁻⁵y²⁵⁻¹⁰
1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x¹⁵y¹⁵
1024x²⁰y²⁵ / 243x⁵y¹⁰ = 1024x¹⁵y¹⁵ / 243
Therefore,
(4x⁴y⁵ / 3xy²)⁵ = 1024x¹⁵y¹⁵ / 243
From the above illustration, we can conclude that the simplified form of (4x⁴y⁵ / 3xy²)⁵ is 1024x¹⁵y¹⁵ / 243
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Explain in words how to solve an equation with a variable on both sides of the equation.
Mrs. Soriano baked 7 5/9 dozens of chocolate cookies. She gave 3 1/3 dozens to her friends. How many dozens of chocolate cookies were left ?
A. 4 3/9
B. 4 2/9
C. 4 5/9
D. 4 1/9
Answer:
4 2/9
Step-by-step explanation:
7 5/9 -3 1/3
68/9 -10/3
(68-30)/9
38/9
4 2/9
Find the height of the figure.
12. A = 12 m²
4.8 m
13. A 11.0625 m²
3.75 m
The height of the figure is 66 m².
How to find height?Finding the triangle's height can be done in a variety of ways. There are numerous other formulas, but the one that uses a triangle's area is the one that is most widely used. You can determine the triangle's area given its sides using an equation known as Heron's formula. Once you are aware of the region, you can use the fundamental equation to determine the triangle's altitude.
You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.
27.5 × 4.8
= 132
132/2
= 66
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Find five consecutive odd integers whose sum is 85.
Answer:
13+15+17+19+21 = 85
Step-by-step explanation:
Hope you got it !
Answer:
The five consecutive odd integers whose sum will be 85 are 13, 15, 17, 19, and 21.
Step-by-step explanation:
To solve this problem, let's assume the first number is n.
Then the consecutive odd integers will be n+2, n+4, n+6, n+8
Thus we can write,
n+(n+2)+(n+4)+(n+6)+(n+8) = 85
In the next step add all the n's,
5n+20 = 85
Then transfer '20' from LHS to RHS,
5n = 85 - 20
5n = 65
Then in the next step '5' needs to be transferred to RHS,
n = 65÷5
n = 13
Therefore, n = 13
n+2 = 15
n+4 = 17
n+6 = 19
n+8 = 21
Thus the five consecutive odd integers are 13, 15, 17, 19, and 21.
:)))))))))))))))))))))))))))))
The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation( please help!!)
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = ln x
The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have
y - 12 = ln (x + 8)
y = ln (x + 8) + 12
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.
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If you were to sketch a circle graph for the data shown in the table below, approximately what
fraction of the circle would represent food?
Vacation Expenses Budget
Expense Amount Budgeted
Activities=600
Food= 450
Souvenirs=270
The fraction of the circle that would represent food is given as 34.09
How to solve for the fraction that would represent foodThe data we have here is given as
Activities = 600
Food = 450
Souvenirs = 270
We would have to sum this up
600 + 450 + 270 = 1320
The proportion that represents food is given as 450
= 450 / 1320
= 0.3409
Then we would have to convert this to percentage
0.341 * 100
= 34.09
34.09 x 360 = 123 degrees
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PLEASE HELP I WILL GIVE BRAINLIEST
For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E
The image of the triangle DEF are formed by the following coordinates: D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5).
How to dilate a triangle centered at a given point
In this problem we need to apply a rigid transformation known as dilation, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Dilation factorWe need to determine the image of triangle DEF. If we know that D(x, y) = (2, - 2), E(x, y) = (4, - 2), F(x, y) = (1, - 4) and k = 1.5, then the images of the vertices of the triangle:
D'(x, y) = (4, - 2) + 1.5 · [(2, - 2) - (4, - 2)]
D'(x, y) = (4, - 2) + 1.5 · (- 2, 0)
D'(x, y) = (4, - 2) + (- 3, 0)
D'(x, y) = (1, - 2)
E'(x, y) = (4, - 2) + 1.5 · [(4, - 2) - (4, - 2)]
E'(x, y) = (4, - 2)
F'(x, y) = (4, - 2) + 1.5 · [(1, - 4) - (4, - 2)]
F'(x, y) = (4, - 2) + 1.5 · (- 3, - 2)
F'(x, y) = (4, - 2) + (- 4.5, - 3)
F'(x, y) = (- 0.5, - 5)
The coordinates of the image of triangle DEF are D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5)
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Sofia is making a batch of slime using a recipe that includes glue, water, and a salt solution. She uses 7. 5 fl oz of glue. The amount of glue is 12. 5 times the amount of salt solution. There are 4. 2 less fluid ounces of salt solution than water.
How many fluid ounces of water does Sofia use to make the batch of slime?
Total amount of fluid ounces of water used by Sofia to make proportionate amount of slime is equal to 4.8 fluid ounces.
Let us consider 'x' amount of salt solution.
Amount of glue used by Sofia = 7.5 fluid ounces
Amount of glue = 12.5 times of salt solution
⇒ 7.5 = 12.5x
⇒ x = 7.5 / 12.5
⇒ x = 0.6
Fluid ounces of water used by Sofia to make the required batch of slime is:
Now, Amount of salt solution = Fluid ounces of Water - 4.2
⇒Fluid ounces of Water = x + 4.2
⇒ Fluid ounces of Water = 0.6 + 4.2
⇒ Fluid ounces of Water = 4.8 fluid ounces
Therefore, the fluid ounces of water used by Sofia with salt solution and glue to make a slime is equal to 4.8 fluid ounces.
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A chef made a blend of cooking oil. 1/5 of his mix was olive oil and 4/5 was corn oil. Write this blend as a ratio of corn oil to olive oil
1 :1 is the blend as a ratio of corn oil to olive oil.
Now, According to the question:
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
"Information available from the question"
A chef made a blend of cooking oil.
1/5 of his mix was olive oil
and 4/5 was corn oil.
To find the blend as a ratio of corn oil to olive oil.
Now, Blend Ratio will be:
olive ratio + corn ratio
1/5 + 4/5
= 5/5 = 1/1
Hence, 1:1 is the blend as a ratio of corn oil to olive oil.
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