The radian measures of the central angle of the sector is 2
Given,
In the question:
Perimeter of sector is 4 times of its radius .
To find the radian measures of the central angle of the sector is?
Now, According to the question:
We know:
The perimeter of the circumference is = 2[tex]\pi[/tex]r
If the perimeter of a sector is 4 times its radius.
then, the arc measure of the sector is (4r-2r) → 2r
So, if 2×[tex]\pi[/tex] radians (full circle) has a length → 2[tex]\pi[/tex]r
X radians → 2× r (the sector)
X=2× r ×(2×[tex]\pi[/tex])/(2[tex]\pi[/tex]r)
X = 2
Hence, The radian measures of the central angle of the sector is 2.
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the length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes what is the probability that a student will take no more than 40 minutes to complete fie examination? select one: a. 0.10 b. 0.00 c. 0.15 d. 0.05
The probability that a student will take no more than 40 minutes to complete tee examination is 0.00.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes.
We have to find the probability that a student will take no more than 40 minutes to complete the examination.
As the time required to complete the statistics examination is uniformly distributed and varies between 40 and 60 minutes so no any student will take less than 40 minutes to complete the examination.
P(X ≤ 40) = 0 where 40 ≤ x ≤ 60
Hence, the probability that a student will take no more than 40 minutes to complete tee examination is 0.00.
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Be sure to show your work where possible-failure to show work will result in
deduction in grade
We know that modern medicine is rich with biology, chemistry and countless other
branches of science. While mathematics does not make a lot of headlines for changing
the way we think about our health and well-being, there are many ways in which
mathematics is informing and improving the way scientists and doctors approach the
world of medicine.
Consider the following data for a group of 2000 women. Of these women, 16 are known
to have breast cancer. All 2000 undergo the same test to determine whether or not they
have breast cancer, and 154 test positive. 14 of the 16 that have breast cancer test
positive and 140 of those that do not have breast cancer test positive.
1. Based on the data presented above, do you think the test for breast cancer is
effective at identifying women who have breast cancer?
The test for breast cancer is not effective at identifying women who have breast cancer.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
It is given that, out of 2000 women, 16 are known to have breast cancer.
But, through the test, the women who do not have breast cancer are also testing positive and the women who have breast cancer are also testing negative.
So, the test for breast cancer is not effective at identifying women who have breast cancer.
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please help solve! cannot find answer and i’m trying to work on math
Answer: 19/21>8/9
Step-by-step explanation:
common denominator is 63
19*3=57 so thats 57/63
8*7=56 so thats 56/63
Fifteen percent of cellphone users use their cell phones to access the Internet. In a random sample of 10 cell phone users, what is the probability that:
Exactly 2 have used their phones to access the Internet?
More than 2 have used their phones to access the Internet?
At least 8 have used their phones to access the Internet?
No more than 5 have used their phones to access the Internet?
Between 1 and 3 people, exclusive, have used their phones to access the Internet?
1) Probability that Exactly 2 have used their phones to access the Internet is; P(X = 2) = 0.2759
2) Probability that more than 2 have used their phones to access the Internet is; P(X > 2) = 0.1798
3) Probability that at least 8 have used their phones to access the Internet is; P(X ≥ 8) = 0.00001
4) Probability that no more than 5 have used their phones to access the Internet is; P(X ≤ 5) = 0.99862
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The formula for binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
Where;
P(X = x) = binomial probability
x = number of times for a specific outcome within n trials
nCx = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
1) We are given;
p = 15% = 0.15
n = 10
Thus;
P(X = 2) = 10C2 * 0.15^(2) * (1 - 0.15)^(10 - 2)
P(X = 2) = 0.2759
2) Probability that more than 2 have used their phones to access the Internet is;
P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
Using binomial probability calculator, we have;
P(X > 2) = 0.1798
3) Probability that at least 8 have used their phones to access the Internet is;
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)
Using binomial probability calculator, we have;
P(X ≥ 8) = 0.00001
4) Probability that no more than 5 have used their phones to access the Internet is;
P(X ≤ 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
P(X ≤ 5) = 0.99862
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Can someone help me figure this out, i’ve been stuck on this question for an hour.
According to the given statement the function representing the points relation is f(x) = 32(3x - 1)
What are the different kinds of functions?An statement, rule, or law in mathematics that establishes the link between an independent variable and a predictor variables (the dependent variable). Equations may be found all around arithmetic, and they are essential for building physical connections in the sciences. A mappings between A and B will only be a function if every member in set A only has end and only 1 photo in set B. Where A & B even be two separate sets.
Briefing:Depicts a few points within the graph of the linear function f given a table.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928
From option first,
f(x) = 32(3x - 1)
Put x = -2
= 32(-2x3-1)
= 32x(-7) = -224
Consequently, f(x) = 32 is the function used to express the points connection (3x - 1)
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what are all of the equivalent ratios to 4.5
Answer:
The two equivalent ratios of 4:5 are 8:10 and 12:15.
Step-by-step explanation:
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The perimeter of a triangle is 204 feet. The longest side of the triangle is 39 feet shorter than twice the shortest side. The sum of the lengths of the two shorter sides is 46 feet more than the length of the longest side. Find the lengths of the sides of the triangle.
The triangle has lengths of 59 feet, 66 feet, and 79 feet.
How to calculate for the sides of the triangle.Let us represent the length of the shortest side of the triangle with x feet, and that of the other shorter side with y feet
The longest side will be (2x - 39) feet
The length of the other shorter side will give us the equation;
y + x = 2x - 39 + 46
so that by subtracting x from both sides, we have
y = 2x - x + 46 - 39
y = (x + 7) feet
From the question,
x + x + 7 + 2x - 39 = 204 feet {which is the perimeter of the triangle}
4x - 32 = 204 {collect like terms}
4x = 203 + 32
4x = 236
x = 236/4
x = 59 feet
Therefore, as the length of the shortest side of the triangle is 48 feet,
the other shorter side is;
y = 59 + 7
y = 66 feet
and the longest side is;
2(59) - 39
118 - 39
79 feet.
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You have 1 2/5 minutes left of
passing time. How many vines
can you watch if each vine is 6
seconds? (Hint: 6 seconds=
1/10 of a minute.)
Answer: You can watch 14 vines.
Step-by-step explanation: 1 2/5 is equal to 1 4/10
1 4/10 is equal to 14/10
So the amount of vines you could watch is 14 in 1 minute and 24 seconds.
find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) (-5,6)
The equation of the circle with endpoints of a diameter at the points (3, 8) and (-5, 6) is x² + y² + 2x - 14y + 33 = 0.
How to determine the equation of a circleThese are the specified parameters:
Endpoints of a diameter at the points (3, 8) and (-5, 6).
Determine the center point of the circle (a, b).
(a, b) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
= ((3 + (-5))/2 , (8 + 6)/2)
= (-2/2 , 14/2)
= (-1, 7)
The center point is (-1, 7).
Determine the radius of the circle (r).
[tex]\begin{aligned} r & = \frac{1}{2} \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\r & = \frac{1}{2} \sqrt{(-5-3)^2 + (6-8)^2} \\ r& = \frac{1}{2} \sqrt{(-8)^2 + (-2)^2} \\ r& = \frac{1}{2} \sqrt{64 + 4} \\ r & = \frac{1}{2} \sqrt{68} \end{aligned}[/tex]
Determine of the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 7)² = (1/2 √68)²
x² + 2x + 1 + y² - 14y + 49 = 1/4 × 68
x² + y² + 2x - 14y + 50 = 17
x² + y² + 2x - 14y + 50 - 17 = 0
x² + y² + 2x - 14y + 33 = 0
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suppose a random variable has population standard deviation 29.5. what is the margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53?
The margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53 is 7.94.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error
z = found by using a z-score table
SD = sample standard deviation = 29.5
n = sample size = 53
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.975, z = 1.96
Plug in the values to the formula and solve for the margin of error.
MOE = z x (SD / √n)
MOE = 1.96 x (29.5/√53)
MOE = 7.94
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A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, then find the length and width.
1. Write a system of equations that will solve the problem
2. Define your variables
3. Solve the problems SHOW YOUR WORK
4. Sketch a graph of your solution
1) The system of equations to solve the given problem are:
2l-3=3b
2(l+ b)=48
2) The variables l and w stands for length and width, respectively.
3) Length l=15 and Width w=9
4) The graph of the solution is shown below:
What is meant by perimeter?A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or a one-dimensional length.
The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference of a wheel/circle specifies how far it will roll in one revolution. Similarly, the amount of string coiled around a spool is proportional to the spool's perimeter; if the length of the string were precise, it would equal the perimeter.
1) The system of equations to solve the given problem are:
2l-3=3b
2(l+ b)=48
2) Here the variables are l, w
The variables l and w stands for length and width, respectively.
3) Given, perimeter of the triangle=48 inches
2l-3=3b
l=(3(b+1))/2
So, 2(l+ b)=48
3b+3+2b=48
5b=45
b=9
l=(3(10))/2
l=15
Therefore, length l=15 and width w=9
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Which graph represents function?
Classify each pair of numbered angles.
Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
[Linear pair ] [ vertical ] [ adjacent ] [none of these ]
Based on the image given above, the angles that are numbered can be classified as:
∠1 and ∠2: vertical angles
∠3 and ∠4: adjacent angles
What are Adjacent Angles?Angles that share the same vertex and also the same side, are said to be angles that lie next to each other which are called adjacent angles.
For example, the angles in the image given that are numbered as 3 and 4, share the same vertex and a common side. Therefore, they are adjacent angles.
What are Vertical Angles?If two angles are formed to lie directly opposite to each other when two lines intersect at a point, the angles share a common point but do not share a common side. These set of angles are called vertical angles.
For example, in the image given, angles 1 and 2 are vertical angles.
Therefore, the angles would be classified as:
Angles 1 and 2: vertical angles
Angles 3 and 4: adjacent angles
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Answer:
3 and 4 are adjacent angles, and 1 and 2 are vertical angles.
Step-by-step explanation:
vertical angles are across from each other while adjacent is next to each other. the other person's explanation is better than mine though. :')
An adult ticket to a museum costs $3 more than a children's ticket. When 200 adult tickets
is $2100. What is the cost of a
and 100 children's tickets are sold, the total revenue
children's ticket?
what is the coefficient of -2 and -3
Answer:
The coefficient of -2 and -3 is -6.
Colleen took out a $48,000 student loan with a fixed interest rate to pay for college. Colleen did not make payments on her loan for a period of 7 years. After this time period interest had accrued, resulting in the loan balance increasing to $78,000. a. What is is the 7-year growth factor for the amount that Colleen owes on the loan? Preview b. What is the 7-year percent change for the amount that Colleen owes on the loan? % Preview c. What is is the 1-year growth factor for the amount that Colleen owes on the loan? Preview d. What is the 1-year percent change for the amount that Colleen owes on the loan? % Preview Submit
a)The 7-year growth factor for the amount on the loan is $4285.71 b) 7-year percentage change for the amount is 6.25% c) 1-year growth factor for the amount $612.244 and d) 1-year percent change for the amount is 0.894%.
a)We know very well that growth factor is ratio of difference of principal amount and loan amount to the time taken, or
Growth factor=(Final loan amount-Initial loan amount)/Total time
=>Growth factor=(78,000-48,000)/7
=>Growth factor=30,000/7=$4285.71
b)To find the percentage change in amount, we need to use initial loan amount and the difference between two amounts, or
percentage change=((78000-48000)/48000)×100
=>percentage change=[(30000)/48000)]×100
=>percentage change=300/48=6.25%
c)Now, we have already find the growth factor for 7 years, we need to find growth rate in 1 year. So, we use unitary method to find it
=>In 7 years growth factor is=$4285.71
∴In 1 years growth factor is=$4285.71/7=$612.244
d)In 7 years percentage change for the given amount is =6.25%
∴In 1 year percentage change for the given amount=6.25/7=0.894%
Hence, answers are a)$4285.71 b)6.25% c)$612.244 d)0.894%
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PLS HELP ASAP>>>>>>Write an equation in slope-intercept form for the line that passes through (3,1) and (1,2). Pls show work
The equation in slope-intercept form is found as; y = -x/2 + 5/2.
State the equation in slope-intercept form?When you understand the slope of a line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y frequency of the y intercept position is denoted by the symbol b in the formula.For the stated question.
Two point are-
(x1, y1) = (3,1)
(x2, y2) = (1,2)
Thus,
slope m = (y2 -y1)/(x2 - x1)
m = (2 - 1)/(1 - 3)
m = -1/2
Equation of line;
y - y1 = m(x - x1)
y - 1 = (-1/2)(x - 3)
y = -x/2 + 5/2
Thus, the equation in slope-intercept form is found as; y = -x/2 + 5/2.
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i honestly don’t know how to do this and if anyone could help it would be appreciated
Is it okay if ya'll can help me on number 5,8,9, and 10
The answer to the following algebra is;
b² at b = 4 is 16
y /5 at y = 15 is 3
27/s at s = 9 is 3
q/3 + 4 at q = 3 is 5
How to solve algebraic expression?Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Given the following:
b² at b = 4
substitute b = 4
= 4²
= 4 × 4
= 16
y /5 at y = 15
substitute y = 15
= 15/5
= 3
27/s at s = 9
substitute s = 9
= 27/9
= 3
q/3 + 4 at q = 3
substitute q = 3
= 3/3 + 4
= 1 + 4
= 5
In conclusion, the algebraic expression is solved by substituting the value of the variables.
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catalina multiplied 842 and 3 and got 3326.how did she check to see if her answer is reasonable?
Answer: Take 3326 and divide by 3
Step-by-step explanation: This will check to see if her answer is correct or not. If 3326 is divided by 3 and gets 842 then her answer is correct!
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3326 ÷ 3 = 1108.666667
Step-by-step explanation:Question: 842 x 3 = 3326?Check:
Take the answer 3326, and divide it by 3, and we should get 842:
3326 ÷ 3 = 1108.666667
It does not equal 842.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Tyrone likes to snack on his big bag of candy. He takes 8 pieces of candy from the bag each time
he snacks. After he has snacked 18 times, there
are only 6 pieces of candy remaining in the bag.
The number c of pieces of candy remaining in the bag is a function of s the number of snacks
Tyrone eats.
Write the function's formula.
C =
Answer:
c = s - (8×18)
Step-by-step explanation:
S = 8×18+6 = 150
c = s - (8×18)
Multiply the following 2 polynomials
(9 + 2x)(9 - 2x)
if the mean of 5 values equals 64, then what is the ∑x?
If the mean of the five values is equals to 64 then the sum of x values i.e., ∑x is 320.
Arithmetic mean:
Arithmetic mean is simply called mean or average. To calculate the arithmetic mean of a set of values, we need to add all the values and then divide the sum by the number of values in the set.
X-bar = ( a₁ + a₂ + -----+ aₙ )/n
Here, there are n items in the set, and each item is represented by one of the a's.
We have given that,
Mean of 5 values , X-bar = 64 , n = 5
we have to calculate the sum of x i.e ∑x
Using Arithmetic mean formula,
sum of x , ∑x = X-bar × n , where x is five values
so, ∑x = 64 × 5 = 320
Hence, the sum of x values is 320.
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Write the equation of the given line in slope-intercept form.
Answer:
SO... y=3x+0b
Or... y = -3x+0b
Step-by-step explanation:
Jack's Car Rental rents out cars, trucks, and SUVs to both individuals and to businesses. For the month of June, they rented out 29 cars, 9 trucks, and 16 SUVs to individuals. They also rented out 13 cars, 22 trucks, and 4 SUVs to businesses. Which of the following matrices could represent this information?
The matrix that represents this information is
| 29 9 16 |
| 13 22 4 |
How to determine which matrices can represent the information?
Matrices (singular matrix) are rectangular arrays or tables where numbers or elements are arranged in rows and columns
Given that:
For the month of June, they rented out 29 cars, 9 trucks, and 16 SUVs to individuals. They also rented out 13 cars, 22 trucks, and 4 SUVs
A defined above, matrices can be viewed as a table. Thus, we can write:
Cars Trucks SUVs
29 9 16
13 22 4
In matrice form:
| 29 9 16 |
| 13 22 4 |
Therefore, the matrix that represents this information is
| 29 9 16 |
| 13 22 4 |
Option D. is the answer
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how many ways can the letters of the word dancer be arranged in a row if d and a must remain together (in order) as a unit?
The number of ways the letters of the word DANCER can be arranged if D and A remain together is 120 ways .
In the question ,
it is given that the word is DANGER ,
the number of letters in the given word is = 6
it is given that the letters D and A are together ,
that means they are a single unit ,
So , the number of letters become = 5 letters
and 5 letters can be arranged in 5! ways ,
which can be simplified as
5! [tex]=[/tex] 5 * 4 * 3 * 2 * 1 [tex]=[/tex] 120 ways
Therefore , the number of ways of arrangement is 120 ways .
The given question is incomplete , the complete question is
How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit ?
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PLEASE HELP ME WITH THIS PROBLEM!!!!!!
Answer:
720
Step-by-step explanation:
100/5 = 20, so 20 tires made in 1 hour and 20 x 36 would be 720 so answer is 720
3. Select all that apply. Which of the following are equal to 600?
A. 400 increased by 50%
B. 500 increased by 25%
C. 300 increased by 75%
D. 800 decreased by 25%
The answer's are A and D!
Let me know if I'm right please!
ANSWER PLEASE
This scatter plot shows the number of siblings 14 students have and each student's grade level.
scatter plot shows the scores of 11 students that took the college algebra final exam and the hours they studied.
Choose the conclusion that is best supported by the data shown in the scatter plot
As hours spent studying increases, grades on the college algebra final exam increase.
As hours spent studying increases, grades on the college algebra final exam increase.
As hours spent studying increases, grades on the college algebra final exam decrease.
As hours spent studying increases, grades on the college algebra final exam decrease.
As hours spent studying increases, grades on the college algebra final exam stay the same.
As hours spent studying increases, grades on the college algebra final exam stay the same.
There is no relationship between the grade on the college algebra final exam and hours spent studying.
Answer:As hours spent studying increases, grades on the college algebra final exam increase.
Step-by-step explanation:
The graph shows the relationship between temperature y (in degrees
Fahrenheit) and altitude x (in thousands feet).
a. Find and interpret the slope of
the graph.
b. Write an equation of the line.
c.Interpret the x-intercept of the graph
Answer:answer will be more exact than the point you found in the first part
Step-by-step explanation:temperature in degrees Fahrenheit,
degrees Celsius
20
40
60
80 100 120 140 160 180 200 220 240
degrees Fahrenheit
a. Mark the point on the graph that shows the temperature in Celsius when it is 60
degrees Fahrenheit
b. Mark the point on the graph that shows the temperature in Fahrenheit when it
is 60 degrees Celsius.
c. Water boils at 100 degrees Celsius. Use the graph to approximate the boiling
temperature in Fahrenheit, or to confirm it, if you knew what it is.
d. The equation that converts Celsius to Fahrenheit is C = (F - 32). Use it to
calculate the temperature in Celsius when it is 60 degrees Fahrenheit. (This
answer will be more exact than the point you found in the first part