Answer:
[tex]\boxed {\boxed {\sf \frac{ 243}{8} \pi , 95.3775, or \ 95.42587686 \ m^2 }}[/tex]
Step-by-step explanation:
When given the central angle in degrees, the formula for sector area is:
[tex]A=\frac{ \theta}{360} * \pi r^2[/tex]
where θ is the central angle and r is the radius.
We are given the diameter, so we must calculate the radius. The radius is half the diameter.
r= d/2The diameter is 18 meters.
r= 18 m/2 r= 9 mNow we know all the variables:
θ=135 r= 9 mSubstitute the values into the formula.
[tex]A=\frac{ 135}{360} * \pi (9)^2[/tex]
Solve the exponent first.
(9)²= 9 m *9 m= 81 m²[tex]A=\frac{ 135}{360} * (81 \ m^2) \pi[/tex]
Solve the fraction.
[tex]A=\frac{ 3}{8} * (81 \ m^2) \pi[/tex]
Multiply the two rational numbers.
[tex]A=\frac{243}{8} \pi \ m^2[/tex]
The answer can be left like this, in terms of pi, or can be multiplied.
Using 3.14 as pi[tex]A=\frac{243}{8} *3.14 \ m^2[/tex]
[tex]A= 95.3775 \ m^2[/tex]
Using the pi button as pi[tex]A= 95.42587685 \ m^2[/tex]
The area is 243/8 π, 95.3775, or 95.42587685 square meters.
what is the slope intercept form of 7x-5y=15?
Answer:
y=7/5x-3 is the slope intercept form
A beachfront hotel is planning for its summer busy season. It wishes to estimate with 95% confidence the average number of nights each guest will stay in a single visit. Using a sample of guests who stayed last year, the average number of nights per guest is calculated at 5 nights. The standard deviation of the sample is 1.5 nights. The size of the sample used is 120 guests and the beachfront hotel desires a precision of plus or minus 0.5 nights.
Required:
a. What is the standard error of the mean in the lakefront resort example?
b. Within what range below can the resort expect with 95% confidence for the true population mean to fall?
Answer:
0.1369
(4.732, 5.268)
Step-by-step explanation:
Given that:
Mean, m = 5
Standard deviation, s = 1.5
Error margin, E = 0.5
Sample size, n = 120
Zcritical at 95% = 1.96
Standard Error of the mean (S. E) :
S. E = s /sqrt(n)
S. E = 1.5 / sqrt(120
S.E = 1.5 / 10.954451
S. E = 0.1369306
S. E = 0.1369
Confidence interval (C. I)
Mean ± (Zcritical * S.E)
5 ± (1.96 * 0.1369)
Lower boundary = 5 - 0.268324 = 4.731676
Upper boundary = 5 + 0.268324 = 5.268324
(4.732, 5.268)
Write 36 + 60 as a product using the GCF as one of the factors.
Answer:
12(3+5)
Step-by-step explanation:
You factor out 12 because it is the GCF, then you divide 36 and 60 by 12.
36 + 60 as a product using the GCF as one of the factors is 12(3 + 5).
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, 36 + 60 now the common factors of 36 and 60 are 2, 3, 6, 12
∴ The GCF of 36 and 60 is 12.
So, 36 + 60 as a product can be written as
36 + 60.
12(3 + 5).
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Which events are independent? Choose all that apply.
A. There is lightning outside. The baseball game is canceled due to lightning,
B. Ahmad flips a coin and records the result. Ahmad flips the same coin again and records the result.
O c. One name is randomly chosen from a bag. The name is not replaced and another name is randomly chosen
D. Jason votes for president of the city council in the morning. Hae Sung votes for president of the city council in the afternoon
Answer:
i'd say the answer is b. i hope this helps
Answer:
B,C,D
Step-by-step explanation:
9X - 5X + 18 = 2X +34
Answer:
x=8
Step-by-step explanation:
1.5.2. You have a six-sided die that you roll once. Let Ri denote the event that the roll is i. Let Gj denote the event that the roll is greater than j. Let E denote the event that the roll of the die is evennumbered. (a) What is PR3 jG1 , the conditional probability that 3 is rolled given that the roll is greater than 1
Answer:
What is PR3 jG1 , the conditional probability that 3 is rolled given that the roll is greater than 1
=0,02
Step-by-step explanation:
Sample Space for rolling a die, S(1,2,3,4,5,6]
Since all the outcomes are equally P( rolling any numebre)=1/6
G1=(2,3,4,5,6)
Hence P(G1) =P (R2)+P (R3)+P (R4)+P (R5)+P (R6)
Hence P(G1) =5/6
and R3= [3]
Hence G1 ∩ R3 = [3] = R3
Hence P(G1 ∩ R3) =P( R3) =1/6
What is PR3 jG1 , the conditional probability that 3 is rolled given that the roll is greater than 1
P(G1 ∩ R3) / P(G1) = (1/6)/ (5/6=
=0,02
A, B & C form the vertices of a triangle.
CAB = 90°, ABC = 60° and AB = 8.6.
Calculate the length of BC rounded to 3 SF.
BC =
Answer:
BC = 17.2.
Step-by-step explanation:
Since CAB = 90º, this is a right triangle.
The triangle format is given below:
C
A B
We have that AB = 8.6, and angle B measures 60º.
Length of BC:
BC is the hypotenyse.
Side AB is adjacent to angle B = 60º.
In a right triangle, angle [tex]\alpha[/tex], it's adjacent side with length s and the hypotenuse h are related by the cosine of the angle, that is:
[tex]\cos{\alpha} = \frac{s}{h}[/tex]
In this question, we have an angle of 60º, with has cosine 0.5. We also have that side AB = s = 8.6, and the hypotenuse h is side BC. So
[tex]\cos{\alpha} = \frac{s}{h}[/tex]
[tex]0.5 = \frac{8.6}{h}[/tex]
[tex]0.5h = 8.6[/tex]
[tex]h = \frac{8.6}{0.5}[/tex]
[tex]h = 17.2[/tex]
BC = 17.2.
Find the mean, median mode(s), range, standard deviation, and variance of the data: 21, 15, 16, 25, 13, 18 5, 3, 2, 6, 5, 2, 5 Eight car sales men sold cars at a dealership. Here is the distribution of cars sold last month: 6, 45, 52, 43, 48, 41, 50, and 48. Find the mean, median mode(s), range, standard deviation, and variance of the data: Which measure of central tendency best represents the data
Answer:
Kindly check explanation
Step-by-step explanation:
Given tbe data :
21, 15, 16, 25, 13, 18 5, 3, 2, 6, 5, 2, 5
Ordered data : 2, 2, 3, 5, 5, 5, 6, 13, 15, 16, 18, 21, 25
Mean, m = Σx /n
Σx = 136
n = sample size = 13
m = Σx / n = 136 / 13 = 10.46
Mode, = 5 (most frequently occurring with frequency of 5)
Median = 1/2(n+1)th term = 1/2(14) = 7th term = 6
Range = maximum - minimum = [25 - 2] = 23
Variance : (V) = Σ(x - m)²/n-1
V = [(2-10.46)^2 + (2-10.46)^2 + (3-10.46)^2 + (5-10.46)^2 + (5-10.46)^2 + (5-10.46)^2 + (6-10.46)^2 + (13-10.46)^2 + (15-10.46)^2 + (16-10.46)^2 + (18-10.46)^2 + (21-10.46)^2 + (25-10.46)^2] / (13-1)
= 745.2308 / 12
= 62.10
Standard deviation = sqrt(V) = sqrt(62.10) = 7.88
2.)
X : 6, 45, 52, 43, 48, 41, 50, 48
Reordered data, X: 6, 41, 43, 45, 48, 48, 50, 52
Mean, m = Σx /n
Σx = 333
n = sample size = 8
m = Σx / n = 333 / 8 = 41.625
Median = 1/2 (n+1)th term = 46.5
Range = 52 - 6 = 46
Mode = 48 (highest occurring frequency of 2)
Variance (V) = Σ(x - m)²/n-1
V = [(6-41.625)^2 + (41-41.625)^2 + (43-41.625)^2 + (45-41.625)^2 + (48-41.626)^2 + (48-41.625)^2 + (50-41.625)^2 + (52-41.625)^2] / 5
= 1541.862251 / 7
= 220.27
Standard deviation = sqrt(Variance)
Standard deviation = sqrt(220.26603)
Standard deviation = 14.84
The median
How much is a 2/9 pound plus 1/9 pound?
Answer:
1/3 pound.
Step-by-step explanation:
2/9 pound +1/9 pound = (2+1)/9 pound.
This can be simplified to 3/9 pound, or 1/3 pound.
Let me know if this helps!
Answer:
33.333 percent
Step-by-step explanation:
Which numbered choice represents the solution to this system?
y=2x+4
-6x+3y=12
1) (2,8)
2) (-3,-2)
3) (0,4)
4) All are solutions.
Answer:4) All are solutions
A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $123 and a standard deviation of $9. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $105
Answer:
At most 25% of homes will have a monthly utility bill of less than $105.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question, we have that:
The mean is $123.
The standard deviation is $9.
What percentage of homes will have a monthly utility bill of less than $105
105 = 123 - 2*9
So 105 is two standard deviations below the mean.
We have that, by the Chebyshev Theorem, at least 75% of the measures will be within 2 standard deviations from the mean, so at most 25% of the measures will be more than two standard deviations of the mean(greater than 141 ou lesser than 105).
So at most 25% of homes will have a monthly utility bill of less than $105
whats the GCF for 1248
Answer:
None or 12 depending on what the question is. See explanation below.
Step-by-step explanation:
If the number is 1248:
A single number cannot have a GCF. The GCF has be for at least two numbers.
If the numbers are 12 and 48, then the GCF can be calculated.
Since 12 is a factor of 48, then the GCF of 12 and 48 is 12.
In general, to calculate the GCF do this:
To calculate it, find the prime factors of 12 and 48.
12 = 2^2 * 3
48 = 2^4 * 3
GCF is the product of common factors with lower exponent.
GCF = 2^2 * 3 = 12
Cho surveyed a random sample of 60 students in the school's library about whether they read the newest magazine. Fifteen of the 60 students said they read the newest magazine. Cho determined that 360 students visit the library each day.
Based on the survey, how many of the 360 students can he expect to read the newest magazine?
Answer:
90 students.
Step-by-step explanation:
Given that Cho surveyed a random sample of 60 students in the school's library, of which 15 said they read the newest magazine, and that a total of 360 students attend the library every day, to determine how many of the 360 students can have expect to read the newest magazine the following calculation should be performed:
60 = 100
15 = X
15 x 100/60 = X
1,500 / 60 = X
25 = X
Thus, 25 percent of the students in the sample read the newest magazine. Since 25% of 360 is 90 (360 x 0.25), that is the number of students he can expect to have read the magazine.
How much water should he use?
enough
lololololololololololol
Answer:
6.25 cups
Step-by-step explanation:
Verify that the following function is a probability mass function, and determine the requested probabilities.
fx = (8/7(1/2)x
x = 0, 1, 2, ...
A. P(X = 2).
B. P(X ≤ 2).
C. P(X > 2).
D. P(X ≥ 1).
Is the function a probability mass function?
Answer:
yes
Step-by-step explanation:
Factor the common expression: 2x + 4 =
Answer:
2(x+2)
Step-by-step explanation:
Hope it helps you
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!
Answer:
both x angles are equal to 40 degrees
Answer:
x would equal 40
Step-by-step explanation:
a line is 180, the angle inside the triangle is 100 and x is on both sides that means x would equal 40 because there is 2 x's and 100 is already a number and 180 is a line.
180 = x + x + 100
x + x + 100 - 100 = 180 - 100
x + x = 80
2x = 80
2 ÷ 2x = 80 ÷ 2
x = 40
A city’s elevation is 140.2 feet below sea level. Between which two integers does this elevation lie?
Answer:
The elevation lies between -140 and -141.
Step-by-step explanation:
The elevation lies between -140 and -141.
what is the difference between 6 and 2 1/5.
Answer:
3.8
Step-by-step explanation:
6 - 2 1/5 = 6 - 11/5
= 6-2.2
=3.8
The difference between the 6 and 2 1/5 will be 3.8
What is a fraction?A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1. A mixed fraction contains a sum of whole number and a proper fraction.
So, WE need to find the difference between the 6 and [tex]2 \frac{1}{5}[/tex].
First we need to convert the mixed fraction into simple fraction.
[tex]2 \frac{1}{5}[/tex] = 11/5
Therefore, the difference between them will be;
6 - [tex]2 \frac{1}{5}[/tex] = 6 - 11/5
= 6 - 2.2
= 3.8
Hence, the difference between the 6 and [tex]2 \frac{1}{5}[/tex] will be 3.8
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HELP!!
Construct the graph of the direct proportion y=kx for k=0
Answer:
Shown in picture UnU
Which soap deal has the lowest price per ounce?
$5.50 for 13.0 oz
$5.75 for 14.0 oz
$3.45 for 3.5 oz
$5.25 for 12.0 oz
Brandon is 5 years older than his brother Hermie. There combined age is 23. How old is Brandon?
Find Brandon's age using the following equation:
2 + (x + 5) = 23
A
9
14
15
Answer:
9
Step-by-step explanation:
9 +5 = 14
14 +9 = 23
What is the y intercept of the line 3y+8x-18=0?
Answer: y= 8/3x + 6
Step-by-step explanation:
Find the scale factor
(-3,-12)--->(-2,-8)
(-6,-15)--->(-4,-10)
(-9,-12)--->(-6,-8)
Answer:
2/3 is the scale factor of the sequence
Kimmie sells custom T-shirts for $12 each at the flea market every Saturday She usually sells 36 T-shirts Kimmie surveys her customers about whether they would buy her T-shirts at a different price. She determines that for every $1 increase in price she would sell two fewer T-shirts and for even $1 decrease in price, she would sell two more T-shirts, Which quadratic function can Kimmie use to model price increments vs. total income so that she can find the price at which her income is maximized?
Answer:
y = -2*x² + 60*x
Step-by-step explanation:
The general form of a quadratic function is:
y = a*x² + b*x + c
We need to determine a ; b ; and c. For that we have three conditions therefore
Condition 1 at x = 12 $ each T-shirts kimmie sells 36 units, then she gets
12* 36 = 432 $ or y = 432 and
432 = a(12)² + 12*b + c or 432 = 144*a + 12*b + c
Second condition selling at 13 $ each T-shirt she sells 34 , then
13*34 = 442
442 = a(13)² + 13*b + c or 442 = 169*a + 13*b + c
And the third condition
11*38 = 418
418 = a* ( 121) + 11*b + c 418 = 121*a + 11*b + c
We have a three equation system
432 = 144*a + 12*b + c (1)
442 = 169*a + 13*b + c (2)
418 = 121*a + 11*b + c (3)
We need to solve it for a, b and c
Subtracting (2) - (1) 10 = 25*a + b and subtracting (2) - (3)
24 = 48*a + 2*b
Then b = 10 - 25*a and 24 = 48*a + 2*( 10 - 25*a )
24 = 48*a + 20 - 50*a
24 - 20 = -2*a
4 = - 2*a
a = - 2 and b = 10 - 25*( -2) b = 60
Finally c is: 432 = 144*a + 12*b + c
432 = 144* ( -2) + 12*60 + c
432 = - 288 + 720 + c
432 = 432 + c
c = 0
The quadratic function is:
y = -2*x² + 60*x
PLZ HELP NEED THIS TO BE RIGHT AS YOU CAN GET IT
Answer of this qn is. option D hope it helps
Jamie has $70 in a savings account. The interest rate is 5%,
compounded annually.
To the nearest cent, how much will he have in 2 years?
*pls hurry . *
Answer:
$77
Step-by-step explanation:
10% of 70$ is $7
$70+$7=$77
Which number line diagram represents the solution to the inequality?
A
B
C
D
Answer:
C
Step-by-step explanation:
A spinner with 8 equal sections labeled 1 through 8 landing on a number less than 9
Answer:
1
Step-by-step explanation:
The probability of that happening is 1. It must always be < 9. The only way it is not true is if you choose not to spin.
Suppose a car travels 174 miles in 3 ours. How far will it travel in 6 hours?
Answer: 348 miles
Step-by-step explanation:
The car will travel 174 miles in 3 hours, if you multiply 174 x 2, the car will travel 348 miles in 6 hours.