Find the length of the arc to 2 decimals places
Answer:
Step-by-step explanation:
The formula for arc length is
[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where theta is the measure of the central angle and r is the radius. We have both of those pieces of info; filling in:
[tex]AL=\frac{30}{360}*2(3.14) (4)[/tex] and simplifying a bit:
[tex]AL=\frac{1}{12}(8)(3.14)[/tex] and a bit more:
[tex]AL=\frac{25.12}{12}[/tex] and finally, to
AL = 2.09 m
are sheep?ои b. At Molebogeng station, a train arrives every 50 minutes the first in domenat z. 122cio Ise minutes. The first train stops at 7:00 a.m. How many trains have stopped at the station just nun before 11:00 p.m.?
Answer:
19 trains
Step-by-step explanation:
Firstly, we need to calculate the difference in the number of hours
From the question, we have 7 am to 11 pm
7 am to 7 pm is 12 hours
7 pm to 11 pm is 4 hours
So total is 16 hours
16 hours to minutes is multiplied by 60 minutes
We have this as;
16 * 60 = 960 minutes
so to get the number of trains, we simply have to divide the number of minutes by 50
Mathematically, we have this as 960/50
= 19.2
Since we cannot have a fractional train stop, it means the number of trains that has stopped is 19
Joe's Auto Insurance Company customers sometimes have to wait a long time to speak to a
customer service representative when they call regarding disputed claims. A random sample
of 25 such calls yielded a mean waiting time of 22 minutes with a standard deviation of 6
minutes. Construct a 95% and 99% confidence interval for the population mean of such
waiting times. Explain what these interval means.
Answer:
The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.
The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{6}{\sqrt{25}} = 2.5[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 22 - 2.5 = 19.5 minutes
The upper end of the interval is the sample mean added to M. So it is 22 + 2.5 = 24.5 minutes
The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{6}{\sqrt{25}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 22 - 3.4 = 18.6 minutes
The upper end of the interval is the sample mean added to M. So it is 22 + 3.4 = 25.4 minutes
The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.
HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.
Please answer!<333 xx
12. X= 6
14. B= -11
16. N= 15
Answer:
q12. [tex]x=6[/tex]
q14. [tex]b=-11[/tex]
q16. [tex]n=15[/tex]
Step-by-step explanation:
Q12.
[tex]-1=\frac{x}{-6}[/tex]
Flip the equation:
[tex]\frac{x}{-6} =-1[/tex]
Multiply both sides by 6/(-1)
[tex](\frac{6}{-1} )[/tex] × [tex](\frac{-1}{6}x )[/tex] = [tex](\frac{6}{-1} )[/tex] × [tex](-1)[/tex]
[tex]x=6[/tex]
Q14.
[tex]5b=-55[/tex]
[tex]b=\frac{-55}{5}[/tex]
[tex]b=-11[/tex]
Q16.
[tex]-3n=-45[/tex]
[tex]n=\frac{-45}{-3}[/tex]
[tex]n=15[/tex]
hope this helps.....
How many outcomes (sample points) for a deal of two cards from a 52-card deck are possible? Report your answer as an integer.
Answer:
1326
Step-by-step explanation:
[tex]{52\choose2}=\frac{52!}{(52-2)!2!}=\frac{52!}{50!*2!}=1326[/tex]
find the value of...
Answer:
1
Step-by-step explanation:
tan(1)tan(2)....tan(89)=?
Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.
tan(89)=tan(90-1)=cot(1)
tan(88)=tan(90-2)=cot(2)
tan(87)=tan(90-3)=cot(3)
...
tan(46)=tan(90-44)=cot(44)
tan(45)=tan(90-45)=cot(45)
So we can replace the last half of the factors with cotangent of the angles in the first half.
The only one that doesn't get a partner is the exact middle factor which is tan(45).
So this is whar we have:
tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)
So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....
So the product equals tan(45) and tan(45)=1 using unit circle.
Which expression is equivalent to -28xy + 35y?
o 7y(-4xy + 5y)
O 7x{-4x+ 5y)
o 7xl-4y+54)
O 7y(-4x+5)
Answer:
[tex]-28xy+35y[/tex]
[tex]GCF ~is~ 7y[/tex]
[tex]=7y(-4+5)[/tex]
The equivalent expression: [tex]7y(-4x+5)[/tex]
-------------------------
hope it helps...
have a great day!!
We deposit $12000 into an account carning 3 % interest compounded continuously, How many years will it take
for the account to grow to $16800? Round to 2 decimal places,
Answer:
The answer is 13.33 year
Step-by-step explanation:
P = $12000
Rate = 3%
Amount = $16800
so,
I = A-P
= $16800 - $12000
= $4800
So,
T = (I × 100)/P×R
= (4800×100)/P×R
= 480000/($12000×3)
= 480000/36000
= 480/36
= 13.33 year
in a class of 50 student,35 are boys.what is the ratio of girls to boys in the class?
Answer:
15:35
Step-by-step explanation:
50-35=Girls
50-35=15
At a hockey game, a vender sold a combined total of 228 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
9514 1404 393
Answer:
152 sodas76 hot dogsStep-by-step explanation:
Of the items sold, sodas were 2/(2+1) = 2/3 of the total.
(2/3)(228) = 152 . . . sodas were sold
152/2 = 76 . . . . hot dogs were sold
An employee at a shoe store has observed that taller customers have larger shoe sizes than customers who are shorter. She knows that shoe sizes are based on foot length, so she hypothesizes: Compared with shorter people, taller people have longer feet.
Question attachment below
Answer and explanation:
Data patterns are repeated data occurrences in a certain way that is recognizable.
In the example below, the data pattern shows taller people require larger shoe sizes(the taller the person the larger the shoe size) but does make some exceptions. Example: while Denver is taller and requires a larger shoe size, Eduardo is shorter than Tim and still requires a larger shoe size than Tim.
The mean temperature for the first 4 days in January was 1°C.
The mean temperature for the first 5 days in January was -1°C.
What was the temperature on the 5th day?
Answer:
The temperature on the 5th day was of -9ºC.
Step-by-step explanation:
Mean of a data-set
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
The mean temperature for the first 4 days in January was 1°C.
This means that during the first 4 days, the sum of the temperatures was 4*1 = 4ºC.
The mean temperature for the first 5 days in January was -1°C.
First 4 days: Sum of 4º
5th day: Temperature of x.
The mean is -1, so:
[tex]-1 = \frac{4 + x}{5}[/tex]
[tex]x + 4 = -5[/tex]
[tex]x = -9[/tex]
The temperature on the 5th day was of -9ºC.
Question 1
Points 3
Rese
A carpet is in the shape of a right triangle. The longer leg
measures 8 feet. The hypotenuse is 4 feet more than the
length of the shorter leg. How long is the shorter leg?
Reset
after
assess
Answer:
6 feetStep-by-step explanation:
Given right triangle with:
Legs s and 8, and hypotenuse s + 4Use Pythagorean and solve for s:
(s + 4)² = s² + 8²s² + 8s + 16 = s² + 648s = 64 - 168s = 48s = 6
Domain and range
O Function
O Not a function
Answer:
Radiation 1- Function
Radiation 2- Not a function
Radiation 3- function
Radiation 4- function
Answer:
1 - Function
2 - Not a function
3 - function
4 - function
Step-by-step explanation:
Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2
Answer:
The area of the square is increasing at a rate of 40 square centimeters per second.
Step-by-step explanation:
The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:
[tex]A = l^{2}[/tex] (1)
Where [tex]l[/tex] is the side length, in centimeters.
Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:
[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)
Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.
If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:
[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]
[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]
The area of the square is increasing at a rate of 40 square centimeters per second.
Please help me i will give brainlest please i need help
Answer:
Since you didn't mention which question.
Step-by-step explanation:
13.
[tex]1.\overline{52}\\[/tex] = 1.525252...
Let x = 1.525252...
10x = 15.2525252....
100x = 152.525252...
100x - x = 151.00
99x = 151
[tex]x = \frac{151}{99}\\\\or\\\\x = 1 \frac{52}{99}[/tex]
14.
4x + 10 = 8x - 26 [ corresponding angles are congruent ]
4x - 8x = - 26 - 10
- 4x = - 36
[tex]x = \frac{-36}{-4} \\\\x = 9[/tex]
15.
Given breadth of a rectangle is ( 2/3) its length.
Let the length be x
Therefore, breadth = ( 2 /3) of x
[tex]= \frac{2}{3} \times x\\\\=\frac{2}{3}x[/tex]
Given perimeter = 40m
Perimeter of a rectangle = 2( length + breadth)
[tex]40 = 2 (x + \frac{2}{3}x )\\\\\frac{40}{2} = \frac{2}{2}(x + \frac{2}{3}x)\\\\20 = x + \frac{2}{3}x\\\\20 = \frac{3x + 2x}{3}\\\\20 \times 3 = 5x \\\\x = \frac{60}{5}\\\\x = 12\\\\Therefore, Length = x = 12 \ m \ and \ breadth = \frac{2}{3}x = \frac{2}{3} \times 12 = 8 \ m[/tex]
16.
Sum of the angles of a triangle = 180°
Given ratio = 2 : 3 : 4
Sum of the ratio = 9
Therefore,
[tex]first \ angle = \frac{2}{9} \times 180 = 2 \times 20 = 40 ^\circ\\\\Second \ angle = \frac{3}{9} \times 180 = 3 \times 20 = 60^\circ\\\\Third angle = \frac{4}{9} \times 180 = 4 \times 20 = 80^\circ[/tex]
17.
Sum of interior angles of a polygon with n sides = ( n - 2) x 180°
Given polygon is pentagon, that is n = 5
Therefore, sum of the interior angles = ( 5 - 2) x 180 = 3 x 180 = 540°
That is ,
x + 125 + 125 + 88 + 60 = 540°
x + 398 = 540°
x = 540 - 398
x = 142°
Answer:
Please can you say which question?
Thank you
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
9514 1404 393
Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
A five-question multiple-choice quiz has five choices for each answer. Use the random number table provided, with O's representing Incorrect answers
and 1's representing correct answers, to answer the following question:
What is the probability of correctly guessing at random exactly one correct answer? Round to the nearest whole number.
Answer:
Step-by-step explanation:
jnow colata
In 1980, the average cost of a pack of cigarettes was $0.88. In 2000, the average cost was $5.31 per pack.
What is the average rate of change of the cost of a pack of cigarettes? What is another name for the average rate of change?
Round your answer to the nearest cent.
Answer:
The average rate of change of the cost of a pack is 22 cents per year.
Another name for the average rate of change is slope.
Step-by-step explanation:
The average rate of change of the cost of a pack ([tex]r[/tex]), in monetary units per year, is equal to the change in the average cost of a pack ([tex]\Delta c[/tex]), in monetary units, divided by the change in time ([tex]\Delta t[/tex]), in years. Then, the average rate of change is:
[tex]r = \frac{\$\,5.31-\$\,0.88}{2000-1980}[/tex]
[tex]r = \$\,0.22\,\frac{1}{yr}[/tex]
The average rate of change of the cost of a pack is 22 cents per year.
Another name for the average rate of change is slope.
The cost of renting a car is $46/week plus $0.25/mile traveled during that week. An equation to represent the cost would be y = 46 + 0.25x, where x is the number of miles traveled.
what is your cost if you travel 59 miles
cost: 60.75
if your cost Is $66.00, how many miles were you charged for traveling?
miles: ?
you have a max of $100 to spend on a car rental. what would be the maximum number of miles you could Travel?
max miles: ?
Answer:
If your cost Is $66.00, how many miles were you charged for traveling?
y = cost = $66[tex]66=46+0.25x\\66-46=0.25x\\20=0.25x\\x=\frac{20}{0.25} =80[/tex]80 miles
You have a max of $100 to spend on a car rental. what would be the maximum number of miles you could Travel?
y = cost = $100[tex]100=46+0.25x\\100-46=0.25x\\54=0.25x\\x=\frac{54}{0.25} =216[/tex]216 miles
if sine Theta is less than 0 and tan Theta is greater than 0 then
Answer:
Sine Theta is a negative number, Tan Theta is a greater number then zero.
Step-by-step explanation:
If Sine Theta is less then zero, she is a negative number. So 0 - y = -y.
So if Tan Theta is a greater number than zero, her number is not negative. So 0 + y = y
I hope this helped! I didn’t really understand the question though.
Using the Fenske equation, calculate the number of theoretical plates for a fractional distillation set up used to separate Ethyl acetate (the more volatile component) from hexane (less volatile component) in a mixture with the following experimental data:
n=log(X/Xb) -log(Y a/Yb)/ log α Fenske Equation
Experimental data: l
The following are the data optained from injection of a 1-microliter sample of the equimolar stock solution used in the distillation experiment into a GČ. The percent of the area under the appropriate peak is idicated.
a = 1.6
GC results of the stock mixture used in the experiment
Component Rt (retention time) Percent Area
Ethyl acetate 1.09 53 82
Hexane 1.58 47 18
GC results of a 1-microliter sample after 3 mL had been collected:
Component Rt (retention time) Percent Area
Ethyl acetate 1.09 82
Hexane 1.58 18
a. 3.9
b. 7.2
c. 7.0
d. 3.0
Compute the total cost per year of the following pair of expenses. Then complete the sentence: On an annual basis, the first set of expenses is _______% of the second set of expenses.
Vern buys seven lottery tickets each week at a cost of $3 each and spends $900 per year on his textbooks.
Answer:
So 912$ is 58% of 1584 $
Step-by-step explanation:
Cho hàm số f(x, y) = ln(x
2 + y
2
).
a) Tính f
′
x
, f′
y
;
b) Tính f
′
x
(2; 1), f′
y
(2; 1).
Answer:
Sorry, I can't understand in which language you have written......
Step-by-step explanation:
So if you tell me the question in English then I can answer
Evaluate:
11x - 8(x - y)
Answer:
11x-8x+8y
3x+8y SEEESH IN DEEZ NU TS
Step-by-step explanation:
Which ratios are less than 8 to 10? Check all that apply.
6/20
3:5
50/100
13:15
9514 1404 393
Answer:
6/20, 3:5, 50/100 are all less than 8/10
Step-by-step explanation:
It can help to give all the ratios a common denominator. (We'll use 100, and fudge the last one a bit.)
8/10 = 80/100 . . . . our reference value
__
6/20 = 30/100 . . . less than 8/10
3/5 = 60/100 . . . . less than 8/10
50/100 . . . . . . . . . less than 8/10
13/15 ≈ 86.7/100 . . . more than 8/10
Please help I’m really stuck this is my last attempt
What is the mode for the set of data?
Ages
Stem Leaves
5 0, 4, 6
6 0, 2, 3, 4, 8, 8, 9
7 0, 2, 3, 4, 4, 4, 8, 9
8 4, 5, 6, 8
5|0 = 50 years old
33
68
4
74
Answer:
I THINK IT IS 74 NOT 4
I HOPE THIS HELPS!!!!!
So for this problem I got the scientific notation however I can not seem to figure out the standard notation. I thought it is the same answer but it is not. Can someone please help me out here please?
Answer:
567000000
Step-by-step explanation:
Standard is the actual number. Multiply 5.67 and 10^8.
Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the smallest measure
O B. angle with the greatest measure
O C. shortest side
D. second-longest side
Answer:
B. angle with the greatest measure
opposite the largest angle
