Answers
Answer:
[tex]\approx 15.9[/tex]
Step-by-step explanation:
The length of an arc with measure [tex]\theta[/tex] and radius [tex]r[/tex] is given by [tex]\ell_{arc}=2r\pi\cdot \frac{\theta}{360}[/tex]. From the figure, we know that the radius of arc ADC is 4, but we don't know the measure of the arc. Since there are 360 degrees in a circle, the measure of arc ADC is equal to the measure of the arc formed by [tex]\angle AOC[/tex] subtracted from 360. The measure of the arc formed by [tex]\angle AOC[/tex] consists of two congruent angles, [tex]\angle AOB[/tex] and [tex]\angle COB[/tex]. To find them, we can use basic trigonometry for a right triangle, since by definition, tangents intersect a circle at a right angle.
In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.
We have:
[tex]\cos \angle AOB=\cos \angle COB=\frac{4}{10},\\\angle AOB=\arccos(\frac{4}{10})=66.42182152^{\circ}[/tex]
Therefore, [tex]\angle AOC=2\cdot 66.42182152=132.84364304^{\circ}[/tex]
The measure of the central angle of [tex]\widehat{ADC}[/tex] must then be [tex]360-132.84364304=227.15635696^{\circ}[/tex]
Thus, the length of [tex]\widehat{ADC}[/tex] is equal to:
[tex]\ell_{\widehat{ADC}}=2\cdot 4\cdot \pi \cdot \frac{227.15635696}{360},\\\ell_{\widehat{ADC}}=15.8585053832\approx \boxed{15.9}[/tex] (three significant figures as requested by question).
Related Questions
What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator
Answers
Answer:
4033
Step-by-step explanation:
An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 - b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:
a^2 = 2017^4
a = 2017^2
b^2 = 2016^4
b = 2016^2
Now, the special product a^2 - b^2 factors to (a + b)(a - b), so we can substitute that for the numerator:
[tex]\frac{(2017^2+2016^2)(2017^2 - 2016^2)}{2017^2+2016^2}[/tex]We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by [tex]\frac{2017^2+2016^2}{2017^2+2016^2}[/tex] which is just one, and will simplify the fraction to just:
2017^2 - 2016^2
This again is just the special product a^2 - b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:
(2017 + 2016)(2017 - 2016)
And, without using a calculator, this is easy to simplify:
(4033)(1)
4033
Solve the simultaneous equations.
Show all your working.
3x + 4y = 14
5x+2y=21
Answers
Step-by-step explanation:
hear is your answer in attachment
Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time. day change Monday +2000 Tuesday -125 Wednesday -127 Thursday +1719 Friday -356 Saturday -782 Sunday 0 2. How many paper cups are left at the end of the week?
Do only number 2
Answers
Answer:
2329
Step-by-step explanation:
2000 - 125 - 127 + 1719 - 356 - 782 = 2329
What's the area of the trapezoid
Answers
Answer:
i dont know just study hard bro
Step-by-step explanation:
Answer:
A =36 ft^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the lengths of the bases
A = 1/2 ( 13+5) *4
A = 1/2 ( 18)*4
A =36 ft^2
1/3(-15 divide 1/2) 1/4 what does it equal
Answers
Answer:
-2.5 or - 2 1/2
Step-by-step explanation:
Writing out the expression Mathematically ;
1/3(-15÷1/2)1/4
Using PEMDAS :
Solving the bracket first
(-15 ÷ 1/2) = (-15 * 2/1) = - 30
We have :
1/3(-30)1/4 = - 10 * 1/4 = - 10 / 4 = - 2.5
-2.5 = - 2 1/2
plaz..mmnj k,mnmnm 1
Answers
Answer:
Option 1
Step-by-step explanation:
3x - 7y = -7y + 3x
They have simply been moved to opposite ends of the equation.
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)
a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Answers
Solution :
a). P(X = x)
= [tex]$p(1-p)^x$[/tex] for x = 0, 1, 2, ....
P(x ≤ 3) = 0.837
b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]
= 1.7397
Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]
= 4.7663726
Standard deviation = 2.1832
Therefore, mean + standard deviation
= 1.7397 + 2.1832
= 3.9229
[tex]$P(x > 3.9229) = 0.1626$[/tex]
So the required P = 2 x 0.1626
= 0.325
2) A block of ice weighs 12 400 kg. It has the shape of a cylinder, with a radius of 1.2 m and
a height of 3 m. What is the density of the ice? Give your answer to one decimal place.
Answers
Answer:
= 3.6
Step-by-step explanation:
Do you know how to find the volume of a cylinder? Like any prism, it's area of base x height, in this case the base is a circle of radius 1.2m.
Density is simply mass / volume (kg / m3 ).
clarify its 1.2 x 3 = 3.6
12400 / 3.6 = 3.444 occuring
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
Answers
9514 1404 393
Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
Can someone please answer this ASAP?
Answers
Answer:
Letter C
Step-by-step explanation:
Given:
[tex]5a+18<-27[/tex]
Subtract 18 from both sides
[tex]5a<-45[/tex]
Divide 5 from both sides to get [tex]a[/tex] alone
[tex]a<-9[/tex]
Letter C is the correct answer choice because the dot is at -9, the arrow is facing to the left, and the dot is open indicating that it's not greater/less than ""or equal to"".
Hope this is helpful
Phân biệt chi phí sản xuất và giá thành sản phẩm?
Answers
Answer:
* Giống nhau: đều là biểu hiện bằng tiền về lao động sống và lao động hóa trong quá trình sản xuất
* Khác nhau:
+ Về thời gian: chi phí sản xuất gắn liền với từng thời kỳ, còn giá thành sản phẩm gắn với thời hạn hoàn thành sản phẩm. ...
+ Có những chi phí được tính vào giá thành nhưng không được tính vào chi phí kỳ này.
+ Mối quan hệ chi phí và tính giá thành sản phẩm: Chi phí là cơ sở để tính giá thành, giá thành là thước đo chi phí sản xuất mà doanh nghiệp bỏ ra để có được khối lượng hoàn thành.
+ Có nhiều chi phí phát sinh trong kỳ nhưng chưa có sản phẩm hoàn thành do đó chưa có giá thành.
Step-by-step explanation:
Graph the line with y-intercept-2 and slope -3/5 .
Answers
Answer:
MATH
Dior H. asked • 01/13/21
graph the line with the slope 1/2 and y-intercept -2
i need help badly i am crying because its hard
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1 Expert Answer
By:
Raymond B. answered • 01/14/21
TUTOR 5 (1)
Math, microeconomics or criminal justice
ABOUT THIS TUTOR ›
y=mx + b is the standard slope intercept form for a line
m=1/2, b =-2
y=(1/2)x -2. y-intercept is -2 or the point (0,-2)
x intercept is found by setting y=0 and solving for x
0=(1/2)x - 2
(1/2)x = 2
x = 4 = the x intercept or (4,0)
plot the 2 intercepts (0,-2) and (4,0)
(4,0) is on the x axis, 4 units to the right of the origin (0,0)
(0,-2) is on the y axis, 2 units below the origin
once you plot those two points, draw a straight line connecting them. That's the graph of the line
Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)
Answers
Answer:
(a) [tex]A = A_0 * e^{kt}[/tex]
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
[tex]A(t) = A_0 * e^{kt}[/tex]
Where
[tex]A_0 \to[/tex] Initial Amount
[tex]k \to[/tex] rate
[tex]t \to[/tex] time
[tex]A(t) \to[/tex] Amount at time t
Solving (b):
We have:
[tex]t = 4.6hr[/tex]
[tex]A_0 = 8[/tex]
[tex]A(4.6) = 4[/tex]
First, we calculate k using:
[tex]A(t) = A_0 * e^{kt}[/tex]
This gives:
[tex]A(4.6) = 8 * e^{k*4.6}[/tex]
Substitute: [tex]A(4.6) = 4[/tex]
[tex]4 = 8 * e^{k*4.6}[/tex]
Divide both sides by 4
[tex]0.5 = e^{k*4.6}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]
This gives:
[tex]-0.6931 = k*4.6[/tex]
Solve for k
[tex]k = \frac{-0.6931}{4.6}[/tex]
[tex]k = -0.1507[/tex]
So, we have:
[tex]A(t) = A_0 * e^{kt}[/tex]
[tex]A(t) = 8e^{-0.1507t}[/tex]
To calculate the time when 1 lb will remain, we have:
[tex]A(t) = 1[/tex]
So, the equation becomes
[tex]1= 8e^{-0.1507t}[/tex]
Divide both sides by 8
[tex]0.125= e^{-0.1507t}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]
[tex]-2.0794= -0.1507t[/tex]
Solve for t
[tex]t = \frac{-2.0794}{-0.1507}[/tex]
[tex]t = 13.7983[/tex]
[tex]t = 14[/tex] --- approximated
The hourly earnings (in dollars) for a sample of 25 railroad equipment manufacturers are:15.60 18.7514.60 15.8014.3513.90 17.5017.5513.8014.20 19.05 15.35 15.20 19.45 15.95 16.50 16.30 15.2515.05 19.10 15.20 16.22 17.75 18.40 15.25Find the median and the mode(s)(if they exist) of the data. What is the interquartile range
Answers
Answer:
[tex]Median = 15.80[/tex]
[tex]Mode = 15.20\ \&\ 15.25[/tex]
[tex]IQR = 2.35[/tex]
Step-by-step explanation:
Given
[tex]15.60,\ 18.75,\ 14.60,\ 15.80,\ 14.35,[/tex]
[tex]13.90,\ 17.50,\ 17.55,\ 13.80,\ 14.20,[/tex]
[tex]19.05,\ 15.35,\ 15.20,\ 19.45,\ 15.95,[/tex]
[tex]16.50,\ 16.30,\ 15.25,\ 15.05,\ 19.10,[/tex]
[tex]15.20,\ 16.22,\ 17.75,\ 18.40,\ 15.25.[/tex]
Solving (a): The median and the mode
First, we sort the data.
[tex]13.80,\ 13.90,\ 14.20,\ 14.35,\ 14.60,\ 15.05,\ 15.20,\ 15.20,\ 15.25,\ 15.25,[/tex]
[tex]15.35,\ 15.60,\ 15.80,\ 15.95,\ 16.22,\ 16.30,\ 16.50,\ 17.50,\ 17.55,\ 17.75,[/tex]
[tex]18.40,\ 18.75,\ 19.05,\ 19.10,\ 19.45.[/tex]
The median position is:
[tex]Median = \frac{n + 1}{2}th[/tex]
[tex]Median = \frac{25 + 1}{2}[/tex]
[tex]Median = \frac{26}{2}[/tex]
[tex]Median = 13th[/tex]
The 13th item is: 15.80
Hence:
[tex]Median = 15.80[/tex]
The modes are:
[tex]Mode = 15.20\ \&\ 15.25[/tex] --- they both have frequency of 2 while others occur once
Solving (b): The interquartile range
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
Since the median is at the 13th position, Q1 is:
[tex]Q_1 = \frac{1 + 13}{2}th[/tex]
[tex]Q_1 = \frac{14}{2}th[/tex]
[tex]Q_1 = 7th[/tex]
The 7th item is: 15.20
[tex]Q_1 = 15.20[/tex]
Similarly, Q3 is:
[tex]Q_3 = \frac{13+n}{2}[/tex]
[tex]Q_3 = \frac{13+25}{2}[/tex]
[tex]Q_3 = \frac{38}{2}[/tex]
[tex]Q_3 = 19th[/tex]
The 7th item is: 17.55
So:
[tex]Q_3 = 17.55[/tex]
Hence,
[tex]IQR = 17.55 - 15.20[/tex]
[tex]IQR = 2.35[/tex]
If P = (7,-4), Find:
(180° (P)
([?], []
Enter
Answers
Step-by-step explanation:
the answer is in the above image
HW HELP ASAP PLZZZZZ
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (x - 5)(x - 4) }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
[tex] {x}^{2} - 9x + 20[/tex]
[tex] = {x}^{2} - 4x - 5x + 20[/tex]
Taking "[tex]x[/tex]" as common from first two terms and "[tex]5[/tex]" from last two terms, we have
[tex] = x(x - 4) - 5(x - 4)[/tex]
Taking the factor [tex](x-4)[/tex] as common,
[tex] = (x - 5)(x - 4)[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Find the zeros of the quadratic function: y = 6x2 + x – 35.
Answers
The zeros of the quadratic function: y = 6x^2 + x – 35 are x = -2.5 or x = 7/3
How to determine the zeros?The function is given as:
y = 6x^2 + x - 35
Expand the function
y = 6x^2 + 15x - 14x - 35
Factorize the function
y = (2x + 5) * (3x - 7)
Set the function to 0
(2x + 5) * (3x - 7) = 0
Split
2x + 5 = 0 or 3x - 7 = 0
Solve for x
x = -2.5 or x = 7/3
Hence, the zeros of the quadratic function: y = 6x^2 + x – 35 are x = -2.5 or x = 7/3
Read more about quadratic functions at:
https://brainly.com/question/1214333
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Given that the length of the figure below is x + 2, its width is
2- 2, and its perimeter is 24, solve for 2.
Answers
Answer:
hear is your answer in attachment please give me some thanks
Find all solutions to the equation.
cos^2 x +2cosx+1=0
Answers
[tex]x= \pi[/tex]
Step-by-step explanation:
[tex]\cos^2x+\cos x+1=0[/tex]
Let [tex]u= \cos x[/tex]
Then [tex]u^2+2u+1=(u+1)^2=0[/tex]
or
[tex]\cos x = -1[/tex]
This gives us [tex]x= \pi[/tex] or all integer multiples of [tex]\pi (n \pi)[/tex]
In practice, the most frequently encountered hypothesis test about a population variance is a _____. a. two-tailed test, with equal-size rejection regions b. two-tailed test, with unequal-size rejection regions c. one-tailed test, with rejection region in upper tail d. one-tailed test, with rejection region in lower tail
Answers
Answer:
c. one-tailed test, with rejection region in the upper tail.
Step-by-step explanation:
One tailed test is statistical test in which critical area of distribution is one sided and greater or less than certain value. One tailed test can be left or right sided depending on the population distribution. Rejection region of the one tailed test will determine whether to accept or reject the null hypothesis.
Use the formula v = IR for current flowing through a resistor, where V is the voltage in volts, I is current in amps, and R is resistance in ohms. Find the current through a resistor with resistance 15 ohms if the voltage across it is 3 volts.
Answers
Answer:
0.2 amps
Step-by-step explanation:
Given data
The formula V=IR is the formula for ohms law
Which state that the voltage is directly proportional to the current and the resistance in an electric circuit
Now
R= 15 ohms
V= 3volts
V= IR
3= I*15
I= 3/15
I= 0.2 amps
Hence he current flowing is 0.2 amps
Which of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1
Answers
Answer:
y=1/4x - 1
Step-by-step explanation:
going off of the picture, I'd say this is your answer
Solve the system 6x -2y+z= -2 2x+ 3y - 3z =11 x+ 6y=31
Answers
Answer:
x = 1
y = 5
z = 2
Step-by-step explanation:
System of equations:
6x - 2y + z = -2
2x + 3y - 3z = 11
x + 6y = 31
Isolate one variable in any of the equations:
x + 6y = 31
x = 31 - 6y
Plug in this value for x in another equation:
6(31 - 6y) - 2y + z = -2
186 - 36y - 2y + z = -2
186 - 38y + z = -2
-38y + z = -188
z = -188 + 38y
Plug in these values in the remaining equation:
2(31 - 6y) + 3y - 3(-188 + 38y) = 11
62 - 12y + 3y + 564 - 114y = 11
626 - 12y + 3y - 114y = 11
626 - 9y - 114y = 11
626 - 123y = 11
-123y = -615
y = 5
Plug in value of y into our other answers to solve for x and z:
x = 31 - 6(5)
x = 31 - 30
x = 1
z = -188 + 38(5)
z = -188 + 190
z = 2
Check your work:
6x - 2y + z = -2
6(1) - 2(5) + 2 = -2
6 - 10 + 2 = -2
-4 + 2 = -2
-2 = -2
Correct!
*Note there are several ways to solve for these types of problems. I used substitution*
Multiply the polynomials.
(4x- + 4x + 6)(7x + 5)
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: 28 {x}^{3} + 48 {x}^{2} + 62x + 30}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex](4 {x}^{2} + 4x + 6)(7x + 5)[/tex]
[tex] = \: 7x(4 {x}^{2} + 4x + 6) + 5(4 {x}^{2} + 4x + 6)[/tex]
[tex] = \: 28 {x}^{3} + 28 {x}^{2} + 42x + 20 {x}^{2} + 20x + 30[/tex]
Combining like terms, we have
[tex] = \: 28 {x}^{3} + (28 {x}^{2} + 20 {x}^{2} ) + (42x + 20x) + 30[/tex]
[tex] = \: 28 {x}^{3} + 48 {x}^{2} + 62x + 30[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Four students want to have their picture taken together. They will stand side-by-side for the picture. In how many different ways can the four students be arranged to take a picture?
Show your work, please :')
Answers
Answer:
24 waysStep-by-step explanation:
This is the permutation of 4:
4P4 = 4! = 1*2*3*4 = 24 ways[tex]\huge\qquad \mathbb{\fcolorbox{red}{lavenderblush}{✰Answer}}[/tex]
✶⊶⊷⊶⊷❍❁❥❀❥❁❍⊶⊷⊶⊷✶
Four students want to have their picture taken together. They will stand side-by-side for the picture. In how many different ways can the four students be arranged to take a picture
so we have to find the permutation of 4
4×3×2×124.°. In 24 different ways can the four students be arranged to take a picture
ASAP. There are three marbles in a bag. When is red and two are black. What is the probability of picking a black marble first, putting it back in the bag and then picking a black marble? Use the following probably need to find the answer.
Answers
Answer:
Number of black balls=2
Total number of balls=3
Probability =2/3
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE SPHERE
Answers
Answer:
Step-by-step explanation:
r = 1/2 unit
[tex]Volume= \frac{4}{3}\pi r^{3}\\\\=\frac{4}{3}\pi *\frac{1}{2}*\frac{1}{2}*\frac{1}{2}\\\\=\frac{1}{3}*\pi *\frac{1}{2}\\\\=\frac{1}{6}\pi[/tex]
2
3
4
9
10
-1
NS
-6
-7
-8
-9
Which three statements correctly describe key features of the function graphed here?
Answers
did u add the attachment of the the statements? cuz i dont see it.
John throws a biased four-sided dice.
The probabilities of getting each number are summarised in the table below.
Number
1
2
3
4
Probability
0.2
x
0.2
0.2
Work out the probability that the dice lands on 2.
Answers
Answer:
0.4
Step-by-step explanation:
0.2+0.2+0.2=0.6
1.0-0.6=0.4
This isn't 0.2 like the others which is why it's a biased dice like it says.
Help me calculate Lim for this lesson
Answers
Answer:
I'm acutally not too sure on this but give me a moment to solve this
Step-by-step explanation:
