Answer:
2/3???
.................
Answer:
0.804% to 3 dec places.
Step-by-step explanation:
If the first 4 throws are a dot and the next 2 are not:
Probability = (1/6)^4 * (5/6)^2
= 25/46656
There are 6C4 ways for this to happen
6C4 = (6*5*4*3)/ (4*3*2*1) = 15 ways.
So The required probability = (25*15)/46656
= 125/15552
= 0.00804
= 0.804%
Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)
Answer:
The third side is increasing at an approximate rate of about 0.444 meters per minute.
Step-by-step explanation:
We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.
Let the angle between the two given sides be θ and let the third side be c.
Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.
First, convert the degrees into radians:
[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]
Hence, dθ/dt = π/90.
From the Law of Cosines:
[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]
Since a = 13 and b = 19:
[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]
Simplify:
[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]
Take the derivative of both sides with respect to t:
[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]
Implicitly differentiate:
[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]
We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:
[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]
Solve for dc/dt:
[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]
Evaluate. Hence:
[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]
The third side is increasing at an approximate rate of about 0.444 meters per minute.
9514 1404 393
Answer:
0.444 m/min
Step-by-step explanation:
I find this kind of question to be answered easily by a graphing calculator.
The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...
c = √(a² +b² -2ab·cos(C))
Since C is a function of time, its value in degrees can be written ...
C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest
Using a=13, and b=19, the length of the third side is ...
c(t) = √(13² +19² -2·13·19·cos(60° +2t°))
Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...
0.443855627418 m/min ≈ 0.444 m/min
_____
Additional comment
At that time, the length of the third side is about 16.823 m.
__
c(t) reduces to √(530 -494cos(π/90·t +π/3))
Then the derivative is ...
[tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
Answer:
b or a
Step-by-step explanation:
area of a triangle 5cm base and 4 cm height
Answer:
1/2 base×height
1/2 .5×4
1/2.20
20 divided by 2 is 10
1/1×10
10cm2
ans
For each kilogram of a persons weight 2.5 milligrams of a drug is to be given. what dosage should be given to a child who weighs 84 pounds? Use the fact that 1 lb = 0.45 kg
Answer:
A child who weighs 84 pounds should be given 94.5 milligrams of the drug.
Step-by-step explanation:
Givens:
1kg=2.5 milligrams of dosage
Weight of child = 84 pounds
1 pound = 0.45 kg
Solution:
Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg
Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.
write the first 10 multiples of 2 and 3 and find LCM.
Answer:
multiples of 2 2,4,6,8,10,12,14,16,18,20
multiples of 3 3,6,9,12,15,,18,21,24,27,30
Step-by-step explanation:
Lcm is 6
look at the image below
Answer:
117.8
Step-by-step explanation:
Surface area = πr²+πrl (whee r = radius and l = slant height)
= π×3²+π×3×9.5
= 75π/2
= 117.8
The difference between the greatest and the smallest 5-digit numbers formed by using each of the digits 2, 0, 4 and 6 at least once is
Answer:
46374
Step-by-step explanation:
The smallest 5-digit number is 20046
While the greatest is 66420
So 66420-20046=46374
pls help Describe how to find the product of the two terms 3x^2y^5 and 4x^3y^7
Answer:
12 x^5y^12
Step-by-step explanation:
3x^2y^5 * 4x^3y^7
Multiply the constants
3*4 = 12
Multiply the x terms
x^2 * x^3
We know a^b* a^c = a^(b+c)
x^(2+3) = x^5
Multiply the y terms
y^6 * y^7 = y&(5+7) = y^12
Put them back together
12 x^5y^12
what is the lub and glb of the following sets, in the set of real numbe if exists E={ 0.2,0.23,0.234,0.2343,0.23434,0.23434,...}
Answer:
Hello,
Step-by-step explanation:
[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]
write your answer in simplest radical form
Answer:
a = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 4[tex]\sqrt{3}[/tex]
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
Step-by-step explanation:
4x - 13 = x + 5 Add 13 to both sides
4x = x + 18 Subtract x
3x = 18 Divide by 3
x = 6
A 3-gallon jug of water costs $15.00. What is the price per quart?
Answer:
1.25 dollars per quart
Step-by-step explanation:
There are 4 quarts per gallon
3 gallons * 4 quarts/ gallon = 12 quarts
15 dollars/ 12 quarts
1.25 dollars per quart
3 to the fourth power
Answer:
It's 81
Step-by-step explanation:
You can use a calculator on go.ogle :D
(2+1/2) (2^2-1+1/4) find the expression in the form of cubes and differences of two terms.
Answer:
Consider the following identity:
a³ - b³ = (a + b)(a² - ab + b²)Let a = 2, b = 1/2
(2 + 1/2)(2² - 2*1/2 + 1/2²) = 2³ - (1/2)³ =8 - 1/8Use the algebraic identity given below
[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]
Here a =2 and b=1/2[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]
[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]
solve for x ! please help (show work)
Answer:
x = 1/2
Step-by-step explanation:
8(-2x+1) =0
Divide each side by 8
-2x+1 = 0
Add 2x to each side
-2x+1+2x = 2x
1 = 2x
Divide by 2
1/2 = 2x/2
1/2 =x
Answer:
1/2
Step-by-step explanation:
8(-2x+1)=0
Use distributive property first
-16x+8=0
Subtract 8 on both sides
-16x=-8
Divide both sides by -16 to get x by itself
x=0.5
Which is also equal to 1/2
Therefore, x is equal to 1/2
find the quotient 1/5 / (-5/7) =
Answer:
-7/25
Step-by-step explanation:
1/5 ÷ (-5/7)
Copy dot flip
1/5 * -7/5
-7/25
Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answer:
m=3*sqrt(2) and n=3
Step-by-step explanation:
tan(45)=3/n
1=3/n, n=3. As it's a right angled triangle, 3^2+3^2=m^2, m=3*sqrt(2)
Help please, but more importantly, I am really trying hard to figure out how, you arrive at the answer. Thanks in advance!
A recent social survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?ocial survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?
Answer:
Step-by-step explanation:
#1
A) P(FEMALE|APPLE)
apple total = 346
apple/female = 194
194/346 = .56 = 56 %
B) P(APPLE|MALE)
male total = 320
apple male = 152
152/320 = .475 = 47.5%
C) female prefer Microsoft
152:168 = 76:84 = 38:42 = 19:21
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I really need help with this
Answer:
G=21, F=9, M=6, L=7, E=20, D=15, B=10, R=12.5, T=16, N=13.5, W=18, H=36, Z=12
*I=5*
Step-by-step explanation:
I basically just found the scale factor/proportion from two given sides and then used that to find the remaining sides.
*I'm not sure about 'I' since the edge of the paper was cut off so I want sure if it was a 5 or a 15 on the left most problem in the third row. I assumed it was 15. If it's not, just shout it out in the comments and I'll fix it! :)*
You can fill the letters in at the bottom XD
I hope this helped! :D
How do I answer this
Answer:
11. Yes
12. No
Step-by-step explanation:
11. The x values only have 1 y value, so it makes it a function.
12. The x value 0 has 2 y values -4 and 4, therefore it is not a function, because in functions that x value can only have one y value,
Solve 6y - 9 + 2y - 5 = -8 y + 17 + 4y
Please Mark my answer brilliant
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a significance level of ? can be found as follows. In the expression
E=z?p1(1?p1)n1+p2(1?p2)n2?????????????????????????
we replace both n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, and p2, by 0.5 (because their values are not known). Then we solve for n, and get
n=(z?)22E2.
Finally, increase the value of n to the next larger integer number.
Use the above formula and Table C to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 99% confidence level and that the error is smaller than 0.07.
n=______.
Answer:
n= (z)22E2
n=10× 99%÷ 0.07
look at the image for the question
Answer:
117.8
Step-by-step explanation:
surface area = πr²+πrl, where r = radius and l = slant height
so,
πr²+πrl
= π×3²+π×3×9.5
= 75π/2
= 117.8 (rounded to the nearest tenth)
The illustration below shows the graph of y as a function of x.
Complete the following sentences based on the graph of the function.
The y-intercept of the graph is the function value y=_____
The smallest positive x-intercept of the graph is located at x=_____
The greatest value of y is y=____ and it occurs when x=____
For x between x and x= 2 π the function value y___ 0
Answer:
below
Step-by-step explanation:
that is the solution above
James purchased five acres of land fo 75,000 what was the cost per acre
Answer:
$15,000
Step-by-step explanation:
James purchased a total of 5 acres of land for a total price of $75,000. To find the cost of each individual acre, simply divide the total cost with the total amount of acres purchased:
[tex]\frac{total price of land bought}{total amount of acres} = \frac{75000}{5} = 15000[/tex]
The cost per individual acre, assuming all of them cost the same, is $15,000.
~
Answer:
15000
Step-by-step explanation:
Since
5 acres = 75000
therefore,
the cost price per acre would be
total cost price ➗ 5
7500/5= 15000
The population p(t) of a culture of the bacterium Pseudomonas aeruginosa is given by ,p(t)= -1683t^2+75,000t+ 10,000 where is the time in hours since the culture was started. Determine the time the population was at its maximum. Round to the nearest hour.
Answer:
22hrs
Step-by-step explanation:
hope it is well understood?
A basketball player averages 22.5 points scored per game with a standard deviation of 6.2 points. In one game, the athlete scored 10 points. What is the z-score for the points scored in this game?
–2.02
–1.63
1.63
2.02
Answer:
Step-by-step explanation:
Z -2.02
x 10
µ 22.5
σ 6.2
Lainey is looking for a new apartment and her realtor keeps calling her with new listings . The calls only take a few minutes , but a few minutes here and there are really starting to add up . She's having trouble concentrating on her work . What should Lainey do ? a ) Tell her realtor she can only receive text messages b ) Limit the time spent on each call c ) Turn off her phone until she is on a break d ) Call her realtor back when customers won't see her on the phone
Answer:
c ) Turn off her phone until she is on a break
The quotient of -8 and the sum of a and b
Hi! I'm happy to help!
To solve this, you need to know what all of the terms mean. Quotient means division, and sum means addition. Knowing this we can set up our expression.
Because there is an operation inside of an operation (addition inside of division) we use parenthesis.
-8÷(a+b)
I hope this was helpful, keep learning! :D
the mean salary if of 5 employees is $35900. the median is $37000. the mode is $382000. If the median payed employee gets a $3100 raise, then…
New median:
New mode:
Answer:
Step-by-step explanation:
New median:40100
New mode:385100
