Answer:
[tex]\frac{dv}{dt} =7239.168 cm/sec[/tex]
Step-by-step explanation:
From the question we are told that:
Rate [tex]\frac{dh}{dt}=1cm[/tex]
Height [tex]h=12cm[/tex]
Radius [tex]r=4h[/tex]
Generally the equation for Volume of Cone is mathematically given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
[tex]V=\frac{1}{3}\pi (4h)^2h[/tex]
Differentiating
[tex]\frac{dv}{dt} =\frac{16}{3}\pi3h^2\frac{dh}{dt}[/tex]
[tex]\frac{dv}{dt} =\frac{16}{3}*3.142*3*12^2*1[/tex]
[tex]\frac{dv}{dt} =7239.168 cm/sec[/tex]
A new car costs $23000. The value decreases by 15% each year.(a) Write the exponential model to represent the cars value after t years. (b) To the nearest dollar, how much will the car be worth after 4 years?
Answer:
(a) 23000(1-15%)^t
(b) about 12006.14375
Step-by-step explanation:
(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t
And with the values, we get the exponential model 23000(1-15%)^t
(b) From question (a) we already have the model and the time period given here is 4 years. So putting it in the formula we get,
23000(1-15%)^4
=23000(1-15/100)^4
=23000(0.85)^4
=23000x0.52200625
=12006.14375 (Ans)
Let the probability of success on a Bernoulli trial be 0.26. a. In five Bernoulli trials, what is the probability that there will be 4 failures
Answer:
0.3898 = 38.98% probability that there will be 4 failures
Step-by-step explanation:
A sequence of Bernoulli trials forms the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Let the probability of success on a Bernoulli trial be 0.26.
This means that [tex]p = 0.26[/tex]
a. In five Bernoulli trials, what is the probability that there will be 4 failures?
Five trials means that [tex]n = 5[/tex]
4 failures, so 1 success, and we have to find P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{5,1}.(0.26)^{1}.(0.74)^{4} = 0.3898[/tex]
0.3898 = 38.98% probability that there will be 4 failures
The rectangular floor of a storage shed has an area of 580 square feet. The length of the floor is 9 feet more than its width (see figure). Find the dimensions of the floor.
Length= ? Ft
Width= ? Ft
9514 1404 393
Answer:
length: 29 ftwidth: 20 ftStep-by-step explanation:
Assuming the dimensions are integer numbers of feet, you're looking for factors of 580 that have a difference of 9.
580 = 1×580 = 2×290 = 4×145 = 5×116 = 10×58 = 20×29
The last pair of factors differs by 9, so ...
the length is 29 feet; the width is 20 feet.
A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. [Binomail Probability] Less than four twos
Answer:
0.5665 = 56.65% probability of less than four twos.
Step-by-step explanation:
For each roll, there are only two possible outcomes. Either it is a two, or it is not a two. The probability of a roll ending up in a two is independent of any other roll, which means that the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 20 times
This means that [tex]n = 20[/tex]
One out of six sides is 2:
This means that [tex]p = \frac{1}{6} = 0.1667[/tex]
Probability of less than four twos:
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.1667)^{0}.(0.8333)^{20} = 0.0261[/tex]
[tex]P(X = 1) = C_{20,1}.(0.1667)^{1}.(0.8333)^{19} = 0.1043[/tex]
[tex]P(X = 2) = C_{20,2}.(0.1667)^{2}.(0.8333)^{18} = 0.1982[/tex]
[tex]P(X = 3) = C_{20,3}.(0.1667)^{3}.(0.8333)^{17} = 0.2379[/tex]
So
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0261 + 0.1043 + 0.1982 + 0.2379 = 0.5665[/tex]
0.5665 = 56.65% probability of less than four twos.
Three student representatives, a president, a secretary, and a treasurer, are to be chosen from a group of five students: Andrew, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men
Answer:
Hence there are 6 different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men.
Step-by-step explanation:
We know that,
Total males = 3,
Total Females = 2,
Now we want 2 males and a female.
Then the choices are,
[tex]= ^{3} C_{2} \times ( ^{2} C_{1} )\\\\= 3 \times 2\\\\=6[/tex]
Write the fraction 24/40 in its simplest form.
Bronson is ordering a sundae at a restaurant, and the server tells him that he can have up to four toppings: butterscotch sauce, caramel, peanuts, and strawberries. Since he cannot decide how many of the toppings he wants, he tells the server to surprise him. If the server randomly chooses which toppings to add, what is the probability that Bronson gets just butterscotch sauce, peanuts, and strawberries
Answer:
20%
Step-by-step explanation:
if zero toppings is an option, then there would be 5 possibilities for toppings
0,1,2,3,or 4
the server randomly chose 3 toppings so that would be one out of 5 or 20%.
(If the server did not have the option to put zero toppings on then there would be only 4 options 1,2,3, or 4 toppings and the correct answer would be one out of 4 or 25%.)
i don’t understand… but thank you if u do answer my question :))
Answer:
7/0
Step-by-step explanation:
This is because if a number is divided by 0 then there is no answer or it is undefined
Think of it like this,
You have 7 apples and wanted to give it to zero friends, is it possible?
Hope this helped :)
Answer:
Second option (7÷0)
Explanation:
Dividing by zero is considered undefined since you can't divide something by nothing. It's like saying you have a pizza and you want to divide it between 7 people but since you're dividing by zero, you're not splitting the pizza between anyone.
Please help.
Evaluate 6!
3,125
720
120
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{6!}\\\large\textsf{= 6}\times\large\textsf{5}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{6(5) = \bf 30}\\\large\textsf{= 30}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{30(4) = \bf 120}\\\large\textsf{= 120}\times\large\textsf{3}\times\large\textsf{2}\times\textsf{1}\\\large\textsf{120(3) = \bf 360}\\\large\textsf{= 360}\times\large\textsf{2}\times\large\textsf{1}[/tex]
[tex]\large\textsf{360(2) = \bf 720}\\\large\textsf{720}\times\large\textsf{1}\\\large\textsf{= \bf 720}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: \bf 720}\huge\textsf{ (option B)}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Calculate trend values by method of least squares
Answer:
It is a mathematical method and with it gives a fitted trend line for the set of data in such a manner that the following tow conditions are satisfied. The sum of the deviation of the actual values of Y and the computed values of Y is zero.
I need help thank you so much !
Answer:
mana saya tau iwnisbagcayabaonsoanuwvsybwiwnusvwuagwyvwkwnwibsyafa
What is an equation of the line that passes through the points (4,-2) and (8,-7)?
Answer:
the slope-intercept form for any line is y = mx + b, where m is the slope and b is the y-intercept.
now, let's calculate the slope:
=
here is the equation we currently have solved: y = x + b
now we have to solve for the y-intercept. to do this, we substitute one of the given points into the equation, and solve for b.
let's use (8, 2). in this ordered pair, the 8 is the x, and the 2 is the y.
2 = 8 + b
2 - 8 = b
b = -6
and now we have our final equation!
y = x - 6
hope this helped! please let me know if you are confused about anything i did smiley
Step-by-step explanation:
Answer:
y = -5/4x + 3Step-by-step explanation:
Find the slope first:
m = (y2 - y1)/ (2 - x1)m = (-7 + 2)/(8 - 4) = -5/4Use point-slope form and the coordinates of one of the points:
y - y1 = m(x - x1)y - (-2) = -5/4(x - 4)y + 2 = - 5/4x + 5y = -5/4x + 3Find MP
Find NL
Hehdjsjsjsjzjxjzjzjjznznznz
Answer:
i dont know
Step-by-step explanation:
hmmm
Let Z be the standard normal random variable. Use a probability calculator to answer the following questions: What is the probability Z will be within one standard deviation of average?
Answer:
0.6826 = 68.26% probability Z will be within one standard deviation of average.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability Z will be within one standard deviation of average?
This is the p-value of Z = 1 subtracted by the p-value of Z = -1.
Z = 1 has a p-value of 0.8413.
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability Z will be within one standard deviation of average.
Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are:__________
a) 0.2 and .04
b) 0.2 and 0.2
c) 20 and .04
d) 20 and 0.2
Answer:
c I think
Step-by-step explanation:
just cuz I did the math but I don't wanna type rn
The population of a city has increased by 33% since it was last measured. If the current population is 39,900, what was the previous population?
=___
Answer:
26,733
Step-by-step explanation:
39,900 - Percentage decrease =
39,900 - (33% × 39,900) =
39,900 - 33% × 39,900 =
(1 - 33%) × 39,900 =
(100% - 33%) × 39,900 =
67% × 39,900 =
67 ÷ 100 × 39,900 =
67 × 39,900 ÷ 100 =
2,673,300 ÷ 100 =
26,733
Hope this helps :)
Which quadratic function has minimum value at x = -b/2a?
O y=-3x2 + 5 X + 6
O y=x2 + 5 x + 6
O y=-x2 + 5x + 6
O y = -4 x2 + 5x + 6
Answer:
The choose (2)
y=x²+5x+6
Step-by-step explanation:
y=x²+5x+6 —> (–5/2 , –1/4)
y=-3x² + 5 X + 6 —> (5/6, 97/12)
y=-x² + 5x + 6 —> (5/2,49/4)
y = -4 x² + 5x + 6 —> (5/8 , 121/16)
How many 10-letter words real or imaginary can. Be formed from the following letters R,S,P,Q,H,J,S,M,B,A
Answer: 3628800
Step-by-step explanation: there are 10 letters so we multiply each with the other 1x2x3x4x5x6x7x8x9x10 or 10! to know all possible combinations so the answer will be 3628800.
Hope it helped!
Answer:
[tex]1,814,400[/tex]
Step-by-step explanation:
The number of ways to arrange a word with [tex]d[/tex] distinct digits is each to [tex]d![/tex]. Since there are 10 letters, there are [tex]10![/tex] permutations initially formed.
However, there is one letter that is repeated, S. We need to account for that fact that switching the placement of the S's does not change the word, as they still appear the same. Therefore, divide [tex]10![/tex] by the number of ways you can arrange the 2 S's, which is simply [tex]2![/tex]. Therefore, our answer is:
[tex]\frac{10!}{2!}=10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3=\boxed{1,814,000}[/tex]
Need Help! ASAP!!! I gave a screen shot. Please someone give me the correct answer.
9514 1404 393
Answer:
x ∈ {-35, 0, 35}
Step-by-step explanation:
We can solve for x and equate those values to find corresponding y-values. Substituting into the original expressions for x gives the possible x-values.
[tex]x+xy^2=250y\ \Rightarrow\ x=\dfrac{250y}{1+y^2}\\\\x-xy^2=-240y\ \Rightarrow\ x=\dfrac{-240y}{1-y^2}\\\\\dfrac{250y}{1+y^2}+\dfrac{240y}{1-y^2}=0\\\\\dfrac{25y(1-y^2)+24y(1+y^2)}{(1+y^2)(1-y^2)}=0\\\\y(-y^2+49)=0=y(7-y)(7+y)\ \Rightarrow\ y\in\{-7,0,7\}\\\\x=\dfrac{250(\pm 7)}{1+(\pm7)^2}=\pm35,\quad=\dfrac{250(0)}{1+0^2}=0\\\\\boxed{x\in\{-35,0,35\}}[/tex]
Solve the right triangle given that mZA= 30°, mZC = 90°, anda = 15. Round your result to one decimal place.
Answer:
[tex]\angle B = 60^o[/tex]
[tex]b =17.3[/tex]
[tex]c = 20[/tex]
Step-by-step explanation:
Given
[tex]a= 15[/tex]
[tex]\angle A = 30^o[/tex]
[tex]\angle C = 90^o[/tex]
See attachment for illustration
Required
Solve the triangle
First, we calculate the measure of B
[tex]\angle A + \angle B + \angle C = 180^o[/tex] --- angles in a triangle
[tex]30^o + \angle B + 90^o = 180^o[/tex]
Collect like terms
[tex]\angle B = 180^o-90^o-30^o[/tex]
[tex]\angle B = 60^o[/tex]
Solve for (c) using sine function
[tex]\sin(30) = \frac{a}{c}[/tex]
Make c the subject
[tex]c = \frac{a}{\sin(30)}[/tex]
Substitute known values
[tex]c = \frac{10}{0.5}[/tex]
[tex]c = 20[/tex]
Solve for (b) using Pythagoras
[tex]c^2 = a^2 + b^2[/tex]
This gives:
[tex]20^2 = 10^2 + b^2[/tex]
[tex]400 = 100 + b^2[/tex]
Collect like terms
[tex]b^2 =400 - 100[/tex]
[tex]b^2 =300[/tex]
Take square roots
[tex]b =17.3[/tex]
Please help!!!! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answers Below:
Answer:
B) 13+14 (n - 1)
Step-by-step explanation:
this is an arithmetic sequence
13 represent the first term
14 is a constant difference
Answer:
The answer is B
Step-by-step explanation:
substitute the value of n in the equation.
Find the value of x. Show your work with proper statements and notation
Answer: x = 14
====================================================
Explanation:
For any triangle, the three inside or interior angles always add to 180
M+N+P = 180
32+64+6x = 180
6x+96 = 180
6x = 180-96
6x = 84
x = 84/6
x = 14
Help please so lost!!!!!!!!!!!!
Answer:
hmmmmm please send the pic again
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Total People=5+7+4=16
Women=7We know
[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]
[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]
Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES
Answer:
A
Step-by-step explanation:
Slope = term that multiply x
y intercept = the number without a variable
1/2-5(2/3x + 6)+4/5x?
Answer:
[tex]-29.5-\frac{38}{15}x[/tex]
Step-by-step explanation:
First, we must expand out the -5.
-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.
Flying with a tailwind, a flight crew flew 500 km in 4 hours. Flying against the tailwind, the crew flew 468 km in 4 hours. Find the speed of the plane in calm air and the speed of the wind, both in km per hour.
Answer:
spped of the plane in calm air=121 km/h
speed of the wind= 4km/h
Step-by-step explanation:
Let say V the speed of the plane in calm air
and v the speed of the wind
Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4
Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4
We divide the 2 equations by 4 and then add the 2 results equations:
(500+468)/4=2V ==> V=121 (km/h)
We replace that value in the first equation:
V+v=500/4=125
v=125-121=4 (km/h)
A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280πcm3. Find the radius of the can if the height is 16cm16cm. Keep your answers in simplified radical form.
Answer:
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Radius of the can:
The radius of the can is given by:
[tex]r^2 = \frac{V}{h\pi}[/tex]
In which V is the volume and h is the height.
In this question:
[tex]V = 1280\pi, h = 16[/tex]
Thus
[tex]r^2 = \frac{V}{h\pi}[/tex]
[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]
[tex]r^2 = 80[/tex]
[tex]r = \sqrt{80}[/tex]
[tex]r = \sqrt{5*16}[/tex]
[tex]r = \sqrt{5}\sqrt{16}[/tex]
[tex]r = 4\sqrt{5}[/tex]
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
URGENT 100 POINTS AND BRAINIEST
Question 9 (Essay Worth 10 points)
(04.01, 04.02 HC)
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Part B: How much time does Ted spend practicing the breaststroke every day? Show your work. (3 points)
Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke if he practices for a total of exactly 50 minutes and practices the breaststroke for 20 minutes longer than he practices the butterfly stroke? Explain your reasoning. (2 points)
Answer:
Part A:
x + y = 50
y = x + 20
Part B:
Ted spends 35 minutes practicing the breaststroke every day.
Part C: It is not possible, as 45 + 65 isn't 50.
Step-by-step explanation:
If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4
PLEASE HELP NEED ASAPPPPPPP
Answer:
a and b are positive
Step-by-step explanation:
We are given that
[tex]a-3>b-3[/tex]
[tex]b>4[/tex]
We have to find that a and b are positive or negative.
We have
[tex]b>4[/tex]
It means b is positive and greater than 4.
[tex]a-3>b-3[/tex]
Adding 3 on both sides
[tex]a-3+3>b-3+3[/tex]
[tex]a>b>4[/tex]
[tex]\implies a>4[/tex]
Hence, a is positive and greater than 4.
Therefore, a and b are positive
