We want to see how long it will take for Lin and Noah to run 1 mile. We will see that:
Lin runs 1 mile in (8/55) hoursNoah runs 1 mile in (2/13) hours.So we know that:
Lin runs (2 + 3/4) miles in 2/5 hours.Noah runs (8 + 2/3) miles in 4/3 hours.The time in which they run a single mile is given by the quotient between the time and the distance.
For Lin we have:
[tex]T = \frac{2/5 }{2 + 3/4} h/mi = \frac{2/5}{11/4} h/mi = \frac{2*4}{5*11} h/mi = \frac{8}{55} h/mi[/tex]
So Lin runs a mile in (8/55) hours
For Noah we have:
[tex]T = \frac{4/3}{8 + 2/3} h/mi = \frac{4/3}{26/3} h/mi = \frac{4}{26} mi/h = \frac{2}{13} h/mi[/tex]
Noah runs 1 mile in (2/13) hours.
If you want to learn more, you can read:
https://brainly.com/question/22610586
Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 10 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks at a rate of 8 cubic feet per minute?
Answer:
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Step-by-step explanation:
Given
Represent radius with r and height with h
[tex]h = 12ft[/tex]
[tex]r = 10ft[/tex]
[tex]Rate = \frac{8ft^3}{min}[/tex] when [tex]h = 10ft[/tex]
Express radius in terms of height
[tex]\frac{r}{h} = \frac{10}{12}[/tex]
[tex]\frac{r}{h} = \frac{5}{6}[/tex]
[tex]r = \frac{5}{6}h[/tex]
First, we need to determine the volume of the cone in terms of height.
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Substitute [tex]r = \frac{5}{6}h[/tex]
[tex]V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^3[/tex]
[tex]V = \frac{25}{108} \pi h^3[/tex]
Differentiate both sides w.r.t time (t)
[tex]\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}[/tex]
Solve for [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}[/tex]
At this point, [tex]h = 10[/tex] and [tex]\frac{dv}{dt} = \frac{8ft^3}{min}[/tex]
So, we have:
[tex]\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{864}{7500\pi}[/tex]
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Hence:
The rate is [tex]\frac{216}{1875\pi} ft/min[/tex]
Using implicit differentiation, it is found that the depth of water changes at a rate of -0.0764 feet per minute.
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
Applying implicit differentiation, we can find it's rate of change, thus:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
In this problem:
Height of 12 ft and radius of 10 ft, thus [tex]h = 12, r = 10[/tex].Radius does not change, thus [tex]\frac{dr}{dt} = 0[/tex].Water leaks at a rate of 8 cubic feet per minute, thus [tex]\frac{dV}{dt} = -8[/tex]Then:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
[tex]-8 = \frac{\pi (10)^2}{3}\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = -\frac{24}{100\pi}[/tex]
[tex]\frac{dh}{dt} = -0.0764[/tex]
The depth of water changes at a rate of -0.0764 feet per minute.
A similar problem is given at https://brainly.com/question/9543179
3. What is the set of ordered pairs such that no twvo
ordered pairs have the same x-value but different y-
values?
A. Function
C. Relation
B. Theorem
D. None of these
Answer:
A
Step-by-step explanation:
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
The mayor of a town saw an article that claimed the national unemployment rate is 8%. They wondered if this held true in their town, so they took a sample of 200 residents to test H_0 : p = 0.08 versus H_a : p != 0.08, where p is the proportion of residents in the town that are unemployed. The sample included 22 residents who were unemployed.Identify the correct test statistic for this significance test to one decimal place.
Answer:
Z = [tex]\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }[/tex] = 1.6
we reject the Null hypothesis
Step-by-step explanation:
The correct test statistic
Assume :
Null Hypothesis : H_0 : p = 0.08
Alternative hypothesis : H_a : p ≠ 0.08
p = proportion of residents that are unemployed
x = unemployed residents = 22
n = sample size = 200
To get the sample of the population that is unemployed we use this equation
[tex]p = \frac{X}{n}[/tex] = 22 / 200 = 0.11
now we apply the test of of significance of single proportion
= Z = [tex]\frac{p - P}{\sqrt{pq/n} }[/tex]
therefore Z = [tex]\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }[/tex] = 1.6
Therefore we reject the Null hypothesis
Testing the hypothesis, it is found that the test statistic used is z = 1.6.
At the null hypothesis, it is tested if the proportion is of 8%, that is:
[tex]H_0: p = 0.08[/tex]
At the alternative hypothesis, it is tested if the proportion is different of 8%, that is:
[tex]H_1: p \neq 0.08[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]p = 0.08, n = 200, \overline{p} = \frac{22}{200} = 0.11[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.11 - 0.08}{\sqrt{\frac{0.08(0.92)}{200}}}[/tex]
[tex]z = 1.6[/tex]
A similar problem is given at https://brainly.com/question/24166849
FIND THE UNIT OF X 5X+17=7 WHEN YOU FIND IT SIOLVE THE EQUATION WITH THE NEW NUMBER OF X
Answer:
x = -2
Step-by-step explanation:
5x + 17 = 7
5x = -10
5x/5 = -10/5
x = -2
i could be wrong but i hope i helped
Answer:
x = -2Step-by-step explanation:
5X + 17 = 7
subtract 17 each side
5x + 17 - 17 = 7 - 17
divide 5 both sides
5x = -10
simplify
5x/5 = -10/5
x = -2
Write out the correct word form of each number.
10) 8,924,600.32
11) 707.91
12) 641,971.44
Solve the question on the interval [0, 2π)
sin^2 θ - cos^2 θ = -3 sin θ - 2
Answer:
[tex]\frac{7\pi }{6} ; \ \frac{3\pi }{2} ; \ \frac{11\pi }{6}.[/tex]
Step-by-step explanation:
if 1=sin²Q+cos²Q, then cos²Q=1-sin²Q, then
2sin²Q+3sinQ+1=0;
[tex]\left[\begin{array}{ccc}sinQ=-1\\sinQ=-0.5\end{array} \ => \ \left[\begin{array}{ccc}Q=3\pi/2+2\pi *n\\Q=(-1)^n*\frac{7\pi }{6}+\pi n \end{array}[/tex]
on the interval Q=3π/2 (from the 1st equation) and Q=7π/6; 11π/6 (from the 2d equation).
what would be the best first step to solving j+18/-4=8:
-add 18 to both sides
-subtract 18 from both sides
-multiply both sides by 4
-multiply both sides by -4
(choose 1)
Of the following statements, which are equivalent?
I. 0
II. x(x−3)<0
III. −5
(A) I and II
(B) I and III
(C) II and III
(D) I, II, and III
(E) none of the above
Answer:
i think its C
Step-by-step explanation:
sorry if i get it wrong
find the value of x.
x=
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
What is the value of -8(17-12)/-2(8-(-2))
Answer:
it's 2 got it right on edg
Step-by-step explanation:
Alison is preparing for a math contest. Each day, she works on multiplication problems for 10 minutes and division problems for 30 minutes.
How many minutes does Alison practice multiplication and division problems in 10 days?
Alison practices multiplication and division problems for blank minutes in 10 days. the answer is 400
Answer:
it's 400-
Step-by-step explanation:
total minutes a day is 40, multiplied by 10 days
Haley makes a total of $400 a part-time job over a two week period. The first week she makes $20 more than her second weeks paycheck. How much money did she make each week
Answer: on the first week she earned 220$ and on the second week she earns 200$
Step-by-step explanation: Haley makes a total of 400$ in a week. divided by 2 would equal 200$ each. but Haley made an extra 20$ in the first week. so, 200$+20$=220$.And the two combined is 420$.
How many solutions exist for the given equation? 3x+13 3(x + 6)+1
zero
one
two
infintely many
Answer:
Two solutions.
hope that will help you
Answer:
A. zero
Step-by-step explanation:
3x + 13 = 3(x + 6) + 1
step 1. distribute 3 through the parantheses:
3x + 13 = 3(x + 6) + 1
step 2. cancel equal terms on both sides of the equation:
3x + 13 = 3x + 18 + 1
13 = 18 + 1
step 3. add the numbers:
13 = 18 + 1
13 = 19
13 ≠ 19, so there is no solution.
may i please have brainliest?
The solution of which inequality is shown by the number line?
-7 -6
-5
-4
-3
-2
Molly has three pairs of shoes. 1 cost $40, 2 cost $20, and 3 cost $25, if she got 50% off for all shoes, what price was each shoe?
Answer:
20, 10, 12.50
Step-by-step explanation:
Multipy (2x + 4 (x - 4)
Zzz
Answer:
6x−16
Step-by-step explanation:
What is the solution to this equation? −5n+5=−15 Enter your answer in the box. n =
Answer:
4.
Step-by-step explanation:
−5n+5=−15
Step 1: Subtract 5 from both sides.
−5n+5−5=−15−5
−5n=−20
Step 2: Divide both sides by -5.
−5n
−5
=
−20
−5
n=4
Can I have Brainlliest? Hope it helps.
Answer:
n=4
Step-by-step explanation:
someone help PLS ASAP! in the figure above, l is a line. if y=96, what is the value of x?
a. 28
b. 30
c. 42
d. 84
Answer:
x=28
So a
Step-by-step explanation:
2x+96+x=180 add like terms (2x+x)
3x+96=180 subtract 96 from both sides (3x+96-96=180-96)
3x=84 divide both sides by 3 (3x/3=84/3)
x=28
The order in which you multiply inverse matrices is not relevant.
True
False
For what value of k will the vector (1, -2, k) in be a linear combination of the vectors (3, 0, -2) and (2, -1, -5) ?
find the single discount equivalent for the series discount 20/10/20 round to the nearest tenth of a percent
Answer: hmmm simple it’s 15
Step-by-step explanation: your welcome
I guess that mean hold him down if he say he can’t breathe
Answer:
[tex]this \: proberbility \: is \: \frac{2}{5} [/tex]
At 2 P.M., the total snowfall is 23 inches. At 7 P.M., the total snowfall is 45 inches. What is the mean hourly snowfall? Write your answer in simplest form as a fraction or mixed number.
Answer:
13 3/5 inches per hour
Step-by-step explanation:
If at 2 there is 23 inches and then at 7 there is 45, it has been 5 hours. Taking the mean (average) is just taking 45+23 and dividing it by 5. That gives you 68/5 which simplified to a mixed number is 13 3/5. So, there was a mean of 13 3/5 inches of snowfall hourly. Hope that helps!
Kyle is a secretary. She earns $12.38 per hour. She worked 42 hours last week. What is her straight time pay?
Answer:
$519.96
Step-by-step explanation:
$12.38 × 42= $519.96
help me asap 40 points in the next 10 minutes a store is going to make a trail mixture of peanuts and chocolate candies. They want the mixture to sell for 3.20 per pound.
peanuts sell for 4.50 per pound and they are going to use 20 pounds of peanuts. If chocolate candies sell for 2.25 per pound how much pounds of the chocolate candies should they use round to the nearest pound.
Answer:
30 pounds
Step-by-step explanation:
took test
The roots of a quadratic equation are
1/ 3 and -2. Determine the equation
Answer: God
Step-by-step explanation:
The reason it’s god is because god created everything so he know everything. So your answer is god
15,420 divided by 20 =
Answer:
771
Step-by-step explanation:
can some one help me please
Can someone help please
Sum of triangle: 180
So we know that:
7x + 3x + 8 + x + 7 = 180
Combine like terms:
11x + 15 = 180
11x = 165
x = 15
Plug in for x in order to find the angles.
You should be able to solve from here!
Answer:
m∠I = 22
m∠J = 53
m∠K = 105
Step-by-step explanation:
m∠I = (x + 7)
m∠J = (3x + 8)
m∠K = (7x)
m∠I + m∠J + m∠K = 180°
(x + 7) + (3x + 8) + (7x) = 180
x + 7 + 3x + 8 + 7x = 180
11x + 15 = 180
11x = 165
x = 15
m∠I = 15 + 7 = 22
m∠J = 3(15) + 8 = 53
m∠K = 7(15) = 105
1) Convince Me!
Suppose each section of the
theater has only 45 seats.
How many sections would be
needed to seat 428 people?