Answer:
a. 24.12 ft³/hr b. 0.0768 ft/hr
Step-by-step explanation:
a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.
The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out
Since volume flow rate in = P(t) and volume flow rate out = R(t),
dV/dt = P(t) - R(t)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
We need to find the rate of change of volume when t = 6.
From the table when t = 6, P(6) = 47 ft³/hr
Also, substituting t = 6 into R(t), we have R(6)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
[tex]\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr[/tex]
dV/dt ≅ 24.12 ft³/hr
So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr
b. How fast is the water level in the pool rising at t=6 hours?
Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet
dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.
So, dV/dt = πr²dh/dt
dh/dt = dV/dt ÷ πr²
Since dV/dt = 24.12 ft³/hr and r = 10 ft,
Substituting the values of the variables into the equation, we have that
dh/dt = dV/dt ÷ πr²
dh/dt = 24.12 ft³/hr ÷ π(10 ft)²
dh/dt = 24.12 ft³/hr ÷ 100π ft²
dh/dt = 0.2412 ft³/hr ÷ π ft²
dh/dt = 0.2412 ft³/hr
dh/dt = 0.0768 ft/hr
So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr
What constant acceleration is required to increase the speed of a car from 30 miyh to 50 miyh in 5 seconds?
Answer:
The acceleration is 1.8 m/s^2.
Step-by-step explanation:
initial velocity, u = 30 mph = 13.4 m/s
Final velocity, v = 50 mph = 22.4 m/s
time, t = 5 s
Let the acceleration is a.
Use first equation of motion
v = u + at
22.4 = 13.4 + 5 a
a = 1.8 m/s^2
Which graph represents the equation x2 = 8y? On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 8), and a directrix at y = negative 8. On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 2), and a directrix at y = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (2, 0), and a directrix at x = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (8, 0), and a directrix at x = negative 8.
Answer:
The parabola x²=8y has,
vertex: (0,0)
focus: (0,2)
directrix: y=-2
so that option is the answer,
btw, the parabola opens up to the top and axis of symmetry is x=0
Answer:
It's A!
Step-by-step explanation:
Got it correct on my test! :)
An ice cream truck started the day with 454545 ice cream sandwiches. During a stop at a busy park they sold sss ice cream sandwiches. After the stop, the truck had 212121 ice cream sandwiches remaining.
Write an equation to describe this situation.
How many ice cream sandwiches did the truck sell at the park?
Answer:
45- s= 21
s= 45- 21
=24
so the answer is 24
Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other
Answer:
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the elements are arranged, so we have to use the arrangements formula.
Arrangements formula:
The number of possible arrangements of n elements is:
[tex]A_{n} = n![/tex]
Desired outcomes:
Pine trees(6!) then the willows(6!) or
Willows(6!) then the pine trees(6!). So
[tex]D = 2*6!*6! = 1036800 [/tex]
Total outcomes:
12 trees, so:
[tex]T = 12! = 479001600 [/tex]
What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?
[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Suppose that 25% of people own dogs If you pick three people at random, what
is the probability that they all three own a dog? (Let me add that we don’t know the
populations size so calculate the probability as if the population is infinite.)
Answer:
1/64
Step-by-step explanation:
25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.
picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.
picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.
so,
1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625
How many proportional relationships are shown in the coordinate plane below?
Answer:
The answer is B) There is one proportional relationship
Step-by-step explanation:
The green line (the one at the top) does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
The blue line (the one in the middle) is a straight line through the origin. This is a proportional relationship.
Reason: It goes through 0,0
----------------------------------------------------------------------------------------------------------------
The purple line (the one at the bottom) does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
Conclusion: Since the green and purple lines are not proportional but the blue line is, this means only 1 line is proportional.
Note:
I know my answer is very late but I wanted to help anyone who needs it for future reference.
The ratio of the number of boys to that of girls in a school is 4:3. If the number of girls in the school is 162, find the number of boys in it. Then find the ratio of the number of girls to the total number of students in the school.
Answer:
total number of boys in skool is 216
And
ratio of girls to boys is a 3:4
Step-by-step explanation:
let total no. of boys be X
ACCORDING TO QUESTION
ratio of boys to girls = 4:3
total number of girls = 162
now
4/3=X/162
or, 4×162= 3x
or, 4×162/3= X
hence
X = 216
therefore total number of boys is 216
and
ratio of girls to boys is =162/216
=3/4
=3:4
Find the length of the leg x
Answer:
12.65
Step-by-step explanation:
Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90 degree angle).
a and b are the side legs.
so, here we have
14² = 6² + b²
196 = 36 + b²
160 = b²
b = sqrt(160) = sqrt(16×10) = 4×sqrt(10) = 12.65
A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 1300 southern residents and 1380 midwestern residents. 39% of the southern residents and 50% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 80% confidence interval for the difference in two proportions. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval
Answer:
The point estimate that should be used in constructing the confidence interval is 0.11.
The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Midwest:
50% of 1380, so:
[tex]p_M = 0.5[/tex]
[tex]s_M = \sqrt{\frac{0.5*0.5}{1380}} = 0.0135[/tex]
South:
39% of 1300, so:
[tex]p_S = 0.39[/tex]
[tex]s_S = \sqrt{\frac{0.39*0.61}{1300}} = 0.0135[/tex]
Distribution of the difference:
[tex]p = p_M - p_S = 0.5 - 0.39 = 0.11[/tex]
So the point estimate that should be used in constructing the confidence interval is 0.11.
[tex]s = \sqrt{s_M^2+s_S^2} = \sqrt{0.0135^2+0.0135^2} = 0.0191[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.11 - 1.28*0.0191 = 0.0856[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.11 + 1.28*0.0191 = 0.1344[/tex]
The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).
Alex purchased
1/2
of a gallon of milk. He put
2/11
of the milk in a smoothie. How much of a gallon of milk did Alex put in his smoothie?
Answer:
1/11 of a gallon
Step-by-step explanation:
He used 2/11 of 1/2 gallon
2/11 * 1/2 = 1/11 of a gallon
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
Step 1: Find how much of a gallon he used
[tex]\frac{2}{11} * \frac{1}{2} =\frac{2}{22}[/tex]
[tex]\frac{2}{22}=\frac{1}{11}[/tex]
Answer: [tex]\frac{1}{11}[/tex]
Marnie just finished setting herself up at a cozy spot at the airport. Her laptop is ready, phone within reach, and her papers are organized, but now, she's hungry. What should she do? a) Take her phone and laptop with her to get something to eat b) Leave her stuff, but get a snack really quickly O c) Put her coat over her laptop to hide it and go get a snack O d) Ask the person next to her to watch her stuff
Answer:
a) someone will steal her stuff in any other situation even if a stranger watches it
Trevor is studying a polynomial function f(x). Three given roots of f(x) are -7, 2i, and 7. Trevor concludes that f(x) must
be polynomial with degree 3. Which statement is true?
Answer:
B Trevor isn't correct because -2i must also be a root
Step-by-step explanation:
A Trevor is correct.
B Trevor is not correct because –2i must also be a root.
C Trevor is not correct there cannot be an odd number of roots.
D Trevor is not correct because there cannot be both rational and complex roots.
statements^^^^^^
The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Since one of the roots is complex (2i), it follows that the coefficients of f(x) must be complex as well, and therefore f(x) must be a polynomial with complex coefficients.
However, it is possible for f(x) to have a higher degree than 3.
For example,
The polynomial (x + 7)(x - 2i)(x + 2i)(x - 7) has degree 4 and has the given roots of -7, 2i, and 7. Therefore, f(x) could be a polynomial with degree 4 or higher.
Thus,
The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.
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rút gọn :
(x+2)^2+(3-x)^2= ?
Step-by-step explanation:
=x^2+2x+4+9-6x+x^2
=2x^2-4x+13
Mark is investing $8,000 in an account paying 5.5% interest compounded daily. What will Mark's account balance be in 6 years?
Picture is the answer
Jenny bought scrapbooking supplies for $156.50. She paid $10.17 in sales tax. What was the sales tax rate on the supplies? If necessary, round your answer to the nearest tenth.
Answer:
6.5%
Step-by-step explanation:
sales price x sales tax rate = sales tax
156.50 x sales tax rate = 10.17
sales tax rate = 10.17/156.50
sales tax rate = .065 or 6.5%
Ed decides to include more fruit in his diet. He goes to the grocery store over the weekend and buys 6 apples, 6 oranges, and 6 avocados. The total cost is $19.50.
Ed finishes the apples very quickly, and has some leftover avocado. The following weekend he buys 12 apples, 2 oranges, and 1 avocado. This time he pays just $9.50.
The following week, Ed reads an article on the benefits of avocado, so over the weekend he buys 5 avocados along with 2 apples and 4 oranges. His total this time is $14.
Assume that Ed pays a unit price rather than a price per pound for the apples, oranges, and avocados.
9514 1404 393
Answer:
apples: $0.50 eaoranges: $0.75 eaavocados: $2.00 eaStep-by-step explanation:
Let a, o, v represent the prices of one each of apples, oranges, and avocados, respectively. Then the equations describing the purchases can be written ...
6a +6o +6v = 19.50
12a +2o +1v = 9.50
2a +4o +5v = 14.00
__
Dividing the first equation by 6 makes it ...
a +o +v = 3.25
Subtracting this from the second equation gives ...
(12a +2o +v) -(a +o +v) = (9.50) -(3.25)
11a +o = 6.25
Subtracting the third equation from 5 times the reduced first equation gives ...
5(a +o +v) -(2a +4o +5v) = 5(3.25) -(14.00)
3a +o = 2.25
The difference of these last two equations is ...
(11a +o) -(3a +o) = (6.25) -(2.25)
8a = 4.00
a = 0.50
Then the other values are ...
o = 2.25 -3(a) = 0.75
v = 3.25 -a -o = 2.00
The unit prices are:
apples -- $0.50
oranges -- $0.75
avocados -- $2.00
_____
Additional comment
Most graphing or scientific calculators will solve systems of equations like these. Using an appropriate tool, it takes less time to find the solution than to read this one.
Note that the last purchase description in the problem statement has the items in a different order than in the first two descriptions. Care must be taken to make sure the correct equations are written.
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate
Step-by-step explanation:
AAS means angle angle side. so, we need 2 angles and 1 side.
the diagram shows us 1 angle in each triangle to be equal or congruent (C and G).
it also shows us implicitly, that the side AB is shared and is therefore truly the same for each triangle.
that means we need one more angle. either the one at A or the one at B. you pick.
evaluate (-1)^6-4^0+(3/7)^0
Answer:
The answer is 1
.............
please mark this answer as brainlist
Let S be a set of linearly dependent vectors in Rn. Select the best statement. A. The set S could, but does not have to, span Rn. B. The set S spans Rn, as long as no vector in S is a scalar multiple of another vector in the set. C. The set S cannot span Rn. D. The set S must span Rn. E. The set S does not span Rn if some vector in S is a scalar multiple of another vector in the set. F. The set S spans Rn, as long as it does not include the zero vector. G. none of the above
Answer:
The set S could, but does not have to, span Rn ( A )
Step-by-step explanation:
Assume S is a set of linearly dependent vectors in Rn
The best statement from the options is ; The set S could, but does not have to, span Rn
This is because S could span Rn ( as stated in option c ) but will not necessary span Rn ( as seen in option D )
Pls help I literally am crying I don’t understand ):
Answer: Passes out in slow
Step-by-step explanation:
Step 1 be Einstein
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 5.1. A sample of 33 honors students is taken and is found to have a mean GPA equal to 5.2. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________.
Answer:
B. The mean GPA of the university honors students
Step-by-step explanation:
Parameter in statistical parlance simply refers to numerical characteristics obtijed from the population dataset or observations. The population itself refers to all observations belonging to a particular or specific experiment or research. Here, the population is the all students belonging to the university's honors programme. The measured characteristic is the mean of the student's GPA. THEREFORE, the parameter will be the mean GPA of the honors student.
Compare the functions shown below:
f(x) = 7x + 3 g(x) tangent function with y intercept at 0, 2 h(x) = 2 sin(3x + π) − 1
if my savings of $x grows 10 percent each year, how much will i have in 2 years?
Answer:
$240
Step-by-step explanation:
A year has 12 month in it so lets multiply the 10 by 12 which is $120,Mean a year is $120 so 2years will be $120×2 which is $240
Answer:
x+1/5x
Step-by-step explanation:
Because the eqaution would be x+10%=x+1/10+10%=1/5+x
Then the equation equals x+1/5
A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue? Choose an answer
Answer: 17 feet
Step-by-step explanation:
51/48 = x/16
(51)(16)/48
The statute is 17 feet tall.
What are the similar triangles?Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.
What is the ratio of any two corresponding sides of similar triangles?The ratio of any corresponding sides in two equiangular triangles is always the same.
Let's visualize the situation according to the given question.
AB is the building ,whose height is 51f
BC is the shadow of the building AB, whose length is 48ft.
QR is the shadow of the tower statue, whose length is 16feet.
Let the height of the statue PR be h feet.
In triangle ACB and triangle PRQ
∠ACB = ∠PRQ = 90 degrees
( the objects and shadows are perpendicular to each other)
∠BAC = ∠QPR
( sunray falls on the pole and tower at the same angle, at the same time )
⇒ΔACB similar to ΔPRQ ( AA criterion)
Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.
⇒ AC/CB = PR/RQ
⇒[tex]\frac{51}{48} =\frac{h}{16}[/tex]
⇒ h = [tex]\frac{(51)(16)}{48}[/tex]
⇒ h = 17 feet.
Hence, the statute is 17 feet tall.
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A certain drug is used to treat asthma. In a clinical trial of theâ drug, 17 of 258 treated subjects experienced headachesâ (based on data from theâ manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11â% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete partsâ (a) throughâ (e) below. â
1-PropZTest
prop<0.11
z=â2.264337000
p=0.0117766978
p=0.0658914729
n=258
a. Is the testâ two-tailed, left-tailed, orâ right-tailed?
b. What is the best statistics?
c. What is the P-value?
d. What is the nut hypothesis and what do you conclude who det hypothesis?
Identify the null hypothesis.
A. H0: pâ 0.11.
B. H0: p=0.11.
C. H0: p<0.11.
D. H0: p>0.11.
Decide whether to reject the null hypothesis.
A. Reject the null hypothesis because theâ P-value is greater than α.
B. Fail to reject the null hypothesis because theâ P-value is less than or equal to α.
C. Reject the null hypothesis because theâ P-value is less than or equal to α.
D. Fail to reject the null hypothesis because theâ P-value is greater than α
e. What is the finalâ conclusion?
A. There is not sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
B. There is not sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
C. There is sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
Solution :
a). The test is a left tailed test.
b). The sample proportion is :
[tex]$\hat p = \frac{x}{n}$[/tex]
[tex]$\hat p = \frac{17}{258}$[/tex]
= 0.065
Determining the Z statistics using the formula :
[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]
= -2.31
∴ Z statistics value is -2.31
c). Using the excel function, the P-value is :
P-value = Normsdist(-2.31)
= 0.0104441
d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]
The level of significance is 0.01
We fail to reject the null hypothesis as the P value is less than or equal to the significant level.
Suppose your Unit Quiz grades have been: 85%, 80%, 96%, 72%, 78%, 85% and 92%
a) What is your average/mean score?
b) What is the median score?
c) What is the mode score?
d) Why is the mean lower than the median?
e) What will your mean be if you get a perfect score of 100% on your next quiz?
Answer:
mean: 84
median: 85
mode: 85
explainations for d and e below.
Step-by-step explanation:
mean:
(85+80+96+72+78+85+92)/7 = 544/7 = 84
median:
sort them in order from least to greatest first
72, 78, 80, 85, 85, 92, 96
find the middle number in that order, that's your median. in this case, it's 85.
mode:
number that appears the most in the order; the frequency. in this case as well, it's also 85.
answer for d:
the reason why the mean is lower than the median is because of the fact we were figuring out the average and had to divide, unlike the median where it's just the middle of the order we have.
answer for e:
(85+80+96+72+78+85+92+100)/8 = 644/8 = 80.5%
p.s: please subscribe to #gauthmath# sub reddit if you can for more help.
Which line is parallel to y = -2x + 8
Answer:
y=-2x-7
Step-by-step explanation:
after putting the choices with the question in a graph I found that that ones stays in a line with the question
Brainliest please!!
Simplify the following expression:
(15b^5)^2
—————-
(5b^2)^3
Answer:
5x
Step-by-step explanation:
(75b x)x×2
---------------
(10b x)×3
=75b x×x×2
-----------------
10b x×3
=25x
-------
5
=5x
which of the following is a polynomial?
A. 15x^4
B. 6x^2/x
C. 4x^2+9x+12
D. 3- √2x
Answer:
C. 4x^2 + 9x + 12
Step-by-step explanation:
4x^2 + 9x + 12 is a polynomial.
Answer:
the answer is c
Step-by-step explanation:
in each figure below find m<1 and m < 2 if a||b
please help i don't have a lot of time I will give brainliest if you help
Answer:
m∠1 = 105°
m∠2 = 75°
Step-by-step explanation:
From the picture attached,
Two lines 'a' and 'b' are parallel and a transversal 't' is intersecting these lines at two distinct lines.
Therefore, m∠2 = 75° [Corresponding angles measure the same]
m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]
m∠1 + 75° = 180°
m∠1 = 105°
