A cube has an edge of 3 feet. The edge is increasing at the rate of 4 feet per minute. Express the volume
of the cube as a function of m, the number of minutes elapsed.
Hint: Remember that the volume of a cube is the cube (third power) of the length of a side.
Answers
Answer:
so it increases by 4 per minute
the volume of a cube is v=side^3
so the side length be 5+4m where m is the number of minutes
therefor the volume can be expressed as V(m)=(5+4m)³
Step-by-step explanation:
The volume of the cube can be expressed as a function of m, the number of minutes elapsed as V(m) = (3 + 4m)³ feet³.
What do we mean by volume?The volume of an object is the total space occupied by the object in the three-dimensional space.
How do we solve the given question?In the question, we are asked to express the volume of a cube as a function of m, the number of minutes elapsed. We are given that the initial length of the edge of the cube was 3 feet, and it increases at a rate of 4 feet per minute.
∴ We can say that the length of the edge after m minutes = 3 + 4m
As 4 feet is the increase per minute and m minutes have elapsed.
We know, that the volume of a cube is the cube of the length of the edge.
∴ The volume = (3 + 4m)³.
Hence, the function of the volume of the cube in m can be written as,
V(m) = (3 + 4m)³ feet³.
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Related Questions
Select the correct answer from each drop-down menu.
Kurt deposited money into his bank account every month. The amount of money he deposited in the first 5 months of 2014 is listed in the table.
Month Amount Deposited
(dollars)
January 1,200.32
February 985.43
March 1,200.65
April 1,987.34
May 1,000.98
The total amount of money that Kurt had deposited into his account at the end of May is
$6,374.72
. The total amount of money that he had deposited into his account at the end of March is
.
Reset
Answers
9514 1404 393
Answer:
$3386.40
Step-by-step explanation:
The amount at the end of March can be found two ways:
add up the deposits for Jan, Feb, Mar:
1200.32 +985.43 +1200.65 = 3386.40
subtract Apr and May from the May total:
6374.72 -1000.98 -1987.34 = 3386.40
The total amount of money that he had deposited into his account at the end of March is $3386.40.
Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 15. The sample of group-participation adolescents had an average of M = 53.8.
Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with α = .05.
Answers
Testing the hypothesis, we can conclude that since the p-value of the test is 0.0114 < 0.05, which means that the sample provides enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population.
At the null hypothesis, we test if the mean is the same of the general population, that is:
[tex]H_0: \mu = 50[/tex]
At the alternative hypothesis, we test if it is different, that is:
[tex]H_1: \mu \neq 50[/tex]
The test statistic is given by:
[tex]z = \frac{M - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
For this problem, the parameters are:
[tex]M = 53.8, \mu = 50, \sigma = 15, n = 100[/tex]
Then, the value of the test statistic is:
[tex]z = \frac{M - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{53.8 - 50}{\frac{15}{\sqrt{100}}}[/tex]
[tex]z = 2.53[/tex]
Two tailed test, so the p-value is P(|z| < 2.53), which is 2 multiplied by the p-value of z = -2.53.
Looking at the z-table, z = -2.53 has a p-value of 0.0057
2(0.0057) = 0.0114
The p-value of the test is 0.0114 < 0.05, which means that the sample provides enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population.
A similar problem is given at https://brainly.com/question/25147864
identify the solutions of the inequality 5 ≤ s − 6
Answers
Answer:
s≥11
Step-by-step explanation:
5 ≤ s -6
=5 + 6 ≤ s
=11 ≤ s or s≥11
The solution to given inequality 5 ≤ s − 6 for s will be s ≥ 11.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
Given the inequality,
5 ≤ s − 6
Subtracting by 5 on both sides,
5 - 5 ≤ s - 6 - 5
0 ≤ s - 11
Adding 11 on both sides
0 + 11 ≤ s - 11 + 11
11 ≤ s or s ≥ 11
Hence "The solution to given inequality 5 ≤ s − 6 for s will be s ≥ 11".
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4(3M - 2) + 2(2M - 1) when M = 5
Answers
Answer:
70
Step-by-step explanation:
4(3m-2)+2(2m-1)
4(3×5-2)+2(2×5-1)
4×13+2×9
52+2×9
52+18
Please answer!no links!!
Picture is included
I selected b but not sure…
Answers
Answer:
B is the correct answer darling
Step-by-step explanation:
don't doubt yourself :)
have a lovely day <3
Answer:
B
Step-by-step explanation:
[tex]\dfrac{-1}{5}(30x-10)=15\\\\ \dfrac{-1}{5}*30x -10* \dfrac{-1}{5}=15\\\\-6x + 2 = 15[/tex]
what is 1\4y+3/8 factored
Answers
Answer:
[tex] \frac{1}{4} (y + \frac{3}{2} )[/tex]
The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
A.
m = 6, A'B' =
B.
m = 21, A'B' = 3.5
C.
m = 21, A'B' =
D.
m = 6, A'B' = 3.5
Answers
Answer:
Step-by-step explanation:
Help!!!! I need this due my 9:30
Answers
Answer:
D. Subtract 15 cents and add 29 cents
Step-by-step explanation:
He should subtract 15 cents and add 29 cents. This is because at 33.85 we estimated to 34 dollars which was 15 cents higher, so we must subtract by 15 to get to the exact cost. We also need to add 29 cents since we rounded down from 16.29 to 16.
Evaluate.
38−(7+2×4)+182
Enter your answer in the box.
the answer is 32
Answers
[tex]205[/tex]
hope it helps
HELP LAST ATTEMPT to ( get marked brainliest show work !
Answers
Answer:
B. 5 3/4 feet
Step-by-step explanation:
33 sq ft is the total area so you need the side lengths, its a square rug, so you just square the number
sqrt 33 = 5 3/4
Answer:
B. 5 3/4 feet
Step-by-step explanation:
33 sq ft is the total area so you need the side lengths, its a square rug, so you just square the number
sqrt 33 = 5 3/4
Let's Create
Fill in the blank with the value that will make the equation true.
1) __+2/3= -1/4
2) __-3/4= -7/12
3) __÷3/4= -2
4) __÷0.04=800
5) (____)(5.6)= -6.72
Let's Analyze
Fill in the blank with the value that will make the equation true.
1) 1/4+___=7/12
2) 5/8-___= -3/8
3) 1/3÷___= 1/9
4) (2.1)(____)=0.63
5)_____-0.98= -7.65
Answers
Answer:
.
1) 1/4+___=7/12
2) 5/8-___= -3/8
3) 1/3÷___= 1/9
4) (2.1)(____)=0.63
value
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $7,200. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)
(a) Find the 90th percentile for an individual teacher's salary.
$
(b) Find the 90th percentile for the average teacher's salary.
$
Answers
Using the normal distribution and the central limit theorem, it is found that:
a) The 90th percentile for an individual teacher's salary is $50,216.
b) The 90th percentile for the average teacher's salary is $43,914.
In a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of $41,000, thus [tex]\mu = 41000[/tex].Standard deviation of $7,200, thus [tex]\sigma = 7200[/tex].Item a:
The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28. Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 41000}{7200}[/tex]
[tex]X - 41000 = 1.28(7200)[/tex]
[tex]X = 50216[/tex]
The 90th percentile for an individual teacher's salary is $50,216.
Item b:
Average for a sample of 10, thus [tex]n = 10, s = \frac{7200}{\sqrt{10}}[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{X - 41000}{\frac{7200}{\sqrt{10}}}[/tex]
[tex]X - 41000 = 1.28\frac{7200}{\sqrt{10}}[/tex]
[tex]X = 43914[/tex]
The 90th percentile for the average teacher's salary is $43,914.
A similar problem is given at https://brainly.com/question/24663213
This is balanced. True or false?
Answers
Answer:
False
Step-by-step explanation:
a=3 b=-2 c=5 d=-4 e=-6
just replace the variables with the numbers.
ex.
e+4ab
-6+4(3)(-2)
-6+12(-2)
-6-24
-30
[tex] \sqrt{27 + {3}^{2} } + 5 \\ \sqrt{27 + 9 + 5 } \\ \sqrt{41 } \\ 6.4[/tex]
Anyone know the answer ? Please help asap :((
Answers
Answer:
Point B
Step-by-step explanation:
Answer:
the answer is point b...
What term describes the amount you must pay in order to be considered “up-to-date” with your credit card payments?
Interest
Minimum payment
Closing balance
Answers
Consider the following formula used to find the volume of a cone.
h
V = ir2
3
Which of the following represents the formula that could be used to find the height of the cone?
Answers
[tex]\\ \sf\longmapsto V=\pi r^2\dfrac{h}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{h}{3}=\dfrac{V}{\pi r^2}[/tex]
[tex]\\ \sf\longmapsto h=\dfrac{3V}{\pi r^2}[/tex]
Option B
Answer:
[tex] \hookrightarrow \: { \rm{V = \pi {r}^{2} \frac{h}{3} }} \\ [/tex]
• simplify making h the subject:
[tex]{ \rm{3V = \pi {r}^{2} h}} \\ \\ { \boxed{ \boxed{ \rm{h = \frac{3V}{\pi {r}^{2} } \: }}}}[/tex]
HELP. FIND X AND EXPLAIN THE ANSWER
ANSWER CHOICES:
A. x=-3
B. x=4
C. x=48
D. x=29
Answers
Answer:
D. x=29
Step-by-step explanation:
(2x-10)+(4x+16)=180
6x+6=180
6x=174
x=29
The sum of two numbers is
17. Their difference is 41. Find the numbers.
Answers
Answer:
The numbers are 12 and −29.
Mark me as the brainlist
solve the equation show each step
-36 = -3x -4 -5x
Answers
i believe that would be the answer. im sorry if its wrong-
Answer:
4 = x
Step-by-step explanation:
To solve for the value of x
-36 = -3x -4 -5x
Transpose and solve
-36 = -8x -4
-36 + 4 = -8x
-32 = -8x
-32 ÷ -8 =x
Both the negative signs will be cancelled
4 = x
A proportional relationship is shown in the table below: What is the slope of the line that represents this relationship?
Answers
Answer:
Step-by-step explanation: The answer is: 2
7 1/3 or 6 2/3 pls help
Answers
Answer:
7 3/3
Step-by-step explanation:
+3221654236583217089
is it normal to forget things almost 4 months after a concussion?
Answers
Answer:
Yes I've had that too
Step-by-step explanation:
I had mine for about 5-6 months
Answer:
Yes, a concussion can cause long-term memory loss and recurring short-term memory loss, even weeks, months, or years after the head trauma. Usually, this is known as a symptom of post-concussion syndrome
Please help me anyone please ????):
Answers
Answer:
Step-by-step explanation:
man the formula is right there!
two points: (3,2) and (7,5)
[tex]y_2=5\\y_1=2\\x_2=7\\x_1=3\\slope=\frac{5-2}{7-3}=.75[/tex]
Deon plans to ride a 15 mile bicycle trail. If his average speed is 20mi/h, which equation can he use to find the time t, in hours, for the ride?
Answers
Answer
15=20t
Step-by-step explanation:
Answer:
t = 15 / 20
Step-by-step explanation:
Given:
Distance traveled by Deon to ride a bicycle trail = 15 mile
Average speed of Deon to ride a bicycle trail = 20 mi/hour
Step-by-Step:
Let 'T' be the time taken to ride the bicycle trail.
We will use distance speed formula to write the equation to find the time 'T' in hours, for the ride.
[tex]Distance=\frac{Speed}{Time}[/tex]
Distance = 15 miles
Speed = 20 miles / hour
Time = 15 / 20
Assuming time is t, the formula would be:
t = 15 / 20
"t = 15 mi/ 20 mi/hr " will help Deon calculate the time he will take.
Therefore, t = 15 / 20
A number is doubled and then increased by seven. The result is fifty-one. What is the original number?
Answers
Answer: I believe it's 22
Step-by-step explanation:
51 - 7 = 44
If the result is 55 and was increased by 7, you'll subtract 7 from 55 and you'll get 44.
44/2 = 22
To find the number that is doubled and makes up 44, you'll divide 2 from 44 and you'll get 22
My work is already late because I was suppose to turn it in at 9:30 PM sooo like help?
Answers
use double number lines to find the missing number
Answers
Answer:
320
Step-by-step explanation:
80 is 25% of:
ok how we do this is 25% of something is 1/4 of something
so 80 is 1/4 of:
yep, 80 x 4.
80 x 4 is 320, there is your answer!
Yw :D
HELP LAST ATTEMPT ( get marked brainliest show work
Answers
Answer:
D
Step-by-step explanation:
Area of H = 25pi
Area of J = 225pi
225pi/25pi = 9
Three times the sum of a number and 9 is 12 find the number
Answers
Answer:
324
Step-by-step explanation:
9 x 12 = 108 x 3 = 324....yay
12345678910121314151617181920 so i can know answer my question yeet help me
Answers
Answer:
1) 529
2) 20.5
3) 7,216
4) 13238.2
5) 254.75
Step-by-step explanation:
1) Multiplication 2) Subtraction and Addition 3) Addition and Multiplication 4) Subtraction 5) Multiplication and Subtraction
-ROR
Answer:
1) 529
2) 20.5
3) 720.6
4) 13238.2
5) 254.75
Step-by-step explanation:
You either multiply, add, subtract or divide the numbers.