The average speed of a vehicle on a stretch of Route 134 between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function f(t) = 12t − (24sqrt t )+ 34 (0 ≤ t ≤ 4) where f (t) is measured in miles per hour, and t is measured in hours, with t = 0 corresponding to 6 A.M. At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
Answers
The traffic is moving at an average speed of 22 miles per hour at 7 A.M.
To find the time of the morning commute when the traffic is moving at the slowest rate, we need to find the minimum value of the function f(t) over the interval 0 ≤ t ≤ 4. We can find this minimum value by taking the derivative of f(t) and setting it equal to 0, then solving for t.
f(t) = 12t − (\(\sqrt{24}\) t )+ 34
f'(t) = 12 - 12/\(\sqrt{(t)}\)
Setting f'(t) = 0, we get:
12 - 12/\(\sqrt{(t)}\) = 0
12 = 12/\(\sqrt{(t)}\)
\(\sqrt{(t)}\) = 1
t = 1
So the slowest rate of traffic occurs at t = 1, which corresponds to 7 A.M.
To find the average speed of a vehicle at that time, we simply evaluate f(t) at t = 1:
f(1) = 12(1) − (24\(\sqrt{(1)}\)) + 34 = 22
Therefore, the traffic is moving at an average speed of 22 miles per hour at 7 A.M.
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Related Questions
4,956,630,210 – 2,148,913,922 =
Answers
The answer is it equals 2807716288
Amount of daylight each day varies
with the time of the year.
Identify the independent variable.
A
daylight
00
time of year
Answers
The independent variable is time of year
Answer:
The number of daylight hours a city in North America receives each day is dependent
ASAP PLEASEEE HELPPP PLEASEEEE
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
Answers
1) A translation of 3 units down, option D.
2) The vertex moves 3 units down.
3) The new range is y ≥ -3, correct option is C.
Which transformation is applied?For a function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N
In this case, we have:
f(x) = |x|
h(x) = |x| - 3
Then h(x) = f(x) - 3
This is a shift of 3 units down, the correct option is D.
How is the vertex affected?
The vertex is translated 3 units down, like the whole graph of the function.
How is the range affected?
The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:
y ≥ -3.
So the correct option is C.
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Lines L and M are parallel find : m<2
Answers
Answer:
38 I believe let me know if I'm right
Step-by-step explanation:
...
Fencing the compound of a house costs ₹5452. If the rate is ₹94 per metre, find the perimeter of the compound. If the breadth is 10 m, find its length.
Answers
Given that: Fencing the compound of a house costs ₹5452. If the rate is ₹94 . We have to find: Perimeter of the compound and its length Formula used.
We know that, Perimeter of the compound = 2(length + breadth)Also, we know that ,Cost of fencing = Rate x perimeter of the compound Calculation: Given ,Rate = ₹94 per metre Cost = ₹5452Therefore,Perimeter of the compound = Cost of fencing / Rate= ₹5452 / ₹94 = 58 m We know that ,Breadth = 10 m Perimeter of the compound = 2(length + breadth)58 = 2(length + 10)Length + 10 = 29Length = 29 - 10 = 19 meters Therefore, the length of the compound is 19 meters.
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anyone know this question: 16) -8(-21 - 2) - 6
Answers
Answer:178
Step-by-step explanation:
distribute, multiply -8 with - 21 and -2 . that would get you 168 + 16 - 6. add the 168 and 16, it equals 184, then subtracts it with a 6.
There are 20 classes at each of two middle schools. The number of students in each class at each school is shown in the dot plots below.
Number of Students in Each Class at Poplar Middle School
A dot plot titled Number of Students in Each Class at Poplar Middle School. A number line going from 20 to 29 labeled Number of students. There are 3 dots above 20, 5 above 21, 7 above 22, 4 above 23, 1 above 24, and 0 above 25, 26, 27, 28, and 29.
Number of Students in Each Class at Oak Middle School
A dot plot titled Number of Students in Each Class at Oak Middle School. A number line going from 20 to 29 labeled Number of students. There is 1 dot above 20, 2 above 21, 2 above 22, 4 above 23, 3 above 24, 2 above 25, 2 above 26, 2 above 27, 1 above 28, and 1 above 29.
What is the difference between the medians in the dot plots?
0
2
3
5
Answers
Answer:
Im sorry for the idiots that stole points, the answer is B.
Step-by-step explanation:
Answer:
the answer is in fact B but pls dont mark me brainliest or anything like that b/cause i answered second. :)
Step-by-step explanation:
PLEASE HELP WILL AWARD BRAINLIEST:)
Answers
Answer:
x = 4 units
Step-by-step explanation:
By geometric mean theorem:
Length of perpendicular
\( =\sqrt{2\times 6}\)
\( =\sqrt{12}\)
Next, by Pythagoras theorem:
\( x^2 = 2^2 + (\sqrt {12})^2 \)
\( \therefore x^2 = 4 + 12 \)
\( \therefore x^2 = 16 \)
\( \therefore x =\sqrt{ 16 }\)
\( \therefore x =4\: units\)
A trapezoid has bases of lengths 14 and 21. Find the trapezoid's height if it's area is 245
Answers
Answer: 8575/2
Step-by-step explanation:
please show the workings
Answers
Find the answer then round it to (3 sf)
At first the answer will be 35.69050361
Then round to 36.0
Hope this help <3
Help me and mark my answer as brainliest plz
Student A can solve 75% of problems, student B can solve 70%. What is the probability that A or B can solve a problem chosen at random?
Answers
The probability that student A or B can solve a problem chosen at random is 0.95.
Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.
Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:
P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:
P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525
Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925
Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).
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Given: DF and DE are midsegments of ∆ABC Prove: DE= 1/2 AC (PLEASE HELP)
Answers
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Step-by-step explanation:
An elevator in an old building can hold four people at a time. The elevator also has an overall weight limit of 800 pounds. The weight of a group of people in the elevator will be represented by w. Choose ALL inequalities that represent w correctly. A) 4 ≥ w ≤ 0 B) 0 ≥ w ≤ 4 C) w ≤ 0 ≤ 800 D) 0 ≤ w ≤ 800 Eliminate E) 800 ≥ w ≥ 0
Answers
Answer:(D and E)
Step-by-step explanation:I know this because I got it right in usa test prep
Answer:
A and C
Step-by-step explanation: I just took the quizz
In Parallelogram WXYZ, diagonals WY and XZ intersect at Point A. Give WA=x^2-48 and AY=x^2-6x. What is WY?
Answers
We know that in a parallelogram, the diagonals bisect each other. WY is 32
Let's solve the problem step by step using the given terms.
In a parallelogram, the diagonals bisect each other. This means that WA = AY. We are given:
1. WA = x² - 48
2. AY = x² - 6x
Since WA = AY, we can set up the equation:
x² - 48 = x² - 6x
- 48 = - 6x
Now, let's solve for x:
x = 48/6
x = 8
Now, we can find the length of WA:
WA = x² - 48 = 8² - 48
= 64 - 48
= 16
Since WA = AY, AY also equals 16. Now we can find the length of the entire diagonal WY:
WY = WA + AY = 16 + 16 = 32
Therefore, the length of WY is 32.
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A strain of peas has 3 green and one yellow for every four peas. If 12 peas are rendomly selected, what is the probability that exactly 8 peas are green
Answers
The probability that exactly 8 peas are green, from the random selection would be 22. 56 %.
How to find the probability ?This is a binomial probability problem as the probability of an exact likelihood from an event needs to be found.
The relevant formula is:
P ( X = k ) = C ( n , k) x p^ k x q ^( n - k)
Solving for the probability, that exactly 8 peas are green gives:
P ( X = 8 ) = C( 12, 8) x ( 3 / 4 ) ^8 x ( 1 / 4 )^4
P ( X = 8 ) = (12! / ( 8 ! ( 12 - 8 )!) ) x ( 3/4 ) ^8 x ( 1 / 4 ) ^4
P ( X = 8 ) = 0. 2256
P ( X = 8 ) = 22. 56 %
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G(Q) = 5 + 3Q + 202 - Q2 C2(Q) = 3 + 4Q + 2 1. Find the MC function for both C1(Q) AND C2(Q). 2. Find AVC function for both Ci(Q) AND C2(Q). 3. Find AFC function for both C1(Q) AND C2(Q). 4. Find AC function for both Ci(Q) AND C2(Q). 5. Find ATC function for both Ci(Q) AND C2(Q).
Answers
For C1(Q) = 3 - 2Q.
For C2(Q) = 4.
2. The AVC function
For C1(Q) = 5/Q + 3 + 20/Q - Q.
For C2(Q) = 3/Q + 4 + 2/Q.
3. The AFC function
For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)
For C2(Q) = 0.
4. To find the AC function
For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5.To find the ATC function
For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)
For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
Find the ATC functions for C1(Q) and C2(Q) given the provided cost functions?
1. To find the MC function, we take the derivative of the cost functions with respect to Q.
For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.
For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.
2. To find the AVC function, we divide the cost functions by Q.
For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.
For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.
3. To find the AFC function, we subtract the AVC function from the ATC function.
For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)
= 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.
4. To find the AC function, we add the AVC function to the AFC function.
For
C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5. To find the ATC function, we divide the AC function by Q.
For
C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q
= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).
For
C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q
= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
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The trapezoid below has an area of 1,575 cm2.
pg616510
Which equation could you solve to find the height of the trapezoid?
A
850.5h = 1,575
B
1,701h = 1,575
C
45h = 1,575
D
90h = 1,575
Answers
The equation to solve the height of the trapezoid is 45h = 1,575
Given data ,
Let the area of the trapezoid be A
Now , the value of A = 1,575 cm²
And , the Top(base2) = 63cm and Bottom(base1) = 27 cm
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
On simplifying , we get
1,575 = (63 + 27) / 2 x h
1575 = 45h
Hence , the equation is 1575 = 45h
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The complete question is attached below :
The trapezoid has an area of 1,575 cm2, Which equation could you solve to find the height of the trapezoid?
A 850.5h = 1,575
B 1,701h = 1,575
C 90h = 1,575
D 45h = 1,575
Top(base2) = 63 cm
Bottom(base1) = 27 cm
the value of sin^2 30° - cos^2 30° is
Answers
Answer:
-1/2
Step-by-step explanation:
Im not going to go into detail about how to compute sin30 and cos 30, but know that sine and cosine are just the ratios between the sides of a 30-60-90 triangle with a hypothenuse of 1.
With that being said:
sin^2 30 - cos^2 30
= (1/2)^2 - ((sqrt3)/2)^2
= 1/4 - 3/4
= -1/2
Answer:
-1/2
Step-by-step explanation:
Explain two ways to find the LCM
Answers
Answer:
1. List the first several multiples of each number.
Look for multiples common to both lists. ...
Look for the smallest number that is common to both lists.
This number is the LCM.
Find the GCF for the two numbers.
Divide that GCF into the either number; it doesn't matter which one you choose, so choose the one that's easier to divide.
Take that answer and multiply it by the other number.
Step-by-step explanation:
Hope this helps!
pls solve this as soon as possible
Answers
Answer:
x³ - y³ = 0
Step-by-step explanation:
Given : \(\frac{x}{y}+\frac{y}{x}=-1\)
To Find : value of (x³ - y³)
Since, \(\frac{x}{y}+\frac{y}{x}=-1\)
\(\frac{x^2+y^2}{xy}=-1\)
x² + y² = -xy
x² + y² + xy = 0 -----(1)
Since, x³ - y³ = (x - y)(x² + xy + y²) [From the formula, (a³ - b³) = (a -b)(a²+ b² + ab)
= (x - y)(0) {From equation (1)]
= 0
Therefore, value of x³ - y³ = 0 will be the answer.
6.given the density calculated for 1 cm2, what would the estimated population be for an area that is 20 cm by 40 cm in size?
Answers
The estimated population for an area can be Red is 2611.2 and Green is 1894.4 respectively.
Given the population for a 1 cm2 area, the population of a 20 cm by 40 cm area is;
Green = 1894.4 Red = 2611.2
How can you determine the population using the population density?
The following are some probable details for a population density of 1 cm2:
The number of people per 6.25 cm2 is;
Red = 20.4
Green ≈ 14.8
Therefore, the density per 1 cm2 is;
Red = 20.4/6.25 = 3.264
Green ≈ 14.8 = 2.368
Consequently, the inhabitants of a 20 by 40 cm region are;
Red = 3.264 × 20 × 40 = 2611.2
Green ≈ 14.8 = 2.368 = 1894.4
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help if your good at maths
Answers
Answer:
\(\frac{1}{p-s}\)
Step-by-step explanation:
\((p+s)(p^2-s^2)^{-1}\)
\((p+s)\frac{1}{(p^2-s^2)}\)
\(\frac{p+s}{p^2-s^2}\)
\(\frac{p+s}{(p+s)(p-s)}\)
\(\frac{1}{p-s}\)
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x 4 - 81) (x - 3).
Answers
The final polynomial equation after synthetic division is \(x^5-3x^4-81x+243\)
We need to solve;
Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.
The polynomial equation given is;
\(\left(x^4-81\right)\left(x-3\right)\)
By using synthetic division;
⇒ \(x^4x+x^4\left(-3\right)-81x-81\left(-3\right)\)
\(x^5-3x^4-81x+243\)
→ The required final equation in descending powers of x is \(x^5-3x^4-81x+243\) .
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Solve for x.
5(x - 2) = -x + 2
/3
x = [?]
![Solve for x.5(x - 2) = -x + 2/3x = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/tillWZR3U7ERLtDDQkAG8WwhbgKBVWEa.png)
Answers
Answer:
x = 2
Step-by-step explanation:
\(\frac{5(x-2)}{3} = -x + 2\)
expand left side:
\(\frac{5(x-2)}{3} = -x + 2\\\\\frac{5x-10}{3} = -x + 2\)
multiply both sides by 3:
\(3(\frac{5x-10}{3}) = 3(-x + 2)\\\\ =5x - 10 = -3x + 6\)
Add 3x to both sides:
5x - 10 + 3x = -3x + 6 + 3x
8x - 10 = 6
add 10 to both sides:
8x - 10 + 10 = 6 + 10
8x = 16
divide both sides by 8:
8x/8 = 16/8
x = 2
what is the slope of y = -x + 7
Answers
Answer:
slope m = - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 7 ← is in slope- intercept form
with slope m = - 1
Please help ASAP
Question is in picture
Answers
Answer:
A,C,D
Step-by-step explanation:
please I've been stuck to long.
Answers
The equivalent expression to (2² x 3^4)^3 is given as follows:
2^6 x 3^12.
(first option).
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Hence the exponents for this problem are given as follows:
(2²)^3 = 2^6.(3^4)^3 = 3^12.And the simplified expression is of:
2^6 x 3^12.
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find the measure of angle 1
Answers
Answer:
123
Step-by-step explanation:
180-57=123
OK OK ok
Answer:
123°
Step-by-step explanation:
A flat line is 180° so that means 57-180=123 so therefore the angle is 123°
Pls I need help!!!Question 6 (Essay Worn 6 points) (06.03) 9(5x + 1) = 37 From the expression above, pronde an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write 'not present."
Answers
Answer:
5x+1=6.136
5x=6.136-1
5x=5.136
x=5.135/5
x=1.03
x=1
A machine produces 264 bolts in 42 minutes. At the same rate, how many minutes would it take to produce 308 bolts?
minutes
Answers
Answer:
49.6 minutes to create 308 bolts
Step-by-step explanation:
hope this helps :)