a) The average rate of change on that interval is 0.1
b) as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1
How to find the average rate of change on the given interval?For any function f(x), the average rate of change on an interval (a, b) is given by:
(f(b) - f(a))/(b - a)
In this case, the function is:
F(x) = −0.005x^2 + 0.8x + 12
And the interval is [60, 80]
Then we have:
F(60) = −0.005*60^2 + 0.8*60 + 12 = 42
F(80) = −0.005*80^2 + 0.8*80 + 12 = 44
Then the average rate of change on that interval is:
R = (44 - 42)/(80 - 60) = 0.1
b) What does that rate means?
F(x) relates the fuel economy and x the speed of the vehicle.
This means that as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1.
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A truck driver is driving on an interstate and is about 150 miles from his planned exit. He is traveling at a speed of 50 miles per hour and plans to stop for a rest within 30 miles of the exit on either side. Find the minimum and maximum numbers of hours the truck driver will drive before stoping for a rest.
The minimum and maximum numbers of hours the truck driver will drive before stoping for a rest will be 3.6 hours and 2.4 hours respectively.
How to illustrate the information?From the information, the truck driver is driving on an interstate and is about 150 miles from his planned exit and he is traveling at a speed of 50 miles per hour and plans to stop for a rest within 30 miles of the exit on either side.
Therefore, the appropriate equation be:
50h - 150 = 30
50h = 30 + 150
50h = 180
Divide
h = 180 / 50
h = 3.6 hours.
The minimum hours will be:
50h = 150 - 30
50h = 120
h = 120/50
h = 2.4 hours.
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Find the equation of the plane that goes through three points:
A (0, 3, 4)
B (1, 2, 0)
C (-1, 6, 4)
I know there are good algorithms to do this problem with, and I've gotten 6x - 2y + z = -2 as my answer, which is correct to my knowledge.
HOWEVER...the teacher wants to go with a three-variable, three-equation system of equations with the format of z = m(x) + n(y) + c for each point.
That would mean the following equations:
4 = m(0) + n(3) + c
0 = m(1) + n(2) + c
4 = m(-1) + n(6) + c
I'm confused as to why anyone would want us to use a system.
How do I proceed from here to get the same answer as the algorithm got?
The equation of the plane that goes through these points is:
6x + 2y + z = 10.
How to find the equation of a plane given three points?The equation of the plane is found replacing the points into the following equation:
ax + by + c = z.
For point A, we have that:
3b + c = 4.
For point B, we have that:
a + 2b + c = 0.
For point C, we have that:
-a + 6b + c = 4.
Hence the system is:
3b + c = 4.a + 2b + c = 0.-a + 6b + c = 4.From the first equation, we have that:
c = 4 - 3b.
Replacing in the second, we have that:
a + 2b + 4 - 3b = 0
a - b = -4.
Replacing in the third, we have that:
-a + 6b + 4 - 3b = 4.
-a + 3b = 0.
a = 3b.
We have that a - b = -4, hence:
3b - b = -4
2b = -4
b = -2.
a = 3b, hence a = -6.
c = 4 - 3b -> c = 10.
Hence the equation is:
ax + by + c = z.
z = -6x - 2y + 10
6x + 2y + z = 10.
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How do you solve this?
The measures of the angles are:
m<7 = 47°
m<8 = 62°
m<1 = 62°
m<2 = 71° [vertical angles theorem]
m<5 = 109°
m<3 = 109°
m<4 = 35°
m<6 = 29°
What is the Alternate Interior Angles Theorem?The alternate interior angles theorem states that two interior angles that are formed along a transversal and lie alternate to each other on two parallel lines are congruent to each other.
Measure of angle 7 = 47° [based on the alternate interior angles theorem]
Measure of angle 8 = 180 - 47 - 71 [triangle sum theorem]
Measure of angle 8 = 62°
Measure of angle 1 = measure of angle 8 = 62° [based on the alternate interior angles theorem]
Measure of angle 1 = 62°
Measure of angle 2 = 71° [vertical angles theorem]
Measure of angle 5 = 180 - 71 [linear angle theorem]
Measure of angle 5 = 109°
Measure of angle 3 = measure of angle 5 = 109° [vertical angles theorem]
Measure of angle 4 = 180 - measure of angle 3 - 36 [linear angle theorem]
Measure of angle 4 = 180 - 109 - 36
Measure of angle 4 = 35°
Measure of angle 6 = 180 - measure of angle 5 - 42 [linear angle theorem]
Measure of angle 6 = 180 - 109 - 42
Measure of angle 6 = 29°
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Question 20 (5 points) The Torre Company has the following stockholders' equity account balances in stockholders equity on December 31. Common Stock - $5 par, 60,000 shares issued 340,000 Paid-In Capital in Excess of Par-Common Stock 650,000 Preferred Stock - $100 par, 5,000 shares issued 590,000 Paid-In Capital in Excess of Par-Preferred 120,000 Retained Earnings 240,000 Treasury Stock (cost-$10 per share) 120,000 If net income for the year was $110,000 and a preferred stock dividend of $30,000 was paid, what was the beginning value of retained earnings?
According to the solving the beginning value of retained earnings:
= $1,60,000.
What is retained earnings?Retained earnings are usually included in the shareholders' equity portion of a company's balance sheet. Retained earnings are computed by adding beginning-period retained earnings to net income (or loss), then deducting dividend distributions.
How do I figure up my retained earnings?To calculate retained earnings, subtract a company's liabilities from its assets to obtain stockholder equity, then locate the common stock line item on your balance sheet and multiply the total stockholder equity by the common stock financial statement figure (if the only two items in your stockholder equity were also common stock).
According to the given data:Retained earnings, ending = $240,000.
Net income = $110,000.
Preferred stock dividend = $30,000.
Retained earning, beginning = ?
Retained earnings, ending = Retained earning, beginning + Net income - Preferred stock dividend
$240,000 = Retained earning, beginning + 110,000 - 30,000
Retained earning, beginning = 1,60,000
According to the solving the beginning value of retained earnings:
= $1,60,000.
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Teresa has a total of 13 coins.
None of them are pennies, and she has at least three each of quarters, dimes, and nickels.
What is the least amount of money she can have?
Answer: $0.65
Step-by-step explanation:
She can have all nickels since at least 3 nickels means that there is a possibility that all 13 of her coins are nickels.
100 cents=1 dollar
Nickel=5 cents
5 cents * 1 dollar/100 cents=
5*1/100=0.05 dollars
Hence, the least total amount of money she could have is:
13*0.05=$0.65
This is equivalent to 140 cents.
==========================================================
Explanation:
"she has at least three each of quarters, dimes, and nickels"
Let's say she has exactly 3 of each for now
3 quarters = 3*25 = 75 cents3 dimes = 3*10 = 30 cents3 nickels = 3*5 = 15 centsSo far she has 75+30+15 = 120 cents (aka $1.20) with the 3*3 = 9 coins mentioned. There are 13-9 = 4 coins remaining
To achieve the least money possible, those missing four coins must be the smallest denomination allowed, i.e. the nickel. We can't go for penny since it states "none of them are pennies". So we add 4*5 = 20 more cents onto 120 to get 120+20 = 140 cents aka $1.40
Calculate the finance charge for a credit card that has given the average daily balance and interest rate. (Round your answer to the nearest cent.) average daily balance: $118.18, monthly interest rate: 1.15%
The finance charge for a credit card that has given the average daily balance and interest rate is 11.170$.
What is finance charge?The finance charge is the cost of credit in dollars. It is calculated on a credit card's unpaid balance. A finance charge, the cost of having the debt a longer time, is added to the outstanding credit card balance.
Given:
Average daily balance: $118.18,
monthly interest rate: 1.15%
According to given question we have
A common way of calculating a finance charge on a credit card is to multiply the average daily balance by the annual percentage rate (APR) and the days in your billing cycle. The product is then divided by 365 .
i.e
[tex]\frac{118.18*1.15*30}{365} \\=11.170[/tex]
Therefore, the finance charge for a credit card that has given the average daily balance and interest rate is 11.170$.
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What is the image of the point
(−9,7) (−9,7) after a rotation of 180∘
counterclockwise about the origin?
The image of the point (-9,7) after a rotation of 180 counterclockwise about the origin is at (9, -7).
What is Dilation?Dilation is a process for creating similar figures by changing the size.
What is the rotation of a point counterclockwise about the origin?Rotation of a point P(x, y) 180 counterclockwise about the origin produces an image at P'(-x, -y).
Here, the point counterclockwise about the origin → (-(-9), -7).
Therefore, the image of the point (-9,7) after a rotation of 180 counterclockwise about the origin is at (9, -7).
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Given the graph below, determine the correct translation rule.
a. (x, y) → (x - 5 , y + 1)
b. (x, y) → (x + 1, y - 5)
c. (x, y) → (x - 1, y + 5)
d.(x, y) → (x + 5, y - 1)
2) a) If the function f(x) = |x| is changed to g(x) = 3|x-1| +3,
how is the graph transformed? (left, right, up, down? By how much?)
b) On the blank graph, graph the function g(x) = 3 |x-1| +6
8
6
21
-10 -8 6-4-2 2468
-24
7
f
8
Step-by-step explanation:
a) right - 1 unit; up - 3 units; angle between branches is decreased. All the details are in the attachment;
b) the required graph is in the attachment.
Point W (-2,4) from square WXYZ is translated 4 units right. What are the coordinates for W’ ?
Answer:
W' (2, 4 )
Step-by-step explanation:
a translation of 4 units right means add 4 to the x- coordinate, that is
W (- 2, 4 ) → W' (- 2 + 4, 4 ) → W' (2, 4 )
Evaluate the expression when a = 3 and c = -4.
-a+7c
Answer: -31
Step-by-step explanation:
a = 3 and c = -4.
-a+7c = -3+(7*-4) = -31
Answer:
- 3 + 7(- 4)
- 3 + - 28
= - 31
Hope this helps :)
3^4 x 10^6
What is the answer ??
cia
Mat
Scien
Simplify the expression 4a + b - 7+ b + a - 3.
7a + 2b - 4
5a + 2b - 4
5a + 2b - 10
за - 10
Answer:
the answer would be 5a+2b-10
The Earth’s total land area is 57,308,738 square miles. The land area of North America is about 16.5% of this total. Estimate the land area of North America. Describe your strategy.
The land area of North America is 9,455,941.77 square miles.
What is the land area of North America?Percentage can be described as the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to represent percentages is %.
In order to determine the land area of North America, multiply the total land area of the Earth by the percentage of the land area of North America.
Land area of North America = percentage of the land area of North America x total land area
16.5% x 57,308,738
0.165 x 57,308,738 = 9,455,941.77 square miles
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mario se fue de compras con 90 soles los cuales gasto de la siguiente manera en chompas gasto el doble que en camisas y en pantalones gasto el triple que en camisas¿ caunto gasto en pantalones?
The amount spent on pants based on the information illustrated is 45 soles.
How to calculate the value?Let the amount spent of shirt = x
Amount spent on sweaters = 2x
Amount spent on pants = 3x
Amount spent = 90
Therefore, the value will be:
x + 2x + 3x = 90
6x = 90
Divide
x = 90/6
x = 15
Therefore, the amount spent on pants will be:
= 3x
= 3 × $15
= 45 soles.
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Solve for h.
V=1/3bh
Answer:
h = 3V /b
Step-by-step explanation:
V=1/3bh
Solve for h
Multiply each side by 3
3V = 3*1/3bh
3V = bh
Divide each side by b
3V/b = bh/b
3V /b = h
h = 3V /b
Answer:
[tex]3v = bh \\ bh = 3v \\ h = \frac{3v}{b} [/tex]
write the answer from top to bottom
Answer:
b
Step-by-step explanation:
state 3 fractors other than $/ hours
True or false is zero is subtracted from an integer the result is the integer
[tex] \chi - 0 = \chi \\ 2 - 0 = 2 \\ y - 0 = y\\ .....[/tex]
TrueAny number take away zero, is still that number.
Simplify −3(5x + 1) + completely. 8 16(x − 9)
The expression is simplified to x - 147
What are algebraic expressions?Algebraic expressions are defined expressions made up of terms, factors, variables, constants , coefficients.
They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc.
Given the expressions;
−3 (5x + 1) + 16(x − 9)
First, we have to expand the bracket
-15x -3 + 16x - 144
collect like terms, we have;
-15x + 16x - 144 - 3
Add or subtract like terms as seen in the expression
x - 147
Note that the expression is simplified to x - 147
Thus, the expression is simplified to x - 147
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it takes 4 cans of paint to paint 1/3 of a room. How many cans of paint do I need to paint 1 room? Solve using a strip diagram
The number of cans of paint which it would take to paint one given the premise that; it takes 4 cans of paint to paint 1/3 of a room is; 12 cans of paint.
What is the number of cans that would be required to paint one room given the premise as in the task content?It follows from the task content that the number of cans of paint that would be required to paint one room according to the task content be determined.
Hence, since it takes 4 cans of paint to paint 1/3 of a room.
Hence, since there are 3 One-thirds in a whole, it follows from proportion that the number of cans of paints required is;
= 3 × 4 cans of paint
= 12 cans of paint.
The number of cans of paint which it would take to paint one given the premise that; it takes 4 cans of paint to paint 1/3 of a room is; 12 cans of paint.
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Muscles Gym has a rack of hand weights. There are four hand weights that weigh 5 pounds each. What is the area of the side of the hand weight shown ?
Answer:
21 7/8 in^2
Step-by-step explanation:
explantation up top
Find the equation of the containing the points (3,0) that is perpendicular to the line y=-3/4x+1
The equation containing the point (9,12) is y = 4/3x.
What are equations?An equation is a mathematical expression that includes the equals sign. Algebra is frequently used in equations. When you don't know the exact number in a calculation, you use algebra. Many professionals, including air traffic controllers, architects, computer programmers, and carpenters, use equations on a daily basis.So, perpendicular = m1 × m2 = -1:
Now,
- 3/4 × 4/3 = -1y = 4/3x + b10 = 1/3(9) + b12 = 12 + bb = 0y = 4/3x + 0y = 4/3xTherefore, the equation containing the point (9,12) is y = 4/3x.
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The correct question is given below:
Find the equation of the line that is perpendicular to y = -3/4x+1 and contains the point (9,12).
Two points have the same y-coordinate but opposite x-coordinates. Which is a possible graph of these points?
The possible graph for two points have the same y-coordinate but opposite x-coordinates is shown below.
In a general point (x,y) , the value x represents the distance from origin to point along x - axis,
and
the value y represents the distance from origin to point along y axis.
It is given in the question that
There are two points in which the y coordinate of both the points is same
the x coordinate is of opposite signs.
Let us take an Example
let the points be A(a,b) and B(c,d)
According to the question
b = d and -a = c
So the points will become (a,b) and (-a,b)
For Example ;
let a=2, b=3
the two points will become (2,3) and (-2,3).
Therefore , the possible graph of these points is shown below .
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1/3 x 3/5 = hgggbbbhbh
Answer:
14/15
Step-by-step explanation:
im so confused on this (help ASAP)
Answer:
x = 4
Step-by-step explanation:
Perimeter of triangle: P = (5x -1) + (5x -1) + (2.2x + 10)
Perimeter of square: P = 4(6.5x - 11.8)
so (5x -1) + (5x -1) + (2.2x + 10) = 4(6.5x - 11.8)
5x - 1 + 5x - 1 + 2.2x + 10 = 26x - 47.2
12.2x + 8 = 26x - 47.2
26x - 12.2x = 8 + 47.2
13.8x = 55.2
x = 55.2/13.8 = 4
3.007 as a fraction?
Decimal > Fraction
Answer:
3 7/100
Step-by-step explanation:
3007/1000 = 3 7
1000
dont mind the answer I put thank y’all!!
Answer:
your right
Step-by-step explanation:
the answer is k and l thats right pls mark brainliest
or hit the thanks button!!!!!!!
pls and thank you!
Part 1: Use complete sentences to explain why solar flares occur.
Part 2: Give two examples in which solar flares impact Earth.
Some consequences of solar flares on Earth are: radio blackouts, intense auroras, damage to communication satellites, among others.
What is a solar flare?A solar flare is a term that refers to a sudden and intense release of electromagnetic radiation in the Sun's Chromosphere. In general, what happens in a solar flare is that the plasma is heated to tens of millions of degrees kelvin; this accelerates electrons, protons, which in turn produces electromagnetic radiation in all wavelengths of the electromagnetic spectrum.
How do solar flares impact the Earth?Strong solar flares can cause different manifestations on Earth such as:
By sending huge clouds of plasma into space that hit the Earth they can cause geomagnetic storms and intense auroras.Some larger waves can trigger radio blackouts.Some waves can cause power outages and damage communication satellites.Some waves can damage electronic equipment and the equipment of astronauts or passengers on high-flying aircraft.Learn more about solar flares in: https://brainly.com/question/2886237
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Which of the following numbers has an odd number of factors
A) 12
b) 24
c) 36
d) 48
what is the value of the algebraic expression if x=1/2, y -1, and z=2?
The value of the given algebraic expression 6x(y²z) is (D) 6.
What are algebraic expressions?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions. 2(x + 8y) is an algebraic expression, for example.So, substitute the values of x, y, and z in the given expression:
6x(y²z)
When x = 0.5, y = -1 and z = 2
= 6(0.5)((-1)²)(2)= 3(1)(2)= 6Therefore, the value of the given algebraic expression is (D) 6.
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The complete question is given below:
What is the value of the algebraic expression if x= 1/2 , y = -1, and z = 2? 6x(y²z)
A. -12
B. -6
C. 1
D. 6
