A rectangle has a height of 5 and a width of 4x^2-2x-6.Express the area of the entire rectangle. Expression should be expanded.
Answers
Answer:
The area of the entire rectangle is [tex]20x^2-10x-30[/tex]
Step-by-step explanation:
Area of a Rectangle
The area of a rectangle of height H and width W is:
A=H.W
The rectangle has a height of H=5 and a width of [tex]W=4x^2-2x-6[/tex]. Calculate the area:
[tex]A=5*(4x^2-2x-6)[/tex]
Expand the product:
[tex]A=20x^2-10x-30[/tex]
The area of the entire rectangle is [tex]20x^2-10x-30[/tex]
Related Questions
The normal distribution An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that x, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months. Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.)
1. If the manufacturer's assumptions are correct, it would reed to replace _______ of its batteries free.
2. The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of ____ results in a 1.07% replacement rate.
3. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
Answers
Answer:
1) if the manufacturer's assumptions are correct, it would reed to replace 0.62% of its batteries free.
2) a standard deviation of 6.0843 results in a 1.07% replacement rate
3) using the revised standard deviation for battery life, 91.9% of the manufacturer's batteries don't get free replacement but qualifies for the prorated credit
Step-by-step explanation:
based on the given data;
x will represent the random variable such that the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months
so
x → N( U = 45, ∝ = 5.6)
Under the warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charges to the consumer.
if the battery fails after 31 months but within 54 months, the manufacturer provides a prostrated credit towards the purchase of anew battery
1) If the manufacturer's assumptions are correct,
p(x < 3) = p( [x-u / ∝ ] < [ 31-45 / 5.6] )
= p( z < -2.5 )
using the standard normal table,
value of z = 0.0062 ≈ 0.62%
so if the manufacturer's assumptions are correct, it would reed to replace 0.62% of its batteries free.
2)
The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect, so a standard deviation of ? results in a 1.07%
so lets say;
p ( x < 31 ) = ( 1.07%) = 0.0107
p ( [x-u / ∝ ] < [ 31-45 / ∝] ) = 0.0107
now from the standard table
-2.301 is 1.07%
so
( 31 - 45 / ∝ ) = -2.301
-14 / ∝ = -2.301
∝ = -14 / - 2.301
∝ = 6.0843
therefore a standard deviation of 6.0843 results in a 1.07% replacement rate
3)
Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
p( 31 < x < 54 ) = p ( [31 - u / ∝ ] < [ x-u / ∝] < [ 54 - 45 / ∝] )
= p ( [31 - 45 / 6.0843 ] < [ x-u / ∝] < [ 54 - 45 / 6.0843] )
= p ( -2.301 < z < 1.4792 )
= p(Z < 1.5) - p(Z < -2.3)
= 0.9393 - 0.0108
= 0.919 ≈ 91.9%
therefore using the revised standard deviation for battery life, 91.9% of the manufacturer's batteries don't get free replacement but qualifies for the prorated credit
1. To rent a van, a moving company charges $30 plus $0.50 per mile. Write an equation
that represents the cost as a function of the number of miles. What does the slope
represent? Find the cost of the van for 150 miles.
Answers
Answer:
Step-by-step explanation:
Suppose that a tea company estimates that its monthly cost is C(c) = 500x² + 100x and its monthly revenue is R(2) = -0.6x3 + 700x2 – 400x + 300, where x is in thousands of boxes of tea sold. The profit is the difference between the revenue and the cost. What is the profit function, p(X)?
O A. P(x) = 0.6x3- 200x2 + 500x+ - 300
OB. P(x) = -0.6x3 + 1200x2 – 300x + 300
O C. P(x) = -0.6x3 + 200x2 – 500x + 300
D. P(xl = 0.6x3 + 200x2 – 500x + 300
Answers
Answer:
p(x) = 0.6x³ - 200x² + 500x- 300
Step-by-step explanation:
Given the cost function and revenue function as:
C(x) = 500x² + 100x
R(x) = -0.6x³ + 700x² – 400x + 300
To get the profit function:
p(x) = C(x) - R(x)
p(x) = 500x² + 100x -(-0.6x³ + 700x² – 400x + 300)
open the parenthesis
p(x) = 500x² + 100x + 0.6x³ - 700x² + 400x - 300
p(x) = + 0.6x³+500x² - 700x² + 100x+ 400x- 300
p(x) = 0.6x³ - 200x² + 500x- 300
Hence the profit function is expressed as p(x) = 0.6x³ - 200x² + 500x- 300
An oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 25 barrels per day.
Required:
How many additional wells should be drilled to obtain the maximum amount of oil per day?
Answers
Answer:
The additional wells for maximum amount of oil per day is 3 wells.
Step-by-step explanation:
Given;
initial number of wells, n = 6
total production, T = 1800
average production per well, = 1800/6 = 300 barrels per day
Let the additional well = y
total number of wells after optimization = 6 + y
new production per well = 300 - 25y
new total production = (6+y)(300-25y)
t = 1800 - 150y + 300y - 25y²
t = 1800 + 150y - 25y²
dt / dy = 150 -50y
for maximum value, dt/dy = 0
150 - 50y = 0
50y = 150
y = 150 / 50
y = 3
Therefore, the additional wells for maximum amount of oil per day is 3 wells.
33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Given that an oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day, and for each additional well that is drilled, the average production per well decreases by 25 barrels per day, to determine how many additional wells should be drilled to to obtain the maximum amount of oil per day, the following calculation must be performed:
1800 x 6 = 10800 1200 x 30 = 36000 1000 x 38 = 38000 950 x 40 = 38000 900 x 42 = 37800 975 x 39 = 38025
Therefore, 33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Learn more in https://brainly.com/question/13581736
What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(1/3x) + 6?
A. Stretched horizontally and shifted up
B. Stretched vertically and shifted right
C. Compressed vertically and shifted left
D. Compressed horizontally and shifted down
Answers
Answer:
A but im not sure
Step-by-step explanation:
write the number whose prime factorization is give: 2×2×2×7
Answers
Answer:
56
Step-by-step explanation:
Multiply it out 2×2×2×7 = 56
Describe the relationship between the point B (16, 24) and the point
B' (8, 12) in terms of dilations.
(x, y) → ()
Answers
Answer:
(x/2,(y/2)
Step-by-step explanation:
(16/2,24/2)
(8,12)
2x + y = 15
Whats the slope
Answers
Answer:
-2
Step-by-step explanation:
Y = mx+c
M here being the number in front of x
M/x =n-p, x for p ??
Answers
Answer:
the answer is A) X=m/n-p
Step-by-step explanation:
m/x=n-p
n-p=m/X
(n-p)×x=m
X=m/n-p
Construct a table of values for the following functions using the integers from -4 to 4.
a. F(x)=6/x-2
b. r(x)=6x+12/x^-4
Answers
Step-by-step explanation:
Find the table attached
a) Given
F(x) = 6/x-2
When x = -4
F(-4) = 6/-4-2
F(-4) = 6/-6
F(-4) = -1
F(x) = 6/x-2
When x = -3
F(-3) = 6/-3-2
F(-3) = 6/-5
F(-3) = -1.2
F(x) = 6/x-2
When x = -2
F(-2) = 6/-2-2
F(-2) = 6/-4
F(-2) = -1.5
F(x) = 6/x-2
When x = -1
F(-1) = 6/-1-2
F(-1) = 6/-3
F(-1) = -2.0
F(x) = 6/x-2
When x = 0
F(0) = 6/0-2
F(0) = 6/-2
F(0) = -3
F(x) = 6/x-2
When x = 1
F(1) = 6/1-2
F(1) = 6/-1
F(1) = -6
F(x) = 6/x-2
When x = 2
F(2) = 6/2-2
F(2) = 6/0
F(2) = infty
F(x) = 6/x-2
When x = 3
F(3) = 6/3-2
F(3) = 6/1
F(3) = 6
F(x) = 6/x-2
When x = 4
F(4) = 6/4-2
F(4) = 6/2
F(4) = 3
b) Given
r(x)=6x+12/x^-4
When x = -4
r(-4) = 6(-4)+12/(-4)^-4
r(-4) = -24+12/(1/256)
r(-4) = -12(256)
r(-4) = -3072
When x = -3
r(-3) = 6(-3)+12/(-3)^-4
r(-3) = -18+12/(1/81)
r(-3) = -6(81)
r(-3) = -486
When x = -2
r(-2) = 6(-2)+12/(-2)^-4
r(-2) = -12+12/(1/16)
r(-2) = -0(16)
r(-2) = 0
When x = -1
r(-1) = 6(-1)+12/(-1)^-4
r(-1) = -6+12/(1)
r(-1) = -6+12
r(-1) = 6
When x = 0
r(0) = 6(0)+12/(0)^-4
r(0) = 0+12/0
r(0) = 12/0
r(0) = infty
When x = 1
r(1) = 6(1)+12/(1)^-4
r(1) = 6+12/1
r(1) = 18(1)
r(1) = 18
When x = 2
r(2) = 6(2)+12/(2)^-4
r(2) = 12+12/1/16
r(2) = 24(16)
r(2) = 384
When x = 3
r(3) = 6(3)+12/(3)^-4
r(3) = 18+12/1/81
r(3) = 30(81)
r(3) = 2430
When x = 4
r(4) = 6(4)+12/(4)^-4
r(4) = 24+12/1/256
r(4) = 36(256)
r(4) = 9216
We want to construct tables of values for the two given functions.
The tables are:
a)
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b)
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
A table will be something like:
[tex]\left[\begin{array}{ccc}x&y\\-4&\\-3&\\-2&\\-1&\\0&\\1&\\2&\\3&\\4&\end{array}\right][/tex]
Where the values of x go from -4 to 4.
To complete the tables, we just need to evaluate the functions in each one of the x-values at the left, and the outcome will be placed at the right.
a) f(x) = 6/x - 2
Now we just need to evaluate the function in all the given points:
f(-4) = 6/(-4) - 2 = -3/2 - 4/2 = -7/2
f(-3) = 6/-3 - 2 = -4
f(-2) = 6/-2 - 2 = -5
f(-1) = 6/-1 - 2 = -8
f(0) is undefined, as we can't divide by zero, here we can write NaN (Not a number).
f(1) = 6/1 - 2 = 4
f(2) = 6/2 - 2 = 1
f(3) = 6/3 - 2 = 0
f(4) = 6/4 - 2 = -1/2
Now we put all of these in the correspondent place of the table:
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b) We do the same thing, here we have:
r(x) = 6*x + 12/x^-4 = 6*x + 12*x^4
Now we evaluate this in the given values:
r(-4) = 6*(-4) + 12*(-4)^4 = 3,048
r(3) = 6*(-3) + 12*(-3)^4 = 954
r(-2) = 6*(-2) + 12*(-2)^4 = 180
r(-1) = 6*(-1) + 12*(-1)^4 = 6
r(0) = 6*0 + 120^4 = 0
r(1) = 6*1 + 12*1^4 = 18
r(2) = 6*2 + 12*2^4 = 204
r(3) = 6*3 + 12*3^4 = 990
r(4) = 6*4 + 12*4^4 = 3,096
Now we place these values in the correspondent place on the table:
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
These are our two tables.
If you want to learn more, you can read.
https://brainly.com/question/8629807
a. Suppose a BMW dealer in Fullerton, CA is trying to calculate the probability of his car sale for next week. The dealer knows that the sale of car is normally distributed with mean 50 and variance 9. The variance 9 was calculated from the weekly car sale data of 20 weeks, as the population variance is not known to the dealer. What is the probability that the dealer will sell 51 or more cars next week? (Hint: use t distribution) (15)
Answers
Answer:
0.45576
Step-by-step explanation:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
Standard Deviation = √variance
Mean = 50
= √9
= 3
z = 51 - 50/3
= 0.11111
Probability value from Z-Table:
P(x<51) = 0.54424
P(x>51) = 1 - P(x<51)
= 1 - 0.54424
= 0.45576
The probability that the dealer will sell 51 or more cars is 0.45576
In 2001, a school population was 1696. By 2007 the population had grown to 2614.
1) How much did the population grow between the year 2001 and 2007?
students
2) How long did it take the population to grow from 1696 students to 2614 students?
years
3) What is the average population growth per year?
students/year
4) What was the population in the year 2000?
students
5) Find an equation for the population,
P
, of the school
t
years after 2000.
P
=
6) Using your equation, predict the population of the school in 2011.
students
Answers
Answer:
grew by 6
Step-by-step explanation:
Most new buildings are required to have a ramp for the handicapped that has a maximum vertical rise of 11 feet for every 132 feet of horizontal distance.
Answers
Answer:
11/132 = 1/12
Step-by-step explanation:
just put the rise over the run and simplify
find the number of terms in the arithmetic sequence
-7,-5.6,-4.2,-2.8,1.4,...,103.6
Answers
Answer:
80
Step-by-step explanation:
use the formula of arithmetic progression
The distance from a point to two is five units. The point could be located at
-7
-6
6
-3
NEXT QUESTION
O ASK FOR HELP
Answers
Answer:
The correct answer is -3
Step-by-step explanation:
attached is a number line to show diagrammatically how to count five units from the chosen point to point 2 on a number line.
Moving five units from -3 to 2 on a number line is given as follows:
-3 ⇒ -2 ⇒ -1 ⇒ 0 ⇒ 1 ⇒ 2
From the motion expression shown above, moving from -3 to 2 involves moving 5 units.
another way of determining the correct answer is to find the difference in interval between the two points as shown below:
Let the point be x
2 - x = 5 units
2 - 5 = x
∴ x = -3
Answer:
-3
Step-by-step explanation:
it was on quiz baby
Can someone help me with number 1 and 2
Answers
The first one is 2 hundredths and the second one is 800+60+3. 01 + 004 +0001
Rico's T-shirt Company sells customized short sleeve T shirts, long sleeve T-shirts, and sweatshirts. Each type of shirt sells in multiples of 5. It costs $25.00 for 5 short sleeve T-shirts, $30,00 for 5 long sleeve T-shirts, and $40.00 for 5 sweatshirts Short sleeve and long sleeve T shirts can be made in any color except navy or black Sweatshirts are only made in navy and black.. Mercedes bought green shirts for $55.00.. Quinn bought 10 navy sweatshirts, Rachel paid $30.00 for several red shirts, Hector bought black and yellow shirts for $65.00. Use the axioms to make three conclusions about the shirts sold.
Answers
Answer:
Hector purchased 5 black sweatshirts at $40, and 5 yellow short sleeve shirts at $25. He spent $65 in total.
Rachel purchased 5 red long sleeves shirts at $30.
Mercedes purchased 5 green short sleeve shirts at $25 and 5 long sleeve shirts at $30. She spent $55 in total.
Quinn purchased 10 navy sweatshirts and spent $80 in total.
which numerical pattern in nonlinear?
A. 3, 11, 19, 27,
B. 1, 3, 9, 27
C. 1, 4, 7, 10,
D. 2, 3, 4, 5
Answers
Answer:
I am going with B.1,3,9,27
Step-by-step explanation:
A,C and D the patterns are from addition ie. A +8, C+3 and D +1 but B it's ×3
please help me with this question
Answers
Answer:
2c^2
Step-by-step explanation:
c3-c1=c2
d2-d2=0
8/4=2
Find the exponential function that satisfies the given conditions: initial value = 70, decreasing at a rate of 0.43% per week
Answer choices:
A) f(t) = 70 x 0.9957^t
B) f(t) = 70 x 1.43^t
C) f(t) = 0.43 x 0.3^t
D) f(t) = 70 x 1.0043^t
Answers
Answer:
a- just took the test
Step-by-step explanation:
Multiply: -12y(y - 6) Enter the correct answer.
Answers
(-12y x y) -(-12y x -6)
= 12y^2 +72y
-18+-6 please help
Answers
Answer:
-24
Step-by-step explanation:
If you are struggling with this here's a tip!
-18+-6 is what you are trying to solve
The 6 is negative, so get rid of the plus sign -18-6
2 negative numbers are just added like positive numbers
So add 18 and 6, you should get 24
Don't forget about the negative!
-24
y/15- 2/3= 4/5
Whats the answer for y
Answers
-3/7 % -1/2 =??
What is the answer to this equation
Answers
Answer:
-0.21428571428
How to solve this without calculator?
sin-1(2/3)
Answers
Answer:-0.560
Step-by-step explanation:
Find the slope of the line
graphed below.
Answers
Answer:
[tex]\frac{3}{5}[/tex] or 0.6
Step-by-step explanation:
This problem requires the slop formula which is [tex]\frac{y2-y1}{x2-x1}[/tex]
You start with the first point which is (-1,1). This will be x1 and y1.
The next point is (4,4). This will be x2 and y2.
You plug these values into your equation which gives you [tex]\frac{4-1}{4-(-1)}[/tex]
To solve, you evaluate, [tex]\frac{4-1}{4-(-1)}[/tex] = [tex]\frac{3}{5}[/tex] or 0.6
If y is 20, what is x?
Answers
When y=20 , x is −5.
Answer:
Depends on the formula given
find the measures of angles 1, 2, and 3
Answers
x = 33°
Then :-
m∠1 = 33° ( angle x and angle 1 are corresponding angles on a transversal )
Which means :-m∠1 + m∠2 = 90° ( angle 1 and angle 2 are complementary angles )
33 + ∠2 = 90
∠2 = 90 - 33
m∠2 = 57°
Then :-m∠1 + m∠3 = 180° ( angle 1 and angle 3 are a linear pair )
33 + ∠3 = 180°
∠3 = 180 - 32
m∠3 = 147°
Therefore , m∠1 = 33°m∠2 = 57° m∠3 = 147°What is the goal of solving equations?
Answers
Answer:
The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, we must reverse the operations acting on the variable.
Step-by-step explanation:
The objective or equation would be to acquire the variables independently. A further explanation is provided below.
The objective is to address an expression by getting the component solely on a single side of this argument as well as a figure while on the other side of the same expression.Throughout the order to isolate variables, procedures that influence somewhat on variables have to be reversed. We achieve this by carrying out several halves of the expression the opposite of every process.
Learn more about equations here:
https://brainly.com/question/20989555
A worker at one farm is paid $486 for the week, plus $0.03 for every pound
of apples she picks. At another farm, a worker is paid $490 for the week, plus
$0.02 for every pound of apples. For how many pounds of apples are the workers
paid the same amount?
Answers
Answer:sorry this probably is t the most helpful but the closest i could get was 399 lbs. it’s is st$497.7 for one and $$497.8.
Step-by-step explanation: