Answer:A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is: f(x)=4x3- 72 x2+320x
The first step to factor it is to extract common factor 4x: f (x)=4x(x2-18=80)
The second step is to factor the quadratic trinomial.
That is made by writing it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is: f(x)=(4x)(x-10)(x-8)
Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
x is the desired (unknown) length
4x is 4 times the desired length
x - 10 is 10 less than the desired length
x - 8 is 8 less than the desired length
Thus, the volume of the prism is the product of the three factors:
Volume = (4x)(x-10)(x-8)
-7r^2= -329 square root property
9514 1404 393
Answer:
r = ±√47
Step-by-step explanation:
-7r^2 = -329 . . . . given
r^2 = 47 . . . . . divide both sides by -7 (multiplication property of equality)
r = ±√47 . . . . square root both sides (square root property of equality)
Answer:
This is what I got.
Step-by-step explanation:
For what value of z would the following system of
equations be true for all real integers?
3x-2y = 14
-12x+8y = 8z
9514 1404 393
Answer:
z = -7
Step-by-step explanation:
The equations will be true for all real integers when they are a dependent set. That will be the case when the second equation is a multiple of the first.
Already, we observe that the ratios of x- and y-coefficients are -4:
-12/3 = -4
8/-2 = -4
The equations will be dependent when the constants have that same ratio:
8z/14 = -4 . . . . desired ratio
8z = -56 . . . . . multiply by 14
z = -7 . . . . makes the equations true for all real numbers
_____
Comment on the question
The system of equations can be made inconsistent (no solutions) or consistent & dependent (infinite solutions) by the choice of z.
However, integer solutions are limited to pairs of the form (2n+2, 3n-4) for integer values of n. The values of x and y are not "all real integers".
Consequently, we have interpreted the question to be asking for the value of z that will make the system of equations have an infinite number of solutions, including both rational and irrational, real and complex values of x and y. They cannot be made to be true for "all real integers" by any choice of z.
Answer:
z = -7 is the answer.Step-by-step explanation:
#CarryOnLearningThe staff commute to work in different ways 2/5 drive, 4/15 catch the bus and 1/3 cycle
order the fractions starting with the largest
Answer:
2/5, 1/3 4/15
Step-by-step explanation:
3x2/5=6/15
5x1/3=5/15
4/15
Correct order:
2/5; 1/3; 4/15
The times that a cashier spends processing individual customers' orders are independent random variables with mean 4.5 minutes and standard deviation 4 minutes. Find the number of customers n such that the probability that the orders of all n customers can be processed in less than 2 hours, is approximately 0.1. (Round your answer to the nearest integer.)
Answer:
n is approximately 29 customers
Step-by-step explanation:
The given parameters are;
The mean duration of an order, μ = 4.5 minutes
The standard deviation, σ = 4
2 hours = 120 minutes
We get;
The z-score when the probability, P = 0.1 is P(z < 0.53983)
We have;
[tex]z = \dfrac{\dfrac{ \sum X_i}{n} - \mu_{\overline x}}{\dfrac{\sigma}{\sqrt{n} } }[/tex]
Therefore, we get;
[tex]z = \dfrac{\dfrac{120}{n} - 4.5}{\dfrac{4}{\sqrt{n} } } = 0.53983[/tex]
[tex]\dfrac{4}{\sqrt{n} } \times 0.53983 = \dfrac{120}{{n} } -4.5[/tex]
With the aid of a graphing calculator, we get;
81·n²-4320·n + 57600 - 18.6506514278·n = 0
Factorizing gives;
(n - 24.3011921023)·(n - 29.2623961869)·81124141329 = 0
Therefore;
n ≈ 24 or n ≈ 29
Therefore, we take the largest number, n ≈ 29, to make the sample approximately normal
What is the perimeter of the square below ?
5 inches
Answer: Where is the square?
Step-by-step explanation:
Heavy general purpose trucks are often used in pipeline operations. They are built to hold up when carrying or pulling substantial loads, and yet still be suitable for regular highway use. A new truck with appropriate options is purchased for $47,000. It is estimated to have a useful life of 5 years and a salvage value of $2,900 at that time.
Required:
Develop a table showing the depreciation.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Purchase price= $47,000
Salvage value= $2,900
Useful life= 5 years
To calculate the annual depreciation, we need to use the following formula:
Annual depreciation= (original cost - salvage value)/estimated life (years)
Annual depreciation= (47,000 - 2,900) / 5= $8,820
The accumulated depreciation is calculated as follow:
Accumulated depreciation= years of depreciation*annual depreciation
For year 4:
Accumulated depreciation= 8,820*4= $35,280
Finally, the book value is:
Book value= purchase price - accumulated depreciation
Year Annual depreciation Accumulated depreciation Book value
1 8820 8820 38180
2 8820 17640 29360
3 8820 26460 20540
4 8820 35280 11720
5 8820 44100 2900
Please someone help me i need this to pass!
Answer:
Step-by-step explanation:
subtrct 2 from every x co-ordinate and add 7 to every y co-ordinate.
Can you help me with this please??
Answer:
.8
Step-by-step explanation:
.8 is the largest
You deposited 750 in an account that pays 5% interest compounded quarterly. How many years do you have two wait until it becomes at least ten times as much? Round answer to the nearest whole year.
A. 47
B. 46
C. 45
D. 48
Simplify the following expression: 7(2x+ 6y)
Answer:
7(2x+ 6y) = 14x + 42y
Step-by-step explanation:
give brainllest plz
A person is standing on the equator of Earth (radius 3960 miles). What are his linear and angular speeds?
Answer:
Linear speed =ωr=2π/86400×3960=11π/120 miles/s.
Step-by-step explanation:
The linear speed and angular speed will be 1036.73 miles / hour and 0.26 radian / hour.
It is given that radius of equator of earth is 3960 miles.
We have to find the linear and angular speeds.
What do you mean by the linear speed ?
The linear speed of a point on the object is equal to the angular speed (ω) multiplied by the distance r.
As per the question ;
radius of equator of earth = 3960 miles
The linear speed will be ;
s = rθ / t
We know that ; at any point of equator would complete 360° or 2π radians revolutions every 24 hours.
So ;
s = (3960 miles × 2π) / 24 hour
s = 330π miles / hour
s ≅ 1036.73 miles / hour
And
The angular speed will be ;
ω = s / r
ω = 1036.73 / 3960 minutes
ω = 0.26 radian/hour
Thus , the linear speed and angular speed will be 1036.73 miles / hour and 0.26 radian / hour.
To learn more about linear and angular speed click here ;
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Need help asap
dadadadadadadadasdasdasd
Answer: -3/5
Step-by-step explanation: -3^3 is 27 and 5^3 is 125. So when you find the cube root of this equation you just simplify it to that.
what solid can be folded from the net?
Answer:
I think it is triangular prisim
Answer:
Triangular prism
Step-by-step explanation:
PLZ HELP THIS IS DUE TODAY AND PLZ NO LINKS.
Answer:
a - they should be large and sturdy
Step-by-step explanation:
The article states that artificial reefs can be made from materials such as concrete, or large pieces of waste such as subway cars, takes, and aircraft carriers. All of these items are large and sturdy.
Hope this helps, have a wonderful day :))
Write the ratio for tan A.
A
25
22
B
Answer:
list
tan (A)=
A=
25=
22=
B=
Step-by-step explanation:
Enter the appropriate value to answer the question or solve the problem.
What is the value of x in the triangle below?
65°
to
75°
Answer:
x = 40 degrees
Step-by-step explanation:
Triangle angle sum is 180 so 180 = 65 + 75 + x.
180 = 65 + 75 + x
180 = 140 + x
40 = x
Simplify 4 − 2(3 − ) + 5
I’m confused on questions 2 3 and 4
Answer:
x = 20
Step-by-step explanation:
60 = x+40
subtract 40 from both sides and you get
20 = x
so x = 20
13. Pls help thank you
No work necessary
A, B, C, or, D ?
Answer: C
Step-by-step explanation:
PLEASE HELPPP!!!!!!!!
Answer:
A
Step-by-step explanation:
If you get that right, follow Sammy Revv on Spotify please
Solve this system of equations using the substitution method y=5x+4 x+12=y
Answer:
(2,14)
Step-by-step explanation:
Since y=5x+4, you can plug that into the other y in the other equation which would give you x+12=5x+4
Now subtract 12 from both sides
x=5x-8
Subtract 5x from both sides
-4x=-8
Now you divide them both by -4 which gives you x=2
Now plug x in to any of the equations
y=5(2)+4
y=10+4
y=14
Your final answer is (2,14)
Which of the g-values satisfy the following inequality?
7 >_ 12 - 9
Choose all answers that apply:
A: g=4
B: g=5
C: g=6
Answer:
B: g=5
C: g=6
Step-by-step explanation:
Given
[tex]7 \ge 12 - g[/tex]
Required
All possible values of g
We have:
[tex]7 \ge 12 - g[/tex]
Collect like terms
[tex]7 - 12\ge - g[/tex]
[tex]-5\ge - g[/tex]
Divide both sides by -1 [The inequality changes because of negative division]
[tex]5\le g[/tex]
Swap both terms
[tex]g \ge 5[/tex]
This implies that g is greater than of equal to 5
i.e.
[tex]g= \{5,6,7.....\}[/tex]
Hence:
(b) and (c) are correct
Can someone help pls
Answer:
[tex] \frac{ - 1}{2} [/tex]
I REALLY NEED HELP with this statistics question, it would mean a lot if someone could answer it, i will give you brainliest for the correct answer :)
Answer:
Best anwser to use is Mode. Where you have the most
Step-by-step explanation:
Given that 2x + 3 > 9, the range of values of x is
Answer:
x>3
Step-by-step explanation:
2x+3>9
2x>6
x>3
So all values of x must be greater than 3 in order for the inequality to be true.
How would you write the equation with a slope of 2/3 and a y-intercept of -3 in slope- intercept form
y=2/3x-2
Explanation:
The equation of a line can be written as y=mx+c
m=slope and c = y-intercept
The point at the x−intercept has coordinates (-3,0)
In y=mx+c
0=2/3(3)+c
0=2+c
-2=c
The equation is y=2/3x-2
Answer:
[tex] y = \frac{2}{3} x - 3[/tex]
Step-by-step explanation:
Slope (m) = 2/3
y-intercept (b) = - 3
Equation of line in slope intercept form is given as:
[tex] y = mx + b[/tex]
Plug the values of m and b in the above equation, we find:
[tex]y = \frac{2}{3} x + ( - 3) \\ \\ y = \frac{2}{3} x - 3[/tex]
A pitcher of iced tea holds 128 ounces. A large orange cooler holds 1792 ounces of iced tea. How many pitchers of iced tea will it take to fill the large orange cooler? * NO LINKS PLZZ!!!
A.12
B.24
C.14
D.18
The big orange cooler will hold 14 pitchers of iced tea. The response is C.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Since a pitcher of iced tea holds 128 ounces, we can find the number of pitchers required to fill the large orange cooler by dividing the total volume of the cooler by the volume of one pitcher:
1792 / 128 = 14
Therefore, it will take 14 pitchers of iced tea to fill the large orange cooler. The answer is C.
Learn more about ratios here:
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A crowd-sourced review platform believes that more and more customers are writing reviews online. The crowd-sourced review platform would like to test the claim that the percent of customers who leave a review online is greater than 72%. They decide to complete a hypothesis test at a 1% significance level. They sample 30 customers, and determine the sample percent to be 90%. The following is the data from this study: Sample size =30 customers Sample proportion =0.90 Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=,≠,<, or > to represent the correct hypothesis.)
Answer:
H0 : P = 0.72
H1 : P > 0.72
Step-by-step explanation:
Claim is to test that percentage of customers who leave a review is greater than 72%
From the information given :
P0 = 72/100 = 0.72
The null hypothesis, H0 : P = 0.72
Alternative hypothesis claims the proportion is greater than 0.72 and from the sampling result obtained, phat = 0.90
Hence,
Alternative hypothesis, H1 : P > 0.72
There are only five possible shapes for a die, if the die is to be considered fair. A fair die means each face has the same shape and the same possibility of appearing on every roll. The five possible shapes are
Tetrahedron: Cube: Octahedron: Dodecahedron: Icosahedron:
If you had five dice, each die being one of the five shapes above with each side containing a number, how many combinations are possible if you were to roll the five dice at the same time? (3 points)
4 faces, each face is an equilateral triangle 6 faces, each face is a square 8 faces, each face is an equilateral triangle 12 faces, each face is a regular pentagon 20 faces, each face is an equilateral triangle
Answer:
46080Step-by-step explanation:
Number of possible combinations:
4*6*8*12*20 = 46080Answer:
Solution given:
Number of possible combinations:
4×6×8×12×20 = 46080 faces
PLEASE HELP WITH MY MOST RECENT QUESTION I NEED IT ILL GIVE BRAINLIEST PLEASE HELP
Answer:
sure
Step-by-step explanation:
but you gotta post the question...