The minimum cost of running the machine is $246. The time for minimum cost will be 16 hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the cost, in dollars, of operating a machine per day is given by the formula C = 3t² – 96t + 1014.
The minimum cost will be calculated as:-
d/dt ( 3t² – 96t + 1014 ) = 0
6t -96 = 0
6t = 96
t = 16 hours
The minimum cost is calculated as:-
C = 3t² – 96t + 1014
C = 3 ( 16)² - 96 x 16 + 1014
C = 768 - 1536 + 1014
C = $246
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Which of these numbers gives -7 when divided by -14
a -98
b -2
c 2
d 98
Answer: d. 98
Step-by-step explanation:
98/-14=-7
The point P(7, −3) lies on the curve y = 3/(6 − x). (a) If Q is the point (x, 3/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9 mPQ = 1
Answer:
The right answer is "3.33333".
Step-by-step explanation:
The given points in the question are:
[tex]P=(7,-3) = (x_1,y_1)[/tex]
[tex]Q=(x,\frac{3}{6-x} )=(x_2,y_2)[/tex]
Now,
The slope of PQ will be:
= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
By putting the values, we get
= [tex]\frac{\frac{3}{6-x}+3 }{x-7}[/tex]
= [tex]\frac{3+18-3x}{(6-x)(x-7)}[/tex]
= [tex]\frac{21-3x}{(6-x)(x-7)}[/tex]
= [tex]\frac{3(x-7)}{(6-x)(x-7)}[/tex]
= [tex]\frac{3}{x-6}[/tex]
hence,
x = 6.9
it's slope will be:
= [tex]3.33333[/tex]
Review the table showing the percentage of
contaminants remaining in a water sample after
passing through each round of filters.
In the exponential regression equation, what does the
value of b indicate?
Round
% of Contaminants
Left in Water Sample
0
100
6.3% of the contaminants remain in the water
sample after each round of filters.
14.9% of the contaminants remain in the water
sample after each round of filters.
O 6.3% of the remaining contaminants are removed
from the water sample after each round of filters.
14.9% of the remaining contaminants are removed
from the water sample after each round of filters.
1
15
2
2
3
0.3
Answer: it’s C
6.3% of the remaining contaminants are removed from water samples after each round of filters
Step-by-step explanation:
I got a good feeling
The value of b indicates 14.9% of the contaminants remains in water after each round of filters.
What is exponential regression?
Exponential regression refers to the process of arriving at an equation for the exponential curve that best fits a set of data.
What is the general form of the exponential regression equation?[tex]y =a b^{x}[/tex] is the general form of the exponential regression equation.
Let the exponential regression equation be [tex]y = ab^{x}[/tex].
Taking natural logarithm both the sides of [tex]y = ab^{x}[/tex]
⇒ [tex]ln y = a + x ln b..(i)[/tex]
For the value of a and b substitute the value of y and x from the given table.
substitute, y = 100 and x = 0 in equation (i)
⇒ [tex]ln100= a + 0[/tex]
⇒ a = 4.6
Substitute, y = 15, x = 1 and a = 4.6 in equation (i)
⇒ [tex]ln15 = 4.6 +( 1)lnb[/tex]
⇒[tex]2.7 - 4.6 = lnb[/tex]
⇒[tex]lnb = -1.9[/tex]
⇒ b = [tex]e^{-1.9}[/tex]
⇒ b = 0.149
⇒b = 14.9%
Hence, the value of b indicates 14.9% of the contaminants remains in water after each round of filters.
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Evaluate the algebraic expression h + h when b = 3, d = 12, h = 2 and r = 7.
A. 12
B. 8
C. 4
D. 0
Answer:
4
Step-by-step explanation:
h + h
h=2
2+2
4
IK THIS ISNT MATH BUT I NEED HELP ASAP!!
The table below gives the temperature at a certain place at different times of the day for 3 days. When did the wind become much colder?
Solve the right triangle. Round decimal answers to the nearest tenth.
Step-by-step explanation:
RS = 15/ tan57° = 9.7
RT = 15/sin57° = 17.9
The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant
Answer: [tex]2\ \text{units}[/tex]
Step-by-step explanation:
Given
Rate of increase in area of the circle is numerically equal to twice the rate of increase to twice the rate of increase in its circumference.
It can be written as
[tex]\Rightarrow \dfrac{d(\pi r^2)}{dt}=2\times \dfrac{(2\pi r)}{dt}\\\\\Rightarrow 2\pi r\dfrac{dr}{dt}=4\pi \dfrac{dr}{dt}\\\\\Rightarrow r=2\ \text{units}[/tex]
Santiago buys a new computer for $3000. He pays it off in 2 years and pays $480 in simple interest. What was the interest rate?
Answer:
8%
Step-by-step explanation:
We can solve this by making use of the simple interest formula
I= PRT/100
480= 3000×R×2/100
480= 6000R/100
Cross multiply
48000= 6000R
R= 48000/6000
= 8%
Hence the rate is 8%
40) A 10 ft. ladder positioned against a house makes a 65 degree angle with the ground. How far away
from the house is the base of the ladder?
A. 4 feet
B. 6 feet
C. 9.06 feet
D. 4.22 feet
Answer:
Distance of ladder from base = 4.22 feet (Approx.)
Step-by-step explanation:
Given:
Length of ladder = 10 feet
Angle with ground = 65°
Find:
Distance of ladder from base
Computation:
Length of ladder (hypotenuse) = 10 feet
Distance of ladder from base (Base)
Using trigonometry function
Cosθ = Base / Hypotenuse
Cosθ = Distance of ladder from base / Length of ladder
Cos65 = Distance of ladder from base / 10
0.4226 = Distance of ladder from base / 10
Distance of ladder from base = 0.4226 x 10
Distance of ladder from base = 4.226
Distance of ladder from base = 4.22 feet (Approx.)
PLS HELP WILL GIVE BRAINLIEST( IN PIC)
Answer:
hahahahahhahahahahahahah
someone please help .. i’m giving 20 points and brialiest
Answer:
D because it goes right then up!
PLEASE HELP I HAVE A C ALREADY I NEED TO GET THIS RIGHT PLEASE
You want to estimate the number of students in your school who support extra funding for the science club. You survey the first 13 students who arrive at a science class.
Determine whether the sample is biased or unbiased.
Answer:
BRO I HAVE THE SAME QUESTION FOR MY TEST....
ITS BIASED IM REALLLLY SURE
Step-by-step explanation:
I WILL GIVE BRAINLIEST PLEASE
Answer:
the answers are pi/6 and radius. hence the statement should read as
the length of the arc intercepted by third central angle is pi/6 times the length of the radius.
A line passes through (-2, 7) and (3, 2).
Find the slope-intercept form of the equation of the line.
Then fill in the value of the slope, m , and the value of the y-intercept, b, below.
m=
b=
[tex]\huge{ \mathfrak{ \underline{ Answer \: \: ✓ }}}[/tex]
Slope of the line :
[tex] \large\boxed{ \mathrm{ \frac{y_2 - y_1 }{x_2 - x_1} }}[/tex]
[tex] \dfrac{7 - 2}{ - 2 - 3} [/tex][tex] \dfrac{ 5}{ - 5} [/tex][tex] - 1[/tex]therefore, m = slope = -1
The equation of the line will be :
y = mx + by = (-1 × x) + by = -x + bNow, let's plug the value of x and y from coordinates of second point,
[tex]y = - x + b[/tex][tex]2 = - 3 + b[/tex][tex]b = 5[/tex]Hence, the required values are :
[tex] \boxed{m = - 1}[/tex][tex] \boxed{ \: \: \: b = 5 \: \: \: }[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
The slope of line passing through (-2, 7) and (3, 2). is -1 and the value of the y-intercept b is 5.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
A line passes through (-2, 7) and (3, 2). We need to find the slope.
x₁=-2, x₂=3, y₁=7, y₂=2
substitute the values in formula of slope
m=2-7/3-(-2)
m=-5/5=-1
The slope intercept form of line is y=-x+b
To find b put the values of (-2,7)
7=-(-2)+b
7=2+b
7-2=b
5=b
y intercept is 5
Hence the slope of line passing through (-2, 7) and (3, 2). is -1 and the value of the y-intercept b is 5.
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Hi I need help with this please help me
Answer:
if I'm correct the answer is 0.45x
What is the value of x in this figure?
Enter your answer in the box.
X
1140
xo
Answer:
114 degrees
Step-by-step explanation:
Because they are vertically opposite angles
Answer:
Step-by-step explanation:
Both angles are opposite of each other, therefore, x = 114
Can someone help me on this?
Answer:
Step 1
Step-by-step explanation:
it should've been 4×[tex]10^{3}[/tex]
Answer:
A
Step-by-step explanation:
step 1
= 4 . 10³ not 4 . 10²
20.3/3.5*0.58 in a standard form
Answer: 3.364
Step-by-step explanation: ?????
Paloma opened a savings account with a deposit of $750. She earns 2% simple interest per year on the account. What will the total amount of money, in dollars, in palomas account after 1 year if there are no other deposits or withdrawals ?
Answer:
$765
Step-by-step explanation:
Given data
Principal= $750
Rate= 2%
Time= 1 year
The simple interest expression is given as
A=P(1+rt)
substitute
A= 750(1+0.02*1)
A= 750(1.02)
A= $765
Hence the final amount is $765
4.
The expression for the area of a rectangle whose Length
(2p + 4) units and breadth 6 units is:
A. 12 + 24p
B. 24 + 12p
C. 4p + 20
D. None of these
Answer:
D. None of this
Step-by-step explanation:
(2p+4) 6
=12p+24
Answer:
None of these
Step-by-step explanation:
area of rectangle=length*breadth
=(2p+4)*6
=6*2p+4*6
=12p+24
You usually buy a 5.4 ounce bottle of lotion. There is a new bottle that says it gives
you 20% more free.
Use the drop-down menus to build an equation that could be used to find the size of
the larger bottle,x
Answer:
5.4 · 0.2
1.08 = 20%
5.4 + 1.08
6.48 ounce bottle
HELP ME PLEASEESWSAS
Solve the following equation for x.
2 + x^2 = 47
6.7
b. 7
22.5
d. 47
Answer:
6.7
Step-by-step explanation:
x² = 45
x = 6.7
is the answer
Please explain this problem fully
Answer:
S2
1. P is represented by -7
2. 1/2
Step-by-step explanation:
1. The P dot is right on the -7 mark, therefore, the number is -7
---------------------------------------------------------------------------------------------------------------
2. There are 3 shaded out of 6, making it 3/6. Once you reduce 3/6, you would get 1/2
-------------------------------------------------------------------------------------------------------------
Have a good day :)
PLZ HELPPPPPP!!!!!!!!!
Answer:
the answer is B
Step-by-step explanation:
A pack of clothes pins has 1 quarter yellow 2 thirds red and the rest blue how much blue pins are there
Answer: 1/12
Step-by-step explanation:
First make all the fractions have the same denominator. To do that, multiply the fractions by a number that will get them the same denominator. In this case, multiply 1/4 by 3, and 2/3 by 4.
1/4 x 3/3 = 3/12
2/3 x 4/4 = 8/12
then you have 3/12 + 8/12 = 11/12
so, blue is 1/12
Answer:
1/12 of the pins are blue
Step-by-step explanation:
¼ yellow & ⅔ red
First you have to find a common denominator.
4×3 =12 & 3×4 =12 so the common denominator is 12.
Now × the numerator on the fraction with the same number that you x the denominator and you will get 3/12 and 8/12.
3/12 +8/12 = 11/12
12/12 - 11/12 = 1/12
Therefor 1/12 of the pins are blue
Hamad wants to buy a video game with a selling price of $55, on sale for 40% off. The sales tax in his state is 3.5%. How much will Hamad have to pay in all?
Answer:
34.16
Step-by-step explanation:
55x.40=22 discount
55-22=33 sales price
33x.035=1.16 sales tax
33+1.16=34.16 total price
Answer:
$33.75
Step-by-step explanation:
hope this helps
PLEASE HELP ILL GIVE BRAINLY
Answer:
Student C
Step-by-step explanation:
The fraction ends up being 3 and you get 3* 3^-1 so you add 1 to the exponent.
3.
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
A. (–1, 1); minimum
B. (–1, 1); maximum
C. (1, –1); minimum
D. (1, –1); maximum
Answer:
C. (1, –1); minimum
Step-by-step explanation:
The answer to your question is letter “C”
The correct answer is c
HELPP(David saves 12 % of his monthly salary.
If he saves $17.75, what is his monthly
salary?)
Answer:
147.92
Step-by-step explanation:
Let the monthly salary be x
He saves 12 % and that is 17.75
x* 12% = 17.75
Change to decimal form
x *.12 = 17.17
Divide each side by .12
x*.12 /.12 = 17.75/.12
x =147.91666666
Rounding to the nearest cent
x = 147.92
Break 5/6 into a sum of unit fractions
plz dont dlete my question this isnt a live test and this isnt being streamed therefore i am not breaking breanlys guidlines
Answer:
1/6+1/6+1/6+1/6+1/6
Step-by-step explanation:
a unit fraction is a fraction with the numerator as 1