find the maximum value of c=6x+2y
Answer:
∞
Step-by-step explanation:
c can have any value you like.
There is no maximum. We say it can approach infinity.
__
Additional comment
There may be some maximum imposed by constraints not shown here. Since we don't know what those constraints are, we cannot tell you what the maximum is.
Find The Sum or Difference
(-6x – 3) + (3x – 9)
Answer:
-3x -12
Step-by-step explanation:
-6x +3x = -3x
-3-9 = -12
What should you substitute for x in the second equation (bottom equation) in order to solve the system by the substitution method?
We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
The given system of equations are 2x-1/3y = -2...(1)
3x+y=1...(2)
We solve this system of equations by using substitution method.
Let us solve for x in equation to substitute it in equation (2).
2x=-2+1/3y
Divide both sides of equation by 2.
x=-1+1/6y
Now plug in the value of x in equation 2.
Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
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For positive acute angles A and B, it is known that sin A=
21/29, and tan B = 28/45.
Find the value of cos(A – B) in simplest form.
Answer:
sin(A+B) = sinAcosB+sinBcosA
if cosA = 9/41 then sinA =j40/41 It's a 9-40-41 right triangle
if tanB =21/20 then sinB =21/29 and cosB= 20/29 It's a 20-21-29 right triangle
plug those values into 1st equation above
sin(A+B) = 40/41(20/29) + 21/29(9/41) = ((40)20 + (21)9))/29(41) = (800+189)/1189 = 989/1189 = 0.832
or you could have just found A and B initially. cosA = 9/41 means A = 77.32 degrees
tanB = 21/20 means B = 46.4
A+B = 123.72
sin(123.72) = 0.832
Exact answer though without rounding is sin(A+B) = 989/1189 Step-by-step
explanation:
I don't know if that makes sense because its kind confusing! i'm sorry if it is hard to understand!
An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 84 feet. What was the speed of the vehicle before the brakes were applied?
Answer:
Step-by-step explanation:
\(\sf Speed = \sqrt{24d}\)
Here, d is the length of the skid marks.
\(\sf Speed = \sqrt{24*84}\\\)
\(\sf = \sqrt{2016}\\\\= 44.9 \ feet \ per \ hour\)
A circle is inscribed in a square. If the perimeter of the square is 40, what is the area of the circle? Use 3.14 for pi.
Answer:
78.5
Step-by-step explanation:
We have the perimeter of the square, which is 40, and 40/4=10. In this picture, we see that the circle's diameter is the same as the length of one side of the square. Therefore, the diameter of the circle is 10. The are formula for circles is \(\pi r^{2}\), where \(r\) is the radius. The radius of the circle is just the diameter divided by 2, and 10/2=5. Now, \(5^2\) is 25, and \(3.14\cdot25=78.5\).
The gas tank in Sharon’s car can hold up to 16.5 gal of gas.
About how many liters of gas can the tank hold?
1 L≈1.06 qt
A:3.9L
B:4.4L
C:62.3L
D:70.0L
Answer:
B 4.4
Step-by-step explanation:
There is 1 gallon in 3.7 liters so you would divide 16.5 by 3.7
The tank has a capacity of 58.90 liters of gas.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculations.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that the gas tank in Sharon’s car can hold up to 16.5 gal of gas
Since one gallon is 4 quarts
Volume in quarts as:
16.5 gallons = 16.5 x 4 quarts = 66 quarts
So quarts = 0.946
66 quarts = 0.946 x 66 = 62.436
So Volume = 62.436q
Volume in liters as:
Given as one litre = 1.06qt
If one liter is 1.06, Then 62.436 will be = 62.436/1.06 = 58.90
The volume in liters of 58.90
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(q1) Find the length of the curve described by the function
The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:
L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2
The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.
Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:
L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral be solved.
We can, however, find a general solution. We use the above formula and substitute the limits of integration.
Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
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A father and son are buying hot dogs and lemonade for a family picnic. They have only a $20 bill to spend. Lemonade costs $3.50 per bottle and they must buy one bottle. Hot dogs cost $2.50 per package. What is the maximum number of packages of hot dogs they can buy?
Answer:
Step-by-step explanation:
subtract 20-3.50 you will get 16.50
Multiply 2.50x6 you will get 15
Subtract 16.50-15.00 you will get 1.50
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.
Labor-Hours per Ski
Maximum Labor-Hours
Available per Day
Department
Fabricating
Finishing
Trick Ski
6
1
Slalom Ski
4
1
132
30
If the profit on a trick ski is $50 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maxi
What is the maximum profit?
The maximum profit will be $2,700.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The profit on a trick ski is $50 and the profit on a slalom ski is $30.
Let the number of Trick ski manufactured = x
And, Number of slalom ski manufactured = y
So, Maximize;
P = 50x + 30y
Subject to we get;
6x + 4y ≤ 108
And, x + y ≤ 24
And, xy ≤ 0
Now, We have to find set of feasible solutions graphically for the number of each type of ski that can be produced.
So, Linear equation in slope form;
6x + 4y = 108
y = -1.5x + 27
And, x + y = 24
y = - x + 24
So, By the graph we get;
The points,
(x , y) = (0, 24) , (6 , 18) (18, 0)
Hence, The maximum profit when 6 trick ski and 18 slalom ski manufactured.
maximum profit = 6 x 50 + 18 x 30 = 840
And, The maximum profit when 18 trick ski and 0 slalom ski manufactured.
maximum profit = 18 x 50 = 900
The maximum profit when 0 trick ski and 24 slalom ski manufactured.
maximum profit = 24 x 40 = 960
Thus, The maximum profit = 840 + 900 + 960
= $2,700
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 8 N acts on a certain object, the accelerstion of the object is 4 m/s2. If the acceleration of the object becomes 9 m/s?, what is the force?
Answer:
18N
Step-by-step explanation:
According to Newtons second law
F ∝ a
F = ka
k is the constant of proportionality
When a force of 8 N acts on a certain object, the acceleration of the object is 4 m/s2, hence;
8 = 4k
k = 8/4
k = 2
If a = 9m/s², F = ?
Recall F = ka
F = 2 * 9
F = 18N
Hence the force will be 18N
On average a clothing store gets 120 customers per day. What is the probability of getting 35 customers in the first four hours? Assume the store is open 12 hours each day.
0.04854
The average number of customers first four hours is 35
the store is open 12 hours each day
the customers per day are 120
so, the equation should be like this
(4÷12)×120=40
probability of getting 35 customers in the first four hours
Therefore, we enter the average number of customers and the number of customers who are expected at random into our Poisson calculator.
P(X=35)=0.04854
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The mean of the data set is 4. Find the absolute deviation of each of the red data values
The absolute deviation of 0 is
The absolute deviation of 3 is
The absolute deviation of 7 is
The absolute deviation of each of the data values are 4, 1 and 3 respectively.
Absolute deviationThe absolute deviatuon gives the distance of any given value in a dataset to the mean value. The absolute deviation is always positive as it does not consider the side to which the value belongs.
Absolute deviation = |value - mean|
Mean = 4
Absolute deviation of 0 = |0 - 4| = 4
Absolute deviation of 3 = |3 - 4| = 1
Absolute deviation of 7 = |7 - 4| = 3
Hence, The absolute deviation of each of the data values are 4, 1 and 3 respectively.
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Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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A marble is selected from a bag containing eight marbles numbered 1 to 8. The number of the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event A.
A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
Step-by-step explanation:MAKE A PLAN:
List The OUTCOMES for EACH EVENT and their COMBINATIONS:
SOLVE THE PROBLEM:a) - EVENT "A": {2, 4, 6, 8}
EVENT "B": {3, 4, 5, 6}
EVENT "A" or "B": {2, 3, 4, 5, 6, 8}
b) - EVENT "A" or "B": {4, 6}
c) - The COMPLEMENT of the EVENT "A": {1, 3, 5, 7}
Draw the conclusion:A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
I hope this helps!
PLEASE HELP ME ?!!!!!
Answer:
b & c for sure
Step-by-step explanation:
............
PLEASE HELP QUICKLY (20 points)!!! Which descriptions of this function are true? Select 4 that apply.
A. the function is increasing
B. the slop of the function is -4/3 and the y-intercept is 9.
C. the slope of the function is -3/4 and the y-intercept is 7.
D. y= -3/4x + 7 represents this function.
E. the function is linear and continuous.
F. y = 7x -3/4 represents this function.
G. the function is decreasing.
H. the function is linear and discrete.
I. y = -4/3x +9 represents this function
C. the slope of the function is -3/4 and the y-intercept is 7.
D. y= -3/4x + 7 represents this function.
G. the function is decreasing.
You toss a fair coin 4 times. What is the probability that:
a. you get all Tails?
b. you get at least one Head?
(round to 4 decimal places)
Answer:
a. 1/16 which is 6.2500%
b. 15/16 which is 93.7500%
Step-by-step explanation:
a. For each 'coin toss' the probability of getting tails is 1/2. If you toss the coin 4 times, the probability of getting tails all times is 1/2 * 1/2 * 1/2 * 1/2 = 1/16.
b. This one is a bit trickier.
When flipping four coins, you either could get all four heads or you could get at least one tail. Both events cannot happen at the same time. This means the two events are complementary.
Complementary events occur when there are only two outcomes, for example passing an exam or passing an exam. The complement means the exact opposite of an event.
Complementary probabilities always add to 1.
We saw in part (a) that the probability you get all tails is 6.25% or 1/16.
0.0625 was the probability of getting all four heads, so 0.9375 is the probability of anything else (getting one or more tails).
The decimal 0.9375 converts to the fraction 15/16.
The probability is 93.75%.
Answer all questions please
Answer:
a) f(1) = 3
b) f(-1) = -0.25
c) x = 0, 3
d) x = -0.75
e) domain [-2, 4]
range [-1, 3]
Step-by-step explanation:
In this graph, f(x) is represented by the y-axis.
a) We can see that f(1) (the y-value when x = 1) is 3.
b) Looking at the graph, we can estimate f(-1) as about -0.25.
c) We need to find the x-values when the y-axis is at 1. We can see that there are two points at x = 0, 3.
d) Looking at the graph, we can estimate that f(x) = 0 around when x = -0.75.
e) The domain of a function is its set of x-values. We can see that f(x) spans from x = -2 to x = 4. That range in interval notation is: [-2, 4]
The range of a function is its set of y-values. We can see that f(x) spans from y = -1 to y = 3. That range in interval notation is: [-1, 3].
If the lengths of the diagonals of a rhombus are 16 cm and 12 cm, find its area.
Answer:
One diagonal is 16 and another 12 then half of both is 8and6.diagonal of rhombus bisect at 90'
8²+6²=h²
64+36=100
Side = 10
Step-by-step explanation:
A restaurant is offering 15 percent off beverages. The check is $90.00 with the beverage total being $15.00. What is the check total after the discount ?
A 77.75
B 76.50
C.75.00
D.87.75
b because 90
15
15
-_____
76.50
Which event will have a sample space of S = {g, b}?
A. Flipping a fair, two-sided coin
B. Rolling a six-sided die
C. Flipping a two-sided coin with one side green and the other side blue
D. Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
An event that will have a sample space of S = {g, b} include the following: C. Flipping a two-sided coin with one side green and the other side blue.
What is a sample space?In Mathematics and statistics, a sample space can be defined as a set or collection of possible outcomes (results or outputs) that are obtainable from a random experiment. Mathematically, a sample space is represented or denoted by using the symbol, "S."
Additionally, a sample space may contain a number of outcomes (results or outputs) that depends on the experiment. Generally speaking, the subset of possible outcomes (results or outputs) of that are obtainable from an experiment is typically referred to as events.
In this context, we can reasonably infer and logically deduce that "Flipping a two-sided coin with one side green and the other side blue" is an event which would have a sample space that is modeled by this mathematical expression;
S = {g, b}
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Answer: C: Flipping a two-sided coin with one side green and the other side blue.
squared root of x-45 equals squared root of x minus 3
Answer:
No solution
Step-by-step explanation:
\(\sqrt{x-45} =\sqrt{x-3} \\(\sqrt{x-45} )^2=(\sqrt{x-3} )^2\\x-45 = x-3\\x-x = 45-3\\0 = 42\\\)
Last year and investor purchased 115 shares of stock A at $90 per share
The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10
The third option is correct.
How do we calculate?For stock A:High price value: 115 shares * $105.19 per share = $12,084.85
Low price value: 115 shares * $103.25 per share = $11,858.75
For stock B:High price value: 30 shares * $145.18 per share = $4,355.40
Low price value: 30 shares * $143.28 per share = $4,298.40
The overall value at high price:
$12,084.85 + $4,355.40
= $16,440.25
The overall value at low price:
$11,858.75 + $4,298.40
= $16,157.15
In conclusion, the difference in overall gain or loss:
$16,440.25 - $16,157.15 = $280.10
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What is the slope of the line that contains the points (2,5) and (4, - 3)?
Answer:
-4
Step-by-step explanation:
The slope would be (5 - (-3)) / (2 - 4) = 8 / -2 = -4.
Answer:
\(\huge\boxed{\text{The slope}\ m=-4}\)
Step-by-step explanation:
The formula of a slope:
\(m=\dfrac{y_2-y_1}{x_2-x_1}\)
(x₁; y₁), (x₂; y₂) - points on a line
We have the points:
\((2;\ 5)\to x_1=2;\ y_1=5\\(4;\ -3)\to x_2=4;\ y_2=-3\)
Substitute:
\(m=\dfrac{-3-5}{4-2}=\dfrac{-8}{2}=-4\)
Help me with this I don’t understand
Answer:
x-int: (2, 0)
y-int: (0, -4)
Step-by-step explanation:
Step 1: Convert to slope-intercept form
2y = -4x - 8
y = -2x - 4
Step 2: Find y-int (Set x to 0)
y = -2(0) -4
y = -4
Step 3: Find x-int (Set y = 0)
0 = -2x - 4
4 = -2x
x = 2
Answer:
The x=-2 and y=-4
Step-by-step explanation:
x=(-2,0)
y=(0,-4)
DO the math and you will get the answer
I hope this helps
Stay safe:)
USe desmo
A submarine was 350 feet below sea level. Then, it rose 75 feet, before diving back down another 100 feet. What is the current elevation of the submarine?
Find the dimensions of a rectangle with area 1,000 m^2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)What is m (smaller value)What is m (Larger value)
10√10 is the dimensions of a rectangle with area 1,000 m² whose perimeter is as small as possible.
a. The smaller value is 10√10 m.
b. The larger value is 10√10 m.
We have to determine the dimensions of a rectangle with area 1,000 m² whose perimeter is as small as possible.
P = 2w + 2L
1000 = Lw
P = 2w + 2(1000/w)
P = 2w + 2000/w
P-prime = 2 -2000/w²
0 = 2 - 2000/w²
Add 2000/w² on both side, we get
2000/w² = 2
Multiply by w² on both side, we get
2000 = 2w²
Divide by 2 on both side
w² = 2000/2
w² = 1000
Taking square root on both side, we get
w = 10√10
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How do I solve this?
Answer:
find all numbers, stick together o make an uqaion and solve . simplifi if needed
Step-by-step explanation:
An analysis of 99 Wall Street traders showed that 32 of their stock picks beat the market average. What is the estimate of the population proportion
Answer:
The estimate of the population proportion is 0.3232.
Step-by-step explanation:
Estimate of the population proportion:
The estimate is the sample proportion, which is the number of desired outcomes divided by the number of total outcomes.
In this question:
32 out of 99, so:
\(p = \frac{32}{99} = 0.3232\)
The estimate of the population proportion is 0.3232.