The fraction 4/3 we get by using the numbers 3 and 4 to make a fraction that is greater than 1 and a fraction less than 1
To make a fraction greater than 1 using the numbers 3 and 4, we can divide 3 by 4 and add 1.
3/4 + 1 = 7/4
The resulting fraction, 7/4, is greater than 1 because the numerator (7) is greater than the denominator (4).
We can also see this by writing 7/4 as a mixed number:
7/4 =[tex]1\frac{3}{4}[/tex]
The whole number part of the mixed number is 1, which means the fraction is greater than 1.
To make a fraction less than 1 using the same numbers, we can divide 4 by 3. This gives us:
4/3
The resulting fraction, 4/3, is less than 1 because the numerator (4) is smaller than the denominator (3).
We can also see this by writing 4/3 as a mixed number:
4/3 =[tex]1\frac{1}{3}[/tex]
The whole number part of the mixed number is 1, which means the fraction is less than 1.
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Suppose that 4 friends are given a vintage arcade game that they want to share. If they decide to divide their time, and they decide that they have 26 hours of available time to play in a week, what is each person's fair share of the playing time?
Answer: 6.5
Step-by-step explanation:
26/4 = 6.5 hours
ASAP.
jack goes for a ride on a ferris wherl thst has a radius of 51 yards. the center of the ferris sherl is 61 yards above the ground. he starts bis rifr at the 9 oclock position and travels counter clockwise. define a function g that tepresents jacks verticL distance above the grihdn in yards in terms of the angel ( meassured in radians) jack has swept out measured grom the 9 oclock positions
Answer:
112 yards
Step-by-step explanation:
The center of the Ferris wheel is 61 yards above the ground and the radius is 51 yards. When Jack is at the 9 o'clock position, he is at a distance of 112 yards from the center of the Ferris wheel (51 yards from the center plus 61 yards above the ground). Let θ be the angle that Jack has swept out measured from the 9 o'clock position, in radians.
The function g that represents Jack's vertical distance above the ground in yards in terms of the angle θ is:
g(θ) = 61 + 51sin(θ)
where sin(θ) represents the vertical component of the distance Jack has traveled.
Note that when θ = 0, sin(θ) = 0, which means Jack is at the very top of the Ferris wheel, 112 yards above the ground. When θ = π/2, sin(θ) = 1, which means Jack is at the 12 o'clock position, 112 + 51 = 163 yards above the ground. Similarly, when θ = π, sin(θ) = 0, which means Jack is at the very bottom of the Ferris wheel, 112 yards above the ground.
A pyramid-shaped building is 318 ft tall and has a square base with sides of 580 ft. The sides of the building are made
from reflective glass. What is the surface area of the reflective glass?
The surface area of the glass is _____ ft².
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places
as needed.)
Answer:
499,237 ft²
Step-by-step explanation:
You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.
AreaTo find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:
A = 1/2bh
There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:
4A = 4(1/2bh) = 2bh
Slant heightThe slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)
h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet
Glass arealateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²
The surface area of the glass is about 499237 square feet.
lamonte car used 5 gallons to travel 125 miles.how many gallons of gas would he need to travel 400 miles
Answer:
Step-by-step explanation:
1. Get mileage per gallon by dividing miles traveled by gallons used
[tex]\frac{125}{5} = 25 mpg\\[/tex]
2. Divide miles you want to travel by the mileage per gallon you got on the first step
[tex]\frac{400}{25} = 16 gallons[/tex]
a) A manufacturer of floor wax has developed two new brands, A and B. To determine which of the
two is superior, both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is
known that the proportion of people that prefer A is 0.4 while the rest prefer brand B. Find the
probability that at least 8 homes would state a preference for brand B.
The probability of at least 8 homes would prefer brand B compare to compare A is given by 0.672.
Sample size 'n'= 25
Proportion of people prefer brand A = 0.4
This implies ,
Proportion of people prefer brand B 'p' = 1 - 0.4
= 0.6
Using the binomial distribution.
Let X be the number of homes that prefer brand B out of the 25 homes surveyed.
Then X follows a binomial distribution with parameters n = 25 and p = 0.6
Probability that at least 8 homes would state a preference for brand B. expressed as,
P(X ≥ 8) = 1 - P(X < 8)
Using the binomial distribution, compute P(X < 8) as follows,
P(X < 8) = Σ [²⁵Cₓ] × 0.6ˣ × 0.4²⁵⁻ˣ, for x = 0, 1, 2, ..., 7
where ²⁵Cₓ is the binomial coefficient which represents the number of ways to choose k homes out of 25.
Use a binomial calculator ,
⇒P(X < 8) = [²⁵C₀] × 0.6⁰× 0.4²⁵⁻⁰ + [²⁵C₁] × 0.6¹× 0.4²⁵⁻¹ + [²⁵C₂] × 0.6²× 0.4²⁵⁻² + .......+ [²⁵C₇] × 0.6⁷× 0.4²⁵⁻⁷
⇒P(X < 8) ≈ 0.328
This implies,
P(X ≥ 8) = 1 - P(X < 8)
≈ 1 - 0.328
= 0.672
Therefore, the probability that at least 8 homes would state a preference for brand B is approximately 0.672.
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The above question is incomplete , the complete question is:
A manufacturer of floor wax has developed two new brands, A and B. which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is known that the proportion of people that prefer A is 0.4 while the rest prefer brand B.
Find the probability that at least 8 homes would state a preference for brand B.
There are 35 boys in the sixth grade. The number of girls in the sixth grade is 42. Lonnie says that means the ratio of the number of boys in the sixth grade to the number of girls in the sixth grade is 5: 7. Is Lonnie correct? Show why or why not.
Answer:
Step-by-step explanation:No, Lonnie is not correct. Step-by-step explanation: Because if we put 35 and 42 in rational form we can write it to its simple form by dividing it and after dividing we get the answer as 5 : 6. so that means Lonnie in incorrect.D
What is the answer to this question
Answer:
The height of the kite is 63.40 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
sin(30) = h / 95
h = 47.5 feet
Therefore the height of the kite is 63.40 feet.
Simplify the expression: 8y + 4 - 3y + 12
The simplified expression is:
8y + 4 - 3y + 12 = 5y + 16
How to simplify the expression?Remember the distributive property:
A*(B + C) = A*B + A*C
Now let's look at our expression, it is:
8y + 4 - 3y + 12
We can reorder the terms to get:
8y - 3y +4 + 12
Now we can take y as a common factor:
(8 - 3)y + 4 + 12
Now simplify the two operations:
(8 - 3)y + 4 + 12 = 5y + 16
That is the expression simplified.
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solve. y=2x^2+8 for the axis of symmetry and the vertex
Need help easy please give right answer
Answer: x < 5, see attached
Step-by-step explanation:
To solve for x, we will isolate the given variable.
Given:
[tex]\displaystyle 1 > \frac{x}{5}[/tex]
Multiply both sides of the equation by 5:
[tex]\displaystyle5 > x[/tex]
Flip equation:
[tex]\displaystyle x < 5[/tex]
To graph, we will first plot a point on 5 with an open circle. Then, we will shade to the left since x is less than 5. See attached.
How many bags of pretzels does Tim buy?
The value of x and y are,
x = 8 and y = 4
We have to given that;
Tim has $20 to buy snacks for 12 people in an office.
And., Tim is buying bags of pretzels that cost $1.50 per bag and bags of crackers that cost $2.00 per bag.
Let x represent bags of pretzels.
And, y represent bags of crackers.
Hence, We can formulate;
x + y = 12 .., (i)
And, 1.5x + 2y = 20 .. (ii)
From (i);
x = 12 - y
Plug in (ii):
1.5 (12 - y) + 2y = 20
18 - 1.5y + 2y = 20
18 + 0.5y = 20
0.5y = 2
y = 2/0.5
y = 4
And, x = 12 - 4
x = 8
Thus, The value of x and y are,
x = 8 and y = 4
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sage team brought 224 cans they brought 3 times cans as asifs team joes team brought 4 times as asifs team how much cans did joes team bring in
The number of cans brought by Joes team is J = 299 cans
Given data ,
Let the number of cans brought by Joes team be J
Now , sage team brought 224 cans
And , sage team brought 3 times cans as asifs team
And , joes team brought 4 times as asifs team
On simplifying the equation , we get
Asif's team brought 224/3 = 74.67 (rounded to the nearest whole number) cans.
Joe's team brought 74.67 x 4 = 298.68
So , J = 299 cans
Hence , the equation is solved and J = 299 cans
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Which of the following functions are vertical translations of f(x)=√x?
Select all that apply.
A. K(x)=√√√-5+x
B. n(x) = -7+ √x
C. g(x)=√x -4
D. h(x)=3+√x
E. m(x)=√5x
Answer:
The function f(x) = √x is the square root function.
A vertical translation of a function is a transformation that shifts the graph of the function up or down without changing its shape.
Option (A) is a vertical translation of f(x) because it shifts the graph of f(x) to the right by 5 and then applies three square root operations. However, it is not a vertical translation that shifts the graph up or down.
Option (B) is a vertical translation of f(x) because it shifts the graph of f(x) down by 7 units.
Option (C) is a vertical translation of f(x) because it shifts the graph of f(x) down by 4 units.
Option (D) is a vertical translation of f(x) because it shifts the graph of f(x) up by 3 units.
Option (E) is not a vertical translation of f(x) because it involves multiplying the input of f(x) by a constant factor of 5.
Therefore, the options that are vertical translations of f(x) are (B), (C), and (D).
Step-by-step explanation:
A line has a slope of 3 and y-intercept of -4. Write its equation in slope- intercept form.
Answer:
y=mx + b
Step-by-step explanation:
y=3x-4
3 is the slope and -4 is the y intercept
Solve the following for θ, in radians, where 0≤θ<2π.
3cos2(θ)+6cos(θ)−4=0
Answer:
0 ≤ < 2
Step-by-step explanation:
Answer:1.02 5.27 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 + 6u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = 6, and c = -4. Substituting these values, we get:
u = (-6 ± sqrt(6^2 - 4(3)(-4))) / 2(3)
u = (-6 ± sqrt(84)) / 6
u = (-3 ± sqrt(21)) / 3
Therefore, either:
POSSIBLE POINTS: 10
Find the area of the composite figure below. Area of Triangle = bh, Area of Rectangle = lb Use Pythagorean formula to find the length () of the
Rectangle.
7 mm
10.4 mm
15.3 mm
The total surface area of the composite figure is: 288.62 mm²
What is the area of the composite figure?From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:
Formula for area of rectangle is:
A = Length * Width
Formula for area of triangle is:
A = ¹/₂ * base * height
Using Pythagoras theorem, length of rectangle is:
L = √(10.4² + 15.3²)
L = 18.5 mm
Thus:
TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)
TSA = 129.5 + 159.12
TSA = 288.62 mm²
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Jake just learned to identify the difference between an oak tree and a
maple tree. He was curious about the concentration of these trees in his
neighborhood, so he went out and identified several trees that were either
by the pond or in the field.
Unfortunately, he smudged his data tables and can't read some of the
values. The absolute and relative frequency tables below show Jake's
salvaged data. Can you help him figure out the rest?
Fill in the missing values from each table.
The value of row total of the column total's is 165.
The value of row total of field is 91
How to calculate the valueColumn total of maple can be found by:
(46.32 /100) * y =44
Or y = (44 *100)/46.32
Or y = 94.991 =95 (approx)
Now we get value of field under maple by
Value of field under maple = (column total - value of pond under maple) = (95 - 44) = 51
Value of row total of the column total's = (column total of oak + column total of maple = (70 + 95) = 165 (total data)
Value of row total of field = ( value of field under oak + value of field under maple) = (40 + 51) = 91
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Need help with his page 20 points
Answer:
m/2 -6= m/4+2 can be solved as follows:
Multiply both sides of the equation by the least common multiple of the denominators, which is 4:
4(m/2 - 6) = 4(m/4 + 2)
2m - 24 = m + 8
Subtract m from both sides:
m - 24 = 8
Add 24 to both sides:
m = 32
Therefore, the value of m is C) 32.
k/12 = 25/100 can be solved as follows:
Multiply both sides of the equation by 12:
k = 12 * (25/100)
k = 3
Therefore, the value of k is A) 3.
9/5 = 3x/100 can be solved as follows:
Multiply both sides of the equation by 100:
100 * (9/5) = 3x
Simplify:
180/5 = 3x
36 = 3x
Divide both sides by 3:
x = 12
Therefore, the value of x is not one of the options provided.
Step-by-step explanation:
Answer:
Question 18:-[tex] \sf \longrightarrow \: \frac{m}{2} - 6 = \frac{m}{4} + 2 \\ [/tex]
[tex] \sf \longrightarrow \: \frac{m - 12}{2} = \frac{m + 8}{4}\\ [/tex]
[tex] \sf \longrightarrow \: 4(m - 12) =2(m + 8)\\ [/tex]
[tex] \sf \longrightarrow \: 4m \: - 48 =2m + 16\\ [/tex]
[tex] \sf \longrightarrow \: 4m \: - 2m = 16 + 48\\ [/tex]
[tex] \sf \longrightarrow \:2m = 64\\ [/tex]
[tex] \sf \longrightarrow \:m = \frac{64}{2} \: \\ [/tex]
[tex] \sf \longrightarrow \:m = 32 \: \\ [/tex]
[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: C) \: \: \: 32 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]
__________________________________________
Question 19:-[tex] \sf \leadsto \: \frac{k}{12} = \frac{25}{100} \\ [/tex]
[tex] \sf \leadsto \: 100(k)= 12(25) \\ [/tex]
[tex] \sf \leadsto \: 100 \times k= 12 \times 25 \\ [/tex]
[tex] \sf \leadsto \: 100 k= 300 \\ [/tex]
[tex] \sf \leadsto \: k= \frac{300}{100} \\ [/tex]
[tex] \sf \leadsto \: k= 3 \\ [/tex]
[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: a) \: \: \: 3 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]
__________________________________________
Question 20:-[tex] \sf \longrightarrow \: \frac{9}{5} = \frac{3x}{100} \\ [/tex]
[tex] \sf \longrightarrow \: 100(9)= 5(3x) \\ [/tex]
[tex] \sf \longrightarrow \: 100 \times 9= 5 \times 3x \\ [/tex]
[tex] \sf \longrightarrow \: 900= 15x \\ [/tex]
[tex] \sf \longrightarrow \: x= \frac{900}{15} \\ [/tex]
[tex] \sf \longrightarrow \: k= 60 \\ [/tex]
[tex]\qquad{\underline{\overline {\boxed{ \sf{ \: \: a) \: \: \: 60 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]
__________________________________________
Can someone help me please
The expansion and simplification of the expression (x - 2)² is x² - 4x + 4.
What is an expression?An algebraic expression is a combination of variables with constants, numbers, and values using the mathematical operands addition, subtraction, multiplication, or division.
Algebraic Expression:(x - 2)²
Expanding the square:
(x - 2)² = (x - 2)(x -2)
Distributing the square:
x(x - 2) - 2(x - 2)
x² - 2x - 2(x -2)
x² - 2x - 2x + 4
Solution:x² - 4x + 4
Thus, after expanding and simplifying the algebraic expression (x - 2)², the solution is x² - 4x + 4.
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A virus takes 5 days to grow from 180 to 230. How many days will it take to grow from 180 to 260? Round to the nearest whole number.
It will take approximately 8 days for the virus to grow from 180 to 260.
We can set up a proportion to solve this problem. Let "x" represent the number of days it will take for the virus to grow from 180 to 260.
The proportion can be set up as follows;
(Change in value) / (Time taken) = (Change in value) / (Time taken)
Using the given information, we have;
(260 - 180) / x = (230 - 180) / 5
Simplifying the fractions on both sides of the equation, we get:
80 / x = 50 / 5
Cross-multiplying, we have;
80 × 5 = 50 × x
400 = 50x
Dividing both sides of the equation by 50, we get;
x = 400 / 50
x = 8
Therefore, it will take 8 days.
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How do you solve for X???
Answer:
x= -18
Step-by-step explanation:
-2/3x + -21/4 = 27/4
-8x-63=81
-8x-63+63=81+63
-8x=144
-8x/-8 = 144/-8
x=-18
Claim: The standard deviation of pulse rates of adult males is 12 bpm. For a random sample of 173 adult males, the pulse rates have a standard deviation of 10.6bpm. Find the value of the test statistic.
Based on the standard deviation given and the sample size, the test statistic can be found to be 134.20.
The test statistic can be found by the formula:
= ((Sample size - 1) x Standard deviation of sample²) / Standard deviation of population
Solving gives:
= ((173 - 1) x 10.6²) / 12²
= 19,325.92 / 144
= 134.20
Hence, the test statistic is 134.20.
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Help 100 pts. I don’t get it
The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.
Given that, the dimensions of rectangular flower bed are length= 6 feet and width = 4 feet.
Dimensions of large rectangle are Length = 6+2x and width = 4+2x
Now, area of large rectangle = (6+2x)×(4+2x)
= 24+8x+12x+4x²
Area of a rectangular flower bed = 6×4
= 24 square feet
Tulips and Daisy have same area to plant
So, the equation is 24+20x+4x²=24
4x²+20x=0
Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.
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a rock is thrown straight up with an initial velocity of 3m/s. The mass of the rock is approximately 0.2kg. Air resistance acts on the rock with a force numerically equal to 0.5v where v is the velocity of the rock. Acceleration due to gravity is 9.8 m/s^2. Set up and solve a differential equation to find the velocity of the rock as a function of time
The velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.
The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:
[tex]m(dv/dt) = -mg - 0.5v[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.
We can simplify this differential equation by dividing both sides by m:
[tex]dv/dt = (-g - 0.5v/m)v[/tex]
This is a separable differential equation, which we can solve using the separation of variables:
[tex](1/(-g - 0.5v/m)) dv = dt[/tex]
Integrating both sides gives:
[tex]-2ln(-g - 0.5v/m) = t + C[/tex]
where C is a constant of integration.
Solving for v gives:
[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]
where C' = exp(C).
We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:
[tex]v(0) = -0.5mg + C' = 3[/tex]
[tex]C' = 0.5mg + 3[/tex]
Substituting this into the equation for v(t) gives:
[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]
Therefore, the velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
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The profit equation for the sale of pressure cookers for the company Kitchen Masters is PP = −120pp2 + 19,800pp − 727,450. Which of the following is a sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300?
Where the above factors are given, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.
Why is this so?The profit equation for the sale of pressure cookers for the company Kitchen Masters is:
P = −120p² + 19,800p − 727,450
To find the sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300,
Let the profit equation = 89,300.
Now, we solve for p:
89,300 = −120p² + 19,800p − 727,450
Adding 727,450 to both sides:
816,750 = -120p² + 19,800p
Dividing both sides by -120:
-6,805 = p² - 165p
Rearrange the equation to make it Quadratic
p² - 165p + 6,805 = 0
Now we can solve for p using the quadratic formula:
p = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = -165, and c = 6,805.
p = (-(-165) ± √((-165)² - 4(1)(6,805))) / 2(1)
p = (165 ± √((27,225 - 27220)) / 2
p ≈ 83.618 or p ≈ 81.382
Therefore, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.
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use the equation 1/5 +s =32/40
The required solution to the equation 1/5 + s = 32/40 is s = 3/5.
To solve the equation 1/5 + s = 32/40 for s, we can begin by subtracting 1/5 from both sides to isolate s:
1/5 + s = 32/40
s = 32/40 - 1/5
We need a common denominator to combine the fractions on the right side of the equation. The least common multiple of 5 and 40 is 40, so we can convert both fractions to have a denominator of 40:
s = (32/40) - (8/40)
s = 24/40
Simplifying the fraction 24/40 by dividing both the numerator and denominator by their greatest common factor, which is 8, we get:
s = 3/5
Therefore, the solution to the equation 1/5 + s = 32/40 is s = 3/5.
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Repartir de forma directamente proporcional 40 000 entre personas de 3,7,10 años a) 3 años = 8 000, 7 años = 12 000, 10 años = 10 000 b) 3 años = 6 000, 7 años = 14 000, 10 años = 20 000 c) 3 años = 4000, 7 años = 8 000, 10 años = 18 000 d) 3 años = 5 000, 7 años = 10 000, 10 años = 10 000
When distributed directly proportionally among the people, using age, the result would be b) 3 years = 6,000, 7 years = 14,000, 10 years = 20,000.
How to distribute the number ?First, find the total age of the people give :
= 10 + 7 + 3
= 20
To amount that would go to 10 as a directly proportional measure is:
= 10 / 20 x 40, 000
= 20, 000
The amount to 7 as a directly proportional value would be:
= 7 / 20 x 40, 000
= 14, 000
The amount to 3 would follow the same pattern :
= 3 / 20 x 40, 000
= 6, 000
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cost minimal of logistic form factory to
warehouse mathematical problem
Answer:
To calculate the minimal cost of logistics from a factory to a warehouse, you would need to consider various factors such as the distance between the factory and the warehouse, the mode of transportation, the weight and volume of the goods being transported, the number of trips required, and any applicable taxes or fees.
To formulate this as a mathematical problem, you could use linear programming, which is a method for optimizing a linear objective function subject to linear equality and inequality constraints.
Let's say we have a factory that produces goods and a warehouse that stores those goods. We want to transport the goods from the factory to the warehouse in a cost-effective way. Let's assume that there are three transportation options available: truck, train, and ship. Each option has a different cost per unit of distance traveled, and a different maximum weight and volume capacity.
Let x1, x2, and x3 be the number of units transported by truck, train, and ship, respectively. Then, the objective function we want to minimize would be:
C = 10x1 + 8x2 + 6x3
where C is the total cost of transportation.
Next, we would need to set up constraints based on the transportation options and the available resources. For example:
Truck capacity: 3x1 <= 15000 (maximum weight capacity of 15000 units for the truck)
Train capacity: 5x2 + 2x1 <= 40000 (maximum weight capacity of 40000 units for the train)
Ship capacity: 2x3 + 3x1 <= 30000 (maximum weight capacity of 30000 units for the ship)
Distance constraint: 2x1 + 3x2 + 5x3 <= 10000 (maximum distance of 10000 units for all transportation modes combined)
The above constraints limit the total weight transported, the capacity of each mode of transport, and the total distance that the goods are transported.
Finally, we would need to add non-negative constraints to ensure that all variables are greater than or equal to zero:
x1 >= 0, x2 >= 0, x3 >= 0
Once we have set up this linear programming problem, we can use optimization techniques to solve for the values of x1, x2, and x3 that minimize the cost of transportation while satisfying all of the constraints.
Step-by-step explanation:
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What value of x satisfies the equation
(793x)3 = 343q36?
The value of x satisfies the equation is 4
What are index forms?Index forms are described as mathematical forms that are used to represent numbers or values that are too large or small in more convenient ways.
From the information given, we have that;
(7q³ˣ)³ = 343q³⁶
expand the bracket for the values
7³. q⁹ˣ = 343q³⁶
Now find the common exponents, we have;
7³. q⁹ˣ= 7³. q³⁶
Divide the values, we have;
q⁹ˣ = q³⁶
Equate the exponents, we get;
9x = 36
Divide both sides by the coefficient of x, we get
9x/9 = 36/9
Divide the values
x = 4
Learn more about index forms at: https://brainly.com/question/15361818
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(Time limit)
Tell me the domain
Tell me the range
Tell me whether the graph is a function or not
The answer choices are below
A relation represents a function when each input value is mapped to a single output value.
On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.
Tracing a vertical line for any x > -3, the vertical line would cross the graph at two points, meaning that the relation is not a function.
As for the domain and the range, we have that:
The domain is: x ≥ -3 -> values of x on the graph.The range is: all real numbers -> values of y on the graph.More can be learned about relations and functions at brainly.com/question/10283950
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