A. We are given that each person weighs 150 lb, each gear
per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.
Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).
So let us say that x is the number of persons, the inequality equation is:
160 x + 200 ≤ 1200
B. There are three groups that wish to rent the boat.
> Solve the inequality equation when x = 4
160 (4) + 200 ≤ 1200
840 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 5
160 (5) + 200 ≤ 1200
1000 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 8
160 (8) + 200 ≤ 1200
1480 ≤ 1200 (FALSE)
So only the 4 people group and 5 people group can safely run the boat.
C. Find the maximum number of people that may safely use the boat, solve for x:
160 x + 200 ≤ 1200
160 x ≤ 1000
x ≤ 6.25
Therefore the maximum number of people that can safely use the boat is 6 people.
A mathematical inequality is created to determine that a maximum of 6 people can rent a boat based on the safety weight limit of 1200 lb. Of the groups provided, only groups with 4 or 5 people can safely rent the boat, while the group with 8 people cannot due to exceeding the weight limit.
To determine the restrictions on the number of people that can possibly fit in a rented boat given the safety weight limit, we start by creating an inequality. Let p represent the number of people, then the total weight of the people is 150 lb times p, and the total gear weight is 200 lb for the boat plus 10 lb per person. The inequality can be represented as:
150p + 10p + 200 \<= 1200
Simplifying the inequality gives us:
160p \<= 1000
Dividing both sides by 160:
p \<= 1000 / 160
p \<= 6.25
Since we cannot have a fraction of a person, the maximum number of people allowed is 6.
For part B, we evaluate if the groups mentioned can safely rent a boat:
Group 1 (4 people): 150(4) + 10(4) + 200 = 840 lb \<= 1200 lb - they can rent.
Group 2 (5 people): 150(5) + 10(5) + 200 = 1000 lb \<= 1200 lb - they can rent.
Group 3 (8 people): 150(8) + 10(8) + 200 = 1480 lb > 1200 lb - they cannot rent as it exceeds the limit.
The maximum number of people who may rent a boat based on the given restrictions and average weights is 6 people.
What is the minimum value for P = x - 2y over the feasibility region defined by the constraints shown below?
A. 8
B. -2
C. -16
D. -14
the answer is -14
Hope this helps : )
"if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility"
The Calvin has a total of 252 utility coming from Oranges and Starfruit.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that oranges cost $2 per pound and starfruit costs $5 per pound.
The utility coming from Oranges and Starfruit, therefore he needs to spend his $26 on buying the oranges and starfruit
Since all in all he also spend $23 on it, and still has remaining $3 in his pocket,
Thus his total utility is 252.
Hence, The Calvin has a total of 252 utility coming from Oranges and Starfruit.
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The complete question is
The oranges cost $2 per pound and starfruit costs $5 per pound. calvin has $26 to spend. if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility?
Which is the directrix of a parabola with equation x^2=y
Determine if the statement is always, sometimes or never true. A natural number is a whole number.
PLEASE HELP!!
What is the length of the midsegment of this trapezoid?
Enter your answer in the box.
Answer:
7 units
Step-by-step explanation:
The length of the midsegment of this trapezoid will be 7 units.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The coordinates of the vertices of the trapezoid are,
A = (-2, 4)
B = (4, 3)
C = (4 , -5)
D = (- 2, - 2)
Now,
Since, We know that;
The length of the midsegment of a trapezoid is always equal to the half of the sum of the parallel sides.
Here, Line AD and BC are parallel lines.
And, The length of AD = √(- 2 - (-2))² + (- 2 - 4)²
= √-6²
= 6
And, The length of BC = √(4 - 4)² + (- 5 - 3)²
= √-8²
= 8
Thus, The length of the midsegment of this trapezoid = (6 + 8)/2
= 14/2
= 7 units.
Therefore, The length of the midsegment of this trapezoid will be 7 units.
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Please help! Use the quadratic function to predict y if x equals 6. Y=2x^2-2x-2
A) y= -58
B) y= 58
C) y=-60
D) y= 60
Answer:
The correct option is B.
Step-by-step explanation:
The given quadratic function is
[tex]y=2x^2-2x-2[/tex]
We have to find the value of the function y at x=6.
Substitute x=6 in the given function.
[tex]y=2(6)^2-2(6)-2[/tex]
[tex]y=2(36)-12-2[/tex]
[tex]y=72-14[/tex]
[tex]y=58[/tex]
The value of the function is 58 at x=6 is 58.
Therefore the correct option is B.
Solve for x: 3 over 4 x + 5 over 8 = 4x. . x = __________________ Write your answer as a fraction in simplest form. Use the \"/\" symbol for the fraction bar
Kanisha has x green apples and y red apples.
Which statement explains why x + y and y + x will each find the total number of apples that Kanisha has?
In addition, the order of the variables matters in the expression.
The expressions are not equivalent because there are two variables.
The first expression has a greater value than the second expression.
In addition, the order of the variables does not matter in the expression.
Answer:
the answer is in addition the order of the variables does not matter in the expression
Step-by-step explanation:
i took the test
what is 3 divided by 7.71?
Using exponents what is the simplified form of the expression 12x^5/6x^2
The required simplified form of the expression 12x⁵/6x² is 2x³.
What are exponential expressions?Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.
The exponential expression is given in the question as:
12x⁵/6x²
To simplify the expression 12x⁵/6x², we can start by dividing 12 by 6 to get:
12x⁵/6x² = (12/6)x⁵/x² = 2x⁵/x²
Then, we can use the quotient of powers rule, which states that when we divide two powers with the same base, we can subtract the exponents to get:
2x⁵/x² = 2x⁵⁻² = 2x³
Therefore, the expression is 2x³ equivalent to the given expression 12x⁵/6x².
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ray OJ bisects angle IOK, if angle IOJ= 2x-5 and measure of angle JOK=x+11, then find measure of angle IOJ
Given ray OJ bisects angle IOK, we can set an equation for angles IOJ and JOK, solve for x and substitute x into the given measure of angle IOJ: 2*(16)-5 equals 27 degrees.
Explanation:Since ray OJ bisects angle IOK, it means that angle IOJ and angle JOK are equal in measurement. Given in the problem, angle IOJ= 2x-5 and angle JOK= x+11. Because they are equal, we can set up the equation 2x-5 = x+11.
To solve for x, we subtract x from both sides of the equation, resulting in x-5 =11. And then, if we add 5 to both sides of the equation, the end result is x = 16.
Substituting x into the given measurement for angle IOJ, which is 2x-5, we would get the measure of angle IOJ as 2*(16)-5 = 27 degrees.
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Q.17
Select the correct numerical form of this number written in scientific notation.
1.2 × 10^4
0.00012
120,000
12,000
1,200
Answer:
its 12,000
Step-by-step explanation:
The sum of two numbers is 68 . the smaller number is 12 less than the larger number. what are the numbers?
Final answer:
To solve the problem, we defined two variables for the larger (x) and smaller (y) numbers. Using the provided information, we set up two equations and solved them to find the numbers: x (the larger number) is 40, and y (the smaller number) is 28.
Explanation:
Step-by-Step Solution to Find the Two Numbers
Let's denote the larger number as x and the smaller number as y. We are given two pieces of information:
The sum of the two numbers is 68.
The smaller number is 12 less than the larger number.
These two statements can be turned into two equations:
x + y = 68 (Equation 1)
y = x - 12 (Equation 2)
Now, we can substitute Equation 2 into Equation 1 to find x:
x + (x - 12) = 68
2x - 12 = 68
Add 12 to both sides:
2x = 80
Divide both sides by 2:
x = 40
Now that we know the larger number, x, we can find y using Equation 2:
y = 40 - 12
y = 28
So, the two numbers are 40 and 28
Which compound inequality has no solution? x ≤ –2 and 2x ≥ 6 x ≤ –1 and 5x ≤ 5 x ≤ –1 and 3x ≥ –3 x ≤ –2 and 4x ≤ –8
Answer:x <= -2 and 2x >= 6 is the smae as
x <= -2 and x >= 3
Step-by-step explanation:
HELP PLEASE
Solve the system by substitution
-4.5x - 2y = -12.5
3.25x - y = -0.75
Solve by substitution-5x+4y=22 x - 3y = 0A) No solution.
b. (6, 2)
c. Infinitely many solutions.
d. (-6, 2)
e. (-6, -2)
Find the slope of the line.
We can use the points (-4, -1) and (0, -2) to solve.
Formula: y2-y1/x2-x1
= -2-(-1)/0-(-4)
= -1/4
Best of Luck!
Please help!
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
Answer:
[tex]y=2x+2[/tex]
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(-4,-6)\ B(2,6)[/tex]
Substitute the values
[tex]m=\frac{6+6}{2+4}[/tex]
[tex]m=\frac{12}{6}=2[/tex]
step 2
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2[/tex]
[tex]B(2,6)[/tex]
substitute and solve for b
[tex]y=mx+b[/tex] ------> [tex]6=(2*2)+b[/tex]
[tex]6=4+b[/tex]
[tex]b=2[/tex]
The equation of the line is equal to
[tex]y=2x+2[/tex]
Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.
Answer:
Pretty sure its the Transitive Property
Step-by-step explanation:
It's a dropdown on Edge so there's no A B C or D
To prove that point C is the midpoint of segment AB, we apply the segment addition property and the definition of congruent segments.
Explanation:To prove that point C is the midpoint of segment AB, we can use the segment addition property. We are given that AB = 12 and AC = 6. By applying the segment addition property, we get AC + CB = AB. Substituting the given values, we have 6 + CB = 12. Solving for CB using the subtraction property, we find that CB = 6.
Now, by using the symmetric property, we can see that 6 = AC. Since CB = 6 and 6 = AC, we can conclude that AC is congruent to CB by the definition of congruent segments. This implies that C is the midpoint of AB, as it divides AB into two congruent segments.
The functions f(x) = –(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.
Final answer:
The completing-the-square method allows rewriting quadratic functions to determine the vertex. The coefficient of the squared term determines if the vertex is a minimum or maximum.
Explanation:
The completing-the-square method allows us to rewrite quadratic functions in a form that reveals the vertex of the parabola. To determine if the vertex is a minimum or a maximum, we need to consider the coefficient of the squared term. In the function f(x) = –(x + 4)² + 2, the coefficient is negative, indicating that the parabola opens downwards, and the vertex is a maximum. In the function g(x) = (x − 2)² − 2, the coefficient is positive, indicating that the parabola opens upwards, and the vertex is a minimum.
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game u welcome
A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 1/4 inches. What should its enlarged height be, in inches?
Two cards are drawn at random without replacement from a standard 52-card deck. what is the probability we see at least one club and at least one ace?
The probability we see at least one club and at least one ace would be 0.019225
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
The Total number of cards in a deck = 52
Number of aces in a standard deck = 4
Number of clubs in a standard deck = 13
The Probability = required outcome / Total possible outcomes
P(ace) = 4 / 52 = 0.0769
P(club) = 13 / 52 = 1/4 = 0.25
Therefore, the probability we see at least one club and at least one ace
0.0769 x 0.25
= 0.019225
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On wensday on a track myles run 7 laps for every 3 laps that elijah run on friday elijahrun 16 more laps than on wensday making the number of laps he run and myles run the same .how many laps did eligah run on wensday
2 sides of an isoceles triangle are 2 and 12. find the length of the third side
The third side of the isosceles triangle with the given sides of 2 and 12 is 12 units.
To find the length of the third side of an isosceles triangle where two sides are given as 2 and 12, we must consider two cases.
In an isosceles triangle, two sides are equal in length and the two angles opposite these sides are also equal. This means either the two given sides are the equal sides, which is not possible since they are different lengths, or one of the given lengths will be the base and the equal sides are yet to be determined.
Case 1: If the side of length 2 is the base, the length of the equal longer sides will both be 12.
Case 2: If the side of length 12 is the base, then the length of the two equal sides must both be 2.
However, we must recognize that the first case is incorrect because it does not form a triangle (a triangle cannot have two sides of length 12 and one side of length 2, as the two longer sides would be parallel and never meet to form a triangle).
Therefore, the correct answer is given by Case 2: the third side of the triangle, which is the base, is 12 units long, and the two equal sides are 2 units long each.
A chess board has 64 squares. if you put one grain of rice on the first square, two grains on the second square, four grains on the third, eight grains on the fourth, and so on. how many grains are on the last square. no calculators.
can you please explain to me which functions are odd?
f(x)=-1/2x^4+5
f(x)=-8x^3+5x
f(x)=-4/x^3-x+1
f(x)=x^5/x^4-1
f(x)=-sqrt2x
f(x)=3sqrtx -x^3
thank you!
HELP ME PLEASE ! I NEED TO DO THIS QUICKLY !!!!! Translate each sentence into an equation!!!!!!!!!!!! 7 berries are 5 less than twice them number of berries Mickey had for lunch! AND also another one Negative 4 times the difference of a number and 7 is 12
the ordered pair (2 16) is a solution to which equation(s)
A. y=(2x)^2
B. y=2x^2
C. y=2x+2
D. y=(x+2)^2
How to find the angle measure of an isosceles triangle if you only know the side lengths?