Answer:
Negative. Because he should run all seven weeks to get positive result.
A student has 30 minutes to complete an exam. There are 9 multiple choice questions worth 3 points each. There are also 3 short answer questions worth 5 points each. It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question. How many multiple choice questions and short answer questions should the student answer to maximize his score in the time remaining (Use x = multiple choice; y = short answer.)
Answer:
9 multiple choice questions and 2 short answer questions
===========================================================
Explanation:
x = number of multiple choice
y = number of short answers
The statement "It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question" means it takes 2x+6y minutes to answer x multiple choice and y short answer questions. We want this total to be 30 minutes or less.
Therefore, [tex]2x+6y \le 30[/tex] is one constraint.
---------------
Another constraint is that [tex]0 \le x \le 9[/tex] since the most multiple choice questions you can answer is 9.
Because there are 3 short answer questions, this means another constraint is [tex]0 \le y \le 3[/tex]
---------------
The list of constraints is:
[tex]\begin{cases}2x+6y \le 30\\0 \le x \le 9\\0 \le y \le 3\\\end{cases}[/tex]
If you were to graph and shade these regions on the xy grid, then you should get a pentagon with the following corner points
A = (0, 0)
B = (0, 3)
C = (6, 3)
D = (9, 2)
E = (9, 0)
We'll plug the coordinates of each vertex into the objective function P(x,y) = 3x+5y which will compute the number of points total after answering x multiple choice and y short answer questions. This computes the maximum points possible.
Plug in the coordinates of point A to get P(0,0) = 0
Repeat for point B to get P(0,3) = 15
Now move onto point C to get P(6,3) = 33
Then point D is P(9,2) = 37 and point E gets us P(9,0) = 27
---------------
Summary:
P(0,0) = 0
P(0,3) = 15
P(6,3) = 33
P(9,2) = 37
P(9,0) = 27
We see that x = 9 and y = 2 produce the largest P(x,y) value of 37
Therefore, you should answer 9 multiple choice questions and 2 short answer questions. This will yield 37 points if you were to get all of those questions correct. In other words, the most points possible are 37 when given 30 minutes.
---------------
Side note:
If you had unlimited time, then the most points possible are 9*3+3*5 = 27+15 = 42 which is the total number of points on the exam.
Getting a 37 out of 42 is a grade of about 37/42 = 0.881 = 88.1%
The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.
To maximize the student's score in the given 30 minutes, we need to create an objective function and constraints based on the time available and the number of questions.
Let:
x = Number of multiple-choice questions to answer
y = Number of short-answer questions to answer
Objective Function (Score):
The score can be calculated as the sum of points obtained from multiple-choice questions and short-answer questions:
Score (S) = 3x (for multiple-choice questions) + 5y (for short-answer questions)
Constraints:
1. Time Constraint: The total time taken to answer all the questions should not exceed 30 minutes:
Time for multiple-choice questions + Time for short-answer questions ≤ 30
2. Number of Questions Constraint: The student can't answer more questions than available:
Number of multiple-choice questions (x) ≤ 9 (total number of multiple-choice questions available)
Number of short-answer questions (y) ≤ 3 (total number of short-answer questions available)
Now, let's consider the time taken to answer each type of question:
- Time for multiple-choice questions: 2 minutes per question
- Time for short-answer questions: 6 minutes per question
Based on the above information, the time constraint can be written as an equation: 2x + 6y ≤ 30
Now, we need to maximize the score (S) by selecting the values of x and y that satisfy the above constraints. This is a linear programming problem that can be solved using various optimization techniques, such as the graphical method, simplex method, or linear programming software.
Since this is a simple problem with a small number of variables and constraints, we can use the graphical method to find the maximum score. We will graph the feasible region defined by the constraints and find the corner points of the feasible region. Then, we will calculate the score (S) at each corner point and select the one with the highest score.
The feasible region will be bounded by the lines:
2x + 6y ≤ 30 (Time constraint)
x ≤ 9 (Number of multiple-choice questions constraint)
y ≤ 3 (Number of short-answer questions constraint)
The corner points of the feasible region are the intersection points of these lines.
Now, calculate the score (S) at each corner point:
For (0, 0): S = 3(0) + 5(0) = 0
For (0, 3): S = 3(0) + 5(3) = 15
For (9, 0): S = 3(9) + 5(0) = 27
The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.
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PLEASE HELP!!
Find the x- and y- intercepts of the function.
(A) x-intercept: (-2,0)
y-intercept: none
(B) x-intercept: (-6,0),(6,0)
y-intercept: (0,-2)
(C) x-intercept: none
y-intercept: none
(D) x-intercept: none
y-intercept: (0,-2)
I think it’s C
Basically you are correct its C , ut go with your gut!
can you use the multiplication property of inequality to solve 8m>-1/10?can you use the division of property to solve -9/2 >3/2?explain your reasoning
HELP ME
The simplification of the given inequalities gives;
1) m > -1/80
2) x < -1/3
How to use Algebraic Properties of Equality?
1) The multiplicative property of inequality states that both sides of an inequality can be multiplied or divided by the same number and an equivalent inequality can be formed.
Thus, applying that to 8m > -1/10, gives;
Multiply both sides by 1/8 to get;
8m * 1/8 > -1/10 * 1/8
m > -1/80
2) The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
Thus, applying that to -9/2x > 3/2 gives;
Divide both sides by -9/2 to get;
x < -1/3
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How many widgets does Widget INC. have to sell to break even?
Answer:
300 widgets
Step-by-step explanation:
Each time the widgets sold goes up by 100, the profits goes up by 400. This shows a ratio/slope of 4 if we were to graph this. To find out when they break even you need to subtract $400 from the first row to get to zero and the equivalent amount of widgets. If each widget is $4 then subtract 100 from 400 to get 300 widgets
well, we know the table has linear relationship, so let's use it to get the Profit function then, to get the equation of any straight line, we simply need two points off of it, so let's use those two points in the picture below.
[tex](\stackrel{x_1}{500}~,~\stackrel{y_1}{800})\qquad (\stackrel{x_2}{700}~,~\stackrel{y_2}{1600}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1600}-\stackrel{y1}{800}}}{\underset{run} {\underset{x_2}{700}-\underset{x_1}{500}}} \implies \cfrac{1600 -800}{700 -500} \implies \cfrac{ 800 }{ 200 }\implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{800}=\stackrel{m}{4}(x-\stackrel{x_1}{500}) \\\\\\ y-800=4x-2000\implies y=4x-1200[/tex]
how many bucks will they lose by selling "0" items?
well, let's find out by setting x = 0.
[tex]\stackrel{profit}{y}=4(0)-1200\implies y=-1200~\hfill \stackrel{\textit{they'd be losing}}{\text{\LARGE 1200}}[/tex]
how many will they need to sell to break-even?
well, to break-even that means no loses, no profits but no loses either, so-called breaking-even, you simply sell enough to cover costs, at that point the profit = y = 0, so
[tex]\stackrel{profit}{0}=4x-1200\implies 1200=4x\implies \cfrac{1200}{4}=x\implies \text{\LARGE 300}=x[/tex]
Please help me with this question.
Part (a)
We need to consider
[tex]x=\frac{1}{k\pi}, k \in \mathbb{Z}[/tex]
[tex]f\left(\frac{1}{k\pi} \right)=\tan (k\pi)
[/tex]
tan(x) has a period of pi, so this is equal to tan(0)=0.
Part (b)
We need to consider
[tex]x=\frac{4}{(4n+1)\pi}, n \in \mathbb{Z} \\ \\ f \left(\frac{4}{(4n+1)\pi} \right)=\tan \left(\frac{(4n+1)\pi}{4} \right) \\ \\ =\tan \left(\pi n+\frac{\pi}{4} \right) \\ \\ =1[/tex]
Part (c)
We see that 1/x approaches infinity, and hence the limit does not exist.
10x-2=102 cry about it
Answer:
Step-by-step explanation:
add 2 to both sides,
10x-2=102
+2 +2
now it is 10x=104
now divide 10 from both sides.
10x/10=104/10
x=10.4
6) Magdalena runs 5 days per week. Her goal is to run a minimum of 60 km each
week. If she runs 50 days, what is the minimum distance she will run?
The required minimum distance she will run is 600 km.
Given that,
Magdalena runs 5 days per week. Her goal is to run a minimum of 60 km each week. If she runs 50 days, what is the minimum distance she will run is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
In 5 days she ran 60 km
In one day she ran = 60 / 5 = 12
Let the number of km run be x
for 50 days minimum run would be,
= 50 * 12
= 600 km
Thus, the required minimum distance she will run is 600 km.
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Refer to ®R .
Is -VU a radius? Explain.
The chord of a circle is defined as the line segment connecting any two points on its circumference.
VU is not a radius it is a chord.
What is a chord in a circle?The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.
A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.
A radius is a segment with ends at the center and circumference of a circle. VU, on the other hand, is a chord because it has both endpoints on the circle.
Therefore, VU is not a radius it is a chord.
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What is the relationship between a and b
Answer:
B. Vertical angles.
look at the image attached.
Find the sum of each finite arithmetic series. (-3)+(-6)+(-9)+. . . . . . +(-30)
The sum of the given arithmetic series (-3)+(-6)+(-9)+. . . . . . +(-30) is -165
The given series is:
(-3)+(-6)+(-9)+. . . . . . +(-30)
First, we need to find how many terms in that arithmetic series.
Recall, the formula for the nth term of an arithmetic sequence is:
a(n) = a(1) + (n-1) . d
From the given series we know that:
the first term : a(1) = -3
the last term: a(n) = -30
the common difference: d = -6 - (-3) = -3
Substitute these parameters into the formula:
a(n) = a(1) + (n-1) . d
-30 = -3 + (n-1) . (-3)
-30 = -3n
n = 10
So there 10 terms in the series.
Use the sum formula:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [-3 + (-30)]
S(10) = -330/2 = -165
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A video game displays 168 frames in 6 seconds on Penelope's computer. What is the rate in frames per second?
Step-by-step explanation:
If theres 168 frames in six seconds, to find out how many there are per second, we simply need to divide 168 by 6. This equals 28. If you know how many there are for 6, and you want to find out how many for 1, you know you're dividing 6 by 6. So you have to do the same to the amount of frames.
please help me! i’m stuck on this problem :((
Answer: x=18
Step-by-step explanation:
2x+8x=180 ==> angles CDE(8x) and ABC(2x) are opposite supplementary angles meaning that they add up to 180 degrees.
10x=180
10x/10=180/10
x=180/10
x=18
Reporte 184 caracoles entre 8 árboles c
cuántos caracoles tendrá cada árbol?
Answer:
23
Step-by-step explanation:
Porque 23 X 8 = 184
Espero te ayude
Hope this helps
yesterday 15 employees in an office were absent if these absentees constitute 30% of the employees, what is the total number of employees
Answer:
total of 50 employees
Step-by-step explanation:
Ms.Nishino uses Zipcar, a rental car service. She only wants to spend $75.00 each month.ziper charges $25 a month, plus $12.50 per hour of car rental.
Ms.Nishino can drive using Zipcar for 4 hours
How is the total cost of of car rental modelled?
The total cost of car rental can be viewed using a straight-line equation, such total cost comprises of the fixed monthly charge and the total cost of hours based on the fact that hourly fee is $12.50 of car rental
y=a+bx
y=total cost=$75.00
a=fixed charge per month for car rental=$25.00
b=hourly charge=$12.50
x=number of hours spent driving in a month=unknown
75=25+12.50x
75-25=12.50x
50=12.50x
x=50/12.50
x=4
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Concluding part of the question:
How many can she drive the rental car to get it in her budget?
plss help ASAP i rly need this
The answer is -0.5.
The source is from calculator soup.
If 4(x+2)-2(x-10)=0 , what is the value of x ?
The value of x is -14.
Rewriting the equation mentioned in question to solve for the value of x -
4(x + 2) -2 (x - 10) = 0
Performing multiplication with brackets on Left Hand Side of the equation
4x + 8 - 2x + 20 = 0
Performing addition and subtraction on Left Hand Side of the equation
2x + 28 = 0
Shifting 28 to other side of equation
2x = - 28
Shifting 2 to other side of equation as denominator
x = - 28/2
Performing division to find the value of x
x = -14
Hence, the value of x is -14.
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Suppose B is the midpoint of -AC. Use the given information to find the missing measure. A B=10 s+2, A C=40, s= ?
Value of s is 1.8.
The midpoint of a line is a point that bisects the line into equal parts. It is equidistant from both end points of the line.
As B is the midpoint of AC,
2AB = AC
∴ 2(10s + 2) = 40
∴ 20s + 4 = 40
∴ 20s = 36
∴ x = 1.8.
Now, AB = 10s + 2
Substituting the value of s,
∴ AB = 10(1.8) + 2
∴ AB = 20 units
Thus, the value of s is 1.8 and the length of AB is 20 units.
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What is the difference ? Show all your steps.
-4-(-7) =
Answer:
Step-by-step explanation:
−4−(−7)=
The opposite of −7 is 7.
−4+7
Add −4 and 7 to get 3.
3
Answer:
3
Step-by-step explanation:
Think of -4-(-7) as -4+7
just remove the negative and add instead
your answer is 3
f(x) = 3x + 10
g(x) = x - 2
Find f(g(x))
Answer:
f(g(x)) = 3x + 4
Step-by-step explanation:
to find f(g(x)) substitute x = g(x) into f(x)
f(g(x))
= f(x - 2)
= 3(x - 2) + 10
= 3x - 6 + 10
= 3x + 4
Answer:
[tex]f\left[g(x)\right]=3x + 4[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x+10\\g(x)=x-2\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The given composite function f[g(x)] means to substitute the function g(x) in place of the x in function f(x):
[tex]\begin{aligned}f\left[g(x)\right] & = f(x-2)\\& = 3(x-2)+10\\& = 3x-6+10\\& = 3x+4\end{aligned}[/tex]
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Which angle is complementary to angle BAC?
The angle which is complementary to angle BAC is ∠ACB which is option (a) .
Two angles are same to be angle if they add up to ninety degrees. In alternative words, once angle are place along, they type a right angle (90 degrees). Angle one and angle two are complementary if the add of each the angles is capable ninety degrees (i.e. angle one + angle two = 90°) and therefore, angle one and angle two are known as enhances of every alternative.From the figure we can see that ΔABC is right angled triangle at B .
∠BAC and ∠ACB on adding gives the right angle ∠CBA .
Hence , on adding ∠ACB to ∠BAC , we get the sum 90° so , ∠ACB is the complementary to angle BAC .
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Open the parallel lines reflection application. The right set of parallel lines is a reflection across the y-axis of the left set of parallel lines. Click the reflect over y-axis button. Are the two sets of parallel lines the same? What does this mean about how parallel lines change when you reflect them?
The first image is before I rotated the angle, and the second image is after I rotated the angle.
Answer:
The lines are the same, they are just in a different position.
A reflection is a type of rigid transformation. Rigid transformations do not
change the size nor the length of the pre-image.
In other words, the pre-image and the image in a rigid transformation are congruent.
Step-by-step explanation:
Hope this helps.
Write an absolute value inequality to represent each situation.
A friend is planning a trip to Alaska. He purchased a coat that is recommended for outdoor temperatures from -15⁰ F to 45⁰F . Let t represent the temperature for which the coat is intended.
Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30
Step-by-step explanation:
To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"
First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15
Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30
Now we can set up our equation,
center (c) = 15
tolerance (t) = 30
|t - 15| ≤ 30
Now that we have our equation, we can set up the inequality
|x - c| ≤ t = -t ≤ x - c ≤ t
so,
-30 ≤ t - 15 ≤ 30
Hope this helps!
(sorry it was so long)
If point B ( -3, -6) is translated 8 units up and 1 unit left what are the coordinates of B’?
If sinx = 0.6 and AB = 12 , what is the area of ΔABC ?
a. 9.6 units²
b. 28.8 units²
c. 31.2 units²
d. 34.6 units²
e. 42.3 units²
If sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².
As given in the question,
In triangle ABC,
AB = Perpendicular side
BC = Base
AC = Hypotenuse
sinx = 0.6
AB = 12
sinx = AB / AC
⇒0.6 = 12/AC
⇒AC = 12 /0.6
⇒ AC = 20
Using Pythagoras theorem,
AB² + BC² = AC²
⇒ BC² = 20² -12²
⇒BC = 16
Area of ΔABC = (1/2)× AB×BC
= (1/2)×12×16
= 96 units²
Therefore, if sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².
The complete question is:
If sin x = 0.6 and AB = 12 as shown in the diagram , what is the area of ΔABC ?
a. 96 units²
b. 28.8 units²
c. 31.2 units²
d. 34.6 units²
e. 42.3 units²
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Which angles are complementary to each other?
Answer:
3 and 2
Step-by-step explanation:
complementary means they add up to 90 degrees. Angle 3 and 2 equal 90 degrees,
Find the coordinates of the circumcenter of the triangle with the given vertices. Explain.
J(5,0), K(5,-8), L(0,0)
The triangle with vertices J(5 , 0), K(5 , -8), and L(0 , 0) has its circumcenter located at Point (5/2 , -4).
Circumcenter of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.
Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.
One method is to calculate the intersection point of any two perpendicular bisectors.
First is to find the midpoint of the two sides given the formula:
midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]
Consider side JK and side KL.
JK : midpoint = [(5 + 5)/2 , (0 + -8)/2] = (5 , -4)
KL : midpoint = [(5 + 0)/2 , (-8 + 0)/2] = (5/2 , -4)
Next, solve for the slope of each side and slope of its perpendicular bisector (-1/m).
m = (y2 - y1)/(x2 - x1)
JK : m = (-8 - 0)/(5 - 5) = -8/0 = 0/8 = 0
KL : m = (0 - -8)/(0 - 5) = 8/-5 = 5/8
Using the midpoint and the slope of the perpendicular bisector, set up its equation using the point-slope form.
(y - ym) = -1/m(x - xm)
JK : (y - -4) = 0(x - 5)
y + 4 = 0
y = -4
KL : (y - -4) = 5/8(x - 5/2)
y + 4 = 5/8 x - 25/16
y = 5/8 x - 89/16
Find the intersection (circumcenter of the triangle) of these two perpendicular bisectors.
Since from the equation 1, y = -4, input this value to the 2nd equation.
y = 5/8 x - 89/16
-4 = 5/8 x - 89/16
5/8 x = 25/16
x = 5/2
y = -4
Hence, the circumcenter is at Point (5/2 , -4).
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In little league,the field is a square with sides of 60 feet. The expression [tex]\sqrt{(s^{2}+s^{2} )} \\[/tex] represents the diagonal distance across a square of side length S.Second base and home plate are in opposite corners across the field.Estimate the distance the catcher at home plate would have to throw the ball to reach the second baseman at second base.
The catcher at home plate had to throw the ball 60 cm to reach the 2nd baseman at second base.
What is defined as the Pythagorean Theorem?The Pythagorean theorem is an extremely useful method for resolving a missing length of a right triangle in mathematics. The square of the longest side, also known as the hypotenuse, is equal to the sum of a squares of the 2 other sides, according to this theorem.The hypotenuse of a right triangle is formed by the line from home plate to 2nd base. The triangle's two sides are each 60 feet long.
We can calculate the length of the hypotenuse using the Pythagorean theorem:
Diagonal² = side² + side²
Side= 60 feet
Diagonal = √s² + s²
Put the value in formula;
(√s² + s²)² = 60² + 60²
2s² = 2 ×60²
Further simplify;
s² = 60²
Taking root on both sides;
s = 60 feet.
Thus, the side of the square field is 60 feet.
Therefore, a catcher at home plate ought to throw the ball 60 cm to reach the 2nd baseman at second base.
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Describe some advantages and some disadvantages of a recursive formula and an explicit formula. When is it appropriate to use each formula?
The explicit formula has the benefit of making it simple to locate any term in the sequence. The recursive formula only includes one addition or multiplication operation, hence this formula's drawback is that it has more operations overall.
What is recursive formula?We discovered that a recursive rule is a rule that repeatedly alters a prior number in order to reach a subsequent number. As an illustration, our formula for counting numbers is recursive since each number is equal to the preceding number plus 1.
A recursive function is one that generates a series of phrases by repeating or using its own prior term as input.
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Please help thank you
