Josh has 40 minutes to complete a government exam. There are 15 multiple-choice questions worth 3 points each. There are also 5 short-answer questions worth 11 points each. It takes about 2 minutes for Josh to answer the multiple-choice questions m and about 8 minutes to complete the short-answer questions s. The system of inequalities that represents this problem is graphed below. Which ordered pair is not a vertex of the feasible region?
Answers
The feasible vertices of the system representing Josh's exam are (0,0), (12,5), and (15,1.25). The non-feasible vertices are (15,0), (0,5), and (20,0). Therefore, the ordered pair (15,0) is not a vertex of the feasible region.
1. System of Inequalities:
- Time constraint: [tex]\(2m + 8s \leq 40\)[/tex]
- Number of multiple-choice questions: [tex]\(m \leq 15\)[/tex]
- Number of short-answer questions: [tex]\(s \leq 5\)[/tex]
2. Feasible Vertices:
- (0,0), (12,5), (15,1.25)
3. Non-feasible Vertices:
- (15,0), (0,5), (20,0)
So, the ordered pair (15,0) is not a vertex of the feasible region.
Related Questions
True or false
Two points determine a plane
Answers
One up and down and add one more
△LMN, with vertices L(2,2), M(3,5), and N(6,1), is rotated 90° about the origin. What is the location of M′?
Answers
The coordinate of M' is (5, -3)
If the x-axis is Quantity and the y-axis is Price, which of the following is the best summarization of the supply shift from S1 to S2?
A)The supply decreased.
B) The supply stayed the same.
C) The supply increased.
D) The supply outweighed demand.
Answers
Correct answer: B
Answer:
Option B is correct.
Step-by-step explanation:
We have been given x-axis representing quantity
And y-axis representing price
S1 and S2 are supply
So, these two supply have parallel lines which means they will never intersect they will remain same throughout the domain.
Therefore, the supply stayed the same.
Option B is correct.
On the blueprint of a house, 45 millimeters represents 10 meters. The length of the living room is 36 millimeters on the blueprint. What is the actual length of the living room?
Answers
45/10= 36/x
cross multiply
360/45X
360/45 = 8
the length is 8 meters
Which double-angle or half-angle identity would you use to verify that 1+cos2a=2/1+tan2a?
Answers
In this case or scenario,
the double-angle identity that should be used is the one for cosine.
In totality, we shall need the following three trigonometric
identities to end up with the equality:
1. cos (2a) = cos² (a) - sin² (a)
2. sin² (a) + cos² (a) = 1
3. tan² (a) + 1 = sec²
(a)
Using identities 1 and 2 on the left-hand side of the
equation, we get the following:
1 + cos (2a) = 1 + cos² (a) - sin² (a) = 2 cos² (a)
Recalling that cos² (a) = 1 / sec² (a) and applying identity
3, we find the following:
2 cos² (a) = 2 / sec² (a) = 2 / (1 + tan² (a))
Therefore giving us:
2 cos² (a) = 2 / (1 + tan² (a))
Answer:
Its C. cos2a=cos^2a-sin^2a on ed
Jenna surveyed the students at her dance class to find out if they like salsa and/or ballet. The results of her survey are shown in the two-way table below:
Like Salsa
Do Not Like Salsa
Total
Like Ballet
32
42
74
Do Not Like Ballet
22
4
26
Total
54
46
100
If a student does not like ballet, what is the probability that student also does not like salsa?
8.7%
15.4%
18.2%
84.6%
Answers
like ballet 32 42 74
hate ballet 22 4 26
total 54 46 100
if a student does not like ballet (there is 26 that do not like ballet)..what is the probability that the student does not like salsa..of those 26 that do not like ballet, 4 do not like salsa...
4/26 = 0.1538 = 15.38% rounds to 15.4% <=
Help plzzzzz!!!!!!!!!!
Answers
1. less than or equal to 5
2. greater than 5
3. less than 5
19. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.
Answers
6 numbers per cube
if one is a 1, then the other one has to be a 2, 4 or 6 to be an odd sum
1+2=3, 1+4=5,1+6=7
since there are 3 numbers you can get that would be a 3/6 ( reduce to 1/2) probability
so 1/2 probability
1/2 is wrong, I put it on my exam and got it wrong:/
Each week Rosario drive to an ice-skating rink that is 60 miles away. The road trip takes 2.75 hours. If he averages 55 mph on his way to the rink, which equation can be used to find X, the number of miles per hour he averages on his way home?
Answers
Answer: The number of miles per hour he averages on his way home is 36 mph.
Step-by-step explanation:
Since we have given that
Distance traveled by Rosario = 60 miles
Time taken for road trip = 2.75 hours
Speed at which he on his way to the rink = 55 mph
Let X be the speed at which he averages on his way home.
So, According to question, we get that,
[tex]\dfrac{60}{55}+\dfrac{60}{x}=2.75\\\\1.09+\dfrac{60}{x}=2.75\\\\\dfrac{60}{x}=2.75-1.09\\\\\dfrac{60}{x}=1.659\\\\x=\dfrac{60}{1.659}\\\\x=36.16\\\\x=36\ mph[/tex]
Hence, the number of miles per hour he averages on his way home is 36 mph.
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x= 12 + y
18x – 12y= 18
Answers
18x – 12y= 18
substitute x= 12 + y into 18x – 12y= 18
18x – 12y= 18
18(12 + y) – 12y= 18
36 + 18y - 12y = 18
6y =-18
y = -3
x= 12 + y
x= 12 -3
x = 9
solution (9, -3)
18(12+y)-12y=18 perform indicated multiplication on left side
216+18y-12y=18 combine like terms on left side
216+6y=18 subtract 216 from both sides
6y=-198 divide both sides by 6
y=-33, which makes x=12+y become:
x=12-33
x=-21
So the solution to this system of equations is the point (-21, -33)
Amy wants to buy a pair of jeans that cost $65. Today the store is offering a straight discount of 25%. Calculate her savings and cost after the discount.
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 65&100\\ x&25 \end{array}\implies \cfrac{65}{x}=\cfrac{100}{25}[/tex]
solve for "x", that's her savings
the cost of the jeans is 65 - x
Answer:
Amy's discount is $16.25, and the cost after the discount is $48.75.
Step-by-step explanation:
A point is on a circle if the distance from the center of the circle to the point is equal to the
a) area.
b)circumference.
c)radius.
d)diameter.
Answers
The distance from the centre of the circle to any point on the circumference of the circle is called the radius.
What is the equation of a quadratic graph with a Focus of (8,-8) and directrix of y=-6
Answers
so hmmm the left-side of the picture, is the focus point and the directrix, notice, the directrix is a horizontal line, that means the parabola is a vertically opening one.
also notice, the focus point is below the directrix, that means the parabola opens downwards
now, the vertex is "p" distance from either the directrix and the focus point, so that means, the vertex is half-way between those two fellows, if you notice the right-side of the picture, that's where the vertex is at.
the distance "p" is clearly just 1unit, however, since the parabola is opening downwards, "p" is negative, thus -1
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{cases} h=8\\ k=-7\\ p=-1 \end{cases}\implies (x-8)^2=4(-1)(y-(-7)) \\\\\\ (x-8)^2=-4(y+7)\implies \cfrac{(x-8)^2}{-4}=y+7 \\\\\\ -\cfrac{1}{4}(x-8)^2-7=y[/tex]
Transform both equations in each system of equations so that each coefficient is an integer.
***I also need it to be solved using substitution method.
Answers
15x -36 = 2y..................(1)
and second multiply by 5:-
2x + y = 9..............(2)
solving:-
from equation (2) y = 9-2x, substitute in equation (1):-
15x - 36 = 2(9-2x) = 18 - 4x
19x = 54
x = 54/19 = 2.84
so y = 9 - 2(2.84) = 3.32
PLEASE HELP!!!! IMAGE ATTACHED FIND THE MEASURE OF ANGLE 3
Answers
m< 3 = 30
answer
30
How would you represent 4 eighth notes as a fraction?
Answers
Which expression represents the area of triangle ABC in square meters?
Answers
The base is 20 + 37 = 57.
Now here is where I am confused. I think it is 14 however. I'm sorry if I'm wrong here.
So the answer is 1/2 * 57 * 14
Answer:
the correct answer is A. 1/2 x 14 x 57
Step-by-step explanation:
i got it right on my test
ind the area of an octagon with a radius of 6 meters. Round your answer to the nearest tenth.
Answers
A = 2 a² ( 1 + √ 2 )
and a = r √ 2
a = 6 √ 2
A = 2 * ( 6 √2 )² * ( 1 + √ 2 ) =
= 2 * 72 ( 1 + √ 2 ) =
= 144 * ( 1 + √ 2 ) m² = 144 + 144 √2 ≈ 347.65 m²
A card is picked from a standard deck of 52 cards. determine the odds against and the odds in favor of selecting a 10
Answers
The odds in favor of drawing a '10' from a standard 52-card deck are 1 to 12, and the odds against are 12 to 1.
Explanation:In a standard deck of 52 cards, there are four '10' cards - one each of hearts, diamonds, clubs, and spades. Hence the probability of drawing a '10' is 4 out of 52, or simplified, 1 out of 13.
Therefore, the odds in favor of selecting a '10' (i.e., the probability of selecting a '10' versus not selecting a '10') are 1 to 12 because for each '10' card there are 12 others that are not '10s'.
The odds against selecting a '10' are simply the inverse of the odds in favor. That is, for every one time you may draw a '10', there are 12 other times when you would draw something else, hence the odds against drawing a '10' are 12 to 1.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
The roof of a house is being reconstructed to accommodate heavy snows. the current 32 foot roofline makes an 18.2° angle with the horizontal. the owner has decided to construct the new roof so that it makes a 50° with the horizontal as shown below. what will be the length of the new roofline?
Answers
To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.
Explanation:To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:
tan(50°) = 32/x
To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:
x = 32/tan(50°)
Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:
x ≈ 32/1.1917
By calculating this, we find that the length of the new roofline is approximately 26.9 feet.
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
Answers
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
Final answer:
To convert 28.7251 degrees to degrees, minutes, and seconds, take the whole number of degrees (28) and multiply the decimals (.7251) by 60 to get the minutes (43). Then multiply the remaining decimal of the minutes (.506) by 60 to get the seconds (30), resulting in 28 degrees, 43 minutes, and 30 seconds (28° 43' 30").
Explanation:
To convert 28.7251 degrees to degrees, minutes, and seconds, you follow a multi-step process which involves converting the decimal part of the degrees into minutes and then into seconds. First, identify the whole number of degrees, which is 28 in this case.
To convert the decimal part (.7251) to minutes, multiply by 60. Using the operation provided in the reference, with 0.7251 × 60, you get 43.506 minutes. The whole number part, 43, is the minutes.
To convert the remaining decimal part of minutes (.506) into seconds, again multiply by 60. This gives you (.506 imes 60) 30.36 seconds, which when rounded to the nearest second is 30 seconds.
Therefore, 28.7251 degrees is equal to 28 degrees, 43 minutes and 30 seconds (28° 43' 30").
The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)?
Number of Hours Distance from Lighthouse
(in oceanic miles)
2 53
4 95.5
6 138
8 180.5
10 223
12 265.5
14 308
16 350.5
y = 42.5x + 10.5
y = 10.5x + 32
y = 21.5x + 10.5
y = 12.25x + 28.5
y = 12.5x + 10.5
Answers
m=(y2-y1)/(x2-x1)
m=(95.5-53)/(4-2)
m=21.25 ? Your equations are wrong, I'll double check with another set of points...
m=(350.5-308)/(16-14)
m=21.25 LOL, yep none of your lines has the correct slope.
Anyway...
y=21.25x+b, using any point we can solve for the y-intercept, or "b", (2, 53)
53=21.25(2)+b
53=42.5+b
10.5=b so the distance to the lighthouse as a function of time is:
y=21.25x+10.5
So essentially, you should fire your teacher or burn that book you are using :)
Answer:
y=21.5x+10.5
Step-by-step explanation:
Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π 3 rad.
Answers
Final answer:
To find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3 rad, we need to differentiate the formula for the area of a triangle with respect to time.
Explanation:
Rate of Change of Triangle Area with Increasing Angle
To find the rate at which the area of the triangle is increasing, we need to differentiate the formula for the area of a triangle with respect to time.
The formula for the area of a triangle is given by: A = 0.5 × a × b × sin(C), where a and b are the lengths of the two sides and C is the angle between them.
By differentiating this formula with respect to time, we can find the rate of change of the area with respect to time.
When the angle between the sides is π/3 rad, substitute the length of the sides and the rate at which the angle is increasing, and solve for the rate of change of area.
I need help and I'm not sure if the answer is A so can you pls help!
Answers
The answer is D because -5 is less than 1 and its not equal to 1.
If one u.s. dollars equals 5.76 egyptian pounds and one u.s. dollar equals 0.56 british pound, how many egyptian pound equal one british pound?
Answers
0,56 p=1s=5,76 e
So
0,56 p=5,76 eWe have to show how much the Egyptian pound was equal to one British pound.
This means that we must obtain the equation 1p=.....
Of 0.56=56/100.56/100 multiply by 100/56 get 1.Multiply both parts of equation by 100/56
1 pound =10.2857 of egyptian pound.
Write the equation of the ellipse with its center at the origin. the height of the ellipse is 12 units and the width is 14 units.
Answers
The general form of the equation of an ellipse centered at (h,k), with semi -major axis of a and semi - minor axis of b is
[tex] \frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} =1[/tex]
Because the width is 14, therefore a = 7.
Because the height is 12, therefore b = 6.
Because the ellipse is centered at the origin, h=0, and k=0.
Answer:
[tex] \frac{x^{2}}{49} + \frac{y^{2}}{36} =1[/tex]
Find the missing number in the proportion. 8/56 = ?/49
Answers
Convert the following using dimensional analysis:
13.2 cm to ft & in
Answers
Use the remainder theorem to determine the remainder when 3t2 + 5t − 7 is divided by t − 5. A. 93 B. 43 C. 107 D. 57
Answers
[tex]P(t) = 3t^{2} + 5t - 7[/tex]
Substitute t = 5 into the equation:
[tex]P(5) = 3(5)^{2} + 5^{2} - 7[/tex]
[tex]P(5) = 75 + 25 - 7 = 93[/tex]
Thus, we get a remainder of 93 or (A)
If five cakes cost 5 pounds how much do 2 cakes cost
Answers
You have five cakes, and it costs 5 pounds. What is the price of each cake?
Well.. It has to be 1! So, if you have two cakes - it will cost 2 pounds. Wanna go extra and get 30 cakes? 30 pounds!