Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]
Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C
Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C
So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]
Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]
Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]
More for reference : https://brainly.com/question/9405925?referrer=searchResults
II NEED HELP!!!!!!!! Are the graphs of the lines in the pair parallel? Explain. y = 2/3x– 17 4x – 6y = –6 4x-6y=-6 Yes, since the slopes are the same and the y-intercepts are the same. A )No, since the y-intercepts are different. B)No, since the slopes are different. C)Yes, since the slopes are the same and the y-intercepts are different.
Answer:
A
Step-by-step explanation:
What is the value of x in the triangle? a 30-60-90 triangle with short leg length x and hypotenuse length 8 A. B. C. D.
In a 30-60-90 triangle with short leg length x and hypotenuse length 8. the value of x in the triangle is 8 [tex]\sqrt{3}[/tex] / 3.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the longest side and is referred to as the hypotenuse.
In a 30-60-90 triangle the ratio of the side lengths is 1 : 2 : [tex]\sqrt{3}[/tex]
To find the length of the short leg, x, you can create this proportion:
x / 8 = 1 / [tex]\sqrt{3}[/tex]
x = 8 × 1 / [tex]\sqrt{3}[/tex]
x = 8 / [tex]\sqrt{3}[/tex]
By rationalizing the denominator by multiplying the numerator and denominator by [tex]\sqrt{3}[/tex].
x = 8 [tex]\sqrt{3}[/tex] / 3
Learn more about the right triangle;
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Find the product. (5p + 2)2^
Answer:
25p^2 + 4 + 20p
Step-by-step explanation:
(5p + 2)^2 = (5p)^2 + (2)^2 + 2 × 5p × 2
= 25p^2 + 4 + 20p
PRST is a trapezium. PQR and PTU are
straight lines. Find the values of x and y.
Answer:
x = 56 degrees
y = 62 degrees
Step-by-step explanation:
Given TS || PR
x = 56 ................. corresponding angles TS, PR parallel sides of trapezium.
VSK = x ...................... correspoinding angles given TU || SV
y = 118 - VSK .......... given VSR = 118
= 118 - 56
= 62
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below.
Answer:
0
Step-by-step explanation:
Answer: it's C. 0
Also Happy early Christmas
Please help me, im in desperate need of help for these questions
Answer:
For the first one, answer is dilation of 2
Step-by-step explanation:
you see the coordinates for triangle A'B'C' are all doubled the coordinates of triangle ABC
PLSSSS HELPPP. The price of a tennis racquet is inversely proportional to its weight. If a 20 oz. racquet cost $30.00, what would a 25 oz. racquet cost?
Answer:
$24 will be the cost of tennis racquet with weight 25 oz.
Step-by-step explanation:
Given that Price of racquet is inversely proportional to its weight.
i.e.
[tex]Price \propto \dfrac{1}{Weight}[/tex]
We can replace the proportional sign with a constant of proportionality.
[tex]Price = \dfrac{C}{Weight}[/tex]
Where C is a constant named as constant of proportionality.
Given that cost of 20 oz. racquet is $30.00
Putting both the values :
[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]
So, the equation becomes:
[tex]Price = \dfrac{600}{Weight}[/tex]
Now, we have to find the price of 25 oz. racquet.
Putting Weight = 25 oz and finding Price:
[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]
So, $24 will be the cost of tennis racquet with weight 25 oz.
I really need help with this question, and I would really appreciate it! I will mark brainliest!
Answer:
These are two equilateral triangles and all the sides of an equilateral triangle are equal. The question even says so so that's the answer, all the sides of the equilateral triangles are equal so all the sides equate to each other
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions ?
Answer:
The width is 23.5 ft and the length is 47 ft
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
141 = 2(l+w)
The length is twice the width
l = 2w
141 = 2 ( 2w+w)
141 = 2( 3w)
141 = 6w
Divide each side by 6
141/6 = 6w/6
23.5 = w
l = 2w = 2(23.5) = 47
The width is 23.5 ft and the length is 47 ft
Answer:
[tex]\boxed{Width = 23.5 \ feet}[/tex]
[tex]\boxed{Length = 47 \ feet}[/tex]
Step-by-step explanation:
Let Length be l and Width be w
Perimeter = 2(Length) + 2(Width)
Condition # 1:
2l+2w = P
=> 2 l + 2 w = 141
Condition # 2:
=> l = 2w
Putting the second equation in the first one
=> 2(2w)+2w = 141
=> 4w + 2w = 141
=> 6w = 141
Dividing both sides by 6
=> Width = 23.5 feet
Given that
=> l = 2w
=> l = 2(23.5)
=> Length = 47 feet
Please help.. ty if you do
Answer:B
Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer
I REALLY NEED HELP FOR THIS ONE
Answer:
A = 27(2√3-π) cm² ≈ 8.71 cm²Step-by-step explanation:
Area of shaded region it is area of hexagon minus area of circle.
A regular hexagon is comprised of six equilateral triangles (of the same sides).
So its area: [tex]A_1=6\cdot\dfrac{S^2\sqrt3}{4}=\dfrac{3S^2\sqrt3}2[/tex] {S = side of the triangle}
Height (H) of such a triangle is equal to radius (R) of a circle inscribed in the hexagon:
[tex]R = H = \dfrac{S\sqrt3}{2}[/tex]
Area of shaded region:
[tex]A=A_1-A_\circ=\dfrac{3S^2\sqrt3}2-\pi R^2=\dfrac{6S^2\sqrt3}4-\pi\left(\dfrac{S\sqrt3}2\right)^2=\dfrac{S^2(6\sqrt3-3\pi)}4[/tex]
S = 6 cm
so:
[tex]A=\dfrac{6^2(6\sqrt3-3\pi)}4=\dfrac{36(6\sqrt3-3\pi)}4=9(6\sqrt3-3\pi)=27(2\sqrt3-\pi)\ cm^2\\\\A=27(2\sqrt3-\pi)\ cm^2\approx8.71\ cm^2[/tex]
What is the greatest common factor of the three terms?
36h, 12h6, 48h5
Answer:
12hStep-by-step explanation:
each term has h^1
each term's coefficient is divisible by 12
12h( 3, h^5, 4h^4)
So, the GCF is 12hA box of God diva chocolate contains 52 identical wrapped chocolates AR troubles 31 have caramel filling the rest of them have walnuts what is the probability of the chocolate chosen at random containing walnuts
Answer:
21/52Step-by-step explanation:
Given the total God diva chocolate contained in a box to be equal to 52 identical chocolates.
If 31 have caramel filling, the amount of walnut filling will be 52-31 = 21. This means 21 remaining chocolate will contain walnuts.
Probability = expected number of outcomes/total outcome
If we are to find the probability that the chocolate chosen at random contains walnuts, then our expected outcome will be 21 and the total outcome will be total God diva chocolate contained in the box which is 52.
The probability that the chocolate chosen at random contains walnuts = 21/52
What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 < r < 12.5)= ____ or ____%
Answer:
0.8185 or 81.85%
Step-by-step explanation:
The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.
The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean the z sore is negative. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.
For 8 inches:
[tex]z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2[/tex]
For 12.5 inches:
[tex]z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1[/tex]
From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%
how to convert 0.16 to fraction
4/25
Step-by-step explanation:
16/100, 8/50, 4/25
(OFFERING ALL THE POINTS I HAVE) Word Problem. Please help!! Part 1 of problem: The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number and use 3.14 for Pi. (Use sphere volume formula) Part 2: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? Part 3: Using the information from part 2, answer the following question by filling in the blank: The volume of the actual tank is __% of the mock-up of the tank.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
Charlie creates and sells jewelry. He has designed a triangular pendant with two 2-inch sides and one 1.5-inch side.Charlie will use wire to form the triangle. He wants to make several of these pendants to sell at his store. How many pendants can Charlie make using 5 feet of wire?
Answer:
Number of pendant made = 10
Step-by-step explanation:
Given:
Sides of triangle = 2 in , 2 in , 1.5 in
Total wire = 5 ft = 5 × 12 = 60 in
Find:
Number of pendant made.
Computation:
Perimeter of 1 pendant = 2 in + 2 in + 1.5 in
Perimeter of 1 pendant = 5.5 in
Number of pendant made = Total wire / Perimeter of 1 pendant
Number of pendant made = 60 / 5.5
Number of pendant made = 10.90
Number of pendant made = 10 and 1 pendant incomplete
pls let me know what you get for the question below
Answer:
233.37
Step-by-step explanation:
so between each gondola is 20.95 so you will multiply it by 35 not 36 (because between the first you go round and come back to the same first you started so no space between first and last) then get circumference as 733.25 using
[tex]c = \pi \: d[/tex]
you get diameter
Which expression can be used to find the surface area of the following square pyramid? I DONT KNOW HOW TO PUT A PHOTO ON PC!!! but it has 4 as the base and 3 as the height PLEASE HELP
Answer:
40 or 16+6+6+6+6
Step-by-step explanation:
To find the surface area of a 3d figure, we can imagine all of its faces laid down on a flat plane. In this case, we would have a square, and four congruent triangles. Now all we have to do is find the areas of each shape and add them up.
4 is the base of the pyramid, so it's also the square's side length. Since a square has four equal sides, our square's length and width are both 4.
4*4 = 16
For every triangle we have, the base is 4 and the height is 3. The area of a triangle can be found using the formula A=(bh)/2. We plug in the values:
A = (4*3)/2
A = (12)/2
A = 6
Since we have 4 triangles, the surface area is:
16+6+6+6+6 = 40
Answer:
16+6+6+6+6
Step-by-step explanation:
KHan
Compare 1/11 to 11/20 using least to greatest
Answer:
0.09
0.55
Step-by-step explanation:
to write least to greatest firstly, start comparing both number
so the answer will be=0.09,0.55
it least to greatest or in assending order.
One day I found a strange thing happening to my watch,the minute hand & the hour hand were coming together every 65 minutes.I decided to get it checked. Was my watch gaining or losing time, and how much per hour?
Answer:
Step-by-step explanation:
The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.
Here M = 64. The clock gains or losses in a day by
=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)
=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.
I need Help!!! Will give Brainliest ABC≅DEF Find the following: 1. x = 2. CB = 3. FE = 4. y = 5. ED = 6. FD = 7. AB = 8. AC = 9. Area =
Answer:
ABC≅DEF
x = 2
CB = 3
FE = 4
y = 5
ED = 6
FD = 7
AB = 8
AC = 9
In triangle ABC=
Side AC= 9 cm
Side CB= 3 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=13.5 cm^2
In triangle DEF=
Side FE= 4 cm
Side FD= 7 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=14 cm^2
In the next four questions, complete the proof of the converse of Theorem 37 (The diagonals of a rectangle are congruent.) by selecting the best reason or statement.
Answer:
Step-by-step explanation:
1) WXYZ is a rectangle 1. Given
2) ∠Z ≅ ∠Y 2. Definition of rectangle
3) WZ ≅ XY 3. Definition of rectangle
4) ZY ≅ ZY 4. Reflexive property
5) ΔWZY ≅ ΔXYZ 5. SAS
6) WY ≅ XZ 6. CPCT -Corresponding parts of congruent triangles
The diagonals of rectangle are congruent
It takes 4 people 2 days to paint a wall. How long would it take if we got 8 people to do it?
Answer:
if it takes 4 people for 2 days
4+4= 8
so it would only take 8 people for 1 day
Answer:
1 day
Step-by-step explanation:
4 people = 2 days
→ Work out how long 1 person takes
4 people = 2 days
( ÷ 4 ) ( × 4 )
1 person = 8 days
→ Work out how long 8 people can do it
1 person = 8 days
( × 8 ) ( ÷ 8 )
8 people = 1 day
Does this graph represent a function? Why or why not?
Answer:
B
Step-by-step explanation:
it is not a function because it fails the vertical line test,
A vertical line intersect the graph no more than once.
What is the difference between a parallelogram and a rectangle? a Both pairs of opposite sides are congruent and parallel. b Contains four right angles. c The diagonals bisect each other. d Both pairs of opposite angles are congruent.
Answer:
b. Contains four right angles.
Step-by-step explanation:
A parallelogram has two pairs of opposite sides that are both congruent and parallel, as does a rectangle.
A parallelogram usually does NOT have four right angles, but a rectangle does. b Contains four right angles is the difference between a parallelogram and a rectangle.
The diagonals of a parallelogram bisect each other, and so do the rectangle's diagonals.
The opposite angles of parallelograms are congruent, and all four angles of a rectangle are congruent, so this is a similar aspect of both a parallelogram and a rectangle.
Hope this helps!
look at the pattern below.How should the tird shape be labeled
Answer:
You havent showed us the pattern
Instructions: Given the preimage reflect over the x-axis then they axis. Find
the new coordinates.
10
8
6
1012
А
-12 -10 8 6 4-2
-2
B
-4
D
-6
С
-12
The coordinates of the preimage are:
A(-8, -2)
B(-4, -3)
C(-2,-8)
D(-10, -6)
Now let's find the coordinates after the reflection over the x-axis.
A'(-8,
B' (-4,
C'(-2,
D' (-10,
Answer:
The coordinates are;
For reflection over the x-axis
A'(-8, 2)
B'(-4, 3)
C'(-2, 8)
D'(-10, 6)
For reflection over the y-axis;
A''(8, 2)
B''(4, 3)
C''(2, 8)
D''(10, 6)
Step-by-step explanation:
When a point (x, y) is reflected over the x, axis, we have;
Coordinates of the pre-image = (x, y)
Coordinates of the image after reflection = (x, -y)
Therefore, for the points A, B, C, D we have;
Pre-image A(-8, -2), Image A'(-8, 2)
Pre-image B(-4, -3), Image B'(-4, 3)
Pre-image C(-2, -8), Image C'(-2, 8)
Pre-image D(-10, -6), Image D'(-10, 6)
When a point (x, y) is reflected over the y, axis, we have;
Coordinates of the pre-image = (x, y)
Coordinates of the image after reflection = (-x, y)
Therefore, for the points A', B', C', D' we have;
Pre-image A'(-8, 2), Image A''(8, 2)
Pre-image B'(-4, 3), Image B''(4, 3)
Pre-image C'(-2, 8), Image C''(2, 8)
Pre-image D'(-10, 6), Image D''(10, 6).
Tom and Harry live 24km from each other, which on the map is 5 cm Given that the distance on the map between Harry and the Sea view is 4cm Find the actual distance between Harry and the Sea view.
Answer:
19.5 km
Step-by-step explanation:
the actual distance between Harry and the Sea view:
if 24 km is 5 cm on map
24*4/5= 19.5 km
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35