The constraints of a problem are listed below. What are the vertices of the feasible region? 2x+3y≥12 5x+2y≥15 x ≥ 0 y ≥ 0
The vertices of the feasible region are (0 , 15/2) , (21/11 , 19/11) and (6 , 0)
Given, the constraints of a problem
2x+3y≥12
5x+2y≥15
x ≥ 0
y ≥ 0
On solving the equations, we get
( 2x + 3y ≥ 12 ) × 2
( 5x + 2y ≥ 15 ) × 3
4x + 6y ≥ 24
15x + 6y ≥ 45
On subtracting, we get
11x ≥ 21
x ≥ 21/11
x = 21/11
On putting the value of x, we get
42/11 + 3y = 12
y = 19/11
Hence, the vertices of the feasible region are (0 , 15/2) , (21/11 , 19/11) and (6 , 0)
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In the problem 14 = 2 = 7, which number is the divisor?
Answer:
14 and 7 or 14 and 2
Step-by-step explanation:
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Answer:
2, assuming you meant 14÷2=7
Step-by-step explanation:
In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25, the F ratio is A) 25 / (30–25) = 5.00
B) (30–25) / 30 = 0.17 C) 25 / 30 = 0.83
D) 30 / 25 = 1.20
The F ratio is 1.2.
What is statistic?
The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
30/25 = 1.2
In an ANOVA, this statistic is used in the F test to test the hypothesis that the group means are not equal to one another. The F ratio is calculated as follows:
Fobs=MSB/MSW
30/25 = 1.2
Where MSB is the mean square between the groups and MSW is the mean square within the groups.
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NO LINKS!! What is the area of this figure? Part 17
Answer:
660 in²
Step-by-step explanation:
The area of this figure looks like it is best computed by subtracting the areas of the empty corners from the area of the "bounding box."
The overall dimensions of the figure are ...
horizontal: 31 in + 10 in = 41 in
vertical: 13 in + 7 in = 20 in
Then the area of the bounding box is ...
A = LW = (41 in)(20 in) = 820 in²
__
The area of the upper left empty space is ...
A = (6 in)(5 in) = 30 in²
The area of the lower right empty space is ...
A = (10 in)(13 in) = 130 in²
Then the area of the figure is ...
total shaded area = (820 -30 -130) in² = 660 in²
__
Additional comment
The formula for the area of a rectangle is ...
A = LW . . . . . . where L is the length, and W is the width
Solution:
Draw the whole rectangle.
Refer to image~
Subtract the area of the unshaded region from the rectangle's area.
{41 x 20} - {(5 x 6) + (10 x 13)} = Area of figure=> 820 - {30 + 130} = Area of figure=> 820 - 160 = Area of figure=> 660 in² = Area of figureMonday 4 7/8
Tuesday 5 3/4
Wednesday 4 7/2
Thursday 4 3/8
Friday 5/8
The chart above shows the number of the boxes an apple picker filled with apples during the week. Which of the following is the total number of boxes he filled in the five days?
A- 17 19/30 boxes
B- 21 ¼ boxes
C- 19 3/8 boxes
D- 20 1/8 boxes
The total number of boxes is the sum of all boxes each day
The total number of boxes he filled in the five days is \(23 \frac 18\)
How to determine the total number of boxThe box each day is given as:
Monday 4 7/8Tuesday 5 3/4Wednesday 4 7/2Thursday 4 3/8Friday 5/8So, the total number of boxes is:
\(Total = 4\frac 78 + 5\frac 34 + 4\frac 72 + 4\frac 38 + \frac 58\)
Add the fractions
\(Total = 23 \frac 18\)
Hence, the total number of boxes he filled in the five days is \(23 \frac 18\)
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An angle measures 87.4° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
Step-by-step Let the angle be x
Given equation
(180-x)=(x-87)
=>180+87=2x
=>267/2=x
=>x=133.5
The second angle=46.5
Greatest comment factor of 14^3 and 13^4
Answer:
14^3 = 2,744. Common factors are 1,2,4,7,8,14,28,49,56...
13^4 = 2,197. Common factors are 1, 13, 169, and 2197.
Dennis is growing tomatoes in his backyard. In one row of his garden, he has 8 plants. Each plant is separated from the next plant by 1.5 feet of space. Ignoring the width of each plant stem, what is the distance from the first plant to the last plant, in feet?
the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.
Why is it?
To find the distance from the first plant to the last plant, we need to add up the distances between each adjacent pair of plants. Since there are 8 plants, there are 7 pairs of adjacent plants, and each pair is separated by 1.5 feet.
So, the total distance from the first plant to the last plant is:
7 ×1.5 = 10.5 feet
Therefore, the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.
Distance refers to the measurement of the physical space between two points or objects. It is a scalar quantity that only considers the magnitude of the separation between two points and does not take into account the direction of the separation.
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I NEED HELP NOWWWW AND I MEAN RIGHT THIS SECOND PLEASE
Answer: See below
Step-by-step explanation:
1 1/2 as mixed fraction = 3/2
3/4 + 3/4 = 3/2
2 2/3 as a mixed fraction = 8/3
7/3 + 1/3 = 8/3
Consider parallelogram QRST below. Use the information given in the figure to find m
The missing values are
<UTQ = 41 degree
x= 1
<UQT = 47 degree
We have a parallelogram QRST.
We know that the opposite sides of the parallelogram is equal and parallel then
QR || ST
QT || SR
Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)
<UTQ = 41
Similarly, <UQT = <SRQ = 47
Now, RU = UT
2x + 1= 3
2x = 2
x= 1
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please help!!!!!!!!!!!!!!!!!1
The area of the cross section for the given cube is 9 sq, in.
What is cross sectional area?Using the area of the cross-section formula for various shapes and figures, the area of the cross-section may be determined. You will be provided information in the question that will allow you to calculate the area of the cross-section of the given shape, such as its length, height, radius, or diameter. You must carefully use several cross-sectional area calculations depending on the shape specified in the questions.
From the figure we observe that the cross - section of the figure is a square.
The area of the square is given as:
A = (s)(s)
Substituting the value of s = 3 in we have:
A = (3)(3)
A = 9 sq. in.
Hence, the area of the cross section for the given cube is 9 sq, in.
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A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
18. A store is having a 38% off sale on every item. Suppose an item in the store has a price of p dollars. Write asimplified expression to represent the discounted price of an item in the store,
Firstly, to have an expression let us represent the discounted price by D.
The original price is represented by p
and the discount is represented by d.
\(\begin{gathered} \text{Discounted price = Original price - Discount} \\ D\text{ = p - d }\ldots\ldots..1 \end{gathered}\)the discount is given to be 38% of the original price.
\(\begin{gathered} \text{Discount d = 38\% of p =}\frac{38}{100}\times p \\ d\text{ = 0.38p} \end{gathered}\)substituting d = 0.38p into equation 1, we have;
\(\begin{gathered} D\text{ = p - 0.38p = (1-0.38)p} \\ D\text{ = 0.62p} \end{gathered}\)Therefore, the simplified expression to represent the discounted price of an item in the store is;
\(D\text{ = 0.62p dollars}\)PLSSS PEOPLE I NEED HELP
Answer:C
Step-by-step explanation:
The vertical line test
A library sells 600 books for a fundraiser. The library claims that 60% of the books are fiction how many of these books are fiction.
A 10
B 36
C 360
D 600
ASAP PLS!!!!!
Answer:
C. 360
Step-by-step explanation:
60% = 0.60
600 x 0.60 = 360
360 fiction books
A conical circus tent has a 20 ft central pole that supports it. The slant height of the tent is 26 ft long. Explain how to find the angle the tent pole makes with the sides of the tent.
The central pole forms a right triangle with the floor of the tent. The (cos , sin , tan)
of the missing angle is the ratio of the length of the central pole to the length of the side of the tent, which is (0.77 , 0.38, 0.65, 1.30). Applying ( arcsine, arctangent, arccosine), we find that the angle the tent pole makes with the sides of the tent is (67.7, 39.6 ,49.5)
Angle that the tent pole makes with the sides of the tent is 39.6°.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given that,
A conical circus tent has a 20 ft central pole that supports it. The slant height of the tent is 26 ft long.
The central pole forms a right triangle with the floor of the tent.
We need the angle tent pole makes with the sides of the tent.
We have the hypotenuse as the slant height and the central pole is the adjacent side of the angle.
The cos of the missing angle is the ratio of the length of the central pole to the length of the side of the tent.
cos x = 20 / 26 = 0.7692 ≈ 0.77
Applying arccosine,
x = cos⁻¹ (1.3) = 39.6°
Hence the required angle is 39.6°.
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44 is 11% of what number?
Answer:
400
Step-by-step explanation:
look it up. it says 400.
The required number is 400 for which 44 is 11%.
The percentage is a way to express a proportion or a fraction as a fraction of 100. It is commonly used to compare values or quantities relative to a whole or a total.
To calculate a percentage, you typically divide a part or a quantity by the whole or the total and then multiply the result by 100. The resulting value represents the percentage equivalent of the part or quantity.
It implies that a percentage value represents a certain number out of 100 parts.
Given that 44 is 11% of the number. The unknown number is calculated as,
x (11%) = 44
\(x \times \dfrac{11}{100} = 44\\x = \dfrac{44\times100}{11}\\x=400\)
Therefore, the number is 400.
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A mover places a cylindrical container on a dolly, as shown. Calculate the angle of elevation, U,
from the base of the dolly to the ground.
A. 52.0°
B. 38.0°
C. 38.6°
D. 51.4°
Check the picture below.
\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)
Make sure your calculator is in Degree mode.
Which is the last operation preformed when evaluating (8-2x)²+4 for x=3
A addition
B multiplication
C subtraction
D applying the exponent
Please hurry
Answer: I think its c sorry if im whrong
some adults and children are watching a musical there are n children there are 25 fewer adults
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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Mr Paul has 4 bars of chocolate. He distributes 1/3
of each bar to 4 children.
a) Write the fraction of chocolate distributed.
b) Write the fraction of cholates left with Mr. Paul
a) The fraction of chocolate distributed is given as follows: 4/3.
b) The fraction of chocolates left with Paul is given as follows: 8/3.
How to obtain the fractions?The fractions are obtained applying the proportions used in the context of this problem.
He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:
4 x 1/3 = 4/3.
(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).
The total number of bars that Paul had initially is given as follows:
4 bars.
Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:
4 - 4/3 = 12/3 - 4/3 = 8/3 bars.
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Math on the Spot Funtime Carnival charges a $3.00 entrance fee and $1.00 per
ride. Crazy Carnival charges a $5.00 entrance fee and $0.50 per ride. For how many
rides will the total charge be the same at both places? What is that cost? Write a system
of equations and solve the system by graphing.
For 4 rides the total charge be the same at both places
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Funtime Carnival charges a $3.00 entrance fee and $1.00 per ride
Crazy Carnival charges a $5.00 entrance fee and $0.50 per ride.
We need to find for how many rides will the total charge be the same at both places and the cost.
For carnival the equation will be 3+1x
Crazy Carnival equation will be 5+0.5x
Now equation both the equations
3+x=5+0.5x
Subtract 0.5x on both sides
3+x-0.5x=5
3+0.5x=5
0.5x=2
x=2/0.5=4
Hence, For 4 rides the total charge be the same at both places
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(50 pts will mark brainliest) The perimeter of a rectangle is 48 inches. The width of the rectangle is 4 inches more than 3 times the length of the rectangle. What are the dimensions of the rectangle?
Answer:
The rectangle is 5 inches long by 19 inches wide.
Step-by-step explanation:
Let's start by listing what we know:
The perimeter of a rectangle is 48 inches.The width of the rectangle is 4 inches more than 3 times the length of the rectangle.Let's represent the width with "w" and length with "l", and make a system of equations based on what we know.
\(\left \{ {{2w + 2l = 48} \atop {w = 3l + 4}} \right.\)
Now, let's solve the system of equations using substitution:
\(2w + 2l = 48\)
\(2 (3l + 4) + 2l = 48\)
\(6l + 8 + 2l = 48\)
\(8l + 8 = 48\)
\(8l = 40\)
\(l = 5\)
The length of the rectangle is 5 inches.
Now, let's use this to solve for the width.
\(w = 3l + 4\)
\(w = 3(5) + 4\)
\(w = 15 + 4\)
\(w = 19\)
The width of the rectangle is 19 inches.
Let's check our work:
\(2w + 2l = 48\)
\(2(19) + 2(5) = 48\)
\(38 + 10 = 48\)
\(48 = 48\)
The results match, so our answer is correct.
The rectangle is 5 inches long by 19 inches wide.
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 4
Blue 4
Green 15
Yellow 9
Purple 3
Based on these results, express the probability that the next spin will land on blue or green or purple as a percent to the nearest whole number.
Step-by-step explanation:
OUT of 35 spins 4 + 15 + 3 = 22 were blue or green or purple
22/35 probability = 63%
A company ships gasoline in tanks. Together, 3 tanks can hold 84 tons of gasoline. How many tanks does the company need to ship 420 tons of gasoline?
A.
12
B.
18
C.
7
D.
15
Answer:
D.
Step-by-step explanation:
To find how much tons each tank can hold, we can use this equation:
84 ÷ 3 = 28So, each tank can hold 28 tons.
To solve for the number of tanks needed to ship 420 tons of gasoline, we can use this equation:
420 ÷ 28 = 15To check, we can use this equation:
15 × 28 = 420Therefore, to ship 420 tons of gasoline with each tank containing 28 tons, the company will need 15 tanks.
AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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A square has a side length of 2x+5, write an expression to find the perimeter of the square
Answer:
4(2x+5) or 8x+20
Step-by-step explanation:
Answer:
8x + 20
Step-by-step explanation:
Side = 2x + 5
Perimeter of square = 4*side
= 4*(2x + 5) {Use distributive rule:a(b +c) = a*b +a*c}
= 4*2x + 4*5
= 8x + 20
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
CAN SOMEONE PLEASE TELL ME THE VALUE OF X, EQUATION, AND ANGLE MEASURES!!
Answer:
8x+10 = 12x - 18
28 = 4x
x = 7
Step-by-step explanation:
A roller coaster car is going over the top of a 13-mm-radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 50 %% of their true weight. How fast is the coaster moving?
Answer:
0.253 m/s
Step-by-step explanation:
radius r of the circular rise = 13 mm = 0.013 m
apparent weight loss = 50%
acceleration of the new weight = 0.5 x 9.81 = 4.905 m/s^2
centripetal acceleration = 9.81 - 4.905 = 4.905 m/s^2
centripetal acceleration = \(\frac{v^{2} }{r}\)
where v is the acceleration at the rise and r is the radius of the rise
centripetal force = \(\frac{v^{2} }{r}\) = \(\frac{v^{2} }{0.013}\)
4.905 = \(\frac{v^{2} }{0.013}\)
\(v^{2}\) = 0.063765
v = \(\sqrt{0.063765}\) = 0.253 m/s