The radius is equal to the length of the given line segment GH, which is 20 units. In this case, r = 20, and θ = 90° = π/2 radians.
Arc GJ is the portion of the circumference of circle H that lies between points G and J. Arc GJ can be calculated using the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = GH = 20 and θ = 90° = π/2 radians. Therefore, l = 20π/2 = 10π. Therefore, the length of arc GJ is 10π units.For example, if the radius of circle H is 10 units, l = 10π/2 = 5π. Thus, the length of arc GJ would be 5π units.To calculate arc GJ, we must first determine the radius of circle H. The radius is equal to the length of the given line segment GH, which is 20 units. We then use the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = 20, and θ = 90° = π/2 radians.
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Write an
explicit formula for an, the nth term of the sequence 8, -4, 2, ....
By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence.
What does "sequence" in mathematics mean?A sequence is a list of objects that is in order in mathematics. (or events). Similar to a set, it has members. (also called elements, or terms). The length of the sequence is the number of many ordered elements (potentially infinite).
Given :
The ratio between consecutive terms in the above sequence is not constant, hence it is not a geometric sequence. The series does, however, appear to rotate between positive and negative numbers.
The explicit formula for the nth term in this sequence is as follows:
a = (-1)^(n+1) * 2^(n-2) (n-2)
By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence. For instance, when n is 1, we obtain:
n = 2 results in:
so forth.
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what value of x makes the two expressions equal (image)
Answer:
[tex]\huge\boxed{\sf x = 6.5 }[/tex]
Step-by-step explanation:
Given that, both the expressions are equal.
So,
7x - 5 = 5x + 8
Subtract 5x from both sides7x - 5x - 5 = 8
2x - 5 = 8
Add 5 to both sides2x = 8 + 5
2x = 13
Divide both sides by 2x = 13/2
x = 6.5[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex] \sf \: x = 6.5[/tex]
Step-by-step explanation:
Given expressions,
→ 7x - 5
→ 5x + 8
Now we have to,
→ Find the required value of x.
Forming the equation,
→ 7x - 5 = 5x + 8
Then the value of x will be,
→ 7x - 5 = 5x + 8
→ 7x - 5x = 8 + 5
→ 2x = 13
→ x = 13 ÷ 2
→ [ x = 6.5 ]
Hence, the value of x is 6.5.
PLEASE HELP!!!!
All I need to know is the area.
Answer:
45
Step-by-step explanation:
Draw an imaginary line from F to S. We then break this into 2 parts:
1. Evaluate the area of triangle SFN
The base of the triangle is FS, who has length 9. The height is the vertical line that passes through point N and FS, and that line has length 6. The area would then be 9*6/2=27.
2. Evaluate the area of rectangle SCWF
WC has length 9. FW has length 2. The area would then be 9*2=18.
The dimensions of a rectangle are 14 centimeters by 48 centimeters. Find, in centimeters, the length of the diagonal of the rectangle
We can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right triangle with legs of length a and b and hypotenuse of length c, we have:
a^2 + b^2 = c^2
In this case, the rectangle has dimensions of 14 centimeters by 48 centimeters, so we can let the length and width of the rectangle be the legs of a right triangle, and the diagonal be the hypotenuse. Then:
a = 14 cm b = 48 cm c = ?
We can plug these values into the Pythagorean theorem and solve for c:
14^2 + 48^2 = c^2 196 + 2304 = c^2 2500 = c^2 c = sqrt(2500) c = 50
Therefore, the length of the diagonal of the rectangle is 50 centimeters.
Answer:
50 cm
Step-by-step explanation:
the equation is d=sqrt(w^2+l^2)
so you get sqrt(14^2+48^2) which equals 50.
Please ASAP Help
Will mark brainlest due at 12:00
Answer: -2
Step-by-step explanation: Find the midpoint of both points so they are equidistant meaning that the ratios between them are 1:1.
To do so, add both quantities given and divide by 2.
[tex](-7+3)/2\\(-4)/2\\-2[/tex]
Which is the answer!
Answer:
plot the point at -2
Step-by-step explanation:
Brainliest will be rewarded+ 100 points!!
Take a screen shot of the work and do the work on the ss
Answer: When do you need it done?
Step-by-step explanation: ?
Answer:
Step-by-step explanation:
x+y=17
x-y = 7
From equation 2, x = 7 + y
put this in equation 1.
(7+y) + y = 17
7+2y = 17
2y = 10
y = 5.
We said that x = 7+y
thus, x = 7 + 5
x = 12.
2x+2y=36
2(x+y) = 36
Thus, x + y = 18.
x+y = 18
x-y=6 using elimination (literally simplifying this)
2x = 24 (y-y=0. ELIMINATED!)
x = 12
When x = 12,
x+y=18
12+y=18
y=6.
3x = y
x + y = 20
From 1, y = 3x.
x + (3x) = 20
4x = 20
x = 5.
when x = 5,
y = 3x
y = 3(5)
y = 15.
x+y = -4
xy = -21
from 1, x = -4-y
=> y(-4-y)= -21
-y²-4y = -21
Therefore,
y² + 4y -21 = 0
y= 3 or -7.
When y = 3,
x + 3 = -4
x= -7.
When y = -7,
x + (-7) = -4
x-7=-4
x = 3.
Hope these help! :)
*fingers cracking*
Kay is standing near 200-foot-high radio tower.
Answer:
265 ft
Step-by-step explanation:
its asking what is the hypotenuse
"SOHCAHTOA"
sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent
use
soh because it has hypotenuse in it
sine equals opposite over hypotenuse
sine 49 = 200 / x
x & sine 49 can switch
x = 200/sin(49°)
x = 200/0.7547
x = 265.005962634
x = 265
using pythagorean theorem other leg is 173.85 or 174
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Pls help!!!
A home has a rectangular kitchen. If listed as ordered pairs, the corners of the kitchen are (7, 6), (−4, 6), (7, −9), and (−4, −9). What is the area of the kitchen in square feet?
Using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.
What is a rectangle?The internal angles οf a rectangle, which has fοur sides, are all exactly 90 degrees. At each cοrner οr vertex, the twο sides cοme tοgether at a straight angle.
Here, Pοints (7,6) and (7.-9) lie οn the same hοrizοntal line as the x values are the same
Sο the distance between these pοints can be taken as the length οf the rectangle.
The distance can be fοund using the distance fοrmula.
Length l = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
= [tex]\sqrt{(7-7)^2 + (6--9)^2} = \sqrt{15^2} = 15[/tex]
Nοw the pοints (7,6) and (-4,6) lie οn the same vertical line as the y values are the same.
Sο the distance between these pοints can be taken as the breadth οf the rectangle.
Breadth b = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex] = [tex]\sqrt{(7--4)^2 + (6-6)^2} = \sqrt{11^2} = 11[/tex]
Since it is a rectangle, the οppοsite sides will have the same measurements.
Nοw the area = l * b = 15 * 11 = 165 sq. feet.
Therefοre using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.
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Match each area to the correct polygon on the coordinate plane. Drag the Items on the left to the correct location on the right.
A 6 square units
B 12 square units
C 4 square units
D 5 square units
(33 points and giving brainilest)
According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 200 executives are randomly surveyed.
a. What is the probability that fewer than 90 of the executives believe employees are most productive on Tuesdays?
b. What is the probability that more than 100 of the executives believe employees are most productive on Tuesdays?
c. What is the probability that more than 82 of the executives believe employees are most productive on Tuesdays?
Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places, the tolerance is +/-0.005.
Therefore , the solution of the given problem of probability comes out to be there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.
Define probability.The primary goal for every procedure's criteria-based methods is to ascertain the probability that a statement is true or that a specific event will occur. Chance can be represented by any number range between 0 and 1, where 0 usually represents probability and 1 usually reflects degree of certainty. A probability illustration displays the possibility that a specific event will take place.
Here,
a.
=> P(X < 90) = F(89)
We can determine: Using a computer or a spreadsheet
=> Binom.dist(89, 200, 0.48, TRUE) = 0.0016 when
=> P(X 90) = F(89) (rounded to 4 decimal places)
Therefore, there is a 0.0016 percent chance that fewer than 90 of the executives agree that workers are most effective on Tuesdays.
b.
=> P(X > 100) = 1 - P(X < 100) = 1 - F(100)
We can determine: Using a computer or a spreadsheet
=> Binom.dist(100, 200, 0.48, TRUE)
=> 0.0668 for P(X > 100) = 1 - F(100) = 1 - (rounded to 4 decimal places)
Therefore, there is a 0.0668 percent chance that more than 100 executives agree that Tuesdays are when workers are most effective.
c.
=> P(X > 82) = 1 - P(X < 82) = 1 - F(82)
We can determine: Using a computer or a spreadsheet
=> Binom.dist(82, 200, 0.48, TRUE) = 0.7569, P(X > 82) = 1 - F(82) = 1
Therefore, there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.
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Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
The solution of the system of equations from the graph is x = 2.
What is point of intersection?The point of intersection formula is used to determine where two lines meet, or the point at which they intersect. In Euclidean geometry, the intersection of two lines can be either an empty set, a point, or a line. Two lines must meet certain requirements in order to intersect, including being in the same plane and not being skew lines. The intersection of these lines may be determined using the intersection formula.
The solution of the system of equations can be determined from the graph by determining the point of intersection between the two lines.
From the graph we observe that the point of intersection of the two lines is at (0, 2).
Hence, the solution of the system of equations is x = 2.
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Determine the quantity of fuel that was utilized by the water tanker in March
The quantity of fuel that was utilized by the water in March is 230.4 liters.
Fuel capacity of the tanker = 460 liters
Fuel consumption rate = 5 km/ℓ
Total distance covered per full tank = fuel capacity * fuel consumption rate = 460 x 5 = 2,300 km
Number of full tanks required to make one round trip = distance per round trip / total distance covered per full tank = 18/2300
=0.0078
Number of round trips made in March 2022 = 1/0.0078 x 2
= 64.1
Total distance covered = number of round trips * distance per round trip
= 64 x 18
= 1,152 km
Therefore, the total distance covered by the water tanker = 1,152 km
Quantity of fuel utilized = total distance covered / fuel consumption rate
= 1152/5
= 230.4 liters.
Therefore, The quantity of fuel that was utilized by the water in March is 230.4 liters.
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Your question is incomplete. The complete question is:
The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 liters. The rate of fuel consumption of the Mercedes water tanker averages 5 km/t. The prices of fuel per liter in March and June 2022 appear below:
MARCH 2022 FUEL PRICES
DIESEL
50 ppm
COST
R19,55
JUNE 2022 FUEL PRICES
DIESEL
50 ppm
Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022.
if you multiply by 1/3 in front of a exponential function what would happen to the graph
Answer:
If you multiply a function by a constant value, it will result in a vertical scaling of the graph. In this case, multiplying by 1/3 would compress the graph vertically by a factor of 3. Specifically, the y-coordinates of each point on the graph would be multiplied by 1/3, resulting in a graph that is one-third as tall as the original.
URGENT! WILL MARK BRIANLIEST!!!!
The caterpillar touches 15 points with two integer coordinates, including the start point (-3, -4) and the end point (25, 38).
What is co-ordinate geometry ?
Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. In coordinate geometry, geometric figures are represented using algebraic equations and analyzed using techniques from algebra and calculus.
The caterpillar moves from (-3, -4) to (25, 38) in a straight line. We can find the equation of the line passing through these two points using the slope-intercept form of the equation of a line:
y - (-4) = (38 - (-4))/(25 - (-3)) * (x - (-3))
y + 4 = 42/28 * (x + 3)
y = 3/2 * x + 19
The caterpillar touches a point with two integer coordinates whenever x and y are both integers. To find these points, we can substitute integer values for x and solve for y. Since the slope of the line is 3/2, every time x increases by 2, y increases by 3.
Starting from x = -3, we can list the integer values of x that the caterpillar touches:
-3, -1, 1, 3, 5, ..., 25
For each value of x, we can compute the corresponding value of y using the equation of the line:
y = 3/2 * x + 1
For example, when x = -3, y = 3/2 * (-3) + 19 = 14.5, which is not an integer. When x = -1, y = 3/2 * (-1) + 19 = 17.5, which is also not an integer. However, when x = 1, y = 3/2 * 1 + 19 = 20, which is an integer. Similarly, we can find the integer values of y for all the other values of x.
Therefore, the caterpillar touches 15 points with two integer coordinates, including the start point (-3, -4) and the end point (25, 38).
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A fish tank contains 90 litres of water, rounded to 1 significant figure.
30 litres of water, rounded to 1 significant figure, are removed from the
tank.
Work out the upper bound of the volume of water left in the fish tank.
Give your answer in litres.
The upper bound of the volume of water left in the fish tank is 60 liters.
What exactly is a litre of water?33.81 fluid ounces make up one litre (US).
One litre of water would fill about one-fourth of a gallon water bottle. Also, you should be aware that there are two different kinds of ounces used globally to measure water volume: (1 litre = 33.814 US ounces).
The maximum allowable mistake can be added to the actual value to determine the upper bound of the amount of water still in the fish tank.
The maximum error for 90 litres, rounded to one significant figure, is half of the value of the last significant figure, or 5. Hence, the actual value of 90 litres might be either 85 or 95.
The largest potential inaccuracy for 30 litres, rounded to one significant figure, is likewise 5. Hence, the actual value of 30 litres might be 25 or 35.
We subtract the lower bound of the withdrawn volume from the higher bound of the original volume to determine the upper bound of the volume of water still present in the tank.
The upper bound of the volume of water left in the fish tank can be found by adding the half of the absolute uncertainty to the measured value of 60 liters (90 - 30):
Upper bound = 60 + 0.5 x 1 = 60.5 liters (rounded to 1 significant figure)
Therefore, the upper bound of the volume of water left in the fish tank is 60 liters.
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A computer must print all natural numbers between 0 and 1,000,000. It can print 9 digits per second. How many seconds will it take to print all these numbers?
What's the 5th term?
Answer:
what term?
Step-by-step explanation:
Explain the question.
If PR = 14 find ST and QR
The values of ST and QR based on the information regarding the square will be 7 and 9.9
How to calculate the valueThe square is a geometric figure that belongs to the parallelograms. The square has the following properties:
All four sides have the same length. The four angles measure 90. The sum of its angles is equal to 360
The diagonals are congruent. The diagonals bisect each other.
We get a PQRS square with PR=14. We are required to find ST and QR.
First, since the figure is a square, we must know that the diagonals are congruent. Therefore, we are required to find ST and QR:
PR = SQ = 14.
ST = 14/2 = 7
QR = sin 45 × 14
QR = 9.9
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how long will it take for the battery to run down one sixth of its capacity of 3600 Milli Ampere hours
Answer:
6 hours
Step-by-step explanation:
[tex]\frac{1}{6}[/tex] of Total battery life = [tex]\frac{1}{6} * 3600 = 600[/tex]milliamps
Assuming the battery takes 100 Milliamps per hour,
Time = Battery Capacity / Current hours
Time = 600 / 100 Mah = 6H
Which describes a possible dependent variable for the given independent variable?
The number of hours you study for a test
1. Your test score
2. The number of students in your study group
3. How many students are taking the test T
4.T he time the test starts
Answer:
1
explanation in head
What is the value of j?
can some one help me please
Answer: 130 degrees
Step-by-step explanation:
The line equals 180 degrees
50+j=180
180-50=130
Answer:
130 Degrees
Step-by-step explanation:
180-50 = 130
if n(r' intersection s') + n(r' intersection s)=3, n(r intersection s)=4 and n(s' intersection r)=7
We can use the principle of inclusion-exclusion to find n(U), which states that for two sets A and B:
n(A union B) = n(A) + n(B) - n(A intersection B)
We can apply this to three sets r, s, and their complements r' and s':
n(U) = n(r union s)
= n(r) + n(s) - n(r intersection s)
= [n(r intersection s') + n(r intersection s)] + [n(s intersection r') + n(s intersection r)] - n(r intersection s)
= [(4 + n(r' intersection s)) + (n(r intersection s') + 7)] - 4
= n(r' intersection s) + n(r intersection s') + 3
= 7 + 3 + 3
= 13
Therefore, n(U) = 13.
When the result of (5x^(2)+x-7)(x-4)-(2x^(3)+5x^(2)-6) is expressed as a polynomial in the form ax^(3)+bx^(2)+cx+d, what is the value of b ?
After expanding the polynomial (5x² + x - 7)(x - 4) - (2x³ + 5x² - 6), b = -24
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
Since we have the polynomial (5x² + x - 7)(x - 4) - (2x³ + 5x² - 6) and we want it expressed as a polynomial in the form ax³ + bx² + cx + d, to find the value of b, we proceeda s follows.
(5x² + x - 7)(x - 4) - (2x³ + 5x² - 6)
Expanding the brackets, we have that
(5x² + x - 7)(x - 4) - (2x³ +5x² - 6) = 5x³ - 20x² + x² - 4x - 7x + 28 - (2x³ + 5x² - 6)
= 5x³ - 20x² + x² - 4x - 7x + 28 - 2x³ - 5x² + 6
Collecting like terms, we have
= 5x³ - 2x³ - 20x²- 5x² + x² - 4x - 7x + 28 + 6
= 3x³ - 24x² - 11x + 34
So, comparing 3x³ - 24x² - 11x + 34 with ax³ + bx² + cx + d, we have that
b = - 24
So, b = -24
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Work out the surface area of the solid cuboid.
3cm, 4cm and 6cm
Answer:
The formula for the surface area of a cuboid is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the cuboid, respectively.
In this case, l = 6 cm, w = 4 cm, and h = 3 cm. Substituting these values into the formula, we get:
SA = 2(6)(4) + 2(6)(3) + 2(4)(3)
SA = 48 + 36 + 24
SA = 108
Therefore, the surface area of the cuboid is 108 square centimeters.
Step-by-step explanation:
Answer: Surface Area is [tex]72cm^2[/tex].
Step-by-step explanation: Let surface area be a.
[tex]a= 2(5*4)+(5*2)+(4*2)\\a= 2(20+10+8)\\a=2(38)\\a=72 cm^2[/tex]
This means the surface area of the solid cuboid is [tex]72cm^2[/tex].
Hope this helps!
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I NEED HELP ON THIS QUICKLYY WILL GIVE BRAINLIESTTT PLEASE HELP!!!
x is the number of HD Big View television produced daily.
y is the number of Mega Tele box television produced daily.
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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What is the resulting costant when (2 - 4/3) is subtracted from (-3/5 plus 5/3)
The resulting constant is 2/5 when (2-4/3) is subtracted from (-3/5 plus 5/3).
What is subtraction?Mathematical subtraction includes calculating the difference between two numbers. It is the inverse of addition and is denoted by the symbol "-". When we subtract one number from another, we are essentially finding out how much smaller the second number is than the first number.
According to question:We can simplify the expressions inside the parentheses first:
2 - 4/3 = 6/3 - 4/3 = 2/3
-3/5 + 5/3 = -9/15 + 25/15 = 16/15
So the expression (-3/5 + 5/3) - (2 - 4/3) becomes:
(16/15) - (2/3)
To subtract these fractions, we need to find a common denominator, which is the least common multiple of 15 and 3, which is 15. Then we can rewrite both fractions with this denominator:
(16/15) - (2/3) = (16/15) - (10/15)
Now we can subtract the numerators and keep the denominator:
(16/15) - (10/15) = 6/15 = 2/5
Therefore, the resulting constant is 2/5.
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What is the length of are AB? Give an exact value
The length of arc AB for the given circle is found to be 13.60 units.
Explain about the arc of the circle?Plotting two lines from the arc's ends to the circle's center, measuring the angle at the point where the two lines intersect the center, and then solving for L by cross-multiplying are useful methods for calculating an arc's length.
And use the arc length method, one may determine a circle's arc length given its radius and center angle.
Length of an Arc = θ × r,in which θ is in radian.Length of an Arc = θ × (π/180) × r,in which θ is in degree.So,
Radius r = 13 units
Central Angle Ф = 60 degree.
Arc length AB = 60 * 3.14 * 13 /180
Arc length AB = 13.60
Thus, the length of arc AB for the given circle is found to be 13.60 units.
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HELP PLSSS....The table shows the result of spinning a color spinner (purple, blue, yellow, and green) in an experiment. PART A: Using the results in the table, what is the experimental probability of a spinner landing on purple (P) in Experiment A? Write your answer as a fraction and as a decimal.
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
part A)
the table shows that in 10 attempts
Blue was hit 5 times
Yellow was hit 2 times
Green was hit 2 times
Purple was hit 1 time
so the experimental probabilities are
Blue 5/10 = 1/2 = 0.5
Yellow 2/10 = 1/5 = 0.2
Green 2/10 = 1/5 = 0.2
Purple 1/10 = 0.1
part B)
the theoretical probability of Purple with an equally spaced spinner of 4 colors is 1/4 = 0.25
Okay, I really need some help with my math questions
1. At a local ballgame the hamburgers sold for 2.50 each and the cheeseburgers sold for 2.75 each. there were 131 total burgers sold for a total value of 342. how many of each kind of burger were sold?
2. Bradford bought a total of 20 medium and large bags of chips. If he spent $53 and bought 6 more large bags of chips as medium bags of chips, how many large and medium bags of chips did he buy? HELP: chips; large-$3, medium-$2, and small-$1
please help I will make you brainliest! Answer the questions fully and show how did you do it.
Answer: Let's use the following system of equations to represent the given information:
h + c = 131 (the total number of burgers sold is 131)
2.5h + 2.75c = 342 (the total value of the burgers sold is $342)
where h represents the number of hamburgers sold and c represents the number of cheeseburgers sold.
We can use the first equation to solve for one of the variables in terms of the other:
h + c = 131
h = 131 - c
Substituting this into the second equation, we can solve for c:
2.5h + 2.75c = 342
2.5(131-c) + 2.75c = 342
327.5 - 2.5c + 2.75c = 342
0.25c = 14.5
c = 58
So, 58 cheeseburgers were sold. We can use the first equation to find the number of hamburgers sold:
h + c = 131
h + 58 = 131
h = 73
Therefore, 73 hamburgers were sold.
Let x be the number of medium bags of chips that Bradford bought. Then, he bought 20 - x large bags of chips.
According to the problem, the total cost of the chips was $53. We can set up an equation for the total cost in terms of x:
diff
2x + 3(20-x+6) = 53
2x + 54 - 3x + 18 = 53
-x = -19
x = 19
So, Bradford bought 19 medium bags of chips and 20 - 19 = 1 large bag of chips.
Enjoy!
Step-by-step explanation:
Consider two natural numbers n,k and p where 0≤k≤p≤n a. Prove that:
P(n+1,k)=P(n,k)+kP(n,k−1) b. Prove that: C(n,k)C(n−k,p−k)=C(p,k)C(n,p)
`C(p,k) * C(n-p,k)`
a. Proof: We will apply the same method we used in formula (1) in our class notes on this question. For this purpose, we choose a set containing `n + 1` elements. It contains all elements of the set of `n` elements and another element `y` that has not been included in the set of `n` elements.Let the number of sets of `n` elements that contain `k` particular elements `a` be `P(n, k)`. To count the number of sets of `n + 1` elements that contain `k` elements, we use the concept of permutations with repetition, such as -{n + 1} can be placed in any of the `k` places of the k-element subsets of `{1, 2,...,n}`, or it can be one of the remaining `n-k+1` elements in each of the `P(n,k)` sets that contain `k` elements.Let us use `A` to denote the set of sets of `n` elements that do not contain the element `y` and `B` to denote the set of sets of `n` elements that contain the element `y`. Then, `P(n+1,k)=|A|+|B|=P(n,k)+(n−k+1)P(n,k−1)`.b. Proof: To count the number of `k` element subsets from a set of `n` elements, we use `C(n, k)`.Let us consider two sets, `A` and `B`, where `|A|=n-k` and `|B|=p-k`. We want to choose `k` elements from these two sets such that the number of subsets we get from `A` is `x` and the number of subsets we get from `B` is `y`. In the set `A`, we select `x` elements by choosing `k-x` elements from the remaining `n-k` elements. Similarly, in the set `B`, we select `y` elements by choosing `k-y` elements from the remaining `p-k` elements.Thus, the total number of ways of choosing `k` elements from `A` and `B` is given by `C(n-k, x) * C(p-k, y)`. The total number of ways of choosing `k` elements from `n` elements is given by `C(n, k)`. Therefore, the total number of ways of choosing `k` elements from `n` elements such that `x` elements are chosen from `A` and `y` elements are chosen from `B` is `C(n-k, x) * C(p-k, y) * C(n, k)`.To get the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B`, we must sum over all possible values of `x` and `y`. Thus, the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B` is given by: `C(p,k) * C(n-p,k)` which is the required result.
Learn more about permutations
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