Answer:
i think its 11.2
Step-by-step explanation:
A patient takes 110 mg of a drug at the same time every day: Just before each tablet is taken, 5% of the drug present in th
preceeding time step remains in the body. What quantity of the drug remains in the body in the long run?
Hint: First find the quantity of drug present in the body after the second tablet, third tablet, etc to generalize the sequenc
formula for the nth tablet. Then use that sequence to predict the drug remains in the long run.
The requried quantity of drug that remains in the body, in the long run, is 220 mg.
Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:
[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]
We can see that the formula for [tex]D_n[/tex] is:
[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]
Simplifying this formula, we get:
[tex]D_n = 220 * (1 - 0.95^n)[/tex]
Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex] as n goes to infinity. Using the formula above, we can see that:
[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]
Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.
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using truth table show that (p^q) =~pv~q please help meeee
The truth table for the given expression can be given using p= T q = T, p^q = T, ~p = F, ~q = F, ~q v ~p = T, and (p ^ q) =~p v ~q = T, thus proving the required.
What is propositional logic?The field of symbolic logic known as propositional logic, also referred to as sentential logic or statement logic, is concerned with propositions or statements, which are declarative phrases that can be true or untrue. To represent propositions and their relationships, propositional logic employs symbols and operators.
Many disciplines, including mathematics, computer science, philosophy, and others, employ propositional logic as a tool for debating the truth or falsity of propositions and analysing arguments.
The truth table for the given expression can be given as:
p | q | p ^ q | ~p | ~q | ~q v ~p | (p ^ q) =~p v ~q
-------------------------------------------------------------
T | T | T | F | F | T | T
T | F | F | F | T | T | T
F | T | F | T | F | T | T
F | F | F | T | T | T | T
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3) Given the formula F=ma where * F represents force, *m represents mass and has units of kilograms (kg), and • a represents acceleration and has units of meters per second squared (). Select an appropriate measurement unit for force.
The appropriate measurement unit for force is kg.m/s²
What is the appropriate measurement unit for force?A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.
From Newton's Second Law, force is expressed as;
F = m × a
Where is mass of object and a is the acceleration
One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
Since F = m × a
Plug in m = kg and a = m/s²
F = kg × m/s²
F = kg.m/s²
Therefore, the unit of measurement is kg.m/s².
Option B is the correct answer.
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A circular garden is surrounded by fence that is 47.1 feet long the surface soil of the entire garden within the fencing needs to be turned prior to planting calculate the square feet of soil that must be turned use 3.14 as a substitute for pi help me please within the next hour
The surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.
What is radius?Radius is a mathematical term that refers to the distance from the center of a circle, sphere, or other curved object to any point on its circumference or surface. It is typically denoted by the letter "r".
According to question:Let's call the radius of the circular garden "r". We know that the circumference of the garden (the length of the fence) is 47.1 feet, so we can set up the equation:
2πr = 47.1
Simplifying this equation by dividing both sides by 2π, we get:
r = 47.1/(2π)
Using 3.14 as a substitute for π, we can calculate:
r ≈ 7.5 feet
Now that we know the radius of the garden, we can calculate the area of the garden by using the formula for the area of a circle:
A = πr²
A = 3.14 * 7.5²
A ≈ 176.625 square feet
Therefore, the surface soil of the entire garden within the fencing that needs to be turned prior to planting is approximately 176.625 square feet.
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An equipment was purchased from China and arrived at Kampala at a value of shs.5,000,000 shs with transport cost of 800,000 shs. and total taxes amounted to 1,500,000 the equipment is expected to be useful for 6 years and an estimated salvage value of 1,300,000 shs. calculate the depreciation expense for each year and accumulated depreciation upto year 6. Using the straight line method.
The depreciation expense for each year is 1,000,000 shs.
Accumulated depreciation up to year 6 is 6,000,000 shs.
How to calculate depreciation using the straight line method?The depreciation using the straight line method is given by the formula:
Depreciation expense per year = (Initial cost - Salvage value) / Useful life
Initial cost = 5,000,000 + 800,000 + 1,500,000 = 7,300,000 shs.
Salvage value = 1,300,000 shs.
Depreciation expense per year = (7,300,000 - 1,300,000) / 6
= 6,000,000 / 6
= 1,000,000 shs.
Thus, the depreciation expense for each year is 1,000,000 shs.
Accumulated depreciation up to year 6 = Depreciation expense per year * Number of years
Accumulated depreciation up to year 6 = 1,000,000 * 6 = 6,000,000 shs.
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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Help corrections due in 3 hours! giving 25 points and brainlist
The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.
How to find the value of GH ?Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.
cos(35°) = adjacent side (FH) / hypotenuse (GH)
We know that FH = 18.4 in. So, we can write the equation as:
cos(35°) = 18.4 / GH
GH = 18.4 / cos(35°)
GH = 18.4 / 0.81915
= 22.46 inches
So, the length of GH, the hypotenuse, is approximately 22.46 inches.
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A hamster running in a wheel of radius 10 cm spins the wheel one revolution in 5 seconds.
a) What is the angular velocity of the wheel?
b) At what linear velocity is the hamster running?
just need the answer
a) The angular velocity = 0.4π rad/s b) The linear velocity of the hamster = 4π cm/s.
What is linear velocity?Linear velocity is the rate of change of an object's position with respect to time. It measures how fast an object is moving in a straight line, and is often expressed in units of distance per time, such as meters per second or kilometers per hour.
According to given information:a) The angular velocity of the wheel can be calculated as follows:
Angular velocity = (2π * number of revolutions) / time
Here, the wheel completes one revolution in 5 seconds, so the number of revolutions is 1 and the time is 5 seconds. Therefore,
Angular velocity = (2π * 1) / 5
Angular velocity = 0.4π rad/s (or approximately 1.26 rad/s)
b) The linear velocity of the hamster can be calculated as follows:
Linear velocity = radius * angular velocity
Here, the radius of the wheel is 10 cm, and the angular velocity we found in part (a) is 0.4π rad/s. Therefore,
Linear velocity = 10 cm * 0.4π rad/s
Linear velocity = 4π cm/s (or approximately 12.57 cm/s)
So the hamster is running at a linear velocity of approximately 12.57 cm/s.
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A bag contains 2 gold marbles, 10 silver marbles, and 29 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $6, if it is silver, you win $4. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answer:
33 thats with the 1 dollar subtracted for the entry fee
Step-by-step explanation:
first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee
Consider the given density curve.
What is the value of the median?
O-10
O-7
O-6
O-2
Note that the median of the distribution or the density curve is -6. (Option C)
What is the explanation for the above response?If the curve is a straight line and the area under the curve appears to be a rectangle, then we can assume that the density curve is a uniform distribution. In this case, the median of the distribution is simply the midpoint of the interval, which would be
(-10 + (-2))/2
= -6.
A density curve is a mathematical model used to describe the overall pattern of a dataset. It is a smooth curve that approximates the distribution of the data and shows the relative frequencies of observations at different values.
The area under the curve represents the total proportion of observations in the dataset, and the curve is normalized such that the total area under the curve equals one. Density curves are used in statistics to analyze and interpret data, and can be used to make predictions about future observations.
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Can someone help me plsssss
Answer:
Tyshawn would have to sell 6 computers on a given day to get paid $225
Step-by-step explanation:
We can use the information in the table to find the equation of the linear relationship between a (the number of computer sales) and p (Tyshawn's total pay):p = 75 + 25aThis equation tells us that Tyshawn's total pay is $75 plus $25 for each computer he sells.To find out how many computers Tyshawn would have to sell in order to get paid $225 on a given day, we can substitute p = 225 into the equation and solve for a:225 = 75 + 25a150 = 25aa = 6
An ice cream stand uses the expression 1 + 0.75x to determine the cost (in dollars) of an ice cream cone that has x scoops of ice cream. How much does an ice cream cone with 3 scoops cost?
Answer:
$3.25
Step-by-step explanation:
An ice cream cone that has x scoops of ice cream costs 1 + 0.75x.
So an ice cream cone that has 3 scoops of ice cream costs
1 + 0.75×3 = 3.25 (dollars)
Write 80cm to 2km as rate
One per 2,500 can be used to represent the rate of 80cm to 2km.
Writing measures as a rate.To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):
80 cm/100,000 = 0.0008 km
Now we can express the rate as:
0.0008 km per 2 km
Or we can simplify it by dividing both the numerator and denominator by 0.0008:
1 per 2,500
Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.
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As seen in the diagram below, Austin is building a walkway with a width of x feet to go around a swimming pool that measures 8 feet by 10 feet. If the total area of the pool and the walkway will be 360 square feet, how wide should the walkway be?
Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
What is a rectangle?In the Euclidean plane, a rectangle is a quadrilateral with four right angles.
A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.
A rectangle with four equal-length sides is a square.
Squares are not always rectangles, but rectangles are always squares.
So, the pool and walkway together have a 360 square foot total space.
Assume that the walkway is w feet in width.
Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).
Thus, we can construct the following equation:
(8 + 2w) x (10 + 2w) = 360
By enlarging and condensing the left side, we obtain:
4w² + 36w - 80 = 0
Using the quadratic formula, we can find w:
w = (-b ± √(b² - 4ac)) / 2a
Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:
w = (-36 ± √(36² - 4(4)(-80))) / 8
w = (-36 ± √(1872)) / 8
w ≈ -5.6 or w ≈ 3.6
We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.
Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
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complete the equatiotin 3 over 4 x 6 =
PLEASE HELP
Answer:
1/8
Step-by-step explanation:
If "over" refers to (4 * 6) as a whole,
[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]
If "over" refers to division,
[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]
I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.
Hope this helps and be sure to mark this as brainliest! :)
Get x an y values for the Photo above
In the given right triangle, by using the Pythagorean theorem, the value of x is 5√2 and the value of y is 5√2
Trigonometry: Calculating the value of x and yFrom the question, we are to determine the value of x and y in the given diagram
The diagram shows a right triangle with a hypotenuse of 10.
The right is a special type of right triangle. The base angles of the triangle are equal.
Thus,
The right triangle is an isosceles right triangle.
This means the legs of the triangle are equal.
That is,
x = y
From the Pythagorean theorem, we can write that
x² + y² = 10²
Since x = y, we can write that
x² + x² = 10²
2x² = 100
x² = 50
x = √50
x = 5√2
Hence,
y = 5√2
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) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
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PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT
what is √29 Place a dot on the number line at the BEST approximation
Answer:
5.4
Step-by-step explanation:
square of 29 = 5.385164807
5.385164807 estimated is 5.4
please answer and explain
Answer:
Trapezoid
Step-by-step explanation:
It's a quadrilateral and it only has one pair of parallel sides.
HELP ME PLEASE!!! HELPPP!!! A backyard pool is in the shape of a rectangle. The pool has a perimeter of 90 feet and an area of 500 ft2. Which of the following could be the pool's length and width? 15 feet and 30 feet, 10 feet and 35 feet ,50 feet and 10 feet, 25 feet and 20 feet
Answer:
(d) 25 feet and 20 feet
Step-by-step explanation:
You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.
AreaThe area is the product of the length and width. The area of the pools offered in the answer choices are ...
(a) 15·30 = 450 . . . square feet
(b) 10·35 = 350 . . . square feet
(c) 50·10 = 500 . . . square feet
(d) 25·20 = 500 . . . square feet
The area requirement eliminates answer choices A and B.
PerimeterThe perimeter is twice the sum of length and width. The perimeters of the possible pools are ...
(c) 2(50 +10) = 120 . . . feet
(d) 2(25 +20) = 90 . . . feet
The perimeter requirement eliminates answer choice C.
The pool's possible length and width are 25 feet and 20 feet, choice D.
__
Additional comment
You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.
If x is the width, then 45-x is the length, and the area is ...
x(45 -x) = 500
x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square
x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension
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(23,000-789) * 19 Explain pls
The expression (23,000-789) * 19 = = 421409.
What is expression?An expression can contain variables, constants, and mathematical operations, and it can be used to represent a wide variety of mathematical concepts and relationships.
According to given information:
To solve the expression (23,000-789) * 19, we need to perform the subtraction operation inside the parentheses first and then multiply the result by 19.
(23,000-789) equals 22,211.
So, we have:
(23,000-789) * 19 = 22,211 * 19
Now, we can multiply the two numbers using the standard multiplication method. We multiply each digit of 19 with the digits of 22,211 starting from the right and then add the results.
22,211 x 19 =
444422 (19 x 1 = 19, write 9 and carry 1) + 420789 (19 x 1 = 19, write 9 and carry 1, 19 x 2 = 38, write 8 and carry 3)
= 421409
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Use the graph to answer the question. Graph of a polygon ABCD with vertices at 4 comma 4, 12 comma 4, 12 comma 8, 4 comma 8 and a second polygon A prime B prime C prime D prime with vertices at 1 comma 1, 3 comma 1, 3 comma 2, 1 comma 2. Determine the scale factor used to create the image. one half 2 one fourth 2.5
Given polygons ABCD and A'B'C'D' have scale factors of 1/4 since their respective side ratios are the same.
What is scale-factor?The amount by which a shape is made smaller or larger is referred to as its scale factor. This method is employed when a 2D polygon, irregular or regular shape, such as a circle, triangle, square, or rectangle, needs to be enlarged larger. In the equation y = px, p is the scale factor for x. One may identify the scale factor between any two shapes or figures by comparing the measurements of the new shape to those of the prior shape.
Scale factor = Dimensions of new shape/Dimensions of original shape
given the original polygon's coordinates:
A(4,4) ; B(12,4) ; C(12,8) ; D(4,8)
Distance AB = X₂ - X₁
= 12 - 4
= 8 units
Distance BC = Y₂ - Y₁
= 8 - 4
= 4 units
Distance CD = X₂ - X₁
= 12 - 4
= 8 units
Distance DA = Y₂ - Y₁
= 8 - 4
= 4 units
Added coordinates for the new polygon:
A'(1,1) ; B(3,1) ; C(3,2) ; D(1,2)
Distance A'B' = X₂ - X₁
= 3 - 1
= 2 units
Distance B'C' = Y₂ - Y₁
= 2 - 1
= 1 units
Distance C'D' = X₂ - X₁
= 3 - 1
= 2 units
Distance D'A' = Y₂ - Y₁
= 2 - 1
= 1 units
Scale factor = [tex]\frac{A^{\prime} B^{\prime}}{A B}=\frac{B^{\prime} C^{\prime}}{B C}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} A^{\prime}}{D A}[/tex]
[tex]\frac{A B}{A^{\prime} B^{\prime}}=\frac{2}{8}=\frac{1}{4}\\\\\frac{B^{\prime} C^{\prime}}{B C}=\frac{1}{4}\\\\\frac{C^{\prime} D^{\prime}}{C D}=\frac{2}{8}=\frac{1}{4}\\\\\frac{D^{\prime} A^{\prime}}{D A}=\frac{1}{4}[/tex]
Scale factor = [tex]\frac{A^{\prime} B^{\prime}}{A B}=\frac{B^{\prime} C^{\prime}}{B C}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} A^{\prime}}{D A}=\frac{1}{4}[/tex]
The image was reduced using a one-fourth scale factor.
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Refer to the attachment for the graph.
Help me on my math question pls!
Answer:
D
Step-by-step explanation:
A rotation and translation preserves the length measures of the sides, so FD is equal to 7 inches
Answer: D
Step-by-step explanation:
Complete the flow chart proof
The flow chart is complete and the answers are given below.
What is meaning of Congruent Figures?Those figures that have same shape and size are called Congruent Figures.
The flow diagram will be completed as follows
∠2 ≅ ∠4 ( vertical angle theorem )
∠1 ≅ ∠2 ( Given )
∠1 ≅ ∠ 3 ( Vertical Angle Theorem)
∠3 ≅ ∠4 ( Transitive Property of congruence)
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Solve for x.
A. 7
B. 4
C. 3
D. 5
The correct option -D. 5; Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
Explain about the secant of circle:A line that precisely intersects a circle at two points is said to be a secant.
The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.
Using the Theorem:
The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:
4(4 + x) = 6²
16 + 4x = 36
4x = 36 - 16
4x = 20
x = 20/4
x = 5
Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
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Help please i dont know
The histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2.The bin from 16 to 25 should be increased by one.The bin from 26 to 35 should be increased by one.The bin from 46 to 55 should be increased by one.What is shown by an histogram?A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.
Then the height of the histogram gives the number of observations into each data interval.
Hence the histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2. -> two measures of 12.The bin from 16 to 25 should be increased by one. -> measure of 16.The bin from 26 to 35 should be increased by one. -> measure of 26.The bin from 46 to 55 should be increased by one. -> measure of 48.More can be learned about histograms at https://brainly.com/question/25983327
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What is the area of the following right triangle?
Let [tex]x[/tex] be the unknown side of the triangle. Find the length of this side from the Pythagorean Theorem;
[tex]x^2+5^2=13^2[/tex][tex]x^2=13^2-5^2[/tex][tex]x^2=144[/tex][tex]x=12[/tex]Another root of the equation is also negative, but we've eliminated it because length can't be a negative value.
To find the area of a triangle, we multiply the height of the triangle by the base length and take half.
[tex]Area=(12.5)/2=30[/tex]Will mark brainliest if answer is correct
According to the information, we know that the term 125x^5y^4 appears in the expansion when n = 6 and the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.
How to solve this equation and fin the expansion terms?We know that the binomial expansion of (x-y)^n is given by the formula:
(x-y)^n = nC0 x^n y^0 - nC1 x^(n-1) y^1 + nC2 x^(n-2) y^2 - ... + (-1)^n nCn x^0 y^nwhere nCk represents the binomial coefficient "n choose k".
We are given that the term 125x^5y^4 appears in the expansion, so we can set up an equation using the binomial coefficient for that term:
nC5 (x)^5 (-y)^4 = 125x^5y^4Simplifying this equation, we get:
nC5 = 125 / (-1)^4 = 125We can solve for n by finding the smallest value of n for which nC5 is greater than or equal to 125. We can use the formula for binomial coefficients:
nCk = n! / (k! (n-k)!)to calculate the values of nCk for different values of n and k. However, it is easier to use Pascal's triangle to find the binomial coefficients quickly. The fifth row of Pascal's triangle is:
1 5 10 10 5 1We see that the sixth term of this row is 10C5 = 252, which is greater than 125. Therefore, we know that the term 125x^5y^4 appears in the expansion when n = 6.
To find the x^6y^7 term in the expansion, we need to find the coefficient of x^6y^7 in the expansion. We can use the same formula as before, but with k = 7 instead of k = 5:
nC7 (x)^6 (-y)^7We can simplify this expression using the fact that (-1)^7 = -1:
nC7 x^6 y^7We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:
6C7 x^6 y^7We see that 6C7 is zero because we cannot choose 7 items from a set of 6. Therefore, the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.
To find the x^7y^2 term in the expansion, we can use the same formula as before, but with k = 2:
nC2 (x)^7 (-y)^2We can simplify this expression using the fact that (-1)^2 = 1:
nC2 x^7 y^2We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:
6C2 x^7 y^2We can use Pascal's triangle to find that 6C2 = 15. Therefore, the coefficient of x^7y^2 in the expansion is 15, and the x^7y^2 term appears in the expansion as:
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A factory that has 6 X 10³ workers makes 2.4 X 105 products each day.
What is the average amount of
products made per worker?
In a a case whereby factory that has 6 X 10³ workers makes 2.4 X 105 products each day, the average amount of products made per worker is 4 *10^1 products per worker
How can the average amount of products made per worker can be calculated?The term "average" in mathematics typically refers to a measure of central tendency, which is a way to describe the typical or common value in a set of numbers. There are several types of averages.
We can calculate the required value as
( 2.4 X 10^5 )/ (6 X 10³)
=4 *10^1 products per worker
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Draw a bar model to represent the expression.
t-2
One such tool that enables us to visualise the given math issue using various-sized rectangles or bars is the bar model.
What is bar model Representation?A bar model in mathematics is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes. To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilised.
To help kids "see" mathematical structure, the bar model is utilised in teaching for mastery. It is not a method for solving issues, but rather a strategy to uncover the mathematical underpinnings of a problem and obtain knowledge and clarity to aid in its resolution.
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Image attached below,