let sn be the sum of the reciprocals of the non-zero digits of the integers from 1 to 10n inclusive. find the smallest positive integer n for which sn is an integer?
The smallest positive integer n for which Sn is an integer is 063.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let [tex]K=^9E_{i=11}\frac{1}{i}[/tex].
Examining the terms in S1, it can be seen that S1 = K + 1 since each digit n appears once and 1 appears an extra time.
Now consider writing out S2.
Each term of K will appear 10 times in the units place and 10 times in the tens place (plus one extra 1 will appear), so -
S2 = 20K + 1
In general, the equation is -
[tex]S_n=(n10^{n-1})K+1[/tex]
Because each digit will appear [tex]10^{n-1}[/tex] times in each place in the numbers [tex]1,2,......,10^{n-1}[/tex]and there are n total places.
The denominator of K is [tex]$D = 2^3\cdot 3^2\cdot 5\cdot 7$[/tex] .
For Sn to be an integer [tex]n10^{n-1}[/tex] must be divisible by D.
Since, [tex]10^{n-1}[/tex] only contains the factors 2 and 5 (but will contain enough of them when n ≥ 3), we must choose n to be divisible by [tex]$3^2\cdot 7$[/tex] .
The smallest such n, the answer is 063.
Therefore, the integer is 063.
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if PX equals to x cube + 3 x square - 2 X + 4 then find value of P2 P - 2 and p0if PX = x³ + 3 x square - 2 X + 4 find the value of p2p minus 2 and p0
Answer: The polynomial P(x) = x³ + 3x² - 2x + 4 is a cubic polynomial with the following properties:
p2 = 2: the coefficient of the x² term in P(x)
p - 2 = -2: the constant term in P(x)
p0 = 4: the coefficient of the x³ term in P(x)
So, p2 = 2, p - 2 = -2, and p0 = 4.
Step-by-step explanation:
Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and 5 3/4 feet high.
The formula for the area of a rectangle is A=bh.
What is the area of the window?
Enter your answer as a mixed number in simplest form by filling in the boxes.
In a case whereby Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and 5 3/4 feet high using the formula for the area of a rectangle is A=bh, the area of the window is 49 5/6.
How can the area of the windowbe calculated?The concept that will be used here is area of a rectangle. Since window can be seen to be like a rectangle then area of window can be take as area of rectangle which can be calculated as
Area = Length × breadth
The Length=82/3 = 26/3
the breadth= 5 3/4 = 23/4
Then Area =( 26/3 * 23/4) = 299/6 = 49 5/6
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Answer: 49 5/6 square feet
Step-by-step explanation: The width/breadth = 8 2/3 = 26/3
the height = 5 3/4 = 23/4
Area = (26/3 * 23/4) = 598/12 = 49 5/6
Use the compound interest formula to compute the total amount accumulated and the interest earned.
$2,000 for 3 years at 5% compounded semiannually.
The amount in the account is $ ( )enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
$12,000
Step-by-step explanation:
2000([tex](1 + \frac{.05}{2}) ^{2(3)}[/tex]
12,000
What is the volume of a sphere with a diameter of 30in
The radius of the sphere is half of its diameter, so the radius is 30/2 = 15 inches.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Substituting the given values, we get:
V = (4/3)π(15)³
V = (4/3)π(3375)
V = 4500π
Therefore, the volume of the sphere is 4500π cubic inches.
Here is a way we can estimate the distance from the earth to the moon. When the moon is seen at its zenith at a point A on the earth, it is observed to be at the horizon from point B. Points A and B are 6156 miles apart on the surface of the earth, and the radius of the earth is 3960 miles.
7319.6 miles is the estimate of the average distance from the earth to the moon
What is Distance?The length along a line or line segment between two points on the line or line segment.
We can use the triangle formed by the earth's center, point A, and the moon to find the distance.
Let us use the law of cosines to find the distance from the earth to the moon.
d = √3960² + 6156² - 2(3960)(6156)cos(90))
The value of cos90 is 0.
d = √3960² + 6156²
d=√15681600+37896336
d=√53577936
d=7319.6 miles.
Hence,7319.6 miles is the estimate of the average distance from the earth to the moon
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Formula for std dev of sampling distribution sampling proportions sample means
This sample proportion is roughly normally distributed for large samples, with a mean of μˆP=p. and a standard deviation of σˆP=√pqn.
A ratio is exactly what?An equation that sets two ratios at the same value is known as a percentage. For instance, if there is one boy and three females, you can phrase the ratio as 1: 3 (there are three girls for every one boy), which means that 3 out of every four girls and one out of every four boys are female.
What does a proportional example consist of?A ratio that links a portion to the whole is a percentage. For instance, there are 80 women and 20 men among the 100 students in the class. Men make up 20% of the population, or 20/100. Women make up 80% of the population.
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Find the distance between the following numbers on the real number line. a=12, b=3
Answer:
Step-by-step explanation:
The distance between two numbers on the real number line is simply the absolute value of their difference. So, to find the distance between the numbers a = 12 and b = 3, we calculate:
distance = |a - b| = |12 - 3| = |9| = 9
Therefore, the distance between the numbers a = 12 and b = 3 on the real number line is 9 units.
Answer:
Step-by-step explanation:
12.1+|-11|=12
Please help??????????
G(x) = 9+ 4x
h(x) =x + 21/5
Write (hog)(x) as an expression in terms of x.
(hog)(x) =
The composite result function (h o g)(x) in the given functions g(x) = 9 + 4x and h(x) = x + 21/5 is 4x + 66/5.
What is the composite result function (h o g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
g(x) = 9 + 4xh(x) = x + 21/5(h o g )(x) = ?To find (h o g)(x), first set up the composite result function h(g(x)).
h(x) = x + 21/5
h( g(x) ) = g(x) + 21/5
Plug g(x) = 9 + 4x
h( g(x) ) = ( 9 + 4x ) + 21/5
Simplify
h( g(x) ) = 9 + 4x + 21/5
h( g(x) ) = 4x + 9 + 21/5
h( g(x) ) = 4x + 66/5
Therefore, the composite function h( g(x) ) is 4x + 66/5.
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Ty and Leo are walking along linear routes in a city. On a map of the city, Ty’s route passes through the coordinates (−1,3) and (0,1) and Leo's route passes through the coordinates (1,4) and (0,2) . Will Ty and Leo pass through a common coordinate, walk along the same route, or never cross routes?
Ty and Leo will
The two lines have same slope with opposite signs thus, the linear routes are perpendicular, and Ty and Leo will pass through a common coordinate.
What is a perpendicular line?A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. If two segments PQ and RS connect at right angles, we may say that they are perpendicular to one another.
For the given coordinates of Ty and Leo let us calculate the slope of the line.
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
For Ty:
m = (1 - 3) / (0 + 1) = -2
For Leo:
m = (2 - 4) / (0 - 1) = 2
The two lines have same slope with opposite signs thus, the lines are perpendicular, and Ty and Leo will pass through a common coordinate.
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In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed.
The average weight was 18 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds. If we wanted to establish the 95% confidence interval estimate, determine the margin of error to be used.
The average weight of carry-on luggage by passengers in airplanes is (15.7, 20.3) pounds.
The margin of error to be used is 2.3 pounds.
Confidence Interval Estimate CalculationThe margin of error can be calculated using the formula:Margin of Error = z * (standard deviation / sqrt(sample size))where z is the Z-score that corresponds to the desired confidence level (95% confidence corresponds to a Z-score of 1.96), standard deviation is the population standard deviation (7.5 pounds), and sample size is the number of items in the sample (25).
Plugging in the values, we get:Margin of Error = 1.96 * (7.5 / sqrt(25)) = 2.3 pounds
So, the 95% confidence interval estimate of the average weight of carry-on luggage would be:(average weight - margin of error, average weight + margin of error)
= (18 - 2.3, 18 + 2.3) = (15.7, 20.3) pounds.
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I have two cans of paint. Can A has 9 parts of blue paint to one part of yellow paint. Can B is 20 percent blue paint and the rest is yellow paint. How much paint should I use from each can to obtain 5 liters of paint which is half blue and half yellow.
3.43 liters of Can A, and 4.57 liters of Can B should be used from each can to obtain 5 liters of paint which is half blue and half yellow.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
From the question,
Can A is 9 parts of blue 1 part yellow= 90% blue, 10% yellow
Can B is 20% blue, 80% yellow.
let
A + B = 8 Liters
90% A + 20% B = 50% (Blue)
10% A + 80% B = 50% (Yellow)
resolving
90% A + 20% B = 10% A + 80% B
80% A = 60% B
Go back to A + B = 8 and solve for one of the variables.
B = 8 - A
80% A = 60% (8 - A)
80% A = 480% - 60% A
140% A = 480%
A = 3 43 liters
B = 8 - A = 4.57 liters
Hence, 3.43 liters of Can A, and 4.57 liters of Can B should be used.
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11 ≥ 2x-5 or 2x-5 > 15
Answer:
Step-by-step explanation:
11≥2x-5
or
2x-5≤11
2x≤11+5
x≤16/2
x≤8
2x-5>15
2x>15+5
2x>20
x>20/2
x>10
so either x≤8
or
x>10
Answer: x</= 8 and x>10
Not sure what you are specifically asking for here is the answers for both
Step-by-step explanation:
Step 1: Move the terms
Step 2: Calculate
Step 3: Divide both sides
find dy/dx, y= 4x²sinxcosx
The derivative of y relative to x is given as follows:
dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).
How to obtain the derivative?The function for this problem is defined as follows:
y = 4x²sin(x)cos(x)
The function is a product of three functions, hence the product rule is applied, as follows:
dy/dx = [4x²]'sin(x)cos(x) + 4x²[sin(x)]'cos(x) + 4x²sin(x)[cos(x)]'.
The derivatives are given as follows:
[4x²]' = 8x.[sin(x)]' = cos(x).[cos(x)]' = -sin(x).Hence the derivative of the function is defined as follows:
dy/dx = 8xsin(x)cos(x) + 4x²cos²(x) - 4x²sin²(x)
dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).
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On the last three physics exams a student scored 84, 87, and 92. What score must the student earn on the next exam to have an average of at least 90?
The student must score at least %.
(Simplify your answer. Type an integer or a decimal.)
The student must score the marks which should be ≥ 97
What is average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
Let x be the marks need to be scored in the next exam
Average = sum of marks/ number of exams
Given: score must the student earn on the next exam to have an average of at least 90
This means,
Average ≥ 90
sum of marks/ number of exams ≥ 90
( 84+ 87 +92+x)/4 ≥ 90
(263+x)/4 ≥ 90
=> 263+x ≥ (90 * 4)
=> 263+x ≥ 360
=> x ≥ 360 - 263
=> x ≥ 97
The student must score the marks which should be ≥ 97
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find the area of the region bounded by the three lines below. [hint: you will have to split up the integral into two parts.] y
The area of the region bounded by the three lines is 4.
The region bounded by the three lines y = 0, y = x and y = 2x is a triangle. To find the area of this region, we need to split the integral into two parts. The first part is the area of the triangle formed by y = 0, y = x and y = 2x. This can be found by integrating y from 0 to x, and x from 0 to 2x. The second part is the area of the triangle formed by y = 0, y = x and y = 0. This can be found by integrating y from 0 to x, and x from 0 to 0.
Therefore, the area of the region bounded by the three lines is given by:
[tex]A = 1/2 ∫x=0 to 2x ∫y=0 to x dy dx + 1/2 ∫x=0 to 0 ∫y=0 to x dy dxA = 1/2[x^2/2]_0^2x + 1/2[x^2/2]_0^0\\A = x^2 \\A = 4[/tex]
The area of the region bounded by the three lines is 4.
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m+c<n<d-m
In the inequality above, c and d are constants.
If m= 1 and n = 2 is a solution of the inequality, which of the following statements concerning c and d must be true?
I. cd is negative
II. d-c>2
III. d+ c> 2
(A) II only
(B) I and II only
(C) II and III only
(D) I, II, and III
Answer: the right option is (A) II only
Step-by-step explanation:
I am so clueless with this mess
Answer:
3 miles
Step-by-step explanation:
The distance between Arati and Ava can be calculated using the Law of Cosines. Let's call the distance between Arati and Ava as "d". We know that:
a = 2 (distance skied by Arati)
b = 3 (distance skied by Ava ) c = d (distance between Arati and Ava) A = 45 (angle between a and b)
Plugging these values into the Law of Cosines formula:
d^2 = 2^2 + 3^2 - 2 * 2 * 3 * cos(45)
d^2 = 4 + 9 - 12 * (√2 / 2)
d^2 = 13 - 12 * √2
d = √(13 - 12 * √2)
To the nearest mile, the distance between Arati and Ava is approximately 3 miles.
The women’s basketball team played 30 home games and won 1/2 of them. They also won 2/3 of their 42 away games. How many games did they win?
Answer:
43 games
Step-by-step explanation:
The number of home games won by the women’s basketball team is 30 * 1/2 = 15.
The number of away games won by the women's basketball team is 42 * 2/3 = 28.
Therefore, the total number of games won by the team is 15 + 28 = 43.
Find the shortest distance between the line L1 passing through the points A =
(3, 2, 1) and B = (2, 1, 0) and the line L2 passing through the points C = (2, 4, −1) and
D = (3, 0, −2).
The shortest distance between the two lines L1 and L2 is 0.
How did we get the value?The shortest distance between two lines can be found using the cross product of their direction vectors.
The direction vectors of line L1 and L2 can be found as:
L1 = B - A = (2 - 3, 1 - 2, 0 - 1) = (-1, -1, -1)
L2 = D - C = (3 - 2, 0 - 4, -2 - (-1)) = (1, -4, -3)
The cross product of the direction vectors of L1 and L2 gives the normal vector to the plane formed by the two lines:
cross(L1, L2) = (1 + 4, -1 - 4, 3 + 1) = (5, -5, 4)
The normal vector of the plane formed by the two lines, and a point on line L1 (A = (3, 2, 1)), can be used to find the equation of the plane:
5x - 5y + 4z = d
5 * 3 - 5 * 2 + 4 * 1 = d
15 - 10 + 4 = d
9 = d
So the equation of the plane formed by the two lines is:
5x - 5y + 4z = 9
The shortest distance between the two lines is equal to the distance between a point on line L1 (A = (3, 2, 1)) and the plane formed by the two lines:
d = abs(9 - (5 * 3 - 5 * 2 + 4 * 1)) / sqrt(5^2 + (-5)^2 + 4^2)
d = abs(9 - 9) / sqrt(29)
d = 0 / sqrt(29)
d = 0
Therefore, the shortest distance between the two lines L1 and L2 is 0.
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Oskar has a map showing this trip is 165 kilometers long. Oskar is from Texas and is more familiar with miles as a unit of measure for distance. Write three paragraphs explaining how to help Oskar determine the distance of his trip in miles.
Paragraph 1: Identify a conversion rate on your formula sheet that will help Oskar? How will this help?
Paragraph 2: Explain the steps Oskar will need to use to convert 165 kilometers into miles.
Paragraph 3: Where do you think Oskar might be traveling in which the maps are labeled in kilometers instead of miles? What is the difference between these two units of measure?
1. Using the conversion rate of 1 kilometer = 0.621371 miles, Oskar determine the distance of his trip in miles.
2. Oskar's 165 kilometer trip is equivalent to 101.87995 miles.
3. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length.
How to Apply Conversion Rate?Paragraph 1: To convert kilometers to miles, Oskar will need to use the conversion rate of 1 kilometer = 0.621371 miles.
This conversion rate can be found on any formula sheet, and it will help Oskar determine the distance of his trip in miles.
Paragraph 2: To convert 165 kilometers into miles, Oskar will simply need to multiply 165 by 0.621371.
The result will give him the distance in miles.
For example, 165 * 0.621371 = 101.87995 miles. Therefore, Oskar's 165 kilometer trip is equivalent to 101.87995 miles.
Paragraph 3: Oskar might be traveling in a country where the maps are labeled in kilometers instead of miles. This is common in many countries, including most of Europe and many countries in Asia. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length. A kilometer is equal to 0.621371 miles, while a mile is equal to 1.60934 kilometers. It's important to be aware of the units used in different countries to ensure accurate navigation.
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K
For each of the following five independent situations, journalize the adjusting entry and the related transaction (either
before or after it). (Record debits first, then credits. Select the explanation on the last line of the journal entry
table. Round amounts to the nearest whole dollar.)
(Click the icon to view the situations.)
a. December 1-business receives $6,000 for a 10-month service contract.
Accounts and Explanation
alculator
Date
December 1
Clear all
Debit
Credit
Check answer
The journal entry for the business receiving $ 6, 000 for a 10 month service contract is :
Date Account and Explanation Debit Credit
December 1 Cash $ 6, 000
Unearned Service Revenue $ 6, 000
Being revenue received for services
not yet rendered
How to record unearned service revenue ?When a business receives money for a service that it is yet to perform for the client, this is called unearned service revenue. The amount is to be debited to the cash account as it is an asset and assets are debited when they increase.
Unearned service revenue will then be credited by the same amount because it represents a liability that the company owes to the client.
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This problem refers to right triangle ABC with C = 90°. Solve for all the missing parts using the given information. Find B, a,c. (Round your answers to three decimal places.) A = 9° 36', b = 5.812 cm.
So, adjusted to three decimal places, the lacking angles in the triangle are B = 80°24', a = 1.042 cm, and c = 5.852 cm.
What is the formula for decimal places?The number of important digits is the total number of digits, excluding the decimal point, all leading zeros, and some following zeroes. The number of decimal points is the number to the left of the decimals.
We are given that triangle ABC is a right triangle with C = 90°, A = 9° 36', and b = 5.812 cm.
To find B, we can use the fact that the sum of the angles in a triangle is 180°. Therefore, we have:
B + A + C = 180°
B + 9°36' + 90° = 180°
B = 80°24'
To find a, we can use the trigonometric function tangent.
We have:
tan A = opposite/adjacent
tan 9°36' = a/b
Solving for a, we get:
a = b tan A = 5.812 cm tan 9°36' ≈ 1.042 cm
The Pythagorean theorem, which says that in a right triangle, the square of the hypotenuse equals the total of the squares of the two sides (a and b), can be used to determine c.
We have:
c² = a² + b²
c² = (1.042 cm)² + (5.812 cm)²
c² ≈ 34.235 cm²
c ≈ √34.235 cm²
c ≈ 5.852 cm
Therefore, the missing parts of the triangle are B ≈ 80°24', a ≈ 1.042 cm, and c ≈ 5.852 cm, rounded to three decimal places.
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sin2 80° + cos2 80° without calculator
Answer:
1
Step-by-step explanation:
Because of the Pythagorean Identity [tex]\sin^2\theta+\cos^2\theta=1[/tex], then the answer is simply 1 as the angle does not matter.
Stefan borrowed twice as much on his 8 % car loan as on his 7% student loan. The annual interest
on the car loan is $360 more than the interest on the student loan. How much did Stefan borrow on
each loan?
a. Write an equation about the principals on the loans, using for the amount of money he borrowed
for his car and y for the amount of money he borrowed for his student loan.
b. Write another equation about the interest on the loans.
c. Solve your system and answer the question for much he borrowed at each rate.
Car: $
Student: $
Answer:
Stefan borrowed $8000 on his car loan and $4000 on his student loan.
Step-by-step explanation:
a. Let x be the amount of money Stefan borrowed on his car loan and y be the amount he borrowed on his student loan. According to the problem, Stefan borrowed twice as much on his car loan as on his student loan, so x = 2y.
b. The annual interest on the car loan is $360 more than the interest on the student loan. We can set up an equation as follows:
0.08x - 0.07y = 360
c. Substituting x = 2y from equation (a) into equation (b), we get:
0.08(2y) - 0.07y = 360
0.16y - 0.07y = 360
0.09y = 360
y = 4000
So, Stefan borrowed $4000 on his student loan. Using equation (a), we can find the amount he borrowed on his car loan:
x = 2y = 2(4000) = 8000
Therefore, Stefan borrowed $8000 on his car loan and $4000 on his student loan.
FIND ALL MISSING VALUES (HELP PLS ). ET
IT
RT = 960 0
Ω
E1
11 = 0.06
R1
E2
12
R21000 2
E3
13
Ω
R3 = 650 02
E4
14
R4 = 950 0
The following currents are present in the circuit: I₁ = 0.492 A, I₂ = -0.428 A, I₃ = 0.920 A. They are found by Kirchoffs law and solving simultaneously.
Inequalities: what are they?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Kirchoff's law and Junction Law will be applied given the various resistances and the circuit.
Apply Kirchoff's law to the left side loop as a starting point.
E₁ + E₂ = (r₁ + R₁ + R₄) I₁ + ( R₂ + r₂ ) I₃
18 + 3 = ( 0.5 + 8 + 15 ) I₁ + ( 10 + 0.25 ) I₃
21 = 23.5 I₁ + 10.25 I₃ —- ( 1 ) ( 1 )
Apply Kirchoff's law to the right side loop as the next step.
E3 - E4 - E2 equals (r3 - r4 - R3) I₂ - ( r₂ + R₂ ) I₃
12 - 24 - 3 = ( 0.75 + 0.25 + 12 ) I₂ - ( 0.25 + 10 ) I₃
-15 = 13 I₂ - 10.25 I₃ —- ( 2 ) ( 2 )
Note: I1 = I2 + I3 when using the Law of Junction.
concurrently solve equations (1) and (2)
I1=0.492A, I2=-0.428A, and I3=0.920A
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claire has a points card for a movie theater. she receives 75 rewards points just for signing up. she earns 13.5 points for each visit to the movie theater. she needs at least 210 points for a free movie ticket. use the drop-down menu below to write an inequality representing vv, the number of visits she needs to make in order to get a free movie ticket.
Using the drop-down menu below to write an inequality is V ≥ 10. The number of visits she needs to make in order to get a free movie ticket is 10.
We have,
75 rewards points just for signing up.
earns 13.5 points for each visit to the movie theater
she needs at least 210 points for a free movie ticket
To write the inequality representing v is,
75 + 13.5v ≥ 210
13.5v ≥ 210 - 75
13.5 v ≥ 135
v ≥ 10
Therefore, by solving inequality the number of visits she needs to make in order to get a free movie ticket is 10.
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Given f(x) = 2x² - 6, find f(7)
Answer:
92
Step-by-step explanation:
2x49=98-6=92
Answer:
f(7) = 92
Step-by-step explanation:
To find f(7), substitute x = 7 into the given function.
[tex]\begin{aligned}f(7)&=2(7)^2-6\\&=2(49)-6\\&=98-6\\&=92\end{aligned}[/tex]
Find the global extreme values of the function f(x, y) = x^2 + 2(y^2)
on the circle x^2 + y^2 = 1.
The global extreme values of the function f(x, y) = x² + 2(y²) on the circle x² + y² = 1 are,
The maximum value of f on the circle x² + y² = 1 is,
⇒ f(0, ±1) = 2
And, the minimum value is,
⇒ f(±1, 0) = 1
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Function is,
f(x, y) = x² + 2(y²)
And, Equations of circle is,
x² + y² = 1
Hence, The maximum value of f on the circle x² + y² = 1 is,
⇒ f(0, ±1) = 0² + 2(1²) = 2
And, the minimum value is,
⇒ f(±1, 0) = 1² + 2 × 0 = 1
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The bag contains 20 red marbles, 30 white marbles, and 40 blue
marbles.
a. What is the ratio of red to blue marbles?
b. What is the ratio of white to red marbles?
c. If one marble is drawn from the bag, what is the probability that
marble will not be white?
When the product of 1 and 1 in subtroter fire no
of 1 and 1
a) The ratio of red to blue marbles is 1:2.
b) The ratio of white to red marbles is 3:2.
c) The probability of drawing a white marble from the bag is 33%.
What is the ratio?The ratio is the relative size of a value compared to another.
Ratios show the quantity of one variable contained in a larger variable.
On the other hand, the probability is the odds or likelihood that an expected outcome occurs given many possible outcomes.
Both ratios and probabilities can be expressed in fractions, decimals, and percentages because they are fractional values.
The number of red marbles in the bag = 20
The number of white marbles in the bag = 30
The number of blue marbles in the bag = 40
The total number of marbles in the bag = 90
a) The ratio of red to blue marbles = 20:40 = 1:2
b) The ratio of white to red marbles = 30:20 = 3:2
The sum of ratios of all marbles = 9 (2:3:4)
c) The probability of drawing a white marble from the bag = 3/9 = 0.33 or 33%
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