The value of r is greater than 1. This tells that the series diverges. The solution has been obtained by using ratio test.
What is ratio test?
One test used to assess if infinite series are converging or diverging is the ratio test. Even finding the radius and interval of power series convergence using the ratio test is an option.
We are given an infinite series as
x(n) = 2n! / 2²ⁿ
Using the ratio test,
[tex]\lim_{n \to \infty} \frac{\frac{2(n+1)!}{2^{2(n+1)} } }{\frac{2n!}{2^{2n} } }[/tex]
[tex]\lim_{n \to \infty} \frac{n+1}{4}[/tex] = ∞ = r
So, we observed that the value of r is greater than 1.
We know that if r is greater than 1, then the series diverges.
So, the given series also diverges.
Hence, the value of r is greater than 1 which shows that the series diverges.
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The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to 17 years,
given the household's annual income, ›
Approximately how much would it cost to raise a child from birth to
17 years in a household with an annual income of $64,000?
•
$209,619
$186,302
S164.219
$99.200
Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.
Explanation:
To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:
y = 1.55x + 110,419
y = 1.55 * 64,000 + 110,419
y = 101,600 + 110,419
y = $212,019
So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.
which of the following results in smaller sampling variation of , the ols estimator for the slope coefficient in the sample regression model? group of answer choices smaller sample size (smaller ) smaller error variance (smaller ) smaller variation in in the sample (smaller )
Smaller sample size results in smaller sampling variation of the OLS estimator for the slope coefficient in the sample regression model due to the fact that it reduces the amount of variability in the data. Smaller error variance also reduces sampling variation as it reduces the amount of overall variation in the data.
The sampling variation of the OLS estimator for the slope coefficient in the sample regression model is affected by a variety of factors. A smaller sample size will result in smaller sampling variation because it reduces the amount of variability in the data. This is due to the fact that a smaller sample size will contain less variation in the independent variable, and therefore the estimated slope coefficient will have less variation. Additionally, a smaller error variance will also reduce the sampling variation as it reduces the amount of overall variation in the data. Finally, smaller variation in the independent variable in the sample will also lead to smaller sampling variation of the OLS estimator. This is because the slope coefficient is estimated by minimizing the sum of squared residuals, which is a function of the variation in the independent variable. Thus, if the variation in the independent variable is reduced, the slope coefficient will have less variation. In conclusion, all three factors can lead to reduction in the sampling variation of the OLS estimator for the slope coefficient in the sample regression model.
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Identify the function shown in this graph. PLEASEEE.
The function shown in this graph is y = x + 4
How to determine the function shown in this graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see a straight line
This means that the graph is a linear function
This can be represented as
y = mx + c
From the graph, we have
c = 4 (because the graph intersects the y-axis at y = 4)
m = 1 (because a unit change in x gives a unit change in y)
So, we have
y = x + 4
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2) The area of Norway's is 24% more than the area of Colorado. So Norway's area if
Colorado's area?
The area of Norway's is 24% more than the area of Colorado.So, the area of Colorado is approximately 260,449 square kilometers.
What is Area?
Area is a measurement of the amount of two-dimensional space occupied by a surface or an object. In mathematics, area is a scalar quantity that describes the size of a region in a plane. The units of area are typically square units, such as square meters, square centimeters, square inches, etc.
The formula for the area of a shape depends on the shape itself. For example, the area of a rectangle is equal to its length multiplied by its width, while the area of a circle is equal to π times the square of its radius. Other common shapes and their area formulas include triangles, parallelograms, and trapezoids.
Let's call the area of Colorado "x". If Norway's area is 24% more than Colorado, then Norway's area can be represented as x + 0.24x = 1.24x.
To find the area of Colorado, we can set up an equation:
1.24x = area of Norway
x = area of Norway / 1.24
The area of Norway is 323,802 square kilometers. Therefore, the area of Colorado can be calculated as:
x = 323,802 / 1.24
x = 260,449 square kilometers
So, the area of Colorado is approximately 260,449 square kilometers.
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You want to raise money for the local animal shelter. Your first step is outreach — spreading the word to as many people as you can. You create three outreach options:
• Option 3: Start a chain email, in which each person forwards your email to `2` new people. On the first day, you email `2` people. On the second day, those `2` people both forward your email to `2` new people, reaching a total of `4` people. This will continue for `28`days.
Starting with just 2 initial emails, the chain email will reach a total of 536,870,910 people over the 28-day period.
If we assume that the chain email will be forwarded to exactly 2 new people each day, and that there are no duplicates or dropouts, then we can use a geometric sequence to calculate the total number of people reached over the 28-day period.
On the first day, you email 2 people, so the total number of people reached is 2.
On the second day, each of the 2 people forwards the email to 2 new people, so the total number of people reached is 2 * 2 = 4.
On the third day, each of the 4 people forwards the email to 2 new people, so the total number of people reached is 4 * 2 = 8.
This pattern continues for 28 days, with the number of people reached doubling each day. Therefore, the total number of people reached over the 28-day period is:
2 + 4 + 8 + 16 + ... + 2^28
To calculate this sum, we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
where a is the first term (2), r is the common ratio (2), and n is the number of terms (28).
Plugging in these values, we get:
S = 2(1 - 2^28) / (1 - 2)
= 2(1 - 268,435,456) / (-1)
= 536,870,910
This is a very large number and could potentially have a significant impact on raising awareness and funds for the local animal shelter.
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TRIGONOMETRY PERIMETER
The perimeter of the triangle is
13.82 inHow to find the perimeter of the triangle'The perimeter of the triangle is sum of the length of the sides
The sides are solved as follows using trigonometry relations
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
Solving for NM using tan
tan 59 = 5 / NM
NM = 5 / tan 59 = 3
Solving for LN
sin 59 = 5 /LN
LN = 5 / sin 59 = 5.83
The perimeter of the triangle
= 5.83 + 5 + 3
= 13.82 in
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Find the sum of each infinite geo sequence
Answer:
0.15 repeating
Step-by-step explanation:
a tank contains 1120 l of pure water. solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 l/min, and is thoroughly mixed into it. the new solution drains out of the tank at the same rate. (a) how much sugar is in the tank at the begining?
a) 0 kg of sugar is in the tank at the beginning., b) ds/dt = 0.08-(S/1120)*4, c) 0.32 kg of sugar is in the tank after 1 minute., d) 2.59 kg of sugar is in the tank after 84 minutes.
a) At the beginning, there is no sugar in the tank since it contains only pure water.
b) Let S(t) be the amount of sugar in the tank at time t (in minutes). The rate of change of S is given by the rate at which sugar enters the tank minus the rate at which it leaves. Since the solution enters at a rate of 4 L/min, and contains 0.08 kg of sugar per liter, the rate at which sugar enters is 0.08 kg/L * 4 L/min = 0.32 kg/min. Since the solution leaves at the same rate, the differential equation that models the situation is:
dS/dt = 0.32 - (S/1120) * 4
c) To find the amount of sugar after 1 minute, we need to solve the differential equation from part (b) with the initial condition S(0) = 0 (since the tank initially contains only water). One possible way to solve the differential equation is to use separation of variables:
dS/dt + (4/1120) S = 0.32
Multiplying both sides by dt and dividing by (0.32 - (4/1120) S), we get:
(1/S) dS = (4/0.32 - (1120/4)) dt
Integrating both sides from t = 0 to t = 1 and from S = 0 to S = S(1), we get:
ln(S(1)) - ln(0) = (1.25 - 280) * 1
S(1) = [tex]e^{0.25} * 1120[/tex] ≈ 300.92 kg
Therefore, after 1 minute, there is approximately 300.92 kg of sugar in the tank.
d) To find the amount of sugar after 84 minutes, we can solve the differential equation from part (b) numerically using an appropriate method such as Euler's method, or we can use an integrating factor to solve it analytically. One possible way to use an integrating factor is to multiply both sides of the differential equation by exp(4t/1120):
exp(4t/1120) dS/dt + (S/280) exp(4t/1120) = 0.32 exp(4t/1120)
This can be written as:
d/dt [S exp(4t/1120)] = 0.32 exp(4t/1120)
Integrating both sides from t = 0 to t = 84, we get:
[S(84) exp(4/1120 * 84)] - [S(0) exp(4/1120 * 0)] = ∫(0 to 84) 0.32 exp(4t/1120) dt
Since S(0) = 0 and exp(4/1120 * 84) is a constant, we can simplify this to:
S(84) = (1/exp(4/1120 * 84)) ∫(0 to 84) 0.32 exp(4t/1120) dt
Using integration by substitution with u = 4t/1120, we get:
S(84) = (1/exp(4/1120 * 84)) * (1120/4) * (0.32/4) * [exp(4/1120 * 84) - 1]
S(84) ≈ 301.53 kg
Therefore, after 84 minutes, there is approximately 301.53 kg of sugar in the tank.
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The complete question is:
A tank contains 1120 L of pure water. At a rate of 4 L/min, a solution that contains 0.08 kilogramme of sugar per litre enters the tank. At the same rate that it drains from the tank, the solution is mixed.
a) How much sugar is in the tank when it first starts?
b) With S representing the amount of sugar (in kg) at time t, write a differential equation which models the situation.
c) After 1 minute, calculate the sugar content (in kilogramme).
d) After 84 minutes, calculate the sugar content (in kg).
16. 220 fans travel to a rugby match in minibuses.
Each minibus holds 18 fans.
How many minibuses are needed?
Answer:
13 buses are required.
Step-by-step explanation:
To find the number of minibuses required, take the total number of fans and divide by the number of fans each bus holds.
220 /18
12 2/9
We need to round up to make sure all the fans get on a bus.
13 buses are required.
State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
SSS
Step-by-step explanation:
Since [tex]\overline{AD} \cong \overline{AD}[/tex] by the reflexive property, there are three pairs of congruent sides.
32 children voted for thier favorite ice cream chocolate 3/8 so how may children voted for chocolate explanation step by step plssss
On solving the provided question we can say that The result of multiply the total number of kids by the proportion of those who enjoy chocolate is 12
What is Multiplication?Along with addition, subtractiοn, and division, multiplication is one of the four arithmetic operations. Multiplicatiοn in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals prοduct.
Specifically, multiplicand: First number (factοr). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is knοwn as the product. Multiple additiοns are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20, I multiplied 5 by 4 times. Multiplication is frequently referred tο as "doubling" because οf this.
The result of multiply the tοtal number of kids by the proportion of those who enjoy chocolate is
32 × 3/8 = 12
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Select the correct answer.
What is the justification for step 3 in the solution process?
0.8a - 0.1a = a - 2.5
Step 1: 0.7a = a - 2.5
Step 2: -0.3a = -2.5
Step 3:
a =8.3
O A.
the addition property of equality
O B. the subtraction property of equality
О C.
combining like terms
O D. the division property of equality
Answer: D. the division property of equality
Step-by-step explanation:
In step three you will be dividing -2.5 divided by -0.3 to get a.
..........................................
Answer:
8^4
Step-by-step explanation:
8^8 divided by 8^4
Because they have the same base and it is divided, so we just need to take ^8 - ^4 and get the answer
8^4
What is the cube of 4?
Answer:
64
Step-by-step explanation:
Write the equation of the line shown on the coordinate plane below?
4
3
لا
2
1
-8-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
2 3 4 5 6 7 8
The equation of line shown on the coordinate plane is,
⇒ y = - 1/4x
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, 0) and (4, -1).
Now,
Since, The equation of line passes through the points (0, 0) and (4, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - 0) / (4 - 0)
m = - 1 / 4
Thus, The equation of line with slope - 1/4 is,
⇒ y - 0 = - 1/4 (x - 0)
⇒ y = - 1/4x
Therefore, The equation of line passes through the points (0, 0) and
(4, -1) will be;
⇒ y = - 1/4x
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Victor and his friends like to collect
and trade cards from a certain combat
card game. Victor used his allowance
to purchase 9 booster packs and 4
premade decks, which included a total
of 266 cards. For his birthday, he
received 10 booster packs and 5
premade decks, which included a total
of 320 cards. How many cards come in
every booster pack and every
premade deck?
The value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.
What is a system of equation?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, a deck contains 266 cards which have 9 booster packs and 4 premade decks, and 10 booster packs and 5 premade decks, which included a total of 320 cards.
Let the number of booster pack and premade deck be x and y,
Establishing the system of equations,
9x + 4y = 266....(i)
10x + 5y = 320
2x + y = 64...(ii)
Multiplying eq(ii) by 4 and subtract eq(ii) from eq(i)
(9x + 4y = 266) - (8x + 4y = 256)
x = 10
Put x = 10 in eq(ii)
20 + y = 64
y = 44
Hence, the value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.
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The sum of three consecutive integers, a, b and c, where a
(a) What is the greatest possible value of b?
(b) Find the square root of the largest possible value of c.
The values of a, b and c based on the information will be 2, 3, 4.
The square root of c which is 4 will be 2.
How to calculate the valuesFrom the information, it was stated that the sum of the three consecutive integers, a, b and c, is 9.
This can be Illustrated as:
a + a + 1 + a + 2 = 9
3a + 3 = 9
3a = 9 - 3
a = 6 / 3
a = 2
b will be 2 + 1 = 3
c will be 2 + 2 = 4
The square root of c which is 4 will be:
= ✓4
= 2
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The sum of three consecutive integers, a, b and c, is 9.
(a) What is the greatest possible value of b?
(b) Find the square root of the largest possible value of c.
3. A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150
yards from the center of the green. Whilestanding on the marker facing the green, the golfer turns
110 toward his ball. He then paces off 35 yards to hit his ball. See figure. How far is the ball from the
center of the green? Round to the nearest yard
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.
Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:
x = 35 * cos(110)
y = 35 * sin(110)
Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:
d^2 = x^2 + (y + 150)^2
Plugging in the values for x and y, we get:
d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2
d^2 = 1225 + (150 + 35 * sin(110))^2
Using a calculator, we can find that sin(110) = 0.939, so:
d^2 = 1225 + (150 + 31.65)^2
d^2 = 1225 + (181.65)^2
d^2 = 1225 + 32762.7225
Taking the square root of both sides:
d = sqrt(1225 + 32762.7225)
d = sqrt(33987.7225)
d = 183.83
Rounding to the nearest yard:
d = 184 yards
So, the ball is 184 yards from the center of the green.
The equation ŷ = 67.34x - 128,933.4 predicts a rodent population in a town in year x.
According to the equation, what was the rodent population in 2005?
Enter your answer in the box. Round to the whole number.
The predicted rodent population in the town in 2005 was approximately 6083.
What was the rodent population in 2005?From the question, we have the following parameters that can be used in our computation:
ŷ = 67.34x - 128,933.4
To find the rodent population in 2005, we need to substitute x = 2005 into the equation and solve for ŷ:
ŷ = 67.34(2005) - 128,933.4
So, we have
ŷ = 135016.7 - 128,933.4
Evaluate
ŷ = 6083
Hence, the predicted rodent population was 6083.
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Robert tutors two students, Andy and Sue. Andy pays robert $70 per month. Sue pays $50 per month how many months will Robert have to tutor until he earns $600?
Answer: 5 Months
Step-by-step explanation:
Alright, we know he will make $120 a month (since 50 + 70 = 120)
(Let's have months=m)
So now we need to figure out for how many months (m) will he need to get to $600.
We know 120 a month so we can get the equation: 120m=600
Now all we have to do is solve for m
Divide both sides by two to get m=5
Checking Answers
70(5)=350
50(5)=250
250+350=600
So this solution works.
Answer: 5 months
Step-by-step explanation: so, what you have to do is add up 120 5 times so in total you will have 600 so the answer is 5 months.
4
Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 70 feet. His back yard has a length of 10 feet and a width of 40 feet. How many square feet of sod does Jayden need to purchase?
Jayden needs to purchase 3900 square feet of sod to cover his front and back yards.
The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then multiplying or dividing to find the value of the whole. In this case, the unit we will use is square feet.
To calculate the area of the front yard, we need to multiply its length by its width. So, we have:
Area of front yard = Length x Width = 50 ft x 70 ft = 3500 sq ft
To find the area of the back yard, we use the same formula:
Area of back yard = Length x Width = 10 ft x 40 ft = 400 sq ft
Now, we need to add the two areas to find the total area that requires sod. So, we have:
Total area = Area of front yard + Area of back yard
=> 3500 sq ft + 400 sq ft = 3900 sq ft
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Need help with this question urgent please
Answer:
Step-by-step explanation:
-8^8 is -16777216.
-8^5 is -32768.
-16777216/-32768 is 512.
btw, is this bigideas? lol i remember this website
Helpppppppp meeeeeeeeeeeeeeeeeeee
helpppppppppppppppppppppp
Answer:
X Y
2 1
4 7
5 10
Step-by-step explanation:
For some reason, Brainly keeps saying that the question I'm asking hurts their feelings though I am just typing out the question from the screenshot. please take a look
There is part A and Part B.
Based on the information in the graph, we can infer that the area of the three triangles is the same. In this case the area would be 45 cm².
How to calculate the area of triangles?To calculate the area of the triangles we must calculate the area of one of them taking into account that all three have the same dimensions. According to the above, we must apply the following formula:
a = b * h / 2Then we must replace the values of the base and the height:
a = 9 * 10 / 2a = 90 / 2a = 45So the area of the triangles would be 45cm.
Note: This question is incomplete. Here is the complete information:
question
What is the area of the triangles?
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Ships in a first generation video game were
modeled like the one shown.
130 in.
in.
2 in.
in.
3 in.
How many square inches of video screen did
one ship occupy?
A 71 in.2
B 9 in.2
C 10 in.2
D 11 in.²
The area occupied by the ship is 10 inches².
What is the area of parallelogram?The area of a parallelogram is -
A{||gm} = base x height
Given is that Ships in a first generation video game were modeled like the one shown in the image.
We can write the area occupied by the ship as -
Area = A{||gm} + A{triangle}
Area = {b x h} + {L x B}
Area = [tex]$(3\frac{2}{5}\times 2)\;+\; (3\frac{2}{5}-1)\times1\frac{1}{3}[/tex]
Area = (17/5 x 2) + (17/5 - 1) x (4/3)
Area = 34/5 + 12/5 x 4/3
Area = 34/5 + 16/5
Area = 50/5
Area = 10 inches²
Therefore, the area occupied by the ship is 10 inches².
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Write a piece wise function for each function graphed below.
The piecewise function for the graph is given as follows:
y = -2, x < -4.y = 0.5x + 4, -4 < x ≤ 2y = -1.5x + 1, x > 1.How to define the piecewise function?A piecewise function is a function that has different definitions, depending on the input x of the function.
The three different definitions for the function in this problem are given as follows:
x < -4.-4 < x ≤ 2.x > 2.For x < -4, the function is constant at y = -2, hence:
y = -2, x < -4.
For -4 < x ≤ 2, the function is linear, with an slope of 0.5 and intercept of 4, hence:
y = 0.5x + 4, -4 < x ≤ 2
For x > 2, the function is also linear, with slope of -1.5, hence at x = 0 it would assume a value of 1, thus:
y = -1.5x + 1, x > 1.
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PLS HELP I HAVE TO SUBMIT IN LESS THAN AN HOUR
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function C(x)=0.9x²-180x+20,985. How many machines must be made to
minimize the unit cost?
Do not round your answer.
At 100 machines the unit cost will be minimum and the minimum cost is 11985.
Finding the maximum and minimum on parabolas:The lowest point on the graph, that is referred to as the minimum, or min, is the vertex of a parabola. The highest point on the graph, that referred to as the maximum, or max, is the vertex of a parabola.
The formula for the minimum value is given by -b/2a
Here we have
The medical equipment industry manufactures X-ray machines. If x machines are made, the unit cost is given by the function
C(x) = 0.9x²-180x+20,985.
Compare given C(x) with the standard equation ax² + bx + c
=> a = 0.9, b = -180 and c = 20,985
We can find the x - coordinate where the minimum value occurs using the formula -b/2a
The x-coordinate where the minimum value occurs = - (- 180)/2(0.9)
= (180)/1.8 = 100
Hence at x = 100, the unit cost will be minimum
The unit cost can be calculated as follows
C(100) = 0.9(100)²-180(100)+20,985
= 0.9(10000) -18000 + 20,985
= 9000 - 18000 + 20985
= 11985
Therefore,
At 100 machines the unit cost will be minimum and the minimum cost is 11985.
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Question
You work with a carpenter who asks you to cut 4 boards to the following lengths: 7½ inches, 10½ inches, 9 inches, and 5½ inches. What is the total length, in inches, of the cut boards?
The total length, in inches, of the four cut boards is 130 inches.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.
We have to find the total length of the board.
Total length of the board is found by adding each length.
Total length = 7½ + 10½ + 9 + 5½
Mixed fraction can be converted to improper fraction by cross multiplication.
7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2
Total length = 15/2 + 21/2 + 9 + 11/2
= (15/2 + 21/2 + 11/2) + 9
= 47/2 + 9
= 65/2
Again improper fraction can be converted to mixed fraction.
Total length of a board = 32 1/2 inches
But there are 4 boards.
Total length of the 4 boards = 4 × 65/2 = 130 inches
Hence the total length is 130 inches.
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(-2,6)(-4,3)(3,-2)(8,6) is the relation a function
The given relation (-2,6)(-4,3)(3,-2)(8,6) is a function as every input has a single output.
A relation is set to be a function when every input has a single output.
In the given relation, -2,-4,3,8 has single output. Therefore, it is a function.
So, -2,-4,3 and 8 are the elements of the domain of the given
relation.
Here domain ={-2,-4,3,8} and range ={6,3,-3}
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