Answers
The absolute values of inequality equations totally depend on the symbols.
x+1 = 3, x = 2x+1 > 3 , x > 2 x+1 < 3 , x< 2x+1 ≥ 3 , x ≥ 2 x+1 ≤ 3, x ≤ 2What is inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.
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Related Questions
Do these data (Mod2-2Commercials (Links to an external site.)Links to an external site.) allow us to infer that the mean number of commercials watched during the game is different from 16? Assume the level of significance is 10%.
Answers
No, the data provided in the link does not allow us to infer that the mean number of commercials watched during the game is different from 16.
To test the hypothesis that the mean number of commercials watched is different from 16, we would need to perform a statistical hypothesis test. The level of significance (10%) would be used to determine the critical value(s) for the test statistic, which would then be used to make a decision about the null hypothesis (that the mean number of commercials watched is equal to 16).
Without the results of such a test, it is not possible to make a conclusion about the difference between the mean number of commercials watched and 16.
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Draw the taste of the values for the relation y = x² for the Interval -3≤x≤4.
Answers
Answer: I don't have the capability to draw images. However, I can explain how to graph the equation y = x² for the interval -3≤x≤4.
To graph the equation, we can plot a set of points by substituting values of x from the given interval into the equation and solving for y.
For example:
when x = -3, y = (-3)² = 9
when x = -2, y = (-2)² = 4
when x = -1, y = (-1)² = 1
when x = 0, y = (0)² = 0
when x = 1, y = (1)² = 1
when x = 2, y = (2)² = 4
when x = 3, y = (3)² = 9
when x = 4, y = (4)² = 16
We can plot these points on a coordinate plane, and then connect them with a smooth curve.
The graph of y = x² for the interval -3≤x≤4 will be a parabola that opens upward and its vertex is located at (0,0) point.
The x-coordinates of the vertex are in the center of the inte
Step-by-step explanation:
row-echelon forms determine if the following matrices are in row-echelon form or reduced row-echelon form. explain why the matrix is in the determined form
Answers
A matrix is in the row-echelon form if:
1. The first nonzero element of each nonzero row (called the leading entry) is to the right of the leading entry of the row above it.
2. Each leading entry is 1 (also called a pivot).
3. Each element above and below a pivot is 0.
A matrix is in the reduced row-echelon form if it is in row-echelon form and also:
4. Each pivot is the only nonzero element in its column.
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers, symbols, or expressions in a matrix are called its entries or elements. Matrices are often used in linear algebra, a branch of mathematics that deals with vector spaces and linear transformations.
They can be used to represent systems of linear equations, perform operations such as matrix addition and multiplication, and solve systems of linear equations.
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A party hat is in the shape of a cone with dimensions shown.
Find the height of the hat. Round to the nearest tenth.
4.3 in.
10 in.
Answers
The height of the hat is 9.0 inches.
How to find the height of a cone?A party hat is in the shape of a cone with dimensions shown . Therefore, the height of the cone can be found as follows:
The radius of the cone is 4.3 inches and the slanted height of the cone is 10 inches.
Therefore, Pythagoras's theorem can be used to find the height of the cone. The radius and the slanted height of the cone forms a right angle triangle.
Therefore,
10² - 4.3² = h²
h² = 100 - 18.49
h² = 81.51
square both sides
h = √81.51
h = 9.02828887442
h = 9.0 inches
Therefore,
height of the hat = 9.0 inches
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Evaluate 2( L+ 8Z) + L, when Z = 3 and L = 4.2
Answers
Answer:
Okay so z is 3.
We are going to put taht into our equation
2(L + 8(3)) + L
2(L + 24) + L
Now we do the 2
2L + 48 + L
Okay now L is 4.2
SO
2(4.2) + 48 + (4.2)
8.4 + 48 + 4.2 = 60.6
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(l + 8z) + l}\\\mathsf{= 2(4.2 + 2(8)(3)) + 4.2}\\\mathsf{= 2(4.2) + 2(8)(3) + 4.2}\\\mathsf{= 8.4 + 16(3) +4.2}\\\mathsf{= \mathsf{8.4 + 48 + 4.2}}\\\mathsf{= 56.4 + 4.2}\\\mathsf{= 60.6}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{\mathsf{60.6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please help.
Find the percent of increase from 5.5 feet to 6 feet. Round the percent to the nearest tenth if necessary.
Answers
The percent of increase from 5.5 feet to 6 feet is 9.1%
What is percentage and its calculation for given terms?Percentage is a way to express a number as a fraction of 100.
It is often used to express a proportion or rate in a convenient and understandable way.
To calculate percentage, you can use the formula: (part/whole) x 100.
For example, if you scored 80 out of 100 on a test, your percentage score would be 80%.
Percentage is often used in many fields such as finance, statistics, and education.
It can be used to express the increase or decrease between two values or to compare the parts of a whole.
You can use the following calculation to determine the percentage increase from 5.5 feet to 6 feet:
Old Value * 100 / (New Value - Old Value) = Percent Increase
In this case:
(6 - 5.5) / 5.5 * 100 = 9.090909090909091%
You can round this to the nearest tenth, which would be 9.1%.
Therefore, the percent of increase from 5.5 feet to 6 feet is 9.1%.
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data consist of weights in grams the unit for population standard deviation would be
Answers
Answer: s squared.s2.sigma i think
Step-by-step explanation:
the distribution system for the herman company consists of three plants, two warehouses, and four customers. plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows: customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows: choose the correct network representation of this problem. (i) (ii) (iii) (iv) formulate a linear programming model of the problem. for subtractive or negative numbers use a minus sign even if there is a sign before the blank. let xij represents relation between plants to warehouses or relation between warehouses to customers. min fill in the blank 2 x14 fill in the blank 3 x15 fill in the blank 4 x24 fill in the blank 5 x25 fill in the blank 6 x34 fill in the blank 7 x35 fill in the blank 8 x46 fill in the blank 9 x47 fill in the blank 10 x48 fill in the blank 11 x49 fill in the blank 12 x56 fill in the blank 13 x57 fill in the blank 14 x58 fill in the blank 15 x59 s.t. 1) fill in the blank 16 x14 fill in the blank 17 x15 < fill in the blank 18 2) fill in the blank 19 x24 fill in the blank 20 x25 < fill in the blank 21 3) fill in the blank 22 x34 fill in the blank 23 x35 < fill in the blank 24 4) fill in the blank 25 x46 fill in the blank 26 x47 fill in the blank 27 x48 fill in the blank 28 x49 fill in the blank 29 x14 fill in the blank 30 x24 fill in the blank 31 x34
Answers
All variables must be greater than or equal to 0, indicating that no shipping is allowed if the cost is negative.
The network representation of the Herman Company distribution system is as follows:
Plants (P1, P2, P3) -> Warehouses (W1, W2) -> Customers (C1, C2, C3, C4).
A linear programming model of the problem can be formulated as:
Minimize Z = 2x14 + 3x15 + 4x24 + 5x25 + 6x34 + 7x35 + 8x46 + 9x47 + 10x48 + 11x49 + 12x56 + 13x57 + 14x58 + 15x59
Subject to:
x14 + x15 ≤ 2
x24 + x25 ≤ 3
x34 + x35 ≤ 4
x46 + x47 + x48 + x49 ≤ 5
x14 + x24 + x34 ≤ 6
x15 + x25 + x35 ≤ 7
x46 + x56 + x66 ≤ 8
x47 + x57 + x67 ≤ 9
x48 + x58 + x68 ≤ 10
x49 + x59 + x69 ≤ 11
All variables ≥ 0
The objective of this problem is to minimize the total shipping cost from plants to warehouses and warehouses to customers. The constraints represent the limited capacities of each plant, warehouse and customer and the maximum number of units that can be shipped from each plant to each warehouse or each warehouse to each customer. All variables must be greater than or equal to 0, indicating that no shipping is allowed if the cost is negative.
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Let $x$ be a real number selected uniformly at random between 100 and 200. If $\lfloor {\sqrt{x}} \rfloor = 12$, find the probability that $\lfloor {\sqrt{100x}} \rfloor = 120$. ($\lfloor {v} \rfloor$ means the greatest integer less than or equal to $v$.)
$\text{(A)} \ \frac{2}{25} \qquad \text{(B)} \ \frac{241}{2500} \qquad \text{(C)} \ \frac{1}{10} \qquad \text{(D)} \ \frac{96}{625} \qquad \text{(E)} \ 1$
Answers
The probability of successful region is =241/2500 Option b is correct.
Since √x=12, 12 ≤√x<13 and thus 144 ≤ x < 169.
The successful region is when 120 ≤ 10√x < 121 in which case 12 ≤√x< 12.1
Thus, the successful region is when
144 ≤ x < 146.41
The successful region consists of a 2.41 long segment, while the total possibilities region is 25 wide. Thus, the probability is
=2.41/25
=241/2500 (B)
In mathematics, a real number is a quantity that can be expressed as an infinite decimal expansion. In contrast to the natural numbers 1, 2, 3,..., which are derived from counting, real numbers are used in measurements of continuously varying quantities such as size and time.
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Round 74,600 to the nearest thousand
Answers
Answer:
75,000
Step-by-step explanation:
We have to round up to nearest thousand ,so we need to check hundred place ...
If hundred place is equal or greater than 5 ,we need to add +1 to the number which is in thousand place , If it is less than 5 we don't need to do so ....
which number rounded to the nearest hundred is 4,700? 4,070 4,617 4,681 4,797
Answers
Answer:
Let's look at each number separately. Look in the tens place to determine which way to round.
4,070 will round up since there's a 7. However, it will only round up to 4,100 so this is not the right answer.
4,617 will round down since there's a 1. However, it will only round down to 4,600 so this is not the right answer.
4,681 will round up since there's an 8. This number will round up to 4,700 so this is the correct answer.
4,797 will round up since there's a 9. However, it will only round up to 4,800 so this is not the right answer.
The correct answer is 4,681.
complete the implementation of the function `same diff ints`, which takes in a list of integers (`ints`) and returns `true` if there exist two list elements $i$ positions apart, whose absolute difference as integers is also $i$. if there are no two elements satisfying this condition, `same diff ints` should return `false`
Answers
The complete implementation of the function 'same diff ints' is written italic below.
How to complete the implementation of the function 'same diff ints'?Below is the implementation for the function same_diff_ints in Python:
def same_diff_ints(ints):
for i in range(1, len(ints)):
for j in range(i, len(ints)):
if abs(ints[j] - ints[j-i]) == i:
return True
return False
The function takes in a list of integers as input and iterates through the list using nested for loops. The outer for loop iterates through the list starting at index 1, and the inner for loop iterates through the list starting at the outer loop's current index.
The function compares the absolute difference between the two elements at index j and j-i with the value of i. If the absolute difference between the two elements is equal to i, the function returns True. If no such pair of elements is found, the function returns False.
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1. Last Monday Micah bought 5 % pounds of plant food. He used 1 7/8 pounds
for his tomato plants and 1 1/2 pounds for his pepper plants.
a. How many pounds of plant food did he have left? Write one or more
equations to show how you reached your answer.
Answers
5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds
What is algebra?The theory used in this question is algebra. Algebra is the branch of mathematics that studies the rules of operations and relations and the constructions and concepts arising from them.
In this question, algebra was used to solve for the number of pounds of plant food that Micah had left after using some for his tomato and pepper plants.
Step 1: Calculate the total amount of plant food that Micah bought: 5 % pounds
Step 2: Calculate the amount of plant food that Micah used for his tomato plants: 1 7/8 pounds
Step 3: Calculate the amount of plant food that Micah used for his pepper plants: 1 1/2 pounds
Step 4: Calculate the amount of plant food that Micah had left by subtracting the total amount of plant food used from the total amount of plant food bought: 5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds
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Below is the data for the unemployment rates from September 2017 issue of the Economist from 10 different countries. Country Unemployment Rates US 4.4 China 4 France 9.8 Spain 17.1 India 5 Greece 21.2 Chile 6.9Mexico 3.2 Egypt 12 Turkey 10.2 You can enter the data into R using this line of code below. GlobalRates<-c(4.4.4,9.8.17.1,5,21.2,6.9.3.2,12,10.2) Constuct a box and whisker plot and deterimine if there are any outliers in the Global Unemployment Rates. O There is one outlier, Greece, O There are two outliers, Greece and Spain.O There are three outliers, Spain, Greece and Turkey. O There are no outliers.
Answers
The answer is -There are no outliers.
According to the question, there are no outliers in the Global Unemployment Rates. From the given data, no outliers are observed.
An outlier is an observation that lies an abnormal distance from other values in a sample from a population. In a sense, this explanation leaves it up to the analyst to decide what will be considered abnormal.
An outlier is a single data point that goes far outside the average value of a set of statistics. Outliers may be exceptions that stand outside individual samples of populations.
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3. If AB = 26 and BD = 20, find AE.
Answers
In a parallelogram, opposite sides are equal in length, which can be used to calculate the length of AE. AB is equal to 26 and BD is equal to 20, so AE is equal to 6.
Is a parallelogram a rhombus?In contrast to a parallelogram, which has equal sides on both sides and diagonals that bisect each other, a rhombus has equal sides on all four sides and diagonals that cross at 90 degrees.
The length of each side is the same. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half.
In a parallelogram, opposite sides are equal in length. Therefore, we can use this fact to calculate the length of AE in the given parallelogram.
Since AB is equal to 26 and BD is equal to 20, we can set up the equation:
26 = AE + 20
Subtract 20 from both sides of the equation to solve for the length of AE:
26 - 20 = AE
6 = AE
Therefore, AE is equal to 6.
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Use the distributive property to write each expression as an equivalent
algebraic expression.
12(y+14)
Answers
Answer: 12y+168
Step-by-step explanation:
Basically, multiply each of the numbers that are in the parenthesis by the number outside the parenthesis (12). So 12·y=12y and 12·14=168. Therfore the answer is 12y+168 .
What is the slope of the line through the points (5, −5) and (6, 0) ?
Answers
Answer:
5
Step-by-step explanation:
the slope is Δy/Δx
0-(-5) =5
6-5 =1
slope is 5
What is the 18th term of the arithmetic sequence where a3 = −6 and a12 = −3?
Group of answer choices
0
1
−3
−1
Answers
Step-by-Step Explanation:
3rd term (a3) = -6
12th term (a12) = -3
We know, nth term of an AP = a1 + (n - 1)d, where d = common difference
a3 = a + (3-1)d = a + 2d = -6...(I)
a12 = a + (12-1)d = a + 11d = -3..(II)
Subtracting (II) from (I), we have
2d - 11d = -6 + 3
=> -9d = -3
=> d = 1/3
Therefore, a + 2×1/3 = -6
=> a + 2/3 = -6
=> a = -6-2/3 = -20/3
Therefore, 18th term
= a + (18-1)d
= -20/3 + 17/3
= -3/3
= -1
Answer:
-1
Hope it helps.
If you have any query, feel free to ask.
What was the price of the ABC bond on the previous day?
a. 100 1/3
B. 100 3/4
C. 104 1/2
D. 104 3/4
Answers
The price of the ABC bond on the previous day is $104 3/4
How to determine the price of the bondFrom the question, we have the following parameters that can be used in our computation:
Rate = $10 per day
Current price = $114 3/4
Using the above as a guide, we have the following:
Previous price = Current price - Rate
Substitute the known values in the above equation, so, we have the following representation
Previous price = $114 3/4 = $10
Evaluate the difference
Previous price = $104 3/4
Hence, the previous price is $104 3/4
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Complete question
ABC bond increase by $10 everyday. If the price on a given is $114 3/4, what was the price of the ABC bond on the previous day?
If the x-intercepts of a function are 2 and 5, then f(2) = _______. and f(5) = ________. The x-intercepts, 2 and 5, are called the _______ of the function.
Answers
If the x-intercepts of a function are 2 and 5, then f(2) = ____0___. and f(5) = ____0____. The x-intercepts, 2 and 5, are called the _zeros_ of the function.
What are the x-intercepts of the function?
The x-intercepts of a function y = f(x) are the values of x such that the graph of the function intercepts the x-axis, that means that are the values of x such that f(x)= 0
Then if 2 and 5 are x-intercepts of the function, then:
f(2) = 0
f(5) =0
The x-intercepts are allso called the zeros of the function.
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❗️PLEASEE HELPPPPPP ILL GIVE YOU BRAINLIESTTTTTT ❗️
Find the value of v that makes quadrilateral PQRS a parallelogram.
P v+38°
s 8v-56°
R 6v–72°
Q v+98°
PLEASEE HELPPPPPP ILL GIVE YOU BRAINLIESTTTTTT
Answers
Answer:
there is no value of v that makes quadrilateral PQRS a parallelogram.
Step-by-step explanation:
Hopefully this helps, may be wrong so...
A quadrilateral is a parallelogram if and only if opposite angles are equal. Therefore, in order for quadrilateral PQRS to be a parallelogram, angle P must be equal to angle S, and angle Q must be equal to angle R. From the given information, we know that:
angle P = v + 38°
angle S = 8v - 56°
angle Q = v + 98°
angle R = 6v - 72°
To find the value of v that makes quadrilateral PQRS a parallelogram, we must set angle P equal to angle S and angle Q equal to angle R:
v + 38° = 8v - 56°
v + 98° = 6v - 72°
Solving for v in the first equation:
v + 38° = 8v - 56°
-7v = -94°
v = 13.428571428571429
Solving for v in the second equation:
v + 98° = 6v - 72°
-5v = -170°
v = 34
We can see that both values of v do not match, therefore there is no value of v that makes quadrilateral PQRS a parallelogram.
A quadrilateral is a parallelogram if and only if the opposite angles are equal. In this case, the opposite angles are P and S, and Q and R.
Therefore, for the quadrilateral PQRS to be a parallelogram, we must have:
v+38° = 8v-56° and v+98° = 6v–72°
Solving the first equation for v:
v+38° = 8v-56°
38 = 7v
v = 38/7
Now we use this value of v to check if the second equation is true:
v+98° = 6v–72°
(38/7) +98 = 6(38/7) - 72
98 = -34
As we can see, the second equation is not true, so the value of v = 38/7 doesn't make quadrilateral PQRS a parallelogram.
No value of v exists that would make quadrilateral PQRS a parallelogram, as the opposite angles are not equal in this case.
First solve the system for x and y.
-3y+8x=18
y=6x-6
Answers
Step-by-step explanation:
given = y = 6x-6 .
therefore ,
=) -3(6x-6)+8x=18 - ( from given ) .
=) -18x+18+8x=18 .
=) -10x=18-18 .
=) -10x = 0 .
=) x = 0/10 = 0.
therefore ,
y=6(0)-6 .
= -6 .
therefore , x = 0 & y = -6 .
[ it takes so much time to write and solve so plzzz => ]
MARK ME AS BRAINLIEST ...
16 multiplied by what gives you 1600?
Answers
Answer:
The answer is 100. One way to find it out is 1600/16, and then you get 100.
lists the parts of the expression shown 8r + 5p + 7 terms variables, coefficient of p constant
Answers
Answer/Step-by-step explanation:
Starting with:
8r + 5p + 7
There are three terms. 8r is a term; 5p is a term; 7 is a term. See how the terms are separated by + or -
r and p are variables. Most often the variable is a letter, that way it can stand for an unknown value. It can vary.
5 is the coefficient of p. Its the number right next to the p. (They are multiplied together)
7 is the constant. Constant means unchanging, right? So 7 is a plain old number, it doesn't change like a variable can. A plain number with no variable is a constant.
Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.
-3x + 3y= 21
4x + 4y= 60
Answers
The given pair of linear equations is consistent.
What are Linear Equations?
An equation is said to be linear if the maximum power of the variable is consistent. Another name for it is a one-degree equation.
Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. a real number equation of the form ax+by+c = 0, with real numbers a, b, and c with the highest power one variable x and y.
In our question, we can see:
a1 = -3 and a2 = 4
b1 = 3 and b2 = 4
c1 = 21 and c2 = 60
a1/a2 = -¾
b1/b2 = ¾
c1/c2 = 7/20
Since a1/a2 is not equal to b1/b2, therefore our pair of liner equation is consistent.
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write in the form a b, where a and b are positive integers:
Answers
The expression of the fraction 256^-3/4 in the form of a / b is equal to 1 / 64 where highest common factor between 1 and 64 is 1.
Expression of the fraction 256^-3/4 in the form a /b .
Where 'a' and 'b' are positive integers .
'a' and 'b' have no common factor than 1.
256^-3/4
= ( 1 / 256^3/4 )
= 1 / 2^ (8 × 3/4 )
= 1 / 2 ^ ( 2 × 3 )
= 1 / 2^6
= 1 / 2⁶
= 1 / 64 in the form of ( a / b )
Greatest common factor between 1 and 64 is equal to 1.
1 and 64 are positive integers.
Therefore, the expression of 256^-3/4 in the a/b fraction form is equal to 1/64.
The given question is incomplete, I answer the question in general according to my knowledge:
Express 256^-3/4 as a fraction. Write the fraction in the form a/b, where a and b are positive integers with no common factor greater than 1 .
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3. Find (a) the net cost equivalent and (b) the single discount equivalent for a
series discount of 5/10/12.
Answers
Answer:(a) To find the net cost equivalent, we can use the formula:
Net Cost Equivalent = Original Cost / (1 - (Discount Rate / 100))
Using this formula, the net cost equivalent for a series discount of 5/10/12 is:
Net Cost Equivalent = Original Cost / (1 - (5/100)) / (1 - (10/100)) / (1 - (12/100))
(b) To find the single discount equivalent for a series discount of 5/10/12, we can use the formula:
Single Discount Equivalent = (1 - (1 - (Discount Rate1 / 100)) x (1 - (Discount Rate2 / 100)) x ... x (1 - (Discount RateN / 100))) x 100
Using this formula, the single discount equivalent for a series discount of 5/10/12 is:
Single Discount Equivalent = (1 - (1 - (5/100)) x (1 - (10/100)) x (1 - (12/100))) x 100
HURRY HAVE A TIMER In the winter fuel line antifreeze must be added at a rate of one can per 8 gal of fuel.
How many cans should be added to an 18-gallon tank
Answers
The number of cans to be added to 18 gallon tank is given by equation
A = 2.25 cans
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of cans for 18 gallon tank be A
Now , the equation will be
The number of cans per 8 gallons = 1 can
So , the number of cans for 1 gallon = number of cans per 8 gallons / 8
On simplifying the equation , we get
The number of cans for 1 gallon = 1/8
The number of cans for 1 gallon = 0.125 can
And ,
The number of cans for 18 gallons A = 18 x number of cans for 1 gallon
Substituting the values in the equation , we get
The number of cans for 18 gallons A = 18 x 0.125
The number of cans for 18 gallons A = 2.25 cans
Hence , the number of cans is 2.25 cans
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Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?
Answers
Answer: 41 years ago, when Sally was 13 and her mother was 39.
Answer: 41 years
Step-by-step explanation:
I reckon the question is asking when her mother was 3 times her age.
S = 54
M = 80
54 - 41 = 13
80 - 41 = 39
39/13 = 3
use ratio test to see if this series converges
Answers
This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] diverges.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given a series, [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] we need to see if the series converges or not.
the ratio test will fail if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | =1[/tex]. Otherwise, the series converges absolutely if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | < 1[/tex] and diverges if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | > 1[/tex]
Testing for the series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}\\[/tex],
=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right |[/tex]
=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{(n+1)!}{n!} \right | \\[/tex]
=> [tex]\lim_{n \to \infty} (n + 1)[/tex]
This value will always be greater than 1 for any positive value of n.
Therefore, This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] does not converge.
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