Answer:
find 3 consecutive numbers such that twice the first , 3 times the second and 4 times the third together make 191 ?
Let n-1,n and n+1 be three consecutive numbers.
Given
2(n-1)+3n+4(n+1)=191
2n-2+3n+4n+4=191
9n+2=191
9n = 189
n = 21
So, n-1=20 and n+1=22
So the answer is 20,21,22
[tex] \huge \bold{\color{red}{ANSWER}}[/tex]
[tex]\pmb { \orange{Given }:} \sf{ Three \: Consecutive \: numbers}[/tex]
[tex]\pmb{\orange{To find}: } \sf{Least \: of \: the \: numbers}[/tex]
[tex]\pmb{\orange{Solution}: }[/tex]
[tex]\sf{Let \: the \: three \: consecutive \: numbers \: be }[/tex]
[tex] \sf\red x, \red {x+1}, \red{x+2}[/tex]
[tex]\sf{Twice \: the \: number = 2\red x}[/tex]
[tex]\sf{3 \: times \: the \: Second \: number = 3(\red{ x+1})}[/tex]
[tex]\sf{4 \: times \: the \: third \: number= 4(\red {x+2})}[/tex]
☆ according to question
[tex] \pmb{2\red x + 3(\red{x+1})+4(\red{x+2})= 191}[/tex]
[tex] \pmb{2\red{x} + 3\red{x}+3+4\red{x}+8= 191}[/tex]
[tex] \pmb{9\red{x}=191-11 = 180}[/tex]
[tex] \pmb{\red{x}=20}[/tex]
[tex] \sf{∴the \: three \: Consecutive \: numbers \: are} [/tex]
[tex] \pmb{\pink{20}, \pink{21}, \pink{22}}[/tex]
_________________......
[tex] \purple{ \pmb{LearningLifeII}}[/tex]
The goal for the size of the Santa on a Christmas Santa cup is 3. 5 cm with an acceptable tolerance of ± 0. 9 cm. The grand mean of the size of the Santa from the samples that were taken is 3. 4 cm and the standard deviation is 0. 28 cm. What is CP? (rounded to three decimals)
The processing capability for the size of the Santa rounded to three decimal places is 1.07.
CP (Process Capability) is a statistical measure that compares the performance of a process to the specifications of that process. It can be calculated using the formula:
CP = (USL - LSL) / (6 * standard deviation)
Where:
USL = Upper Specification Limit (3.5 + 0.9) = 4.4 cm
LSL = Lower Specification Limit (3.5 - 0.9) = 2.6 cm
Standard deviation = 0.28 cm
Substituting these values into the formula:
CP = (4.4 - 2.6) / (6 * 0.28) = 1.8 / 1.68 = 1.07
So, CP rounded to three decimal places is 1.07
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Do 5 - x > 8 and x - 5 < 8 have the same solution set? If so, describe the solution set. If not, give a example of a number that belongs to one solution set but not to the other.
The given equation does not give same solution set.The first equation gives negative number and second equation gives positive number as a solution.
What is inequality in math example?The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally,Compare the two values whether it is less than or greater than,then different inequalities are used.
How do we solve an inequality in math?Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number.
Now we solve
5-x>8 x-5<8
5-5-x>8-5 x-5+5<8+5
-x>3 x<13
Hence given equation does not give same solutions.
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HELP!!! Find the inverse of the matrix..
Answer:
The matrix does not have an inverse (D)
Step-by-step explanation:
The matrix is singular, therefore doesn't have an inverse
Suppose the average yearly salary of an individual whose final degree is a master's is $ 41 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $ 109 thousand. Find the average yearly salary of an individual with each of these final degrees.
Suppose the average yearly salary of an individual whose final degree is a master's is $ 41 thousand less than twice that of an individual. the average yearly salary of an individual with each of these final degrees is: $50,000 (Bachelor's degree) and $59,000 (Master's degree )
How to find the average yearly salary?Let x represent the average yearly salary of an individual with the bachelor's degree
Let (2x-41000) represent the average yearly salary of an individual with the master's degree
Let the sum of these salaries = 109000
So, x + (2x-41000) = 109000
Simplify and solve:
3x = 109000 + 41,000
3x = 150,000
Divide both side by 3x
x= 150,000/3
x = 50,000 (Bachelor's degree)
So,
(2x-41000)
= 2(50,000) - 41,000
=100,000 - 41,000
= $59,000 (Master's degree )
Therefore the average yearly salary is $50,000 (Bachelor's degree) and $59,000 (Master's degree )
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What is the slope of the line that passes through the points (-7,-8) and
(-5, 6)?
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-7)}}} \implies \cfrac{6 +8}{-5 +7} \implies \cfrac{ 14 }{ 2 } \implies \text{\LARGE 7}[/tex]
Alyssa just accepted a job at a new company where she will make an annual salary of $53000. Alyssa was told that for each year she stays with the company, she will be given a salary raise of $5000. How much would Alyssa make as a salary after 3 years working for the company? What would be her salary after
t
t years?
Answer:
68,000
Step-by-step explanation:
53,000+5,000x3
5,000x3=15,000
53,000+15,000=68,000
32. Hannah's gross wage is 1250perweek, buther' takehome' payisonly785 What percentage is this of her gross wage? Give your answer correct to the nearest whole percentage.
Therefore , the solution of gross pay problem is 62% is this of her gross wage.
What percentage is this of her gross wage?Hannah's take home pay of percentage 785 is 62.8% of her gross wage of 1250. This can be calculated by dividing 785 by 1250 and multiplying the answer by 100.
Here,
62.8% is the same as 0.628.
This can be calculated by dividing 785 by 1250.
To get the answer to the nearest whole percentage, we round up 0.628 to 0.63 which is 63%.
This means that Hannah's take home pay of 785 is 63% of her gross wage of 1250.
63% is the answer to the question: what percentage is Hannah's take home pay of her gross wage? This is correct to the nearest whole percentage.
To summarise, Hannah's take home pay of 785 is 63% of her gross wage of 1250, correct to the nearest whole percentage.
Hannah's take-home pay is 62.8% of her gross wage. This percentage is the result of taxes and other deductions taken by her employer.
Knowing this percentage can help Hannah better understand how much money she is taking home each week and how much money is being withheld from her paychecks.
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Simplifying algebraic expression
Answer:
42
Step-by-step explanation:
2 + 3(5) + 5(5)
2 + 15 + 25
Which equals..
42
Answer:
42
Step-by-step explanation:
IF b=5
Now,
2+3b+5b
=. 2 + 3*5 + 5*5
=. 2 + 15 + 25
=. 42
Please help. This is the last problem from my homework.
A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number
On solving the provided question, we can say that number 12 is the smallest natural number is abundant
What is natural number?Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.
number 12 is the smallest natural number is abundant
factor of 12 = 1,2,3,4,6,12,
1~1
2>1
3>1
4>2+1
.............
10> 1+2+5
11>1
therefore, number 12 is the smallest natural number is abundant
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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?
Please help Polynomial
The degree of the given polynomial is 4.
What is the polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
The given polynomial is y=3x²-7x⁴+5-9x.
a) The polynomial in standard form is -7x⁴+3x²-9x+5.
b) The degree of the polynomial is 4.
c) The number of terms in the polynomial are 4.
d) Use the degree and the leading coefficient to determine the behavior.
Falls to the left and falls to the right
e) Use the derivative to find the maximum and minimum.
(−0.78859507, 11.25584002) is a local maxima
f) Here the y-intercept is (0, 5)
g) The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x. x≈−1.33755842,0.5797309.
h) Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
i) Range: (−∞,11.25584002],{y|y≤11.25584002}
Therefore, the degree of the given polynomial is 4.
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A pattern follows the rule "Starting with three, every consecutive line has 2 less than twice the previous line. "
1. How many marbles must be in the fifth line?
Therefore , the solution to the given problem of unitary method comes out to be 34 marbles are therefore on the sixth line.
Define the unitary method.The term unitary refers to a single or unique or variable unit. As a result, the purpose of this strategy is to construct values with regard to a single unit. For instance, if a car drives 44 kilometres on two litres of fuel, the unitary technique can be used to determine how many kilometers it will travel on one.
Here,
Every subsequent line, beginning with one, contains two less characters than the one before it.
This signifies that your starting line contains three marbles. The 3 marbles are multiplied by 2 to get 3x2=6, and the result is subtracted to get 6-2=4.
This implies that you will receive 4 marbles for the following line.
As a result, in order to determine the sixth line, you must first determine the fifth line by counting the number of marbles on the fourth line because your diagram does not include a fifth line.
(4) = ten marbles.
10×2=20
20-2=18
(5) line = (18)
18×2=36
36-2=34
Therefore , the solution to the given problem of unitary method comes out to be 34 marbles are therefore on the sixth line.
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Wyatt says that 0.6 has the same value as 0.600 do you agree explain
Answer:
Yes, the zeros can be used as place holders. When using place holders, the value does not change.
To win the game, the team must score at least 8 goals. What inequality represents the number of goals, g, the team must score
So, on solving the provided question, we can say that to form a inequality - x * y > 8
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
here to form a inequality-
let x = goals by each player
y = no. of players
x * y > 8
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together Larry and Lenny have $\$$35. Larry has two-fifths of Lenny's amount. How many more dollars than Larry does Lenny have
The answer which we get after calculating from the data given is that Larry has 15 dollars more than Lenny.
Let the amount which Lenny is having be x
then the amount which Larry is having will be (2/5)x
and on combining them it makes $35 .
Which means, x + 2x/5 = 35
On simplifying this equation we will get ,
(7/5)x= 35 ,
multiplying both the sides by 5/7
x= (5/7)*35 = $25
Therefore , Lenny is having 4 25.
So Larry must be having , $(35 - 25) = $10
So , we can conclude that Lenny has more dollars. The difference is of 15 dollars.
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The length of some material is 8.3m correct to 2 significant figures. Write the error int
length, x, of the material.
Therefore , the solution of the given problem of equation comes out to be the error range for x is [1250, 1350].
Explain the equation.A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.
Here,
Given: Some material has a length of 8.3 meters
We have provided a number, x, that has been rounded to two significant numbers with the supplied error.
Next, we must determine the x error interval.
It is necessary for x to have a value that is both bigger than or equal to 1250 and less than or equal to 1300.
i.e.,1250 ≤ x ≤ 1300 ---(1)
2. The value of x is more than 1300 but not equal to 1350.
1300 ≤ x ≤ 1350--- (2)
When (1) and (2) are combined, we obtain
1250≤ x ≤ 1350
As a result, 1350 is not part of the error-interval for x.
As a result, the interval notation is [1250, 1350].
As a result, the error range for x is [1250, 1350].
Therefore , the solution of the given problem of equation comes out to be the error range for x is [1250, 1350].
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What is an example of substitution method?
Substitution method is a method used to solve equations. It involves replacing a variable with its given value, which helps to isolate it and solve for the unknown. For example, if we have the equation 2x+5=17, we can solve for x by substituting 17 for 2x+5 and then subtracting 5 from both sides to obtain x=12.
The substitution method is a technique used to solve systems of equations. An example of the substitution method would be solving the system of equations:
x + 2y = 5
3x + 6y = 15
First, solve the first equation for x:
x = 5 - 2y
Substitute the expression for x into the second equation:
3(5 - 2y) + 6y = 15
Simplify:
15 - 6y + 6y = 15
Solve for y:
15 = 15
Now substitute the value of y back into the expression for x:
x = 5 - 2(3)
Solve for x:
x = -1
Therefore, the solution to the system of equations is:
x = -1, y = 3
Substitute x in equation 1 into equation 2, solve, then substitute y back into equation 1.
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1. Circle which of the following ways to prove that a quadrilateral is a parallelogram. (5 pts.)
I. quadrilateral with both pairs of opposite sides congruent
II. quadrilateral with both pairs of opposite angles congruent
ILI. quadrilateral with one pair of opposite sides both congruent and parallel
A. I only
B. II only
C. I, II and III
D. III only
E. I and II
quadrilateral with both pairs of opposite sides congruent
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
If both pairs of opposite sides of a quadrilateral are congruent , then the quadrilateral is a parallelogram.
So, the option I only is correct
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If an object is propelled upward from ground level with an initial velocity of 80. 1 feet per second? It’s height h in feet t seconds later is giving by the equation h= -16ft+ 80. 1t after how many seconds does the object hit the ground
The object will hit the ground after 5.01 seconds.
When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,
h= -16t^2+ (80.1)t
When the object hit the ground, the height of the object h would be zero.
To find: time (t) when h = 0
Substitute h = 0 in given equation.
h = -16t^2+ (80.1)t
0 = -16t^2+ (80.1)t
16t^2 - (80.1)t = 0
t (16t - 80.1) = 0
t = 0 or 16t - 80.1 = 0
t = 0 OR t = (80.1)/16
t = 0 OR t = 5.01
Therefore, it will hit the ground after 5.01 seconds.
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How do you find the equation of a vector given the point and direction?
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).
The equation of a vector is typically written like this:
v = (x, y, z)
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation. For example, let's say you are given the point (1,2,3) and the direction of the vector is (2,3,4). The components of the vector, v, would be x = 2, y = 3, and z = 4, so the equation for that vector would be:
v = (2, 3, 4)
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).
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A package of salt waits 25 KG and a packet of sugar weighs 35 KG find the ratio of weight of salt to the weight of sugar
[tex] \longmapsto \: =25/35 [/tex]
[tex] \longmapsto \: =5/7[/tex]
[tex] \longmapsto \: =5:7[/tex]
The cost of 3 cheese sandwiches and 2 bottles of water is £7. 80. The cost of 5 cheese sandwiches and 4 bottles of water is £14. 20. What is the cost of: (a) one cheese sandwich? (b) one bottle of water?
One cheese sandwich costs $1.4 and one bottle of water costs $1.8.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Let x be the cost of cheese sandwiches and y be the cost of one bottle of water.
3x+2y=7.8
5x+4y=14.2
(3x+2y=7.8)*2
6x+4y=15.6
5x+4y=14.2
x=$1.4
y=$1.8
The cost of one cheese sandwich is $1.4 and that of one bottle of water is $1.8.
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What are the different types of time complexity analysis available?
There are five different types of Time complexity analysis:
Constant Time ComplexityLogarithmic Time Complexity Linear Time Complexity O(n log n) Time ComplexityQuadratic Time ComplexityWhat is Time complexity?
The computational complexity that describes the amount of computer time required to run an algorithm is known as time complexity in computer science. The time complexity of an algorithm is commonly estimated by counting the number of elementary operations performed by the algorithm, assuming that each elementary operation takes a fixed amount of time to perform.
As a result, the time required and the number of elementary operations performed by the algorithm are assumed to be proportional. Because the running time of an algorithm varies among different inputs of the same size, the worst-case time complexity, which is the maximum amount of time required for inputs of a given size, is commonly considered.
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-15x+4x+2-x= x+ as a no solution
The equation -15x + 4x + 2 - x = x has solution and the solution is 2/13
How to determine if the equation has no solutionFrom the question, we have the following parameters that can be used in our computation:
-15x+4x+2-x= x+
Express the equation properly
So, we have the following representation
-15x + 4x + 2 - x = x
Collect the like terms in the equation
This gives
-x - 15x + 4x - x = -2
Evaluate the like terms
So, we have the following representation
-13x = -2
Divide both sides by -13
This gives
x = 2/13
Hence, the solution is 2/13
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The number of acres in a landfill is given by the function A=3000e−0. 05t, where t is measured in years. How many acres will the landfill have after 9 years? (Round to the nearest acre. )
Is this exponential growth or decay?
A function A = 3000 e^(-0. 05t) is an exponential decay function.
And the landfill after 9 years = 1912.8 acres
From given information, the number of acres in a landfill is given by the function A = 3000 e^(-0. 05t), where t is measured in years.
To find: the landfill after 9 years
Substitute t = 9 years in above function.
A = 3000 × e^(-0. 05t)
A = 3000 × e^(-0.05 × 9)
A = 3000 × e^(-0.45)
A = 3000 × 0.6376
A = 1912.8 .............(1)
Substitute t = 9 years in given function.
A = 3000 e^(-0. 05t)
A = 3000 × e^(-0.05 × 0)
A = 3000 × e^(0)
A = 3000 × 1
A = 3000
This means, initially a landfill was 3000 acres.
From (1) we can observe that after 9 years, the landfill is 1912.8 acres.
A landfill has been reduced.
So, a function is exponential decay function.
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A $280 suit is marked down by 30%. Find the sale price.
Answer: The Sale price is $196
Step-by-step explanation:
We can start by converting 30% to a decimal 0.3, then we will multiply the $280 by the decimal (280*0.3 = $84) This means it is marked down by $84, so to get the sale price we subtract the mark down by the original price, ($280-$84 = $196).
Answer:
The suit's sale price is $196.
Step-by-step explanation:
⭐What is "mark down"?
the percentage the price of an item is reduced byTo find the sale price, we need to form an equation representing the given situation.
MARK DOWN:
original price - (mark down percentage)(original price) = sale price
Substitute the known values.
280 - (0.3)(280) = sale price
Compute.
280 - 84 = sale price
∴ $196 = sale price
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Quesuon Help
An exponential function has an initial value of 500 and a decay rate of 15%. Compare the average rate of change for the interval 0<x<4 to the average rate for the
interval 4<x<8. What do you think will happen to the rate of change for intervals beyond x = 8? Explain.
For 0<x<4, the average rate of change will be
(Round to the nearest integer as needed. )
The slope of the straight line connecting the break's ends to the function's diagram.
For 0 < x < 4 will be -60
For 4 < x < 8 will be -31
What is meant by exponential function?The mathematical formula f (x) = [tex]$$a^{x[/tex] denotes an exponential function. a constant known as the function's base and a variable called x are present. The transcendental number e, roughly equivalent to 2.71828, is the most frequent exponential-function base.
When a positive constant other than 1 is raised to a variable exponent, the function is said to be exponential. Solving at a certain input value yields the evaluation of a function. If you know the growth rate and the starting point, you can find an exponential model.
We have to use the knowledge of functions to describe the average rates of each one of them, so:
For 0 < x < 4 will be -60
For 4 < x < 8 will be -31
It is a measurement of how much the function changed for one person on average throughout that interval. It results from the slope of the straight line connecting the break's ends to the function's diagram.
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What is value of tan 90?
Answer:
Step-by-step explanation: infinity or undefined.
the perimeter of the trapezoid is 18x +18 find the missing length of the lower base
PLEASE HURRY
Answer:
Step-by-step explanation:
8x+18=2x+x+4x-3
8x+18=7x-3
perimeter = x+21
Is 9x² 30x 25 a perfect square trinomial?
Yes, [tex]9x^2-30x +25[/tex] is a perfect square trinomial.
How can you tell if a trinomial is a perfect square?A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial of the form [tex]ax^2 + bx + c[/tex] meets the requirement [tex]b^2 = 4ac[/tex], it is said to be a perfect square.
What trinomial has a perfect square?Two of your terms will be perfect squares in a perfect square trinomial. This trinomial is not a perfect square trinomial if it lacks two perfect square terms. The square root of each perfect square word should now be determined, combine the two square roots, then multiply the result by two.
This trinomial is a perfect square. The only thing left to determine is whether the middle term matches when you square (3x-5) because both [tex]9x^2=(3x)^2\ and\ 25=52[/tex] are perfect squares. The minus sign was used to at least produce a negative coefficient for the middle term.
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