So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.
Define Factorial.The factorial of a non-negative integer n, represented by n! is the product of all positive integers less than or equal to n. It is the mathematical operation that is applied to a non-negative integer.It is also used in many areas of mathematics, including calculus and number theory, as well as in many areas of science, including physics, chemistry, and computer science.
What is variables and constants ?A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.
To factor a trinomial of the form "ax² + bx + c," we can use the following steps:
First, we need to determine two numbers that multiply to give us "c" and add to give us "b." In this case, the two numbers are 4 and 5 because 4 x 5 = 20 and 4 + 5 = 9, which is equal to "13m".
Next, we can factor the trinomial into the form (ax + b)(cx + d) by grouping the middle term and the constant term together.
So, the factored form of the trinomial is (2m + 4)(m + 5)
So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.
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Sergio purchased 4 items for $1.50 each. Sales tax was 8.25%. What was the total price?
please explain if you can, thxs!
Answer:
6.495.Step-by-step explanation:
The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.
The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.
So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.
√≈≈≈≈≈Which of the following is a one-to-one function? y = [[2x]], y = x^2, f(x) = { 4x + 1;x < -2
The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
A function can either have one-to-one or many-to-one mapping.
One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.
The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.
They can be examined one by one as follows,
(a) y = [2x]
It is a greatest integer function.
At x = 1.1, y = [2 × 1.1] = [2.2] = 2
And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(b) y = x²
Find values of the function at two different x as,
x = -2, f(x) = (-2)² = 4
And, for x = 2, f(x) = 2² = 4.
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(c) f(x) = 4x + 1
It is a equation of a straight line.
Which implies it has different values for different values of x.
Thus, it is a one-to-one function.
Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.
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What is the numerical coefficient of the term − 6xy?
The numerical coefficient of xy in the given expression 6xy is 6.
In mathematical terms, a coefficient is a numerical value that is multiplied by a variable in an algebraic expression. The coefficient is the number that appears in front of the variable.
For example, in the expression 3x, the coefficient is 3. In the expression 2[tex]y^2[/tex], the coefficient is 2. In the expression -5[tex]z^3[/tex], the coefficient is -5.
In the case of a constant term in an expression, the coefficient is the constant term itself.
For example, in the expression 3x + 4, the coefficient of x is 3 and the coefficient of the constant term 4 is 4.
Here, in the expression 6xy, the numerical coefficient of xy is 6.
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Look at the graph, then select the correct answer.
Which distribution has the greatest spread?
A. Distribution 1
B. Distribution 2
C. Distribution 3
D. Distribution 4
The distribution has the greatest spread is
C. Distribution 3What is standard deviation?The term standard deviation refers to a measurement of the data's dispersion or spread from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed or spread out.
In the given problem the distribution that has a higher value of standard deviation is the one that has the highest spread spread
This is distribution 3 with a standard deviation of 7.2
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A neighbor of yours is getting ready to
plant a garden of flowers in his backyard.
He asks you for ideas on how to
conserve soil. You notice that his
backyard has a lot of hills. What do you
suggest?
In order to maintain soil fertility and productivity, soil must be protected from erosion and other forms of deterioration. Water use and watershed management are typically included.
What comes first in gardening?Eliminating the existing vegetation is the first step in making a garden bed. Weeds can be manually pulled. Just be certain to remove the roots to prevent regrowth. You might want to rent a gas-powered sod cutter to get rid of the grass if you're starting with a lawn.
What is an example of soil conservation?Better soil conservation techniques that affect both erosion and fertility include crop rotation, cover crops, conservation tillage, and installed windbreaks.
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the survey is a research method in which: group of answer choices individuals are carefully observed in their natural environments. a representative, random sample of individuals are questioned regarding their attitudes or behaviors. an individual is studied in great depth. an investigator determines the extent to which two variables influence each other.
The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.
B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.
C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.
D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.
Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
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The domain of y = √√√x-5-1 is
DONE
3 of 8
P
10
1000
098
7
6
5
4
3
12
y
2
19
Ð
6
8x
The function domain is X≥5 Or in interval notation [5, ∞)
What is Domain definition?The domain of a function is the set of input or argument values for which the function is real and definedThe domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limitedIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by {\displaystyle \operatorname {dom} } or {\displaystyle \operatorname {dom} f}, where f is the functionFind non-negative values for radicals x≥5solve x-5≥0:x≥5 function domain is X≥5 Or in interval notation [5, ∞)To learn more about Domain definition refers to:
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When can parallelism make your algorithms run faster when could it make your algorithms run slower?
When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.
What algorithm is parallelizable?The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.
When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.
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A company has two manufacturing plants with daily production levels of 5x +14 items and 3x - 5 items, respectively. The first plant produces how many more items daily than the second plant?
Answer:
21x
Step-by-step explanation:
5x+14=19x
3x-5=-2x
-2x-19x=21x
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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Using the graph below with the following point find the length of the two diagonals to determine if TUVW is a rectangle or not T(-5,0) U(7,3) V(9,-6) W(-3,-9)
The lengths of each diagonal are given as follows:
[tex]TV = \sqrt{232}[/tex][tex]WU = \sqrt{244}[/tex]As the lengths are different, the polygon TUVW is not a rectangle.
How to obtain the diagonals?The diagonal length is obtained using the formula for the distance between two points, presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.
The first diagonal is TV, and the length is given as follows:
[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]
The second diagonal is WU, and the distance is given as follows:
[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]
A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.
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What if Aya and Sakura could only afford a monthly payment of $1800?
What would be the maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
a) The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same = $369,181.93.
b) The total amount that would be paid to the lender over 25 years = $540000
To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.
Here, future value = 0
number of periods = 25 years
= 25 × 12 months per year
= 300
payment amount = -1800 dollars
interest rate = 4.25% per year
= 0.3542% per month
the maximum mortgage amount they could afford = $369,181.93.
And the total payments would be equal to 300 × 1800 = 540000
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The complete question is:
Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.
What if Aya and Harumi could only afford a monthly payment of $2,000?
What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
2 diagonals of a regular nonagon (a 9-sided polygon) are chosen. What is the probability that their intersection lies inside the nonagon
The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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what is the rate of decay f(x)=(.8)^x
9th grade AP algebra
The provided function, f(x)=(.8)^x, has a 20% rate of decay.
What is the Rate of decay or growth?
A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
given, a function f(x)=(.8)^x. To calculate the decay rate of this function.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a (1 - r)x is the general form.
Where
a = the initial amount
1-r is the decay factor
x = time span
from the given expression,
Decay factor = 0.8
That is also equal to 1 - r
1 - r = 0.8
r =0.2
Thus, rate of decay = r * 100%
rate of decay = 0.2 * 100 = 20%
therefore, The rate of the of the given function f(x)=(.8)^x is 20%.
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(25 points for the answer)
If John save 1/5 of his paycheck how much money would it take him to get to 14,500$ for his holiday trip? He earns $9062.5 each paycheck. (Unrealistic question unless you are under paid severely)
Use multiplication or division ONLY!
The amount of john would save 2900 rs
14500*1/5=2900
How much he earns on paycheck?A paycheck, also spelled paycheque, pay check or pay cheque, is traditionally a paper document issued by an employer to pay an employee for services rendered.a check used to pay an employee the amount of money the employee has earned.A paycheck can be an actual piece of paper (a check) that a person can take to the bank to deposit to their account or exchange for cash. Alternatively, a paycheck can be money a company electronically deposits directly into the employee's bank account.Take a look at how each common payroll interval works: Weekly: Once a week (52 paychecks per year) Biweekly: Once every other week (26 paychecks per year) Semimonthly: Twice per month (24 paychecks per yearTo learn more about paycheck refers to:
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Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars? Main Street Auto Leasing has more cars since it has cars while Airport Auto Leasing has cars only
If the ratio of cars to truck in Main Street Auto Leasing Company is 9 to 4 and in the airport Auto Leasing Company is 5 to 3 , then the Main Street Auto Leasing Company has more number of cars .
The Ratio of cars to truck in Main Street Auto Leasing Company is = 9:4 ;
the ratio of cars to truck in Airport Auto Leasing Company is = 5:3 ;
the number of trucks in each Leasing Company is = 24 trucks ;
Case (i) : Main Street Auto Leasing Company ;
Since the ratio is = 9:4 ,
So , the number of cars is = 9x and
the number of trucks = 4x ;
That means , [tex]4x = 24[/tex] ;
[tex]x = 6[/tex] ;
the number of cars in Main Street company is = [tex]9 \times 6[/tex] = 54 cars .
Case (ii) : Airport Auto Leasing Company ;
the ratio is = 5:3 ;
So , the number of cars is = 5x and
the number of trucks = 3x ;
That means , [tex]3x = 24[/tex] ;
[tex]x = 8[/tex] ;
the number of cars in Airport Auto company is = [tex]5 \times 8[/tex] = 40 cars .
Therefore , the Main Street Auto Leasing Company has more number of Cars .
The given question is incomplete , the complete question is
Main Street Auto Leasing has a ratio of cars to trucks that is 9 to 4. Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars ?
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Mrs Anderson has 185 pieces of wood he sold 25 peacas of wood to his neighbor and distract the rest of the world into piles around his house each pile of wood contained 40 pieces of wood which equation can be used to find peat the number of piles of wood Mr. Anderson made?
Answer: Let x be the number of piles of wood that Mr. Anderson made.
We know that he sold 25 pieces of wood to his neighbor, and the rest of the pieces of wood were divided into piles around his house, with each pile containing 40 pieces of wood.
Therefore, we can set up the equation:
185 pieces - 25 pieces = x * 40 pieces
Simplifying the equation:
160 = x * 40
To find the value of x, we need to divide 160 by 40
160/40 = x
x = 4
Therefore, Mr. Anderson made 4 piles of wood after he sold 25 pieces of wood to his neighbor.
It's worth noting that this equation was used to find the number of piles of wood Mr. Anderson made after selling 25 pieces to his neighbor, and assuming that he didn't use the rest of the wood for anything else except for making the piles.
Step-by-step explanation:
How many terms are there in the expression 7x2 5x?
There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.
Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.
An algebraic expression with three terms is called a trinomial.
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Angle J and Angle M are base angles of isosceles trapezoid JKLM. If angle j= 23x+5, and angle m = 13x+15 , find measure k .
The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:
23x + 5 = 13x + 15
23x - 13x = 15 - 5 {collect like terms}
10x = 10 {divide through by 10}
x = 1
angle J = 23(1) + 5 = 28°
Angle K and angle J are supplementary so:
K = 180 - 28
K = 152°
Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°
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Which of the following is correctly written in Standard Form?
Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.
An equation's definitionAn equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.
Here,
Given : 4x-3y = 6
-4x + 2y =8
=> y = 4/5x + 4
=> 4/5x + 2y = 6
Thus ,
From the above following equations we get ,
4x-3y = 6
as a standard equation in all the above options.
Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.
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PLEASE HURRY!!
Find the value of x
Answer:
Step-by-step explanation:
3x=24
x=8
A line passes through the points (-2,8) and (5,-20)
The linear equation that passes through these two points is:
y = -4x
How to find the equation for the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (-2, 8) and (5, -20), so the slope is:
a = (-20 - 8)/(5 + 2) = -28/7 = -4
So the line is:
y = -4*x + b
To find the value of b, we can replace the values of the point (-2, 8), so we will get:
8 = -4*(-2) + b
Now we can solve this for b.
8 = -4*(-2) + b
8 = 4*2 + b
8 = 8 + b
8 - 8 = b
0 = b
Then the linear equation is:
y = -4*x
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How do you calculate seed multiplication ratio?
The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.
What is Seed?A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.
Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.
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The function
h
defined by
h(t) = (49 + 4. 9t)(10 – t)
models the height, in meters, of an object
t
seconds after it is dropped from a helicopter.
1. Find or approximate the time when the object hits the ground. Explain or show your
reasoning
2. From what height is the object dropped? Explain or show your reasoning.
Answer:
55555555546776546567
You use a technical support company for your computer. The company bills you at a rate of $10 per month and $35 per hour for phone support.
a. Identify the fixed cost (the constant).
b. Identify the independent variable (x).
c. Identify the dependent variable (y).
d. Write an equation that describes the situation above.
e. If you were billed $97.50 for last month, how many hours of phone support did you need? Show all work.
Answer:fixed cost=10
Independent variable=months paid
Dependent=hours on support
month=x,h=hour,10x+35h=total cost
97.50=10+35h
87.50=35h
h=2.5 hours
Step-by-step explanation:
showed work
Write a ratio of the following in three ways.
Write your answers on the blanks.
1) 6 Weeks to 12 days_____
2) 10 decimeters to 10 centimeters_______
3) 4 days to 36 hours___
4) 4 months to 8 weeks___
5) 30 seconds to 6 minutes__
6) 24 girls to 16 boys___
7) 12 mangoes to 36 fruits__
8) 2. Years to 36 months__
9) 45 points to 9 games__
10) 468 students for 9 classrooms___
Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.
1. 6 Weeks to 12 days:
6:12 (using the same unit of measurement, weeks)42:12 (converting weeks to days, 6 weeks x 7 days/week = 42 days)3:1 (simplifying the ratio to its simplest form)2. 10 decimeters to 10 centimetres:
10:10 (using the same unit of measurement, decimeters)100:10 (converting decimeters to centimeters, 10 decimeters x 10 centimeters/decimeter = 100 centimeters)10:1 (simplifying the ratio to its simplest form)3. 4 days to 36 hours:
4:36 (using the same unit of measurement, days)24:36 (converting days to hours, 4 days x 24 hours/day = 96 hours)2:3 (simplifying the ratio to its simplest form)4. 4 months to 8 weeks:
4:8 (using the same unit of measurement, months)16:8 (converting months to weeks, 4 months x 4 weeks/month = 16 weeks)2:1 (simplifying the ratio to its simplest form)5. 30 seconds to 6 minutes:
30:6 (using the same unit of measurement, seconds)180:6 (converting seconds to minutes, 30 seconds x 6 minutes/60 seconds = 0.5 minutes)30:1 (simplifying the ratio to its simplest form)6. 24 girls to 16 boys:
24:16 (using the same unit of measurement, girls and boys)3:2 (simplifying the ratio to its simplest form)7. 12 mangoes to 36 fruits:
12:36 (using the same unit of measurement, mangoes and fruits)1:3 (simplifying the ratio to its simplest form)8. 2 years to 36 months:
2:36 (using the same unit of measurement, years and months)6:36 (converting years to months, 2 years x 12 months/year = 24 months)1:6 (simplifying the ratio to its simplest form)9. 45 points to 9 games:
45:9 (using the same unit of measurement, points and games)5:1 (simplifying the ratio to its simplest form)10. 468 students for 9 classrooms:
468:9 (using the same unit of measurement, students and classrooms)52:1 (simplifying the ratio to its simplest form)To learn more about the ratio, visit:
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4/5 + 3/4= asap PLEASEEE
Write the answer to 3^4 x 3^7
(i) in the form 3^x
(ii) as an integer
Answer:
I)3^4 x 3^7=3^4+7(b/c the base is similar)
3^4 x 3^7=3^11
Ii) first 3^4=3x3x3x3=81
3^7=2187
then 81 x 2187=177147
3. ) Mary is the director of the Washington Performing Arts Center. Her employer offers a pension. Mary’s employer uses a formula to calculate the pension. Marina is planning on retiring at the end of this year after 30 years of employment. A retiring employee receives 1. 6% of his or her average salary for the last 5 years of employment multiplied by the number of years worked. Mary would receive this amount each year until her death. Her salaries for the last 5 years are $80,900; $90,200; $95,000; $99,000; and $104,000. Calculate Marina’s pension
Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.
1.6% x $80,900 = $1,282.40
1.6% x $90,200 = $1,444.32
1.6% x $95,000 = $1,520.00
1.6% x $99,000 = $1,584.00
1.6% x $104,000 = $1,664.00
Total = $7,604.72
Pension amount = $7,604.72 x 30 years
= $228,141.60
Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.
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What is the degree of 3x³?
Answer:
3x³ is a polynomial of degree
The degree of the polynomial 3x³ is 3