Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.
what is unitary method ?In mathematics, the unitary approach entails determining the value of a single unit in a certain circumstance and using that value to resolve other issues that are connected to it. It is a quick and efficient method for handling issues involving direct proportion, indirect proportion, and other circumstances of a same nature. In disciplines including mathematics, science, business, and engineering, the unitary technique is widely employed.
given
Let V be the computer's starting value.
The computer's value drops to V/2 after four years.
The computer's value is decreased to V/2 1/2 = V/4 after six years.
We are informed that the PC will be worth $835 after six years. When we set this equal to V/4, we obtain:
V/4 = 835
Adding 4 to both sides results in:
V = 4 × 835 = $3340
Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.
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3n^2 can it be in standard form
Answer:
No it can,t be in standard for
Answer
D =
E =
Please help
Answer:
d = 3.75
e = 8/3
Step-by-step explanation:
8/6 = 5/d = e/2
4/3 = 5/d
4d = 3 × 5
d = 3.75
4/3 = e/2
3e = 4 × 2
e = 8/3
13. The area of the kite is 30 m². What is the value
of x? Explain.
4m
xm
6 m
xm
14.
Answer:
answer is 3
Step-by-step explanation:
Help me pls, i need the process too!
Option A,B,C,D : Elias might have gotten the answer by calculating the percentage discounts of each item and comparing them to see which ones are the same.
To find which items have the same percent discount, we need to calculate the percent discount for each item.
For the sweater, the percent discount is (20/50) x 100% = 40%.
For the shorts, the percent discount is (12/30) x 100% = 40%.
For the shirt, the percent discount is (14/35) x 100% = 40%.
For the jeans, the percent discount is (24/60) x 100% = 40%.
Therefore, all items have the same percent discount of 40%, and option C (jeans and shirt only) is incorrect. The correct answer is A, sweater and shorts only, B, sweater, shorts, and shirt only, and D, sweater, shorts, and jeans only, have the same percent discount. Elias may have chosen C because he overlooked that the percent discount is the same for all items.
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Which items have the same percent discount?
A. sweater and shorts only
B. sweater, shorts, and shirt only
C. jeans and shirt only
D. sweater, shorts, and jeans only
Elias chose C as the correct answer. How might he have gotten that answer?
for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. 5.1
Bending moment curve equation below point A will be:
M = 15x - 3x² for 0 ≤ x ≤ b
Determination of shear and bending moment curves.
For the beam and loading shown, we can do the following:
Equation of shear curve (above point A):V = RA - w.x
For x = a,V = RA - w.a
For x = b,V = RA - w.b
Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b
Equation of shear curve (below point A):
V = RA - w.x
For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a
The shear curve equation becomes;
V = 15k for 0 ≤ x ≤ a
V = 15 - 6a for a ≤ x ≤ b
Equation of bending moment curve (above point A):
M = RAx - ½w.x²For 0 ≤ x ≤ a,
M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,
M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²
The bending moment curve equation above point A becomes:
M = 15x - 3x² for 0 ≤ x ≤ a
M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b
Equation of bending moment curve (below point A):
M = RAx - ½w.x²For 0 ≤ x ≤ b,
M = 15x - ½(6x²) = 15x - 3x²
The bending moment curve equation below point A becomes;
M = 15x - 3x² for 0 ≤ x ≤ b
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I need help with this problem. Joe bought a gallon of gasoline for 2. 85 per gallon and c cans of oil for 3. 15 per can
From the given information provided, the expression that need to determine the total amount is Total cost = $2.85/gallon x g gallons + $3.15/can x c cans.
The expression that can be used to determine the total amount Joe spent on gasoline and oil is:
Total cost = Cost of gasoline + Cost of oil
We can represent the cost of gasoline as:
Cost of gasoline = price per gallon x number of gallons
Substituting the given values, we get:
Cost of gasoline = $2.85/gallon x g gallons
Similarly, we can represent the cost of oil as:
Cost of oil = price per can x number of cans
Substituting the given values, we get:
Cost of oil = $3.15/can x c cans
Putting it all together, we get:
Total cost = $2.85/gallon x g gallons + $3.15/can x c cans
Expression that can be used to determine the total amount Joe spent on gasoline and oil is:
Total cost = $2.85/gallon x g gallons + $3.15/can x c cans
Question - Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
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a 336-m long fence is to be cut into pieces to make three enclosures, each of which is square. how should the fence be cut up in order to minimize the total area enclosed by the fence?
The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.
To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:
12x = 336
Addressing for x, we get:
x = 28
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Can somebody please help with this? you don't have to understand Spanish its just a word search, please.
Answer: sure....... i actually understand Spanish so this is gonna be easy.
Step-by-step explanation:
Give me a few minutes to do it
Ok for startes when you find a word cross it off the word bank that is where your first mistake is......
The angles of an irregular pentagon is x, 90, x, 150, x degrees.
Calculate the size of the largest angle.
Answer:
x=130°
Step-by-step explanation:
The sum of the angel of the pentagon is equal to 540°
X+90+x+150+x=540
3x+240=540
3x=540-150
3x=390
X=130
Factor
[tex]64h^3+216k^9[/tex]
Answer:
Factor 64h^3+216k^9
Step-by-step explanation:
The given expression is a sum of two terms:
[64h^3+216k^9
Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:
64h^3+216k^9 = 64h^3(1 + 3k^6)
This expression cannot be factored any further, so the final answer is:
64h^3+216k^9 = 64h^3(1 + 3k^6)
If you can, give me brainliest please!
sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, what minimal sample size of the random sample should be used?
Sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, 368 is the minimal sample size of the random sample should be used
The appropriate sample size for probability estimates of the sample proportion of female students in the business statistics class is determined by the margin of error (m) and the level of confidence (Z).
The formula for sample size calculation is as follows:
N = [tex](Z^2\times p \times q) / m^2[/tex]
where
N is the sample size
Z is the z-score that corresponds to the level of confidence
p is the estimated proportion of female students
q is 1 - p (proportion of male students)m is the margin of error.
Since we don't have any margin of error, we can assume it to be a standard value of 5%. And a z-score of 1.96 is appropriate for a 95% level of confidence.
As a result, the sample size for estimating the sample proportion of female students in the business statistics class is given by
N = [tex](1.96^2\times0.60\times0.40) / (0.05^2)[/tex]
N = 368 students
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Write the ratios for sin A and cos A. The diagram is not drawn to scale.
sin A= 14/50 cos A 48/50
sin A= 48/50 cos A 14/50
sin A 48/14 cos A 14/50
sin A= 48/50 cos A 14/48
The ratio of SINA and COSA = 48/50 and 14/50
What is trignometric ratios?This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
According to our question,
sina = perpendicular\ hypotenuse
= 48/50
cosa= base\ perpendicular
=
14/50
Hence, The ratio of SINA and COSA = 48/50 and 14/50
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julio has $31.00 he earns half of that much mowing a lawn. How much money does he have in all?
Answer: $ 46.50
First divided 31 by 2
Which equals...
15.50
Then add 15.50 to 31.
46.50
The answer is $46.50
help please?!This sphere has a radius of 6 cm.
What is the surface area of the sphere?
Enter your answer, in exact form, in the box.
Answer:
Step-by-step explanation:
It's[tex]288\pi in2[/tex]Answer:
Step-by-step explanation:
Here is real answer :>
Tammy said the product of 5/7
and 1 1/4
is 1 3/4
.
How can you tell that this answer is wrong?
Answer:
Step-by-step explanation:
To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.
First, we need to convert 1 1/4 to an improper fraction:
1 1/4 = (4 x 1 + 1)/4 = 5/4
Then, we can multiply the fractions:
5/7 x 5/4 = 25/28
As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.
a die is rolled twice and the sum of numbers appearing on the upper faces of them is observed to be 7. what is the probability that the number 2 has appeared atleast once? hint: use the concept of conditional probability)
The probability of getting at least one 2 given that the sum of the numbers is 7 is 2/6 or 1/3.
To find the probability that the number 2 has appeared at least once given that the sum of the numbers is 7, we need to use the concept of conditional probability.
Let's consider the possible outcomes when two dice are rolled. The total number of outcomes is 36, as each die has six possible outcomes.
Out of these 36 outcomes, there are six outcomes in which the sum of the numbers appearing on the upper faces is 7. These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Out of these six outcomes, there are two outcomes in which the number 2 appears at least once: (1,6) and (2,5).
We can use the formula for conditional probability to verify our answer:
P(2 appears at least once | sum is 7) = P(2 appears at least once and sum is 7) / P(sum is 7)
P(2 appears at least once and sum is 7) = 2/36 = 1/18 (as there are two outcomes with a sum of 7 that have a 2 in them)
P(sum is 7) = 6/36 = 1/6
So, P(2 appears at least once | sum is 7) = (1/18) / (1/6) = 1/3, which is consistent with our previous answer.
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a sock drawer contains 18 black socks and 12 red socks. if you randomly choose two socks at once, what is the probability you get a matching pair?
There are 12 red socks and 18 black socks in a sock drawer. If you randomly choose two socks at once, the probability you get a matching pair is 50%.
The probability of getting a matching pair of socks can be calculated as follows:
First, we can calculate the total number of ways to choose 2 socks out of 30:
C(30, 2) = 30! / (2! * (30-2)!) = 435
Now, we need to calculate the number of ways to choose 2 socks such that they are both black or both red:
Number of ways to choose 2 black socks: C(18, 2) = 153
Number of ways to choose 2 red socks: C(12, 2) = 66
Therefore, the total number of ways to choose a matching pair of socks is 153 + 66 = 219.
Finally, we can calculate the probability of getting a matching pair of socks by dividing the number of ways to choose a matching pair by the total number of ways to choose 2 socks:
P(matching pair) = 219 / 435 ≈ 0.5034
Therefore, the probability of getting a matching pair of socks is approximately 0.5034 or 50.34%.
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The population of a country is initially two million people and is increasing at a rate of 4% per year. The country’s annual food supply is initially adequate for four million people and is increasing at a constant rate adequate for an additional 0.5 million people per year.If the country doubled its initial food supply and maintained a constant rate of increase in the
supply adequate for an additional 0.5 million people per year, would shortages still occur? In
approximately which year? . If the country doubled the rate at which its food supply increases, in addition to doubling its
initial food supply, would shortages still occur?
in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.
How to calculate the rate?
To answer these questions, we need to calculate the population and food supply at different points in time and compare them.
Let's first calculate the population after t years:
Population after t years = 2,000,000 * (1 + 4%) raise to the power t
And the food supply after t years:
Food supply after t years = 4,000,000 + 0.5 million * t
Now, let's answer the first question:
If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?
If the country doubles its initial food supply, the new food supply would be 8,000,000, and it would still increase at a rate of 0.5 million people per year. Let's calculate the year when the population exceeds the food supply:
Population = Food supply
2,000,000 * (1 + 4%)^t = 8,000,000 + 0.5 million * t
Solving for t, we get t ≈ 17.77 years.
So, in approximately 18 years, the population would exceed the food supply, even if the country doubles its initial food supply and maintains a constant rate of increase in the supply adequate for an additional 0.5 million people per year.
Now, let's answer the second question:
If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?
If the country doubles the rate at which its food supply increases, the new rate would be 1 million people per year. Let's calculate the year when the population exceeds the food supply:
Population = Food supply
2,000,000 * (1 + 4%) raise to the power t = 16,000,000 + 1 million * t
Solving for t, we get t ≈ 21.96 years.
So, in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.
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Determine the magnitude of the force P for which the resultant of the four forces acts on the rim of the plate. Given: F= 320 N. 30° 120 N 80 N P x 250 mm F 7 The magnitude of the force P is N.
The magnitude of the force P is 464.77 N.
STEP BY STEP EXPLANATION:
Step 1: Break down each force into components.
F = 320 N at 30°
Fx = F * cos(30°) = 320 * cos(30°) = 277.13 N (horizontal)
Fy = F * sin(30°) = 320 * sin(30°) = 160 N (vertical)
120 N is in the horizontal direction (assume positive x-direction):
Fx2 = 120 N
80 N is in the vertical direction (assume positive y-direction):
Fy2 = 80 N
Step 2: Sum up the components.
Total horizontal force (Fxtotal) = Fx + Fx2
= 277.13 + 120 = 397.13 N
Total vertical force (Fytotal) = Fy + Fy2
= 160 + 80 = 240 N
Step 3: Find the magnitude of the resultant force.
Resultant force (R) = sqrt(Fxtotal^2 + Fytotal^2)
= sqrt(397.13^2 + 240^2) = 464.77 N
Step 4: Determine the magnitude of the force P.
Since the resultant of the four forces should act on the rim of the plate, it means that the force P should be equal in magnitude and opposite in direction to the resultant force R.
The magnitude of the force P is 464.77 N.
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there are 3 soccer games in a month, and 8 are played at night. the season is 4 months. how many games are the season?
There are a total of 48 soccer games in the season.
Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:
Number of day games = Total number of games - Number of night games
= 12 games/month x 4 months - 8 night games/month x 4 months
= 48 games - 32 games
= 16 games
Therefore, the total number of games in the season is:
Total number of games = Number of day games + Number of night games
= 16 games + 32 games
= 48 games
So, there are 48 soccer games in the season.
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Hellppppppppppppppppp
Tonya's income is four times as much as Nora's income. Write an Algebraic expression representing Nora's income in terms of Tonya's
An algebraic expression for representing the Nora's income in form of Tonya's income is given by y = ( x / 4 ) .
Let us consider 'x' represents the Tonya's income.
And variable 'y' represents the Nora's income.
Tonya income is equal to four times of Nora's income.
This implies,
Nora's income is equal to one fourth times of Tonya's income.
⇒ y = ( x / 4 )
Rewrite an algebraic expression to represents Tonya's income in terms of Nora's income we have,
Simplify by multiplying both the sides of the algebraic expression by 4 we get,
⇒ x = 4y
Therefore, an algebraic expression to represents the Nora's income in terms of Tonya's income is equal to y = ( x / 4 ).
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what is the difference between 6 holes and 1/2 and 10 holes?
10-hole harmonicas, which can produce a wider range of notes and are more commonly used in professional music settings.
What is equation?An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.
Given by the question.
The terms "6 holes and 1/2" and "10 holes" are often used to refer to harmonicas, which are small wind instruments that produce sounds when air is blown into or drawn out of them.
The main difference between a 6-hole harmonica and a 10-hole harmonica is the number of holes on the instrument. As the name suggests, a 6-hole harmonica has 6 holes, while a 10-hole harmonica has 10 holes.
In addition to the number of holes, the two types of harmonicas may also differ in their size, range, and the specific notes that they can produce. 6-hole harmonicas are typically smaller and produce a more limited range of notes compared
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Determine which property(s) the following relation R on the set of all integers satisfy(s)?( a , b ) ∈ R iff a b ≥ 1 .
In conclusion, the relation R on the set of all integers satisfies reflexivity and symmetry but not transitivity.
To determine which properties the relation R on the set of all integers satisfy, we need to check for reflexivity, symmetry, and transitivity.
1. Reflexivity: A relation R is reflexive if for every element a in the set, (a, a) ∈ R.
In this case, we need to check if a * a ≥ 1 for all integers a.
Since any integer squared (a * a) is greater than or equal to 1, R is reflexive.
2. Symmetry: A relation R is symmetric if for every pair (a, b) ∈ R, (b, a) also ∈ R.
In this case, we need to check if a * b ≥ 1 implies b * a ≥ 1.
Since multiplication is commutative (a * b = b * a), the condition holds true, and R is symmetric.
3. Transitivity: A relation R is transitive if for every (a, b) ∈ R and (b, c) ∈ R, (a, c) also ∈ R.
In this case, we need to check if a * b ≥ 1 and b * c ≥ 1 imply a * c ≥ 1.
Let's take the counterexample: a = -1, b = 2, and c = -1. We have -1 * 2 ≥ 1 and 2 * -1 ≥ 1, but -1 * -1 ≥ 1 is false.
Therefore, R is not transitive.
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Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down.
A′(−4, −1), B′(0, 1), C′(−2, −4)
A′(−4, 7), B′(0, 9), C′(−2, 4)
A′(0, 3), B′(4, 4), C′(3, 0)
A′(−8, 7), B′(−4, 9), C′(−6, 4)
The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).
What is meant by preimage?
In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.
To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:
A′(-4, 3-4) = (-4, -1)
B′(0, 5-4) = (0, 1)
C′(-2, 0-4) = (-2, -4)
Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).
So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).
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Subtract the following polynomials.
The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x
How to subtract polynomials?A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.
(3.1x + 2.8z) - (4.3x - 1.2z)
open parenthesis
3.1x + 2.8z - 4.3x + 1.2z
combine like terms
3.1x - 4.3x + 2.8z + 1.2z
-1.2x + 4x
Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.
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PLEASE HELPP I NEED HELP WITH THIS MATHS PLEASE
1. It will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.
2. An annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.
3 A principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.
How to solve the questionsa. Using the TVM Solver function in Excel, we can input the following information:
Present value (PV): -$35,000 (since it's an outgoing cash flow)
Future value (FV): $70,000 (since we want the tithe to double in value)
Interest rate per period (Rate): 7.75%/12 (since the APR is compounded monthly)
Number of periods (Nper): unknown (what we're solving for)
Payment (Pmt): 0 (since there are no recurring payments)
Solving for Nper, we get 96.16 months, or approximately 8 years.
Therefore, it will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.
b. Present value (PV): -$22,500 (since it's an outgoing cash flow)
Future value (FV): $50,000
Interest rate per period (Rate): unknown (what we're solving for)
Number of periods (Nper): 14*2=28 (since the interest is compounded semi-annually, we need to double the number of years)
Payment (Pmt): 0
Solving for Rate, we get 4.84% APR.
Therefore, an annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.
c. Using the TVM Solver function in Excel, we can input the following information:
Present value (PV): unknown (what we're solving for)
Future value (FV): $40,000
Interest rate per period (Rate): 4%/4 (since the APR is compounded quarterly)
Number of periods (Nper): 9*4=36 (since the interest is compounded quarterly, we need to multiply the number of years by 4)
Payment (Pmt): 0
Solving for PV, we get $26,512.18.
Therefore, a principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.
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2. Claire earns $92, 400 a year gross pay as a company president. She has 5%of her gross pay deposited into a 401(k) retirement plan. How much money does Claire's company deposit into her 401(k)
retirement plan each month?
$300
$385
$275
$325
Therefore , the solution of the given problem of unitary method comes out to be choice B $385 is the correct response.
An unitary method is what ?The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.
Here,
We must first determine how much is deducted from Claire's gross salary annually for the 401(k) plan in order to determine
how much money is deposited into her retirement account by her employer each month.
Since we are aware that Claire contributes 5% of her total income to her 401(k),
we can figure out how much she contributes as follows:
=> 0.05 x $92,400 = $4,620
As a result, Claire's 401(k) plan deducts $4,620 from her total income each year. We can reduce this amount by 12 (the number of months in a year) to determine how much it is per month:
=> $4,620 ÷ 12 = $385
As a result, Claire's employer contributes $385 each month to her 401(k) savings account.
Therefore, choice (B) $385 is the correct response.
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What is 2.5 as a fraction?
Answer: 5/2
fraction of 2.5 is 5/2
Answer:
2 1/2 or 5/2 as improper fraction
2 is a whole number and you have .5 left over
To convert to fraction .5 is the same as 1/2
So it gives you 2 1/2
By the way thanks for the Brainly points :)
For any acute angle A if sin A = 2x-1/2x+1, what is the value of cos A cot A?
The trigonometric expression cosAcotA = 8x/(4x² - 1)
What is a trigonometric expression?A trigonometric expression is an expression that contains trigonometric ratios.
Given that for any acute angle A if sin A = 2x-1/2x+1, we desire to find the value of cos A cot A?
So, we proceed as follows
cosAcotA = cosA × cosA/sinA (since cotA = cosA/sinA)
= cos²A/sinA
Now using the trigonometric identity
sin²A + cos²A = 1
⇒ cos²A = 1 - sin²A
So, substituting this into the equation, we have that
cosAcotA = cos²A/sinA
= (1 - sin²A)/sinA
= 1/sinA - sin²A/sinA
= 1/sinA - sinA
Substituting the value of sinA into the equation, we have
= 1/(2x - 1)/(2x + 1) - (2x - 1)/(2x + 1)
= (2x + 1)/(2x - 1) - (2x - 1)/(2x + 1)
Taking the L.C.M, (2x - 1)(2x + 1), we have
= [(2x + 1)² - (2x - 1)²]/[(2x - 1)(2x+ 1)]
= [(2x + 1)² - (2x - 1)²]/[(2x)² - 1²)]
= [(2x + 1 + 2x - 1)(2x + 1 - (2x - 1)]/(2x)² - 1²)
= [(2x + 1 + 2x - 1)(2x + 1 - 2x + 1)]/4x² - 1)
= [(4x)(2)]/4x² - 1)
= 8x/(4x² - 1)
So, cosAcotA = 8x/(4x² - 1)
Learn more about trigonometric expresion here:
https://brainly.com/question/29321762
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