What is the first step in evaluating the expression shown below?
(12.9-3.1) 6.2-2 + 43

Answer:

Rs 6900

Step-by-step explanation:

To calculate the tax amount the girl should pay in a year, we need to determine the taxable income and then apply the corresponding tax rates.

The taxable income is calculated by subtracting the tax-free allowance from the girl's early income:

Taxable Income = Early Income - Tax-Free Allowance

Taxable Income = 150,000 - 100,000

Taxable Income = 50,000

Now, we can calculate the tax amount based on the given tax rates:

For the first 20,000 rupees, the tax rate is 12%:

Tax on First 20,000 = 20,000 * 0.12

Tax on First 20,000 = 2,400

For the remaining taxable income (30,000 rupees), the tax rate is 15%:

Tax on Remaining 30,000 = 30,000 * 0.15

Tax on Remaining 30,000 = 4,500

Finally, we add the two tax amounts to get the total tax she should pay in a year:

Total Tax = Tax on First 20,000 + Tax on Remaining 30,000

Total Tax = 2,400 + 4,500

Total Tax = 6,900

Therefore, the girl should pay 6,900 rupees in tax in a year.

v · (2u - 3~v) equals -18.

What is Distributive Property?

This is the definition of distributive property:

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For example:

3 (2+4)

According to the distributive property, you first have to add these two numbers (2+4 = 6) and then multiply the result 6 by 3 = 18.

To find v · (2u - 3~v), we can use the properties of the dot product and the given information.

Let's break down the expression step by step:

v · (2u - 3~v)

Using the distributive property, we can expand the expression:

= v · 2u - v · 3v

Now, let's calculate each term separately.

v · 2u:

Since ~u · ~v = -3, we can substitute this value:

= v · 2u

= 2(~v · ~u)

= 2(-3) (substituting ~u · ~v = -3)

= -6

Next, we calculate the second term:

v · 3v:

The dot product of a vector with itself gives us the square of its magnitude:

= v · 3v

= 3(|~v|²)

= 3(2²) (substituting |~v| = 2)

= 3(4)

= 12

Now, let's substitute the values back into the original expression:

v · (2u - 3~v)

= -6 - 12 (substituting v · 2u = -6 and v · 3v = 12)

= -18

Therefore, v · (2u - 3~v) equals -18.

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Answer: 216cm2

Step-by-step explanation: 36x6

The loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with Simple interest, as it results in a lower overall cost compared to the other options.

Part A: To calculate the total value of the loan with simple interest, we use the formula: Total Value = Principal + (Principal * Rate * Time).

Here, the Principal (P) is $50,000, the Rate (R) is 4.35% or 0.0435, and the Time (T) is 3 years and 4 months, which is equivalent to 3.33 years.

Plugging the values into the formula, we have:

Total Value = $50,000 + ($50,000 * 0.0435 * 3.33)

Total Value ≈ $50,000 + $7247.5

Total Value ≈ $57,247.50

Part B: To calculate the total value of the loan with quarterly compounded interest, we use the formula: Total Value = Principal * (1 + (Rate / n))^(n * Time).

Here, n represents the number of compounding periods per year, which is 4 (quarterly compounding).

Plugging the values into the formula, we have:

Total Value = $50,000 * (1 + (0.0435 / 4))^(4 * 3.33)

Total Value ≈ $50,000 * (1.010875)^13.32

Total Value ≈ $50,000 * 1.156977

Total Value ≈ $57,848.85

Part C: To calculate the total value of the loan with continuously compounded interest, we use the formula: Total Value = Principal * e^(Rate * Time).

Here, e represents the mathematical constant approximately equal to 2.71828.

Plugging the values into the formula, we have:

Total Value = $50,000 * e^(0.0435 * 3.33)

Total Value ≈ $50,000 * e^(0.145005)

Total Value ≈ $50,000 * 1.15514

Total Value ≈ $57,757.00

Part D: Comparing the total values of the loans, we find that:

- The total value with simple interest is $57,247.50.

- The total value with quarterly compounded interest is $57,848.85.

- The total value with continuously compounded interest is $57,757.00.

Based on these calculations, the loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with simple interest, as it results in a lower overall cost compared to the other options.

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The probability of a song being played on a single day is 0.5. We need to find the probability of the song being played on 2 days out of 4 days. This can be solved using the binomial probability formula, which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful events, p is the probability of success, and (n choose k) is the binomial coefficient. Substituting the values, we get P(X=2) = (4 choose 2) * 0.5^2 * 0.5^2 = 0.375. Therefore, the probability that this song will be played on 2 days out of 4 days is 0.375.

The problem can be solved using the binomial probability formula because we are interested in finding the probability of a particular event (the song being played) occurring a specific number of times (2 out of 4 days) in a fixed number of trials (4 days).

We use the binomial probability formula P(X=k) = (n choose k) * p^k * (1-p)^(n-k) to calculate the probability of k successful events occurring in n trials with a probability of success p.

In this case, n=4, k=2, p=0.5. Therefore, P(X=2) = (4 choose 2) * 0.5^2 * 0.5^2 = 0.375.

The probability that a particular song will be played on 2 days out of 4 days at radio station wmzh is 0.375 or 37.5%.

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Step-by-step explanation:

Here is your answer in the photo

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The exponential functions are identified as follows

exponential function     growth / decay        rate

y =3,500(1,12)^ t             growth                      12%

y = 10000 * (0.9)^ t        decay                       10%

y = 5 * (1.025)^t              growth                      2.5%

y = 160 * (0.79) ^ t          decay                        21%

y =1,950(0.875)^ t          decay                        12.5%

graph

f(x) = 2(1.5)^x                  growth                       50%

f(x) = 2(0.8)^x                 decay                         20%

Considering the given problem,  f(x) = a(b)^x

the starting = a

the base = b

the exponents = x

The base is what determines exponential growth or decay

b > 1 growth function

0 < b < 1 decay function

y =3,500(1,12)^ t

b = 1.12 (growth) = 1 + r

rate, r = b - 1 = 1.12 - 1 = 0.12 = 12%

y = 10000 * (0.9)^ t

b = 0.9 (decay) = 1 - r

r = 1 - b = 1 - 0.9 = 0.1 = 10%

y = 5 * (1.025)^t

b = 1.025

r = 1.025 - 1 = 0.025 = 2.5%

y = 160 * (0.79) ^ t  

b = 0.79

r = 1 - 0.79 = 0.21 = 21%

y = 1,950(0.875)^ t  

b = 0.875

r = 1 - 0.875 = 12.5%

the graph

red f(x) = 2(1.5)^x

b = 1.5 (growth)

r = 1.5 - 1 = 50%

blue f(x) = 2(0.8)^x

b = 0.8 (decay)

r = 1 - 0.8 = 20%

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The whisper is approximately 360.4 times more intense than the rock concert.

The difference in the intensity between two sound levels is calculated using the formula:

Difference in intensity (in decibels, dB) = 10 * log10(I2 / I1)

where I1 and I2 are representing the intensities of the two sounds.

In this case, we have a whisper measuring 45 dB and a rock concert measuring 120 dB.

To convert decibels to intensity, we use the formula:

Intensity (I) = \(10^{(dB/10)\)

For the whisper (45 dB):

\(I1 = 10^{(45/10)} 10^{(4.5)}\)

≈ 3162.28

For the rock concert (120 dB):

\(I2 = 10^{(120/10)} = 10^{(12)}\)

= 1,000,000,000,000

Difference in the intensity = 10 * log10(I2 / I1) = 10 * log10(1,000,000,000,000 / 3162.28)

Now, calculate the logarithm using a calculator or software:

log10(1,000,000,000,000 / 3162.28) ≈ 36.04

Finally, calculate the difference in intensity:

Difference in the intensity ≈ 10 * 36.04 ≈ 360.4

Therefore, we have, the whisper is approximately 360.4 times more intense than the rock concert.

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Answer:

i think it is -1

Step-by-step explanation:

The total installment price is 34 and the carrying charges is 34

A sort of contract or arrangement known as an installment loan involves a loan that must be returned over period with a predetermined number of periodic instalments; typically, at least two each payment is required.

a) Total charge of the Installment price = 146 × 30 = $5256

b) The carrying charges = $5256 - $4000 = $1256

c) Number of months needed to save money = $4000 ÷ 36 = 111.11..

Therefore 11.11 months or 12 months is needed to save money to buy the car.

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The value of h in the triangle shown above is calculated using proportion as: h = 4.

The two triangles shown are similar to each other based on the Angle-angle (AA) Similarity theorem. This implies that the length of their corresponding pair of sides would be proportional to each other.

Therefore, we have:

8/18 = h/9 [proportional sides of similar triangles]

Cross multiply:

h * 18 = 8 * 9

18h = 72

Divide both sides by 18:

18h/18 = 72/18 [Division property of equality]

h = 4

Therefore, the length of h in the given image is determined as: 4 units.

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Answer:

None of them, 3x + 15 is correct.

Step-by-step explanation:

In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:

\(3(x+5)\)

We multiply everything in the parentheses by 3

\(3x+15\)

Looking at out choices, none of them uses the distributive property correctly.

(C)

Given data:

The given inequalities.

The graph of the given inequalities is shown below.

the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.

StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot

= 25x9y3 / 64x6y11

StartRoot is the beginning of the root expression and StartFraction is the beginning of the fraction within the root expression. 25x9y3 is the numerator of the fraction and 64x6y11 is the denominator of the fraction. Superscript is used to raise the numbers to the power indicated. Baseline is the number which the Superscript is raised to. EndFraction indicates the end of the fraction and EndRoot indicates the end of the root expression.

Therefore, the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.

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Answer:

S = 3

S = 5

S = 7

S = 9

Step-by-step explanation:

t = 3s + 2

when t = 11

11 = 3s + 2

11 – 2 = 3s

9 = 3s

s = 3

t = 3s + 2

when t = 17

17 = 3s + 2

17 – 2 = 3s

15 = 3s

s = 5

t = 3s + 2

when t = 23

23 = 3s + 2

23 – 2 = 3s

21 = 3s

s = 7

t = 3s + 2

when t = 29

29 = 3s + 2

29 – 2 = 3s

27 = 3s

s = 9

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Answer:

-10 and -10

Step-by-step explanation:

Can you use the same number twice?

To test the effect of living environment on cholesterol levels using samples from rural and urban areas, the best statistical test to utilize would be the two-sample t-test.

The two-sample t-test is appropriate in this case because it compares the means of two independent groups (rural and urban residents) to determine if there is a significant difference between their cholesterol levels.

This test will help researchers determine if living environment has an impact on cholesterol levels.

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Answer:

D

Step-by-step explanation:

6x7x4= 168

Answer:

x2 + 4x +4

Step-by-step explanation:

did this

If there were 1000 births in 1995 in a given community and of these 90 died before Jan. 1, 1996 and 50 died after Jan. 1, 1996 but before reaching their first birthday then, the cohort probability of death before age 1 for 1995 is 0.140.

To calculate the cohort probability of death before age 1, we need to determine the proportion of infants who died before their first birthday relative to the total number of births. This proportion represents the likelihood of an infant in the given community dying before reaching the age of 1.

Given, Birth in 1995 = 1000

Died before Jan. 1, 1996= 90

Died after Jan. 1, 1996= 50

We need to find the cohort probability of death before age 1.

The total number of births in 1995 = 1000

The number of infants who died before Jan. 1, 1996= 90

Therefore, the number of infants who survived up to Jan. 1, 1996= 1000 - 90 = 910

Number of infants who died after Jan. 1, 1996, but before their first birthday = 50

Therefore, the number of infants who survived up to their first birthday = 910 - 50 = 860

The cohort probability of death before age 1 for 1995 can be calculated as follows:

\text{Cohort probability of death before age 1 }= \frac{\text{Number of infants died before their first birthday}}{\text{Number of births in 1995}}

\text{Cohort probability of death before age 1 }= \frac{90 + 50}{1000}

\text{Cohort probability of death before age 1 }= 0.14

Therefore, the cohort probability of death before age 1 for 1995 is 0.140.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:

She will actually do it on the 35th day of gym

In FEA process, the step that assembles stiffness matrix of all elements to form the global stiffness matrix [K] of the entire system belongs to Preprocessing phase.

The phases of the FEA process are given below:

Preprocessing phase

Solution phasePostprocessing phaseValidation phase

The preprocessing phase is the first and most critical phase of the finite element analysis process.

It encompasses all of the tasks that must be completed before launching the actual finite element solution of the problem, including geometry creation and cleanup, meshing, material specification, and load and boundary condition application.

In FEA process, the assembly of the stiffness matrix of all elements to form the global stiffness matrix [K] of the entire system is done in the Preprocessing phase.

The assembly of the stiffness matrix of all elements is done by assembling the element stiffness matrices.

Once the element stiffness matrices have been calculated, they can be put together to make up the global stiffness matrix K.

This matrix is then utilized in the solution phase of the FEA process to solve the governing equations for the unknown nodal displacements.

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Answer:

The initial number of gallons of gas that were in the car

Step-by-step explanation:

The gallons left needs a starting value.  16 is the initial gallons of gas, from which gas consumed is subtracted.

Answer:

I would have to say C.) VA

Step-by-step explanation:

i obviously can't sketch it out but in a triangle there is the hypotenuse, the opposite, and the adjacent. this is going by the right angle in the triangle.

ok the triangle we are working with is YAV. in this triangle, the segment VA is the shortest

Answer:

18

Step-by-step explanation:

5/6 is 15, so you divide 15 by 5 to get 3. That means it goes up by 3. 3x6 will answer 18.

Answer:

The answer is 2

Step-by-step explanation:

I did the assignment and got it right             *>*                                                            

The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>

A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.

In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.

To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.

The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.

Therefore, the matrix equation can be written as Ax = 40 27 32.

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7) Angles around a point add to 360 degrees, so b = 23.

8) Angles that form a linear pair add to 180 degrees, so b = 131.

9) Vertical angles are equal, so b = 90.

10) Vertical angles are equal, so b = 73.

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad