Re write the statement 19+7 divided by 2-5 by including one pair of brackets to make the total equal to 8

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.

The 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).

To get started, let's put the mother's age into the given equation to determine the mean birth weight. Then, we'll use the RMS value to calculate the standard deviation.The equation for predicting baby birth weight in grams given the mother's age is: Y = -1163.45 + 245.15XWhere X is the mother's age, and Y is the baby's birth weight. We are given X=22, so let's use that to find the predicted mean birth weight:Y = -1163.45 + 245.15(22) = 4486.95 gramsThe RMS is given to be 589.3 grams. Because we're told that the distribution is approximately normal, we can use the 68-95-99.7 rule to find the 95% prediction interval. Here are the steps:Subtract the RMS from the mean to find the lower endpoint of the interval:4486.95 - (2 x 589.3) = 3308.35Add the RMS to the mean to find the upper endpoint of the interval:4486.95 + (2 x 589.3) = 5665.55Round both values to four decimal places, as instructed in the problem:3308.35 rounds to 3308.4 grams5665.55 rounds to 5665.6 gramsTherefore, about 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).

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i didn’t realize u were chill like that

Answer:

Step-by-step explanation:

G(fx)= 2x+4÷5×6x+2

G(fx)= 2x+0.8×6x+2

G(fx)= 2x×6x+0.8+2

G(fx)= 12x+2.8

The standard deviation of the distribution of the number of girls among the 3 children is 0.866. This means that the number of girls among the 3 children will typically vary from the mean of 1.5 by 0.866, in either direction. the correct answer is D.

The standard deviation of the distribution is a measure of how much the data values in the distribution typically vary from the mean. To calculate the standard deviation of the distribution, we need to find the variance of the distribution and then take the square root of the variance. The variance of the distribution is the average of the squared differences between each data value and the mean.

Here are the steps to calculate the standard deviation of the distribution:

1. Find the mean of the distribution (μX): μX = 1.5
2. Find the difference between each data value and the mean: (X - μX)
3. Square each difference: (X - μX)²
4. Find the average of the squared differences: (Σ(X - μX)²) / N
5. Take the square root of the average of the squared differences:

√((Σ(X - μX)²) / N)

The standard deviation of the distribution is 0.866. This means that the number of girls among the 3 children will typically vary from the mean by 0.866.

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The cumulative downtime per year of an SLA percentage of 99.95 is 4 hours, 21 minutes, 58 seconds.

The  SLA Downtime refers to the time duration that a machine or service is unavailable.

The SLA Uptime is the amount of time a machine or service is available.

The cumulative downtime per year of an SLA percentage of 99.95 will give the following:

An SLA percentage of 99,95 gives 43 seconds daily downtime.

In a year, cumulative downtime = 43 seconds  * 365 = 15695 seconds

Converting to hours and minutes give a downtime of 4 hours, 21 minutes, 58 seconds.

In conclusion, downtime refers to unavailability of a given machine or service.

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Company A has a higher risk percentage (55%) compared to Company B (3%).

To compute the Coefficient of Variation (CV) for each company, we need to use the formula:

CV = (Standard Deviation / Mean) * 100

Let's calculate the CV for each company:

For Company A:

Risk Percentage = 55%

Return = 14%

For Company B:

Risk Percentage = 3%

Return = 14%

Since we don't have the standard deviation values for each company, we cannot calculate the exact CV. However, we can still compare the riskiness of the two companies based on the provided information.

The Coefficient of Variation measures the risk relative to the return. A higher CV indicates higher risk relative to the return, while a lower CV indicates lower risk relative to the return.

In this case, Company A has a higher risk percentage (55%) compared to Company B (3%), which suggests that Company A is riskier. However, without the standard deviation values, we cannot make a definitive conclusion about the riskiness based solely on the provided information. The CV would provide a more accurate measure for comparison if we had the standard deviation values for both companies.

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Answer:

\((\frac{12}{-4n^{2}})\)

Step-by-step explanation:

\((\frac{3}{-2n})(\frac{4}{2n})=(\frac{3*4}{-2n*2n})=(\frac{12}{-4n^{2}})\)

Answer:

\( -\dfrac{3}{n^2} \)

Step-by-step explanation:

\( \dfrac{3}{-2n} \times \dfrac{4}{+2n} = \)

\( = \dfrac{3 \times 4}{-2n \times 2n} \)

\( = \dfrac{12}{-4n^2} \)

\( = -\dfrac{3}{n^2} \)

Therefore, the result is 133/20

To find the result, we'll first calculate the difference between 1 1/4 and 1/5.

1 1/4 is equivalent to 5/4, and 1/5 can be written as

1/5 * 4/4 = 4/20.

Subtracting these fractions, we get

(5/4) - (4/20) = 25/20 - 4/20 = 21/20.

Next, we add this difference to 5 6/10. 5 6/10 is equivalent to 56/10. Adding the fractions, we get

(21/20) + (56/10) =

(21/20) + (112/20) = 133/20.

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1/81(C)

(3)^4=81

if 3^-1=1/3

so, 3^-4=1/81(C)

The sale price of the laptop is $414 after the use of the coupon.

Answer:

$385.00

Step-by-step explanation:

Original Price - Discount = Sale price

Since the discount is 30%, we would multiply 0.30(550) to get the amount of the discount.

0.30(550) = 165

550 - 165 = $385

Answer:

1) 7/12 is rational

2) √28 is irrational

3) √13/25 is irrational

4)  -15 is irrational

5) 5π is irrational

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

38.47 Hope this helps. Thats how much she has left.

To derive \(cos(x/2) = +sqrt(1+cosx)/2\), we can use the half-angle formula for cosine, which states that:

\(cos(x/2) = ±sqrt((1 + cos x) / 2)\)

To determine the sign of the square root, we need to know the quadrant in which x/2 lies. Since x/2 is half of the angle x, we can use the properties of cosine to determine the sign of cos x.

Specifically:

If x lies in the first or fourth quadrant, then cos x is positive.

If x lies in the second or third quadrant, then cos x is negative.

Now, let's consider the two cases separately:

Case 1: x/2 lies in the first or fourth quadrant.

In this case, cos x is positive, so we take the positive sign in the half-angle formula:

\(cos(x/2) = +sqrt((1 + cos x) / 2)\)

Case 2: x/2 lies in the second or third quadrant.

In this case, cos x is negative, so we take the negative sign in the half-angle formula:

\(cos(x/2) = -sqrt((1 + cos x) / 2)\)

Therefore, we have two possible values for cos(x/2), depending on the quadrant in which x/2 lies. However, if we want to find a single expression for cos(x/2) that is always positive, we can take the positive square root in the half-angle formula:

\(cos(x/2) = +sqrt((1 + cos x) / 2)\)

This expression is valid for all values of x, and it is always positive.

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Complete Question

Recall that the trash bag manufacturer has concluded that its new 30-gallon bag will be the strongest such bag on the market if its mean breaking strength is at least 50 pounds. In order to provide statistical evidence that the mean breaking strength of the new bag is at least 50 pounds, the manufacturer randomly selects a sample of n bags and calculates the mean _ x of the breaking strengths of these bags. If the sample mean so obtained is at least 50 pounds, this provides some evidence that the mean breaking strength of all new bags is at least 50 pounds. Suppose that (unknown to the manufacturer) the breaking strengths of the new 30-gallon bag are normally distributed with a mean of m 5 50.6 pounds and a standard deviation of s 5 1.62 pounds. a Find an interval containing 95.44 percent of all possible sample means if the sample size employed is n=4

Answer:

\(X=(48.98,52.22)\)

Step-by-step explanation:

From the question we are told that:

Sample Mean \(\mu=50.6\)

\(\sigma =1.62\)

Sample size \(n=4\)

Level of significance \(\alpha 100-95.4=>4.56\)

Therefore

\(Z-value( \alpha/2)=2\)

Generally the equation for Interval is mathematically given by

\(X=\mu \pm z(alpha/2)* \frac{sd}{sqrt(n)}\)

\(X= 50.6 \pm z(0.0456/2)* \frac{1.62}{sqrt(4)}\)

\(X=50.6 \pm 2*\frac{1.62}{2}\)

\(X=(48.98,52.22)\)

The indicated probability P(z ≥ 1.33) is 0.0918 or approximately 0.0919 when rounded to four decimal places.

To find the probability P(z ≥ 1.33) with z being a standard normal distribution, we can use a standard normal table or a calculator that has the capability to find normal probabilities. Using a standard normal table, we look up the area to the right of 1.33 (since we are looking for P(z ≥ 1.33)). The value we find is 0.0918, rounded to four decimal places.

Alternatively, we can use a calculator to find the probability directly. We can use the normalcdf function in a calculator or statistical software, specifying a lower limit of 1.33 and an upper limit of infinity (since we want the probability of z being greater than or equal to 1.33). This gives us a probability of 0.0918, rounded to four decimal places.

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Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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The value of integral ∫ c ( x 2 y 2 z ) d s ∫c(x2 y2 z)ds is 156.864.

To evaluate the line integral ∫c(x^2 y^2 z)ds, we need to parameterise the curve C and then compute the integral along that curve.

The parameterization of C is given by → r ( t ) = ⟨ 2 cos ( 2 t ) , 2 sin ( 2 t ) , 5 t ⟩ r→(t)=〈2cos(2t),2sin(2t),5t〉 for 0 ≤ t ≤ 4 0≤t≤4.

To compute the line integral, we first need to get the unit tangent vector →T(t) of the curve C. The unit tangent vector is :

→T(t) = →r'(t)/|→r'(t)|

Taking the derivative of →r(t) gives:

→r'(t) = ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩So, the magnitude of →r'(t) is:

|→r'(t)| = √( (-4 sin(2t))^2 + (4 cos(2t))^2 + 5^2 ) = √( 16 + 25 ) = √41

Therefore, the unit tangent vector is:

→T(t) = (1/√41) ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩

Now, we can compute the line integral as follows:

∫c(x^2 y^2 z)ds = ∫0^4 (x^2 y^2 z) |→T(t)| dt

Substituting the parameterization and the unit tangent vector, we get:

∫c(x^2 y^2 z)ds = ∫0^4 (4 cos^2(2t) 4 sin^2(2t) 5t) (1/√41) dt

= (20/√41) ∫0^4 (16 cos^2(2t) sin^2(2t) t) dt

Using the identity sin(2θ) = 2sin(θ)cos(θ), we can simplify the integrand as follows:

16 cos^2(2t) sin^2(2t) = 4 sin^2(4t) = 2 (1 - cos(8t))

Substituting this back into the integral, we get:

∫c(x^2 y^2 z)ds = (20/√41) ∫0^4 [ 2 (1 - cos(8t)) t ] dt

Integrating by parts with u = t and dv = 1 - cos(8t), we get:

∫c(x^2 y^2 z)ds = (20/√41) [ t^2/2 - (1/8) sin(8t) ] |_0^4

= (20/√41) [ 8 - (1/8) sin(32) ]

≈ 156.864

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Step-by-step explanation:

5x-16 = 3 (10+x)

=> x= 23

Answer:

1,374.00

Step-by-step explanation:

.

Given:

Last year Lira earned $12,000 less than her husband Todd.

Together they earned $75,000.

To find:

The amount earned by Lira in last year.

Solution:

Let x be the amount earned by Lira's husband inn last year.

Last year Lira earned $12,000 less than her husband Todd.

Amount earned by Lira = \(x-12000\)

Total amount earned by Lira and her husband = \(x+(x-12000)\)

                                                                             = \(2x-12000\)

Together they earned $75,000.

\(2x-12000=75000\)

\(2x=75000+12000\)

\(2x=87000\)

\(x=\dfrac{87000}{2}\)

\(x=43500\)

Now,

Amount earned by Lira = \(x-12000\)

                                       = \(43500-12000\)

                                       = \(31500\)

Therefore, the amount earned by Lira in last year is $31500.