Mr Signorelli is buying a new suit for a wedding. The suit costs $250, but he found a coupon for 20% off. What is the sale price of the suit?

Answer:

152 feet^2

Step-by-step explanation:

1: Set up the formula of the surface area of a rectangular prism:

2: (Solving)

Therefore, the answer is 152 feet^2.

We can eliminate x from the second equation by differentiating it and substituting for x' using the first equation:

y'' = (x + 2y)' = x' + 2y' = x + 2(x + 2y) = 3x + 4y

So we have the system:

x' = x

y'' = 3x + 4y

The characteristic equation is:

r^2 - 1 = 0

which has roots r = ±1. So the general solution is:

x = c1e^t + c2e^(-t)

y = c3e^(2t) + c4e^(-2t) - (3/4)x

where c1, c2, c3, and c4 are arbitrary constants.

To write this as a linear combination of two vector solutions, we can let:

u1 = [e^t, e^(2t)]

u2 = [e^(-t), e^(-2t)]

Then the general solution can be written as:

[x, y] = c1 u1 + c2 u2 - (3/4)[e^t, e^(2t)]

b. We can eliminate y from the second equation by adding the two equations together:

x' + y' = (x - y) + (x + y) = 2x

So we have the system:

x' - y' = x - y

x' + y' = 2x

Multiplying the first equation by 2 and adding it to the second equation gives:

2x' = 3x

So x = c1e^(3t/2) and y = c2e^(t/2) + c3e^(-t/2) - (1/2)x. The general solution is:

x = c1e^(3t/2)

y = c2e^(t/2) + c3e^(-t/2) - (1/2)c1e^(3t/2)

To write this as a linear combination of two vector solutions, we can let:

u1 = [e^(3t/2), e^(t/2)]

u2 = [0, e^(-t/2)]

Then the general solution can be written as:

[x, y] = c1 u1 + c2 u2 - (1/2)[e^(3t/2), 0]

c. We can eliminate y from the first equation by differentiating it and substituting for y' using the second equation:

x'' = (x + 2y)' = x' + 2y' = x' + 2x = 3x

So we have the system:

x' = x + 2y

x'' = 3x

The characteristic equation is:

r^2 - r - 2 = 0

which has roots r = -1, 2. So the general solution is:

x = c1e^(-t) + c2e^(2t)

y = (1/2)(c2-c1)e^(2t) + c3

where c1, c2, and c3 are arbitrary constants.

To write this as a linear combination of two vector solutions, we can let:

u1 = [e^(-t), (1/2)e^(2t)]

u2 = [e^(2t), (1/2)e^(2t)]

Then the general solution can be written as:

[x, y] = c1 u1 + c2 u2 + [0, c3]

d. We can eliminate y from the second equation by differentiating it and substituting for y' using the first equation:

y'' = 2x - y' = 2x - (-x - 2y) = 3x + 2y

So we have the system:

x' = -x - 2y

y'' = 3x + 2y

The characteristic equation is:

r^2 + r + 2 = 0

which has roots r = (-1 ± i√7)/2. So the general solution is:

x = e^(-t/2)(c1cos((√7/2)t/2) + c2sin((√7/2)t/2))

y = (-1/√7)e^(-t/2)((c1/2)sin((√7/2)t/2) - (c2/2)cos((√7/2)t/2)) + c3e^(-t)

where c1, c2, and c3 are arbitrary constants.

To write this as a linear combination of two vector solutions

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Answer:

5. 1=112º

5. 2=68º

5. 3=112º

6. 1=45º

6. 2=45º

6. 3=135º

Step-by-step explanation:

5. 1 is a vertical angle to 112º, so they are equal (1 is obtuse)

5. 2 and 112º form to create a straight angle (line/180º) (supplementary angles) so subtracting the known number (112) from the total (180) gives you the number of the missing angle (2 is acute)

5. 3 is the same as 1 (3 is obtuse)

6. 1 and 45º are equal to each other (1 is acute)

6. 2 and 1 and 45º are equal and vertical angles (2 is acute)

6. 3 and 45º form to create a straight angle (line/180º) (supplementary angles) so subtracting the known number (45) from the total (180) gives you the number of the missing angle (3 is obtuse)

Answer:

q = - \(\frac{7}{18}\)

Step-by-step explanation:

q + \(\frac{5}{9}\) = \(\frac{1}{6}\)

Multiply through by 18 ( the LCM of 9 and 6 ) to clear the fractions

18q + 10 = 3 ( subtract 10 from both sides )

18q = - 7 ( divide both sides by 18 )

q = - \(\frac{7}{18}\)

Answer:

x = -2

Step-by-step explanation:

-6x + 5 = 17

First, combine the constants by subtracting 5 from each side.

-6x = 17 - 5

-6x = 12

Now you want x by itself, so divide both sides by -6.

x = -2

Check your answer by plugging x = -2 into the original equation.

-6(-2) + 5 = 17

12 + 5 = 17

17 = 17

Your answer is correct.

Answer:

-2

Step-by-step explanation:

-6x + 5 = 17

-6x = 17 - 5

-6x = 12

-6x = 12

6 6

-x = 2

-x = 2

-1 -1

x = -2

Answer: subtract 5 from the input to get the output.

Step-by-step explanation:

There are 60 different ways could you choose a car and this can be determined by using arithmetic operations.

What are arithmetic operations?

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-") Multiplication ("×") Finding the quotient in division ("÷").

Given :

A car dealership has five exterior color choices.

A car dealership has six interior color choices.

A car dealership has two model choices.

The following steps can be used to determine the different ways could you choose a car:

Multiply 5 and 6 that is multiply five exterior color choices and six interior color choices.

= 5 * 6

Multiply the above expression by 2 which is with two model choices.

= 30 * 2

Further, simplify the above expression.

= 60

Hence, There are 60 different ways could you choose a car.

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Answer:

4

Step-by-step explanation:

(a,a),(a,b),(b,a),(b,b)

change 3/4 to 6/8 and add 6/8 and 1/8 to get 7/8

he walked 7/8 miles in total :)

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

If he plans to get 5 cans of soup, then deal a would be the best, because you save $1.50.

The leak is approximately 4.61 meters above the ground. The minimum radius of the flattened suction cup is approximately 1.397 meters.

To find the height above the ground where the leak is located, we can use the equation of motion for vertical projectile motion. The equation is:

h = (v²) / (2g)

where:

h is the height above the ground,

v is the initial vertical velocity (speed),

g is the acceleration due to gravity (approximately 9.8 m/s^2).

Given that the water shoots out at a speed of 9.5 m/s, we can substitute the values into the equation:

h = (9.5²) / (2 * 9.8)

h = 90.25 / 19.6

h ≈ 4.61 meters

Therefore, the leak is approximately 4.61 meters above the ground.

To solve this problem, we can use the principle of fluid pressure. The pressure difference between the inside and outside of the suction cup holds it in place. The formula for pressure is:

P = F / A

where:

P is the pressure,

F is the force applied (in this case, the weight of the table),

A is the area over which the force is distributed (the contact area of the suction cup).

Given that the pressure in the room is 100.407 Pa and the mass of the table is 63 kg, we can calculate the force applied:

F = m * g

F = 63 kg * 9.8 m/s²

F ≈ 617.4 N

Now, we can rearrange the pressure formula to solve for the area:

A = F / P

A = 617.4 N / 100.407 Pa

A ≈ 6.141 m²

Since we are looking for the minimum radius of the flattened suction cup, we can assume it has a circular shape. The area of a circle is given by the formula:

A = π * r²

where:

A is the area,

r is the radius of the circle.

Substituting the calculated area into the equation:

6.141 m² = π * r²

Solving for r:

r² = 6.141 m² / π

r² ≈ 1.955 m²

r ≈ √(1.955)

r ≈ 1.397 meters

Therefore, the minimum radius of the flattened suction cup is approximately 1.397 meters.

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Answer:

Sorry it doesn't look like you attached any link for this.

Answer: n-8

Step-by-step explanation: n represents the unknown number. You need to subtract 8 from the number since "less than" is another phrase to describe subtraction.

I hope this helps, have a nice day.

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

D

Step-by-step explanation:

Every time there is a number outside the parenthesis, you have to distribute that number to each number within the parenthesis. The numbers are multiplied but the symbol in the middle stays the same.

The GCF of the given literal terms m⁷ n⁴ p³ and mn¹² p⁵ is mn⁴p³.

To find the greatest common factor (GCF) of the given literal terms, we need to identify the highest power of each variable that appears in both terms.

The variables present in both terms are m, n, and p.

For m, the highest power is m⁷ in the first term and m¹ in the second term. Therefore, the common factor for m is m¹.

For n, the highest power is n⁴ in the first term and n¹² in the second term. Therefore, the common factor for n is n⁴.

For p, the highest power is p³ in the first term and p⁵ in the second term. Therefore, the common factor for p is p³.

Combining these common factors, we get the GCF of the given literal terms:

GCF = m¹ * n⁴ * p³

Therefore, the GCF of the given literal terms m⁷ n⁴ p³ and mn¹² p⁵ is mn⁴p³.

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Answer:

You didn't provide any choices or options to pick from but here are the possible answers is:

- Encourage the use of the incentive spirometer every 2 hours

-Instruct to splint incision when coughing and deep breathing.

-Reposition the client every 2 hours

-Assist with early ambulation.

Step-by-step explanation:

Hope I could help!

In the plan of care to prevent postoperative atelectasis, interventions should not include the use of tobacco products or exposure to secondhand smoke.

The nurse should include several interventions in the plan of care to prevent postoperative atelectasis, but there are specific interventions that should not be included. Atelectasis is the partial or complete collapse of the lung, and preventing it is crucial after surgery. Here are some interventions that should be included:

Incentive Spirometry: The nurse should encourage the client to use an incentive spirometer to promote deep breathing and lung expansion.

Early Ambulation: Encouraging the client to get out of bed and walk as soon as possible after surgery helps improve lung function.

Pain Management: Adequate pain control measures should be in place to ensure the client can take deep breaths without discomfort.

Coughing and Deep Breathing Exercises: The nurse should teach and encourage the client to perform regular coughing and deep breathing exercises to clear the airways and prevent mucus buildup.

Positioning: Proper positioning, such as elevating the head of the bed, can aid lung expansion.

What should not be included in the plan of care is the use of tobacco products or exposure to secondhand smoke, as smoking and smoke exposure are detrimental to lung health and can worsen atelectasis. These should be strictly avoided to prevent postoperative complications.

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Jill's overtime pay is $137.9 and her gross pay is $531.9

For calculating, Hourly and overtime pay

Some employers pay a set amount for every hour an employee works. This is called regular pay. An employee may also earn overtime pay for all hours worked over 40 within a pay period. The overtime rate is usually 1.5 times an employee’s regular hourly pay.In some cases, such as on Sundays, an employer may pay double time or 2 times an employee’s regular pay.

Formulas for calculating earnings,

Hours Worked x Hourly Rate = Regular Pay

Overtime Hours Worked x Overtime Rate = Overtime Pay

Regular Pay + Overtime Pay = Gross Pay

Jill work for one day = 8 hours

She work from Monday to Friday i.e, 5 days which is = 8 * 5 = 40 hours

On Saturday and Sunday she worked 4 hours on each day,

so, for Saturday her payment is = (1.5 * 9.81) * 4

                                                     = 59.1

And, for Sunday her payment is = 2 * ( 4 * 9.85)

                                                    = 78.8

Now, find her overtime pay (add her's Saturday and Sunday payment)

Overtime pay = 59.1 + 78.8

                       = $137.9

Now, find her Gross pay = Regular pay + Overtime pay

Regular pay = 9.85 * 40

                    = 394

So, the Gross pay = 394 + 137.9

                              = $531.9

Therefore, Jill's overtime pay is $137.9 and her gross pay is $531.9.

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\( \sqrt{4x} = 3a - y \\ \sqrt{4} \times \sqrt{x} = 3a - y \\ 2 \sqrt{x} = 3a - y \\ \frac{2 \sqrt{x} }{2} = \frac{3a}{2} - \frac{y}{2} \\ \sqrt{x} = \frac{3a}{2} - \frac{y}{2} \\ ( { \sqrt{x} })^{2} = {( \frac{3a}{2} - \frac{y}{2} })^{2} \\ x = ( \frac{3a}{2} - \frac{y}{2} ) ^{2} \)

ATTACHED IS THE SOLUTION

Answer:

Part A: The appropriate design for the study includes;

Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

Step-by-step explanation:

I understand not

Oh the anSwer Is a

Answer:

We need to determine 50% of 166

So,

Step-by-step explanation:

Step 1: In the given case Output Value is 166.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 166 = 100%.

Step 4: In the Same way, x = 50%.

Step 5: On dividing the pair of simple equations we got the equation as under

166 = 100% (1).

x = 50% (2).

(166%)/(x%) = 100/50

Step 6: Reciprocal of both the sides results in the following equation

x%/166% = 50/100

Step 7: Simplifying the above obtained equation further will tell what

is 50% of 166

x = 83%

Therefore, 50%

of 166 is 8

3

Part 1/3:a sample of 382 children aged 8-10 living in New York is required to obtain a margin of error of 0.047 and a 95% confidence interval.Part 2/3:a sample size of 2719 children aged 8-10 living in New York is required to obtain a margin of error of 0.04 and a 99.8% confidence interval.

Part 1/3:Using the formula, n = (z² * p * q) / E²

Where z = 1.96 (for a 95% confidence interval)

P = 0.42

q = 0.58

E = 0.047

By plugging in the values into the formula we getn = (1.96)² * 0.42 * 0.58 / (0.047)²

n = 381.92 ≈ 382

Therefore, a sample of 382 children aged 8-10 living in New York is required to obtain a margin of error of 0.047 and a 95% confidence interval.

Part 2/3:When the proportion is not available, use 0.5 instead.Using the formula n = z² * p * q / E²

Where z = 3.09 (for a 99.8% confidence interval)

P = 0.5q = 0.5E = 0.04

By plugging in the values into the formula we getn = (3.09)² * 0.5 * 0.5 / (0.04)²n = 2718.87 ≈ 2719

Therefore, a sample size of 2719 children aged 8-10 living in New York is required to obtain a margin of error of 0.04 and a 99.8% confidence interval.

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Answer:

25.05

Step-by-step explanation:

12.26 + 7 + 5.79 = 25.05

Lydia earns $52.5 more than Gabrielle after 3 years.

percentage, a relative value indicating hundredth parts of any quantity.

we can use the formula for compound interest:

\(A = P(1 + r/n)^n^t\)

where A is the final amount,

P is the principal (initial investment),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the number of years.

For Lydia (n=365)

A=1000(1+0.0525/365)¹⁰⁹⁵

A=1115.7

For Gabrille, we use the same formula but with n = 2 (compounded semi-annually):

A = 1000(1 + 0.0525/2)⁶

A = 1000(1.0265625)⁶

A = 1168.2

To find the difference in the amounts earned, we subtract Gabrielle's amount from Lydia's:

1168.2- 1115.7 = 52.5

Hence, Lydia earns $52.5 more than Gabrielle after 3 years.

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Given that IQ is normally distributed with a mean of 100 and a standard deviation of 15 and the sample size, n=16

We need to find the probability that a randomly selected sample has a mean greater than 105.

The z-score is given by;\(z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\\)

The sample mean of size n=16 is \(\bar{x}=105\), the population mean is \(\mu=100\) and the standard deviation is \(\sigma=15\). Now we need to find the probability that the z-score is greater than z. Since the sample size is greater than 30, we can use the z-distribution to approximate the standard normal distribution. Since the sample size is n=16 which is less than 30, we cannot use the z-distribution to approximate the standard normal distribution. Instead, we use the t-distribution, which is a set of distributions that are similar to the standard normal distribution but are dependent on the sample size. The formula for the t-score is given by;

\(t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\)Where \(s\) is the sample standard deviation. Since the population standard deviation is unknown, we use the sample standard deviation instead.

The sample mean of size n=16 is \(\bar{x}=105\),

the population mean is \(\mu=100\),

the sample standard deviation is \(s=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{16}}=3.75\).

The t-score is given by\(t=\frac{105-100}{\frac{3.75}{\sqrt{16}}}=4.267\\)

The degrees of freedom is given by n-1 = 16-1 = 15. Using the t-table with 15 degrees of freedom and a two-tailed test at the 0.05 level of significance, the critical value is 2.131. Since the t-score is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the sample mean is greater than the population mean. The p-value is the area under the curve to the right of the t-score. We find the p-value using the t-table. The p-value is 0.0002. Hence, the probability that a randomly selected sample has a mean greater than 105 is 0.0002 (or 0.02%). Therefore, the option with the correct answer is 0.0002.

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Answer:

f(x)+41 f(-10)=7

Step-by-step explanation:

Answer:

$19.2

Step-by-step explanation:

The school mascot is rectangular in nature.

Perimeter P = 2(L+W)

L is the length = 4feet

W is the width = 12 feet

Perimeter = 2(4+12)

Perimeter = 2(16)

Perimeter  = 32 feet

Convert to inches

12in = 1feet

x = 32 feet

Cross multiply

x = 12 * 32

x = 384in

Hence the perimeter of the school mascot is 384in

If it is to be completely framed using a single row of square tiles each 2inches on an edge

2 inches = 1 tiles

384inches = y tiles

Cross multiply

2y = 384

y = 384/2

y = 192 tiles

The number of tiles needed is 192 tiles

Get the cost of 192tiles

If the tiles are $0.10 each. 192 tiles will cost 192 * 0.1 = $19.2

Hence the cost of the tiles needed is $19.2