4/5 cm * 3/8 cm
please answer fast ​

The face value of the non-interest-bearing note for the woman's loan should be approximately $500.26. The face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.

To find the face value of a non-interest-bearing note, we can use the formula:

Face Value = Proceeds / (1 - Discount Rate * (Days to Maturity / 360))

1. Calculation for the woman's loan:

Proceeds = $485

Discount Rate = 13.22%

Days to Maturity = 80 (from April 10 to June 29)

Face Value = $485 / (1 - 0.1322 * (80 / 360))

Face Value = $485 / (1 - 0.1322 * 0.2222)

Face Value = $485 / (1 - 0.0294)

Face Value = $485 / 0.9706

Face Value = $500.26 (approximately)

Therefore, the face value of the non-interest-bearing note for the woman's loan should be approximately $500.26.

2. Calculation for the man's loan:

Amount needed = $2350

Discount Rate = 14.4%

Days to Maturity = 70 (from July 10 to September 18)

Face Value = $2350 / (1 - 0.144 * (70 / 360))

Face Value = $2350 / (1 - 0.144 * 0.1944)

Face Value = $2350 / (1 - 0.0279)

Face Value = $2350 / 0.9721

Face Value = $2417.91 (approximately)

Therefore, the face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.

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3.31×\(10^-^5\) g is equivalent to 0.0331 μg which is obtained by using the conversion factor.

To convert from grams to micrograms, we need to consider the conversion factor that relates the two units. The prefix "micro-" represents a factor of \(10^-^6\), which means there are 1,000,000 micrograms in a gram. Therefore, to convert grams to micrograms, we multiply the given value by 1,000.

In this case, we have 3.31×\(10^-^5\) g. To convert this value to micrograms, we can multiply it by 1,000:

= 3.31×\(10^-^5\) g × 1,000

= 3.31×\(10^-^5\) × 1,000

= 3.31×\(10^-^5\) × \(10^{3}\)

= 3.31×\(10^(^-^5^+^3^)\)

= 3.31×\(10^-^2\)

= 0.0331 μg

Therefore, 3.31×\(10^-^5\) g is equivalent to 0.0331 μg.

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Given the dimensions of the triangle, QPR is as follows:

angle QPR =90^circle

Side QP = 8 sqrt3 units

Side PR = 8 units

To find, side QR =? units

Please refer to the attached figure for the representation of the given dimensions.

The base is side QP,

Perpendicular is side PR and

Hypotenuse is side QR.

In a right-angled triangle, the Pythagorean theorem holds i.e.

According to Pythagoras theorem:

text {Hypotenuse}^ {2} = text {Base}^ {2} + text {Perpendicular}^ {2}

=            QR^ {2} = QP^ {2} + PR^ {2}

Putting the values of QP and PR:

=           QR^ {2} = (8sqrt3) ^ {2} + 82} = QR^ {2} = 64 times 3+ 64 QR^ {2}

= 64 times 4 QR = 8 times 2 QR = 16 units.

So, the value of the length of the side QR is 16 units.  

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cot(θ) = -3/4: The cotangent of angle θ, when the terminal side passes through the point (-3, -4), is -3/4. .

Given that the terminal side of an angle θ passes through the point (-3, -4), we can determine the value of cot(θ), which is the ratio of the adjacent side to the opposite side in a right triangle. To find cot(θ), we need to identify the adjacent and opposite sides of the triangle formed by the point (-3, -4) on the terminal side of angle θ.

The adjacent side is represented by the x-coordinate of the point, which is -3. The opposite side is represented by the y-coordinate, which is -4. Using the definition of cotangent, cot(θ) = adjacent/opposite, we substitute the values:

cot(θ) = -3/-4

Simplifying the fraction gives us:

cot(θ) = 3/4 . Therefore, the exact value of cot(θ) when the terminal side of angle θ passes through the point (-3, -4) is 3/4.

In geometric terms, cotangent is a trigonometric function that represents the ratio of the adjacent side to the opposite side of a right triangle. By identifying the appropriate sides using the given point, we can evaluate the cotangent of the angle accurately.

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Answer:

c＝√(a²+b²)

C is hypotenuse

Answer: 18 mins

Step-by-step explanation

there is 3600 secs in an hour so do the same for this.

6 mins is 360 secs and times 360 by 3 is 1080 and then double it they figure out how many mins is 2160 im sorry if thats confusing.

To proceed with this analysis, we assume that the individuals in the sample were randomly selected and that the samples are independent.

Additionally, the sample sizes are large enough to apply the normal approximation to the sampling distribution of the difference in proportions.Using these assumptions, we can calculate the confidence in is 37/77 ≈ 0.481. The proportion of men who follow a regular exercise program is 44/85 ≈ 0.518. The difference between these proportions is 0.518 - 0.481 ≈ 0.037.

The 95% confidence interval for the difference in proportions can be calculated using the formula: difference ± (critical value) * sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)] where p1 and p2 are the proportions of women and men, n1 and n2 are the respective sample sizes, and the critical value corresponds to a 95% confidence level. Performing the calculations, the 95% confidence interval for the difference in proportions is approximately 0.037 ± 0.129, which gives us a range from -0.092 to 0.166.

Interpreting this interval, we can say that with 95% confidence, the true difference between the proportions of women and men who follow a regular exercise program lies within the range of -0.092 to 0.166. This means that there is insufficient evidence to conclude that there is a significant difference in the proportions of women and men who follow a regular exercise program. The interval includes zero, indicating that the difference could be negligible or non-existent.

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Answer:

Step-by-step explanation:The answer would be 28 because if you divide 16 by 4 you would get 4 and multiply it by 3 and you would get 12 so add 16+12=28

Answer:

Step-by-step explanation:

espera y termino y te ayudo vale que me falta poco vale

Answer:

ABCD-AEFG

Step-by-step explanation:

Answer:

x + 37 ≥ 65

Step-by-step explanation:

Given:

Money Micah wants = $65

Money Micah had = $37

Find:

Money Micah need

Computation:

Money Micah need(x)

x + 37 ≥ 65

So,

Money Micah need = 65 - 37

Money Micah need = $28

Answer:

11y + 7

Step-by-step explanation:

4y + 5 + 2 + 7y

4y + 7y + 5 + 2 <== combine the like terms

11y + 7

Hope this helps!

Answer:

11y+7

Step-by-step explanation:

4y+5+2+7y

combine like terms

5+2=7

then you have

4y+7+7y

combine the y's

4y+7y=11y

then you got

11y+7  

Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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Answer:

Step-by-step explanation:

16y² - 24y + 9 = 16(y-0.75)² = (4y-3)²

Answer:

16y² - 24y + 9

Step-by-step explanation:

Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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Answer:

The fraction of the pencils that are red is 4/10. The fraction of the pencils that are black is 6/10.

Step-by-step explanation:

[I can't draw you a model but I reccomend that when you do, you seperate it into 10 pieces and mark 4 as red pencils and 6 as black pencils. You could also simplify 4/10 to 2/5 and 6/10 to 3/5, but instead you'd seperate the model into 5 pieces and mark 2 as red pencils and 3 as black pencils.]

First, let's add this up so we have our denominator.

4 + 6 = 10.

Now that we know that the denominator is 10, we apply it to the question.

The box has 4/10 red pencils and 6/10 black pencils.

The box has 4/10 red pencils and 6/10 black pencils.If you were to simplify, it'd be 2/5 red pencils and 3/5 black pencils.

Answer:

Multiply to remove the fraction, then set equal to 0 and solve.

Exact Form: y = − 1/10

Decimal Form: y = − 0.1

Step-by-step explanation:

Answer:

y = -1/10 or -0.1

Step-by-step explanation:

Multiply both sides of the equation by 100.

To find the opposite of 5y−17, find the opposite of each term.

The opposite of −17 is 17.

Combine 155y and −5y to get 150y.

Subtract 17 from both sides.

Subtract 17 from 2 to get −15.

Divide both sides by 150.

​Reduce the fraction  

​ to lowest terms by extracting and canceling out 15.

There are 364 different committees of 3 people. There are 436 different committees of 4 people.

There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:

To calculate the number of different committees of 3 people, we can use the combination formula, which is:

\(${n \choose k} = \frac{n!}{k!(n-k)!}$\)

where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:

\(${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$\)

Therefore, there are 364 different committees of 3 people that can be formed from this group.

To solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:

\(${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$\)

Next, we calculate the number of committees that do not include a freshman, which is:

\(${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$\)

Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:

\(${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$\)

\(${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$\)

\(${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$\)

Now we can apply the principle of inclusion-exclusion, which is:

Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.

Plugging in the values, we get:

$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$

Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.

Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.

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She will have run a total of 2.25 racers in 27 racers

From the question, we have the following parameters that can be used in our solution:

Total number of racers = 27 racers

Number of racers in a run = 12 racers

From the above parameter, we can calculate the total number of racers using the following equation

The total number of racers is calculated as

Total number of racers in the run = Total number of racers/Number of racers in a run

Substitute the known values in the above equation

So, we have the following equation

Total number of racers in the run = 27/12

Evaluate the quotient

Total number of racers in the run = 2.25

Hence, the total number of racers in the run is 2.25 racers

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It is important to consider scholarships and grants before loans to pay for higher education because Scholarships and grants are free money that do not need to be paid back. That is option A.

Scholarship and grants are defined as payments that are being granted to an individual upon an academic achievement which usually involves a stipulated amount of money.

Scholarship and grants are important due to the following reasons:

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Here's a step-by-step explanation on how to approach this task:

1. Start by listing the main rooms and spaces you want to include in your house, such as living room, kitchen, dining room, bedrooms, bathrooms, garage, and any additional rooms (e.g., office, laundry room).

2. Consider the flow and layout of the house, taking into account factors like natural light, privacy, and ease of movement between rooms. For example, it's common to have the living ro om, dining room, and kitchen connected for better social interaction.

3. Sketch the floor plan using a piece of paper or digital software. Begin by drawing the exterior walls, then add interior walls to separate the rooms. Make sure to label each room to avoid confusion.

4. Add doors and windows to your floor plan, ensuring that there is easy access to each room and that windows are placed to take advantage of natural light.

5. Consider the placement of furniture and appliances in each room to ensure that there is enough space for them, as well as clear pathways for movement.

6. Once you've sketched the floor plan, analyze it by reviewing the layout and ensuring that it meets your needs and preferences. Make any necessary adjustments to improve the design.

By following these steps, you'll be able to sketch a floor plan of a house and determine the essential parts of the house that should be included.

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Answer:

It is answer A) 5x^8y^8z^3 (sq rt 2y)

Step-by-step explanation:

1. Factor out the perfect square

(sqr rt) 5^2 × 2x^16 × y^16 xyz^6

2. Split each factor to their own square root

3. Simplify these roots

Answer:

A

Step-by-step explanation:

First let's factor 50. This will look like this: 2*5*5. Since there are two 5s, together they form a perfect square so we can bring it out of the square root. This is what we have so far now: \(5\sqrt{2x^{16} y^{17} z^{6} }\). Now we should move on to \(x^{16}\), since 16 is an even number, we can just divide it in half and put x to the power of 16/2 outside the square root. This is what we have so far: \(5x^{8} \sqrt{2y^{17}z^{6} }\). Now let's work on \(y^{17}\). Since 17 is an odd number, we will separate it like this: 16 + 1. Now we can divide 16 by 2 and put y to the power of 16 divided by 2 outside of the square root, but the last \(y^{1}\) will need to continue inside. So this is what we have so far: \(5x^{8}y^{8} \sqrt{2y z^{6}}\). Now all we have to do is take care of the \(z^{6}\). Since 6 is even we can just divide it by 2 and put the z to the power of 6 divided by 2 outside of the square root. This is what we have: \(5x^{8}y^{8} z^{3} \sqrt{2y}\).

We are done!

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The ratios that are equivalent to 2:3 are:

6 to 9

8 to 12

To determine which of the given ratios are equivalent to 2:3, we need to simplify each ratio and check if they result in the same reduced form.

12 to 36:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 12:

12 ÷ 12 = 1

36 ÷ 12 = 3

The simplified ratio is 1:3, which is not equivalent to 2:3.

6 to 9:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 3:

6 ÷ 3 = 2

9 ÷ 3 = 3

The simplified ratio is 2:3, which is equivalent to 2:3.

8 to 12:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 4:

8 ÷ 4 = 2

12 ÷ 4 = 3

The simplified ratio is 2:3, which is equivalent to 2:3.

16 to 20:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 4:

16 ÷ 4 = 4

20 ÷ 4 = 5

The simplified ratio is 4:5, which is not equivalent to 2:3.

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At the 0.05 significance level, the hypothesis test supports the claim that the mean amount of juice in the 16-ounce bottles is less than 16.3 ounces, based on the sample data and calculations.

To test the claim that the mean amount of juice in the 16-ounce bottles is less than 16.3 ounces, we can perform a one-sample t-test.

State the null hypothesis (H₀) and the alternative hypothesis (H1):

- Null hypothesis (H₀): The mean amount of juice in the 16-ounce bottles is equal to or greater than 16.3 ounces (μ >= 16.3).

- Alternative hypothesis (H₁): The mean amount of juice in the 16-ounce bottles is less than 16.3 ounces (μ < 16.3).

Choose the significance level. In this case, the significance level is 0.05.

Calculate the test statistic. We'll use the formula for the one-sample t-test:

t = (\(\bar{x}\) - μ) / (σ / √(n))

where \(\bar{x}\) is the sample mean, μ is the hypothesized mean, σ is the population standard deviation, and n is the sample size.

Sample mean (\(\bar{x}\)) = 16.14 ounces

Hypothesized mean (μ) = 16.3 ounces

Population standard deviation (σ) = 0.9 ounces

Sample size (n) = 70

Substituting these values into the formula:

t = (16.14 - 16.3) / (0.9 / √(70))

t ≈ -1.69

Determine the critical value or p-value. Since we have a left-tailed test, we'll find the critical value using the t-distribution with (n - 1) degrees of freedom (df = 69) and a significance level of 0.05. Looking up the critical value in the t-table, we find it to be approximately -1.666.

Compare the test statistic with the critical value. Since the test statistic (-1.69) is less than the critical value (-1.666), it falls in the critical region.

Make a decision and interpret the results. Since the test statistic falls in the critical region, we reject the null hypothesis. This means that there is sufficient evidence to support the claim that the mean amount of juice in the 16-ounce bottles is less than 16.3 ounces.

Therefore, at the 0.05 significance level, the claim that the mean amount of juice for all 16-ounce bottles is less than 16.3 ounces is supported.

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Complete Question:

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places. A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.3 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 16.14 ounces. nbspTest whether the claim that the mean amount of juice for all 16 dash ounce bottles is less than 16.3 ounces is supported or not supported. Assume that sigma equals 0.9 ounces.

supported or not supported?

Answer:

73.1 cm

Step-by-step explanation:

In the drawing, the rubber track is in black and the wheels are in light gray.

As we can see in the figure, the rubber track will have a length of two halfs of a circunference of radius 8 cm plus six diameters of 8 cm. So the total length is:

Length of rubber track = pi * 8 + 6 * 8 = 25.13 + 48 = 73.133 cm

Rounding to one decimal place, we have that the length is 73.1 cm

This question is incomplete because it lacks the diagram of the 4 circular wheels.

Find attached to this answer the appropriate diagram

Answer:

100.5cm

Step-by-step explanation:

The formula to be used in this calculation is the circumference of a circle.

The circumference of a circle can be defined as the actual length of a circle when it is stretch out(opened up) or the distance around a circle.

The formula for the circumference of a circle is given as 2πr where r = radius of the circle

Or πD where D = Diameter of the circle

In the question, we are given the diameter of the circle = 8cm

So we use the Formula

= πD

The length of the rubber track around one wheel is

= π × 8cm = 25.132741229cm

From the attached diagram, we can see we have 4 wheels.

The length of the rubber track that goes around the four wheels is calculated as

4 × 25.132741229cm = 100.53096491cm.

Approximately to one decimal place = 100.5cm

Therefore, the length of the rubber track that goes around the four wheels to one decimal place is 100.5cm

Answer:

8 x 50 + 8 x 4.

The value of x (hypotenuse) by using trigonometry is 2√5.

What is trigonometry ?

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

In the triangle height = √15  and hypotenuse as x

The value of the angle is  60°

by using trigonomtry we can write

sin60° = height/ hypotenuse

√3/2 = √15/ x

x = (√15 * 2)/√3

x = 2√5

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Answer:

6 possible outcomes

Step-by-step explanation:

To solve this problem, we have to make use of the Fundamental Counting Principle formula.

The formula counting principle states that when we are given two or more distinct events, in order to get the total number of possible outcomes, we multiply such events together.

In the above question, we are given two events.

Event 1

3 varieties of cheese: Cheddar, Gouda, and Swiss.

Event 2

2 styles of cheese: Shredded and Sliced

The possible outcomes for the variety and style of cheese = Event 1 × Event 2

= 3 × 2

6 possible outcomes.

These 6 Possible outcomes are listed below:

1) Cheddar cheese , Shredded

2) Cheddar cheese , Sliced

3) Gouda cheese , Shredded

4) Gouda cheese , Sliced

5) Swiss cheese , Shredded

6) Swiss cheese , Sliced