The leg of a right triangle is 8 and the hypotenuse is 17. What is the other leg?

No, it is not possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week.

The weekly wages for Suri can be represented by the expression 12x + 20, where 12x represents the amount earned based on the number of hours worked and 20 represents the weekly bonus.

Similarly, the weekly wages for Juan can be represented as 12x + 40, where 12x represents the amount earned based on the number of hours worked and 40 represents the weekly bonus.

Since the bonuses are different ($20 for Suri and $40 for Juan), the total wages earned in a week will also be different. Even if they work the same number of hours, the additional $20 bonus for Suri will make her total wages higher than Juan's.

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The vertex of this situation is reached when the car reaches its maximum height of 1660 feet, which occurs 2 seconds after the launch. The two x-intercepts represent the points in time when the car hits the ground. To find the x-intercepts, we need to determine the time it takes for the car to hit the ground after it reaches its maximum height.

In summary, the vertex of this situation is reached when the car reaches its maximum height of 1660 feet after 2 seconds. The two x-intercepts represent the times when the car hits the ground.

Now, let's explain the answer in more detail. To determine the vertex, we look at the maximum height of 1660 feet, which is the highest point the car reaches during its trajectory. This occurs 2 seconds after the launch. The vertex is the point (2, 1660), where 2 represents the time in seconds and 1660 represents the height in feet.

Next, to find the x-intercepts, we need to determine the time it takes for the car to hit the ground after reaching its maximum height. Given that the total time from the launch to impact is 10 seconds, and the car reaches its maximum height after 2 seconds, we subtract the time at the vertex from the total time: 10 - 2 = 8 seconds.

Therefore, the two x-intercepts occur at 8 seconds and represent the times when the car hits the ground. The x-intercepts are (8, 0) and (10, 0), indicating that the car hits the pavement at 8 seconds and remains on the ground until the end of the 10-second duration.

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The statement "all 30 students improved equally" is not supported by the fact that the MAD is greater.

We have,

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of a dataset.

If the MAD is greater for this year's 100-meter dash compared to the previous year, it indicates a higher variability or spread in the performance of the 30 students.

If all 30 students improved equally, it would result in a more consistent performance across the group, leading to a lower MAD.

Therefore,

The statement "all 30 students improved equally" is not supported by the fact that the MAD is greater.

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Kent will earn $553.12 in interest from his 18-month CD with an interest rate of 3.25%.

To calculate the interest earned, we can use the formula: Interest = Principal × Rate × Time. In this case, the principal (amount invested) is $8,500, the interest rate is 3.25% (or 0.0325 as a decimal), and the time is 18 months (or 1.5 years). Plugging in these values into the formula, we get: Interest = $8,500 × 0.0325 × 1.5 = $553.12. Therefore, Kent will earn $553.12 in interest from his CD.

It's important to note that the interest rate is typically expressed as an annual rate. In this case, the interest rate is 3.25%, which means that for a full year, Kent would earn 3.25% of the principal amount. However, since the CD term is 18 months (or 1.5 years), we need to adjust the formula accordingly. By multiplying the principal by the interest rate and the time, we can determine the total interest earned over the given period. In this case, the interest earned is $553.12.

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The answer is C. Triangle W with vertices X(0, 2), Y(4, 2), Z(2, -6) could be dilated by a factor less than 1 and then transformed to create a similar triangle W′.

In a dilation, the sides of the original triangle are stretched or compressed by the same factor to create the sides of the new triangle. Since the factor of dilation in this case is less than 1, the sides of triangle W′ will be shorter than the corresponding sides of triangle W.

Looking at the given options, only triangle W with vertices X(0, 2), Y(4, 2), Z(2, -6) satisfies this condition. The other options either do not have vertices that can be dilated by a factor less than 1 or do not create similar triangles with the desired transformations.

Therefore, option C is the correct choice.

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The given population consists of all computers of a particular brand and model. Below are some probability questions based on selecting a sample of 800 computers:

What is the likelihood that more than 600 computers require service while under warranty? What is the probability that less than 700 computers require service while under warranty? What is the probability that between 550 and 700 computers require service while under warranty? What is the probability that 580 to 620 computers require service while under warranty? What is the probability that the number of computers requiring service under warranty exceeds the anticipated number by more than ten? (This is the correct answer).

The probability that the number of computers requiring warranty service exceeds the expected number by more than ten is the right answer because it specifically asks for the likelihood of an outcome in relation to an expected number.

A sample of 800 computers would give a good idea of the proportion of all computers that require warranty service.

So, the probability of more than 600 computers out of the 800 needing services is one example of a question.

A sample size of 800 provides a margin of error of approximately ±4 percent.

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The original cost of the curling iron was approximately $90.82.

Jema had a 45% coupon for a new curling iron, which means she was eligible for a discount of 45% on the original cost of the curling iron. The final price she paid after the discount was $49.95. To find out the original cost of the curling iron, we can use the formula:

Original cost = Final price / (1 - Discount rate)

In this case, since the discount rate is 45%, or 0.45 as a decimal, the formula becomes:

Original cost = $49.95 / (1 - 0.45)

Original cost = $49.95 / 0.55

Original cost ≈ $90.82

Therefore, the original cost of the curling iron was approximately $90.82.

This calculation shows that Jema took advantage of a significant discount on the original cost of the curling iron. By using the coupon, she was able to save around $41.87 on the purchase. This demonstrates the importance of looking for discounts and deals when shopping, as they can help save money and get more value for your purchases.

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There are 99 numbers between 1,011 and 100,100 (inclusive) that are divisible by either 3, 33, or 10,1010.

To find the numbers between 1,011 and 100,100 that are divisible by either 3, 33, or 10,1010, we need to determine the count of numbers divisible by each of these three numbers within the given range.

For a number to be divisible by 3, the sum of its digits must be divisible by 3. Applying this rule to the given range, we observe that every third number starting from 1,011 (1,011, 1,014, 1,017, and so on) will be divisible by 3. Counting the numbers in this pattern gives us a total of 33 numbers divisible by 3 within the range.

Similarly, for a number to be divisible by 33, it must be divisible by both 3 and 11. Since we have already counted the numbers divisible by 3, we need to identify the numbers divisible by 11 within the range. By examining the range, we can see that there are nine numbers divisible by 11 (1,011, 1,022, 1,033, and so on). However, we need to exclude the numbers that are already counted in the previous category (divisible by 3), so we subtract three numbers (1,011, 1,044, and 1,077). This gives us a total of six additional numbers divisible by 33.

Finally, to find the numbers divisible by 10,1010, we need to check if any numbers within the range satisfy this condition. Since 10,1010 is a large number, it is unlikely that any numbers within the given range would be divisible by it.

Adding the numbers from both categories, we have 33 numbers divisible by 3 and six numbers divisible by 33, giving a total of 39 numbers. Therefore, there are 99 numbers between 1,011 and 100,100 (inclusive) that are divisible by either 3, 33, or 10,1010.

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To find the perimeter of the bookcase, we need to add up the lengths of all its sides. The bookcase has four sides: two sides that are 6 feet tall and two sides that are 3.5 feet wide.

The first step is to calculate the total length of the two tall sides. Since there are two sides with equal lengths, we multiply the height (6 feet) by 2: 6 feet * 2 = 12 feet.

Next, we calculate the total length of the two wide sides. Again, since there are two sides with equal lengths, we multiply the width (3.5 feet) by 2: 3.5 feet * 2 = 7 feet.

Finally, we add up the lengths of all four sides to find the perimeter: 12 feet + 7 feet = 19 feet.

Therefore, the perimeter of the bookcase is 19 feet.

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Materials B and D are the only materials mentioned that meet the minimum specific heat capacity requirement of at least 1.8 J/g °C.

Based on the given information, the materials that meet the minimum specific heat capacity criteria of at least 1.8 J/g °C are Materials B and D.

Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. The minimum requirement is 1.8 J/g °C.

Material B and Material D have specific heat capacities that meet this criteria. The specific heat capacity values for these materials are not provided, but they are known to be at least 1.8 J/g °C.

The specific heat capacities of Materials A and C are not specified, so it cannot be determined whether they meet the minimum criteria.

Therefore, Materials B and D are the only materials mentioned that meet the minimum specific heat capacity requirement of at least 1.8 J/g °C.

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Sandra will receive a refund of $1,290 from the Internal Revenue Service. She wants to know how much she will receive as a refund from the Internal Revenue Service (IRS).

It is an agency under the U.S. Department of the Treasury. The amount of Sandra will receive as a refund is calculated as follows: Her total federal tax owed is calculated as a percentage of her taxable income. For the 2019 tax year, the percentage tax rates for single filers are as follows:10% on taxable income from $0 to $9,700,12% on taxable income over $9,700 to $39,475, and 22% on taxable income over $39,475 to $84,200. Sandra's taxable income is within the 12% tax bracket.

She owes 12% of her taxable income in federal taxes. This can be calculated as follows:

12% x $39,250 = $4,710

Her total federal tax owed is $4,710. However, she already paid $6,000 in federal withholding tax. Therefore, her refund can be calculated as follows:

Refund = Amount withheld - Amount owed Refund

= $6,000 - $4,710

Refund = $1,290

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The x-interval over which the function is increasing is:x < -1 or x > -1

Given function:[tex]y=-3x^{2} -6x+8[/tex]

The x-interval over which the function is increasing.

The given function is a quadratic function of the form f(x) = ax² + bx + c. We will determine the intervals for which the function is increasing.

To know the increasing intervals of the given function f(x), we need to determine the intervals for which f'(x) > 0 where f'(x) is the first derivative of the function.

So, Let's find the first derivative of the given function:

[tex]\begin{aligned}f(x)&=-3x^{2}-6x+8\\\Rightarrow f'(x)&=-6x-6=-6(x+1)\end{aligned}[/tex]

Now, we have to check the sign of f'(x) to find the interval(s) where the function is increasing.

Sign of f'(x) changes at x = -1. If x < -1, f'(x) > 0, so the function is increasing in that interval. Similarly, if x > -1, f'(x) > 0, so the function is increasing in that interval as well.

Therefore, the x-interval over which the function is increasing is:x < -1 or x > -1

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The sum of f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3 is 5x^2 + x + 5, while the difference is x^2 + 5x - 1. These results are obtained by adding and subtracting the corresponding terms of the two functions.



To find the sum and difference of the functions f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3, we add and subtract the corresponding terms.

For the sum, we add the like terms: (3x^2 + 2x^2) + (3x - 2x) + (2 + 3) = 5x^2 + x + 5.

For the difference, we subtract the like terms: (3x^2 - 2x^2) + (3x + 2x) + (2 - 3) = x^2 + 5x - 1.

Therefore, the sum of the functions is given by f(x) + g(x) = 5x^2 + x + 5, and the difference of the functions is given by f(x) - g(x) = x^2 + 5x - 1.

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The best description of the correlation is a weak positive correlation, and it is not likely causal.

The values of the radius and circumference show a positive trend, but the correlation is weak, indicating that the relationship between the variables is not very strong. Additionally, the measured data alone does not provide enough evidence to establish a causal relationship between the radius and circumference of the objects.

The correlation between the radius and circumference of the objects is considered weak and positive. This means that as the radius increases, the circumference tends to increase as well, but the relationship is not very strong. The measured data points show some level of association, but the correlation is not strong enough to make definitive predictions or draw causal conclusions. In other words, the data does not provide enough evidence to establish that changes in the radius directly cause changes in the circumference. Additional information or experiments would be needed to establish a causal relationship.

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The selling price of the novel would be Rs 375. The bookseller should sell the novel for Rs 375 to earn a profit of 25%. Profit percentage is a measure of the profit earned as a percentage of the cost price.

In this case, the bookseller earns a profit of 25%. To calculate the selling price, we need to determine the profit earned and add it to the cost price.

To find the profit earned, we multiply the cost price by the profit percentage. In this case, the cost price of the novel is given as Rs 300, and the profit percentage is 25%. To calculate the profit, we multiply Rs 300 by (25/100) or 0.25. The result is Rs 75, indicating that the bookseller earns a profit of Rs 75.

To obtain the selling price, we add the profit to the cost price. In this case, the cost price is Rs 300, and the profit is Rs 75. Adding them together, we get Rs 375 as the selling price of the novel.

To calculate the selling price, we need to determine the profit earned by the bookseller and add it to the cost price.

Given:

Profit percentage = 25%

Cost price of the novel = Rs 300

To calculate the profit, we multiply the cost price by the profit percentage:

Profit = 25% of Rs 300 = (25/100) * 300 = Rs 75

The selling price is obtained by adding the profit to the cost price:

Selling price = Cost price + Profit = Rs 300 + Rs 75 = Rs 375.

Therefore, the selling price of the novel is Rs 375.

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The coordinates of point M is located between lines d and e

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

M = (3 1/2, 1)

The above means that the x and the y coordinates of M are

x = 3 1/2 and y = 1

From the attached figure, we can see that

The point M with the given coordinates is located between lines d and e

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Question

Miley will place point m at the coordinate (3 1/2, 1) on the coordinate grid below

Point M will be between which 2 lines

The total length of road they built is 5 15/21 kilometers.

Here, we have,

given that,

A construction crew has just finished building a road. The crew worked for 2 2/3 days. If they built 2 1/7 kilometers of road each day.

so, we get,

The total number of days that it took the construction crew to finish the road 2 2/3.

Converting 2 2/3 days to improper fraction, it becomes 8/3 days.

If they built 2 1/7 kilometers of road each day,

converting 2 1/7 kilometers to improper fraction, it becomes 15/7 kilometers.

so, we have,

The total number of days that it took the construction crew to finish the road is 8/3 days.

they built 15/7 kilometers of road each day

Therefore, the total length of road that they built is

15/7 × 8/3

= 120/21 kilometers

Converting to mixed fraction, it becomes

5 15/21 kilometers.

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Therefore, the measures of the angles AGB, BGC, and AGC are given by:$$m\angle AGB=\frac{180^\circ}{\pi}\cdot \arctan\frac{z}{x+y+z}$$$$m\angle BGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{y}{z}$$$$m\angle AGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{x}{z}$$Thus, the solution is obtained.

Given that G is the incenter of the triangle AABC.The incenter of a triangle is the intersection point of the angle bisectors of the triangle's three angles.We have to find the measure of the angles AGB, BGC, and AGC.

Solution:Let us consider the figure below: [asy]
pair A,B,C,I; A=(-6,-3); B=(4,-3); C=(0,6); draw(A--B--C--A); I=incenter(A,B,C); draw(incircle(A,B,C)); draw(A--I--B); draw(I--C); dot(A); dot(B); dot(C); dot(I); label("$A$",A,WSW); label("$B$",B,ERS); label("$C$",C,N); label("$G$",I,NW); label("$a$",(B+C)/2,E); label("$b$",(A+C)/2,NW); label("$c$",(A+B)/2,SW); label("$x$",(I+B)/2,W); label("$y$",(I+C)/2,NE); label("$z$",(A+I)/2,NW); [/asy]

We can use the angle bisector theorem to determine the measure of the angles AGB, BGC, and AGC.Let $AB=c$, $AC=b$, and $BC=a$. Let $x$, $y$, and $z$ be the lengths of the line segments as shown in the figure above.

By the angle bisector theorem, we know that:$$\frac{AG}{BG}=\frac{b}{a}$$$$\frac{BG}{CG}=\frac{c}{b}$$$$\frac{CG}{AG}=\frac{a}{c}$$

Multiplying these three equations, we get:$$\frac{AG}{BG}\cdot \frac{BG}{CG}\cdot \frac{CG}{AG}=\frac{b}{a}\cdot \frac{c}{b}\cdot \frac{a}{c}=1$$

Thus, we have:$$\frac{x}{z}\cdot \frac{z}{y}\cdot \frac{y}{x}=1$$$$\Rightarrow \frac{x}{y}=\frac{z}{x+y+z}$$

Therefore:$$m\angle AGB=\frac{180^\circ}{\pi}\cdot \arctan\frac{x}{y}=\frac{180^\circ}{\pi}\cdot \arctan\frac{z}{x+y+z}$$

Similarly, we can show that:$$m\angle BGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{y}{z}$$$$m\angle AGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{x}{z}$$.

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The statement that correctly describes the location of the incenter of a triangle is that the incenter is equidistant from all three sides of the triangle. Therefore, the correct answer is C. The incenter is equidistant from all three sides of the triangle.

The equation for the perpendicular bisector of a segment that has endpoints (–1, 10) and (3, 6) is y

= x + 2.

The steps to solve for the equation of the perpendicular bisector are as follows:Find the midpoint of the segment by averaging the x-coordinates and the y-coordinates of the endpoints:Midpoint

= ( (-1 + 3) / 2, (10 + 6) / 2 )

= (1, 8)

Find the slope of the segment: Slope

= (6 - 10) / (3 - (-1))

= -1Use the negative reciprocal of the slope of the segment to find the slope of the perpendicular bisector:

Slope of perpendicular bisector

= 1 Use the slope and the midpoint to write the equation of the perpendicular bisector in slope-intercept form: y

= mx + b, where m is the slope and b is the y-intercept.8

= 1(1) + b, so b

= 7The equation of the perpendicular bisector is y

= x + 7.

Therefore, the correct answer is A. y

= x + 7.

The incenter is the center of the inscribed circle. Therefore, the correct answer is A. inscribed.The statement that correctly describes the location of the incenter of a triangle is that the incenter is equidistant from all three sides of the triangle. Therefore, the correct answer is C. The incenter is equidistant from all three sides of the triangle.

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The expression -12 + 10c consists of two terms: -12 and 10c. The coefficient of the variable term 10c is 10, and the constant term is -12.

In the expression -12 + 10c, we can identify the terms, coefficients, and constants as follows:

Terms:

A term is a combination of a constant and a variable, separated by an operation (usually addition or subtraction). In this expression, we have two terms: -12 and 10c.

Term 1: -12

Term 2: 10c

Coefficients:

The coefficient of a term is the numerical factor that multiplies the variable. In this expression, the coefficient of the second term (10c) is 10.

Coefficient of 10c: 10

Constants:

A constant is a term that does not contain any variable. In this expression, the constant term is -12.

Constant: -12

To summarize:

Terms:

Term 1: -12

Term 2: 10c

Coefficients:

Coefficient of 10c: 10

Constants:

Constant: -12

It's important to distinguish between terms, coefficients, and constants as they provide information about the components of the expression and their respective roles.

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He travels: (i) C is 4 km north of A. (ii) C is 6 km east of A.

(i) North of A:

The northward component from A to B is 8 km on a bearing of N30°E. To find the northward distance, we can use trigonometry. Since the bearing is N30°E, we can split it into two right-angled triangles: one facing north and one facing east.

In the northward triangle:

Opposite side = 8 km * sin(30°)

Opposite side = 8 km * 0.5

Opposite side = 4 km

Therefore, C is 4 km north of A.

(ii) East of A:

The eastward component from B to C is 6 km due East. Since this distance is directly east, it does not change the eastward position of C relative to A. Therefore, C is 6 km east of A.

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The dilation is a transformation in which a figure is enlarged or decreased. The dilation scale factor is the ratio of the distances between two pairs of corresponding points in a dilation. The distances in a dilation are measured from the center of dilation.

The relationships between point D (6, 9) and point A (8, 12) in terms of dilations are given below:Step 1: To determine the center of dilation and the scale factor, first find the distance between the two points. Let us use the distance formula to determine the distance between the two points. Distance formula Since the distance between the two points is not 1, the center of dilation is not located on the segment between the two points. As a result, we'll use the midpoint of the segment that connects the two points as the center of dilation. Center of dilation.

To find the scale factor, we must find the ratio of the distance between each point and the center of dilation.Hence, the relationship between the point D(6, 9) and the point A(8, 12) in terms of dilations is that the point D(6, 9) can be enlarged or decreased to reach the point A(8, 12) using a center of dilation of E(7, 21/2) and a scale factor of $\frac{{2\sqrt {793} }}{{61}}$.

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This interval does not contain the null hypothesis value of 7.2 hours, we can reject the null hypothesis and conclude that there is enough evidence to suggest that college students do not sleep for an average of 7.2 hours on Friday night to Saturday morning.

a) The researcher has committed a type I error in this scenario.

A type I error occurs when a null hypothesis is rejected when it is actually true. In this case, the null hypothesis is that college students sleep for an average of 7.2 hours on Friday night to Saturday morning.

The researcher has rejected this null hypothesis and concluded that college students sleep for more than 7.2 hours, but this may not be the case.

b) The confidence interval can be calculated as follows:

Margin of error = zα/2 * (σ/√n),

where α = 0.05, zα/2 = 1.96 (from the z-table for a 95% confidence level), σ = 1.2, and n = 15

Margin of error = 1.96 * (1.2/√15) ≈ 0.70

The 95% confidence interval is then (8.3 - 0.70, 8.3 + 0.70) = (7.60, 9.00)

Interpretation:

We can be 95% confident that the true mean number of hours that college students sleep on Friday night to Saturday morning is between 7.60 and 9.00 hours.

Since this interval does not contain the null hypothesis value of 7.2 hours, we can reject the null hypothesis and conclude that there is enough evidence to suggest that college students do not sleep for an average of 7.2 hours on Friday night to Saturday morning.

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To calculate the number of moles of hydrogen in a 45.3-liter container under the same conditions as Sample #1, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

Given that Sample #1 contains 2.98 moles of hydrogen at 35.1 degrees C (308.25 K) and 2.3 atm in a 32.8 L container, we can use these values to find the value of R.

R = (PV) / (nT) = (2.3 atm * 32.8 L) / (2.98 moles * 308.25 K)

Once we have the value of R, we can use it to calculate the number of moles in the 45.3-liter container at the same conditions:

n = (PV) / (RT) = (2.3 atm * 45.3 L) / (R * 308.25 K)

By substituting the appropriate values and solving the equation, we can determine the number of moles of hydrogen in the 45.3-liter container.

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The width of the river is approximately 9.17 m.

Let us consider the given figure. Using trigonometry ratios, we can find the width of the river. Suppose the width of the river is AC or BC = x meters. We need to find the value of x.

Given: AB = 10 m, ∠A = 45°, and ∠B = 60°Step 1:Find ∠AOC and ∠BOC using ∠A = 45°, and ∠B = 60°.∠AOC = ∠A + ∠C = 45° + ∠C∠BOC = ∠B + ∠C = 60° + ∠CStep 2:Find the value of ∠COC from the sum of the angles of the triangle OAC.

∠COC = 180° − (∠AOC + ∠AOC) =

180° − (45° + 45°) = 90°

Step 3:Now, we can find the length of OC.OC = AC tan ∠COC = x tan 90° = Undefined (As the tan 90° = Undefined)Step 4:Next, we can find the length of OA and OB using the sin function.

OA = AC / sin ∠AOC

= x / sin (45° + ∠C) OB

= BC / sin ∠BOC

= x / sin (60° + ∠C)

Step 5:We know that OA + OB = AB = 10 m.

Substitute the values of OA and OB in the above equation and simplify. OA + OB = x / sin (45° + ∠C) + x / sin (60° + ∠C)

= 10sin (45° + ∠C)sin (60° + ∠C)

= 10 / [2(√2 + √6)] sin (45° + ∠C)sin (60° + ∠C)

= (5 − √3) / 8 cos (30° − ∠C) / cos (30° − ∠C) × sin (45° + ∠C) / sin (60° + ∠C)

= (5 − √3) / 8 × 2 / √3 = (5 − √3) / 4 cos (30° − ∠C) / cos (30° − ∠C) × (1 / sin (45° + ∠C)) = (5 − √3) / 4cos (30° − ∠C) / sin (75° + ∠C)

= (5 − √3) / 4(1 / 2 cos (30° − ∠C)) = (5 − √3) / 4 tan (30° − ∠C)

= (5 − √3) / 3∠C

= 30° − tan −1[(5 − √3) / 3]

Putting the value of ∠C in x tan (90°) = x × Undefined, and the value of x in OA, we get, OA = x / sin (45° + ∠C)OA = 9.17 m (approx)Therefore, the width of the river is approximately 9.17 m.

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312 users accessed Schoology on mobile devices in 2016.

Given that there were 608 students using Schoology in IRSD in 2016.

Schoology is a learning management system for corporations and educational institutions that allows users to create, organise, and share materials and assignments.

Therefore, in 2016, the total number of users accessing Schoology will be 608.

Now we have to calculate the number of users who accessed Schoology on mobile devices.

Let the number of users accessing Schoology on mobile devices in 2016 be x.

Therefore, 51.5% of all users accessing Schoology on mobile devices can be given by the expression:

51.5/100 × 608 = 312.32

Hence, 312 users accessed Schoology on mobile devices in 2016.

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To find the temperature (°F) when they sell 95 ice cream cones using the model y=1.8x−76.9, we substitute 95 for x in the equation. This will give us the approximate temperature in degrees Fahrenheit.

The given model equation y=1.8x−76.9 represents the relationship between the temperature (°F) and the number of ice cream cones sold. The variable x represents the number of ice cream cones sold, and y represents the temperature in degrees Fahrenheit.

To find the temperature when they sell 95 ice cream cones, we substitute 95 for x in the equation:

y = 1.8(95) - 76.9

Calculating the expression gives us:

y = 171 - 76.9

y = 94.1

Therefore, when they sell 95 ice cream cones, the temperature is approximately 94.1°F.

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The confidence limits for the proportion of voters planning to vote for the Democratic incumbent are approximately 0.558 and 0.662.

We have,

To find the confidence limits for the proportion of voters planning to vote for the Democratic incumbent, we can use the formula for a confidence interval for a proportion.

Given:

Sample size (n) = 500

Number of respondents voting for the Democratic incumbent (x) = 305

Confidence level (1 - α) = 0.99

First, we calculate the sample proportion (p-hat):

p-hat = x / n = 305 / 500 = 0.61

Next, we calculate the standard error (SE) of the proportion:

SE = √((p-hat x (1 - p-hat)) / n)

= √((0.61 x (1 - 0.61)) / 500)

= 0.020

Using the z-score corresponding to a 0.99 confidence level, which is approximately 2.576, we can calculate the margin of error (ME):

ME = z x SE = 2.576 x 0.020 = 0.052

Finally, we can calculate the confidence interval:

Confidence Interval = p-hat ± ME

Confidence Interval = 0.61 ± 0.052

Therefore,

The confidence limits for the proportion of voters planning to vote for the Democratic incumbent are approximately 0.558 and 0.662.

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Let's denote the cost of each coffee as 'c'.Neveah bought a cupcake for $5, which we can represent as 5.

She also bought coffees for 5 coworkers, so the total cost of the coffees can be represented as 5c.

The total amount Neveah spent is $35.

Putting it all together, we can set up the equation:

5 + 5c = 35

To solve for 'c', we can isolate the variable by subtracting 5 from both sides:

5c = 30

Then, we divide both sides by 5 to solve for 'c':

c = 30/5

Simplifying the expression, we find that each coffee costs $6.

Therefore, each coffee was bought for $6.

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