Given a right triangle with the longer leg three less than three times the shorter leg and the hypotenuse
is seven less than four times the shorter leg. What are the lengths of the three sides of the triangle? Be
sure to check both solutions to answer the question correctly.

The standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided. The average expenses of the sample is $4400, but the standard deviation of these expenses is not given.

The standard deviation is a measure of the variability or dispersion of the data in a set and is calculated using a complete dataset of the expenses of all 200 patients. Without this dataset, it is not possible to determine the standard deviation of the average expenses.

Option A, less than $400, Option B, at least $400, and Option C, between $0 and $400, are all based on assumptions about the standard deviation that cannot be made without a complete dataset of expenses.

In conclusion, the standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided and a complete dataset of expenses would be needed to make any assumptions about the standard deviation.

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Complete Question: A sample of 200 patients who were hospitalised at the rwj hospital in New Brunswick incurred $4400 on average in costs. The patients' average monthly costs have a standard deviation of

A. less than $400.

B. $400 or more.

C. from $0 to $400

D. Unable to determine D.

The fraction of the area of the triangle that would be shaded in stage 7 is equal to 2,187/16,384.

No, there isn't a stage when the fraction of area shaded would be equal to 0.

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Next, we would determine the area of the triangle that would be shaded in stage 2 is as follows;

Fraction of the area = 3/4 × 3/4 = 9/16.

The area of the triangle that would be shaded in stage 3 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 = 27/64.

The area of the triangle that would be shaded in stage 4 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 = 81/256.

Therefore, the area of the triangle that would be shaded in stage 7 is as follows;

Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 = 2,187/16,384.

In this context, we can reasonably infer and logically deduce that there isn't a stage when the fraction of area shaded in this triangle would be equal to zero (0) because there is a linear relationship between the shaded and unshaded area.

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Answer:

x=1, y=3

Step-by-step explanation:

Answer:

x = 1, y = 3

Step-by-step explanation:

y = x + 2

y = -5x + 8

Using substitution:
x + 2 = -5x + 8

6x = 6
x = 1

y = 1 + 2
y = 3

The number of seats in the front row can be represented as: s = x - (n - 1) * (2y / n - x) / (n - 1) = x - (2y - nx) / n

Let's call the number of seats in the first row "s". Then, the number of seats in the second row is s + d, the number of seats in the third row is s + 2d, and so on. The total number of seats in the theater can be represented as:

s + (s + d) + (s + 2d) + ... + (s + (n - 1)d) = y

Expanding this equation and combining like terms, we get:

ns + (d * (n - 1) * n) / 2 = y

Now that we have an equation for the total number of seats in terms of n, d, and y, we can use the number of seats in the last row to solve for s, the number of seats in the first row:

s + (n - 1)d = x

ns + (d * (n - 1) * n) / 2 = y

Solving for s in terms of n, x, and y:

s = x - (n - 1)d

ns + (d * (n - 1) * n) / 2 = y

Substituting this expression for s into the equation for the total number of seats:

(x - (n - 1)d) + (d * (n - 1) * n) / 2 = y

Expanding and solving for d:

x + (n - 1)d = 2y / n

d = (2y / n - x) / (n - 1)

Finally, substituting this expression for d back into the equation for s:

s = x - (n - 1) * (2y / n - x) / (n - 1)

So the number of seats in the front row can be represented as:

s = x - (n - 1) * (2y / n - x) / (n - 1)

= x - (2y - nx) / n

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The complete question is:

A theater has n rows of seats, and each row has d more seats than the row in front of it. There are x seats in the last (nth) row and a total of y seats in the entire theater. How many seats are in the front row of the theater? Write your answer in terms of n, x, and y.

Answer:To find the number of students who want to be both a doctor and a social worker, we can use the Principle of Inclusion-Exclusion (PIE). This principle states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.

So, the number of students who want to be both a doctor and a social worker can be calculated as:

|Doctor ∩ Social worker| = |Doctor| + |Social worker| - |Doctor U Social worker|

|Doctor ∩ Social worker| = 40 + 20 - 65

|Doctor ∩ Social worker| = -5

However, this result is negative which is not possible, therefore, no students want to be both a doctor and a social worker.

To find the number of students who want to be both, we have to find the number of students who want to be both a doctor and a social worker which is 0 in this case.

Step-by-step explanation:

The answers are a) the area of wallpaper needed to cover the wall is 84 ft², b) (i) the area of a roll = 49.5 ft², (ii) the number of the roll required to cover the wall is 2 rolls, c) the cost of the rolls needed to cover the wall = 2 x 11.99 = $23.98 and d) the cost of the paint for painting the wall is $19.3116

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Given that, a wall is 8 ft high and 16 ft long, having a window, mirror and a fireplace, with dimensions, 18 in(1.5 ft) by 14 ft, 5 ft by 3 ft and 4 ft by 2 ft respectively,

a) The area of wallpaper needed to cover the wall =

The area of wallpaper = area of wall - (sum of areas of the  window, mirror and the fireplace)

= 8x16-(14x1.5+5x3+4x2)

= 128-(21+15+8)

= 84 ft²

Therefore, the area of wallpaper needed to cover the wall is 84 ft²

b) (i) The area of one roll =

The dimensions of the roll are 1.5 ft by 33 ft, area = 49.5 ft²

(ii) The number of the roll required to cover the wall = 84 ft² / 49.5 ft²

= 1.7 ≈ 2

Therefore, the number of the roll required to cover the wall is 2 rolls.

c) The cost of the rolls needed to cover the wall = 2 x 11.99 = $23.98

d) A gallon of the paint can cover 200 ft², costing $22.99/gallon,

1 ft² = 1/200 gallons

Therefore,

168 ft² = 168 x 1/200 = 0.84 gallons

Cost = 0.84 x $22.99

= $19.3116

Therefore, the cost of the paint for painting the wall is $19.3116

Hence, the answers are a) the area of wallpaper needed to cover the wall is 84 ft², b) (i) the area of a roll = 49.5 ft², (ii) the number of the roll required to cover the wall is 2 rolls, c) the cost of the rolls needed to cover the wall = 2 x 11.99 = $23.98 and d) the cost of the paint for painting the wall is $19.3116

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The complete question is attached :-

Answer:

Step-by-step explanation:

Let's call the number of cans Reggie collected as "x".

According to the problem, Tanner collected 360 cans, which was 40% of what Reggie collected, so:

360 = 40/100 * x

To find the value of x, we can isolate x by dividing both sides by 40/100:

x = 360 * 100/40

x = 900

So Reggie collected 900 cans.

Answer:

900 cans

Step-by-step explanation:

We know

360 cans = 40%

We have to find 1% by taking

360 divided by 40 = 9 cans

How many cans did Reggie collect?

We take

9 x 100 = 900 cans

Answer:  To find the ratio of the length of the shorter stick to the length of the longer stick, we need to divide the length of the shorter stick by the length of the longer stick:

11 inches ÷ 14 inches = 11/14

So, the ratio of the length of the shorter stick to the length of the longer stick is 11/14.

Step-by-step explanation:

Answer:

5.196103885259%

Step-by-step explanation:

Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).

Answer:

To solve the polynomial (g^2 + 9g + 18 = 0) using the X or Box method, you need to factor the polynomial into two binomials. To do this, you need to find two numbers that multiply to 18 and add up to 9. The two numbers are 6 and 3, so the polynomial can be factored as:

g^2 + 9g + 18 = (g + 6)(g + 3) = 0

To find the solutions, you set each factor equal to 0 and solve for g:

g + 6 = 0, so g = -6

g + 3 = 0, so g = -3

The solutions to the polynomial are g = -6 and g = -3.

Step-by-step explanation:

The area of the region bounded by the two lines is 19 square units.

The two lines intersect at the point where they have the same

y-coordinate, so we can set y=3x-6 equal to y=-2x+8 and solve for x:

3x - 6 = -2x + 8

5x = 14

x = 2.8

Therefore the two lines intersect at x=2.8, and the corresponding y-coordinate is y = 3(2.8) - 6 = 6.4.

We can find the coordinates of the two other corners of the region by setting x=0 and x=5:

x=0: y = 3(0) - 6 = -6

x=5: y = 3(5) - 6 = 13

So the other two points are (0, -6) and (5, 13).

We will use the Shoelace Theorem to find the area:

A = 1/2 * |(0 * 6.4) + (2.8 * 13) + (5 * -6) - (6.4 * 5) - (13 * 2.8) - (-6 * 0)|

A = 1/2 * |(0 * 6.4) + (37.4) + (30) - (32) - (36.4) - 0|

A = 1/2 * |37.4 + 30 - 32 - 36.4|

A = 1/2 * |38| = 19

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Answer:

Step-by-step explanation:

The solution for side b is 12.4 cm

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

< A = 50⁰, < B = 72º and a = 10cm.

Uing the law of sines, we have

a/sin(A) = b/sin(B)

Substitute the known values in the above equation, so, we have the following representation

10/sin(50) = b/sin(72)

So, we have

b = sin(72) * 10/sin(50)

Evaluate

b = 12.4

Hence, the length is 12.4 cm

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Yes, 6xy² is the greatest common factor of 12xy², 36x²y², and 42 xy⁴. The Greatest common factor is the highest common factor of all the given numbers.

We can find the greatest common factor by applying the prime factorization method. There are two steps involved to find the highest common factor.

Step 1

The factors of the numbers are

Factors of 12 are 1,2,3,4,6,12

Factors of 36 are 1,2,3,4,6,9,12,18,36

Factors of 42 are 1,2,3,6,7,14,21,42

The common factor for 12,36,42 are 1,2,3,6

Therefore, the greatest common factor for 12,36,42 is 6.

Step 2

We have to find the common factors for the variable parts x¹,y²,x²,y²,x¹,y⁴

The factor for x¹ is x itself.

The factors for y² is y⋅y

The factors for x² are x⋅x

The factors for y² are y⋅y

The factor for x¹ is x itself.

The factors for y⁴ are y⋅y⋅y⋅y

Hence, the common factors for the variables

x¹,y²,x²,y²,x¹,y⁴ are x⋅y⋅y

The GCF for the variable part is xy².

Now, multiply the GCF of the numerical part i.e.6 and the GCF of the variable part i.e. xy².

Therefore, it comes out to be 6xy².

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The artist reportedly got $225 or $275 for her paintings this week, depending on the statement provided.

We might, for instance, move to the city. Most likely, he will start classes again in the fall. If we could finish the job by tomorrow, that would be perfect. In the worst-case scenario, we would have to commence the project over.

Let x become the sum the artist got this week for her works in Part A.. The situation is represented by the absolute value equation:

|250 - x| = 25

Part B: To solve the equation, we can split it into two cases:

Case 1: 250 - x = 25

Solving for x, we get:

x = 250 - 25 = 225

Case 2: 250 - x = -25

Solving for x, we get:

x = 250 + 25 = 275

Therefore, the artist received either $225 or $275 for her prints this week.

Part C: The minimum amount the artist received is $225, which is $25 less than her goal of $250. The maximum amount the artist received is $275, which is $25 more than her goal of $250.

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The given assertion states that the sequence's nth element is -k² + (2n-3)k + 1.

Sequential is a derivative of the Latin word consecutus, which means "following closely" without a pause. Similar to those snowstorms, which occurred back-to-back each day for five months in a succession. Additionally, consecutive numbers progress in the correct sequence or follow one another. For instance, the numerals 5, 6, 7, 8, 9, and 10 follow one another.

Looking at the differences between consecutive terms, we have:

(k+2) - (-k²-k+1) = k²+3k+3 - (k+2) = k²+2k+1 = (k+1)²

(k²+3k+3) - (k+2) = k²+2k+1 = (k+1)²

(2k²+5k+4) - (k²+3k+3) = k²+2k+1 = (k+1)²

We can see that the differences between consecutive terms are all the same, which means that the sequence is an arithmetic sequence.

To find tₙ, we need to find the common difference d. From the differences above, we have:

d = (k+1)² - (k²+k-1) = 2k

So, the nth term of the sequence is given by:

tₙ = t₁ + (n-1)d

tₙ = (-k²-k+1) + (n-1)(2k)

tₙ = -k²-k+1 + 2nk - 2k

tₙ = -k² + (2n-3)k + 1

Therefore, the nth term of the sequence is -k² + (2n-3)k + 1.

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The intensity of the transmitted light, [tex]I_{t}[/tex], is equal to half of the original intensity, [tex]I_{0}[/tex].

Given θ = 45° and cosθ = [tex]\sqrt\frac{I_{t} }{I_{0} }[/tex]

When polarized light with intensity [tex]I_{0}[/tex] strikes a polarized filter with its axis at an angle θ with the vertical, the intensity of the transmitted light, [tex]I_{t}[/tex], depends on the angle θ and the original intensity [tex]I_{0}[/tex]. The relationship between [tex]I_{t}[/tex] and [tex]I_{0}[/tex] is described by the equation cosθ = [tex]\sqrt\frac{I_{t} }{I_{0} }[/tex].

If θ = 45°, then the equation θ can be simplified to cos 45° =[tex]\sqrt\frac{I_{t} }{I_{0} }[/tex].

The cosine of 45° is equal to [tex]\frac{1}{\sqrt{2} }[/tex], so we have:

[tex]\frac{1}{\sqrt{2} }=\sqrt\frac{I_{t} }{I_{0} }[/tex]

On Squaring both sides, we have:

[tex]\frac{1}{{2} }=\frac{I_{t} }{I_{0} }[/tex]

Multiplying both sides by [tex]I_{0}[/tex], we have:

[tex]I_{t}=\frac{I_{0} }{2}[/tex]

Therefore, if θ = 45°, the intensity of the transmitted light, [tex]I_{t}[/tex], is equal to half of the original intensity, [tex]I_{0}[/tex].

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Answer:

$ 31.45

Step-by-step explanation:

15% = 0.15 x 37 = 5.55$ off the original price so 31.45$ is the final price for the tee shirt. Give brainlist please

Sale price for the given shirt will be $32.

According to question given are-

Percentage of the reduction rate of the shirt is = 15%

Reduction Percentage refers to the percentage rate at which the Initial Per Certificate Entitlement will diminish daily, assuming that the daily rate will be calculated as the annual rate given in the Final Terms divided by 365 and applied as necessary.

Actual cost of the shirt is = $37.

decreased rate "Reduced rate" refers to a contribution rate that is lower than the standard rate required by State law, while "standard rate" refers to the rate used to compute variances from that rate.

So, accordingly Reduction rate = (Actual rate X Reduction Percentage)/100

Reduction = (37×15)/100 = Rs 5.55$ ≅ 5$

So the sale price = 37−5 = 32$

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The graph of the problem depicts the rate of the temperature change.

To graph temperature change, you can use a line graph. The horizontal axis represents time, while the vertical axis represents temperature. You plot points on the graph corresponding to the recorded temperature at specific times, and then connect the points to form a line.

The slope of the line represents the rate of temperature change, with a steep line indicating a rapid increase or decrease in temperature and a gentle slope indicating a slow change. The line graph helps to visually represent changes in temperature over time and can be used to analyze patterns and trends.

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The probability that the chip drawn from urn II is red is 4/15. Let's call the event that the chip drawn from urn I and transferred to urn II is red "R1", and the event that the chip drawn from urn II is red "R2".

The probability of event R1 is 2/6 = 1/3.

Given that event R1 has occurred, the number of red chips in urn II becomes 4, and the number of total chips becomes 4+1=5. The probability of event R2 is 4/5 = 4/5.

The probability of both events occurring is (1/3) * (4/5) = 4/15.

So, the probability that the chip drawn from urn II is red is 4/15.

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The evaluation of the possible graph and table in the question, which indicates proportional relationships are presented as follows;

Part A: The rate of change of a bushel of corn in the current year is; 8 dollars per bushel of corn

Part B: Tnhe price of a bushel of corn in the current year is three dollars ($3) more than the price in the previous year.

A proportional relationship is one in which the output variable of the relationship, is a multiple of the input variable and factor.

The points on the graph in the question, obtained from a similar question posted on the website are;

(0, 0), (3, 24), (6, 46), (9, 72), (12, 76), (15, 120), (18, 144)

Part A: The slope is the rate of change of the bushel of corn. Therefore, the rate of change for the current year can be found by finding the slope as follows;

The graph is a straight line graph, indicating a proportional relationship therefore, the slope of the graph is a constant, which can be found as follows;

Slope = (24 - 0)/(3 - 0) = 8

The rater of change of the bushel for the current year is; 8 dollars per bushel of corn

Part B: Whereby the values in the table for the number of bushels to the price of corn for the previous year can be presented as follows;

Number of Bushels [tex]{}[/tex]   Price of Corn (dollars)

2        [tex]{}[/tex]                            10

4        [tex]{}[/tex]                            20

6        [tex]{}[/tex]                            30

8        [tex]{}[/tex]                            40

The rate of change of the price for the previous year is therefore;

Rate of change = (20 - 10)/(4 - 2) = 5

The rate of change for the previous year is therefore 5 dollars per bushel

The price of a bushel in the current year is three more dollar than the price of a bushel in the previous year.

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Answer:

I. 11%
II. ₹ 1110 in interest over 3 years

Step-by-step explanation:

To solve for the interest rate and the total interest earned, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where A is the maturity amount, P is the principal, r is the interest rate, n is the number of times compounded per year, t is the time in years, and

Since we know the maturity amount (A = ₹ 10,110), the principal (P = 250 * 12 * 3 = 9,000), and the time (t = 3 years), we can rearrange the formula to solve for the interest rate:

r = n * ((A/P)^(1/nt) - 1)

We'll assume that the interest is compounded monthly, so n = 12. Then:

r = 12 * ((10110/9000)^(1/36) - 1)

r ≈ 0.11

So, the interest rate is approximately 11% per year.

To find the total interest earned, we can use the formula:

Interest = A - P

Interest = 10110 - 9000

Interest = 1110

So, Mr Sharma earned ₹ 1110 in interest over 3 years.

Answer:

The equation is not true.

Step-by-step explanation:

Starting with the left side,

sin²(θ) - cos²(θ) = 1 - cos²(θ) - cos²(θ) = 1 - 2cos²(θ)

The right side,

2 sin²(θ) - 1 = 2(sin²(θ) - 0.5)

Thus, in general, sin²(θ) - cos²(θ) ≠ 2 sin²(θ) -1.

Answer:

Step-by-step explanation:

x will be the original weight.

2x - 20 = 180

2x = 200

x = 100

If a car was driving at a speed of 40 miles per hour and slams on its brakes the vehicle will produce a skid mark that measures around 64.2 feet.

Equation v = √(32fd), where f is the surface's coefficient of friction, relates the speed, v (in feet per second), to the length of the skid mark, d (in feet).

To begin, we may convert the car's starting speed from miles per hour to feet per second:

25 miles/hour × 5280 feet/mile / 3600 seconds/hour ≈ 36.7 feet/second

In order to solve for d, we may then enter the above numbers into the equation v = √(32fd):

36.7 = √(32 × 0.5 × d)

36.7² = 32 × 0.5 × d

d = (36.7²)/(32 × 0.5) ≈ 64.2 feet

As a result, the vehicle will produce a skid mark that measures around 64.2 feet.

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Quinn will need 8 cups of sugar to make 16 pies based on the table that shows the ratio of pies and sugar.

What we know from the question:

3 pies = 1 ½ cups of sugar

5 pies = 2 ½ cups of sugar

9 pies = 4 ½ cups of sugar

16 pies = ?

To make it easier, the answer will be explained through sentence:

First, we find out how much sugar it takes to make one pie. Use one of the ratio provided above by dividing the pie amount with the sugar’s. For example, 3 divided by 1 ½ equals ½ .

Therefore, one pie would require only ½ cups of sugar. Crosscheck with the other ratio to make sure it is correct using the same method earlier.

Second, we find out how much sugar it takes to make 16 pies. Multiply the amount of pies with the amount of sugar. So 16 x ½ equals 8.

Here are the summary

1 pies = ½ cups of sugar

16 pies = 8 cups of sugar

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The mean for boxplot #3 should be less than its median. In a negatively skewed distribution, the mean is less than the median.

This is because the few small values in the data pull the mean down, while the median is still at the middle value. A boxplot can give us an idea of the shape of the distribution, and if it is negatively skewed, it suggests that the mean will be less than the median.

It's important to note that without actually seeing the boxplot, this conclusion may not be accurate. There could be other factors that affect the mean and median, such as outliers or the size of the sample. However, based on the information given that the boxplot is negatively skewed, it is likely that the mean will be less than the median.

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Answer:

486 Calories

Step-by-step explanation:

175/9 = # of Calories for EACH Starburst

25 x 175/9

4375 / 9 = 486 1/9

Answer: 486 calories

Step-by-step explanation:

175 / 9 = 19.4444444444 calories per piece

25 starbursts = 19.4444444444 * 25= 486.111111111

Rounded = 486 calories

(5, 1, -3, 5.8, -11,)

Step-by-step explanation:

basically rage is y value. and domain is x value. so in this question the domain value are given so since domain is the value of x you have to substitute the number into the x. then you get the range. the answer are (5, 1, -3, 5.8, -11,)

The volume of the cylinder is approximately 6058.73 cubic meters.

A cylinder is a three-dimensional geometric shape that is similar to a tube. It has two parallel bases that are circular in shape, and its lateral surface is a rectangle. The height of the cylinder is the distance between the two bases. The cylinder has a top base and a bottom base, and these are both circles with the same diameter. The volume of a cylinder can be found by multiplying the area of one of its circular bases by its height. The surface area of a cylinder can be found by adding up the areas of the two circular bases and the lateral surface. Cylinders are widely used in mathematics, engineering, and physics, and they play an important role in the study of various geometric and physical concepts.

Given the diameter of a cylinder is 34m and its height is 27m, we can find the volume of the cylinder using the formula:

Volume = π × (diameter / 2)² × height

Plugging in the values, we get:

Volume = 3.14 × (17 / 2)² × 27

Volume = 3.14 × (8.5)² × 27

Volume = 3.14 × 72.25 × 27

Volume = 6058.73 cubic meters

So, the volume of the cylinder is approximately 6058.73 cubic meters.

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