In 1852, an Indian mathematician, Radhanath Sikdar, used measurements and trigonometry to calculate the height of Peak XV in the Himalayas (later to be named Mount Everest). This required the use of a device that measured angles from the ground to the top of an object. By measuring the angle to the top of Peak XV from two different spots, and knowing the distance between these spots, Sikdar may have come up with a drawing like the following: The angle of elevation to the top of the peak (from point B) was measured to be 32 degrees. From a point 17409.7 feet closer (point A), the angle of elevation was 45 degrees. Find the height Sikdar calculated for Peak XV.

In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2, then the slope of AB is 2.

What is the diameter of the circle?

The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle.

We have that,

ABC is a right triangle

so,

AB is perpendicular to BC

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1.

so,

m1 * m2 = -1

in this problem

mAB * mBC =-1

solve for mAB

mAB = -1 / mBC

mAB = -1 / -1/2

mAB = 2

therefore, In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2, then the slope of AB is 2.

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Complete Question:

In the diagram, AC is the diameter of circle O. If the slope of BC is -1/2, what is the slope of AB?

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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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.

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 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:

Step-by-step explanation:

x will be the original weight.

2x - 20 = 180

2x = 200

x = 100

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.

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:

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

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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The surface area of the cube of side length 0.125 inches is given as follows:

S = 0.09375 in².

The surface area for a cube of side length a is given by the equation presented as follows:

S = 6a².

The side length in this problem has the value given as follows:

a = 1/8 = 0.125 in.

Hence the surface area of the cube is calculated as follows:

S = 6(0.125)²

S = 0.09375 in².

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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:

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.

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 :-

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 correct Option for this question is option C i.e. x= 4tan34°. The other options which are given in the question are incorrect.

The Right angled triangle along with the base angle of 34°. The base is equal to 4.

θ= 34°

To find the value of x which is equal to the perpendicular of the right-angled triangle

According to the trigonometric ratio

tanθ = Perpendicular ÷ base

According to the above formula

tan 34 = x ÷ 4

Now, we have to multiply each side by 4.

x= 4× tan34° which means x= 4tan34°

tan 34° = 0.6745

x= 4× 0.6745

X=2.70

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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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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:

Step-by-step explanation:

Domain: The domain of the function is all real numbers.

Range: The range of the function is all real numbers less than or equal to 8. To see this, note that the leading coefficient of the polynomial is negative (-x^3), so the function approaches negative infinity as x approaches positive or negative infinity. The largest y-value the function can attain is 8, which occurs at x = 2.

Relative maxima and minima: To find the relative maxima and minima, we find the critical points of the function, which are the values of x that satisfy f'(x) = 0 or f'(x) does not exist. The first derivative of the function f(x) is given by:

f'(x) = -3x^2 + 16x - 15

Solving f'(x) = 0, we get:

-3x^2 + 16x - 15 = 0

x = 1, 5

We also need to determine the concavity of the function near each critical point to determine whether each is a relative maximum or minimum. To do this, we find the second derivative of the function and evaluate its sign at each critical point. The second derivative of f(x) is given by:

f''(x) = -6x + 16

Since f''(x) is always negative, the function is concave down and therefore has a relative maximum at x = 1 and a relative minimum at x = 5.

End behavior: The leading term of the function is -x^3, which means the function approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity. The end behavior of the function is therefore negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

Increasing and decreasing intervals: To find the increasing and decreasing intervals of the function, we find the critical points and the sign of f'(x) in the intervals between the critical points.

f'(x) = -3x^2 + 16x - 15

Since f'(x) is negative for x < 1 and positive for x > 1, the function is decreasing for x < 1 and increasing for x > 1. Similarly, since f'(x) is positive for x < 5 and negative for x > 5, the function is increasing for x < 5 and decreasing for x > 5. So, the increasing intervals are (negative infinity, 1) and (1, 5) and the decreasing intervals are (5, positive infinity).

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 number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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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

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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(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 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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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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