Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°. Find the height, h, of the lighthouse. Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse. To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations

Final answer:

To convert the temperature of Savannah's liquid from Celsius to Fahrenheit, use the equation °F = (°C × 9/5) + 32. Savannah's temperature in Celsius is 50°, so her temperature in Fahrenheit is 122°F.

Explanation:

To convert the temperature from Celsius to Fahrenheit, you can use the equation:
°F = (°C × 9/5) + 32.
In this case, Savannah's temperature in Celsius is 50°. Using the equation, we can calculate her temperature in Fahrenheit as:
°F = (50 × 9/5) + 32 = 122°F.
Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.

Savannah's liquid, initially measured at 50°C, converts to 122°F using the formula F = C x (9/5) + 32.

To convert the temperature from degrees Celsius to degrees Fahrenheit, we use the conversion formula: F = \( C \times \frac{9}{5} + 32 \), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.

In Savannah's case, she measured the temperature as 50°C. Applying the conversion formula:

Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.

To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:

z = (x – u) / s

Where,

u = the sample mean = 68

s = standard deviation of the samples = 12

x = sample value = 70

In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.

z = (70 – 68) / 12

z = 2 / 12

z = 0.17

Therefore finding for P at z ≥ 0.17 using the standard distribution tables:

P (z = 0.17) = 0.5675

But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:

P (z ≥ 0.17) = 1 - 0.5675

P (z ≥ 0.17) = 0.4325 = 43.25%

The probability that the sample mean is larger than 70 is 43.25%

The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.

To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).

The standard error of the mean is calculated using the formula:

SE = σ / √n

Where σ is the population standard deviation and n is the sample size.

In this case:
σ = 12
n = 40

Therefore,

SE = 12 / √40 ≈ 1.8974

The z-score is calculated using the formula:

z = (M - μ) / SE

Where M is the sample mean,
μ is the population mean,
SE is the standard error.

Given,
μ = 68
M = 70

Therefore,

z = (70 - 68) / 1.8974 ≈ 1.054

Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.

However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,

1 - 0.8531 ≈ 0.1469

Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.

By multiplying the course options together for Humanities, Sociology, Science, Math and Music (2*2*6*6*8), we found that there are a total of 576 different sets of five courses.

To answer this question, we have to calculate the number of different sets of five courses. This can be done by multiplying the number of choices available for each requirement. So, if you have 2 humanities​ courses, 2 sociology​ courses, 6 science​ courses, 6 math​ courses, and 8 music courses to decide from, the calculation would be as follows:

We then multiply these options together (2*2*6*6*8) to get the total number of different sets of courses possible, which is 576.

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To find the total number of different sets of five courses, multiply the number of choices for each course category: 2 (Humanities) × 2 (Sociology) × 6 (Science) × 6 (Math) × 8 (Music). This results in 1152 different sets of five courses.

To determine the number of different sets of five courses possible, we need to consider the choices available for each category:

- Humanities: 2 choices

- Sociology: 2 choices

- Science: 6 choices

- Math: 6 choices

- Music: 8 choices

The total number of different sets of five courses can be found by multiplying the number of choices in each category together. Here is the calculation:

2 × 2 × 6 × 6 × 8

Let's calculate this step-by-step:

1. 2 × 2 = 4

2. 4 × 6 = 24

3. 24 × 6 = 144

4. 144 × 8 = 1152

Therefore, the number of different sets of five courses possible is: 1152

Final answer:

The warehouse has a volume of 252,000 cubic feet, calculated using the corrected dimensions of 140 feet in length, 100 feet in width, and an 18-foot ceiling.

Explanation:

To calculate the volume of a warehouse, we use the formula for the volume of a rectangular prism, which is length × width × height. However, the question contains a typo about the width of the warehouse.

We are informed that the correct width is 100 feet, not 610 feet.

Given the corrected dimensions (140 feet by 100 feet with an 18 foot ceiling), we can now calculate the volume of the warehouse.

Volume = length × width × height
= 140 feet × 100 feet × 18 feet
= 252,000 cubic feet.

Therefore, the warehouse has a volume of 252,000 cubic feet of space.

Answer:

[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]

Step-by-step explanation:

Here the "X" Values are given, thus the corresponding "Y" values will be

[tex]Y = log (3 X)\\a) X = \frac{1}{1} , Y =  log (3 * \frac{1}{3} ) = log (1) = 0\\b) X = 1, Y = log (3*1) = log (3) = 0.477\\c) X = 3, Y = log (3*3) = log (9) = 0.954\\d) X = 9, Y = log (3*9) = log (27) = 1.43\\e) X = 27, Y = log (3* 27) = log (81) = 1.90\\f) X = 81, Y = log (3 * 81) = log (243) = 2.385\\[/tex]

So the pattern would be

[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]

The area of the smaller polygon with a side ratio of 3:4 is 180 m2 for the smaller polygon.

When dealing with the areas of similar polygons, if the ratio of corresponding sides is given, such as 3:4 in this case, the ratio of their areas is the square of the ratio of their sides. This is because the area is a two-dimensional measure, so each dimension is scaled by the ratio.

Given that the area of the larger polygon is 320 , we establish that the scale factor is 3 for the smaller polygon and 4 for the larger one.

To find the area of the smaller polygon, we use the fact that the ratio of the areas is (3/4)2 = 9/16.

This means that the area of the smaller polygon is 9/16 times the area of the larger polygon. Therefore, focusing on the comparison of areas, we calculate:

Area of smaller polygon = (9/16) x Area of larger polygon

= (9/16)  x 320

Area of smaller polygon = 180

Answer:

Answer: Reference angle is π/3 Radians

Step-by-step explanation:

The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

I. -(-6) = 6 and -(-4) > -4

Here -(-4) > -4 is incorrect

-(-4) = 4 is correct

These statements are not true

III. 5 + 6 = 11 or 9 - 2 = 11

Here 9 - 2 = 11 is incorrect

So 9 - 2 = 7  is correct

These statements are not true

II. -(-4) < 4 or -10 > 10 - 10

Here -(-4) < 4 is incorrect

So -(-4) = 4 is correct

These statements are not true

IV. 17 > 2 or 6 < 9

Here 17 is greater than 2 and 6 is less than 9 is always true.

Hence, the correct answer would be an option (D)

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Answer:

D.  [tex](x-7)^3[/tex]

Step-by-step explanation:

Given functions are,

[tex]f(x) = x-7-----(1)[/tex]

[tex]g(x)=x^3-----(2)[/tex]

Now,

[tex]g(f(x))=g(x-7)[/tex]     ( From equation (1) ),

[tex]=(x-7)^3[/tex]            ( From equation (2) ),

[tex]\implies g(f(x)) = (x-7)^3[/tex]

Hence, Option D is correct.

a. The required equation is x² - 16x + 48 = 0

b. I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

a.

The required equation is x² - 16x + 48 = 0

Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.

So, y = -10x² + 160x - 430

-10x² + 160x - 430 = 50

-10x² + 160x - 430 - 50 = 0

-10x² + 160x - 480 = 0

Dividing through by -10, we have

x² - 16x + 48 = 0

So, the required equation is x² - 16x + 48 = 0

b.

I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

To determine the method you would use to solve the equation, you would need to determine the value of the discriminant.

For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac

Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48

= 256 - 192

= 48

= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,

So, x² - 16x + 48 = 0

x² - 4x - 12x + 48 = 0

x(x - 4) - 12(x - 4) = 0

(x - 4)(x - 12) = 0

x - 4 = 0 or x - 12 = 0

x = 4 or x = 12

I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

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Answer:

A is the answer

Final answer:

The mean test score for the group is calculated by summing the products of each unique score and the number of students who received it, then dividing by the total number of students. In this case, the mean test score is 77.

Explanation:

To calculate the mean test score for the group, you multiply each score by the number of students who received it, then sum all those products, and finally divide by the total number of students. Four students scoring 90 would contribute 4 x 90 = 360 to the total sum. Three students scoring 70 contribute 3 x 70 = 210. Two students scoring 60 contribute 2 x 60 = 120. One student scoring 80 adds 80 to the sum. The total sum of all scores is 360 + 210 + 120 + 80 = 770. Since there are a total of 10 students (4 + 3 + 2 + 1), the mean score is calculated as 770 ÷ 10 = 77. Therefore, the mean test score in this group is 77.

The number of words Jean will type when she completes 60 minutes of typing is  3,000, This is further explained below Option C is correct

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, The graph and table show the relationship between y and x

And the graph shows 3000 at "the number of words Jean has typed for her essay" axis denoted by y, for what she completes 60 minutes.

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Answer:

A

Step-by-step explanation:

The sum of measures of all the exterior angles of ANY POLYGON is 360°.

The measure of each exterior angle of ANY POLYGON is [tex]\frac{360}{n}[/tex]

where [tex]n[/tex] is the number of sides of the polygon

A hexagon has 6 sides, thus the measure of each exterior angle of a hexagon is:

[tex]\frac{360}{6}=60[/tex] degrees

Answer choice A is correct.

The solution would be like this for this specific problem:

f(x) = x^2 + sin(x) 

f '(x) = 2x + cos(x) 

The minimum value is at f '(x) = 0, 

So, let g(x) = 2x + cos(x) 

Thus, g '(x) = 2 - sin(x) 

x(new) = x - g(x) / g '(x) 
or 
x(new) = x - [2x + cos(x)] / [2 - sin(x)] 

Calculation 

x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)] 
= -0.4506266931 
x2 = -0.4501836476 
x3 = -0.4501836113 
x4 = -0.4501836113 

This value for x, f(x) = -0.2324655752. 

After converting to 6 decimal places: the minimum point is (-0.450184, -0.232466).

Final answer:

To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.

Explanation:

To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).

Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.

The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).

Answer:

the answer is the first option : A

Step-by-step explanation: