Tom is driving towards a building. When he first looks up at the top of the building, he looks up at an angle of elevation of 47 degrees. After driving 500 feet towards the building, he is now looking up at an angle of elevation of 54 degrees. How tall is the building?

The probability that the sample mean would differ from the true mean by less than 5.4 months is approximately 1.0000 or 100%.

We are given the following information:

1. The mean life of a television set (µ) is 138 months.
2. The variance (σ²) is 324 months.
3. We have a sample of 83 televisions (n).
4. We want to find the probability that the sample mean (X) differs from the true mean by less than 5.4 months.

First, let's find the standard deviation (σ) by taking the square root of the variance:
σ = √324 = 18 months

Next, we'll find the standard error (SE) using the formula SE = σ / √n:
SE = 18 / √83 ≈ 1.974

Now, let's find the Z-score corresponding to the desired difference of 5.4 months:
Z = (5.4 - 0) / 1.974 ≈ 2.734

Using a Z-table or calculator, we find the probability corresponding to Z = 2.734 is approximately 0.9932. Since we're looking for the probability that the sample mean differs from the true mean by less than 5.4 months, we need to consider both tails of the distribution (i.e., the probability of the sample mean being 5.4 months greater or 5.4 months lesser than the true mean). So, we need to calculate the probability for -2.734 as well, which is 1 - 0.9932 = 0.0068.

Finally, we'll add the probabilities for both tails to get the answer:
P(-2.734 < Z < 2.734) = 0.9932 + 0.0068 = 1.0000

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If a random sample of 29 time intervals between eruptions has a mean greater than 106, it may be concluded that the average time between eruptions is longer than 106 units of time. However, it is important to note that the sample size of 29 may not be representative of the entire population of time intervals between eruptions, and therefore the conclusion drawn may not be entirely accurate.
Additionally, it is important to consider the variability of the data. If the standard deviation of the sample is high, it may indicate that there is a wide range of time intervals between eruptions, making it difficult to draw a definitive conclusion. On the other hand, if the standard deviation is low, it may indicate that the time intervals are more consistent, and the conclusion drawn may be more reliable.

Overall, it is important to consider both the mean and variability of the sample when drawing conclusions about the population of time intervals between eruptions. Further research and analysis may be necessary to validate the findings and provide a more accurate answer.

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Answer:

54°

Step-by-step explanation:

\(\sin A = \cos B \: \: \: (Given) \\ \\ \implies \: \sin 36 \degree = \cos B \\ \\ \implies \: \cos(90 - 36 ) \degree = \cos B \\ \\ \implies \: \cos \: 54\degree = \cos B \\ \\ \implies \:m \angle B = 54\degree\)

Answer:

523.6 cm^3

Step-by-step explanation:

We know the diameter is 10. The radius is half the diameter, so 10/2=5.

Knowing the radius is 5, we just need to plug it into the formula.

Volume=(4/3)pi5^3

≈523.6

Answer:523.6 cm^3

a. The probability that the sample mean score is less than 589 is approximately 0.0455.

b.  The probability that the sample mean score is between

575 and 610 is 0.2576.

c. The 85th percentile of the sample mean is 620.65

d.  It would be somewhat unusual if the sample mean were greater than 620.

e. It would not be unusual for an individual to get a score greater than 620, since the probability is relatively high (about 54%).

(a) To find the probability that the sample mean score is less than 589, we need to calculate the z-score and then use a normal distribution table or calculator to find the corresponding probability. The z-score is calculated as:

z = (x - μ) / (σ / √n) = (589 - 605) / (136 / √76) = -1.69

Using a normal distribution table or calculator, the probability corresponding to a z-score of -1.69 is 0.0455.

(b) To find the probability that the sample mean score is between 575 and 610, we need to calculate the z-scores for both values and then use a normal distribution table or calculator to find the area between them. The z-scores are:

z1 = (x1 - μ) / (σ / √n) = (575 - 605) / (136 / √76) = -2.21

z2 = (x2- μ) / (σ / √n) = (610 - 605) / (136 / √76) = 0.61

Using a normal distribution table or calculator, the probability corresponding to a z-score of -2.21 is 0.0138, and the probability corresponding to a z-score of 0.61 is 0.2714. Therefore, the probability that the sample mean score is between 575 and 610 is approximately 0.2714 - 0.0138 = 0.2576.

(c) To find the 85th percentile of the sample mean, we need to find the z-score that corresponds to an area of 0.85 to the left of it. Using a normal distribution table or calculator, we can find that the z-score is approximately 1.44. Therefore, the 85th percentile of the sample mean is:

x = μ + z(σ / √n) = 605 + 1.44(136 / √76) ≈ 620.65

(d) To determine whether it would be unusual if the sample mean were greater than 620, we need to find the corresponding probability. The z-score is calculated as:

z = (x - μ) / (σ / √n) = (620 - 605) / (136 / √76) ≈ 1.33

Using a normal distribution table or calculator, the probability corresponding to a z-score of 1.33 is approximately 0.0918. Therefore, it would be somewhat unusual (but not extremely rare) if the sample mean were greater than 620.

(e) To determine whether it would be unusual for an individual to get a score greater than 620, we need to convert the score to a z-score and then find the corresponding probability. Assuming that the variable is normally distributed, the z-score is calculated as:

z = (x - μ) / σ = (620 - 605) / 136 ≈ 0.11

Using a normal distribution table or calculator, the probability corresponding to a z-score of 0.11 is approximately 0.5440. Therefore, it would not be unusual for an individual to get a score greater than 620, since the probability is relatively high (about 54%).

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Answer:

£9

Step-by-step explanation:

1:8=9

?:72

72÷9=8

9×1=9

The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.

To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.

Given:

f(x) = 2(3 - x) - 2x, we have:

-10 = 2(3 - x) - 2x

Let's simplify the equation step by step:

-10 = 6 - 2x - 2x

-10 = 6 - 4x

-10 - 6 = -4x

-16 = -4x

To solve for x, divide both sides by -4:

x = (-16) / (-4)

x = 4

Therefore, when f(x) = -10, the value of x is 4.

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Answer:

Using the 30-60-90 triangle to find sine and cosine

sin(60 degrees) = 2√3 4.

sin(60 degrees) = √3 2.

sin(30 degrees) = 2 4.

sin(30 degrees) = 1 2.

cos(60 degrees) = 2 4.

cos(60 degrees) = 1 2.

cos(30 degrees) = 2√3 4.

cos(30 degrees) = √3 2.

The equilibrium point is (60, 2400), the consumer surplus at the equilibrium point is $48,000, and the producer surplus at the equilibrium point is $36,000.

(a) The equilibrium point occurs when the quantity demanded by consumers equals the quantity supplied by producers. To find this point, we need to set the demand function equal to the supply function and solve for x.

Demand function: D(x) = 3000 - 10x

Supply function: S(x) = 900 + 25x

Setting D(x) equal to S(x):

3000 - 10x = 900 + 25x

Simplifying the equation:

35x = 2100

x = 60

Therefore, the equilibrium point occurs at x = 60.

(b) Consumer surplus at the equilibrium point can be found by calculating the area between the demand curve and the equilibrium price. Consumer surplus represents the difference between the price consumers are willing to pay and the actual market price.

At the equilibrium point, x = 60. Plugging this value into the demand function:

D(60) = 3000 - 10(60)

D(60) = 3000 - 600

D(60) = 2400

The equilibrium price is $2400 per unit. To find the consumer surplus, we need to calculate the area of the triangle formed between the demand curve and the equilibrium price.

Consumer surplus = (1/2) * (2400 - 900) * 60

Consumer surplus = $48,000

(c) Producer surplus at the equilibrium point represents the difference between the actual market price and the minimum price at which producers are willing to sell their goods.

To find the producer surplus, we need to calculate the area between the supply curve and the equilibrium price.

At the equilibrium point, x = 60. Plugging this value into the supply function:

S(60) = 900 + 25(60)

S(60) = 900 + 1500

S(60) = 2400

The equilibrium price is $2400 per unit. To find the producer surplus, we need to calculate the area of the triangle formed between the supply curve and the equilibrium price.

Producer surplus = (1/2) * (2400 - 900) * 60

Producer surplus = $36,000

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Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

The percentage off of the coupon is 25%

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

Normal price = $24

Amount saved = $6

The above parameters mean that

Percentage of the coupon = Amount saved/Normal price

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

Percentage of the coupon = 6/24

Evaluate

Percentage of the coupon = 25%

Hence, the percentage is 25%

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Answer: 75%

Step-by-step explanation:

35% of 5 liters is 1.75 liters

1.75 liters + 8 liters = 9.75 liters (only juice)

(5 liters + 8 liters = 13 liters) (the whole thing)

So, 9.75/13 is 75%

Answer:

x=147°

Step-by-step explanation:

BEING THE CORRESPONDING ANGLES ARE ALWAYS EQUAL.....

Answer:

By the Parallelogram Consecutive Angles Theorem, ∠NQL is supplementary to ∠QNM

Step-by-step explanation:

By the Parallelogram Consecutive Angles Theorem, ∠NQL is supplementary to ∠QNM

This means m∠NQL + m∠QNM = 180

80 +  m∠QNM = 180

m∠QNM = 180 - 80 = 100

By the Parallelogram Consecutive Angles Theorem, ∠NQL is supplementary to ∠QNM

which theorem is used in this parallelogram?

By the Parallelogram Consecutive Angles Theorem, ∠NQL is supplementary to ∠QNM

This means m∠NQL + m∠QNM = 180

80 +  m∠QNM = 180

m∠QNM = 180 - 80 = 100

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Answer:

okay so first you have the original height (2,000 feet) than subtract by 450. add 1750 giving you 3300

Answer:

g(1) = 12(1) - 2 = 10

Step-by-step explanation:

Where is f(x)?

If you meant to type g(1), then:

g(x) = 12x - 2 and g(1) = 12(1) - 2 = 10

The derivative of y = sin(x)cos(x) is 2sin(x)cos(x).Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)

The rule for derivatives of trigonometric functions states that the derivative of a trigonometric function is the product of the coefficient and the derivative of the other function in the product. This rule can be expressed mathematically using the following formula: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) For example, let's say that we want to calculate the derivative of the function y = sin(x)cos(x). Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x) Therefore, the derivative of y = sin(x)cos(x) is 2sin(x)cos(x).

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Yes, you can still cover the remaining squares with dominoes. The necessary and sufficient condition for this to work is that the chessboard originally had an even number of squares.


A standard chessboard has 64 squares. If one corner square is missing, we are left with 63 squares. Each domino covers exactly 2 squares, so we need 31.5 dominoes to cover the remaining squares. Since we cannot use half a domino, this means we need a whole number of dominoes. Therefore, the number of squares must be even.

Conversely, if the chessboard originally had an even number of squares, then we can remove any one square and still have an odd number of squares left. Since each domino covers 2 squares, it is easy to see that we can always cover an odd number of squares with dominoes, by placing one domino vertically in the middle of the board. Therefore, in this case we can also cover the remaining squares with dominoes.

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The vectors u, v, and w are linearly independent if and only if k ≠ -8.

To understand why, let's consider the determinant of the matrix formed by these vectors:

| -4   -3    -4   |

| -3   -3    -11+k |

| 5    -11+k  7    |

If the determinant is nonzero, then the vectors are linearly independent. Simplifying the determinant, we get:

(-4)[(-3)(7) - (-11+k)(-11+k)] - (-3)[(-3)(7) - 5(-11+k)] + (-4)[(-3)(-11+k) - 5(-3)]

= (-4)(21 - (121 - 22k + k^2)) - (-3)(21 + 55 - 55k + 5k) + (-4)(33 - 15k)

= -4k^2 + 80k - 484

To find the values of k for which the determinant is nonzero, we set it equal to zero and solve the quadratic equation:

-4k^2 + 80k - 484 = 0

Simplifying further, we get:

k^2 - 20k + 121 = 0

Factoring this equation, we have:

(k - 11)^2 = 0

Therefore, k = 11 is the only value for which the determinant becomes zero, indicating linear dependence. For any other value of k, the determinant is nonzero, meaning the vectors u, v, and w are linearly independent. Hence, k ≠ 11.

In conclusion, the vectors u, v, and w are linearly independent if and only if k ≠ 11.

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Answer:

C.) 2.7 with the line over the 7

Answer:

x=-3

Step-by-step explanation:

we can fill the y into the first equation since we already know what it is equal to

5x+4(1-x)=1

5x+4-4x=1

x+4=1

  -4. -4

x=-3

Hopes this helps please mark brainliest

Answer:

5x + 4y = 1

Answer: x = 1/5 - 4y/5

y = 1 - x

Answer: x = −y + 1

Step-by-step explanation:

Please give the brainliest, really appreciated.

Answer:

2 cups of popcorn and 1/2 cups of cereal per cup

Step-by-step explanation:

khan told me

Colin was able to make 33.75 ounces of bubble bath .

It is given that Colin fills 4.5 ounce per bottles .

We apply division because we need to find the cost of one item given the  cost of many items. If you need to find the cost of many items from the cost of one item,  apply the multiplication operation.

Using unitary method , we get

1 bottles have = 4.5 ounces

7.5 bottles will have = \(7.5\times 4.5=33.75\) ounces

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Answer:

Step-by-step explanation:

5:8

50:80

Hope this was right :)

The missing information for the SAS congruence theorem is given as follows:

B. SU = JL.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The congruent angles for this problem are given as follows:

<S and <J.

Hence the proportional side lengths are given as follows:

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Answer:

x ≈ 25.73

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = \(\frac{opposite}{adjacent}\) = \(\frac{12}{x}\) ( multiply both sides by x )

x × tan25° = 12 ( divide both sides by tan25° )

x = \(\frac{12}{tan25}\) ≈ 25.73 ( to 2 dec. places )

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The measure of the length 'x' is calculated by the tangent of angle 25°. The tangent of an angle is the ratio of the perpendicular to the base of the right-angle triangle. Then we have

tan 25° = 12 / x

x = 12 / tan 25°

x = 12 / 0.466

x = 25.75 units

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

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Square the two smallest values and then add them together. If they are greater than the square of the largest number in the set, than it is obtuse. If smaller it is acute. If it is the same it is a right triangle.

9514 1404 393

Answer:

Step-by-step explanation:

The Law of Cosines tells you the largest angle C will be found from ...

  C = arccos((a² +b² -c²)/(2ab))

where c is the longest side of the triangle.

For the purpose of classifying the triangle as acute, right, or obtuse, you need only look at the sign of the argument of the arccos function. Since all side lengths are positive, this means you only need to look at the sign of the "form factor" a²+b²-c².

When f = a²+b²-c² is negative, the cosine is of an angle larger than 90°, so the triangle is obtuse. When it is 0, the angle is 90°, so a right triangle. (That condition is recognizable as related to the Pythagorean theorem.) When f > 0, the triangle is acute.

__

In the attached spreadsheet, we have done these calculations by summing the squares of all three sides, then subtracting twice the square of the longest side. (This makes the formula fairly simple.) It shows ...

  Triangle 1: f < 0 — obtuse triangle

  Triangle 2: f > 0 — acute triangle

_____

In summary, you can compute a form factor ...

  f = a² +b² -c² . . . . . . . triangle with side lengths a, b, c with c longest