gravel is being dumped from a conveyor belt at a rate of 4 cubic feet per minute. it forms a pile in the shape of a right circular cone whose height and base diameter are always equal to each other. how fast is the height of the pile increasing when the pile is 5 feet high?

Solution

For this case the confidence interval is given by:

(0.27; 0.33)

We can find the estimaed proportion in the following way:

then the sample proportion would be 0.30

This is the expression your question creates 13-6•x

Answer:

This can be written as (13-6)n. Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

First find the hyp..

6^2 + 20^2 = x^2

x = 20.88

Using x, we now know the extra height missing from the original tree height, so we add 6 to find the original.

20.88 + 6 = 26.88ft

The tree was 26.88 feet tall before the storm.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have Perpendicular = 6 feet

and, base = 20 feet

Using Pythagoras theorem we get

H² = P² + B²

H² = 6²+ 20²

H²= 36+400

H² = 436

H = 20.88 feet

thus, the height of the tree = 20.88 + 6 = 26.88 feet

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Answer:

Step-by-step explanation:

Remark

You have an isosceles triangle. That means that the angles opposite the marked sides are equal. So mark the angle on the lower left of the triangle as 50 degrees.

The solution to problem depends on the fact that the sum of the two inside angles of the triangle (each of which is marked as 50 degrees) not supplementary to the exterior angle, are still equal to the exterior angle.

Givens

<1 = 50 degrees

<2 = 50 degrees

Exterior angle = 15x + 25   Substitute the givens into the equation

Equation

<1 + <2 = 15x + 25

Solution

50 + 50  = 15x + 25                       Combine the left side

100 = 15x + 25                               Subtract 25 from both sides

100 - 25 = 15x + 25 - 25                Combine

75 = 15x                                          Divide both sides by 15

75/15 = 15x/15                      

5 = x

Answer

<1 = 50 degrees

<2 = 50 degrees

15x + 25 = 75 + 25 = 100

The age of “Old Fred” is approximately 487.6 years old.

We are given that;

Thickness=0.5cm

Circumference=766cm

Now,

To estimate the age of “Old Fred”, we can use the formula:

Age=Circumference​/π×Average ring thickness

Note that this is only an estimate based on the average ring thickness. The actual age of the tree may vary depending on the environmental factors that affect its growth.

Plugging in the given values, we get:

Age=π×0.5766​≈487.6

Therefore, by the given circumference the answer will be 487.6 years old.

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1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?

Answer:

- 1

Step-by-step explanation:

The average rate of change of g(x) in the close interval [ a, b ] is

\(\frac{g(b)-g(a)}{b-a}\)

Here [ a, b ] = [ 3, 6 ] , then

g(b) = g(6) = 6² - 10(6) + 19 = 36 - 60 + 19 = - 5

g(a) = g(3) = 3² - 10(3) + 19 = 9 - 30 + 19 = - 2

average rate of change = \(\frac{-5-(-2)}{6-3}\) = \(\frac{-5+2}{3}\) = \(\frac{-3}{3}\) = - 1

Answer:

1

Step-by-step explanation:

\(\log_{b} x=0 \\ \\ b^0 =x \\ \\ x=1\)

Answer:

24 cm

Step-by-step explanation:

the perimeter is the circumference, the way to go one time fully around the object.

now think, what distances do you have to go when walking around a rectangle ?

well, there are 2 times the length and 2 times the width or breadth. that's it.

P = 2×7 + 2×5 = 14 + 10 = 24 cm

Answer:

Step-by-step explanation:

Correct choice is C

Answer:

4

Step-by-step explanation:

Hence, there are 4 zeros for the square of 200.

Answer:

What is the question

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4x + 11)° is suplementary angle to angle corresponding to (6x + 19)° angle

Therefore:

m║n    ⇒    (4x + 11)° = 180° - (6x + 19)°

(4x)° + 11° = 180° - (6x)° + 19°      {add (6x)° to both sides}

(10x)° + 11° = 161°                     {subtract 11° from both sides}

(10x)° = 150°                       {divide both sides by 10°}

 x = 15

Rounded to the nearest whole dollar, the administrative fee for the year is $433.

To calculate the administrative fee for your variable annuity, you can use the following formula:
Administrative fee = (Average account value) × (Annual rate of administrative fees)
In this case, the average account value is $228,000 and the annual rate of administrative fees is 0.19 percent (0.0019 as a decimal).
Administrative fee = ($228,000) × (0.0019)
Administrative fee = $433.20

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\(a^3 \cdot a^4 = a^{3 + 4} = a^7\)

Option B is correct

Answer: Jesse

Step-by-step explanation:

Elizabeth - 50f/10s

Jesse - 55f/10s

Reagan - 53.3333333/10s

Jesse is the fastest

Answer:

I think that Jessie swam the fastest

Step-by-step explanation:

Jessie swam the fastest bc Reagan only swims 160 feet in half a minute and 110 is less than 160 and 20 + 20 =40 so if Jessies swimming speed and time was multiplied by 2, she would still swim faster!

(sorry Im not the best at math but I hope you can understand my logic lol)

Answer:

Its 108 because you have to split up the rectangles so when you cut them in half you will have 2 separate rectangles 1 with a base of 8 and a height of 9 so you will multiply those so 9 x 8 = 72 then just do the other two so 6 x 6 = 36 now you add those together 36 + 72 = 108 hope that helps

The Answer Is 108

Find the top length by adding 8+6=14

And the sides are the same length, meaning the sides are equivalent to 6.

6x14=84.

To find the sides for the the other rectangle, do 9-6 to get the side 3.

3x8=24

Add both areas to get 108 Inches Squared.

Answer:

994

Step-by-step explanation:

If the choir raised $700, and they plan to make 42% more, what you have yo do is divide 700 by 100, which will bring you to 7$ is 1% of 700. Then, you must multiple 7 by 42 (which is 294). Finally, you need to add 294 to 700, which will bring you to 994 total dollars ($) raised by the choir this year.

The number of permutations of putting the 28 cards into the envelopes is 1024.

A permutation is the arrangement of objects in a specific order. When we are counting the number of permutations of a set of objects, we are finding the total number of ways that the objects can be arranged.

In your question, you have 28 cards and 10 envelopes. To find the number of permutations of putting the 28 cards into the envelopes, we need to consider a few factors.

Firstly, each envelope can only hold a maximum of

=> 28/10 = 2 cards.

Secondly, the order in which the cards are placed into the envelopes matters,

Since each envelope can only hold a maximum of 2 cards, we have two options for each envelope: either 0 cards or 2 cards.

We can use a binary code of 0 and 1 to represent this, where 0 means the envelope is empty and 1 means the envelope has 2 cards.

Therefore, the total number of permutations can be calculated as

=> 2¹⁰ = 1024

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer: 1/28, 3/14, 1/28

Step-by-step explanation: There are two Jokers in the deck. This is 2/56 chance, which is reduced to 1/28. There are 12 face cards: 4 Kings, 4 Queens, and 4 Jacks. This is 12/56, which reduces to 3/14. There are two red aces: The Ace of Diamonds and the Ace of Hearts. This is a s2/56 chance, which reduces to 1/28 chance.

The lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

The mid-range or mid-extreme is the arithmetic mean of the highest and minimum values of the data set and is used in statistics as a measure of a sample's central tendency.

The difference between the greatest and minimum values, which is a measure of statistical dispersion, is strongly related to the mid-range.

The two measurements are complementary in that one can determine the sample's maximum and minimum values by knowing the range and the midpoint.

Therefore, the lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

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The alpha level for each hypothesis test made on the same set of data is called B. experimentwise alpha

When numerous suppositions are examined concurrently, the likelihood of committing at least one type I mistake grows.

In order to manage the probability of erroneously rejecting the null hypothesis in all tests, scientists usually modify the alpha level for each test, with the purpose of maintaining an experimentwise alpha that reflects the probability of making a type I error in the entire set of tests.

The Bonferroni procedure is a technique utilized to regulate the experimentwise error rate by adjusting the alpha level for each hypothesis test.

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The decision rule for rejecting the null hypothesis is that if the test statistic is greater than 1.708, we reject the null hypothesis.

To determine the decision rule for rejecting the null hypothesis, we need to calculate the critical value for the given level of significance. The level of significance is 0.1.

Step 1: Determine the critical value
Since the sample size is small (26 students), we need to use the t-distribution. The critical value can be found using a t-table or a t-distribution calculator.

The degrees of freedom (df) for this test is n - 1, where n is the sample size. In this case, the sample size is 26, so the degrees of freedom is 26 - 1 = 25.

Using a t-table or t-distribution calculator with a significance level of 0.1 and degrees of freedom of 25, we find the critical value to be approximately 1.708.

Step 2: Determine the decision rule
The decision rule for rejecting the null hypothesis is as follows:
- If the test statistic is greater than the critical value (1.708), reject the null hypothesis.
- If the test statistic is less than or equal to the critical value (1.708), fail to reject the null hypothesis.

Therefore, the decision rule for rejecting the null hypothesis is that if the test statistic is greater than 1.708, we reject the null hypothesis.

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Answer:

Pete

Step-by-step explanation:

Given that:

Mandy's Estimate :

Number of spins , n = 20

Pete's Estimate:

Number of spins, n = 200

A good probability estimate is one which has narrow margin of error with a high degree of confidence. These two variables are affected by sample size.

A high sample size give a narrower margin of error and increases the confidence level probability

Based on the sample size used by each of Pete and Mandy, we can conclude that, Pete's probability estimate would be better due to its significantly higher sample size.

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The dimensions will be x = 7.5 cm and y = 7.5 cm where x is the side of the base and y is the height of the solid.

We are given that:

The solid has a square base.

So, the area of the base will be:

A = x²  ( where x = side of the square)

Also, it is a rectangular solid, so let the height be y.

Volume will be:

V = x² × y

V = x²y

The surface area is given as:

S = 337.5 cm²

x² + x² + xy + xy + xy+ xy = 337.5 cm²

2x² + 4 x y = 337.5 cm²

y = (337.5- 2 x²) / (4 x)

Plug into the equation of volume:

V = x² (337.5- 2 x²) / (4 x)

V = (337.5 x- 2 x³) / 4

Differentiate with respect to x:

V' = (337.5 - 6 x²) / 4

Put it equal to 0:

337.5 - 6 x² = 0

x² = 337.5 / 6

x = ±7.5

Dimension will be:

x = 7.5 cm ( as it cannot be negative)

y = 7.5 cm.

Therefore, the dimensions will be x = 7.5 cm and y = 7.5 cm where x is the side of the base and y is the height of the solid.

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Your question was incomplete. Please refer the content below:

A rectangular solid (with a square base) has a surface area of 337.5 square centimeters. Find the dimensions that will result in a solid with maximum volume.

(A)6  Polar form as 6(cos 0° + I sin 0°).

(B) 4i polar form as 4(cos π/2 + i sin π/2).

(C) -9 + 5i polar form as √106(cos 2.628 + i sin 2.628).

(a) To express the number 6 in polar form, we need to find its magnitude (r) and angle (θ). Since 6 is a positive real number, its angle θ is 0 degrees (or 0 radians) because it lies on the positive real axis. The magnitude r is simply the absolute value of the number, which is 6.

Therefore, 6 can be written in polar form as 6(cos 0° + I sin 0°).

(b) To express the number 4i in polar form, we need to find its magnitude (r) and angle (θ). Since 4i is a purely imaginary number, it lies on the positive imaginary axis. The angle θ is 90 degrees (or π/2 radians) because it forms a right angle with the positive real axis. The magnitude r is simply the absolute value of the number, which is 4.

Therefore, 4i can be written in polar form as 4(cos π/2 + I sin π/2).

(c) To express the number -9 + 5i in polar form, we need to find its magnitude (r) and angle (θ). We can use the Pythagorean theorem to find the magnitude r:

r = √((-9)² + 5²) = √(81 + 25) = √106.

θ = arctan(5/-9) = -0.514 radians (approximately).

Since the number -9 + 5i lies in the third quadrant, we need to add π to the angle to obtain a positive value. Therefore, θ ≈ π - 0.514 ≈ 2.628 radians.

Therefore, -9 + 5i can be written in polar form as √106(cos 2.628 + I sin 2.628).

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