HELPPP!! which of the following could be the ratio between the lengths of two legs of a 30,60,90 triangle
check all that apply:
whoever gives me the correct answer gets brianliest

Answer:

a = b/4

Step-by-step explanation:

Let a be the altitude to the hypotenuse and b be the hypotenuse. The 15° angle faces a and the right angle faces b.

Using the sine rule,

a/sin15 = b/sin90

a = bsin15/sin90

= 0.25b

= 25b/100

= b/4

Answer:

62.5 miles per hour

Step-by-step explanation:

Assuming she had the same speed the whole time and never stopped, just divide the miles driven by the time to get miles per hour. 437.5/7 = 62.5, so she drove 62.5 miles per hour.

Hopefully this helps- let me know if you have any questions!

Answer:

1.283.5

2.34.56

3.92.96

4.39.9

5.34

6.18.7

Step-by-step explanation:

Answer:

48 pipes

Step-by-step explanation:

3/4 of 1 foot = 0.75 foot

36/0.75=48

Answer:

The answer would be 2,240

Step-by-step explanation:

Answer:

2240

Step-by-step explanation:

1. 5x4=20x7 and keep on going

Option B. The function that represents the profit, P(m), where m is the number of minutes the platform uses on advertisements is: P(m) = -1.6(x - 150)² + 10000.

The capability that addresses the benefit, P(m), where m is the quantity of minutes the stage utilizes on promotions is:

P(m) = - 1.6(x - 150)² + 10000

This is on the grounds that we know that the greatest benefit of $10,000 happens when the stage utilizes 150 minutes daily on notices, and the benefit capability ought to have a most extreme as of now. The capability is in the vertex structure, which is P(m) = a(x - h)² + k, where (h,k) is the vertex of the parabola and a decides if the parabola opens upwards or downwards.

The negative worth of an in the capability shows that the parabola opens downwards and has a most extreme worth at the vertex (h,k). The vertex is at (150,10000), and that implies that the most extreme benefit of $10,000 happens when the stage utilizes 150 minutes daily on ads.

In this way, the capability that addresses the benefit, P(m), where m is the quantity of minutes the stage utilizes on ads is P(m) = - 1.6(x - 150)² + 10000. The other given capabilities don't match the given circumstances for the most extreme benefit, and in this way, they are not fitting to address the benefit capability of JP Creations.

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Answer:

41300 a x + 123900

Step-by-step explanation:

Answer:

4√5

Step-by-step explanation:

Use Pythagorean theorem

a^2=21^2-19^2

a^2=441-19^2

a^2=441-361

a^2=80

a= √80

simplify

The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

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An urn contains 4 blue and 3 yellow chips, two are removed in succession without replacement. The probability both chips are blue is 15/14

Since the balls are to be removed in succession,

For removing first ball:

Total probability to remove the ball from 7 balls = 7c1

The probability for removing one blue ball out of 4 blue balls = 4c1

So final probability = 4c1/7c1

Now the remaining balls = 7-1 = 6

The remaining blue balls = 4-1 = 3

For removing second ball:

Total probability to remove one ball out of 6 balls = 6c1

The probability for removing one blue ball out of 3 blue balls = 3c1

So final probability = 3c1/6c1

The final probability to remove two blue balls in succession out of 7 balls is = 4c1/7c1 + 3c1/6c1

   = 4/7 + 3/6

   = 15/14

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The website which is cheaper for Caroline to buy the spice mix is French website.

Given data ,

Let's calculate the total cost for Caroline from both websites and determine which one is cheaper.

British website:

Price for 100 g = (£0.90 / 25 g) * 100 g = £3.60

Since the British website offers free delivery, the total cost remains £3.60.

French website:

Price for 100 g = (€1.20 / 50 g) * 100 g = €2.40

Delivery cost = €0.80

On simplifying the equation , we get

To convert the price and delivery cost to pounds, we'll use the conversion rate: €1 = £0.85.

Price in pounds = €2.40 * £0.85 = £2.04

Delivery cost in pounds = €0.80 * £0.85 = £0.68

Total cost = Price in pounds + Delivery cost = £2.04 + £0.68 = £2.72

Comparing the total costs:

British website: £3.60

French website: £2.72

Hence , Caroline would pay £2.72 for the spice mix from the cheaper website, which is the French website.

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Answer:  In bold

Step-by-step explanation:

The formula they gave is a rate

Let's solve for the rate first.

This equation is done for 3 years 2018-2021  that's why ^3

3.55 =  2.90(1+x)³                 >divide both sides by 2.90

1.224 = (1+x)³                         > take cube root of both sides

1.0697 =  1+x

x= .0697

so let's make our generic formula

\(y = 2.90(1+.0697)^{t}\)        let t be years and let y=  price  

Let's calculate 2018, so this would be year 0

\(y = 2.90(1+.0697)^{0}\)

y=$2.90   this is for 2018

They already gave you 2021 price

y=$3.55   this is for 2021

Rate of increase is .0697 

In 2025

That's 7 years=t

\(y = 2.90(1+.0697)^{7}\)

y=$4.65    for 2025

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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False. The expression \((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

The expression\((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

To simplify \((3ab - 6a)^2\), we need to apply the exponent of 2 to the entire expression. This means we have to multiply the expression by itself.

\((3ab - 6a)^2 = (3ab - 6a)(3ab - 6a)\)

Using the distributive property, we can expand this expression:

\((3ab - 6a)(3ab - 6a) = 9a^2b^2 - 18ab^2a + 18a^2b - 36a^2\)

Simplifying further, we can combine like terms:

\(9a^2b^2 - 18ab^2a + 18a^2b - 36a^2 = 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\)

The correct simplified form of \((3ab - 6a)^2 is 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\).

The statement that\((3ab - 6a)^2\) is the same as 2(3ab - 6a) is false.

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Answer: D

Step-by-step explanation:

There are 14 students who chose vanilla, and 6 of those are male. 6/14 = 3/7.

Using the area formula,

Area of the prism = 40mm².

Define area?

The word "area" designates a vacant region. The length and width of a form are used to calculate its area. The units of unidimensional length are feet (ft), yards (yd), inches (in), etc. Yet, the area of a shape is a two-dimensional quantity. Measurements like square inches (in²), square feet (ft²), square yards (yd²), etc. are used to measure anything in a square.

In the figure,

We have 2 equal rectangles and 2 equal triangles.

Now dimensions of the rectangles, l = 4mm and b = 3mm.

Area of 2 rectangles = 2 × 4 × 3

= 24mm².

Height of triangle, h = 4mm and base, b = 4mm.

Area of 2 triangles = 2 × 1/2 × b × h

= 4 × 4

= 16mm².

Therefore, total area of the prism = 24 + 16 = 40mm².

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the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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Answer: its 1 2 6

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 6 common factors of 36 and 48, i.e. 1, 2, 3, 4, 6 and 12. Therefore, the highest common factor of 36 and 48 is 12.

Answer: Simple!! 1, 2, 6!

<3

The product of the sum and difference of two terms can be found using the distributive property and the FOIL (First, Outer, Inner, Last) method.If you have two terms, A and B, the sum and the difference of these terms can be represented as:

Sum: A + B Difference: A - B

To find the product of the sum and difference, you can multiply the sum and the difference together:

(A + B)(A - B)

Using the distributive property, we can expand the product:

AA - AB + AB - BB

Which is equal to:

A^2 - B^2

This is the difference of squares of the terms.

It's worth noting that this is a very common pattern in algebra, and it's called the difference of squares. It is the product of the sum and difference of two terms. The distributive property and FOIL method can be used to expand the product of two binomials, but it's important to recognize patterns, like this one to solve the problem in a faster way.

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Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

Answer:

(2,-2)

I hope this helps:

The required probability is 3/4.

We have to compute the probability

P(Female |Junior) because we have to find the probability of the female student and the given condition is that the student is junior.

Determine the total number of juniors.

Juniors=2+6=8

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Since the number of females who are junior is 6, determine the required probability.

P(Female|Junior)=6/8=3/4

Therefore, the required probability is 3/4.

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The diagonal matrix from given elements is

| 16   0    0    0    0  |

|  0  -8.7  0    0    0  |

|  0   0   5.4   0    0  |

|  0   0    0   1.3   0  |

|  0   0    0    0  -6.9 |

A diagonal matrix is a special type of matrix in which all the non-diagonal elements are zero. In other words, only the diagonal elements have non-zero values.

Diagonal matrices are often used in linear algebra because they are easy to work with and have some interesting properties.

In the given problem, we are asked to construct a diagonal matrix using the given elements.

To do this, we simply place the given elements on the diagonal of the matrix, and set all the other elements to zero. The resulting matrix is a 5 x 5 diagonal matrix with the given elements on the diagonal.

Therefore, the matrix is

| 16   0    0    0    0  |

|  0  -8.7  0    0    0  |

|  0   0   5.4   0    0  |

|  0   0    0   1.3   0  |

|  0   0    0    0  -6.9 |

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--The given question is incomplete, the complete question is given below " A diagonal matrix has the elements shown below.

a 11 = 16

a 22=-8.7

a 33= 5.4

a 44= 1.3

a 55=-6.9

CONSTRUCT  the diagonal matrix containing these elements"--

a. The possible results of a measurement of Ln is λn = ½ sin θ (e^-iφλ+ + e^iφλ-) + cos θ μ

b. The expectation values of Ln and L²ⁿ is μ₂

The angular momentum operator in spherical coordinates can be written as:

L = -i h sin φ (∂/∂θ) + i h (1/sin θ) (∂/∂φ)

So, the component of angular momentum in the direction n, denoted by Ln, can be written as:

Ln = n·L = sin θ cos φ Lx + sin θ sin φ Ly + cos θ Lz

where Lx, Ly, and Lz are the x, y, and z components of the angular momentum, respectively.

To express Ln in terms of ladder operators L+ and L-, we use the following identities:

Lx = ½ (L+ + L-)

Ly = ½i (L+ - L-)

Substituting these expressions into the equation for Ln, we get:

Ln = sin θ cos φ (½ (L+ + L-)) + sin θ sin φ (½i (L+ - L-)) + cos θ Lz

Simplifying and rearranging, we obtain:

Ln = ½ sin θ (e^-iφL+ + e^iφL-) + cos θ Lz

(a) The possible results of a measurement of Ln are given by the eigenvalues of the operator Ln. Since Ln is expressed in terms of Lx, Ly, and Lz, which all commute with L^2 and Lz, we can use the commutation relations between Lz and L± to show that Ln also commutes with L^2 and Lz.

Therefore, the possible results of a measurement of Ln are simply the eigenvalues of the operator Ln, which are given by the expression derived above:

λn = ½ sin θ (e^-iφλ+ + e^iφλ-) + cos θ μ

where λ± and μ are the eigenvalues of L± and Lz, respectively.

(b) The expectation value of Ln can be calculated as follows:

<Ln> = <n|Ln|n> = ½ sin θ (<n|e^-iφL+ + e^iφL-|n>) + cos θ (<n|Lz|n>)

Since the system is in a simultaneous eigenstate of L² and Lz, we have:

L²|n> = i(i+1)h²|n>

Lz|n> = mh|n>

Substituting these expressions into the above equation, we get:

<Ln> = ½ sin θ (e^-iφ<λ+> + e^iφ<λ->) + cos θ <μ>

where <λ±> and <μ> are the expectation values of L± and Lz, respectively.

The expectation value of L²n can be calculated similarly:

<L²n> = <n|Ln²|n> = ¼ sin² θ (<n|L+L- + L-L+|n>) + cos² θ (<n|Lz^2|n>)

Using the commutation relations between L± and Lz, we can show that:

L+L- + L-L+ = L² - Lz² - Lz

Substituting this expression into the above equation, we get:

<L²n> = ¼ sin² θ (<n|L² - Lz² - Lz|n>) + cos² θ <μ²>

where <μ²> is the expectation value of Lz^2.

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Answer:

b^3c^2/a^3

Step-by-step explanation:

Answer:

\(\frac{b^{3}c^{2} }{a^{2} }\)

Step-by-step explanation:

The probability that the amount of time Gary takes to assist the next customer is:

To solve this problem, assume that the time it takes Gary to assist a customer follows an exponential distribution with a rate parameter λ = 1/3 customers per minute (since he assists three customers per hour on average).

a) To determine the probability that the time is between 6 and 12 minutes, calculate the cumulative distribution function (CDF) of the exponential distribution at t = 12 and subtract the CDF at t = 6.

P(6 < X < 12) = F(12) - F(6) = (1 - exp(-λ × 12)) - (1 - exp(-λ × 6))

Substituting λ = 1/3:

P(6 < X < 12) = (1 - exp(-(1/3) × 12)) - (1 - exp(-(1/3) × 6))

= 0.4168.

b) To determine the probability that the time is between 26 and 35 minutes, use the same approach:

P(26 < X < 35) = F(35) - F(26) = (1 - exp(-λ × 35)) - (1 - exp(-λ × 26))

Substituting λ = 1/3:

P(26 < X < 35) = (1 - exp(-(1/3) × 35)) - (1 - exp(-(1/3) × 26))

= 0.0404.

c) To determine the probability that the time is either less than 14 minutes or greater than 24 minutes, calculate the complementary probabilities:

P(X < 14) = 1 - exp(-λ × 14)

P(X > 24) = 1 - F(24) = 1 - (1 - exp(-λ × 24))

Substituting λ = 1/3:

P(X < 14) = 1 - exp(-(1/3) × 14)

P(X > 24) = 1 - (1 - exp(-(1/3) × 24))

= 0.6032

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Answer:

x = 10

Step-by-step explanation:

\(6(x - 1) = 9(x - 4)\)

➡️ \(6x - 6 = 9x - 36\)

➡️ \(6x - 9x = - 36 + 6\)

➡️ \( - 3x = - 30\)

➡️ \(x = 10\) ✅

The probability that all of them get the same number is 1/36.

Given :

Three people are asked to throw a fair die.

Probability :

Probability is a branch of mathematics that deals with the occurrence of a random event.

In one dice probable outcomes 1, 2, 3, 4, 5 and 6

Total out comes in three dice = ( 6 * 6 * 6 = 216 )

Probability of getting 1 = 1/216

Similarly for 2, 3, 4, 5 and 6

Probability of getting same number = 6 * 1/6 * 1/6 * 1/6

= 6*1/6 * 1 * 1 / 6 * 6

= 6/6 * 1/36

= 1 * 1/36

= 1/36

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