n airplane took off from an airport and traveled at a constant rate and angle of elevation. When the airplane reached an altitude of 500 m, its horizontal distance from the airport was found to be 235 m. What was the angle when the airplane rose from the ground?

Answer:

They are congruent

Step-by-step explanation:

The SSS congruency theorem states that the triangles are congruent. They have a shared line which is congruent becasue it si a shared line. The I and II marking on each triangle show that those lines are congruent to eachother. So II is congruent to II and I is congruent to I.

Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

To reflect a point across the y-axis, we keep the x-coordinate the same but change the sign of the y-coordinate.

Point B is located at (2, -3), so it looks like

     |

     |

     |

     |

------B(2, -3)

     |

     |

     |

     |

To reflect point C across the y-axis, we change the sign of the y-coordinate, but keep the x-coordinate the same. If point C is located at (x, y), then its reflected image, C', would be located at (-x, y).

Since we don't have the coordinates for point C, we cannot plot it accurately. However, we know that its reflected image would be located at (-x, y), so we can label it as C' for now.

So, the reflected image of point C across the y-axis, C', would be located at (-x, y). Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

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Answer:

n=-5

Step-by-step explanation:

Do the equation backwards:

-26 - 4 = -30

-30 / 6 = -5

Check:

-5*6 = -30

-30+4 = -26

Hope this helps!

Answer:

k = - \(\frac{3h}{h+1}\)

Step-by-step explanation:

Given

h(k + 6) = 3h - k ← distribute parenthesis on left side

hk + 6h = 3h - k ( add k to both sides )

hk + k + 6h = 3h ( subtract 6h from both sides )

hk + k = - 3h ← factor out k from each term on the left side

k(h + 1) = - 3h ( divide both sides by (h + 1) )

k = - \(\frac{3h}{h+1}\)

The simple multiplier of the economy represented by the system of equation above is: 4/7.

The simple multiplier is the ratio of the change in equilibrium output to a change in autonomous expenditures, such as government spending or investment.

To find the simple multiplier in the economy, we need to first determine the equation for equilibrium output, which is where aggregate demand (AD) equals aggregate supply (AS).

Setting y in both equations equal to each other, we get:

710 - 30p + 5g = 10 + 5p - 2s

Simplifying and rearranging, we get:

35p = 700 + 2s - 5g

p = (20/7) + (2/35)s - (1/7)g

Now that we have the equilibrium price, we can substitute it back into the AD equation to find the equilibrium output (y):

y = 710 - 30[(20/7) + (2/35)s - (1/7)g] + 5g

y = (400/7) + (6/7)s + (4/7)g

The simple multiplier is then equal to the change in equilibrium output divided by the change in government purchases:

simple multiplier = Δy/Δg = 4/7

Therefore, the simple multiplier in the economy is 4/7.

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Approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in a bank account that has grown to $150,000 today.

To calculate the number of years, we can use the compound interest formula:

\(A = P(1 + r/n)^ {nt}\)

where A is the final amount, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal amount is $2, the final amount is $150,000, the annual interest rate is 5.5% (0.055 as a decimal), and the interest is compounded weekly (n = 52), we can solve for t:

\(50,000 = 2(1 + 0.055/52)^{52t}\)

Dividing both sides by $2 and isolating the exponent, we get:

\(75,000 = (1.0010576923076923)^{52t}\)

Taking the logarithm of both sides, we have:

\(log(75,000) = log(1.0010576923076923)^{52t}\)

Using logarithm properties, we can rewrite the equation as:

log(75,000) = 52t * log(1.0010576923076923)

Solving for t by dividing both sides by 52 * log(1.0010576923076923), we find:

t ≈ 204.11 years

Therefore, approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in the bank account.

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We can conclude that there is no measurable effect of immersing them in water or dropping them. Thus, we cannot conclude that the treatment has any significant effect.

To answer whether there appears to be any measurable effect of immersing the devices in water or dropping them, we have to compare the average scores of each group before and after submerging them in water or dropping them.

The null and alternative hypotheses are stated as follows:

Null Hypothesis H0:

µ1 = µ2 = µ3

Alternative Hypothesis Ha:

µ1 ≠ µ2 ≠ µ3

The level of significance is α = 0.05.

ANOVA table helps us to calculate the test statistic.

The calculated F-value of 1.56 is less than the critical F-value of 3.05 at the 0.05 level of significance.

Since the calculated F-value is less than the critical F-value, we fail to reject the null hypothesis.There is no significant difference in the scores between the groups.

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Answer:4610

Step-by-step explanation:

$4564 is the amount in account after 5 years.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Madison invested $3,300 in an account paying an interest rate of 6.7% compounded daily.

We need to assume no deposits or withdrawals are made, then we need to find money in account after 5 years.

Madison invested = $ 3300

Rate of interest = 6.7 %

Time = 5 years

\(A=P(1+\frac{r}{100} )^{t}\)

P is the principle amount

t is the time

r is the rate of interest

\(A=3300(1+\frac{6.7}{100} )^{5}\)

A=3300(1+0.067)⁵

A=3300(1.067)⁵

A=3300(1.383)

A=4563.9

A=4564

Hence, $4564 is the amount in account after 5 years.

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The expression obtained by simplifying is 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9.

What is an expression?

A mathematical expression consists of its own components, at least two additional variables or integers, and one or more arithmetic operations.

We are given an expression as

(\(x^{2}\) + 6x + 9) (3x - 1)

Now, for simplifying the expression, we will multiply the terms.

So, we get

⇒ (\(x^{2}\) + 6x + 9) (3x - 1)

⇒ 3\(x^{3}\) - \(x^{2}\) + 18\(x^{2}\) - 6x + 27x - 9

Now, by combining the like terms, we get

⇒ 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9

Hence, the expression obtained by simplifying is 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9.

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Question: Simplify the following

(x² + 6x + 9) (3x - 1)

Answer:

B and C

Step-by-step explanation:

The lower bound of Ω(m log n) for the disjoint-sets data structure implemented using union-by-rank without path compression.

When implementing the disjoint-sets data structure using union-by-rank without path compression, a sequence of union and find operations can be constructed to take Ω(m log n) time, where m represents the number of operations and n represents the number of elements.

To achieve this lower bound, we need to create a specific scenario where the height of the trees in the disjoint-sets structure grows logarithmically with the number of elements. We can achieve this by performing a series of union operations on disjoint sets with a specific pattern.

Let's consider the following scenario:

Start with n disjoint sets, each containing one element.

Perform a sequence of m/2 union operations by merging two disjoint sets together in a specific pattern. Each union operation merges two sets of roughly equal sizes.

Perform a sequence of m/2 find operations on the resulting disjoint sets.

In this scenario, the union operations will create a tree-like structure where each disjoint set is represented as a tree, and the height of each tree is approximately log(n). This is because each time we merge two sets of similar size, the resulting tree's height increases by 1.

Now, when we perform the m/2 find operations, without path compression, each find operation will traverse the tree from the root to the corresponding element. Since the height of the tree is approximately log(n), each find operation will take logarithmic time.

Considering that we have m union operations and m find operations, the total time complexity will be Ω(m log n), as the find operations alone contribute Ω(m log n) to the overall time complexity.

Therefore, by carefully designing a sequence of union and find operations where the tree height increases logarithmically with the number of elements, we can achieve a lower bound of Ω(m log n) for the disjoint-sets data structure implemented using union-by-rank without path compression.

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Answer:

1183

Step-by-step explanation:

75th term of Arithmetic sequence is 1183 Given: -1, 15, 31,... is Arithmetic series To find: The 75th term of the arithmetic sequence -1, 15, 31

Answer:

C. 164

Step-by-step explanation:

its self explanitory

The half life for this radioactive substance is 40.76 years

As we know that radioactive decay is a first order reaction

For first order reaction, we can write

N = \(N^{0}\)\(e^{-kt}\)

Where N = Amount of substance at time ‘t’

N0 = Initial amount of substance

K = rate constant for first order reaction

t = time in years

Now, as per the question,

This substance is decaying at a rate of 1.7% that means 98.3% will remain after decaying.

For time t = 1 years , N/\(N^{0}\) = 0.983

Therefore, we have

N/\(N^{0}\) = \(e^{-kt}\)

0.983 = \(e^{-k }\)

-k = ln(0.983)

-k = -0.017

K = 0.017 \(year^{-1}\)

Now for half life, We can write N/\(N^{0}\) = 0.5

Therefore, N/\(N^{0}\) = \(e^{-kt}\)

              0.5 = \(e^{-0.017t}\)

ln(0.5) = -0.017t

-0.693 = -0.017t

t = 0.693/0.017 = 40.76 years

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Step-by-step explanation:

pure acid is a 100% acid solution.

x = ml of 100% solution

1×x + 0.3×400 = 0.75×(400 + x)

x + 120 = 300 + 0.75x

0.25x = 180

x = 720 ml

we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).

Answer:

In Q39, the value 3x should be positive and in Q40, the final answer is missing 8x and the fact that 4x^2 is negative (-4x^2)

Step-by-step explanation:

39:

1. \(-(-3x)\) is presented as \(-3x\) when it should be \(+3x\), as 2 negatives make a positive.

2. Again, \(-3x\) is shown instead of \(+3x\)

3. The answer \(-x^2-2x\) should instead be \(-x^2+4x\), as \(-3x\) is used to reach this incorrect answer instead of the correct \(+3x\)

40:

1. \((x^3-4x^2+3)+(-3x^3+8x-2)=(x^3-3x^3)-4x^2+8x+(3-2)=-2^3-4x^2+8x+1\),

The final answer is wrong as it is missing the 8x and the fact that it is \(-4x^2\)and not \(+4x^2\)

Answer:

2*f

Step-by-step explanation:

because all the rest are negative

In Tableau, a filter allows a visualization developer or user to dynamically remove rows from the visualization.  Thus, Option A is the answer.

What is Tableau?

Tableau is an interactive and intuitive data visualization tool that enables people to see and understand data. It provides a variety of data exploration, modelling, and visualization options. Tableau is one of the best data visualization software available in the market. It provides an easy way to integrate data from various sources. With Tableau, you can easily create interactive and visually appealing charts, graphs, and other types of visualizations that are easy to understand and interpret.

What is a filter?

In Tableau, a filter is a tool that allows you to selectively display data from a larger dataset based on certain conditions. Filters help you to narrow down your data to the most relevant information so you can make better decisions based on your analysis. Filters can be applied to different dimensions and measures to help you get a better view of your data. Tableau allows you to filter your data using various types of filters such as categorical, continuous, and relative filters. You can also create custom filters using calculated fields and parameters.

A filter allows a visualization developer or user to dynamically remove rows from the visualization. Therefore, the correct option is (a) Filter.

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Answer:

728

Step-by-step explanation:

(9x3)^2-4^0

First solve in parenthesis,

Then solve exponents.

27^2 - 4^0

729 - 1

728

Answer:

Step-by-step explanation:

You want a system of equations, their solution, and the interpretation of the solution for the scenario that Apple will be buying 12 ounces total of rice (x) at $1.73 per ounce and veggies (y) at $3.38 per ounce.

The given relations can be expressed in two equations:

The solution to these equations is shown in the attached graph. It is ...

  (x, y) ≈ (7.61, 4.39)

For Apple to buy 12 ounces of ingredients at a total cost of $28, Apple needs to buy 7.61 ounces of rice and 4.39 ounces of veggies.

__

Additional comment

If you understand the definitions of the variables, the interpretation is pretty straightforward:

  x = ounces of rice to purchase: x = 7.61 means Apple needs to purchase 7.61 ounces of rice.

  y = ounces of veggies to purchase: y = 4.39 means Apple needs to purchase 4.39 ounces of veggies.

My graphing calculator offers at least 3 different ways to solve a system of equations like this. I like the graphical solution, because it is convenient to type the equations in their original form, and the solution is given as an ordered pair.

Answer:

i think songs it might be correct but im not sure

The inequality that represents the number of songs and videos Patrick can buy using only his gift certificate is s + 2.50v ≤ 25

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

Let's suppose the number of songs is 's' and number of videos is 'v'

Total cost for songs = $s

Total cost for videos = $2.50v

Patrick has a gift certificate for $25

Then the inequality that represents the number of songs and videos Patrick can buy using only his gift certificate is:

s + 2.50v ≤ 25

Thus, the inequality that represents the number of songs and videos Patrick can buy using only his gift certificate is s + 2.50v ≤ 25

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So, the probability that the next car to drive by Pablo's house will be red or blue is 12/25 that is option C.

Probability is a measure of the likelihood or chance that a particular event or outcome will occur, expressed as a number between 0 and 1, where 0 represents impossibility (an event that will not occur) and 1 represents certainty (an event that will definitely occur). Probability is used to quantify uncertainty and randomness in various fields, such as mathematics, statistics, physics, economics, engineering, and many other areas of science and everyday life.

Here,

To find the probability that the next car to drive by Pablo's house will be red or blue, we need to add up the number of cars that are red or blue and divide it by the total number of cars recorded.

From the table provided, we can see that the number of blue cars is 70 and the number of red cars is 50. Therefore, the total number of cars that are either red or blue is 70 + 50 = 120.

The total number of cars recorded is given as 250, so the probability of the next car being red or blue is:

Probability = Number of red or blue cars / Total number of cars recorded

Probability = 120 / 250

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 120 and 250 is 10.

Probability = 12 / 25

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a. The truck rental cost when you drive 85 miles is  $85.7.

b. The number of miles driven when the cost is $65.96 is 0.42x.

a. To find the truck rental cost when driving 85 miles, we can substitute the value of x into the given function.

f(x) = 0.42x + 50

Substituting x = 85:

f(85) = 0.42(85) + 50

= 35.7 + 50

= 85.7

Therefore, the truck rental cost when driving 85 miles is $85.70.

b. To determine the number of miles driven when the cost is $65.96, we can set up an equation using the given function.

f(x) = 0.42x + 50

Substituting f(x) = 65.96:

65.96 = 0.42x + 50

Subtracting 50 from both sides:

65.96 - 50 = 0.42x

15.96 = 0.42x

To isolate x, we divide both sides by 0.42:

15.96 / 0.42 = x

38 = x

Therefore, the number of miles driven when the cost is $65.96 is 38 miles.

In summary, when driving 85 miles, the truck rental cost is $85.70, and when the cost is $65.96, the number of miles driven is 38 miles.

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To compute 101^(4,800,000,023) mod 35 using the Chinese Remainder Theorem, we need to first decompose 35 into its prime factors: 35 = 5 × 7.

Next, we need to compute 101^(4,800,000,023) mod 5 and 101^(4,800,000,023) mod 7 separately.

To compute 101^(4,800,000,023) mod 5, we can use Fermat's Little Theorem, which states that if p is a prime number and a is a positive integer not divisible by p, then a^(p-1) ≡ 1 mod p. Since 5 is prime and 101 is not divisible by 5, we have 101^(4) ≡ 1 mod 5. Therefore, 101^(4,800,000,023) ≡ 101^(4 × 1,200,000,005 + 3) ≡ (101^4)^1,200,000,005 × 101^3 ≡ 1^1,200,000,005 × 101^3 ≡ 1 × 101^3 ≡ 1 mod 5.

To compute 101^(4,800,000,023) mod 7, we can use Euler's Totient Theorem, which states that if a and m are coprime positive integers, then a^φ(m) ≡ 1 mod m, where φ(m) is Euler's totient function. Since 7 is prime and φ(7) = 6, we have 101^6 ≡ 1 mod 7. Therefore, 101^(4,800,000,023) ≡ 101^(6 × 800,000,003 + 5) ≡ (101^6)^800,000,003 × 101^5 ≡ 1^800,000,003 × 101^5 ≡ 101^5 ≡ 4 mod 7.

Now we can use the Chinese Remainder Theorem to combine the results. Let x ≡ 1 mod 5 and x ≡ 4 mod 7. Then we can write x = 5k + 1 for some integer k. Substituting this into the second congruence, we get 5k + 1 ≡ 4 mod 7, or equivalently, k ≡ 6 mod 7. Therefore, x = 5k + 1 ≡ 5(6) + 1 ≡ 31 mod 35.

Hence, 101^(4,800,000,023) mod 35 = x = 31.

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The surface area of the regular three-sided prism is 26√3 cm².

Now, For the surface area of the prism, We can find the area of each of its five faces and add them together.

First, let's find the length of the base edge.

Let's take it "s".

We know that the surface area of the base is 4√3 cm²,

Hence, We get;

A = (sqrt(3)/4)s = 4√3

Solving for "s", we get:

s = 2 cm

Next, we need to find the height of the prism.

We know that the height is 3 times greater than the length of the base edge, so:

h = 3s = 6 cm

Now we can find the area of each face of the prism using the formula for the area of an equilateral triangle:

A = (√(3)/4)s

A = (√(3)/4)(2 cm)

A = √3 cm²

Since, The prism has five faces.

Therefore, the total surface area of the prism is:

A = 2(4√3 cm²) + 3(√3 cm²)(6 cm)

A = 8√3 cm² + 18√3 cm²

A = 26√3 cm²

Therefore, The surface area of the regular three-sided prism is ,

= 26√3 cm².

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==========================================================

Explanation:

We'll break things up into cases. The phrasing "at least 3" means "3 or more".

We either will have 3 kings or 4 kings.

----------------------------------------------

Case A) There are exactly 3 kings.

Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.

Put another way: there are 4 ways to leave a certain king out of the hand.

Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128

To recap, we found

That gives 4*1128 = 4512 ways to have case A happen.

----------------------------------------------

Case B) There are exactly 4 kings

4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.

Overall there are 1*48 = 48 ways to have case B play out.

----------------------------------------------

There were 4512 ways to have case A happen, and 48 ways to have case B happen.

These cases are mutually exclusive to allow us to simply add the counts:

4512+48 = 4560

This is why the final answer is 4560

9514 1404 393

Answer:

  21.  3x^2 +7x

  22.  6x^3 +3x

Step-by-step explanation:

21. The perimeter is the sum of the side lengths.

  P = (x^2 +3x +1) +(4x -1) +(2x^2)

  P = x^2(1 +2) +x(3 +4) +(1 -1) . . . . combine like terms

  P = 3x^2 +7x

__

22. The area is the product of the dimensions.

  A = (3x)(2x^2 +1)

  A = 6x^3 +3x . . . . . use the distributive property

Answer:

3

Step-by-step explanation:

The interquartile range is where the 2nd and 5th dots are, on the opposite ends of the square, from 15-18.

Answer:

3

Step-by-step explanation:

The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁).

In a box plot:

From inspection of the given box plot:

Therefore:

IQR = Q₃ - Q₁

      = 18 - 15

      = 3

So the interquartile range of the given box plot is 3.