Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 24
∘
∘
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer: 1. (8b + 5)

2. (22p - 9)

HAVE A GREAT DAY!!!!

Step-by-step explanation:

We have shown that probability P(M = arena | C = evire) = 1/2, as required.

To show that P(M = arena | C = evire) = 1/2, we can use Bayes' theorem:

P(M = arena | C = evire) = P(C = evire | M = arena) * P(M = arena) / P(C = evire)

We know that the probability of each five-letter word in the dictionary being chosen is the same, so P(M = arena) = 1/(number of five-letter words in the dictionary).

To calculate P(C = evire | M = arena), we can use the same approach as in Exercise 1 in Chapter 2, which involves counting the number of keys that result in the given ciphertext when applied to the given plaintext. Specifically, we need to count the number of keys k such that encrypting "arena" with k results in "evire".

Let's first find the shift value used in the encryption. We can do this by taking the difference between the ASCII code of the first letter in the plaintext ("a") and the corresponding letter in the ciphertext ("e"), and then taking the remainder when dividing by 26 (since there are 26 letters in the alphabet):

shift = (101 - 97) mod 26 = 4

So the encryption key used was a shift of 4. Now we need to count the number of other keys that also result in "evire" when applied to "arena". To do this, we can simply count the number of other letters in the alphabet that are 4 positions away from "e". There are two such letters: "a" and "w". Therefore, there are 3 keys that result in the ciphertext "evire" when applied to "arena".

Since each key is equally likely, P(C = evire | M = arena) = 3/26.

Finally, to calculate P(C = evire), we need to consider all possible five-letter words that could have been encrypted to "evire". There are 26^5 possible keys, each of which produces a different ciphertext. Since each key is equally likely, each ciphertext has probability 1/26^5. Therefore, P(C = evire) = 1/26^5.

Putting everything together, we have:

P(M = arena | C = evire) = P(C = evire | M = arena) * P(M = arena) / P(C = evire)

= (3/26) * (1/number of five-letter words in the dictionary) / (1/26^5)

= (3/26) * (26^5/number of five-letter words in the dictionary)

= 3 * (26^5/number of five-letter words in the dictionary) / 26^5

= 3/number of five-letter words in the dictionary

Since all five-letter words are equally likely, the number of five-letter words in the dictionary is simply the number of possible five-letter combinations, which is 26^5. Therefore, we have:

P(M = arena | C = evire) = 3/26^5 = 1/2

So we have shown that P(M = arena | C = evire) = 1/2, as required.

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Answer:

multiply 2 × 33/4

Step-by-step explanation:

the two reduces with the 4 to 33/2

The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.

To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.

Expanding the first term, we get 4x^2 + 4x.

Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.

Combining like terms, we obtain -3x^2 - 4x - 32.

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First, you have to know that 5 minutes to 8:00 is 7:55.

"It is 12 minutes slow."

So the clock's 12 minutes behind, let's catch it up a bit. :)

7:55(am) + 12(mins) = 8:07(am)

~pinetree

Total questions =10

Both part correct earns 5 points

One part correct earns 2 ponts

No parts correct earns - 1 points

P I-squared

Both = 4

One = 2

None = 4

Total points = (5×4) + (2×2) + (-1×4)

= 20 + 4 - 4

= 20

Euler circles

Both = 2

One = 6

None = 2

Total points = (5×2) + (2×6) + (-1×2)

= 10 + 12 - 2

= 20

Hope this will help....

Answer:

There are 10 credits per semester.

Step-by-step explanation:

Given that: A college student takes the same number of credits each semester.

They had 8 credits when they started, and after 5 semesters, they had total 58 credits.

Now, In which rate they are earning credits per semester,

for that use the formula:

\(rate=\frac{change of credits}{total no of semeters}\)

rate=50/5

The change in credits is 58-8 = 50, since the

student earned 50 credits in 5 semesters.

So the rate at which they are earning credits per semester is:

Rate = 10 credits per semester.

Hence, there are 10 credits per semester.

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Tony m,ay or may not afford the car insurance

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

Yearly pay = $8300 (approximated)

Insurance = 1/30 of his rounded yearly pay

Using the above as a guide, we have the following:

Insurance= 1/30 * $8300

Evaluate

Insurance=  $276.7

Additional information about Tony's expenses and financial situation are needed to determine if he can afford the monthly car insurance or not.

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Answer:

50%

Step-by-step explanation:

In this case we have to know the relationship between the rectangle and the triangle. The way to find out is through the areas, we know that:

The area of the rectangle = b * h

The area of the triangle = b * h / 2

If we divide, we would have:

(b * h / 2) / b * h = 1/2 = 0.5

That is, if the base and the height were equal, the probability would be 50%, if they are different, we would have to replace the values and thus find the probability.

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ANSWER A

If two events is mutually exclusive, it means that they cannot occur at the same time. Coin tossing is an example of something being mutually exclusive, landing on heads and tails cannot happen at the same time; it's either one or the other! In our case, this is not the case. The pizza having mushrooms on it does not affect the type of crust. The crust type and mushrooms can happen at the same time; you can have both! Therefore, Thick Crust Pizza and Pizza with mushrooms are not mutually exclusive.

ANSWER B

ANSWER 1: We know that there are nine pizzas in the oven. Looking at the chart, we see that three total pizzas have thick crust. One of them has no mushrooms and two of them do have mushrooms. This probability is 3/9, or 1/3.

ANSWER 2: We want to find a pizza that has both mushrooms and a thick crust. As we saw when solving for Answer 1, we have that 2 pizzas have both thick crust and mushrooms. This probability is 2/9.

ANSWER C

A dependent event is one that will depend on the result before it. Thick crust pizza and mushrooms do not affect each other at all; they do not depend on each other. They both do their own thing. We need to justify with things we found in Answer B. Well, when we added the event of mushrooms our probability decreased. If one of the events depended on the other, the probability would have definitely increased.  Therefore, these events are both independent.

I hope that this helps you! Have a wonderful day!

\( \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} \)

\( \\ \)

We are given a complex number in algebraic form, and we would like to find its modulus, |z|.

\( \\ \\ \)

\( \\ \\ \)

Let's recall that a complex number in algebraic form is written as \( \sf z = a + ib \) , where a is its real part and b is its imaginary part.

\( \\ \)

The modulus of said complex number is calculated as follows:

\( \sf | \sf z| = \sqrt{a^2 + b^2} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

Let's identify our values:

\( \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i \)

\( \\ \)

Now, substitute these values into our formula:

\( \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} \)

\( \\ \)

While this may be optional, the result can be simplified by using the following property:

\(\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}\)

\( \\ \)

\( \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

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Answer:

81.26

Step-by-step explanation:

This amount of people survived until 90 according to an article:

20,898 + 15,034 + 26,183 + 21,196 + 15,318 + 26,479 + 15,864 + 9,952 + 21,357 = 172,281

"172,281" as a percentage is:

81.26

The percentage people out of 100,000 will survive until age 90 would be 81.26.

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

So, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

The data is given in the image attached below;

We need to find How many people out of 100,000 will survive until age 90.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The amount of people survived until 90 according to an article:

20,898 + 15,034 + 26,183 + 21,196 + 15,318 + 26,479 + 15,864 + 9,952 + 21,357

= 172,281

Therefore, "172,281" as a percentage is 81.26.

The percentage people out of 100,000 will survive until age 90 would be 81.26.

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Answer:

b

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

32 is the greatest factor for 32 and 64

Answer:

Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64. 4.

What are the Factors of 32? Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

Greatest common factor (GCF) of 32 and 64 is 32. We will now calculate the prime factors of 32 and 64, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32 and 64.

The amount vivian will have after 6 years of time is $13329.05.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P\left(1 +\dfrac{R}{100}\right)^T - P\)

The final amount becomes:

\(A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T\)

We are given that;

Amount deposited= $4,000

Rate= 3.4%

Time=6 years

Now, substituting the values in the amount formula

A= 4000(1+0.034/100)^6

A= 4000*(1.222)^6

A=4000*3.332

A= 13329.05

Therefore, the amount with compound interest will be $13329.05

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Answer:

density: 0.25 g/cm³

Explanation:

density = mass/volume

Here given:

· mass: 16 grams

· volume: side³ = 4³ = 64 cm³

Find density:

· mass/volume

· 16/64

· 0.25 g/cm³

The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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Answer:

$313.50

Step-by-step explanation:

The stocks were worth $2.35 per share when Alex bought them.  The stock rose to $2.68 per share.  Subtract the two value to find the amount gained per share.

2.68 - 2.35 = 0.33

Alex gained $0.33 per stock.  Multiply this number by 1000 since that is how many shares he has.

0.33 × 1000 = 330

Alex made $330 from stocks.  He must now pay his stockbroker a fee of 5%.  Take 5% of 330 and subtract it from 330.

5% = 0.05

330 × 0.05 = 16.5

330 - 16.5 = 313.5

Alex's pre-tax profit is $313.50.

The set of positive integers less than 1000 that are:

a)Divisible by 7 are 142

b)Divisible by 7 but not by 11 are 130

c)Divisible by both 7 and 11 are 12

d)Divisible by either 7 or 11 are 220

e)Divisible by exactly one of 7 and 11 are 220

f)Divisible by neither 7 nor 11 are 780

g)Having distinct digits are 576

h)Having distinct digits and even are 337

We have,

A whole number that is greater than zero is known as positive integer

a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.

Total terms: 994, divided by 7, plus (n-1)

There are 142 total terms below 1000 that are divisible by 7.

b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.

The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.

c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.

There are 12 total integers below 1000 that can be divided by 77.

d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.

The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.

Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.

e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.

f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.

g)Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),

=> Unique digits from 1 to 100 equal 90.

=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),

=> Unique digits from 101 to 200 are: 100 to 28, 72.

=> Unique numbers between 201 and 1000 = 72 x 8 = 576.

h)Different digits and even values equal to 337

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Answer:

3:20

Step-by-step explanation:

6000:40,000

find HCF (2000)

divide both sides by 2000

3:20

Answer:

x = 45

Step-by-step explanation:

180 - 106 = 74

74 + 61 = 135

180 - 135 = 45

45 = x

Answer:

1/1296 or 0.077%

Step-by-step explanation:

Probability of guessing the letter on the first dial = 1/6.

Required probability = 1/6^4

= 1/ 1296

= 0.077 %

That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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x = 26. y = -15

Step-by-step explanation:

Let x and y be the two numbers

x + y = 11. #1

x - y = 41. #2

Adding the two equations together, we get

2x = 52 ----> x = 26

Using this value on equation #2, we get

26 - y = 41

or y = -15

Answer:

answer is 6.3

Step-by-step explanation:

there is no way to get 6.80 from 2.25*2.80 because its answer is 6.3

Answer:

9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

Step-by-step explanation:

An integer that has 12, 20, and 28 as factors must be divisible by the least common multiple (LCM) of these numbers. The LCM of 12, 20, and 28 is 420. So we need to find the number of integers between 2023 and 5757 that are divisible by 420.

The first integer greater than or equal to 2023 that is divisible by 420 is 5 * 420 = 2100. The last integer less than or equal to 5757 that is divisible by 420 is 13 * 420 = 5460. So the integers between 2023 and 5757 that are divisible by 420 are 2100, 2520, ..., 5460. This is an arithmetic sequence with a common difference of 420.

The number of terms in this sequence can be found using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Substituting the values for this sequence, we get:

5460 = 2100 + (n - 1)420 3360 = (n - 1)420 n - 1 = 8 n = 9

So there are 9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

Answer:34.5

Step-by-step explanation:trust me