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The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

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Answer: 64

Step-by-step explanation:

(47 + 39) - 22

= 86 - 22

= 64

Answer:

Step-by-step explanation:

\(\frac{(12a - 6bc - 3)}{20ab-5c)} \\\\\frac{3 . (4a - 2bc - 1)}{5 . (4ab - c)}\\\\\)

Answer:

Step-by-step explanation:

What is the rate in miles per gallon:

gallons used:           28        39        42

miles;                      628.4  947.7  1020.6

The answer is below

Solution:

A linear function is a function in the form:

y = mx + b; where y is a dependent variable, x is an independent variable, m is the rate of change of y with respect to x, and b is the initial value of y when x is zero.

From the table, we are given the gallon used to cover a distance in miles. To calculate the rate, we can select two points from the table. Using the points in the form (miles, gallons used): (628.4, 28) and (1020.6, 42) we get:

\(m=\frac{1020.6-628.4}{42-28}\\\\m=28\ miles\ per\ gallon\)

The approximation of the expression ln(6.9 * e⁻⁶) is (b) -4.0685

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

ln(6.9 * e⁻⁶)

Evaluate the exponent

So, we have

ln(6.9 * e⁻⁶) = ln(6.9 * 0.002479)

When the products are evaluated, we have

So, we have

ln(6.9 * e⁻⁶) = ln(0.0171051)

Take the natural logarithm

ln(6.9 * e⁻⁶) = -4.06837861433

Approximate

ln(6.9 * e⁻⁶) = -4.0685

Hence, the approximation of the expression is (b) -4.0685

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Answer:

15

Step-by-step explanation:

I hope you have a great day and welcome to brainly!

Answer:

= 33.3333% decrease

Step-by-step explanation:

(200−300)|300|×100

=−100300×100

=−0.333333×100

=−33.3333%change

=33.3333%decrease

The factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

y =x³-4x²-17x+60x

Let us assume that the factors are

(x−a), (x−b) and (x- c)

So, if x is either equal to a or b or c, y=0

and a⋅ b⋅ c=−60, which means a or b and c are factors of 60.

Thus, which factor of 60 (such as 2, 3, 5, 6, 10 etc.) makes y=0.

It is given that (x−3) is a factor of y

and, When we divide y by (x−3), we get x²−x−20

Similarly x=5 makes x²−x−20 equal and Dividing x2−x−20 by (x−5), we get (x+4)

Hence, the factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)

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Answer:

supplementary angles

Step-by-step explanation:

Answer:

supplementary angle

The expression that can be factored by grouping is pr + ps + qr + qs. We can group the terms into two groups, factor out the common factors from each group, and simplify the expression to get (p+q)(r+s). So, the correct answer is D).

The expression that could be factored by grouping is

pr + ps + qr + qs

To factor this expression by grouping, we can first group the first two terms and the last two terms

(pr + ps) + (qr + qs)

We can then factor out the common factors from each group

pr + ps = p(r+s)

qr + qs = q(r+s)

We can see that both groups have a common factor of (r+s), so we can further simplify the expression

(p+q)(r+s)

Therefore, the final factored form of the expression pr + ps + qr + qs is (p+q)(r+s).

None of the other expressions given can be factored by grouping.

For pq + ps - pr + pt, we cannot group any two terms that have a common factor. For pq + rs - pq + rs, we can simplify it as 2rs, but it cannot be factored by grouping. For pr + ps - qr - qs, we cannot group any two terms that have a common factor. So, the correct option is D).

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Answer:

7

Step-by-step explanation:

since the whole line is 10 and QR Is a part of the line and is 3. we subtract 3 from 10 to get our answer which is 7.

As each side of the cube has a surface area of 24in².the total amount of wrapping paper needed is 64in².

Surface area is the total area of a three-dimensional object's surface, including the area of its faces and any curved surfaces.

To calculate the amount of wrapping paper needed for the cube, we can use the formula for the surface area of a cube:

SA = 6 x (side)²

In this case, the side of the cube is 2in,

so the SA = 6 x (2in)² = 24in²

To get the amount of wrapping paper needed, we would need to multiply this by 4, as each side of the cube has a surface area of 24in².

Therefore, the total amount of wrapping paper needed is

24in² x 4 = 96in²

To convert this to a square, we would need to divide it by 4, as each side of the square is equal in length.

Therefore, the total amount of wrapping paper needed is

96in² / 4

= 24in x 4

= 64in².

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The null hypothesis for the test would be that there is no difference between the ratings for the existing coffee flavors and the newly introduced holiday flavor. The alternative hypothesis would be that there is a significant difference between the ratings.If the p-value of the test is less than the level of significance, the company can reject the null hypothesis and conclude that there is a significant difference between the ratings for the two sets of flavors. This would indicate that the holiday flavor is preferred more than the existing flavors and the company can introduce it as a new flavor for the holiday season.

The coffee company can use a hypothesis test for matched pairs in a situation where they want to compare the preferences of their customers for the existing coffee flavors with the newly introduced holiday flavor. By conducting a matched-pairs hypothesis test, the company can determine whether the holiday flavor is preferred more than the existing flavors.Matched-pairs hypothesis test is a statistical test used to determine the difference between two related variables. In this case, the related variables are the preferences of the customers for existing coffee flavors and the newly introduced holiday flavor. The test involves measuring the differences between the paired variables and determining whether the differences are significant enough to indicate a preference for one flavor over the other.
For instance, the coffee company can conduct a survey among its customers to determine their preferences for the different coffee flavors. The survey can involve asking the customers to rate the existing coffee flavors and the newly introduced holiday flavor on a scale of 1 to 10. The company can then compare the ratings for each customer to determine whether the holiday flavor is preferred more than the existing flavors.After collecting the data, the company can use a paired t-test to determine whether the differences in the ratings are significant.

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Answer:

x = 7

Step-by-step explanation:

Given

4x - 2(x - 2) = - 4 + 5x - 13 ← distribute left side and simplify

4x - 2x + 4 = 5x - 17

2x + 4 = 5x - 17 ( subtract 5x from both sides )

- 3x + 4 = - 17 ( subtract 4 from both sides )

- 3x = - 21 ( divide both sides by - 3 )

x = 7

Answer:

y=x-9

Or

m=1

b= -9

Step-by-step explanation:

m is slope so we know since it is a parrellel line both lines need the same slope and it’s 1

Now to find y intercept we just fill in the coordinates to find b

-2=7+b

-7 -7

-9=b

y=x-9

Hopes this helps please mark brainliest

Answer: 150 degrees

Step-by-step explanation:

The number of degrees did it rotate altogether should be considered as the 150 degrees.

Since A sprinkler rotates 75°, pauses, and then rotates another 75

So, here total degrees be like

= 75 degrees + 75 degrees

= 150 degrees

hence, The number of degrees did it rotate altogether should be considered as the 150 degrees.

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Step-by-step explanation:

42=2b-14 where b=price of the blouse

42+14=2b

56=2b

b=56/2

b=$28 is the price of the blouse

Answer: 42-14=28$

Step-by-step explanation:

       Hence, OPTION (C) is your answer:  X  =  44

Step-by-step explanation:

       √x + 5 - 3 = 4

        √x +  5   =  3  +  4

        √x +  5   =   7

         (√x  +   5)2     =     (7)2

            x   +   5         =   49

        x   -  44     =   0

             +44      =   44

       X                =   44

       Hence,  X  =  44

        Equation: √x  +  5  =  7

      √(44)  +  5  =  7

    √49  =   7

            Hence,   x   =   44

        I hope this helps!

The presence of duplicate numbers in a random sample does not indicate a higher probability. Each run of random numbers is independent of any specific number is not affected by its occurrence in previous runs.

Random numbers are generated independently from each other, and each number has an equal chance of being selected in each run. The occurrence of duplicate numbers in a single run is purely coincidental and does not impact the probability distribution of subsequent runs. In fact, the presence of duplicates in one run has no bearing on the occurrence or absence of duplicates in future runs.

The probability of a specific number appearing in each run remains constant, regardless of its past occurrences. Each number is selected randomly and independently, following the distribution and range of the random number generator used. Therefore, the appearance of duplicates in one run does not imply that those numbers will have a higher likelihood of appearing again in subsequent runs. Each run should be treated as a separate and independent event when analyzing random numbers.

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The probability of Sam having a cheeseburger along with an apple juice  is 1/6. can be found by multiplying the probabilities of choosing a cheeseburger and an apple juice.

Step 1: Determine the probability of choosing a cheeseburger.
Since Sam has the options of a hamburger, a cheeseburger, or a chicken burger, and there are three choices in total, the probability of Sam choosing a cheeseburger is 1/3.

Step 2: Determine the probability of choosing an apple juice.
Similarly, since Sam has the options of orange juice or apple juice, and there are two choices in total, the probability of Sam choosing an apple juice is 1/2.

Step 3: Calculate the probability of having a cheeseburger and an apple juice.
To find the probability of two independent events occurring together, we multiply the individual probabilities. Therefore, the probability of Sam having a cheeseburger along with an apple juice is (1/3) * (1/2) = 1/6.

So, the probability of Sam having a cheeseburger along with an apple juice is 1/6.

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the answer is b. x =7

steps

176=(3x+5)+(21x+3)

176=24x+8

168=24x

x=7

Answer:

3

Step-by-step explanation:

30 ×10%/100%=3

percentage is always out of 100 that's why 10%over 100%

hope this will help mate

the only critical number of g(y) is -1/4.

To find the critical numbers of the function g(y) = y - 2y^2 - 2y + 4, we need to find its derivative and set it equal to zero.

g'(y) = 1 - 4y - 2

Setting g'(y) = 0, we get:

1 - 4y - 2 = 0

-4y - 1 = 0

y = -1/4

what is number?

A number is a mathematical object used to represent a quantity or value. Numbers can be classified into different types based on their properties and the set of numbers they belong to. Some common types of numbers include:

Natural numbers: These are the counting numbers, such as 1, 2, 3, and so on.

Whole numbers: These are the natural numbers plus zero, such as 0, 1, 2, 3, and so on.

Integers: These are the whole numbers plus their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3, and so on.

Rational numbers: These are numbers that can be expressed as a ratio of two integers, such as 1/2, 0.75, or -3/4.

Irrational numbers: These are numbers that cannot be expressed as a ratio of two integers, such as pi (3.14159...) or the square root of 2 (1.41421...).

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the probability that a tomato grown in the special soil will be a winner is approximately 0.0228 or 2.28%.

To find the probability that a tomato grown in the special soil will be a winner, we need to determine the probability that its diameter is greater than 4 inches.

Let's denote the mean diameter as μ and the standard deviation as σ.

Given:

Mean diameter (μ) = 3.2 in.

Standard deviation (σ) = 0.4 in.

To calculate the probability, we need to standardize the value 4 inches using the standard normal distribution.

The standardized value (z-score) can be calculated using the formula:

z = (x - μ) / σ

Substituting the values into the formula:

z = (4 - 3.2) / 0.4

z = 0.8 / 0.4

z = 2

Now, we need to find the probability of a z-score greater than 2. This can be determined using a standard normal distribution table or a calculator.

Looking up the z-score of 2 in a standard normal distribution table, we find that the probability associated with it is approximately 0.9772.

However, since we are interested in the probability of the tomato's diameter being greater than 4 inches, which corresponds to the right tail of the distribution, we subtract this probability from 1 to obtain the desired probability:

P(diameter > 4) = 1 - 0.9772 ≈ 0.0228

Therefore, the probability that a tomato grown in the special soil will be a winner is approximately 0.0228 or 2.28%.

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Let Z be a standard normal random variable. We want to determine the value of z if the area between –z and z is 0.754.Step 1: Sketch a standard normal curveThe standard normal curve is a normal curve with a mean of 0 and a standard deviation of 1.

The total area under the standard normal curve is equal to 1.Step 2: Shade the area under the curveWe want to shade the area between –z and z. We do not know the value of z, but we know that the area between –z and z is 0.754. Therefore, the area to the right of z is (1 – 0.754)/2 = 0.123 and the area to the left of –z is also 0.123.Step 3: Look up the z-scoreUsing a z-score table, we find that the area to the right of z is 0.123. The closest value to 0.123 in the table is 0.1226, which corresponds to a z-score of 1.16. Therefore, the value of z is 1.16.Answer: d. 1.16

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Answer:

36,000

Step-by-step explanation:

Area formula- A=LW (length x width)

450 (length) x 80 (width)

450

 80

-------

36,000

(45 x 8 and add two zeros :))