a method to solving a system of equations by getting rid of one of the variables first to solve for the other variable

The length of the diagonal of this rectangle is equal to: B. 21.25.

In order to determine the length of the diagonal of this rectangle, we would have to apply Pythagorean's theorem.

In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

By substituting the side lengths of this rectangle, we have:

z² = x² + y²

z² = 12.75² + 17²

z² = 451.56

z = √451.56

z = 21.25 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:37.5

Step-by-step explanation:

that's the answer

The required expression for Jose's height is 2j + 7.

Given that,

Height of Jose = j

Here we have to find the mathematical expression for the given statement.

And we know that Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

The proceed formation of expression,

The twice of Jose's height = 2j

Therefore,

7 more than Jose's height can be represented as

⇒ 2j + 7

Hence the expression is   2j + 7

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The area of the largest circular rug that she can buy to fit the space is given as follows:

B. 30.2 ft².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The side length of the square is of 6.2 ft, which is equivalent to the diameter of the circle, hence the radius is given as follows:

r = 0.5 x 6.2

r = 3.1 ft.

Hence the area of the rug is obtained as follows:

A = 3.14 x 3.1²

A = 30.2 ft².

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Answer:

Step-by-step explanation:

Without knowing the cost of college or the student's financial aid package, it is difficult to make definitive statements about the possible choices for college. However, based on the given information, we can make some assumptions and estimates.

Assuming the student saves $50 per month for 60 months (5 years), they will have an additional $3,000 ($50 x 60 = $3,000). Adding the initial savings of $1,200, the total savings would be $4,200.

If we assume the cost of college to be $10,000 per year, the $4,200 in savings would not be sufficient to cover even one year of college expenses. However, if the student receives financial aid or scholarships, their savings may be sufficient to cover some of the remaining costs.

If outliers are present in a dataset, but their removal is justified and results in a data set for which the z-test is appropriate, then the z-test can be used to test a hypothesis about the mean of the dataset.

The z-test is a parametric test that assumes the data is normally distributed and that the population standard deviation is known or can be estimated from the sample.

Outliers can affect the normality assumption and the estimation of the standard deviation, leading to incorrect results if not handled properly.

If outliers are identified and can be removed based on a valid justification (e.g., measurement error, data entry error), then the resulting dataset can be checked for normality using methods such as the Shapiro-Wilk test or visual inspection of a normal probability plot.

If the dataset is approximately normal, and the sample size is sufficiently large, then the z-test can be used to test a hypothesis about the mean.

However,

It is important to note that outlier removal should be done with caution and based on valid justifications. ++

Arbitrarily removing outliers without justification can lead to bias and incorrect conclusions.

Additionally,

There are also non-parametric tests that can be used to test hypotheses about the median or other measures of central tendency that are robust to outliers.

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The mean of the data is 1268/5 = 253.6

The median of the data is 248.

To find the mean of the data, we will first add up all the figures and divide the result by the total number of data available to us. This can be obtained thus: 248 + 176 + 379 + 263 + 202 = 1268

Now, we divide this sum by 5 which equals 253.6

Next, to find the median of the data, we first organize in ascending order as follows:

173, 202, 248, 263, 379.

Now, we will chack the middle number and this is 248.

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The angle relationship between each pair of angles include:

∠4, and ∠5, ∠3  and ∠6, ∠11  and  ∠14, ∠12 and ∠13 are alternate interior angles.

∠2 and ∠7, ∠1 and ∠8, ∠9 and ∠16, ∠10 and ∠15 are alternate exterior angles.

∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠9 and ∠13, ∠11 and ∠15, ∠10 and ∠14, ∠12 and ∠16 are corresponding angles.

∠3 and ∠5, ∠4 and ∠6, ∠11 and ∠13, ∠12 and ∠14 are consecutive interior angles

Corresponding angles - Two angles are corresponding if they are in the same position relative to two parallel lines and a transversal, and are equal in measure. Alternate interior angles - Two angles are alternate interior angles if they are on opposite sides of the transversal and inside the two parallel lines, and are equal in measure.

Alternate exterior angles - Two angles are alternate exterior angles if they are on opposite sides of the transversal and outside the two parallel lines, and are equal in measure.

Interior angles on the same side of the transversal: Two angles are interior angles on the same side of the transversal if they are on the same side of the transversal and inside the two parallel lines, and their measures add up to 180 degrees.

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This means that the weight of the ear of corn is 0.55 standard deviations below the mean weight of the distribution for the Ohio farm's corn.

To determine how many standard deviations an observation is from the mean of a distribution, we need to calculate its z-score. The z-score measures the number of standard deviations an observation is above or below the mean.

Let's assume we know the mean and standard deviation of the distribution of weights for the Ohio farm's corn. For example, let's say that the mean weight is 1.5 pounds and the standard deviation is 0.2 pounds.

Then, we can calculate the z-score for an ear of corn that weighs 1.39 pounds using the formula:

z = (x - μ) / σ

where x is the weight of the ear of corn, μ is the mean weight of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have:

z = (1.39 - 1.5) / 0.2

z = -0.55

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The longest list of numbers that an average person can remember without any repetition is around 7 ± 2, according to Miller's Law.

Miller's Law suggests that the capacity of human short-term memory is limited to around 7 ± 2 items, or "chunks" of information. This means that if the professor reads a list of numbers to you without giving you a chance to repeat them, the longest list you are likely to remember is around 7 ± 2 numbers.

However, this capacity can be increased through the use of various memory strategies such as chunking, which involves grouping pieces of information into meaningful units. Additionally, the ability to remember numbers or any other type of information can vary greatly between individuals depending on factors such as age, cognitive ability, and previous experience with the material.

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The expression which represents the country's population after m months is 11.8 [(1.0066)^m].

Given a expression which is defined as,

11.8 (1.082)^y

This is the function which represents the future population, in millions, of a country after y years.

Here after m months, y changes to m/12 months.

11.8 (1.082)^(m/12)

= 11.8 [(1.082)^(1/12)]^(m)

= 11.8 [(1.006589)^m]

≈ 11.8 [(1.0066)^m]

Hence the correct option is A. 11.8 [(1.0066)^m].

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The answers to all parts are shown below.

1. The number of ways are

= 11!/ (11-1)!

= 11! /10!

= 11

2. The favorable outcomes of the event

Triangle= 1

star = 4

Not square= 9

Not circle= 8

3. C( 12, 1)= 12!/ 1! 11!

= 12 ways

4. Choose a cat = C(18, 12)= 18! / 12! 6!

= 18564

5. Choose a dog

= C(18, 6)

= 18!/ 6! 12!

= 18564

6. Bus arrive on time= 1-2/7 = 5/7

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The company's expected net gain from this 1-year term-life insurance policy is $30.

Determine the total cost of the insurance policy:

In this case, the cost of the policy is $450.
Calculate the payout if the man dies:  

If the man dies, the insurance company will have to pay out the policy value, which is $21,000.
Determine the probability of each outcome:

The probability that the man will live for another year is given as 0.98.

Since there are only two possible outcomes (the man either lives or dies), the probability that he will die within the year is 1 - 0.98 = 0.02.

Calculate the company's expected gain/loss for each outcome:
  - If the man lives, the company's gain will be the cost of the policy ($450) since no payout is made.
  - If the man dies, the company's loss will be the policy value ($21,000) minus the cost of the policy ($450), which equals $20,550.

Find the company's expected net gain by multiplying each outcome's gain/loss by its respective probability and adding the results:
  - Expected gain if the man lives = 0.98 * $450 = $441
  - Expected loss if the man dies = 0.02 * (-$20,550) = -$411
Add the expected gain and expected loss to find the company's expected net gain: $441 + (-$411) = $30.

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Hi! the answer to this question is C.

It will always be something in front of the square root as well. Since 45-45-90 has two congruent sides, the other legs will be equivalent to each other, except for the hypotnuse.

An example of what I mean below :). Hope this helps!

The numbers that replace A, B and C are given as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

y  = x² + x.

The letter A is replaced by the numeric value at x = -1, hence:

y = (-1)² + (-1)

y = 1 - 1

y = 0.

The letter B is replaced by the numeric value at x = 0, hence:

y = (0)² + (0)

y = 0.

The letter B is replaced by the numeric value at x = 1, hence:

y = 1² + 1

y = 2.

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Part A. The robot must have started 15 feet behind its position at t=0, which is at = (-3, -4) feet.

Part B. The location the robot will hit the edge of the prototype field is at ≈ (32.61, 100) feet.

We shall find out where the robot started by determining the robot's velocity vector.

Part A:

We can find the robot's velocity vector by dividing the displacement vector by the time elapsed:

Velocity vector = (15-9, 36-28) / (7-(-3)) = (6, 8) / 10 = (0.6, 0.8) feet per second.

Since the robot moves at a constant speed, we use the distance formula to find how far it traveled in the 3 seconds from t=-3 to t=0:

Distance = √((9-6)² + (28-8)²) = √(225) = 15 feet

Therefore, the robot started 15 feet behind its position at t=0, which is (6, 8) - (150.6, 150.8) = (6-9, 8-12) = (-3, -4) feet.

Part B:

Since the robot moves in a straight line, we find the equation of the line that it follows, and then find where it intersects the boundaries of the field.

The line passes through points (6,8) and (15,36), so, its slope is (36-8)/(15-6) = 28/9, and its y-intercept is 8 - (28/9)*6 = -4/3.

Therefore, the equation of the line is y = (28/9)*x - 4/3.

To find where the line intersects the left and right boundaries of the field, we plug in x=0 and x=100:

y = (28/9)*0 - 4/3 = -4/3

y = (28/9)*100 - 4/3 = 3112/9

Since the robot is in the top half of the field, we shall only find where the line intersects the top boundary, which is y=100:

100 = (28/9)x - 4/3

x = (9/28)(100 + 4/3)

= 32.61 feet (rounded to 2 decimal places)

Therefore, the robot will hit the edge of the prototype field at ≈ (32.61, 100) feet.

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2x⁴+2x³-12x² is the correct option.

Given is an expression, 2x²(x+3)(x-2), we need to expand it,

To expand the given expression, we must multiply each term of every expression to each term of the other two expressions.

The expansion is as follows :

= 2x²(x+3)(x-2)

= 2x²(x²+3x-2x-6)

= 2x²(x²+x-6)

= 2x⁴+2x³-12x²

Thus, the required expended form is 2x⁴+2x³-12x².

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The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use.

Memoization is a technique where we store the results of expensive function calls and return the cached result when the same inputs occur again. Here's a recursive function that uses memoization to calculate the n-th Bessel polynomial at x:

```
memo = {}  # Memoization cache

def B(n, x):
   if n == 0:
       return 1
   elif n == 1:
       return x + 1
   elif (n, x) in memo:
       return memo[(n, x)]
   else:
       result = (2 * n - 1) * x * B(n - 1, x) + B(n - 2, x)
       memo[(n, x)] = result
       return result
```

The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use. This approach avoids redundant calculations and can significantly speed up the computation of Bessel polynomials for large values of n.

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The problem is to count the number of prime numbers less than a non-negative number n.  # Count the number of prime numbers less than n
   return sum(is_prime)
```

The problem of counting the number of prime numbers less than a non-negative number n is a classic problem in number theory and has many practical applications in computer science and cryptography.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are the first 10 prime numbers.

To count the number of prime numbers less than n, we can use the Sieve of Eratosthenes algorithm. The algorithm works by iteratively marking the multiples of each prime number, starting with 2. For example, we start by marking all multiples of 2, then move to the next unmarked number (which must be a prime), and mark all of its multiples, and so on. At the end of this process, all unmarked numbers less than n are prime.

Here is an example implementation of the Sieve of Eratosthenes algorithm in Python:

```
def count_primes(n: int) -> int:
   if n < 2:
       return 0

   # Initialize a list of boolean values indicating whether each number is prime
   is_prime = [True] * n
   is_prime[0] = is_prime[1] = False

   # Iterate over all numbers less than the square root of n
   for i in range(2, int(n ** 0.5) + 1):
       if is_prime[i]:
           # Mark all multiples of i as not prime
           for j in range(i ** 2, n, i):
               is_prime[j] = False

   # Count the number of prime numbers less than n
   return sum(is_prime)
```

This implementation has a time complexity of O(n log log n), which is much faster than checking each number for primality individually.

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One mile will take her 13.4 minutes to walk. the correct answer is an option (B).

We can start by converting the units of speed to miles per hour (mph) and the distance to miles to make the calculations easier.

2.0 m/s = 2.0 x 3600/1609.34 = 4.47 mph

1 mile = 1 x 1609.34 = 1609.34 m

Time taken to walk one mile = distance ÷ speed = 1609.34 m ÷ 2.0 m/s = 804.67 seconds

Converting seconds to minutes, we get:

804.67 seconds ÷ 60 seconds/minute = 13.41 minutes

Therefore, one mile will take her 13.4 minutes to walk.

Hence, the answer is an option (B) 13.4 minutes.

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To find the length of the hypotenuse c in a right triangle with legs a = 16 and b = 30, we can use the Pythagorean theorem:

c^2 = a^2 + b^2

Substituting the given values, we get:

c^2 = 16^2 + 30^2

c^2 = 256 + 900

c^2 = 1156

Taking the square root of both sides, we get:

c = √1156

c ≈ 34.0 (rounded to the nearest tenth)

Therefore, the length of the hypotenuse c in the right triangle is approximately 34.0 units.

Their hourly wage in 3 more years (after a total of 13 years) will be 17.43 per hour.

We can solve this problem using the formula for exponential growth, which is:

[tex]A = P(1 + r)^t[/tex]

Where:

A = the amount after t years

P = the initial amount

r = the annual growth rate (expressed as a decimal)

t = the number of years

Let's use this formula to solve the problem:

Find the initial amount

The initial hourly wage is 7.40, so P = 7.40

Find the annual growth rate

The wages grew from 7.40 to 14.56 in 10 years, so we can use this information to find the annual growth rate:

[tex]14.56 = 7.40(1 + r)^{10}\\(1 + r)^{10} = 14.56/7.40\\(1 + r)^{10} = 1.97297\\1 + r = (1.97297)^{(1/10)[/tex]

1 + r = 1.076

r = 0.076 or 7.6%

So the annual growth rate is 7.6% (expressed as a decimal).

Find the amount after 13 years

We want to find the hourly wage in 3 more years, which is a total of 13 years (10 years of past growth + 3 more years). So t = 13.

[tex]A = P(1 + r)^t\\A = 7.40(1 + 0.076)^{13}\\A = 7.40(1.076)^{13}\\A = 7.40(2.355)[/tex]

A = 17.43 (rounded to two decimal places)

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The correct answer is option a. The slope of the least-squares regression line is 0.0298. This means that for every additional one mile increase in the flight distance, the predicted air fare increases by $0.0298.

In other words, there is a positive relationship between the distance of the flight and the air fare. As the distance of the flight increases, the air fare also increases. It is important to note that this is only a rough linear relationship and there may be other factors that affect the air fare such as seasonality, demand, and competition. The slope of the least-squares regression line helps us understand the direction and strength of the relationship between the two variables (distance and air fare). However, it is important to interpret this slope in context with other information such as the correlation coefficient, residual plots, and other regression diagnostics.

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The leading coefficient is 7, the degree of the polynomial is 2, the name of the polynomial is a quadratic polynomial, the number of terms is 2, and the type of polynomial is a quadratic trinomial.

Given that:

Expression, 5 + 12x + 7x²

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed.

Convert the equation into vertex form, then we have

⇒ 7x² + 12x + 5

⇒ 7[x² + (2·6/7)x + 36/49] - 36/7 + 5

⇒ 7 (x + 6/7)² - 1/7

The leading coefficient is 7, the degree of the polynomial is 2, the name of the polynomial is a quadratic polynomial, the number of terms is 2, and the type of polynomial is a quadratic trinomial.

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The radius of the cylinder is of 17 inches.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The parameters for this problem are given as follows:

V = 289π in³, r = 1 in.

Hence the radius of the cylinder is obtained as follows:

r² = 289

[tex]r = \sqrt{289}[/tex]

r = 17 inches.

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The requried Ricardo has 115 pitcher's cards in his collection.

If 46% of the cards in Ricardo's collection show players that are pitchers, then the number of pitcher's cards he has can be found by multiplying the total number of cards in his collection by 46%.

Using the decimal form of 46%, we have:

0.46 x 250 = 115

Therefore, Ricardo has 115 pitcher's cards in his collection.

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The constant of proportionality that relates the number of cups of cereal, y, to the number of cups of pretzel sticks, x is y= 5/2x.

We have,

A snack mix recipe calls for 10 cups of cereal and 4 cups of pretzel sticks.

Using constant of proportionality

y = kx

where k is the constant

So, put y= 10 and x= 4 then

10 = k (4)

k = 10/4

k= 5/2

Thus, the constant of proportionality is 5/2.

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Answer:

2(30(12) + 30(10) + 12(10)) + π(4^2)

+ 2π(4)(5) = 1,560 + 56π = 1,735.9 units^2

Answer:

0.75

Step-by-step explanation:

The probability that neither time A occurs is 361/400.

Given that a fair die has 20 sides and a different letter on each side, with no repeated letter, is rolled twice,

We need to find the probability that neither time the letter A shows up,

So, probability of a not event = 1 - probability of the event.

So, P(getting A) = 1/20

P(not getting A) = 1-1/20 = 19/20

For two times it will be = 19/20 × 19/20 = 361/400

Hence, the probability that neither time A occurs is 361/400.

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