the sum of two rational numbers is 85. if one number is 5 more than the other, then what are the numbers?

In total, there are 126 cans in the showcase.

We will use the method for the sum of an arithmetic sequence to solve this problem. The formulation is:

S = (n/2)(a + l)

Wherein S is the sum of the sequence, n is the range of terms, a is the first term, and l is the last term.

In this example, the primary time period is 20, and the closing term is 4. The common difference among the terms is -2, given that we are subtracting 2 cans from each row. we will discover the number of terms using the formulation:

l = a + (n-1)d

Wherein d is the common distinction. solving for n, we get:

n = (l - a)/d + 1

n = (4 - 20)/(-2) + 1

n = 9

Now we can plug within the values for a, l, and n into the system for the sum:

S = (n/2)(a + l)

S = (9/2)(20 + 4)

S = 126

Thus, there are 126 cans in the display in total.

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Answer:

Let x = the cost of a movieLet y = the cost of a gameUsing these variables,

we can set up equations.3x + 5y = 42 eq19x + 7y = 72 eq2

We have here a system of equations, where we have two or more equations with two or more different variables.

We use the elimination method to solve for the variables.

Multiply eq1 by 3. Keep eq2.

9x + 15y = 126 eq1

9x + 7y = 72 eq2

Subtract eq2 from eq1 to eliminate the x terms.

8y = 54y  

= 6.75

This rental cost of one video game is $6.75

Substitute the value of y into eq1 to solve for x.

This will give you the rental cost of one movie.

Step-by-step explanation:

Therefore, the expression that would give the total number of elements in the array list is n*m.

The Student question is given below :Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization.

[tex]Item[][] list= new Item[n][m];[/tex]

What expression would give the total number of elements in the array list?

The expression that would give the total number of elements in the array list is n*m. The given array declaration and initialization is Item[][] list= new Item[n][m]; This declaration and initialization signify that the array list is a 2D array with n rows and m columns. The total number of elements in this array can be determined by computing the product of the total number of rows (n) and the total number of columns (m).

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Answer:

Sales tax: $90 × .05 = $4.50

Total cost: $90 + $4.50 = $94.50

Answer:

Step-by-step explanation:

You want to know the dimensions of a cuboid cereal box with volume 975 cm³ that is 3 times as wide as deep, and 2 cm shorter than wide.

Let x represent the depth of the box. Then the width is 3 times that, or 3x. The length is 2 cm less than the width, so is (3x -2). The volume is the product of these dimensions.

  V = DWL

  975 = x(3x)(3x -2)

We like to graph an equation like this in the form ...

  f(x) = 0

so the solution is the x-intercept of the graph of f(x). Subtracting 975 puts the equation in that form:

  x(3x)(3x -2) -975 = 0

The attachment shows the graph of x(3x)(3x -2), and that it has its only real solution at x=5. This means the dimensions are ...

__

Alternate solution

Sometimes finding the solution to a cubic isn't easy. As a starting point, we can recognize that 3x-2 is about the same as 3x, so the value of x will be approximately the solution to ...

  975 = x(3x)(3x) = 9x³

  x = ∛(975/9) ≈ 4.8

The nearest integer to this value is x=5, so that can be a good value to check: 5(3·5)(3·5 -2) = 5·15·13 =975. (x = 5 works!)

Iterated solution

We can rewrite the equation as ...

  975 = 3x²(3x -2)

  325 = x²(3x -2)

  325/(3x -2) = x²

  x = √(325/(3x -2))

A value of x will be a solution to this equation if it makes the right side equal to the left side. This equation works as an "iterator," meaning we can use a value of x on the right side, and the value of that function will give a value of x on the left that is closer to the solution. The table in the second attachment shows this convergence to x=5.

It isn't always easy to find a suitable iteration function for a cubic or higher degree polynomial equation. The usual tools are Descartes' Rule of Signs, and the Rational Root Theorem. The best iteration functions are found using calculus.

Xavier rode 7.5 miles and Aiguo rode twice as much, or 15 miles.

Let x be the number of miles Xavier rode. Since Aiguo rode twice as many miles as Xavier, let 2x be the number of miles Aiguo rode.

Together, they rode a total of 22.5 miles, so we have the equation:

x + 2x = 22.5

Simplifying, we will get:

3x = 22.5

x = 22.5/3

x = 7.5

We can check our answer by verifying that the sum of their distances is indeed 22.5 miles:

= 7.5 + 15

= 22.5

Therefore, the solution is x = 7.5 and y = 15.

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Answer:

23 but not

Step-by-step explanation:

The mass of dog having weight as 19 kg has its mass in grams as 1.9 x 10⁴ grams, option C.

In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.

Measuring units to determine the size, weight, or quantity of any object. Seven fundamental measurement units are utilized in daily life and across the globe.

A dog has a mass of 19 kg

The mass of the dog in grams is:

1 kilogram = 1000 grams

19.5 kg × (10³ g/1 kg) = 1.95 × 10⁴ g.

Thus, the mass of the dog in grams is 1.95 × 10⁴ g.

1000 grammes make to 1 kilogram (kg) (g).

1 kg = 1000 g

The mass m in kilogram (kg) multiplied by 1000 gives the mass m in grams (g)

m(g) = m(kg) × 1000.

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A Home Equity Conversion Mortgage (HECM) is a type of mortgage specifically designed for homeowners over the age of 62. It allows the homeowner to access their home’s equity without having to sell it. The HECM loan is secured by the equity in the home and is repaid when the homeowner passes away or sells the home. This type of mortgage is popular with the elderly due to the lack of monthly payments and the flexibility to use the loan proceeds in any way they want. The funds can be used for medical expenses, home repairs, travel, or to supplement retirement income. A HECM is a great way for an elderly homeowner to access the equity in their home without having to make a large upfront payment or sell the home.

A Home Equity Conversion Mortgage (HECM) is a type of mortgage specifically designed for homeowners over the age of 62. It allows the homeowner to access their home’s equity without having to sell it. The HECM loan is secured by the equity in the home and is repaid when the homeowner passes away or sells the home. This type of mortgage is popular with the elderly due to the lack of monthly payments and the flexibility to use the loan proceeds in any way they want. The funds can be used for medical expenses, home repairs, travel, or to supplement retirement income. A HECM is a great way for an elderly homeowner to access the equity in their home without having to make a large upfront payment or sell the home.

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The mean for the sample is 14.5.

We are asked to select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. We then have to calculate the mean for the sample. The given numbers are: 12, 17, 8, 13, and 20. Therefore, there are five numbers in the population.

Now, we have to choose any two numbers randomly from the population. Let us suppose that we select 12 and 17 randomly from the population. Therefore, the sample will be {12, 17}. Now, we have to calculate the mean of the sample.

The formula to calculate the mean is: mean = sum of all numbers in the sample / total number of items in the sample. The sum of 12 and 17 is 12 + 17 = 29. Therefore, the sum of all numbers in the sample is 29. Also, the total number of items in the sample is 2.

Therefore, we can calculate the mean as: mean = 29 / 2mean = 14. 5. Therefore, the mean for the sample is 14.5.

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The values of sides x and y of the triangle are 6.75 and 11.25 units respectively.

The square of the hypotenuse side of the right-angled triangle equals the sum of the squares of the other two sides, according to Pythagoras' Theorem. The three sides of this triangle are referred to as the perpendicular, base, and hypotenuse.

by using the Pythagorean theorem:

Equation1:  y ² =x ² + 9²

Equation2:  (12 + x) ² =1 5 ² + y ²

Putting values of equation1  in 2 we get

(12 + x) ² =1 5 ² +x ² + 9²

144 + x²+ 2×12x = 225 + x²+ 81

x=6.75

Putting value of x in equation1

y ² =6.75 ² + 9²

y=11.25

Hence, the values of x and y are

x = 6.75 unit

y =11.25 unit

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The relation R is a partial order for the given set of data regarding over the set of people.  (Option 1)

A partial order is a binary relation that is reflexive, antisymmetric, and transitive. In this case, the relation R is reflexive since a person is always born before themselves. It is also transitive since if person A is born before person B, and person B is born before person C, then person A must be born before person C.

However, the relation R is not symmetric, since if person A is born before person B, then person B cannot be born before person A. Therefore, the relation R is not a total order.

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Complete Question:

in a relation r over a set of people, we have that a person x is related to person y if x's birth date is prior to y's birth date. no two people in the group have the same birth date. indicate the choice that correctly describes the relation r.

The volume of Laura's gold ring is 21.6 cubic centimeters.

To find the volume of the gold ring, we need to determine the volume of water that is displaced when the ring is dropped into the glass.

The initial volume of water in the glass can be calculated as the product of the base area and the height of the water:

V1 = base area x height of water = 7 cm x 4.5 cm x 8.8 cm = 277.2 cm³

When the gold ring is dropped into the glass, it displaces some of the water, causing the water level to rise. The new volume of water in the glass can be calculated using the same formula, but with the new height of the water:

V2 = base area x height of water with ring = 7 cm x 4.5 cm x 9.2 cm = 298.8 cm³

The volume of the gold ring can be calculated by subtracting the initial volume of water (before the ring was added) from the new volume of water (after the ring was added):

Volume of gold ring = V2 - V1 = 298.8 cm³ - 277.2 cm³ = 21.6 cm³

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Th given question is incomplete, the complete question is:

Laura wants to know the volume of her gold ring in cubic centimeters. She gets a rectangular glass with a base 7 cm by 4.5 cm and fills the glass 8.8 cm high with water. Laura drops her gold ring in the glass and measures the new height of the water to be 9.2 cm. What is the volume of Laura'5 ring in cubic centimeters? cm? 8.8 cm 9.2 cm 4.5 cm 4.5 cm 7cm 7 cm

Answer:

THE OTHER GUY IS WRONG  the answer is 3.6cm

Step-by-step explanation:

I had this question on khan

Probability that exactly four workers carpool to work is 0.214990847, or approximately 21.5%.

We must apply the binomial distribution formula to resolve this issue. The number of successes in a certain number of independent trials that all have the same chance of success are described by the binomial distribution, which is a type of probability distribution. In this scenario, the number of successes is the number of workers who carpool, and the probability of success is 0.1.

The binomial distribution's formula is:

[tex]P(X=k) = to (n pick k) * p*k*1-p (n-k)[/tex]

Where n is the total number of trials (in this case, 8), p is the success probability (0.1), and (n choose k) is the binomial coefficient, which is equal to [tex]n! / (k! * (n-k)![/tex] and P(X=k) is the probability of obtaining exactly k successes.

This formula can be used to determine the likelihood that four employees will carpool to work:

[tex]P(X=4) = (8 pick 4) * 0.14 * 0.94 * 0.214 = 0.214990847.[/tex]

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The algebraic expression to represent the cost of buying r records and c CDs is given as, Cost = 3r + 1.5c

The music store is selling the records for a price of $3.00 and the CDs for $1.50 each. Let us say someone buys r number of record and c number of CDs.

So, the final algebraic expression that we will get from the above mentioned information is Cost = 3r + 1.5c.

Here, 3r represents the cost of buying "r" number of records at $3.00 each, and 1.5c represents the cost of buying "c" number of  CDs at $1.50 each. By adding these two costs together, we can find the total cost of buying r number of records and c number of CDs.

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The percent change in size from 983 to 2,349 square feet was 138.8%.

The average American home swelled from 983 square feet in 1950 to 2,349 square feet in 2004, representing a change of 1366 square feet. This change can be expressed as a percent change by dividing the change (1366 square feet) by the starting value (983 square feet). The resulting percent change is 138.8%.

To calculate the percent change, we can use the following equation:
Percent Change = (Ending Value - Starting Value) / Starting Value x 100
Using this equation, the percent change in the size of the average American home is calculated as follows:
Percent Change = (2349 - 983) / 983 x 100 = 138.8%

This means that the average American home increased by 138.8% in size between 1950 and 2004. This is an impressive rate of growth and may be attributed to a number of factors. In 1950, the United States was in the midst of a period of rapid economic growth, and this may have allowed people to buy larger homes and upgrade to more luxurious accommodations. In addition, advances in technology and manufacturing may have made larger homes more affordable for more people.

Whatever the cause of the growth in home size, it is clear that the average American home saw a substantial increase in size between 1950 and 2004. The percent change in size from 983 to 2,349 square feet was 138.8%.

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Number of measurements that must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm is 16

To estimate the diameter with an uncertainty of 0.5 mm, we need to reduce the uncertainty to that level. Let's call the number of measurements we need to make "N". We can use the formula for the standard deviation of the mean

σ_mean = σ / sqrt(N)

where σ is the standard deviation of the individual measurements. In this case, the uncertainty of each measurement is given as 1.4 mm, which we can assume is the standard deviation.

To reduce the uncertainty to 0.5 mm, we need

0.5 = 1.4 / sqrt(N)

Solving for N, we get

N = (1.4 / 0.5)^2 = 15.68

≈ 16

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Answer:

To find the simple interest on a principal of $600 at a rate of 2% for a time period of 2 years, we can use the formula:

Simple Interest = (Principal * Rate * Time)

where Rate is the annual interest rate as a decimal, and Time is the time period in years.

In this case, we have:

Principal = $600

Rate = 0.02 (2% expressed as a decimal)

Time = 2 years

So, the formula becomes:

Simple Interest = ($600 * 0.02 * 2)

= $24

Therefore, the simple interest on a principal of $600 at a rate of 2% for 2 years is $24.

"The speed of a randomly selected car on a highway" and "the percent change in the price of a share of IBM stock in a month" are examples of continuous random variables. Options A and C are the correct answers.

Continuous random variables are those that can take on any value within a given range, as opposed to discrete random variables, which can only take on certain values.The speed of a randomly selected car on a highway and the percent change in the price of a share of IBM stock in a month are examples of continuous random variables.

These variables have a range of values and can take on any value within that range.The number of claims on a medical insurance policy on a given year, the number of customers that enter a particular store on a randomly selected day, and the time that elapses between two customer service calls are examples of discrete random variables. These variables can only take on certain values, such as whole numbers or specific times.

Thus option A and option C are the correct answers.

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Let p be the probability of an adult over 50 wearing glasses for driving. Since we don't know the value of p, we can't use the binomial distribution directly. However, we can use the normal approximation to the binomial distribution since n is large (assuming n * p >= 10 and n * (1-p) >= 10).

Let X be the number of adults over 50 wearing glasses for driving in a random sample of n adults. Then X ~ Binomial(n, p) can be approximated by a normal distribution with mean µ = n * p and standard deviation σ = sqrt(n * p * (1-p)).

We want to find the probability that at least six adults over 50 in a random sample of n wear glasses for driving. This is equivalent to finding P(X >= 6) = 1 - P(X < 6) using the normal approximation.

To apply the normal approximation, we need to standardize the random variable X:

Z = (X - µ) / σ

Using continuity correction:

P(X >= 6) = P(X > 5.5)

Z = (5.5 - n * p) / sqrt(n * p * (1-p))

We can use the standard normal distribution table or calculator to find the probability:

P(Z >= (5.5 - n * p) / sqrt(n * p * (1-p)))

Since we don't know the value of p, we can use a conservative estimate of p = 0.5 (assuming 50% of adults over 50 wear glasses for driving). Then:

P(Z >= (5.5 - n * 0.5) / sqrt(n * 0.5 * (1-0.5)))

For example, if we sample n = 100 adults over 50, the probability of at least six wearing glasses is:

P(Z >= (5.5 - 100 * 0.5) / sqrt(100 * 0.5 * (1-0.5)))

= P(Z >= 0.5)

Using a standard normal distribution table or calculator, P(Z >= 0.5) = 0.3085.

Therefore, the probability of at least six adults over 50 wearing glasses for driving in a random sample of 100 is approximately 0.3085 or 30.85%.

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The experimental probability of drawing the cards, 2, 3, or 4, from the deck of 52 cards, with the frequency obtained from 200 draws is about 15.5%

An experimental probability is the probability of a specified event taking place, based on repeated trials or sampling.

The number of draws Rayna drew from the standard deck of cards = 200 draws

The frequency of the cards drawn, obtained from the frequency table are;

Frequency of 2 = 8

Frequency of 3 = 12

Frequency of 4 = 11

The experimental probability of drawing a card that has a value of 2 or a card that has a value of 3 or a card that has a value of 4 is therefore;

P(2, 3, 4) = (Frequency of 2 + Frequency of 3 + Frequency of 4)/The total number of draws Rayna drew

P(2, 3, 4) = (8 + 12 + 11)/200 = 0.155 = 15.5%

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Answer:

39°

Step-by-step explanation:

angles are alternate exterior angles making them congruent

for example:

The correct option is A) 3; 4; no money. Ned should eat 3 pounds of oranges and 4 pounds of starfruit, as this combination maximizes his total utility and fully utilizes his $26 budget, resulting in a total utility of 280.

He should eat 3 oranges and 4 pounds of star fruits and he will have no money left over

Because by comsuming this combination it will maximize Calvin's total utility and his money will be distributed correctly according to the utility maximization

Like if he consume 8 orange and 2 pound of star fruit in option(B)

8 units of orange consumption is not given but we'll assume it will give total utility of 84

And 2 pound of star fruit will give 130

130 + 84 = 214

Opt (c) = only 5 star fruit no orange

= 5 Star fruit = 250 total utility

Opt (D) = is not possible because

4 orange will take $2 each = 4×2 = $8

And 5 pounds of star fruit takes $5 each = $5×5 = $25

$25 +$8 = $33 but he have only $26 so option (d) cant be considered

Opt (a)

3 orange = 60

And 4 pounds of star fruit = 220

220 + 60 = 280 total utility so this option gave us maximum total utility and the $26 is Fully utilized

3×$2 = $6

4 × $5  = $20

$6 + $20 = $26

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Complete question is in the image attahed below

The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

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Answer:

x = -4

y = 1

Step-by-step explanation:

I added a photo of my solution

Answer:

3x = y

x + 4 = y

Step-by-step explanation:

Letter C

Answer:

(9x10^4)+(7x10) = 90,000 + 70 = 90,070

The matrix that shows the prices in U.S. dollars is:

[1.81  6.32  0.56 0.36]

Here we have a simple row matrix which can be written as:

[80  280  25  16]

You can see this as a row vector or something like that, notice that if we multiply this by an scalar, we just need to multiply each element by an scalar.

Now, we know that:

1 dollar = 44.32 Nu

then:

1 Nu = (1/44.32) dollars.

So to get the matrix in dollars, just multiply each number by (1/44.32), then we will get:

(1/44.32)*[80  280  25  16] = [80/44.32  280/44.32  25/44.32  16/44.32]

= [1.81  6.32  0.56 0.36]

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The Existence and Uniqueness Theorem states that if a system of linear equations has a unique solution, then the solution can be found by solving the associated augmented matrix.

To determine whether a system of linear equations has a unique solution, the number of equations must equal the number of unknowns. Additionally, the equations must not be linearly dependent. If these criteria are met, then the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution.

To illustrate, consider the system of equations:

x1 + x2 - x3 = 2  

2x1 - x2 + 2x3 = 8

3x1 + 2x2 - 4x3 = 0

= 4. Therefore, the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution for this system.

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