The sum of two numbers is 35 and the difference is 1. What are the numbers

Using proportions, it is found that the correct statement is given by:

C There were 56 more people who ate a turkey sandwich than ate a chicken sandwich.

A proportion is a fraction of a total amount.

In this problem, one third out of 840 people ate Turkey Sandwich, hence the number is given by:

nT = 840/3 = 280.

One sixth ate Vegetarian Sandwich, hence the number is given by:

nV = 840/6 = 140.

4/15 ate Chicken Sandwich, hence the number is given by:

nC = 4 x 840/15 = 224.

7/30 ate Salad, hence the number is given by:

nS = 7 x 840/30 = 196.

Thus, option C is correct.

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In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.

It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.

These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.

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Equation BBB is obtained from Equation AAA by simplifying and combining like terms.

To get Equation BBB from Equation AAA, we can simplify the expression by combining like terms and applying the rules of algebra.

In Equation AAA, we have:

5x - 2 + x / (5x + x) = x - 4

First, we can simplify the denominator in the fraction by combining the terms 5x and x:

5x + x = 6x

So, the equation becomes:

5x - 2 + x / 6x = x - 4

Next, we can multiply both sides of the equation by 6x to eliminate the fraction:

(5x - 2 + x) * 6x / 6x = (x - 4) * 6x

This simplifies to:

(6x)(5x - 2 + x) = 6x(x - 4)

Expanding both sides:

\(30x^2 - 12x + 6x^2 = 6x^2 - 24x\)

Combining like terms:

\(36x^2 - 12x = 6x^2 - 24x\)

Subtracting 6x^2 and adding 24x from both sides:

\(30x^2 + 12x = 0\)

Dividing both sides by 6x:

5x^2 + 2x = 0

Now we have Equation BBB:

\(5x^2 + 2x = 0\)

So, Equation BBB is obtained from Equation AAA by simplifying and combining like terms.

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Answer:

4

Step-by-step explanation:

4 is the GCF od 12, 16 and 20

Answer:

4

Step-by-step explanation:

The greatest common factor is the largest number that is a shared factor of all 3 numbers (the greatest number they can all divide into). To find the GCF, we can list all the factors of the 3 numbers and then find the largest one that is common to all three sets.

Factors of 12 are: 1,2,3,4,6,12

Factors of 16 are: 1,2,4,8,16

Factors of 20 are: 1,2,4,5,10,20

We can see that 1,2 and 4 are the numbers common to all three sets but 4 is the largest so 4 is our greatest common factor.

Hope this helped!

the amount of vertical change in your position when you drive 200 feet is 16 feet

you are driving on a road that has a 8% uphill grade.

this means that the slope of the road is 8/100.

approximate the amount of vertical change in your position when you drive 200 feet

Therefore our proportion is: (where x is the "vertical" rise)

Slope is defined as rise so

8/100 = x/200

(8*200)/100 = x

16 feet = x

Hence ,  the amount of vertical change in your position when you drive 200 feet is 16 feet

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To convert 72 feet per day to a different unit, we can use unit conversion factors:

1 day = 24 hours

1 hour = 60 minutes

1 foot = 12 inches

So, we can set up the following calculation:

72 feet/day × (1 day/24 hours) × (1 hour/60 minutes) × (12 inches/1 foot) = 0.1 inches/minute

Therefore, the converted rate is in units of inches per minute.

Answer: (4) inches/minute

To solve the equation 4tanθ = 3 + tanθ for θ with 0 ≤ θ < 2π, we can use algebraic manipulation and trigonometric identities. By subtracting tanθ from both sides and simplifying the equation, we obtain tanθ = 3. Then, we can take the inverse tangent (arctan) of both sides to find the value of θ. However, it is important to note that the equation has multiple solutions due to the periodic nature of the tangent function.

Given the equation 4tanθ = 3 + tanθ, we can simplify it by subtracting tanθ from both sides:

4tanθ - tanθ = 3

Simplifying further, we have:

3tanθ = 3

Dividing both sides by 3, we find:

tanθ = 1

To solve for θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(1)

The inverse tangent of 1 is π/4 (45 degrees). However, it's important to note that the tangent function has a periodicity of π (180 degrees), so there are infinitely many solutions for θ. In the given range 0 ≤ θ < 2π, the solutions for θ are θ = π/4 (45 degrees) and θ = π + π/4 (225 degrees).

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Answer:

y= 1/2x+1

Step-by-step explanation:

Solving a simple linear equation we can see that the value of b is 7.

Here we have the point (5, b - 7) and we want to find the value of b such that the point lies on the x-axis.

Remember that a point lies on the x-axis only if the y-value is zero, so we need to solve the linear equation:

b - 7 = 0

Adding 7 in both sides we get:

b - 7+ 7 = 0 + 7

b = 7

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The area of the parallelogram formed by the given vertices A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), and D(0, 3, 2) is 2√21 square units.

To calculate the area of a parallelogram, we can use the cross product of two vectors formed by the sides of the parallelogram. The vectors AB and AD can be calculated by subtracting the coordinates of the initial and final points.

The cross product of these vectors gives us a vector representing the area of the parallelogram. Taking the magnitude of this vector gives us the area of the parallelogram. The magnitude of the cross product of AB and AD is 24, so the area of the parallelogram is 24 square units.

In this case, the vector AB is (-3, 7, 3), and the vector AD is (-1, 3, 3). Taking the cross product of these vectors gives us the vector (-12, 6, 24). The magnitude of this vector is √(12² + 6² + 24²) = √756 = 2√21. Therefore, the area of the parallelogram is 2√21 square units.

Complete Question:

Find the area of the parallelogram whose vertices are A(1, 0, −1), B(1, 7, 2), C(2, 4, −1), D(0, 3, 2).

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Answer:

ok

1 divide the area A÷ 3.1416

2 find the square root of the number for example 3×3=9 so the square root of 9 is 3

3 the results is you radio.

4 do this formula 2×3.1416× the number you got.

To find the log of 45.3 using a calculator, first enter 45.3 into the calculator, then press the "log" key. This should give you the result of 1.654221564 rounded to the nearest ten-thousandth.

Knowing the nature of logarithms, in mathematics, logarithms are the opposite or inverse of exponents or exponents. In simple terms, logarithms can be interpreted as an inverse or the opposite of the power used in determining the power of a base number.

So the point is that by studying logarithms, you will be able to find the exponential value of a number whose exponent is known.

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Based on the properties of rectangles, the angles and the side lengths are KN = 11 and NLK = 32

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

JN = 2x + 7, LN = 6x - 1

NKJ = 58 degrees

The diagonals or a rectangle are equal

So, we have

2x + 7 = 6x - 1

Evaluate the like terms

4x = 8

Divide

x = 2

So, we have

KN = 2 * 2 + 7

KN = 11

Adjacent angles in this case add up to 90 degrees

This gives

NLK = 90 - 58

Evaluate

NLK = 32

Hence, the measure of the angle is 32 degrees

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Answer:

The formula of a trapezoid is:

B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)

In this case 9 and 3 are your bases so add them together to get 12.

Now we multiply 12 to the height! 12 x 3(height) = 36. Now we multiply 36 to 1/2 which is just dividing by 2, so 36 divided by 2 = 18

Answer:

Step-by-step explanation:

A.  There is a ± to show that there are 2 possible answers

Ex:

x²=16

x can be 4 or -4 for this statement to be true.

Answer:whats the question

Step-by-step explanation:

Here, given the equation in the question, we want to make y the subject of the formula;

From the given sequence we can observe that, each term is obtained by dividing the previous term by 3.

A recursive function is one that uses a known prior term to define each word in a series, meaning that the next term is reliant on one or more known previous terms (s).

A recursive formula is one that defines each term in a series by reference to the one before it (s). The following parameters are defined using the recursive formulas: The opening phrase of the series The formula to calculate any phrase from its previous term.

Also, the first term is 18.

Thus, the recursive formula is given as:

aₙ = aₙ₋₁ ÷ 3

Now, the nth term is obtained by using the nth term formula:

a = 18 ÷ 3 ⁽ⁿ⁻¹⁾

Hence, the recursive formula is aₙ = aₙ₋₁ ÷ 3 and the nth term of the sequence is a = 18 ÷ 3 ⁽ⁿ⁻¹⁾.

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Answer:

2. There are 2 pints in 32 fluid oz.

Let me know if this helps!

Answer: 2 pints

Step-by-step explanation:

Divide the volume by 16

32/16=2 and you can also draw the gallon king to help

Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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In Monogram, Robert Rauschenberg created combine-paintings by assembling everyday objects through collage and painting techniques. This artwork showcased his unique approach of combining various elements to form a cohesive artistic composition.

Robert Rauschenberg's Monogram exemplifies his innovative approach of combining different mediums and materials in his artwork. He coined the term "combine-paintings" to describe these pieces that brought together everyday objects, such as a stuffed goat, tires, and various found materials, with painting and collage techniques.

Rauschenberg's aim was to challenge traditional boundaries and definitions of art by blurring the lines between painting and sculpture, two-dimensional and three-dimensional forms. By incorporating familiar objects into his artworks, he explored themes of consumerism, popular culture, and the relationship between art and everyday life. Through his combine-paintings, Rauschenberg pushed the boundaries of artistic expression and opened up new possibilities for artistic creation.

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The eigenvalues of the matrix H are λ₁ = 1 + 3i, λ₂ = 1 - 3i, and λ₃ = 5. The corresponding eigenvectors are v₁ = [7i, 0, 1], v₂ = [-7i, 0, 1], and v₃ = [0, 1, 0].

To find the eigenvalues and eigenvectors of the given matrix H, we will first perform block diagonalization. The matrix H can be written as:

H =\(BDB^(^-^1^)\),

where D is the diagonal matrix of eigenvalues and B is the matrix of eigenvectors. We can find B by solving the equation H·B = B·D.

Finding the eigenvalues

To find the eigenvalues, we solve the secular equation |H - λI| = 0, where I is the identity matrix. Substituting the values of H, we have:

|1 - λ   0      7i  |

|0       3 - λ   0   | = 0

|-7i     0       5 - λ|

Expanding the determinant, we get:

(1 - λ)[(3 - λ)(5 - λ) + 7i·(-7i)] - 7i[0 - (-7i)·(7i)] = 0

Simplifying further, we obtain:

(1 - λ)[(3 - λ)(5 - λ) + 49] + 49 = 0

Expanding and collecting terms, we get:

(λ - 1)λ² - 8λ - 250 = 0

Solving this quadratic equation, we find the eigenvalues λ₁ = 1 + 3i, λ₂ = 1 - 3i, and λ₃ = 5.

Finding the eigenvectors

To find the eigenvectors, we substitute each eigenvalue into the equation H·v = λv, where v is the eigenvector corresponding to the eigenvalue.

For λ₁ = 1 + 3i:

(1 - (1 + 3i))v₁₁ + 0v₁₂ + (7i)v₁₃ = 0

(0)v₁₁ + (3 - (1 + 3i))v₁₂ + (0)v₁₃ = 0

(-7i)v₁₁ + (0)v₁₂ + (5 - (1 + 3i))v₁₃ = 0

Simplifying each equation, we get:

-3iv₁₁ + 7iv₁₃ = 0

2v₁₂ = 0

-4iv₁₁ + 4iv₁₃ = 0

Solving these equations, we find v₁ = [7i, 0, 1].

Similarly, for λ₂ = 1 - 3i, we find v₂ = [-7i, 0, 1].

For λ₃ = 5, we find v₃ = [0, 1, 0].

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To calculate the probability of getting returns greater than 5%, we need additional information such as the distribution of returns.

To calculate the probability of getting returns greater than 5%, we need more information about the distribution of returns. The mean return of 15% and the standard deviation of 22% provide some information about the stock's return characteristics, but they do not fully determine the probability distribution.

If we assume a normal distribution for the returns, we can use the properties of the standard normal distribution to estimate the probability. We can standardize the value of 5% using the mean and standard deviation, and then find the probability of obtaining a value greater than the standardized value.

However, it's important to note that stock returns may not follow a perfectly normal distribution, and other factors such as skewness and kurtosis can impact the probability calculation. Therefore, a more comprehensive analysis would require additional information or assumptions about the distribution of returns.

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Based on the given temperature data, the forecasted high temperature for today using a three-day moving average is 93°F, and using a two-day moving average is 89°F. The mean absolute deviation for the two-day moving average is 1°F, and the mean squared error is 1. The mean absolute percent error for the two-day moving average is approximately 1.13%.

These metrics provide a way to assess the accuracy of the temperature forecasts and the variability of the actual temperatures from the moving averages.

a) To forecast the high temperature today using a three-day moving average, we take the average of the temperatures from the last three days. So, (95 + 96 + 88) / 3 = 93°F.

b) To forecast the high temperature today using a two-day moving average, we take the average of the temperatures from the last two days. So, (88 + 90) / 2 = 89°F.

c) The mean absolute deviation (MAD) based on a two-day moving average is calculated by finding the absolute difference between each temperature and the two-day moving average, summing up those differences, and then dividing by the number of observations.

The two-day moving average is 89°F. The deviations from the moving average are: |88 - 89| = 1 and |90 - 89| = 1. The sum of these deviations is 1 + 1 = 2. Since we have two observations, the MAD is 2 / 2 = 1°F.

d) The mean squared error (MSE) for the two-day moving average is calculated by squaring the differences between each temperature and the two-day moving average, summing up those squared differences, and then dividing by the number of observations.

The differences are: (88 - 89)^2 = 1 and (90 - 89)^2 = 1. The sum of squared differences is 1 + 1 = 2. Since we have two observations, the MSE is 2 / 2 = 1.

e) The mean absolute percent error (MAPE) for the two-day moving average is calculated by finding the absolute difference between each temperature and the two-day moving average, dividing that difference by the actual temperature, summing up those absolute differences, and then dividing by the number of observations.

The two-day moving average is 89°F. The absolute percent differences are: |88 - 89| / 88 = 0.0114 and |90 - 89| / 90 = 0.0111. The sum of these absolute differences is 0.0114 + 0.0111 ≈ 0.0225. Since we have two observations, the MAPE is 0.0225 / 2 ≈ 0.0113 or 1.13%.

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The probable question may be:

A Canadian tourist travelling to Miami learned that the local temperatures in Fahrenheit for the last week were as follows: 93, 94, 93, 95, 96, 88, 90 (yesterday).

a) Forecast the high temperately today, using a three-day moving average.

b) Forecast the high temperature today, using a two-day moving average.

c) Calculate the mean absolute deviation based on a two-day moving average.

d) Compute the mean squared error for the two-day moving average.

e) Calculate the mean absolute percent error for the two-day moving average.

Step-by-step explanation:

AB=DC

-x+6 = 3x-14

4x= 20

x= 5

AB=1

DC=1

Answer:

Yes

Step-by-step explanation:

The answer I got was Yes

sorry if it's wrong

Answer:

13 i think

Step-by-step explanation:

The average length of the queue and the Average number in the system.

the average time spent in the system can be calculated as:

W = Wq + (1 / μ)

The  M/G/1 system, we need to calculate the following parameters:

a. The probability that the system is idle.

b. The average length of the queue.

c. The average number in the system.

Let's solve each part step by step:

a. Probability that the system is idle (ρ):

The utilization factor (ρ) represents the ratio of the average arrival rate (λ) to the average service rate (μ). In an M/G/1 system, the probability that the system is idle can be calculated as:

P(Idle) = 1 - ρ

In this case, λ = 6 and μ = 9, so:

ρ = λ / μ = 6 / 9 = 2 / 3

Therefore,

P(Idle) = 1 - ρ = 1 - 2/3 = 1/3

b. Average length of the queue (Lq):

The average length of the queue can be calculated using Little's Law, which states that Lq = λ * Wq, where Wq represents the average time spent in the queue.

In an M/G/1 system, the average time spent in the queue (Wq) can be calculated using the Pollaczek-Khinchine formula:

Wq = ρ^2 / (2 * (1 - ρ)) * (σ^2 + (μ^2 / λ^2))

In this case, σ = 0.03, λ = 6, and μ = 9, so:

Wq = (2/3)^2 / (2 * (1 - 2/3)) * (0.03^2 + (9^2 / 6^2))

Simplifying the equation will give us the value of Wq.

c. Average number in the system (L):

The average number in the system (L) can be calculated as L = λ * W, where W represents the average time spent in the system. In an M/G/1 system,

Substituting the values of Wq and μ into the equation will give us the value of W. Then, we can calculate L by multiplying λ and W.

Lq and L, we can determine the average length of the queue and the average number in the system, respectively.

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sorry but the digits after 18 are unclear. are they singular or going together in 2s or is it one big number?

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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