X+y=8
Y=3x

Solve with substitution

Correct answer gets Brainliest!!

Answer:

6:50 p.m.

Step-by-step explanation:

150 miles / 60 mph = 2.5 hours

2 hours after 4:20 p.m. is 6:20 p.m.

30 minutes (1/2 hour) after 6:20 p.m. is 6:50 p.m.

In the given scenario, where there is one infinitely long track and overtaking is impossible, the initial situation consists of three equally spaced trains, each moving at a different speed. The trains have the capability to link up when one catches up to the other, resulting in a single train moving at the speed of the slower train.

As the trains move, they will eventually reach a configuration where the fastest train catches up to the middle train. At this point, the fastest train will link up with the middle train, forming a single train moving at the speed of the middle train. The remaining train, which was initially the slowest, continues to move independently at its original speed. Over time, the process continues as the new single train formed by the fastest and middle trains catches up to the remaining train. Once again, they link up, forming a single train moving at the speed of the remaining train. This process repeats until all the trains eventually merge into a single train moving at the speed of the initially slowest train. In summary, on this strange railway line, where trains can only link up and cannot overtake, the initial configuration of three equally spaced trains results in a sequence of mergers where the trains progressively combine to form a single train moving at the speed of the initially slowest train.

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Answer:

About 700 billion bacteria

Step-by-step explanation:

Given

\(1oz \approx 28g\)

\(1g = 25\ billion\ bacteria\)

Required

Number of bacteria in 1 oz

\(1g = 25\ billion\ bacteria\)

Multiply both sides by 28

\(28 * 1g = 25\ billion\ bacteria * 28\)

\(28g = 700\ billion\ bacteria\)

Recall that

\(1oz \approx 28g\)

This means:

\(1oz \approx 700\ billion\ bacteria\)

xm denotes the number of the page that was added twice. By solving the equation, we can find xm = (S' - S)/2, which is the number of the page that was added twice.

Let the page numbers be denoted by x1, x2, x3, ... , xn.

The sum of the page numbers is given by S = x1 + x2 + x3 + ... + xn.

The sum of the page numbers with the page number added twice is S' = x1 + x2 + x3 + ... + xn + xm + xm

Therefore, S' = S + 2xm

Since S' = S + 2xm, then 2xm = S' - S

Therefore, xm = (S' - S)/2

Therefore, the number of the page that was added twice is xm = (S' - S)/2.

Let x1, x2, x3, ... , xn denote the page numbers of a book. The sum of the page numbers is denoted by S. When the page numbers were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of S'. Therefore, S' = S + 2xm, where xm denotes the number of the page that was added twice. By solving the equation, we can find xm = (S' - S)/2, which is the number of the page that was added twice.

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Answer:

h = 20.5 yards

Step-by-step explanation:

Volume of Rectangular Pyramid: lwh/3

492 = (18) * (4) (h) /3

Multiply 3 on both sides

1476 = (18) (4) (h)

1476 = 72h

Flip the equation.

72h = 1476

h = 41/2 or 20.5 yards

Important notice:

/\2 = Power 2

Answer:

D. 1,047.2

Step-by-step explanation:

The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed.

The silo is made up of a cylinder with the height of 10 feet and base radius of 5 feet and two cones, each having the height of 5 feet and base radius of 5 feet.

The formulas volume of cylinder πr /\2 h and volume of cone 1/3  πr/\2h can be used to determine the tatol volume of the silo.

Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is:

V = π(5)/\2 (10) + (2) ( 1/3) π(5) /\2 (5)

= ( 4/3 ) (250)π

= 1,047.2 cubic feet.

The length of AC is 29.98516 in.

5. We have,

AB = 25 in, <b= 79 ad CB = 22 in

Using the law of cosine

b² = a² + c² + 2ac cos B

b² = 22² + 25² -2 x 25 x 22 cos (79)

b = 29.98516 in

Thus, the length of AC is 29.98516 in.

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Answer:

(4c + 1)(16c² - 4c + 1)

Step-by-step explanation:

64c³ + 1 ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

64c³ + 1

= (4c)³ + 1³ [ with a = 4c and b = 1 ]

= (4c + 1)((4c)² - 4c(1) + 1²)

= (4c + 1)(16c² - 4c + 1)

Answer:

A = 47 degrees

Step-by-step explanation:

cosineA = adjacent/hypotenuse

cosineA =  34/50

cosineA = 0.68

reverse cosine

A = 47 (rounded to the nearest whole number)

The lightest shape that can handle a tensile load of 850 kips in yielding, assuming Fy = 50 ksi, is the W12x58.

The lightest rectangular HSS shape that can handle a tensile load of 376 kips in rupture, assuming Fy = 46 ksi, is the HSS10x4x5/8.

The lightest shape below that can handle a tensile load of 850 kips in yielding, and Fy = 50 ksi is the W12x58.

The load capacity of the shape is given by the expression: (5/3)Fy x Mp / Lp

where Mp = 1.5Mn = 1.5 x 230 = 345 k-ft and Lp = 1.10 x rts = 1.10 x 8.2 = 9.02 ft

W12x72

Mp = 1.5 x Mn = 1.5 x 280 = 420 k-ft

Lp = 1.10 x rt = 1.10 x 8.72 = 9.59 ft

Load capacity = (5/3)50 x 345,000 / 9.02 = 809 kips

W14x68

Mp = 1.5 x Mn = 1.5 x 327 = 491 k-ft

Lp = 1.10 x rt = 1.10 x 8.6 = 9.46 ft

Load capacity = (5/3)50 x 491,000 / 9.46 = 840 kips

W12x58

Mp = 1.5 x Mn = 1.5 x 214 = 321 k-ft

Lp = 1.10 x rt = 1.10 x 8.36 = 9.20 ft

Load capacity = (5/3)50 x 321,000 / 9.20 = 865 kips (ANSWER)

W14x53

Mp = 1.5 x Mn = 1.5 x 264 = 396 k-ft

Lp = 1.10 x rt = 1.10 x 8.22 = 9.04 ft

Load capacity = (5/3)50 x 396,000 / 9.04 = 870 kips

The lightest rectangular HSS shape below that can handle a tensile load of 376 kips in rupture, and Fy = 46 ksi is the HSS10x4x5/8.

The load capacity of the shape is given by the expression: Fy x A / √3

HSS8x6x1/2

A = 5.53 in^2

Load capacity = 46 x 5.53 / √3 = 3.19 kips/in

HSS8x8x3/8

A = 5.87 in^2

Load capacity = 46 x 5.87 / √3 = 3.38 kips/in

HSS10x4x5/8 (ANSWER)

A = 5.92 in^2

Load capacity = 46 x 5.92 / √3 = 3.39 kips/in

HSS6x4x1/2

A = 3.24 in^2

Load capacity = 46 x 3.24 / √3 = 1.86 kips/in

Therefore, the lightest rectangular HSS shape below that can handle a tensile load of 376 kips in rupture, and Fy = 46 ksi is the HSS10x4x5/8.

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The number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.

In a farm, there is food to feed 300 rabbits for 60 days.

Let x be the number of rabbits that must be sold if they want to be fed for 15 more days.

From the given data, we have the following equation:

300 * 60 = (300 - x) * 75

The equation represents the amount of food for 300 rabbits that can last 60 days is equal to the amount of food for 300 - x rabbits that can last 75 days.

Solving for x, we get:

x = 150 rabbits

Hence, the number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.

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After the second outer loop iteration, the list is [6,1,7,8,9].

To determine the list after the second outer loop iteration, let's assume we're working with a simple bubble sort algorithm. Here are the steps:
1. First outer loop iteration:
  - Compare 6 and 9; no swap.
  - Compare 9 and 8; swap to get [6,8,9,1,7].
  - Compare 9 and 1; swap to get [6,8,1,9,7].
  - Compare 9 and 7; swap to get [6,8,1,7,9].
2. Second outer loop iteration:
  - Compare 6 and 8; no swap.
  - Compare 8 and 1; swap to get [6,1,8,7,9].
  - Compare 8 and 7; swap to get [6,1,7,8,9].

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Answer:

Step-by-step explanation:

Rational numbers:

(150+160)/2 = 310/2 = 155

(150+155)/2 = 305/2= 152.5

(155 +160)/2 = 315/2= 157.5

155, 152.5 , 157.5 are rational numbers between 150 and 160

Irrational numbers:

Irrational numbers are numbers that are non terminating and non repeating numbers

155.502003000.....

155.202002000......

156.3120578.......

Answer:

1st rational number

= a + b/2

= 150 + 160/2

= 310/2 (1)

2nd rational number

Middle term of 150 and 160 is 155

= 150 + 155/2

= 305/2

3rd rational number

= 160 + 155/2

= 315/2

\( \\ \)

Answer:

well I don't have a picture to explain it but (0,8) would be on the y axis and 8 on the x-axis ( it would go up 8 times and stay on the same line)

it would be -3 on the y axis and it wouldn't move up or down (move 3 points to the left)

Step-by-step explanation:

(x,y) when the x is 0 it doesn't move on the x-axis (left or right) and when it is 0 it doesn't move on the y-axis (up or down)

hope that makes sense!

The correct option regarding the numeric values of the functions at x = -3 is given as follows:

f(-3) < g(-3).

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

At x = -3, the definition of function f(x) for this problem is given as follows:

f(x) = 3x + 4.

(piece-wise function has different definitions depending on the input, -3 is less than 1 hence the first definition is applied).

Hence the numeric value is:

f(-3) = 3(-3) + 4 = -9 + 4 = -5.

From the table, the numeric value of function g(x) at x = -3 is given as follows:

g(-3) = 0.

0 is greater than -5, hence the correct option is given as follows:

f(-3) < g(-3).

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The sale price of the backpack is $25.5, the sale price of the soccer ball is $13.005, and the sale price of one jacket is 17.918.

Given:

The sale price of every item in a store is 85 percent of its regular price.

1. The regular price of a backpack is $30.

Then, the sale price = 85% of (the regular price of a backpack )

= 0.85  x ($30)

= $25.5

Hence, the sales price of the backpack = $25.5

2. The regular price of a soccer ball is = $15.30

The sale price of the soccer ball is 85% of its regular price.

Therefore, the sale price = 85% of $15.30

= $13.005

So, the sale price of the soccer ball is $13.005.

3. The regular price of a jacket is $21. 08

The sale price of a jacket is 85% of its regular price.

Therefore, the sale price = 85% of $21. 08

= $17.918

So, the sale price of a jacket is $17.918.

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Answer:

30°, 70°, 80°

Step-by-step explanation:

Let the measures of the angles be 3x, 7x and 8x.

Since, sum of the measures of all the three angles of a triangle is 180°.

Therefore,.

3x + 7x + 8x = 180°

18x = 180°

x = 180°/18

x = 10°

3x = 3*10° = 30°

7x = 7*10° = 70°

8x = 8*10° = 80°

Thus, the measures of the angles are 30°, 70°, 80°.

For the given mean of 50 and standard-deviation of 10, the expected value will be 50.

The "Expected-Value", also known as the mean or average, is a measure of central tendency. It represents the average value that we would expect to obtain if we were to repeatedly sample from a distribution.

In this case, We have a mean of 50 and a standard-deviation of 10. The mean is the average value of the data set, and it serves as an estimate of the expected value. So, when the mean is given as 50, the expected value is also 50.

The standard deviation, quantifies the variability or dispersion of the data points around the mean. While the standard deviation provides valuable information about the spread of the data, it does not directly affect the expected-value calculation.

Therefore, the required expected-value is 50.

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The given question is incomplete, the complete question is

How to find expected value for given mean as 50 and standard deviation as 10?

The expected value can be found by using the formula: Expected Value = mean. It represents the average outcome of a random variable.

The expected value, also known as the mean or average, is a measure of central tendency in probability and statistics. It represents the average outcome of a random variable. To find the expected value given the mean and standard deviation, you can use the formula:

Expected Value = Mean

The mean is the sum of all the values divided by the number of values. It gives us a measure of the central location of the data. The standard deviation, on the other hand, measures the spread or variability of the data. It tells us how much the values deviate from the mean.

The formula for standard deviation is the square root of the variance. Variance is the average of the squared differences from the mean. By knowing the mean and standard deviation, you can calculate the expected value.

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Answer: Pressure and Volume have an inverse and Temperature and Moles have an inverse relationship

Step-by-step explanation:

There is an inverse relationship between the following variables that define the properties of a gas:

1. Pressure (P) and Volume (V): According to Boyle's Law, when the temperature (T) is held constant, the product of pressure and volume remains constant for a given amount of gas. Mathematically, PV = constant. As one variable increases, the other decreases, indicating an inverse relationship.

2. Temperature (T) and Volume (V) in certain cases: In the case of Charles's Law, when the pressure is constant, the volume is directly proportional to temperature. However, if we consider a constant product of temperature and volume (TV = constant), and the pressure increases, then we observe an inverse relationship between temperature and volume.

Remember, these inverse relationships occur while keeping other variables constant. This is a multiple response question as both relationships mentioned above display an inverse relationship between different variables that define the properties of a gas.

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The correct option of the given statement "Janice's funds to triple if she has $5,000 invested in a bank that pays 9.4% annually" is 11.86 years.

To solve the problem, we can use the formula for the future value of a single sum.

FV = PV (1 + i)ⁿ

Where,

PV is the present value of the investment

"i" is the annual interest rate

n is the number of years

FV is the future value of the investment.

So, we can say that the future value (FV) of Janice's investment will be 3 times her present value (PV). Thus,

FV = 3 PV

    = 3 × 5,000

    = $15,000

Now, we can substitute the given values in the formula:

FV = PV (1 + i)ⁿ

15,000 = 5,000(1 + 0.094)ⁿ

Dividing both sides by 5,000, we get:

3 = (1 + 0.094)ⁿ

Taking the logarithm of both sides:

log 3 = log (1 + 0.094)ⁿ

log 3 = n log (1 + 0.094)

n = log 3 / log (1 + 0.094)

n = 11.86 years

Therefore, it will take approximately 11.86 years for Janice's funds to triple.

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To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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Answer:

The correct answer is 111.

Step-by-step explanation:

Each time, the number increases by the number it increased by before, plus 2.

The full sequence would be:

3, 9, 17, 27 , 39, 53, 69, 89, 111.

Hope this helps:) Goodluck!

Answer:

The parametrization of the curve on the surface is

\(c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]\)

Where

   \(x =  \frac{\sqrt{97} }{2} cost - 4\)

    \(y = \frac{\sqrt{97} }{2}  sint  + \frac{5}{2}\)

\(z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}\)

Step-by-step explanation:

From the question we are told that

The equation for the paraboloid is \(z = x^2 + y^2\)

The equation of the plane is \(8x - 5y + z -2 = 0\)

Form the equation of the plane we have that

\(z = 5y -8x +2\)

So

\( x^2 + y^2 = 5y -8x +2 \)

=> \( x^2 + 8x + y^2 -5y = 2 \)

Using completing the square method to evaluate the quadratic equation we have

\((x + 4)^2 + (y - \frac{5}{2} )^2 = 2 +(\frac{5}{2} )^2 + 4^2\)

\((x + 4)^2 + (y - \frac{5}{2} )^2 = \frac{97}{4}\)

\((x + 4)^2 + (y - \frac{5}{2} )^2 = ( \frac{\sqrt{97} }{2} )^2\)

representing the above equation in parametric form

\((x + 4) = \frac{\sqrt{97} }{2} cost\) , \((y -\frac{5}{2} ) = \frac{\sqrt{97} }{2} sin t\)

\(x = \frac{\sqrt{97} }{2} cost - 4\)

\(y = \frac{\sqrt{97} }{2} sint + \frac{5}{2}\)

So from \(z = 5y -8x +2\)

\(z = 5[\frac{\sqrt{97} }{2} sint + \frac{5}{2}] -8[ \frac{\sqrt{97} }{2} cost - 4] +2\)

\(z = 5\frac{\sqrt{97} }{2} sint + \frac{25}{2} -8 \frac{\sqrt{97} }{2} cost + 32 +2\)

\(z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}\)

Generally the parametrization of the curve on the surface is mathematically represented as

\(c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]\)

To find the derivative of the function y = 3 + sin(6x), we can apply the derivative rules. The derivative of sin(u) with respect to x is cos(u), and the derivative of a constant (in this case, 3) is 0.

Using the chain rule, we multiply the derivative of the inside function (6x) by the derivative of the outside function (sin(6x)):

dy/dx = 0 + cos(6x) * d(6x)/dx

The derivative of 6x with respect to x is simply 6, as the derivative of x is 1.

dy/dx = cos(6x) * 6

= 6cos(6x)

Therefore, the derivative of the function y = 3 + sin(6x) is dy/dx = 6cos(6x).

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If 75 grams of ice cream contains 10 grams of fat, then 150 grams of ice cream would contain 20 grams of fat. The amount of fat is directly proportional to the weight of the ice cream.


We can set up a proportion to solve the problem. Let x represent the unknown amount of fat in 150 grams of ice cream. According to the given information, we have the proportion:
10 grams of fat / 75 grams of ice cream = x grams of fat / 150 grams of ice cream
To solve for x, we can cross-multiply and then divide:
10 * 150 = 75 * x
1500 = 75x
X = 1500 / 75 = 20
Therefore, 150 grams of ice cream would contain 20 grams of fat. This is because the ratio of fat to ice cream remains constant, so we can use this proportion to find the missing value.

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The correct answer is x = 9.

Making use of the logarithm table, Compute the characteristic that the provided integer's whole number component dictates. Using the significant digits of the given number, find the mantissa. Add a decimal point after combining the characteristic and mantissa.

The student's solution has a division by zero error. The wrong step is when ln(x2) = ln(3x) - 0. It would have been better to first simplify the addition of ln(9) - 2ln(3) as follows:

The formula is ln(9) - 2ln(3) = ln(9) - ln(32) = ln(9/32) = ln(1/3).

When we substitute this number into the first equation, we get:

ln(1/3) - ln(3x) = 2ln(x)

ln(3x/1/3) = 2ln(x)

2ln(x) = ln (9x)

If we multiply both sides by their exponential, we get:

E = 2ln(x) + eln (9x)

x^2 = 9x

x^2 - 9x = 0

x(x - 9) = 0

As a result, the solutions are x = 0 and x = 9, but since ln(0) is undefined, we must determine whether x = 0 is a valid solution. So x = 9 is a workable answer.

Hence, the right response is x = 9.

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a) The system of linear equation for the data to fit the curve is

y = a + b + c

y = 4a + 2b + c

y = 9a + 3b + c

b) The solution of the system is y = 0.1833t² - 10.33t + 15.8.

c) The graph of the equation is illustrated below.

d) The polynomial function provides a reasonable approximation of the revenue data, but it is not a perfect fit.

(a) To create a system of linear equations for the data to fit the curve y = at² + bt + c, we need to find the values of a, b, and c. Since we have three data points, we can create three linear equations using the revenue data from each year.

Using the given information, we can substitute t = 1 for 2011, t = 2 for 2012, and t = 3 for 2013, and we get the following three linear equations:

y = a + b + c (for t = 1, or 2011)

y = 4a + 2b + c (for t = 2, or 2012)

y = 9a + 3b + c (for t = 3, or 2013)

(b) To use Cramer's Rule to solve the system of linear equations, we need to create a matrix of coefficients and a matrix of constants. The matrix of coefficients is created by writing down the coefficients of each variable in the equations, and the matrix of constants is created by writing down the constants on the right-hand side of each equation.

The matrix of coefficients is:

| 1 1 1 |

| 4 2 1 |

| 9 3 1 |

The matrix of constants is:

| 156.8 |

| 161.7 |

| 177.2 |

The determinants are then divided by the determinant of the matrix of coefficients.

The determinant of the matrix of coefficients is -6, so we have:

a = |-1.1| / |-6| = 0.1833

b = | 62 | / |-6| = -10.33

c = |-94.8| / |-6| = 15.8

Therefore, the equation that fits the data is y = 0.1833t² - 10.33t + 15.8.

(c) We can plot the data as a scatter plot and the polynomial function as a line graph on the same axes. The resulting graph will show us how well the polynomial function fits the data.

(d) After plotting the data and the polynomial function, we can see that the polynomial function fits the data fairly well. The function captures the overall trend of the data, which is an increase in revenue over time. However, there are some discrepancies between the function and the data at each point.

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Answer:

- 125

Step-by-step explanation:

The length AB represents the length of the minor arc in the circle. The formula required to find the length is given as:

We substitute the values of the angle = 140 degrees and the radius= 8m, to find the length of the arc AB

In conclusion, the length AB = 19.55m