The sum of four consecutive odd numbers is 80 find the number

Answer:

\(w=\frac92\)

Step-by-step explanation:

Let's remember that the slope of a line measures the ratio of the variation in y over the variation in x. Let's plug the numbers we have and see what we get

\(m= \frac {\Delta y}{\Delta x}; \frac18 = \frac{w-4}{-6-(-10)}\rightarrow\\\frac18 = \frac{w-4}{4}\rightarrow 2w-8=1 \rightarrow w=\frac92\)

Answer:

C. \(\frac{9}{2}\)

Step-by-step explanation:

Hi there!

We are given the points (-6, w) and (-10,4), and that the slope that passes between these two lines is 1/8

We want to find the value of w

We can do that by plugging in our given values into the equation \(\frac{y_2-y_1}{x_2-x_1}=m\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points, and m is the slope

We have everything we need to solve the equation, let's just label their values to avoid any confusion.

\(x_1=-6\\y_1=w\\x_2=-10\\y_2=4\\m=\frac{1}{8}\)

Now plug all of these values into the formula (remember: we have NEGATIVE values, and the formula contains SUBTRACTION)

\(\frac{y_2-y_1}{x_2-x_1}=m\)

\(\frac{4-w}{-10--6}=\frac{1}{8}\)

Simplify:

\(\frac{4-w}{-10+6}=\frac{1}{8}\)

Add the values together

\(\frac{4-w}{-4}=\frac{1}{8}\)

Now we can cross multiply; multiply -4 by 1 and (4-w) by 8

-4=32-8w

Subtract 32 from both sides

-36=-8w

Divide both sides by 8

w=\(\frac{9}{2}\)

The answer is C

Hope this helps!

The probability that only one phone call passes through a given minute, provided that the relay follows a Poisson distribution with a mean of 5 is 0.033689.

Here it is given that the number of phone calls that pass through a particular cell phone relay system follows a Poisson distribution. The time interval given here is of a minute.

For any Poisson distribution

P(X = x) = λˣ X e^(-λ) / x!

where λ = mean of the distribution.

x = the no. of times the event occurs in the time interval.

It is given that

λ = 5 calls per minute.

We need to find the probability that only n a given minute, the relay receives only one phone call.

Hence, x = 1

Therefore, the probability that only one phone call passes through in a given minute is

P(X = 1) = 5¹ X e^(-5) / 1!

= 0.033689

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Answer:

The anwser is B forsho

Step-by-step explanation:

'Direct measurement' refers to measuring exactly the thing that you are looking to measure, while 'indirect measurement' means that you're measuring something by measuring something else. For example of direct measurement is weight, distance, and so on.

The tangent of y(x) at x = 1 is y'(1) = 4 + C₁, and the value of f(1) is 5, we can solve for C₁ to get C₁ = 1. Therefore, the function y(x) = x⁴ / 4 + x + C₂, where C₂ is another constant.

The given equation is  f (x) = 5, and it is the tangent of the function y = x³ / 3 at x = 1.To get y = x (x² / 2 + C), we integrate the second derivative of y with respect to x.∫(d²y/dx²)dx = ∫(12x²)dx => y = 4x³ + C₁ Solve for C₁ by applying the point-slope equation at the point x = 1:f(1)

= 5

= y(1)

= 4(1)³ + C₁

=> C₁ = 1Therefore, the equation of y is: y = 4x³ + 1.For a more in-depth and better explanation, here are 150 words: A second derivative represents the rate of change of the first derivative with respect to x.

Therefore, if we have a second derivative of y with respect to x, we can integrate it twice to get a function of y with respect to x. Given y''(x) = 12x², we can integrate it once to obtain y'(x) = 4x³ + C₁, where C₁ is a constant. We integrate y'(x) once again to get y(x) = x⁴ / 4 + C₁x + C₂, where C₂ is another constant. Now, to find C₁ and C₂, we need to use the fact that the function f(x) = 5 is tangent to y(x) at x = 1.

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The tangent of y(x) at x = 1 is y'(1) = 4 + C₁, and the value of f(1) is 5, we can solve for C₁ to get C₁ = 1. Therefore, the function y(x) = x⁴ / 4 + x + C₂, where C₂ is another constant.

The given equation is  f (x) = 5, and it is the tangent of the function

y = x³ / 3 at x = 1.

To get y = x (x² / 2 + C),

we integrate the second derivative of y with respect to x.

∫(d²y/dx²)dx = ∫(12x²)dx

=> y = 4x³ + C₁

Solve for C₁ by applying the point-slope equation at the point

x = 1:f(1)

= 5

= y(1)

= 4(1)³ + C₁

=> C₁ = 1Therefore, the equation of y is: y = 4x³ + 1

.For a more in-depth and better explanation, here are 150 words: A second derivative represents the rate of change of the first derivative with respect to x.

Therefore, if we have a second derivative of y with respect to x, we can integrate it twice to get a function of y with respect to x.

Given y''(x) = 12x²,

we can integrate it once to obtain

y'(x) = 4x³ + C₁, where C₁ is a constant.

We integrate y'(x) once again to get

y(x) = x⁴ / 4 + C₁x + C₂, where C₂ is another constant.

Now, to find C₁ and C₂, we need to use the fact that the function

f(x) = 5 is tangent to y(x) at x = 1.

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Answer:

\(y=\frac{3}{4}x\)

Step-by-step explanation:

The graph represents direct variation since it is a line passing through the origin.

The constant of proportionality is \(\frac{18}{24}=\frac{3}{4}\), so \(y=\frac{3}{4}x\).

the given expression is

so the answer is - 141/4

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).

Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:

Loss Amount | Probability

$10 million | 0.5%

$1 million | 99.5%

To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.

The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.

The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.

Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:

VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)

VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)

VaR = $50,000 + $995,000

VaR = $1,045,000

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

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Options a, b, d, and g are the correct conditions for a Binomial Distribution.

The four conditions necessary for X to have a Binomial Distribution are:

a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.

b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.

d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.

g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.

The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.

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The equation of a line in different forms are:

1. The slope-intercept form: y = mx + b.

2. The point-slope form: y - y₁ = m(x − x₁).

3. The standard form: ax + by = c.

There are three ways that an equation that represents a line can be written in, they are as follows:

1. The slope-intercept form: this is expressed as y = mx + b. In this form, we have the following values and what they each represent:

m = the slope of the line.

b = the y-intercept of the line,

x and y are the coordinates of a point on the line.

2. The point-slope form: this is expressed as y - y₁ = m(x − x₁). In this form, the variables represented are:

m = the slope of the line.

x₁ and y₁ are the coordinates of a point that the line passes through.

3. The standard form: this is expressed as ax + by = c. In this form, the variables a, b, and c are integers.

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Step-by-step explanation:

if you are satisfied with the results then plz make me genius

Sari said that her estimate is slightly greater than the actual answer. This is wrong.

A quotient simply means the number gotten when a division is done.

In this case, the quotient of 120.78 ÷ 9.9 will be:

= 120.78 ÷ 9.9

= 12.2

Here, Sari estimated the quotient of 120.78 ÷ 9.9 to be 12. The answer is 12.2 and this is higher than 12. Therefore, she's wrong.

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Based on the given information, person C would take 600 minutes to finish the job by himself.

Let's break down the steps to find out how long it would take person C to finish the job by himself.

1. Determine the rate at which person A completes the job. We can find this by dividing the total job by the time it takes person A to complete it: 1 job / 100 minutes = 1/100 job per minute.

2. Similarly, determine the rate at which person B completes the job: 1 job / 120 minutes = 1/120 job per minute.

3. When person A and person B work together, we can add their rates to find the combined rate: (1/100 job per minute) + (1/120 job per minute) = (12/1200 + 10/1200) = 22/1200 job per minute.

4. After 40 minutes of working together, person C joins them, and together they finish the job in an additional 10 minutes. So the total time they take together is 40 minutes + 10 minutes = 50 minutes.

5. Calculate the total job done by person A and person B working together: (22/1200 job per minute) * (50 minutes) = 22/24 = 11/12 of the job.

6. Since person C helped complete 11/12 of the job in 50 minutes, we can calculate the rate at which person C works alone by dividing the remaining 1/12 of the job by the time taken: (1/12 job) / (50 minutes) = 1/600 job per minute.

7. Now we can find how long it would take person C to finish the job by himself by dividing the total job (1 job) by the rate at which person C works alone: 1 job / (1/600 job per minute) = 600 minutes.

Therefore, it would take person C 600 minutes to finish the job by himself.


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It would take c approximately 3.75 minutes to finish the job by himself. To find out how long it would take c to finish the job by himself, we need to first calculate how much work a and b can do together in 40 minutes.

Since a can finish the job in 100 minutes, we can say that a completes \(\frac{1}{100}\)th of the job in 1 minute. Similarly, b completes \(\frac{1}{120}\)th of the job in 1 minute.

So, in 40 minutes, a completes \(\frac{40}{100}\) = \(\frac{2}{5}\)th of the job, and b completes \(\frac{40}{120}\) = \(\frac{1}{3}\)rd of the job.

Together, a and b complete 2/5 + 1/3 = 6/15 + 5/15 = 11/15th of the job in 40 minutes.

Since a, b, and c complete the entire job in an additional 10 minutes, we can subtract 11/15th of the job from 1 to find out how much work c did in those 10 minutes. This comes out to be 1 - 11/15 = 4/15th of the job.

Therefore, c can complete 4/15th of the job in 10 minutes.

To find out how long it would take c to complete the whole job by himself, we can set up a proportion:

    (4/15) / x = 1 / 1

Cross-multiplying gives us:

    4x = 15

=> x = 15/4 = 3.75 minutes.

Therefore, it would take c approximately 3.75 minutes to finish the job by himself.

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Answer:

- 10, - 40

Step-by-step explanation:

200, 170, 140, .... - 10, - 40 ....

30 × 5 = 150

140 - 150 = - 10

- 10 - 30 = - 40

The requried solutions with the help of the quadratic formula have been shown.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
1.
To solve the equation x² + 2x - 3 = 0 using the quadratic formula, we'll first identify the coefficients:

a = 1
b = 2
c = -3

Now we can plug these values into the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

x = (-2 ± √(2² - 4(1)(-3))) / 2(1)

x = (-2 ± √(16)) / 2

x = (-2 ± 4) / 2

This gives us two possible solutions:

x₁ = (-2 + 4) / 2 = 1

x₂ = (-2 - 4) / 2 = -3

Therefore, the solution set is {least: -3, greatest: 1}.

Similarly,
2. the solution set is {least: 3 - √(5), greatest: 3 + √(5)}.
3. the solution set is {least: -5, greatest: -1}.
4. the solution set is { -5/2, 1/2 }

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The graph indicates that the line segment's domain and range are [-5, 1] and [-4, 7, respectively.

The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.

The range refers to all potential values of y, while the domain refers to all conceivable values of x.

The graph indicates that the line segment's domain and range are [-5, 1] and [-4, 7, respectively.

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Answer:

x = 4

x is 4 (which is the answer)

Answer:

x = 4

Step-by-step explanation:

1) Multiply 3 from both sides to get rid of the denominator

2) Subtract 6 from both sides

3) Divide 3 from both sides

4) Get the answer

The range of a function may refer to either of two closely related concepts: The codomain of the function The image of the function

MARK BRAINLIEST PLEASE DEAR...THANKS I LOVE U

Answer:

x = 2

Step-by-step explanation:

The 2 triangles are similar, thus the ratios of corresponding sides are equal, that is

\(\frac{x}{8}\) = \(\frac{3.5}{14}\) ( cross- multiply )

14x = 28 ( divide both sides by 14 )

x = 2

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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i cant see anything???????

Answer:

$17.85 for the 21 fancy cupcakes

Step-by-step explanation:

Answer:

A fancy cupcake costs $0.85 to make. Fill in the table to show how much it would cost to make 21 fancy cupcakes.

Step-by-step explanation:

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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Answer:

Select both Table A and Table B

Step-by-step explanation:

Both Tables show all 3 colors and 2 possible sizes

For proof here is a screenshot of the answer being correct:

Answer:

Step-by-step explanation:

by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. v(x).

The length of the rectangle is equal to \(L < 11\;inches\).

Given the following data:

To write an equation and solve for the length of the rectangle:

Mathematically, the area of a rectangle is given by this formula:

\(A=LW\)

Where:

Substituting the given parameters into the formula, we have;

\(5L < 55\\\\L < \frac{55}{5} \\\\L < 11\;inches\)

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Answer:

n = - 6

Step-by-step explanation:

Given

- 6n - 5 = 31 ( add 5 to both sides )

- 6n = 36 ( divide both sides by - 6 )

n = - 6

Answer:

n= -6

Step-by-step explanation:

-6n=31+5

-6n=36

n=36÷-6

n= -6

The solution (10, 7) represents that the box contains 10 batteries that provide 1.5 volts each and 7 batteries that provide 9 volts each.

Option C is the correct answer.

We have,

The solution (10, 7) in the given equation represents the values for x and y that satisfy the equation 1.5x + 9y = 78.

In the context of the problem,

x represents the number of batteries that provide 1.5 volts each, and y represents the number of batteries that provide 9 volts each.

The equation 1.5x + 9y = 78 represents the total voltage provided by all the batteries in the box, which is 78 volts.

By substituting the values x = 10 and y = 7 into the equation, we can verify if it holds true:

1.5(10) + 9(7) = 15 + 63 = 78

Since the equation is satisfied by these values, (10, 7) is a solution to the equation.

Therefore,

The solution (10, 7) represents that the box contains 10 batteries that provide 1.5 volts each and 7 batteries that provide 9 volts each.

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