what two numbers multiply to -49 and add to +6

Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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The solid that could have resulted in a two-dimensional cross section in the shape of a rectangle is a rectangular pyramid.

A prism is a solid figure with two parallel, congruent faces called bases. The other faces of a prism are rectangles. If a plane is passed through a prism parallel to one of its bases, the resulting cross section will be a rectangle.

A rectangular pyramid could indeed have a rectangular base and therefore could have resulted in a cross section in the shape of a rectangle.

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A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?

Rectangle

Trapezoid

Cylinder

Rectangular pyramid.

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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Given:

• x - 3 = x + 3

Let's solve the equation above

x - 3 = x + 3

x - x = 3 + 3

0 = 6

Therefore, since 0 = 6, we can say the equation has no solution.

Equation 2:

-4x - 8 = 4x + 8

Let's solve the equation.

-4x - 4x = 8 + 8

-8x = 16

Divide both sides by -8:

Since x = -2, we can say the equation has one solution

ANSWER:

a) No solution

b) One solution

The possible value of positive constant b for an absolute maximum value of function g(x), \(g(x) = xe^{-x} + be^{-x} \) at x = \( \frac{2}{3} \) is equals to the \( \frac{1}{3} \).

An absolute maximum point is a point where the function acquires its largest possible value. To drive the max or min absolute value, we have to substitute the derivative value of function equals to zero. We have a function, \(g(x) = xe^{-x} + be^{-x} \), where b is positive constant. We have to determine the possible value of b for absolute maximum of g at x= 2/3.

Differentiating the function g(x) with respect to x

=> \(g'(x) = - x e^{-x} + e^{-x} - be^{-x} \)

\(= (1 - x - b )e^{-x}\)

\(= \frac{1 - x - b }{e^{x}}\)

For obtaining absolute maximum value put, g'(x) = 0

=> \(\frac{1 - x - b }{e^{x}} = 0\)

Substitute x = 2/3, in above expression,

\( \frac{1 - \frac{2}{3} - b }{e^{\frac{2}{3}}} = 0\)

=> \(1 - \frac{2}{3} - b = 0\)

=> \( b = \frac{1}{3}\)

Hence, the required value of b is \( \frac{1}{3} \).

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Complete question:

Let g(x)=xe^(-x)+be^(-1), where b is a positive constant. For what positive value of b does g have an absolute maximum at x=2/3 .Justify your answer.

Answer:

y=-x+5

Step-by-step explanation:

Hope this helps!

And can I have brainliest!

Answer:

The last choice is correct

\(LCM=120a^4b^7c^5\)

Step-by-step explanation:

Least Common Multiple (LCM)

To find the LCM we can follow this procedure:

List the prime factors of each monomial.

Multiply each factor the greatest number of times it occurs in either factor.

We have two monomials:

\(12a^4b^2c^5\)

\(40a^3b^7c^1\)

The prime factors of the first monomial are:

\(2^2,3,a^4,b^2,c^5\)

The prime factors of the second monomial are:

\(2^3,5,a^3b^7c^1\)

LCM = Multiply \(2^3*3*5*a^4*b^7*c^5\)

These are all the factors the greatest number of times they occur.

Operating:

\(LCM=8*15*a^4*b^7*c^5\)

\(\boxed{LCM=120a^4b^7c^5}\)

The last choice is correct

Answer:

x+1

Step-by-step explanation:

Since it's a consecutive integer it's 1 added to the smaller integer, which is x.

Answer:

the answer is 8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

ADB is congruent to CBD and CD=8 because CPCTC.

Answer:

D. 26

Step-by-step explanation:

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Brainliest?

The center of the circle is (0, 2) and the radius is √3

The equation of a circle is;

In this case, we have:

Then:

r is the radius, then we know that already.

Now the center is (h, k) from the equation of a circle, above

In this case, the number that is resti

The ordered pair is plotted in the graph attached in the solution.

Given that Timony has three friends, the table shows the time taken by him to reach at his friends place and the distance of the homes of each of his friend.

We need to plot the ordered pair formed by the time and distance on the graph,

The ordered pair are:

(5, 10)

(11, 15)

(18, 20)

Plot the ordered pairs on the graph according to the given values:

Hence the ordered pair is plotted.

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The expression that can be used to find the third number in Mark's pattern is 3[3(5) - 1]. The correct option is C.

In Mark's pattern, the rule is to subtract 1 from the previous number and then multiply the result by 3.

Starting with 5 as the first number, we can apply this rule step by step to find the subsequent numbers.

First step: Subtract 1 from 5, giving us 4.

Second step: Multiply 4 by 3, which equals 12.

So, the second number in Mark's pattern is 12.

Now, to find the third number, we apply the same rule.

First step: Subtract 1 from 12, giving us 11.

Second step: Multiply 11 by 3, which equals 33.

Therefore, the third number in Mark's pattern is 33.

Option C, 3[3(5) - 1], correctly represents this calculation, where 5 is subtracted by 1, multiplied by 3, and then multiplied by 3 again.

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The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.



To build a deterministic finite automaton (DFA) for the language L3 = {x ∈ {a, b, c}* | x has strictly more than 3 'c' symbols and does not end in 'c'}, we can design the following DFA M3:1. Start with an initial state q0.

2. Create a loop on q0 for 'a', 'b', and 'c' inputs, leading back to q0.

3. From q0, transition to a state q1 on input 'c'. This represents the first 'c' encountered.

4. From q1, create a loop for 'a' and 'b' inputs, leading back to q1.

5. Transition from q1 to q2 on input 'c'. This represents the second 'c' encountered.

6. Similarly, create a loop on q2 for 'a' and 'b' inputs, leading back to q2.

7. Transition from q2 to q3 on input 'c'. This represents the third 'c' encountered.

8. From q3, create a loop for 'a', 'b', and 'c' inputs, leading back to q3.

9. Create a final accepting state q4 and transition from q3 to q4 on 'a' or 'b' inputs.

In this DFA, any string that ends with 'c' or has less than three 'c' symbols will not reach the accepting state q4, hence not belonging to L3.

Therefore, The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.

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Let:

The slope m is given by:

Answer:  -2x + 5y = 8

Step-by-step explanation:

Since the lines must be parallel, the slopes must be the same, so keep the coefficients of x and y

Substitute the values of x and y from the given coordinate  (6,4) to find the new constant, b, the y-intercept.

-2x + 5y = b

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

-12 + 20 = b

8 = b

Rewrite the original equation substituting the new b for the original -15

-2x + 5y = 8

The dairy farmer used the relative frequency method of probability to reach his conclusion.

Relative frequency is a method of calculating probability that is based on the observation of how often an event occurs in a sample. The farmer likely observed how often he gets between 12 and 14 gallons of milk in a day and used that data to calculate the probability of it happening.

In contrast, theoretical probability is based on the assumption that all possible outcomes are equally likely. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

Therefore, the correct answer is relative frequency.

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There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

116.66666667

Step-by-step explanation:

3 inches = 50 miles

so 1 inch = 16.6666666667

x 7 = 116.66666667

:) hope this helps

The range of the function c = 50t + 200 is given by [200, ∞).

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the y intercept.

Let c represent the distance travelled in t hours, hence:

c = 50t + 200

The range of the function c = 50t + 200 is given by [200, ∞).

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It is not reasonable to use the least-squares regression model to predict attendance per game for 0 wins because it involves extrapolation beyond the range of the observed data

Using the least-squares regression model to predict attendance per game for 0 wins is not reasonable because it would involve extrapolating the regression line beyond the range of the data.

In other words, the least-squares regression model is designed to capture the relationship between two variables within the range of the observed data. If we attempt to use this model to make predictions outside of this range, the results may not be reliable or accurate.

For example, if we were to use a least-squares regression model to predict attendance per game based on the number of wins a sports team had, and the range of wins in our data set was from 10 to 80, then any predictions we make for 0 wins (which is outside of this range) would be extrapolations rather than interpolations.

Extrapolation can be risky because it assumes that the relationship between the two variables continues beyond the range of the data. However, this assumption may not hold true in reality, and therefore the predictions made using extrapolation may not be accurate.

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The p-value of 0.072 represents the probability of obtaining a sample mean length as extreme as 53 centimeters or more extreme (in the direction of being lower) under the assumption that the expected mean length is 50.5 centimeters.

In hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true. In this case, the null hypothesis would be that the expected mean length of fish is 50.5 centimeters.

The appropriate test to determine if the expected mean length is low would be a one-sample t-test, comparing the sample mean (53 centimeters) to the hypothesized population mean (50.5 centimeters). The p-value of 0.072 indicates that there is a 7.2% chance of obtaining a sample mean length of 53 centimeters or more extreme (lower) if the true mean length is 50.5 centimeters.

The p-value of 0.072 suggests that there is some evidence (though not strong) that the expected mean length of 50.5 centimeters may be low based on the random sample of 100 fish with a mean length of 53 centimeters. However, it is important to note that the interpretation of the p-value depends on the significance level chosen for the test. If the significance level (commonly denoted as α) is set at 0.05, for example, the p-value of 0.072 would not be considered statistically significant, and the null hypothesis of a mean length of 50.5 centimeters would not be rejected.

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Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Fixed costs= $7,900

Unitary cost per sandwich= $1.7

Selling price per unit= $7.75

To calculate the break-even point in units and dollars, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 7,900 / (7.75 - 1.7)

Break-even point in units= 1,306 sandwiches

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 7,900 / (6.05 / 7.75)

Break-even point (dollars)= $10,120

Required Laplace transform is

\(L{ Cesia 49 ( 3 + 4 \times cos(a) )^3 } \\ = Cesia 49 [ -81/s + (172/3)/(s^2 + 1) + 54/(s^2 + 4) + (128/9)/(s^2 + 9) ]\)

To solve the Laplace transform of the given function, we use the following formula:

\(L{f(t)} = ∫[0,∞) e^{(-st)} f(t) dt\)

where s is the complex frequency parameter.

Using the formula, we have:

\(L{ Cesia 49 ( 3 + 4 \times cos(a) )^3 }\)

\(= ∫[0,∞) e^{(-st)} Cesia 49 ( 3 + 4 \times cos(a) )^3 da\)

\(= Cesia 49 ∫[0,π] e^{(-st)} ( 3 + 4 \times cos(a) )^3 da\) [since cos(a) is an even function]

\(= Cesia 49 ∫[0,π] e^{(-st)} (3^3 + 33^24cos(a) + 334^2cos^2(a) + 4^3*cos^3(a)) da\)

We can simplify the integrand by using the identity,

\(cos^2(a) = (1 + cos(2a))/2 and cos^3(a) = (cos(a) + 2cos(3a))/3\)

which gives:

\(L{ Cesia 49 ( 3 + 4×cos(a) )^3 }\)

\(= Cesia 49 ∫[0,π] e^(-st) [ 3^3 + 33^24cos(a) + 334^2(1 + cos(2a))/2 + 4^3 \times (cos(a) + 2cos(3a))/3 ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 27 + 363cos(a) + 548(1 + cos(2a))/2 + 64 \times (cos(a) + 2cos(3a))/3 ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 27 + 108cos(a) + 216(1 + cos(2a)) + 64 \times (3cos(a) + 2cos(3a))/3 ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 27 + 108cos(a) + 216 + 216cos(2a) + 64cos(a) + 128/3cos(3a) ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 243/3 + (172/3)cos(a) + 216cos(2a) + (128/3) \times cos(3a) ] da \\ = Cesia 49 [ (243/3)/(-s) + (172/3)/(s^2 + 1) + 216/(s^2 + 4) + (128/3)/(s^2 + 9) ] \\ = Cesia 49 [ -81/s + (172/3)/(s^2 + 1) + 54/(s^2 + 4) + (128/9)/(s^2 + 9) ]\)

Therefore, the Laplace transform of the given function is

\(L{ Cesia 49 ( 3 + 4 \times cos(a) )^3 } \\ = Cesia 49 [ -81/s + (172/3)/(s^2 + 1) + 54/(s^2 + 4) + (128/9)/(s^2 + 9) ]\)

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Correct answer is "Solve the Laplace Transforms- for the function Cesia 49 ( 3 +4cosa )³"

The Laplace transform of the given function is (3s + 4) / (s^2 + 1)^3.

To find the Laplace transform of the given function, we apply the properties and formulas of Laplace transforms. The function can be rewritten as (3s + 4) / (s^2 + 1)^3.

The Laplace transform of 3s is 3/S, and the Laplace transform of 4 is 4/S. The Laplace transform of 1 is simply 1/S.

For the term (s^2 + 1)^3, we can use the formula for the Laplace transform of t^n. In this case, n = 3, so the Laplace transform of (s^2 + 1)^3 is 6!/s^6.

Therefore, applying linearity and the Laplace transform properties, the Laplace transform of the given function is (3s + 4) / (s^2 + 1)^3.

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Answer:

Step-by-step explanation:

\(4x^2-12x+9=0\\4*9=36\\6+6=12\\6*6=36\\4x^2-(6+6)x+9=0\\4x^2-6x-6x+9=0\\2x(2x-3)-3(2x-3)=0\\(2x-3)(2x-3)=0\\(2x-3)^2=0\)

Answer:

\((x-\frac{3}{2}) ^{2}\)

Step-by-step explanation:

When we complete the square, we take the b value from the equation:

a\(x^{2}\) + bx + c = 0, and plug it into \((\frac{b}{2})^{2}\) ..

First step is to make the coefficent of x go away. By dividing by 4.

x^2 - 3x + 9/4 = 0

now plug into the equation

(-3/2)^2 = 9/4 <-- because the square is parantheses, the negative goes away. Notice how there is a 9/4 already in our equation, meaning we dont have to do anything and simply can find the answer!

(x - 3/2)^2 = 0

The equation is c = -5f + 35. f is the independent variable while c is the dependent variable

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

The variable f(number of friends) is the independent variable (input value) while c(number of carrots) is the dependent variable (output value)

From table, using pairs (1, 30) and (2, 25):

c - 30 = [(25 - 30)/(2 - 1)](f - 1)

c - 30 = -5(f - 1)

c = -5f + 35

The equation is c = -5f + 35

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Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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