when 5 times a number is increased by 10, the answer is the same as when 100 is decreased by the number. What is the number?

Intersection AND

Union AND, MOSTLY

Disjunction OR

Conjunction AND

For these words, we have:

Intersection, when we and the common results between two sets

So, Intersection A ∩ B A and B

A ={1,2,3} B= {3,4,5} A ∩ B ={3}

Disjunction, OR

When some conditions apply either to one set or to another.

A V B = OR

He is American OR He is British

A OR B

Union, AND, Mostly

When we want all the elements that belong to both Sets

So A ∪ B means A and all the elements from A and all the elements from B, no need no repeat the same element.

A = {1,2,3} B= {3,4,5} A ∪ B ={ 1,2,3,4,5}

Conjunction

A ^ B = AND,

In Logic and Set Theory and we have conjunction, we can use the word

He is a New Yorker AND He is American.

Answer:

yes it is a right triangle

The principles of reinforced pre-stressed concrete involve designing a reinforced concrete beam to meet the requirements set by the American Concrete Institute (ACI). In this case, we will focus on designing the beam for shear.

To design the beam for shear, we need to consider the following information:

- The shear strength of the concrete, which is given by the equation: Vc = 0.17√(fc')bw'd
 - Vc: Shear strength of concrete
 - fc': Compressive strength of concrete (given as 28 MPa)
 - bw': Width of the web of the beam (not provided)
 - d: Effective depth of the beam (not provided)

- The shear strength of the reinforcement, which is given by the equation: Vs = Asfy / s
 - Vs: Shear strength of the reinforcement
 - As: Area of the shear reinforcement
 - fy: Yield strength of the reinforcement (given as 420 MPa)
 - s: Spacing of the shear reinforcement (not provided)

- The total shear strength of the beam, which is the sum of the shear strength of the concrete and the shear strength of the reinforcement: Vt = Vc + Vs

To proceed with the design, we need the values of bw' (width of the web of the beam), d (effective depth of the beam), and s (spacing of the shear reinforcement). These values are not provided in the given information, so we cannot calculate the shear strength of the beam accurately.

However, let's assume some values for bw' and d to illustrate the design process. Let's assume bw' = 200 mm and d = 400 mm.

We can now calculate the shear strength of the concrete, Vc, using the given compressive strength of concrete, fc', and the calculated values of bw' and d. Using the equation mentioned earlier, we have:

Vc = 0.17√(28)200400 = 5.95 kN

Next, let's assume a spacing for the shear reinforcement, s. Let's assume s = 150 mm.

Now, we can calculate the shear strength of the reinforcement, Vs, using the given yield strength of the reinforcement, fy, and the assumed spacing, s. Using the equation mentioned earlier, we have:

Vs = Asfy / s

To determine the required area of shear reinforcement, we need to ensure that the total shear strength, Vt, is greater than or equal to the factored shear force. In this case, the factored shear force is not provided, so we cannot determine the required area of shear reinforcement accurately.

In conclusion, without the necessary information such as the width of the web of the beam, the effective depth of the beam, and the factored shear force, we cannot design the reinforced concrete beam for shear in accordance with the ACI requirements accurately. It is essential to have these values to ensure the structural integrity and safety of the beam.

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Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690   [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: \(\hat{p}=\dfrac{368}{2690}\approx0.137\)

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Using synthetic division, we can divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1. Performing the synthetic division, we obtain a quotient of x² + 6x - 6 and a remainder of 8.

To divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1 using synthetic division, we set up the synthetic division table as follows:

1  |   1   7  -12   14

We begin by bringing down the coefficient of the first term, which is 1, and place it on the line below the division bar. Then we multiply the divisor, 1, by the value we brought down and write the result under the next coefficient. Adding the values in the second row, we obtain the new value. We continue this process for each term until we reach the last term.

1  |   1   7  -12   14

 1   8  -4     10

The values in the last row represent the coefficients of the quotient polynomial. Therefore, the quotient is x² + 6x - 6. The remainder, which is the last value in the last row, is 10. Since the divisor is 1, the remainder does not affect the quotient. Hence, the result of the division is x² + 6x - 6 with a remainder of 10.

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One drink of an alcoholic beverage contains approximately 100 to 150Kcal. That is option D

An alcoholic beverage is a type of beverage that contains ethanol which is also a type of alcohol.

The three main types of alcoholic beverage are beer, wine and spirits.

Alcoholic drinks contain a lot of kilojoules and have no nutritional benefits

One drink of an alcoholic beverage contains approximately 100 to 150Kcal.

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Answer: 15

Step-by-step explanation:

Factors:

75: 1, 3, 5, 15, 25,

15: 1, 3, 5, 15

Write out all the factors of each number and circle the highest factor that both numbers have

The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.

Data;

Using poission formula,

\(P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute\)

Let's substitute the values into the formula.

For 50 calls in 150 hours

For 150 hours = x = 0.3 * 150 = 45

\(p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431\)

b)

The probability the next call arrives after 2 hours.

\(\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488\)

c)

The number of calls recieved each day is recorded for 50 consecutive days.

for 50 days;

\(\lambda = 0.3 * 50 * 24 = 360\)

The mean = 360

The standard deviation is given as

\(S.D = \sigma =\sqrt{360} = 18.974\\\)

The probability the sum of these 50 number is less than 356 is

\(p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165\)

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Answer:

72 = -6r

r= -72/6

r = -12

is the answer

Answer:

three      parts     1/3

Step-by-step explanation:

The company's profit if there are no price increases is $120.

We have,

The problem provides a function P(x) that models the profit of a natural sponge company.

The function takes as input the number of $0.15 increases in the price of each sponge, denoted by x.

When the value of x is 0, it means that there are no price increases, and therefore the initial price of each sponge is unchanged.

Now,

If there are no price increases, then the value of x in the function P(x) is 0, since x represents the number of price increases.

Substituting x = 0 into the function, we get.

P(0) = -0.1(0)^2 + 15(0) + 120 = 120

Therefore,

The company's profit if there are no price increases is $120.

We can also see this from the graph of the function, which starts at (0, 120) and represents the profit when there are no price increases.

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The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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One-to-one: Since f(2) = f(-2) = -4, the function is not one-to-one.

(a) f: R → R. f(x) = x^2

The function f is neither onto nor one-to-one. To see why, consider the following:

Onto: A function is onto if every element of the co-domain has at least one pre-image in the domain. In this case, f(x) = x^2 can never be negative, so it does not take on every value in the co-domain R (since R includes negative numbers). Therefore, the function is not onto.

One-to-one: A function is one-to-one if each element in the co-domain corresponds to exactly one element in the domain. However, since f(-x) = f(x) for all x, the function is not one-to-one. For example, f(2) = f(-2) = 4.

(b) g: R → R. g(x) = x^3

The function g is both onto and one-to-one. To see why:

Onto: For any y in the co-domain R, we can find x in the domain R such that g(x) = y by taking the cube root of y. Therefore, g is onto.

One-to-one: Suppose g(a) = g(b) for some a, b in the domain R. Then, we have a^3 = b^3, which implies a = b. Therefore, g is one-to-one.

(c) h: Z → Z. h(x) = x^3

The function h is onto but not one-to-one. To see why:

Onto: For any y in the co-domain Z, we can find x in the domain Z such that h(x) = y by taking the cube root of y. Therefore, h is onto.

Not one-to-one: For example, h(-1) = (-1)^3 = -1 and h(1) = 1^3 = 1, so h is not one-to-one.

(d) f. 2+2, f(x) = -4

The function f is neither onto nor one-to-one. To see why:

Onto: The co-domain is not specified, so it is not clear whether the function is onto or not.

Not one-to-one: Since f(2) = f(-2) = -4, the function is not one-to-one.

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An equation about a point A on a number line could involve finding the distance between A and another point, finding the midpoint between two points, or finding the equation of a line passing through A. The specific method used would depend on the context of the problem and the information given.

To find the distance between point A and another point B on the number line, we can subtract the coordinates of the two points and take the absolute value of the result. For example, the distance between point A at 3 and point B at 7 would be |3-7| = 4.

To find the midpoint between two points on the number line, we can add the coordinates of the two points and divide the sum by 2. For example, the midpoint between point A at 3 and point B at 7 would be (3+7)/2 = 5.

To find the equation of a line passing through point A, we would need to know at least one other point on the line and use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

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The method of integration by substitution to solve for y. The final solution was given as y = (1/7) (r²/√2) sin(14r) - (1/r) sin(u) + C.

(a) To determine the general solution of the differential equation, √(1 + y²) = rcos7r we will make use of the substitution

v = y'v = dy/dx

Then, we get:

y' = dv/dx(dx/dy) = dx/dv

dx = vdv/dx

x = ∫vdv

Solving for y' in terms of v: y' = v

Substituting v back in for y':

√(1 + v²) = rcos7r

Squaring both sides:

(1 + v²) = r²cos²7r = r²(1 + cos14r)/2v² = (r²(1 + cos14r)/2) - 1y = ∫vdx = ∫(√((r²(1 + cos14r)/2) - 1))dx

In order to integrate, we use the substitution

u = arccos(√(r²/2)(1 + cos14r))

Then, du = -(r/√2)sin(14r) dr

So we have:

y = (1/7) (r²/√2) sin(14r) - (1/r) sin(u) + C(b)

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Step-by-step explanation:

Given :-

Adding the equations :-

\(: \implies\) 10y = -10

\(: \implies\) y = -1

Put it (i) :-

\(: \implies\) 4x - 8 = 20

\(: \implies\) 4x = 20 + 8

\(: \implies\) 4x = 28

\(: \implies\) x = 28/4

\(: \implies\) x = 7

The transfer price set by the selling division should be equal to the selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally. Option D.

The transfer price refers to the price at which goods or services are transferred between divisions within the same organization. When the selling division sets the transfer price, it needs to consider various factors. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, is the most appropriate choice.

The selling price less the variable costs ensures that the selling division covers its direct costs associated with the transferred goods or services. This ensures that the division remains financially viable and does not incur losses. However, it is also important to consider the opportunity cost of making the transfer internally.

The foregone contribution to the organization represents the potential profit or contribution that the selling division could have made if it had sold the goods or services to external customers instead of transferring them internally. By including this foregone contribution in the transfer price, the selling division accounts for the potential value it could have added to the organization.

In conclusion, the transfer price set by the selling division should consider both the variable costs associated with the transfer and the foregone contribution to the organization. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, captures both of these factors and provides a comprehensive approach to setting the transfer price.

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Answer:

(See the attachment)

Step-by-step explanation:

None

The graph of the inequality 8x - 5y < 3 is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

8x - 5y < 3

The graph of this inequality is given below.

Thus,

The graph is given below.

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The possible coordinates of the rectangle's other two vertices are

Given that:-

Coordinates of the rectangle : (3,7) and (-4,7).

Perimeter of the rectangle = 30units

We have to find the possible coordinates of the rectangle's other two vertices.

Let the length and breadth of the rectangle be l and b respectively.

We know that,

Perimeter of rectangle = 2(l + b)

Hence,

2(l + b) = 30

l + b = 15 units.

Distance between the points (3,7) and (-4,7) =

\(\sqrt{(7-7)^2+(-4-3)^2}=\sqrt{0^2+(-7)^2}=\sqrt{49} =7 units\)

Let b = 7 units.

l + 7 = 15

l = 8 units.

Hence,

Possible Coordinates of rectangle:-

(3, 7+8) or (3,7-8) = (3,15) and (3,-1) and,

(-4,7+8) or (-4, 7-8) = (-4, 15) and (-4,-1).

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Answer:

Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Step-by-step explanation:

Answer:

x<7, The third option

Step-by-step explanation:

-1.1x+6.4>-1.3

We are trying to isolate x so we can move all the constant to one side.

-1.1x>-1.3-6.4

-1.1x>-7.7

Lastly, we need to divide both sides by -1.1.

-1.1x>-7.7/-1.1

Note that if you multiply or divide both sides of an inequality by a negative, then you need to flip the sign.

x<7

Hope this helps :)

Answer:

I believe it is the third option. It is really hard to explain. Lots of workout and I don't have enough time for it nut it is the third option...

Answer:

Janet would save 4 dollars a month while Mike saves 2 dollars a month.

Step-by-step explanation:

5 x 2 = 10

4 x 2 = 8

10 + 8 = $18

Answer:

18

Step-by-step explanation:

50%

since 98/2 = 49

Thats it

Answer:

2, 11, 38

Step-by-step explanation:

Multiply by 3 and then add 5 each time

1st term : 2

2nd term : 2*3 + 5 = 6 + 5 = 11

3rd term : 11*3 + 5 = 33 + 5 = 38

Answer:

A = 67.4°

Step-by-step explanation:

\(tan(A)=\frac{24}{10}\)

\(tan(A)=2.4\)

\(A=tan^{-1} (2.4)=67.38\)

Hope this helps

Answer:

840

Step-by-step explanation: