Evaluate the expression if a= -5 and b=-2.
a + 3b
A:4
B:1
C:11
D: -11

On solving the provided question, we can say that - the area of the provided circle is A = \(113.04 cm^2\)

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

radius, r = 6 cm

Area of circle = \(\pi X r^2 = 3.14 X 6 X 6 \\\)

A = \(113.04 cm^2\)

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Answer:

96

Step-by-step explanation:

im right

The statement "the horizontal, continuous lintel on a classical building supported by columns is called a stylobate" is False.

The horizontal, continuous lintel on a classical building supported by columns is called an entablature, while the stylobate is the platform on which the columns stand.

In classical architecture, the entablature is the horizontal, continuous lintel that rests on top of the columns and consists of three parts: the architrave (the bottom layer), the frieze (the middle layer), and the cornice (the top layer). The entablature helps to unify the columns and create a sense of continuity across the facade of the building.

The stylobate, on the other hand, is the platform or base upon which the columns stand, and is usually elevated above ground level. Together, the stylobate and entablature form the colonnade, a defining feature of classical architecture.

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a. To calculate velocity, we need to take the derivative of the position function, r(t). So, the formula for velocity is v(t) = r'(t) = [sqrt(2)(e^t - e^-t) + sqrt(2)t(e^t + e^-t)]a.

b. To calculate acceleration, we need to take the second derivative of the position function, r(t). So, the formula for acceleration is a(t) = r''(t) = [sqrt(2)(e^t + e^-t) + sqrt(2)t(e^t - e^-t) + 2sqrt(2)t(e^t + e^-t)]a.

c. To calculate distance, we need to integrate the velocity function, v(t), over a certain time interval. So, the formula for distance is d(t1, t2) = ∫[t1, t2] v(t) dt = ∫[t1, t2] [sqrt(2)(e^t - e^-t) + sqrt(2)t(e^t + e^-t)]a dt.

d. To calculate position, we need to integrate the acceleration function, a(t), twice over a certain time interval. So, the formula for position is r(t1, t2) = ∫[t1, t2] ∫[t1, t] a(s) ds dt + r(t1), where r(t1) is the initial position at time t1.


a. Velocity (v) can be calculated using the derivative of the position function r(t). In this case, v(t) = dr(t)/dt.

b. Acceleration (a) can be calculated using the derivative of the velocity function v(t). So, a(t) = dv(t)/dt.

c. Distance (d) can be calculated by finding the definite integral of the velocity function v(t) with respect to time over a specific interval. In other words, d = ∫|v(t)|dt, where the integration limits correspond to the interval of time you're interested in.

d. Position (r) is given by the function r(t) = sqrt(2)t * e^t * e^(-t), which represents the position of the object at any given time t.

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hi

(x+3)^2 -4 = ( (x+3) +2) ( (x+3)-2 )

= ( x+5) (x +1)

so

solutions are : x+5=0 so x=-5

x+1= 0. so x= -1

solution are -5 +and -1

Are you asking for the formula of a line that passes through these points?

Answer:

5,809

Step-by-step explanation:

I took the application

A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.

It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.

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The normal distribution curve gives useful information regarding the distribution of students' grades, such as the average grade, the dispersion of grades, the likelihood of receiving a specific grade, and the presence of any outliers.

The normal distribution curve generated by the educator offers multiple insights into the distribution of academic achievement among her pupils. The analysis of the curve yields various informative data such as:

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Answer:

96

Step-by-step explanation:

year 1: 6

year 2: 12

year 3: 24

year 4: 48

year 5: 96

Answer:

96

Step-by-step explanation:

A shelving company shipped 2,483 shelving units to each of 417 warehouses 1035411 shelving units did the company ship in all.

Total shelving to one = 2483

Total shelving to 417 warehouse = 417 x 2483 = 1035411

A flexible display system that can be moved and altered to meet various product dimensions is a shelving unit. A gondola is an open-sided island shelving unit. Overstocks are kept on the riser, the top shelf atop a shelving unit.

Pallet racks are used for products placed onto pallets, whereas used shelving is often used for single things or boxes. The styles of used shelving include enclosed, nut and bolt, modular, wire, clip, and record storage, among others.

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An off-by-one error is a common type of error that occurs when programming or solving mathematical problems.

It refers to a situation where a programmer or mathematician makes an error by including or excluding an element that they should have not. This can lead to unexpected results and bugs in the code or calculation. The error is typically caused by a misunderstanding of the boundaries of an array, list or any other data structure. These types of errors can be difficult to spot and can cause serious problems, especially in situations where precision is important.

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Answer:

A = $122.99

Step-by-step explanation:

A = P + I where

P (principal) = $100.00

I (interest) = $22.99

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 100.00(1 + 0.03/1)(1)(7)

A = 100.00(1 + 0.03)(7)

A = $122.99

Therefore:

The total amount accrued on a principal of $100.00 at a rate of 3% per year compounded 1 time per year over 7 years is $122.99.

Answer:

113.1 yards

Step-by-step explanation:

...........

Answer:

9 pi yards squared

Step-by-step explanation:

By definition, the circumference of a circle is equal to 2pi(radius) or pi(diameter).

Since the circumference is 6 pi yards, we can work backwards to find the area.

Set the equation of the circumference of a circle and the circumference given to you equal to each other in order to find your radius. With the radius we can calculate your area.

2pi(radius)=6 pi yards

Divide both sides by 2

pi(radius)=3 pi yards

Divide both sides by pi

radius=3 yards

Now that we know the radius we can find the area.

By definition, the area of a circle is pi(radius)^2 (This reads as pi times the radius squared)

Squaring the radius is just multiplying it by itself. In this case you would multiply 3 by 3 to get 9.

pi(9 yards squared)=Area

Area=9 pi yards squared

Answer:

16+(-21+4) = -1

Step-by-step explanation:

16 added to .. is 16 + ..

the sum of -21 and 4 is (-21 + 4)

So we get 16+(-21+4), that equal -1

Given statement solution is :- The new cost of a table is:

New cost of a table = T + (T * 20%)

New cost of a table = T + (T * 0.2)

New cost of a table = 1.2T

The new cost of a chair is:

A new chair would cost $900 plus ($900 * 20%)

A chair would cost $900 new plus ($900 * 0.2)

A new chair would cost $900 plus $180.

New cost of a chair = $1,080

Let's assume that a chair originally cost C and a table originally cost T.

The price of two chairs, based on the information provided, is $1,800. So we can set up the following equation:

2C = $1,800

When we multiply the two sides of the equation by 2, we get:

C = $1,800 / 2

C = $900

This indicates that a chair once cost $900.

After a month, the price of every chair and every table has now gone up by 20%. This means the new cost of a chair is 120% of the original cost, and the new cost of a table is also 120% of the original cost.

The new cost of a chair is:

A new chair would cost $900 plus ($900 * 20%)

A chair would cost $900 new plus ($900 * 0.2)

A new chair would cost $900 plus $180.

New cost of a chair = $1,080

Similarly, the new cost of a table is:

New cost of a table = T + (T * 20%)

New cost of a table = T + (T * 0.2)

New cost of a table = 1.2T

According to the given information, the office bought 6 chairs and 2 tables at $4,800. Using the updated costs, we can construct the following equation:

(6 * $1,080) + (2 * 1.2T) = $4,800

Simplifying the equation, we have:

6,480 + 2.4T = 4,800

Subtracting 2.4T from both sides, we get:

6,480 = 4,800 - 2.4T

Subtracting 4,800 from both sides, we have:

1,680 = -2.4T

Dividing both sides by -2.4, we find:

T = 1,680 / -2.4

T ≈ -$700

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Answer:

2(p - 32)(p + 2)

Step-by-step explanation:

2p² - 60p - 128 ← factor out common factor 2 from each term

= 2(p² - 30p - 64) ← factor the quadratic

consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)

the factors are - 32 and + 2 , since

- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then

p² - 30p - 64 = (p - 32)(p + 2) , so

2p² - 60p - 128 = 2(p - 32)(p + 2)

The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:

a = 2, b = -60, c = -128

The product of a and c is:

ac = 2 × (-128) = -256

We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:

1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256

We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.

We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.

We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:

2p² - 60p - 128 = 2(p - 4)(p - 32)

Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).

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Recent research has confirmed the Spillover Hypothesis by demonstrating a favourable association between life and job happiness.

According to the spillover hypothesis, behaviour or affect in a family system might flow immediately from one place or connection to another. Transfer takes place in the same valence, which means that one subsystem's negative affect is connected to another's negative affect, or stress at work spills over and intensifies stress at home. The compensatory hypothesis offers a different perspective by arguing that transfer between family subsystems occurs in the opposite valence, leading a person to seek fulfilment in one relationship or environment in order to make up for shortages in another.

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Answer: y/y+x

Step-by-step explanation: Reduce the fraction at the bottom (1 - x/y) (1 + x/y) = 1 + x/y = simplify and you get y/y+x

Answer:

10. 3 musicians

11. a) 10 feet

   b) can't read all of it

Step-by-step explanation:

Answer:

#10 should be 3

Step-by-step explanation:

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

0.2800 is the probability of an american airlines flight arriving late

The foundational ideas of probability theory were established by Blaise Pascal and Pierre de Fermat, who are recognized as the fathers of probability.

Calculating or predicting how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using terms like "certain," "impossible," or "probable." Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

The probability serves as a gauge for how likely an event is to occur. It gauges how likely an occurrence is. The probability equation is stated by the following notation: P(E) = number of favorable outcomes/number of total outcomes.

Let us assume ,

n = 150 be the total number of Airlines flights.

Out of 150 , 108 are on time.

That means 150 - 108 = 42 will be late.

Next, required probability is:

= 42/150

= 0.2800

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In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

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Answer:

Discrete

Step-by-step explanation:

Discrete is the type of variable in which the number of auto accidents reported in a given month q

Discrete data is a count that uses integers and has a finite number of potential values. This sort of information can't be broken down into smaller chunks. Discrete data consists of finite, numeric, countable, and non-negative integers with discrete variables.

As we know that the number of auto accidents that can be reported in a month will be always a whole number, therefore, the number of accidents can be represented as 0, 1, 2,..., 1000, etc.

Thus, the type of variable is the number of auto accidents reported in a given month is Discrete.

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Approximately 68% of completed pregnancies fall within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations from the mean.

The given information states that the duration of completed pregnancies follows a normal distribution. With a mean of 270 days and a standard deviation of 15 days, we can utilize the properties of the normal distribution to determine the percentages of pregnancies falling within different standard deviations from the mean.

According to the empirical rule, approximately 68% of observations fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

Therefore, in the context of completed pregnancies, around 68% will have durations between 255 and 285 days, 95% will fall within the range of 240 to 300 days, and 99.7% will have durations ranging from 225 to 315 days.

These percentages provide a statistical understanding of the distribution of completed pregnancy durations and allow for the assessment of likelihoods within different ranges.

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Complete Question:

What percentages of completed pregnancies fall within one standard deviation, two standard deviations, and three standard deviations from the mean?

The highest blank is (D)

The second highest blank is (E)

The third highest blank is (A)

The fourth highest blank is (C)

In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78) and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case.

1. In the Stackelberg case, let Firm 1 choose output y1 first, and then Firm 2 decides y2 after observing y1. Firm 1 is the leader and Firm 2 is the follower. Thus, the optimization problem for Firm 2 is as follows:

Max p(y1 + y2) * y2 - c2(y2), where y1 is chosen by Firm 1.

Thus, the profit function of Firm 2 is Π2(y1, y2) = (100 − 2(y1 + y2))y2 − 4y2

                                                                              = (100 − 2y1 − 2y2)y2

Differentiating with respect to y2, we obtain:

∂Π2(y1, y2) / ∂y2 = 100 − 2y1 − 4y2

Setting this equal to zero, we obtain:

50 − y1 = 2y2

Thus, Firm 2's best response function is: yˆ2(y1) = (50 − y1)/2

Now, Firm 1 knows that Firm 2 will choose yˆ2 given that it already chose y1.

Firm 1 chooses y1 to maximize its own profit, which is:

Π1(y1) = (100 − 2(y1 + yˆ2(y1)))y1 − 2y1

= (100 − 2y1 − 25 + 0.5y1)y1

= (75 − 1.5y1)y1

Differentiating with respect to y1, we obtain:

∂Π1(y1) / ∂y1 = 75 − 3y1

Setting this equal to zero, we obtain:

y1 = 25

Thus, yˆ1 = 25, and yˆ2 = (50 − y1)/2 = 12.5.

The profit of Firm 1 is Π1(y1) = (75 − 1.5y1)y1 = 562.5, and the profit of Firm 2 is

= Π2(y1, y2)

= (100 − 2y1 − 2y2)y2

= 156.25.2.

In the simultaneous-move case, the optimization problem for Firm 1 is as follows:

Max p(y1 + y2) * y1 - c1(y1) - c2(y2)

Similarly, the optimization problem for Firm 2 is: Max p(y1 + y2) * y2 - c1(y1) - c2(y2)

These two problems can be combined into a single problem by substituting

p(y1 + y2) = 100 − 2(y1 + y2) and

c1(y1) = 2y1 and c2(y2) = 4y2.

Thus, the profit function of each firm is:

Π1(y1, y2) = (50 − y1 − y2)y1Π2(y1, y2) = (50 − y1 − y2)y2

The first-order conditions for maximizing these profit functions are:

= ∂Π1(y1, y2) / ∂y1

= 50 − 2y1 − y2

= 0

∂Π2(y1, y2) / ∂y2 = 50 − y1 − 2y2 = 0

Solving these equations simultaneously, we obtain:

y1 = 16.67, y2 = 16.67, and Π1(y1, y2) = Π2(y1, y2) = 277.78.

Comparing this to the Stackelberg case, we see that both firms are worse off in the simultaneous-move case. In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78), and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case. Thus, Firm 1 is better off in the Stackelberg case, and Firm 2 is worse off.

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Answer:

525 mL

Step-by-step explanation:

Never mind it is not 175 that is what is left he drank 525ml