What is the value of the expression 2 + x to the second power. 5
when x = 3? =​

Answer:

Step-by-step explanation:

-10.9p + 3.9

-10.9p turns positive.

The (p) is isolated.

10.9 - 3.9= 9.18 = -9.18

Answer

-9.18

Answer:

K, here fr

Step-by-step explanation:

The length of the side marked x is 15, and the scale factor is 1.5, Similar figures have the same shape, but they may be different sizes. The ratio of the corresponding side lengths of two similar figures is called the scale factor.

In the problem, we are given that the two hexagons are similar. We are also given that the side length of the smaller hexagon is 10. We can use this information to find the scale factor and the length of the side marked x.

The scale factor is the ratio of the corresponding side lengths of the two similar figures. In this case, the scale factor is 10/15 = 2/3. This means that every side of the larger hexagon is 2/3 times as long as the corresponding side of the smaller hexagon.

The side marked x is a side of the larger hexagon, so its length is 10 * 2/3 = 15.

Therefore, the length of the side marked x is 15, and the scale factor is 2/3.

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GIVEN:

We are given a circle with center A and diameter CB.

The length of arc CDB is 14;

Required;

We are required to calculate the lenght of the radius.

Step-by-step solution;

The length of an arc with the central angle measured in radians is;

The length of the arc is given, so also is the angle theta (180 degrees, that is half the circle).

We can convert the degree measure of the angle into radians as follows;

Now we substitute the value of d (degree measure);

Now we take the formula for the length of an arc as follows;

Divide both sides by pi;

Therefore, the radius is

ANSWER:

Answer:

C: (4,5)

Step-by-step explanation:

The solution is where the two lines intersect.

Answer:

29) 60°

30) 80°

Step-by-step explanation:

29)

8x + 4 = 11 + 7x

x = 7

∴ ∠ = 11 + 7(7) = 60

30)

14x - 4 = 12x + 8

2x = 12

x = 6

∴ ∠ = 14(6) - 4 = 80

For:

Use distributive property:

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

Let:

x = Unknown number

When the number x is increasesd by 35 the result is 38, so:

Answer:

area = 160 cm²

Step-by-step explanation:

area = (8x 4 x 4) + (4 x 4 x 2) = 160 cm²

Answer: 160

Step-by-step explanation:

(8×4 + 8×4 + 4×4) × 2 = 160

Recall that tangent is the ratio of sine over cosine

tan = sin/cos

This means we'll have sin(theta+2pi) up top and cos(theta+2pi) in the bottom

\(\tan(\theta+2\pi) = \frac{\sin(\theta+2\pi)}{\cos(\theta+2\pi)}\)

Now because both sine and cosine have a period of 2pi, this means,

\(\sin(\theta+2\pi) = \sin(\theta)\\\cos(\theta+2\pi) = \cos(\theta)\)

The graph of each repeats itself every 2pi units, which is why we're back to the original version of each.

So,

\(\tan(\theta+2\pi) = \frac{\sin(\theta+2\pi)}{\cos(\theta+2\pi)}\\\\\tan(\theta+2\pi) = \frac{\sin(\theta)}{\cos(\theta)}\\\\\tan(\theta+2\pi) = \tan(\theta)\\\\\)

This seems to suggest that tangent also has a period of 2pi. This is false or misleading. It turns out the period of tangent is pi. The proof of this is a bit more involved. See the screenshot below to see those steps.

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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Answer:

0.375

Step-by-step explanation:

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

three two digit numbers and 8 total so 3/8

Hives, itching, and pale or flushed skin are examples of allergies. reduced blood pressure (hypotension) breathing difficulties and wheezing can result from airway constriction and swelling of the tongue or throat.

What causes allergies?

Why do allergies occur?

If your immune system overreacts to something that is typically harmless but causes an allergic reaction in someone who is sensitive to it, you will experience allergy symptoms. We call this chemical an allergy.

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No, there is not a SAA congruence rule. There is ASA congruence Rule.

According to the ASA congruence rule, two triangles are considered congruent if two angles of a triangle and the side between them are equal to two angles of another triangle and the side between them respectively .

According to the ASA congruence rule, two triangles are considered congruent if two angles of a triangle and the side between them are equal to two angles of another triangle and the side between them respectively . For two triangles to be congruent, the principal elements, primarily the three angles and three sides, of one triangle must be equal to the corresponding angles and corresponding sides of another triangle. Therefore, if two triangles have the same size and shape, they are said to be congruent. All six corresponding elements in both triangles need not be the same to determine congruence.

Look at the image below and see if the two given triangles ΔABC and ΔXYZ are congruent according to the ASA rule.

In the ASA standard, ∠B = ∠Y, ∠C = ∠Z, side BC = YZ, so Δ ABC ≅ ΔXYZ. Since ΔABC ≅ ΔXYZ, the other two sides of the third angle ∠A and ΔABC must be equal to the corresponding sides of angles ∠X and ΔXYZ.

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1/6 is the probability of rolling a number greater than or equal to 5.

solving-

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Approximately 38% of deaths among 16 to 19 year-olds are related to motor vehicles.

According to the Centers for Disease Control and Prevention (CDC), motor vehicle crashes are the leading cause of death for teenagers in the United States.

In 2019, a total of 2,375 teenagers aged 16-19 years died in motor vehicle crashes, and an additional 258,000 were treated in emergency departments for injuries sustained in motor vehicle crashes.

These deaths accounted for 62% of all deaths among teenagers aged 16-19 years.

Therefore, around 38% of fatalities among individuals aged 16 to 19 are connected to automobiles.

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The area of the region on is left side of the line x ≤ 1 will be considered.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

8 ≥ 3x + 5

Simplify the equation, then we have

8 ≥ 3x + 5

3 ≥ 3x

x ≤ 1

The area of the region on is left side of the line x ≤ 1 will be considered.

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Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

Answer:The opposite sides are parallel.

They have four right angles.

Step-by-step explanation: I know it because we all learn it in 5 grade.

Answer:

0.4 = 40%

0.26 = 26%

Step-by-step explanation:

Multiply the decimal by 100, and convert to percentage.

Answer:

0.4 = 4%, 0.26 = 26%

Step-by-step explanation:

hope this helps :)

24. The answer is False. Plants will not turn ideas into practical action.
25. The answer is True, Shapers will see the "small picture" and make sure that the solution results in a change of direction.


24. Plants are the creative innovators in an organization. They are characterized by their creativity, originality, and unorthodox problem-solving abilities. They generate new ideas and approaches to problem-solving. However, they may not have the necessary drive to see those ideas through to fruition. So, it is not true that plants will turn ideas into practical action. Thus, the statement is false.

25. Shapers are dynamic individuals who thrive on challenge, possessing the drive and courage to overcome obstacles and make things happen. They provide the necessary impetus to ensure that ideas are turned into action and that decisions are taken quickly and efficiently. They are the ones who see the "small picture" and make sure that the solution results in a change of direction. So, it is true that shapers will see the "small picture" and make sure that the solution results in a change of direction. Thus, the statement is true.


The correct answer for statement 24 is False and for statement 25 is True.

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Answer:

8 - 2/x is the algebraic equation (if that's what you're looking for)

Hi there!

\(\large\boxed{ \lim_{x \to 0} x^{2} - 2= -2}\)

In direct substitution, simply plug in the x-value given to solve for the limit as x approaches zero:

\(\lim_{x \to 0} x^{2} - 2 \\\\ \lim_{x \to 0} (0)^{2} - 2\\\\ \lim_{x \to 0} x^{2} - 2= -2\)

Answer:

First we write y and its derivatives as power series:

y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2

Next, plug into differential equation:

(x+2)y′′+xy′−y=0

(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

Move constants inside of summations:

∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0

∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0

Change limits so that the exponents for  x  are the same in each summation:

∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0

Pull out any terms from sums, so that each sum starts at same lower limit  (n=1)

∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0

Combine all sums into a single sum:

4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0

Now we must set each coefficient, including constant term  =0 :

4a2−a0=0⟹4a2=a0

2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0

We would usually let  a0  and  a1  be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since  a0=4a2 , I’ll choose  a1  and  a2  as the two arbitrary constants. We can still express all other constants in terms of  a1  and/or  a2 .

an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)

a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2

a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2

a5=−(4⋅3)a4+2a32(5⋅4)=15!a2

a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2

We see a pattern emerging here:

an=(−1)(n+1)n−4n!a2

This can be proven by mathematical induction. In fact, this is true for all  n≥0 , except for  n=1 , since  a1  is an arbitrary constant independent of  a0  (and therefore independent of  a2 ).

Plugging back into original power series for  y , we get:

y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯

y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯

y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)

Notice that the expression following constant  a2  is  =4+  a power series (starting at  n=2 ). However, if we had the appropriate  x -term, we would have a power series starting at  n=0 . Since the other independent solution is simply  y1=x,  then we can let  a1=c1−3c2,   a2=c2 , and we get:

y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)

y=c1x+c2∑n=0∞(−1)n+1n−4n!xn

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Answer:

It’s the bottom answer.

Step-by-step explanation:

hope I helped

The corresponding angles of the triangles are equal. Then the triangles ΔFGH and ΔMLN are similar triangles.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In triangle ΔLMN, the measure of the third angle is calculated as,

∠N + ∠M + ∠L = 180°

∠N + 51° + 36° = 180°

∠N = 93°

In triangle ΔFGH, the measure of the third angle is calculated as,

∠H + ∠F + ∠G = 180°

∠H + 51° + 36° = 180°

∠H = 93°

In triangles ΔFGH and ΔMLN, the corresponding angles are equal. Then the triangles ΔFGH and ΔMLN are similar triangles.

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a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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a. The mean is 569.5 minutes and the standard deviation is approximately 8.7366 minutes. b. The probability that a flight arrives late (later than 9:25 am) is approximately 0.68.

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is a way to express the uncertainty associated with a particular outcome or set of outcomes in a given situation.

a. To calculate the mean and standard deviation of the continuous uniform distribution, we first need to convert the time data to a minute scale.

Early arrival time: 9:17 am = 9 * 60 + 17 = 557 minutes

Late arrival time: 9:42 am = 9 * 60 + 42 = 582 minutes

The continuous uniform distribution is defined by the following formula:

Mean (μ) = (early arrival time + late arrival time) / 2

Standard Deviation (σ) = (late arrival time - early arrival time) / √12

Plugging in the values:

Mean (μ) = (557 + 582) / 2 = 569.5 minutes

Standard Deviation (σ) = (582 - 557) / √12 ≈ 8.7366 minutes (rounded to 4 decimal places)

Therefore, the mean is 569.5 minutes and the standard deviation is approximately 8.7366 minutes.

b. To calculate the probability that a flight arrives late (later than 9:25 am), we need to find the area under the probability density function (PDF) curve beyond 9:25 am.

Since the distribution is continuous uniform, the PDF is a rectangle with a base of (late arrival time - early arrival time) = 582 - 557 = 25 minutes and a height of 1/(late arrival time - early arrival time).

The probability of a late arrival can be calculated as:

Probability of late arrival = (late arrival time - 9:25 am) / (late arrival time - early arrival time)

Converting 9:25 am to minutes: 9 * 60 + 25 = 565 minutes

Probability of late arrival = (582 - 565) / (582 - 557)

= 17 / 25 ≈ 0.68 (rounded to 2 decimal places)

Therefore, the probability that a flight arrives late (later than 9:25 am) is approximately 0.68.

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Answer:

The first term is -3 and the common difference is 6

Step-by-step explanation:

Recall that the nth term of an arithmetic progression AP is given as

Tn = a + (n - 1)d

where

Tn is the nth term

a is the first term and

d is the common difference while n is the number of terms

Given that the 18th term of Arithmetic progression is 99 and 29th term is 165 then

substituting the given values into the formula

a + 17d = 99

a + 28d = 165

solve both equations simultaneously

11d = 165 - 99

11d = 66

d = 66/11

= 6

recall that a + 17d = 99

a + 17(6) = 99

a + 102 = 99

a = 99 - 102

= -3

hence the first term is -3 and the common difference is 6

There are 24 different ways to arrange the cards in the boxes.

How to arrange the card in the box?

Because there are four boxes and four cards, there are four ways to arrange the first card, three ways to arrange the second card (because one box is already occupied), two ways to arrange the third card, and one method to arrange the fourth card. As a result, the total number of possible ways to arrange the cards in the boxes is:

4 x 3 x 2 x 1 = 24

So there are 24 different ways to arrange the cards in the boxes.

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Answer:

w=6 in

l=3 in

Step-by-step explanation:

let w = width and length be 'w-3'

Two sides of w and two sides of (w-3) equal 18 sq in

18=2(w)+2(w-3)

18=2w+2w-6

4w=24

w=6

The width of rectangle is, 6 in.

And, Length of rectangle is 3 in.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is 3 inches less than its width

And, the area of the rectangle is 18 in.²

Now, We know that;

Area of rectangle = Length × Width

Let the width of rectangle = x

Hence, Length of rectangle = x - 3

Thus, We get;

Area of rectangle = Length × Width

18 = x (x - 3)

18 = x² - 3x

x² - 3x - 18 = 0

x² - (6 - 3)x - 18 = 0

x² - 6x + 3x -18 = 0

x(x - 6) + 3 (x - 6) = 0

(x - 6) (x + 3) = 0

x = 6 , x = - 3

But dimensions are not negative.

Hence, We get;

x = 6

Thus, the width of rectangle = 6 in.

Hence, Length of rectangle = x - 3

                                           = 6 - 3 = 3 in.

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