(9-3)+18÷8
show your work ​

Answer:

\(\huge\boxed{\cot\dfrac{3\pi}{2}=0}\)

Step-by-step explanation:

\(\text{We know}\ \cot x=\cot(x\pm\pi)\ \text{and}\ \cot(-x)=-\cot x.\\\\\text{We have}\ \cot\dfrac{3\pi}{2}=\cot\dfrac{\pi+2\pi}{2}=\cot\bigg(\dfrac{\pi}{2}+\dfrac{2\pi}{2}\bigg)=\cot\bigg(\dfrac{\pi}{2}+\pi\bigg)=\cot\dfrac{\pi}{2}\\\\\cot\bigg(\dfrac{\pi}{2}\bigg)=0\\\\\text{Therefore}\ \cot\dfrac{3\pi}{2}=0.\)

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

V = \(\frac{7}{8}\) units³

Step-by-step explanation:

the volume (V) of the prism is calculated as

V = Ah ( A is the area of the base and h the height ) , then

V = \(\frac{1}{2}\) × 1 \(\frac{3}{4}\) ( change mixed number to improper fraction )

   = \(\frac{1}{2}\) × \(\frac{7}{4}\)

   = \(\frac{1(7)}{2(4)}\)

   = \(\frac{7}{8}\) units³

Answer:

5√10

Step-by-step explanation:

I always teach my students this one method, and that is to take the number inside the square root and factor it into a SQUARE NUMBER multiplied by ANOTHER NUMBER.

A square number is a number that is a perfect square, in the sense that it is the product of a certain number multiplied by itself. For instance, 16 is a square number because 16 = 4*4.

So, what is a square number in 250? Well, firstly, let's list the factors of 250.

1, 250

2, 125

5, 50

10, 25
These are all the factors of 250. The ONLY perfect square/square number in this list of factors is 25, which is 5*5. Therefore, 250 = 25*10. 25 is the square number and the other number is 10.

To simplify the square root, we split √250 into √25 * √10. When you have a composite number in a square root, you can split it like this. √25 = 5, and you cannot simplify √10 because it doesn't have any factors that are square numbers. Therefore 5*√10 = 5√10. This is the answer to the problem.

If you have any other questions, just let me know. I hope this helps and have a great day.

The simplified form of the given square root number is 5√10.

The given square root number is √250.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

Here, 250 = 2×5×5×5

Thus, √250=√2×5×5×5

= 5√10

Therefore, the simplified form of the given square root number is 5√10.

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H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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The probability that the call arrived when the switchboard was not fully busy, given that it arrived at random within the one-minute interval, is P(B) or 7/12.

The probability that the call arrived when the switchboard was not fully busy can be calculated using the concept of conditional probability. Let's define the event A as the call arriving during the 25-second period when the switchboard was fully busy, and event B as the call arriving during the remaining 35-second period when the switchboard was not fully busy. Since the call arrived at random within a one-minute interval, the probability of event A happening is 25/60 or 5/12 (25 seconds out of 60 seconds).
The probability of event B happening can be calculated as the complement of event A, which is 1 - 5/12 or 7/12 (35 seconds out of 60 seconds).
Therefore, the probability that the call arrived when the switchboard was not fully busy, given that it arrived at random within the one-minute interval, is P(B) or 7/12.

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Answer:

First Section:4km per hour

Second Section:0km per hour

Third Section:1.5km per hour

Step-by-step explanation:

From the first section to the second section the distance remains the same therefore he didn't travel at all that's why it is 0km. For the third section he has to travel 6 kilometers in 4 hours which is 1.5.

0 5/3 21 On the number line, we need to position three numbers: 0, 5/3, and 21.

The number 0 is the starting point and should be placed on the leftmost box. Next, we have the number 5/3. To determine its placement, we can convert it to a decimal. Dividing 5 by 3 yields 1.666..., which is approximately 1.67.

Since 5/3 is greater than 1 but less than 2, it falls between 1 and 2 on the number line. Finally, we have the number 21, which is significantly larger than 5/3. It should be placed on the rightmost box, well past the midpoint between 0 and 5/3. Therefore, the correct placement along the number line would be: 0, 5/3, 21.

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Answer:

B. Point E

Step-by-step explanation:

Your point is (2,5) for the reptile house ((8,3) is extra unnecessary information) to find the house you go to the right 2 units and then 5 units up. The only one that matches is point E so therefore it's your answer.

The gain of $5 can be represented as +5 and the loss of $3 can be represented as -3.

We know that there are two types of integers

To represent the gain of $5 on one day, we can use the positive integer +5.

To represent the loss of $3 on the next day, we can use the negative integer -3.

Therefore, the gain of $5 can be represented as +5 and the loss of $3 can be represented as -3.

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A) La probabilidad de que la cantidad total de la solución contenida en 50 tambores sea mayor a 1 500 L es del 50%.

B) La probabilidad de que puedan llenarse 80 tambores sin que se acabe la solución es del 75%.

C) La tina debe contener 2160 litros para que la probabilidad sea 0,9 de que puedan llenarse 80 tambores sin que se acabe la solución.

Dado que unos tambores, con una etiqueta de 30 L, son llenados con una solución proveniente de una tina grande, y se agrega una cantidad aleatoriamente de la solución en cada tambor con media de 30.01 L y desviación estándar de 0.1 L, para determinar A) ¿Cuál es la probabilidad de que la cantidad total de la solución contenida en 50 tambores sea mayor a 1 500 L?; B) Si la cantidad total de la solución en la tina es de 2 401 L, ¿cuál es la probabilidad de que puedan llenarse 80 tambores sin que se acabe la solución?; y C) ¿Cuánta solución debe contener la tina para que la probabilidad sea 0,9 de que puedan llenarse 80 tambores sin que se acabe la solución?, se deben realizar los siguientes cálculos:

A)

B)

C)

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The number of people in the survey is 25, s = 2 and mean = 33, the margin of error is given as 0.5532

Given,

In the question:

25 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $33 and standard deviation of $2.

To find the margin of error at a 80% confidence level.

Now, According to the question;

How to solve for the margin of error?

The margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.

We would have to calculate the amount of error using the data that we have below.

We have the following values

number n = 25

mean u = 33

standard deviation (sd) = 2

The level of confidence c i = 80% = 0.80

we have to find the critical value

degree of freedom = 1 - 0.80

= 0.20

zα/2

= 0.20 / 2 = 0.10

= 1.383

The margin of error

= zα / 2 x s / √n

= 1.383 x 2/√25

= 1.383 x 2/5

= 0.5532

Hence,  the number of people in the survey is 25, s = 2 and mean = 33, the margin of error is given as 0.5532

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The outcomes of A ∪ B are {1, 2, 3, 5, 7, 9, 11, 13, 17, 19} and the outcomes of A ∩ B are {3, 5, 7, 11, 13}.

The set A represents the prime numbers less than 20, while the set B represents the odd numbers less than 15.

Listing the outcomes of A ∪ B (union of A and B) will provide all the elements present in both sets without duplication.

On the other hand, listing the outcomes of A ∩ B (intersection of A and B) will give the common elements between the two sets.

Set A: {2, 3, 5, 7, 11, 13, 17, 19}

Set B: {1, 3, 5, 7, 9, 11, 13}

To find the outcomes of A ∪ B, we need to combine all the elements from sets A and B without duplication.

Taking the union of A and B gives us the following elements: {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}.

Therefore, the outcomes of A ∪ B are {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}.

These numbers represent all the prime numbers less than 20 and all the odd numbers less than 15, combined without duplication.

To find the outcomes of A ∩ B, we need to identify the elements that are present in both sets A and B.

In this case, the common elements between A and B are {3, 5, 7, 11, 13}.

Therefore, the outcomes of A ∩ B are {3, 5, 7, 11, 13}.

These numbers represent the prime numbers less than 20 that are also odd numbers less than 15.

The intersection of A and B shows the elements that satisfy both conditions simultaneously.

By finding the outcomes of A ∪ B and A ∩ B, we have identified the elements that belong to both sets without duplication and the elements that are common between the sets, respectively.

This helps in understanding the combined elements and the overlapping elements between sets A and B.

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The complete question is:

A = {prime numbers less than 20} B = {odd numbers less than 15}

List the outcomes of A ∪ B and explain?

List the outcomes of A ∩ B and explain?

Answer:

2x + 5

ok.. slightly silly question...

you will eventually learn that this formula is the

formula for the "derivative" in calculus....

A\(x^{b}\) becomes (a*b)  \(x^{b-1}\)

2x + 5

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

x = 1500 /  12

  =  125

The two-column proof are properties written with reason statements.

Two column proof is always written in two columns. This proof is consist of two parts, first one is the statement part which contain the exact statement of theorem and second part is reason part which consist of reason for that particular statement or equation. Both the parts are written in different columns, thus the proof is called as two-column proof.

In the given question , two-column proofs are as below :

for part 7 - Reflexive Property of Segment Congruence

To prove:  (AB)' ≅ (AB)'

Proof :

            Statements                               Reasons

           segment AB                                Given

           AB = |(AB)'|                                   Definition of segment length

           (AB)' = (AB)'                                  Reflexive property

           (AB)' ≅ (AB)'                                 Definition of congruent segments

for part 8 - Transitive Property of Angle Congruence

To prove: ∠A ≅ ∠C

Proof :

            Statements                               Reasons

           ∠A ≅ ∠B                                      Given

           ∠B ≅ ∠C                                      Given

            m∠A = m∠B                                Definition of congruent angle

            m∠B = m∠C                                Definition of congruent angle

            m∠A = m∠C                                Definition of Transitive property

            ∠A ≅ ∠C                                     Congruence property

for part 9 - Transitive Property of Segment Congruence

To prove: ∠A ≅ ∠C

Proof :

            Statements                               Reasons

           ∠A ≅ ∠B                                      Given

           ∠B ≅ ∠C                                      Given

            ∠A ≅ ∠C                                     Transitive Congruence property

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The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

A mathematical statement is a sentence that can be either true οr false and cοntains mathematical expressiοns οr variables, such as numbers, variables, οperatiοns, relatiοns, οr lοgical cοnnectives.

Mathematical statements can take many fοrms, such as equatiοns, inequalities, geοmetric theοrems, and lοgical prοpοsitiοns. Fοr example, "2 + 2 = 4" is a mathematical statement that is true, while "1 + 1 = 3" is a mathematical statement that is false.

Nοw,

Given statement can be written as

Twο times=2x

six less than 2 times=2x-6

is nο mοre than 17= 2x-6≤17

where x is the number.

Hence,

          The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

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The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The expression is given below.

⇒ 8² + 3 × 78² + 3 × 7

Simplify the expression, then we have

⇒ 8² + 3 × 78² + 3 × 7

⇒ 64 + 3 × 6084 + 21

⇒ 85 + 18252

⇒ 18337

The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.

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Answer:

-26

Step-by-step explanation:

The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle

To find the length of the arc subtended by the angle's rays, we need to know the angle measure. Since we know that 1/360th of the circumference is 0.04 cm long, we can find the circumference by multiplying 0.04 cm by 360, which gives us 14.4 cm.

Now, we need to find the angle measure. Since the circle is centered at the vertex of the angle, the angle measures half the arc it subtends. Thus, we can find the angle measure by dividing the circumference by 2 and then multiplying by 1/360.

Angle measure = (14.4/2) x (1/360) = 0.02 radians

Finally, we can find the length of the arc subtended by the angle's rays by multiplying the angle measure by the radius of the circle.

Length of arc = 0.02 x radius


The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle. The given information of 1/360th of the circumference being 0.04 cm long helped us find the circumference and subsequently the angle measure.

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Time intervals = 14/7 = 2

Final Amount = 40(1/2)² = 10

Step-by-step explanation:

For x = 2,6

\( = 3{x}^{0} \)

\( = 3 \times {2,6}^{0} \)

\( = 3 \times1 \)

\( = 3 \)

\( \: \)

For a = -3 and b = -8

\( = 10 \times {a}^{2} \times {b}^{0} \)

\( = 10 \times {( - 3)}^{2} \times {( - 8)}^{0} \)

\( = 10 \times 9 \times 1\)

\( = 90\)

The volume of the smaller solid is approximately 8.85 cubic meters.

Since the two solids are similar, their corresponding side lengths are proportional. Let the ratio of the corresponding side lengths be k. Then the ratio of the surface areas is k², and the ratio of the volumes is k³.

Let V be the volume of the smaller solid, then we have:

(k²) * 49 = 169  (equation 1)

(k³) * V = 114   (equation 2)

Solving equation 1 for k, we get:

k = √(169/49) = 13/7

Substituting k into equation 2, we get:

(13/7)³ * V = 114

V = 114 / (13/7)³

V ≈ 8.85 m³

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Answer:

x = -25

Step-by-step explanation:

\(3 - \frac{x}{5} = 8\)

\(5(3 - \frac{x}{5} ) = 5 \times 8\)

\(5 \times 3 - 5 \times \frac{x}{5} = 5 \times 8\)

\(15 - 5 \times \frac{x}{5} = 40\)

\(15 - x = 40\)

\( - x = 40 - 15\)

\( - x = 25\)

\(x = - 25\)

Answer:

x = - 25

Step-by-step explanation:

Given

3 - \(\frac{x}{5}\) = 8 ( subtract 3 from both sides )

- \(\frac{x}{5}\) = 5 ( multiply both sides by 5 to clear the fraction )

- x = 25 ( multiply both sides by - 1 )

x = - 25

The problem can be modeled as a linear programming problem. We need to minimize the total cost of shipping the boots, which can be represented as a linear combination of the shipment quantities.

Thus, the objective function to be minimized can be written as:

Minimize Z = 4x11 + 5x12 + 7x13 + 6

32 + y33 ≤ 40 (capacity limit at warehouse 3)

y41 + y42 + y43 ≤ 30 (capacity limit at warehouse 4)

y51 + y52 + y53 ≤ 45 (capacity limit at warehouse 5)

xij, yjk ≥ 0 (non-negativity constraint)

Thus, the complete linear programming problem can be formulated as:

Minimize Z = 4x11 + 5x12 + 7x13 + 6x21 + 4x22 + 5x23 + 4y11 + 3y12 + 6y13 + 5y21 + 5y22 + 4y23 + 6y31 + 7y32 + 5y33 + 4y41 + 6y42 + 5y43 + 5y51 + 4y52 + 6y53

Subject to:

x11 + x12 + x13 ≤ 60

x21 + x22 + x23 ≤ 90

x11 + x21 = y11 + y21 + y31 + y41 + y51

x12 + x22 = y12 + y22 + y32 + y42 + y52

x13 + x23 = y13 + y23 + y33 + y43 + y53

y11 + y12 + y13 ≤ 35

y21 + y22 + y23 ≤ 50

y31 + y32 + y33 ≤ 40

y41 + y42 + y43 ≤ 30

y51 + y52 + y53 ≤ 45

xij, yjk ≥ 0

Solving this linear programming problem using a suitable solver will provide us with the optimal values of xij and yjk, which will help us in determining the minimum cost required for shipping the boots while satisfying all the constraints.

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Answer:

is there more in the question

Answer:

B

Step-by-step explanation:

8f=10

f=1 1/4

Answer:

A

Step-by-step explanation:

A linear function is a straight line when graphed so is not B.

For confirmation of A note how for each increase of 3 in x we get the same increase of 5 in y.