A sample of 1 can be drawn from an automatic storage and retrieval rack with 9 different storage racks and 6 different trays in each rack, find the number of different ways of obtaining a tray?

1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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Step-by-step explanation:

the middle one has to be the same for both part ratios.

the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there

for that (as a ratio is a fraction) we also have to adapt the A element in the same way.

so, we get

4×2 : 5×2 : 9 =

= 8 : 10 : 9

and that is also shown in the graphic.

Answer:

X:Y:Z= 8:10:9

Step-by-step explanation:

Let x be the number of students in class A

Let y be the number of students in class B

Let z be the number of students in class C

x:y = 4:5

y:z= 10: 9

x:y:z = ?

Find the LCM of the y terms (5 and 10 ) which is 10

Divide 10 by the first y term (5) = 2

Divide 10 by the second y term(10) = 1

X: y = (4 x 2) :(5 x 2)= 8:10

y:z =(10 x 1) : (9:1)= 10:9

x:y:z= 8:10:9

Answer:

35

Step-by-step explanation:

Well if m<YVW = (12x-1) and x=3 then just plug in x

So,

m<YVW = (12(3)-1)

m<YVW = 36-1

m<YVW = 35

Answer:

Slope: -1/4; Y-Intercept: 1.5

Step-by-step explanation:

Step 1: Find the slope. The best way to do this is to transform the two given points to y=mx+b form. When given two points, the best way to find the slope will be to do y2-y1/x2-x1. In this equation it would be -2-0/2+6, which is -2/8, simplified is -0.25 or -1/4. So we have the slope, which can determine the length of the line.

Step 2: Find the Y-Intercept. Finding the Y-intercept is so much simpler when given a graph, since all you have to do is find where the line goes through the y-axis, which in this case is (0,1.5), meaning that the y-intercept is 1.5 (note: the y-intercept can also be found when x=0, for example (0,9).

Hope this helped, good luck!

Answer:

55

Step-by-step explanation:

all angles shoudl equal 180. 180-80=100// 100= (x+67)+(x+57)// 100=2x+124// -24=2x//x=-12// -12+67= 55

Answer:

see below

Step-by-step explanation:

given function: \(Cos(x)=\frac{1}{3}\)

Cosine - (In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.)

#1: Take the inverse cosine of both sides of the equation to extract \(x\) from inside the cosine.

\(x=arccos\frac{1}{3}\)

#2: Evaluate

\(x=1.23095941\)

#3: The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from \(2\)π to find the solution in the fourth quadrant.

\(x=2(3.14159265)-1.23095941\)

#4: Simplify the equation above.

- Multiply \(2\) by \(3.14159265\)

\(x=6.2831853-1.23095941\)

- Subtract \(1.23095941\) from \(6.2831853\)

\(x=5.05222588\)

#5: Find the period.

- The period of the function can be calculated using \(\frac{2\pi }{|b|}\).

\(\frac{2\pi }{|b|}\)

- Replace \(b\) with \(1\)  in the formula for period.

\(\frac{2\pi }{|1|}\)

#6: Solve the equation.

- The absolute value is the distance between a number and zero. The distance between \(0\) and \(1\) is \(1\).

\(\frac{2\pi }{1}\)

- Divide \(2\pi\) by \(1.\)

\(2\pi\)

The period of the \(cos(x)\) function is \(2\pi\) so values will repeat every \(2\pi\) radians in both directions.

\(x=1.23095941+2\pi n,5.05222588+2\pi n\), for any integer \(n\)

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

The correct conclusion that interprets the results within the context of the hypothesis test is that "We should not reject the null hypothesis because to > tn.(C)

So, at the 10% significance level, the data do not provide sufficient evidence to conclude that the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%."

In hypothesis testing, the null hypothesis assumes that there is no significant difference between the observed and expected data. (C)

The alternative hypothesis suggests otherwise and will be used to determine the significance level. In this case, the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%.

To interpret the result, the t-value is compared to the critical value. When the t-value is greater than the critical value, the null hypothesis is rejected. If the t-value is less than the critical value, the null hypothesis is not rejected. In this case, the t-value is less than the critical value, and thus, the null hypothesis is not rejected.

Therefore, at the 10% significance level, there is no sufficient evidence to conclude that the average percentage of tips received by waitstaff in Chicago restaurants is less than 15%.

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Answer:

50 grams

Step-by-step explanation:

From the above question:

Chicken : Turkey

= 4:1

Sum Proportions = 4 + 1 = 5

We have to find the weight in grams of the entire pie

Let us represent the weight in grams of the entire pie = x.

The pie contains 200g of Chicken.

Hence:

4/5 × x = 200g

4x/5 = 200g

Cross Multiply

4x = 200g × 5

x = 200g × 5/4

x = 250g

The amount turkey that is in the pie is calculated as:

Total weight of pie - Amount of Chicken in the pie

= 250g - 200g

= 50 g

The data structures are true:  Option (1,3)

Data structures are ways of organizing and storing data in a computer so that it can be accessed and manipulated efficiently. There are several types of data structures, including arrays, linked lists, stacks, queues, trees, and graphs. Each structure has its own unique features and advantages, making it suitable for different scenarios.

For example, arrays are used for storing and accessing data in a linear fashion, while trees and graphs are used for representing hierarchical relationships between data. Data structures are a fundamental concept in computer science and are used in many applications, including databases, compilers, and operating systems. Understanding and implementing data structures is essential for efficient programming and software development

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Full Question: Which of the following statements about the data structures are true? Select ALL CORRECT answers.

Answer:

2.23

Step-by-step explanation:

tune able to find the area you should x one side by the other side to find the area 2.23 * 2.23 equals close to 5 square feet

The left Riemann sum approximation is 14.892

From the question, we have the following parameters that can be used in our computation:

f(x) = 3^x

The left Riemann sum can be expressed as:

\(R_n = h \sum_{i=1}^{n} \frac{4}{a + ih}\)

Such that:

h = (b - a)/n

In this case, a = 2, b = 3.5, n = 3, and f(x) = 3^x

So, the left Riemann sum approximation is:

Approximation = (3.5-2)/3 * (f(2 + 1/3 * (3.5-2)) + f(2 + 2/3 * (3.5-2)) + f(2 + 3/3 * (3.5-2)))

Approximation = 0.5/3 * (3^(2 + 1/3 * (3.5-2)) + 3^(2 + 2/3 * (3.5-2)) + 3^(2 + 3/3 * (3.5-2)))

Approximation = 14.892

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0 ≤ x < 2, where x is an integer. Option C

The appropriate domain for the function f(x) = 42 - 15x in the given context can be determined by considering the constraints of the problem.

Tyson has a $50 gift card, and he wants to purchase a belt that costs $8 and x number of shirts that cost $15 each. The function f(x) represents the balance on the gift card after Tyson makes the purchases.

The number of shirts Tyson can purchase depends on the remaining balance on the gift card. Since each shirt costs $15, the maximum number of shirts he can buy is limited by the amount of money left on the gift card.

If we subtract the cost of the belt ($8) and the cost of x shirts ($15x) from the initial balance ($50), we should get a non-negative result, indicating that Tyson has enough money on the gift card to make the purchases.

Therefore, we can set up the inequality:

50 - 8 - 15x ≥ 0

Simplifying, we have:

42 - 15x ≥ 0

Now, we can solve for x:

-15x ≥ -42

Dividing by -15 (remembering to flip the inequality sign), we get:

x ≤ 42/15

x ≤ 2.8

Since x represents the number of shirts Tyson can buy, it should be a whole number. Therefore, the appropriate domain for the function f(x) is:

0 ≤ x ≤ 2, where x is an integer.

Option C.

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Answer: y = -4x + 3

Step-by-step explanation:

   First, we will write 8x+2y=14 in slope-intercept form.

8x+2y=14

2y = -8x + 14

y = -4x + 7

   Next, we will take this new slope-intercept form equation, y = -4x + 7, and use the slope from it to substitute the coordinate point given to find the y-intercept of the equation we are trying to find.

y = -4x + b

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

-5 = -8 + b

b = 3

   Lastly, we will write our equation with a slope of -4 and a y-intercept of 3.

         y = -4x + 3

The distance covered by light in 2 weeks is \(3.6288*10^{14}\) m.

It is given that:-

Speed of light = \(3*10^8 m/s\)

We have to find the distance travelled by the light in 2 weeks.

We know that,

1 week = 7 days

Hence,

2 weeks = 14 days

Also,

1 day = 24 hours

1 hour = 60 minutes

1 min = 60 seconds

Hence, we can write,

1 day = 60*60*24 seconds = 86,400 seconds

14 days = 86400*14 = 12,09,600 seconds

We know that,

Speed = distance/time

Hence,

distance = speed * time

Hence, distance travelled by light in 2 weeks = \(3*10^8*1209600 = 3628800 * 10^8 = 3.6288*10^{14} m\)

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The numerical value in this sentence, "the average price of a house in the new subdivision is $257,000" describes a Population Parameter.

A population parameter is a figure that describes a fact about a whole population. In this sentence, we can see that the figure quoted is representative of an entire population. A sample statistic, on the other hand, describes something about a part of a population.

So, for the statement above, we can see that the average price is representative of all the houses in the new subdivision. Thus, the figure is a population parameter.

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Answer:

\( \overline{XY} = 1.5 \)

Step-by-step explanation:

Given:

AB = 3

BC = 5

CA = 6

Required:

Length of XY

SOLUTION:

According to the Triangle Midsegment Conjecture, midsegment \( \overline{XY} \) is half the length of \( \overline{AB} \).

Therefore:

\( \overline{XY} = \frac{1}{2}(\overline{AB}) \)

Thus:

\( \overline{XY} = \frac{1}{2}(3) \)

\( \overline{XY} = \frac{3}{2} \)

\( \overline{XY} = 1.5 \)

The problem that Camilla could she be trying to solve is D. a person can afford a $480-per-month loan payment.

It should be noted that a loan simply means an amount of money that's taken for future repayment.

In this case, the information given shows that the problem will be that the person can afford a $480-per-month loan payment and she is being offered a 2-year loan with an APR of 1.2%, compounded monthly.

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The solution of the system of equations is (x, y) = (1/3, 1/3).

To solve the given system of equations, we can use any of the following three methods; the substitution method, the elimination method (also known as the addition/subtraction method), and the graphical method. Below, we will solve it using each of these methods.

1. Substitution method:

We will use the substitution method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2) From equation (1), we have

Y + 2x = 3y ...(3)Now substitute equation (3) into equation

(2)2y = 3x - 2 ...(2)Y + 2x = 3y ...(3)2(3y - 2x) = 3x - 2

Multiplying both sides by 2:

6y - 4x = 3x - 2 Grouping like terms:

6y - 3x = 2 Adding 3x to both sides:

6y = 3x + 2Dividing both sides by 6:

y = (3/6)x + 2/6y = (1/2)x + 1/3

Therefore, the solution of the system of equations is (x, y) = (1/3, 1/3).

2. Elimination method:

We will use the elimination method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2)Multiplying equation (1) by 2,

we get;2Y = 6y - 4x ...(3)Multiplying equation (2)

by -3, we get;-6y = -9x + 6 ...(4) Adding equations (3) and (4),

we get;-4x = -9x + 8

Simplifying;-4x + 9x = 8x = -8x = -2

Therefore, we found the value of x, which is -2.

Substitute the value of x in either equation (1) or (2);

If we substitute x = -2 in equation (1), we get;

Y = 3y - 2(-2)Y = 3y + 4Y - 3y = 4Y = 4/2Y = 2Substitute the value of y in equation (1)

;Y = 3y - 2xY = 3(2) - 2(-2)Y = 6 + 4Y = 10

Therefore, the solution of the system of equations is (x, y) = (-2, 10/2).3.

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The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.

Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).

The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:

P(A and C) = P(C|A) * P(A)

Substituting the given values:

P(A and C) = 0.17 * 0.08

P(A and C) = 0.0136

Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.

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Using sine rule formula to resolve the value for angle D

The sine rule formula is,

Given:

Therefore,

Simplify

Hence, the answer is

To find the z-score of a person who scored 775 on the exam, we can use the formula:

z = (x - μ) / σ

where x is the individual's score, μ is the mean, and σ is the standard deviation.

In this case, the individual's score is 775, the mean is 750, and the standard deviation is 25. Plugging these values into the formula, we get:

z = (775 - 750) / 25 = 1

Therefore, the z-score of a person who scored 775 on the exam is 1.

A z-score represents the number of standard deviations an individual's score is away from the mean. It is a measure of how a given value relates to the average value of a set of data, taking into account the variability of the data.

By calculating the z-score, you can determine whether a data point is relatively high or low compared to the rest of the data set. A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that it is below the mean.

In this case, a z-score of 1 indicates that the person's score is 1 standard deviation above the mean.

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Step-by-step explanation:

Given

No. of employees \(N(t)=500(0.02)^{0.7^{t}}\)

(a)When the company opens i.e. at t=0

\(N(0)=500(0.02)^{1}=10\)

There are 10 employees at the beginning

(b)when N=100

\(100=500(0.02)^{0.7^{t}}\\0.2=0.02^{0.7^{t}}\)

Taking log both sides

\(\ln (0.2)=0.7^t \cdot \ln (0.02)\)

\(0.7^t=\frac{\ln (0.2)}{\ln (0.02)}=0.4114\)

again taking log

\(t\times \ln (0.7)=\ln (0.4114)\)

\(t=\dfrac{\ln (0.4114)}{\ln (0.7)}=2.49\)

(c)when t tends to \(\infty\), \((0.7)^t\rightarrow 0\)

So, \(N(\infty)=500\cdot(0.02)^0=500\times1=500\)

i.e. there can be 500 employees at max

Answer:

The answer is 6

Step-by-step explanation:

4.5 = 75% × Y

4.5 =  

75

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 75 we will arrive at:

Y = 4.5 ×  

100

75

Y = 4.5 × 100 ÷ 75

Y = 6

Step-by-step explanation:

D) (-3, 1)

I is 3 steps away from the y axis, so counting 3 steps further you'll have (-3,1)

The area of the largest rectangle is 46.47 square root.

Consider a semi-circle with a rectangle ABCD inscribed in it.

Let, O = centre of the semi-circle

A and B lies on the base of the semi-circle

OA = OB = x

D and C lie on the semi-circle

BC = AD = y

AB = CD = 2x

By Pythagorean theorem,

CB² + OB² = OC²

⇒ y² + x² = (6)²

⇒ y² = 36 - x²

⇒ y = √(36 - x²)

Now, area of rectangle in terms of x,

Area, A = 2x × y

= 2x × √(36 - x²)

Differentiating,

A' = 2 × √(36 - x²) - 2x²/(36 - x²)

When x = 0, y = 6 and when x = 6, y = 0, area = 0.

It implies that area is maximum when the value of x lies between 0 and 6.

This will occur where A’ = 0.

⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0

⇒ 2 × √(36 - x²) = 2x²/(36 - x²)

On simplification, we get,

⇒ 2 × (36 - x²) = 2x²

⇒ 36 - x² = x²

⇒ 2x² = 36

⇒ x² = 36/2

⇒ x = √36/2

Now, y = √(36 - x²) becomes

⇒ y = √(36 - (√36/2)²)

⇒ y = √(36 - 36/2)

⇒ y = √(96 - 36)/2

⇒ y = √60/2

Maximum area = 2xy

= 2(√36/2)(√60/2)

= 46.47

Therefore, the area of the largest rectangle = 46.47 square units.

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Answer:

sam did the most

Step-by-step explanation:

let's find box packed per day

sam - 15 boxes in 5 days

so 3 boxes in 1 day

Dylan - 60 boxes in 4 weeks and 2 days

that is 60 in 30 days

that will make 2 boxes in 1 day

It has 816 ways to 3-element subsets, such that no two consecutive integers are in the subset.

You need three digits from 1 to 20, but you don't want any consecutive ones. You should call them a, b, and c.

Without loss of generality, a < b < c.

We use combinations,

Remember that we can write a + 1 b if a b and they're not sequential. With the aid of this insight, we can see the number of desired the number of methods for choosing a, b, and c from among the integers so that,

(1 ≤ a) & (a + 1 < b) & (b + 1 < c) & (c ≤ 20)

In other words, you want to know how many possibilities there are to choose the three numbers a, b, and c so that;

1 ≤ a < b − 1 < c − 2 ≤ 18

As a result, the question is equal to asking how many ways there are to select three integers (a, b - 1, and c - 2) from a range of 1 to 18. In other words, we are interested in how many ways we can select three items from a total of 18 options.

So, the response is:

\((^1^8_3)\) = 816 ways

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