Problem 1 (2 points). A large investment firm wants to review the distribution of the ages of its stock-brokers. The ages of a sample of 25 brokers are as follows: 53 42 63 70 35 47 55 58 41 49 44 61

Answer:

\(\displaystyle \cos(\alpha+\beta)=\frac{21}{221}\)

Step-by-step explanation:

First, we can draw two right triangles to represent the given information.

Please refer to the attachment.

We will ignore the negatives for now.

The triangle on the left represents the ratio:

\(\displaystyle \tan(\alpha)=\frac{15}{8}\)

And the triangle on the right represents the ratio:

\(\displaystyle \sin(\beta)=\frac{5}{13}\)

And the unknown side, c and d, were determined using the Pythagorean Theorem.

We want to find:

\(\displaystyle \cos(\alpha+\beta), \; \pi/2<\alpha<\pi, \; \pi/2<\beta<\pi\)

So, both α and β are in QII.

Using the Sum Identity, we can write our expression as:

\(\displaystyle\cos(\alpha+\beta) =\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)\)

Now, we will use our triangles and what we know about our angles and quadrants.

Since α and β are in QII, cosine is always negative, sine is always positive, and tangent is always negative.

Now, we can use our trig ratios. Recall SohCahToa.

According to the first triangle, cos(α) is 8/17.

However, since α is in QII, cos(α) must be -8/17.

Likewise, according to the second triangle, cos(β) is 12/13.

Since β is in QII, cos(β) is -12/13.

Now, we can determine our sine ratios.

According to the first triangle, sin(α) is 15/17.

And since α is in QII, this stays positive.

And, sin(β), as given to us, is 5/13.

Therefore, we will substitute this into our equation. So:

\(\displaystyle \cos(\alpha+\beta)=(-\frac{8}{17})(-\frac{12}{13})-(\frac{15}{17})(\frac{5}{13})\)

Evaluate:

\(\displaystyle \cos(\alpha+\beta)=\frac{96}{221}-\frac{75}{221}\)

Hence:

\(\displaystyle \cos(\alpha+\beta)=\frac{21}{221}\)

The total cost for Beck to attend the fair and go on 4 rides can be calculated as follows:

Cost of admission: $10

Cost of 4 rides: 4x

Total cost: $10 + 4x

Since we are not given the value of x, we cannot calculate the total cost. However, we know that each ride costs x dollars, so we can use this information to find the cost of each ride if we are given the total cost. Alternatively, if we are given the cost of each ride, we can find the total cost by substituting the value of x into the equation.

As the question does not provide any information about the value of x or the total cost, we cannot provide a specific answer to this question.

Answer:

-65/33

Step-by-step explanation:

The solution to the given expression negative four and one third ÷ two and one fifth is -1 32/33

negative four and one third ÷ two and one fifth

-4 1/3 ÷ 2 1/5

= -13/3 ÷ 11/5

= -13/3 × 5/11

= (-13 × 5) / (3 × 11)

= -65 / 33

= -1 32/33

Therefore, the solution to the fraction is -1 32/33

Learn more about fraction:

https://brainly.com/question/11562149

#SPJ1

The area of one wall based on area of floor and height of room is 28 feet².

Finding the length of one side of floor to find the area of wall. The formula to be used in the calculation of side of floor is area = side².

Area of floor = side²

side = \( \sqrt{49} \)

side = 7 m

Area of wall will be calculated by finding the product of length and breadth.

Area of one wall = 7 × 4

Performing multiplication on Right Hand Side of the equation

Area of one wall = 28 feet²

Thus, the area is 28 feet².

Learn more about room calculations -

https://brainly.com/question/84323

#SPJ4

The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

Read more on probability here:https://brainly.com/question/13604758

#SPJ1

Constructive criticism refers to feedback or advice given in a positive and collaborative manner with the intention of improving a specific outcome or behavior.

Constructive criticism refers to feedback or advice given in a positive and collaborative manner with the intention of improving a specific outcome or behavior. It involves providing specific and actionable feedback that is timely and favorable to the individual receiving it, with the goal of helping them improve their performance or achieve a particular objective.

Unconstructive criticism, on the other hand, is feedback that is negative, unhelpful, or delivered in a manner that is not collaborative or respectful. It may focus on faults or mistakes without offering solutions or guidance on how to improve, and may be delivered in a way that is hurtful or demotivating to the person receiving it.

It's important to remember that constructive criticism should always be delivered in a positive and supportive manner, with the aim of helping the individual improve and succeed. Providing feedback in a way that is respectful, specific, and actionable can help build trust and foster a positive working relationship between individuals, while also driving better outcomes and results.

To know more about constructive criticism, refer here:

https://brainly.com/question/1953632

#SPJ11

The area of the shaded region is 36.3  to 3  significant figures

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Step one: find the two diagonals of the kite.

The Horizontal diagonal can be obtained using the cosine rule:

AC² = OA²- OC² - 2 *OA*OC* cosθ

       = 10²+ 10² - 2* 10 *10 * cos(120)

AC² = 200

=> AC=√200 = 14.1

The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:

Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.

This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.

cos(60)= 10/OB

=> OB= 10/ cos(60) = 20 m

Step two: Use the dimensions of the two diagonals of the Kite to find the area:

The area of a Kite is obtained using this formula:

area = pq/2, , where p and q are the two diagonals.

area =( 14.1*20)/2 = 141 m²

Step three: Calculate the area of the sector of the circle.

Area of the sector is obtained using this formula

Area =θ/360 * πr²  = 120/360 * 3.14 * 10²  = 104.66 m²

Step Four: Subtract the area of the sector from the area of the kite:

Area of the shaded region will be  141 m²  -  104.66 m²  = 36.34 m²

To learn more about the area from the given link

https://brainly.com/question/25292087

#SPJ1

1264₈ = 1•8³ + 2•8² + 6•8¹ + 4•8⁰

1264₈ = (2³)³ + 2•(2³)² + 3•2•2³ + 2²

1264₈ = 2⁹ + 2⁷ + 3•2⁴ + 2²

1264₈ = 512 + 128 + 3•16 + 4

1264₈ = 692

After converting the base, 1264 base 8 is equal to 692 base 10.

To convert a number from base 8 (octal) to base 10 (decimal), we need to evaluate the value of each digit in the base 8 number and then calculate the equivalent decimal value.

Given the number 1264 in base 8, we can break it down into its digits:

1 * 8³ + 2 * 8² + 6 * 8 + 4 * 1

Simplifying this expression:

1 * 512 + 2 * 64 + 6 * 8 + 4 * 1

Evaluating the multiplication:

512 + 128 + 48 + 4

Adding the products together:

692

In summary, to convert a number from base 8 to base 10, we evaluate the value of each digit by multiplying it with the corresponding power of 8, and then sum up the results. This gives us the equivalent decimal value of the number.

To learn more about conversion click on,

https://brainly.com/question/33187951

#SPJ2

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162

To rewrite the expression 1 - cos^2(theta) without using absolute values for the given values of theta (2.5 < theta < 3), we can utilize the trigonometric identity for cosine squared:

cos^2(theta) = 1 - sin^2(theta)

Now, let's substitute this identity into the expression:

1 - cos^2(theta) = 1 - (1 - sin^2(theta))

= 1 - 1 + sin^2(theta)

= sin^2(theta)

Therefore, for the given range of theta (2.5 < theta < 3), the expression 1 - cos^2(theta) is equivalent to sin^2(theta).

To know more about identity visit-

brainly.com/question/31054770

#SPJ11

To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

Learn more about square feet here : brainly.com/question/30678567

#SPJ11

Answer: I am going to evaluate this question. The anwser is 99

According to the question the correct solution is to find the number of ways to reach the Nth step, you can calculate the Nth Fibonacci number.

To find the number of ways to reach the Nth step, we can use the concept of Fibonacci numbers.

Let's consider the base cases:

- If N = 1, there is only one way to reach the 1st step (by taking one step).

- If N = 2, there are two ways to reach the 2nd step (by taking two single steps or one double step).

For N > 2, the number of ways to reach the Nth step can be calculated by summing the number of ways to reach the (N-1)th step and the (N-2)th step.

Let's denote the number of ways to reach the Nth step as F(N). Then we have:

F(N) = F(N-1) + F(N-2)

Using this recursive relation, we can calculate the number of ways to reach the Nth step for any positive integer N.

Here's a table to illustrate the calculation of Fibonacci numbers for the number of ways to reach each step:

Step (N)   |  Number of Ways (F(N))

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

1          |  1

2          |  2

3          |  3

4          |  5

5          |  8

6          |  13

...        |  ...

As we can see, the number of ways to reach the Nth step follows the Fibonacci sequence. Therefore, to find the number of ways to reach the Nth step, you can calculate the Nth Fibonacci number.

To know more about sequence visit-

brainly.com/question/13034574

#SPJ11

Answer:

1089

Step-by-step explanation:

The original number is A0CD, We have that DC0A = 9 x A0CD.

If A =1, then D = 9 and we have:

9C01 = 9 x 10C9

In order for this expression to be true, the following must also be true:

(C x 9) + 8 must be divisible by 10, which means that C x 9 must end in a 2.

The only multiple of 9 (from 9 to 81) that ends in a 2 is 72.

72 = 9 x 8.

Therefore, C must be 8 and the original number is 1089. Multiply it by 9 to check the answer:

1089 x 9 = 9,081

Therefore, 1089 is correct.

Answer:

24

Step-by-step explanation:

it is correct

...,..............

The solution to the given indices are 1/2^7, 11^4 and -1/64

Give the following indices expression

\(\frac{(2^{-4})^2\times 2^{-5}}{2^{-6}} \\\)

This can be further simplified according to the law of indices as:

\(\frac{(2^{-4})^2\times 2^{-5}}{2^{-6}} =\frac{2^{-8-5}}{2^{-6}}\)

Determine the result

\(\frac{2^{-8-5}}{2^{-6}} = 2^{-7} = 1/2^7\)

For the indices expression

\(11^{-4}\times 11^{8} = 11^{-4+8}=11^4\)

For the indices expression

\(-4^4\times4^{-7}\\=-(4^{4-7})\\= -4^{-3}\\=-1/4^3\\=-1/64\)

Hence the solution to the given indices are 1/2^7, 11^4 and -1/64

Learn more on indices here: https://brainly.com/question/170984

#SPJ1

The post image coordinates are - A'(12,3), B'(10, -5) and C'(7,0)

Here, we are given 3 points A (-6, 15), B (-8,7) and C (-11, 12)

We are given the following translation rule- (x + 18) and (y - 12)

Let us take each point one by one-

A (-6, 15)

here x = -6

⇒ x + 18 = -6 + 18 = 12

and y = 15

⇒ y - 12 = 15 - 12 = 3

Thus the post image of A is (12, 3)

B (-8,7)

here x = -8

⇒ x + 18 = -8 + 18 = 10

and y = 7

⇒ y - 12 = 7 - 12 = -5

Thus the post image of B is (10, -5)

C (-11, 12)

here x = -11

⇒ x + 18 = -11 + 18 = 7

and y = 12

⇒ y - 12 = 12 - 12 = 0

Thus the post image of C is (7, 0)

Learn more about graphical transformations here-

https://brainly.com/question/4025726

#SPJ9

Answer:

Step-by-step explanation:

Correct option is c)

\( \huge \bf{explanation}\)

\( {i}^{54} \)

=>( i^2)^24

=> (-1)^27

=> -1

Answer: A. approximately 37.33° above the ground

Step-by-step explanation:

edge2020

The correct solution to the problem is that the direction of the resultant force will be approximately 37.33° from the horizontal above the ground.

For 30° Vector of 40 pounds :-

If we divide it in components it will become

40 cos 30° Î + 40 sin 30° Ĵ

40 × ( √3 / 2 ) Î + 40 × ( 1 / 2 ) Ĵ

34.64 Î + 20 Ĵ    ( approximately )

For 45° Vector of 35 pounds :-

If we divide it in components it will become

35 cos 45° Î + 35 sin 45° Ĵ

35 × ( 1 / √2 ) Î + 35 × ( 1 / √2 ) Ĵ

24.75 Î + 24.75 Ĵ    ( approximately )

Now adding both vectors

( 24.75 + 34.64 ) Î + ( 24.75 + 20 ) Ĵ    ( approximately )

59.39 Î + 44.74 Ĵ    ( approximately )

Now Using formula of Tan θ to find the value of θ

( Tan θ = Perpendicular / Base )

Tan θ =  44.74 / 59.39

Tan θ =  0.75    ( approximately )

θ =  Tan⁻¹ (0.75)    ( approximately )

θ =  36.87°    ( approximately )

We are calculated the value of θ as 36.87° which is approximate value as we used a lot of approximations while calculating and, the closest option given is 37.33° which is again an approximate value.
So we can say that the correct answer to this problem is The direction of the resultant force will be approximately 37.33° from the horizontal above the ground.

Learn more about Vectors here:

https://brainly.com/question/25705666

#SPJ2

Answer and Step-by-step explanation:

Ok, so all we have to do is input the values into the equation.

We are told Adam bought 2 mechanical pencils and 8 spiral notebooks, which cost $13

and that

Kia bought 3 mechanical pencils and 5 spiral notebooks, which cost $12.50.

Adam: 2p + 8n = 13

Kia:     3p + 5n = 12.5

This is the answer.

#teamtrees #WAP (Water And Plant)

Answer: Adam: 2p + 8n = 13

Kia:     3p + 5n = 12.5

Step-by-step explanation:

i think its b so yeah

Answer:  5²⁻⁵

Step-by-step explanation:

\(4^x-4^{x-1}=24\\\\\\3(4^{x-1})=24\\\\\\4^{x-1}=8\\\\\\2^{2(x-1)}=2^3\\\\\\2(x-1)=3\\\\\\x-1=\dfrac{3}{2}\\\\\\x=\dfrac{5}{2}\quad \rightarrow x=2.5\)

\((2x)^x\quad =(2\cdot 2.5)^{2.5}\quad =\large\boxed{5^{2.5}}\)

Answer:

Step-by-step explanation:

To find the total area of the track, we need to calculate the area of each section and then add them together.

Area of a semi-circle with radius 31m:

A = (1/2)πr^2

A = (1/2)π(31m)^2

A = 4795.4m^2

Area of a rectangle with length 92.7m and width 31m (the straight parts):

A = lw

A = (92.7m)(31m)

A = 2873.7m^2

To find the total area, we need to add the areas of the two semi-circular ends and the two straight sections:

Total area = 2(Area of semi-circle) + 2(Area of rectangle)

Total area = 2(4795.4m^2) + 2(2873.7m^2)

Total area = 19181.6m^2

Rounding this to 1 decimal place, we get:

Total area ≈ 19181.6 m^2

Therefore, the total area of the track is approximately 19181.6 square meters.

Answer:

6.5 feet

Step-by-step explanation:

V = lwh

Plug-in the numbers given and solve for h

312 = 8(6)h

312 = 48h

312/48 48h/48

h = 6.5 feet

\(\huge\mathfrak\red {Answer:}\)

Value of 3⁰ × 3⁴ = 1 × 81

\(\mathfrak\purple {Hope\: this\: helps\: you...}\)

Step-by-step explanation:

It's a system of equations.

From the first one we isolate x:

x = 9-y

And we substitute in the second one:

(9-y)y = 14

-y^2 + 9y - 14 = 0

y^2 - 9y + 14 = 0

D = 25

y1/2 = (9 +- 5)/2 = 2 or 7

y = 2 => x = 7

y = 7 => x = 2

x^2 + y^2 = 7^2 + 2^2 = 53

Answer:

Es falso.

Step-by-step explanation:

Es falso.

En una recta numérica tenemos los enteros positivos ubicados a la derecha del 0 (punto central) y los enteros negativos ubicados a la izquierda del cero.

 |__|__|__|__|__|__|__|__|                              

-4   -3  -2  -1   0   1    2   3  4

En la recta numérica los números son cada vez mayores hacia la derecha y cada vez menores hacia la izquierda, por lo que cada número será mayor que el número ubicado a su izquierda y menor que el número ubicado a su derecha. Por ejemplo:        

- El 3 es mayor que el 2 y menor que el 4

- El -2 es mayor que -3 y menor que -1      

Entonces, los enteros positivos y los enteros negativos son mayores a la derecha. Por lo tanto el enunciado es falso.  

Espero que te sea de utilidad!  

The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.

Nadia had the highest score on a test.

According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.

Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.

Additionally, the highest score by Nadia is 100 while that for Ben is; 99.

Hence, Nadia had the highest score on a test.

Read more on median in box plots;

https://brainly.com/question/14277132

#SPJ1

The event containing the outcomes belonging to a or b or both is the union of a and b.

Let us consider two sets a and b, and say events or the elements in set a are: (x, y, z), and the elements in set b are: (o, p, q)

The union of these two sets will give:

aUb=(x, y, z, o, p, q)

Now, a union of two sets (denoted by U), for our case a and b, is the set or event containing the elements belonging to a or b or both the elements in a and b altogether.

Thus, the even containing the outcomes belonging to a or b or both in a and b altogether is the union of a and b.

Learn more about union of a set here:

https://brainly.com/question/23337676

#SPJ4