The angle of elevation from a point on the ground to the top of a pyramid is 35 degrees 30 seconds. The angle of elevation from a point 135 feet farther back to the top of the pyramid is 21 degrees 10 seconds. Find the height of the pyramid

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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A vector object for holding integers is defined as a container class that can hold a dynamic array of integers.

A vector object is a container class in C++ that provides dynamic arrays. It allows the programmer to create an array of any size at runtime and easily manipulate its elements. To define a vector object for holding integers, we need to use the following syntax:
```
vector vec;
```
This creates an empty vector object that can hold integers. We can then use various member functions of the vector class to add, remove, or modify the elements of the vector.

In C++, a vector object is a dynamic array container that can hold elements of any data type. To define a vector object for holding integers, we need to specify the data type as "int" and create an empty vector object using the following syntax:

```
vector vec;
```

This creates an empty vector object named "vec" that can hold integers. We can then use various member functions of the vector class to add, remove, or modify the elements of the vector. For example, we can add elements to the vector using the push_back() function as follows:

```
vec.push_back(10); // adds the integer 10 to the end of the vector
vec.push_back(20); // adds the integer 20 to the end of the vector
vec.push_back(30); // adds the integer 30 to the end of the vector
```

We can access the elements of the vector using the square bracket notation as follows:

```
int x = vec[0]; // assigns the value 10 to x
int y = vec[1]; // assigns the value 20 to y
int z = vec[2]; // assigns the value 30 to z
```

We can also use the size() function to get the number of elements in the vector:

```
int size = vec.size(); // assigns the value 3 to size
```

Overall, a vector object for holding integers is a very useful data structure in C++ that provides dynamic arrays with convenient member functions for manipulating the elements.

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The average hourly wage for KwikFix is $11.10 per hour.

What are average hourly wages?
Average hourly wages refer to the average amount of money earned by an employee per hour worked. This is calculated by dividing the total amount of wages paid by the total number of hours worked.

To calculate the average hourly wage, you will need to know the total wages paid and the total number of hours worked by the employees. Here's the formula:

Average Hourly Wage = Total Wages Paid / Total Hours Worked

For example, let's say a company pays its employees a total of $5,000 in wages for 400 hours of work. The average hourly wage for the employees would be:

Average Hourly Wage = $5,000 / 400 = $12.50 per hour

This means that on average, each employee earned $12.50 for every hour they worked.

It's important to note that when calculating average hourly wages, you need to ensure that you are including all wages paid to employees, including overtime pay and any other bonuses or incentives. Additionally, this calculation is only accurate when all employees are paid on an hourly basis and do not have varying pay rates.

Using the information provided, we can calculate the average hourly wage for each company.

For MongoRama, there are a total of 10 employees. Nine of them make $9.00 per hour, while one makes $30.00 per hour. To find the average hourly wage for the company, we can use the formula:

Average hourly wage = Total wages paid / Total number of hours worked

The total wages paid by MongoRama is:

(9 * $9.00) + (1 * $30.00) = $99.00 + $30.00 = $129.00

The total number of hours worked is:

9 * 1 hour + 1 * 1 hour = 10 hours

Therefore, the average hourly wage for MongoRama is:

$129.00 / 10 hours = $12.90 per hour

For KwikFix, there are a total of 10 employees. Two of them make $9.00 per hour, five make $10.50 per hour, two make $12.00 per hour, and one makes $16.50 per hour. To find the average hourly wage for the company, we can again use the formula:

Average hourly wage = Total wages paid / Total number of hours worked

The total wages paid by KwikFix is:

(2 * $9.00) + (5 * $10.50) + (2 * $12.00) + (1 * $16.50) = $18.00 + $52.50 + $24.00 + $16.50 = $111.00

The total number of hours worked is:

2 * 1 hour + 5 * 1 hour + 2 * 1 hour + 1 * 1 hour = 10 hours

Therefore, the average hourly wage for KwikFix is:

$111.00 / 10 hours = $11.10 per hour

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Answer: SA=5183.62788

Step-by-step explanation:

A=2πrh+2πr2=2·π·15·40+2·π·152≈ 5183.62788

~Find the radius- 30 divided by 2= 15 so radius =15

Answer:

130

Step-by-step explanation:

Step 1: write equations:

Company A: y = 0.20x + 110

Company B: y = 0.50x + 80

Step 2: graph your lines

Step 3: Find your intersect point

Step 4: find the points: (100,130)

The number of miles is y, so at 130 miles, both trucks are the same cost

Hope that helps

E is halfway between A and C

coordinates are

-2a , -2b

you could basically see it in the picture.

the formula is alrdy given, so I just gave you the solution

Answer:

\( \sqrt{8} \)

or

\(2 \sqrt{2} \)

Step-by-step explanation:

Since the legs are equal this is a 45-45-90 triangle.

The ratio of side length for a 45 45 90 triangle

\((1)(1)( \sqrt{2} )\)

where 1 is the legs length and sqr root of 2 is the length of the hypotenuse.

Since we are trying to find the length of the legs side we can set up a proportion.

We know the hypotenuse is 4 so our proportion looks like

\( \frac{1}{x} = \frac{1}{x} = \frac{ \sqrt{2} }{4} \)

Let see how far sqr root of 2 goes into 4.

\( \sqrt{2} \times x = 4\)

\( \sqrt{2} \times x = \sqrt{16} \)

\(x = \sqrt{8} \)

so that means the answer for the legs length is

\( \sqrt{8} \)

or

\(2 \sqrt{2} \)

Answer:

Step-by-step explanation:

hello :

use  phtagor - rule:  let  x  the length of each side

x² +x² =4²

2x² =16

x² = 8  

x = √8

but :  8 = 4×2 = 2²×2

x = √(2²×2) = √2²× √2 =2√2      ......   √2² =2

x  =  2√2 metres.

Answer:

Part A:

From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team. The Red Team's box is the smallest, indicating that their times are more tightly clustered together.

Part B:

Blue Team:

Q1: 75

Q2: 82

Q3: 87

IQR: 12

Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105

There are no outliers

Green Team:

Q1: 70

Q2: 75

Q3: 80

IQR: 10

Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95

There is one outlier at 90

Red Team:

Q1: 80

Q2: 83

Q3: 87

IQR: 7

Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5

There are no outliers

Step-by-step explanation:

N/A

Answer:

8

Step-by-step explanation:

This man is cutting 6.5 ft of wood into pieces that are .75 ft long.

Divide 6.5/.75 and there's ur answer chief

Answer:

Don't have an answer but I will explain what to do.

Step-by-step explanation

You're going to mark the point's on your graph paper, then make a right triangle, after that you're going to count over how many square's there are until you run to the end of the right triangle and also do that for both sides. After you found out what the number is you are going to multiply that number by it for both of them. Then after you found that out your going to take your calculator and press 2nd and X2 and put your number after that. Hope this helps!

The rationalized form of the surd is;

1) 25/13

2) 144/3

3) 36

We have to note that the term surd would have to refer to an irrational number as we know it.

1) The conjugate of the surd is;

5/4 + √3

Rationalizing we have;

5/4 -  √3 * 5/4 + √3

25/16 + 4√3 - 4√3 -3

25/13

2) The conjugate is √7 - 2

Rationalizing we have;

12/√7 + 2  * 12/√7 - 2

144/7 -2√7 + 2√7 -4

144/3

3) The conjugate of the surd is √2 + √3

Rationalizing we have;

6/ √2 -  √3  * 6/ √2 + √3

36/4 +√6 - √6 - 3

36/1 = 36

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Answer:

\(x {}^{3} \)

Step-by-step explanation:

\(\frac{(x {}^{5} )}{( {x}^{2} )}\)

\(x {}^{3} \)

Answer:

Tanya is correct.

Step-by-step explanation:

a). Tanya has the equation,

   x - 2 = 2x - 4

   x - 2x = 2 - 4

  -x = -2

   x = 2

  By adding (x + 2) on both the sides of the equation,

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

  2x = 3x - 2

  2x - 3x = -2

  x = 2

Tanya is correct.

b). By Diego's statement

   (x - 2)(x + 2) = (2x - 4)(x + 2)

   x² - 4 = 2x²- 8

   x² - 2x² = 4 - 8

   -x² = -4

    x² = 4

    x = ±2

 Therefore, Diego's statement is incorrect.

If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3

Given,

The number of siblings each person has = 1,2,3,4 and 10

Arrange them in ascending order =1,2,3,4 and 10

We know the median is the middle term of the ordered pair

The number of terms n= 5

Middle term is = \(\frac{n+1}{2}\)

=\(\frac{5+1}{2}\)

=3

The 3rd term is 3.

The median = 3

Hence, If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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Answer:

Rate of return = 16%

Step-by-step explanation:

The computation of the rate of the return is shown below:

Data provided in the question

Current value of the investment = $20,880 = C

Originally cost = $18,000 = O

N = Net earnings = C - O

= $20,880 - $18,000

= $2,880

Based on the above information, the rate of return is

\(= \frac{N}{O} \\\\ = \frac{\$2,880}{\$18,000}\)

= 16%

Hence, the rate of return is 16%

The coordinates form a right triangle and the coordinates are within the parallelogram .

What is parallelogram explain?

A right triangle cutout from the parallelogram has the vertices (13,10), (13,14) and (11,10)

The coordinates of the parallelogram are given as -

(5, 17), (10, 20). (18,9), and (13,6)

The question is incomplete, as the options are not given.

So,  use of a general explanation

For the right triangle to be a cutout from the parallelogram, then the vertices of the right triangle must be within the coordinates  (5, 17), (10, 20). (18,9), and (13,6)

An example of such coordinates are = (13,10), (13,14) and (11,10)

Note that you can use any coordinates, as long as the coordinates form a right triangle and the coordinates are within the parallelogram.

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The complete question is -

A parallelogram has coordinates of (5, 17), (10, 20). (18,9), and (13,6). Which right triangle represents one of the cutouts from the box method ?17​

Answer:

It will be C

Step-by-step explanation:

Answer:

5) 12  6) -12  7) -6  8) 2  9) 80 degrees  10) 40 degrees

Step-by-step explanation:

:)

As per the borrowed amount, the value of IRR is 6.40%

The term IRR is the internal rate of return is a metric used in financial analysis to estimate the profitability of potential investments.

Here we have know that Maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200.

Now, we have to calculate the value of IRR,

The general form of the IRR formula is written as,

=> NPV = \(\sum\limits^T_{t=1} {\frac{C_t}{(1+r)^t} }\ -C_0\)

where r is the discount rate / interest rate and T is the number of cash flow periods with t denoting a specific period, C0 is the initial investment while Ct is the return during period t.

Here we apply the values on it, then we get,

=> \(NPV = \sum\limits^5_{t=1} {\frac{1200_t}{(1+r)^t} }\ -5000\)

When we simplify this one then we get,

=> Internal Rate of Return = 6.402%

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The statement that correctly compares the two functions is B, They have the same y-intercept but different end behavior.

From the graph that the exponential function passes through the points (-0.5, 8), (0, 4), (1, 1), and (5, 0). Use this information to find the equation of the exponential function.

Assume that the exponential function has the form f(x) = a × bˣ, where a and b = constants to be determined, use the points (0, 4) and (1, 1) to set up a system of equations:

f(0) = a × b⁰ = 4

f(1) = a × b¹ = 1

Dividing the second equation by the first:

b = 1/4

Substituting this value of b into the first equation:

a = 4

So the equation of the exponential function is f(x) = 4 × (1/4)ˣ = 4 × (1/2)²ˣ.

Now, compare the two functions. Since the exponential function has a y-intercept of 4, and the equation of the other function is not given.

However, from the graph that the exponential function approaches the x-axis (i.e., has an end behavior of approaching zero) as x gets larger and larger. Therefore, the exponential function and the other function have different end behavior.

So the correct answer is (B) "They have the same y-intercept but different end behavior."

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Answer:

C) ATUS-ABCS

Step-by-step explanation:

ΔTUS ΔBSC would also be a right answer, but remember that the order of the points matter.

Both of these triangles share a point S, so the order of where the S is placed should be the same.

In this answer, ΔTUS ΔBCS, notice that the S is in the end of the triangle notation.

However, in this answer,  ΔTUS ΔBSC, the S is in the end of ΔTUS while the S is in the middle of ΔBSC even S is the correspondent point for both triangles.

Hence, ΔTUS ΔBCS is the correct notation and correct answer.

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Answer:

the first one

Step-by-step explanation:

I do not believe either of them because of the heights of both the R.F. Mitte Building and the tallest building in San Marcos.

The height that a projectile can reach in ideal conditions (i.e., without air resistance) can be estimated by the physics formula for kinetic and potential energy equivalence:

mgh = 1/2mv²

The R.F. Mitte Building is 100 feet tall, and the tallest building in San Marcos is 150 feet tall. The velocity of a baseball thrown at the top of these buildings would need to be at least 44.27 m/s and 54.22 m/s, respectively, in order for it to reach the top.

This is a very high velocity, and it is unlikely that a person could throw a baseball with that much force. The fastest recorded pitch in Major League Baseball was by Aroldis Chapman at 105.1 mph, which is approximately 47 m/s.

Therefore, while the claim to throw a ball on top of the R.F. Mitte Building might be achievable by a person in excellent physical condition but the claim to throw a baseball on top of the tallest building in San Marcos seems impossible.

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Full question is:

A person claims they can toss a baseball on top of the R.F. Mitte Building. Not to be outdone, his buddy boasts he can throw a baseball on top of the tallest building in San Marcos.

Do you believe either of them and why?

The most appropriate inference procedure for the researchers to use to analyze the results is a matched-pairs t-interval for a population mean difference.

A matched-pairs t-interval for a population mean difference is suitable for this study because it involves comparing the pretest and posttest scores of the same individuals.

The researchers are interested in determining whether there is a significant difference in the number of correct answers before and after the adult reading program.

By using a matched-pairs t-interval, the researchers can analyze the mean difference in scores and determine the range within which the true population mean difference is likely to fall. This inference procedure takes into account the paired nature of the data, accounting for individual differences and increasing the precision of the estimate.

It is important to use this procedure as it considers the correlation between the pretest and posttest scores for each individual, providing a more accurate assessment of the program's effectiveness.

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9x-5x=24 :x=5

steps

9x-5x=24

add similar elements 9x-5x=4x

dive both sides by 4

4x/4=24/4

simplify

x=6