Map of the city zoo a triangle with points zebras, monkeys, and lions. the distance from zebras to monkeys is 52 feet and from monkeys to lions is x feet. a triangle with points lions, tigers, elephants. the distance from lions to tigers is 96 feet and from tigers to elephants is 78 feet. the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants. what is the distance between the lions and monkeys? 1. proportion: 52 78 = x 96 2. cross-multiply: 4992 = 78x 3. solve: the distance between the lions and the monkeys is feet.

The domain and range of the graphs shown above include the following:

Domain: [2, ∞]                 Domain: [-∞, ∞]

Range: [1, ∞]                    Range: [-2, ∞]

Domain: [-∞, ∞]                 Domain: [1, ∞]

Range: [-∞, ∞]                   Range: [-∞, 2]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graphs shown in the image attached above, we can reasonably and logically deduce the following domain and range for graph 1:

Domain = [2, ∞].

Range = [1, ∞] or y ≥ 1

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Answer: $15

Step-by-step explanation:

6 times 10 = 60

(6 is tickets, $10)

He has $45 but needs $15 more dollars to pay.

60-45=15

(a) The expected number of board-feet of timber next year is 102.9. (b) The interest rate at the bank matters in deciding to cut the trees down now or in the future due to the opportunity cost of waiting and potential earnings from investing the proceeds. (c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower.

(a) To calculate the expected number of board-feet of timber next year, we multiply the probabilities of each outcome by the corresponding timber quantity and sum them. With a 98% probability of growth and a 5% increase in timber, and a 2% probability of fire and no timber, the expected number of board-feet of timber next year would be: (0.98 * 100 * 1.05) + (0.02 * 0) = 102.9 board-feet.

(b) The interest rate at the bank matters in deciding to cut the trees down now or in the future because it represents the opportunity cost of waiting. By cutting the trees down now and selling the timber, you can invest the proceeds in the bank and earn interest over time. If the interest rate is high, the present value of the future timber may be lower compared to the immediate cash flow from selling the timber now, making it more favorable to cut the trees down earlier.

(c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower. A lower interest rate implies that the present value of future cash flows (from selling the timber next year) is higher relative to the immediate cash flow (from selling the timber now). Therefore, a lower interest rate makes it more advantageous to delay cutting the trees and wait for them to grow, maximizing the forester's profit.

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Distance from the summit of Mount Everest to the horizon, Rounded to the nearest mile, the distance from the summit of Mount Everest to the horizon is 210 miles.

Distance refers to the space between two points or the length of a line between them. It may also refer to a range, extent, or magnitude that separates one point from another. Distance may be a physical concept, such as the distance between two cities or the distance traveled by a moving object.

The distance between two points can be calculated using a number of mathematical techniques, including the Pythagorean theorem, the distance formula, and vector addition.

d = √(2Rh + h²)

where d is the distance to the horizon, R is the radius of the Earth (4000 miles), and h is the height of the observer (in this case, the height of the summit of Mount Everest, which is 29,030 feet).

We need to convert the (h) height of the summit to miles:

29,030 ft = 29,030/5280 miles ≈ 5.49 miles

Now we can plug in the values and solve for d:

d = √(2 × 4000 × 5.49 + 5.49^2) =209.64288 ≈ 210 miles

Therefore, the distance from the summit of Mount Everest to the horizon is approximately 210 miles when rounded to the nearest mile.

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The statement "TRUE" is the answer to the question "TRUE or FALSE: residuals measure the vertical distance between two observations of the response variable.

Residuals are the difference between the predicted value and the actual value. It's also referred to as the deviation. The error or deviation of an observation (sample) is computed with a residual in statistical analysis. The residual is the deviation of an observation (sample) from the prediction value or the mean value of a sample.In a linear regression, the residual is the vertical distance between the actual and predicted values.

The vertical distance between the actual and predicted values is used to compute the deviation (error) of the observation. Therefore, the statement "TRUE" is correct because residuals measure the vertical distance between two observations of the response variable.

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Trapezoidal Rule: \((b-a)^3 / 96n^2,\) Simpson's Rule: \((b-a)^5 / 2880n^4\\\).  Both approximations have error of 0.0208.

For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get \(|E| ≤ 2^3/12(4)^2(2)\) or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get\(|E| ≤ 2^5/180(4)^4(2)\) or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.

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Pascal's triangle can be used to expand the binomial (d-3)^6. The expansion involves applying the binomial theorem and using the coefficients from the corresponding row of Pascal's triangle.

In this case, the sixth row of Pascal's triangle is 1 6 15 20 15 6 1, which represents the coefficients for each term in the expansion of (d-3)^6.

The binomial theorem states that for any binomial expression (a+b)^n, the expansion can be represented as the sum of terms of form C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient obtained from Pascal's triangle.

In this case, we have (d-3)^6, so the expansion will have seven terms corresponding to the powers of d from 6 to 0. Using the coefficients from the sixth row of Pascal's triangle, we can write the expanded form as:

(d-3)^6 = 1d^6 + 6d^5*(-3) + 15d^4(-3)^2 + 20d^3(-3)^3 + 15d^2(-3)^4 + 6d(-3)^5 + 1*(-3)^6.

Simplifying the terms and raising -3 to different powers, we can obtain the expanded form of (d-3)^6.

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Answer:

square and rectangle

Step-by-step explanation:

The drawing of the plan is attached and the height of the plan is 18.54 cm

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

ab = 20 cm

ac = 20 cm

bc = 15 cm

Next, we draw the plan

See attachment for the figure of the plan (not drawn to scale)

Represent the height of the plan with h

The variable h can be calculated using the following pythagoras theorem

h² = 20² - (15/2)²

So, we have

h² = 343.75

Take the square root of both sides

h = 18.54

Hence, the height of the plan is 18.54 cm

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Answer:

the price would be $3.93

Step-by-step explanation:

18%of 3.33 is .6 so just add that to the original amount

Answer:

El recolector recoge un total diario de 50 kilogramos.

Step-by-step explanation:

(The following problem is written in Spanish and for such reason explanation will be held in the same language)

La masa total diaria recogida es igual al número de cajas recogidas por día y la capacidad de la caja. Entonces:

\(m = n \cdot m_{unit}\)

\(m = (4\,cajas)\cdot \left(\frac{25}{2}\,\frac{kg}{caja} \right)\)

\(m = 50\,kg\)

El recolector recoge un total diario de 50 kilogramos.

Answer:

G=12.4

Step-by-step explanation:

3633 is the difference of these numbers.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.

Subtraction can be applied in a variety of real-world situations. Assume you had five apples and your friend had three. We may calculate the quantity of remaining apples by subtracting: 5 - 3 = 2.

Given Data

9832 - 6199

Subtracting,

= 9832 - 6199

= 3633

3633 is the difference of these numbers.

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Answer:

x=-1.87 y = -1.95

Step-by-step explanation:

10x - 3y = 24.5

5(2x-5y = 13.5)

10x - 3y = 24.5

- 10x -25y = 67.5

22y = -43 , y = -1.95

10x - 3(-1.95) = 24.5

x = -1.87

Answer: 90 and 110

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Explanation is in the file

tinyurl.com/wpazsebu

From Section 1, understanding the gradient of a function and the directional derivative can be useful for optimization problems and understanding system behavior.

From Section 2, knowledge of second-order partial derivatives and the Hessian matrix can be useful for modeling complex systems and analyzing function behavior for optimization and machine learning.

Two things from Section 1 that could be useful for a scientist, engineer, mathematician, or in your personal life are:

1) Understanding how to calculate the gradient of a function, which can be useful in optimization problems, such as finding the maximum or minimum values of a function.

2) Knowing how to calculate the directional derivative of a function in a particular direction, can be useful in understanding how a system or process behaves under different conditions.

Moving on to Section 2 on Second Order Partial Derivatives, two things that could be new and exciting are the concepts of the Hessian matrix and the Laplacian operator.

These are advanced mathematical tools that allow us to analyze the curvature and behavior of functions in higher dimensions. However, they can also be tricky and frustrating because they involve more advanced calculus and linear algebra.

Two things from Section 2 that could be useful for a scientist, engineer, mathematician, or in your personal life are:

1) Understanding how to calculate second-order partial derivatives, which can be useful in modeling and analyzing complex systems, such as fluid dynamics, electromagnetics, or financial markets.

2) Knowing how to use the Hessian matrix to analyze the curvature and behavior of a function, which can be useful in optimization problems, machine learning, or image processing.

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Answer:

9π

Step-by-step explanation:

Area of Circle: πr²

Diameter = radius * 2

Diameter = 3 * 2 = 6

Plug into the formula πr²

(3)²π ≈ 28.274 or 9π

The most appropriate test statistic for constructing confidence intervals for the population mean when the population is normally distributed, but the variance is unknown, is the t-statistic.

The t-statistic is used when the sample size is small (typically less than 30) and the population standard deviation is unknown. It takes into account the uncertainty introduced by estimating the population standard deviation from the sample.

To construct a confidence interval using the t-statistic, follow these steps:

Take a random sample from the population.
Calculate the sample mean and sample standard deviation.
Determine the desired level of confidence, often expressed as a percentage (e.g., 95% confidence).
Look up the appropriate critical value from the t-distribution table based on the sample size and desired level of confidence.
Calculate the margin of error by multiplying the critical value by the standard error of the sample mean.
Construct the confidence interval by adding and subtracting the margin of error from the sample mean.
Write the conclusion, stating the confidence interval and interpreting it in the context of the problem.

The t-statistic is the most appropriate test statistic for constructing confidence intervals when the population is normally distributed but the variance is unknown. The t-statistic takes into account the uncertainty introduced by estimating the population standard deviation from the sample.

The steps to construct a confidence interval using the t-statistic include calculating the sample mean and sample standard deviation, determining the desired level of confidence, looking up the appropriate critical value, calculating the margin of error, and constructing the confidence interval.

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Answer:

Assuming that Jerry is at ground level and Tom is sitting on a table 41 feet away from Jerry, we can use trigonometry to find the angle of elevation that the board would make with the floor.

Let's call the height that the board reaches on the table "h". From the information given, we know that the distance from Jerry to the point where the board touches the table is 57 feet (the length of the board), and the distance from that point to Tom is 41 feet. We can set up a right triangle with these distances as the legs and "h" as the hypotenuse, as shown in the diagram below:

         |\

         | \

        h|  \ 41 ft

         |   \

         |____\

          57 ft

Using the Pythagorean theorem, we can find the value of "h":

h^2 = 57^2 + 41^2

h^2 = 3241 + 1681

h^2 = 4922

h = sqrt(4922)

h ≈ 70.1 ft

Now we can use trigonometry to find the angle of elevation of the board. We want to find the angle whose tangent is equal to the opposite side (h) divided by the adjacent side (57 ft):

tan(theta) = h / 57

theta = arctan(h / 57)

theta ≈ arctan(70.1 / 57)

theta ≈ 51.1 degrees

Therefore, the angle of elevation that the board would make with the floor is approximately 51.1 degrees.

Answer:

16:81

Step-by-step explanation:

explanation: Scale factor for the sides of these triangles. k=49. Therefore the ratio of the area will be k2=Area Triangle area.

Answer:

These are the intervals of the people who are at least adults and are mature enough to take the survey seriously and answer correctly

Step-by-step explanation:

Answer:

-½ + (root2 / 2) i + root½ i

Step-by-step explanation:

\( \frac{a}{b} - \frac{c}{d} = \frac{ad - cb}{bd} \)

I used this formula to do it but let me know if it's enough or you have to simplify it further

Answer:

45

Step-by-step explanation:

Answer:

4 students per teacher

Step-by-step explanation:

its a ratio I think if not then a unit rate but still its 4 because u divide 48 by 12 and then use that number per teacher

Answer:

use math w.a.y works like a dream

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.

\(x+4=3x-8\\x=3x-12\\-2x=-12\\x=6\)

The length of AC is simply x, therefore 6

Answer:

5

Step-by-step explanation:

-9-(-9)+5=5