Mr. and Mrs. McClurrie are debating on whether or not to remove a tall tree in their front yard. Mr. McClurrie is concerned that the tree could fall during a storm and land on their home. Mrs. McClurrie disagrees. She thinks the tree poses no danger to their home and wants to keep the tree because of the wonderful shade it provides. They decide to estimate the height of the tree using special right triangles.

They stood 25 feet from the base of the tree to create a 30° angle from the ground to the top of the tree.

If their home is 20 feet from the base of the tree, could the McClurrie's wait a few more years before cutting down the tree or does it pose a risk now?

The ratio of 4 tulips to 6 daffodils will be 2:3.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

The ratio of 4 tulips to 6 daffodils will be calculated as below:-

Ratio = 4 tulips : 6 daffodils  = 2 tulips : 3 daffodils

Therefore, the ratio of 4 tulips to 6 daffodils will be 2:3.

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3rd place to the left of the decimal point is the hundreds place

 so the number 4 represents 4 hundred

Answer:

The changing rate of the amount of water in the watering can is a constant rate of 0.15 gallon per minute.

The initial volume of water in the can at time = 0 is 5 gallons

The function will be a linear function in the form of  where

is the volume of water in the can after  minutes

is the changing rate

is the initial volume when time is 0

Substitute all the values into the form we have

Step-by-step explanation:

y=0.15x +5

Given the following which is the mean and standard deviation of the dune’s movement over one year and need to find out what the ten year mean and the standard deviation will be.

The ten-year mean is ten times the one year mean or 110 feet per decade. The ten-year standard deviation is somewhat more complicated. Multiple independent trials accumulate standard deviation as the square root of the number of trials since an unusually high level of movement ten years in a row. The decade is going to be 2 feet per year x square root of ten will result to 6.32 feet.

The answer will to question A. will be:

  90           < 110 + z (6.32 feet)

 -20           < z (6.32 feet)

    z            > - 3.16

By using the z table, it shows the probability of 0.9992. This result shows that as 90 feet is lesser than the mean travel that is expected over decade. 

To find the probability that a sand dune moves more than 90 feet in 7 years, one must calculate a z-score using the mean annual movement, standard deviation, and the 7-year period, then find the corresponding probability in a standard normal distribution table or calculator.

The question involves calculating the probability that a random variable, X, will exceed a certain value over a period using the normal distribution. The random variable X in this context represents the movement of sand dunes per year, which is assumed to be normally distributed with mean (μ) of 11 feet per year and a standard deviation (σ) of 2 feet per year.

To find the probability of the dune moving more than 90 feet in 7 years, we first calculate the mean movement for 7 years, which is 7 × μ = 7 × 11 feet = 77 feet. Next, we calculate how much more than 77 feet does 90 feet represent. This difference is 90 - 77 = 13 feet. Then, we standardize this difference by dividing by the standard deviation over the square root of 7 years to get the z-score:

Z = (90 - 7×11) / (σ × √7) = (90 - 77) / (2 × √7) = 13 / (2 × √7)

The z-score helps us find the probability that X is more than the calculated mean for 7 years. We look up this z-score in the standard normal distribution table or use a calculator to find the probability that corresponds to this z-score. This gives us the probability that a dune will move more than 90 feet in 7 years. The answer should be rounded to four decimal places as per the instruction in the question.

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Answer:

Ben needs more than 200 points to unlock the next level in the game

He already has 45 points

For every win, he receives 5 points

No. of wins required: x

5x + 45 > 200

Answer:

There are 73.38 gallons in the tank.

Step-by-step explanation:

The diameter of the tank is = 2.5 feet

So, the radius is = [tex]2.5/2=1.25[/tex] feet

The depth of the tank = 2 feet

The volume of the cylinder is = [tex]\pi r^{2} h[/tex]

V=[tex]3.14\times(1.25)^{2} (2)[/tex]

= 9.81 cubic feet

Now, 1 cubic feet = 7.48 gallons

So, 9.81 cubic feet = [tex]7.48\times9.81=73.38[/tex] gallons

So, there are 73.38 gallons in the tank.

A fraction is a way to describe a part of a whole. The given fraction 18/13 in the form of a decimal will be equal to 1.38.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The given fraction 18/13 in the form of a decimal can be written as,

18/13

= 1  5/13 (In the form of a mixed fraction)

= 1 + 0.384615

= 1.384615 ≈ 1.38 (In the form of a Decimal)

Hence, The given fraction 18/13 in the form of a decimal will be equal to 1.38.

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Examples in real life and physics provide contexts for understanding situations where a direct solution is not possible or applicable.

An absolute value problem with no solution is one where the absolute value expression is set to a negative number. Since the absolute value of any number represents its distance from zero on a number line, it can never be negative. Consequently, an equation like |x| = -3 has no solution because there is no real number x that, when taken as an absolute value, results in a negative number.

Real-world Example...

In everyday life, think of a scenario such as locking oneself out of an encrypted system without any means of retrieval. The problem can't be solved directly (as there is no way to bypass encryption), but one might approach the matter sideways by resetting the system entirely, which doesn't address the original issue of being locked out.

Physics Context

In physics, an example of a situation where there is a force and a displacement but no work is done is when the force is applied perpendicular to the direction of the displacement. Since work is defined as the dot product of force and displacement, when the angle between them is 90 degrees, this product and thus work is zero.

To determine the actual size of an ice fishing hut from a 1:35 scale model, multiply each model dimension by 35, resulting in a real hut approximately 5.95 meters tall, 6.3 meters wide, and 6.895 meters long.

The dimensions of the actual ice fishing hut, based on the 1:35 scale model, can be found by multiplying each dimension of the model by 35. To find the height, multiply 17 cm by 35, which gives 595 cm or 5.95 meters. To find the width, multiply 18 cm by 35, which gives 630 cm or 6.3 meters. Finally, to find the length, multiply 19.7 cm by 35, resulting in 689.5 cm or 6.895 meters. Therefore, the actual dimensions of the ice fishing hut are approximately 5.95 meters tall, 6.3 meters wide, and 6.895 meters long.

value = v

v = 0.05n + 0.10d

Answer: v = 0.05n + 0.10d

Step-by-step explanation: