Using the above​ technique, find the equation of the line containing the points (-2,7) (4,-2)

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

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A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

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We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

Step-by-step explanation:

Probability = favorable outcome / total number of outcomes

5 numbers left and 3 of them are even.

So combined probability is:

Answer:

7x3=45 so substitute

Step-by-step explanation:

Answer:

57.5 %

Step-by-step explanation:

First find out the number of workers that do not arrive by 8 am

200 -85 = 115

Take this number divided by the total

115/200 = .575

Change to percent form

57.5 %

The inverse of the linear equation is y = x/58 - 12/29. After an evaluation of the inverse function at an input of 227, the output is equal to 223/58 or 3.85.

An inverse function is a type of function that is created by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of the given function y = 58x + 24, we would interchange both the input value (x) and output value (y) as follows:

y = 58x + 24

x = 58y + 24

Subtracting 6 from both sides of the function, we have the following:

x - 24 = 58y + 24 - 24

x - 24 = 58y

Dividing both sides of the function by 58, we have:

y = (x - 24)/58

y = x/58 - 24/58

y = x/58 - 12/29

At an input value of 227, we have:

y = 227/58 - 12/29

y = (227 - 24)58

y = 223/58 or 3.85.

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Answer:

$159.75

Step-by-step explanation:

137.45/252.60 + x = 1/3

252.60 + x = 412.35

x = 412.35 - 252.60

x = 159.75

Answer:

297.2

Step-by-step explanation:

549.8 ÷ 4 = 137.45

549.8 - 252.60 = 297.2

There are 191 different patterns of mail delivery possible for the 19 houses on the northern side of the street, satisfying the given conditions.

To determine the number of different patterns of mail delivery in this scenario, we can use a combinatorial approach.

Let's consider the possible patterns based on the number of houses in a row that receive mail on the same day: If no houses in a row receive mail on the same day: In this case, all 19 houses would receive mail on different days. We have a single pattern for this scenario.

If one house in a row receives mail on the same day: We have 19 houses, and we can choose one house in a row that receives mail on the same day in 19 different ways. The remaining 18 houses would receive mail on different days. So, we have 19 possible patterns for this scenario.

If two houses in a row receive mail on the same day: We have 19 houses, and we can choose two houses in a row that receive mail on the same day in C(19, 2) = 19! / (2! * (19-2)!) = 171 different ways. The remaining 17 houses would receive mail on different days. So, we have 171 possible patterns for this scenario.

Therefore, the total number of different patterns of mail delivery in this scenario is: 1 (no houses in a row) + 19 (one house in a row) + 171 (two houses in a row) = 191 different patterns.

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The derivative (dy)/(dt) for the given pair of functions is (dy)/(dt) = 2t - 6. To find (dy)/(dt), we need to differentiate the function y with respect to t.

Let's start with the given functions:

1. y = x^2 - 6x

2. x = t^2 + 4

First, let's find dx/dt by differentiating the second function with respect to t:

dx/dt = d/dt(t^2 + 4)

      = 2t

Now, we can find (dy)/(dt) by substituting the value of dx/dt into the derivative of y:

(dy)/(dt) = d/dt(x^2 - 6x)

         = d/dt((t^2 + 4)^2 - 6(t^2 + 4))  [Substituting x = t^2 + 4]

         = d/dt(t^4 + 8t^2 + 16 - 6t^2 - 24)

         = d/dt(t^4 + 2t^2 - 8)

         = 4t^3 + 4t

Therefore, the derivative (dy)/(dt) for the given pair of functions is (dy)/(dt) = 2t - 6.

To find the derivative (dy)/(dt), we first differentiate the function y = x^2 - 6x with respect to x, using the power rule of differentiation. The derivative of x^2 is 2x, and the derivative of -6x is -6.

Next, we need to find dx/dt by differentiating the function x = t^2 + 4 with respect to t. The derivative of t^2 is 2t, and the derivative of 4 is 0 (since it is a constant).

To find (dy)/(dt), we substitute the values of dx/dt and dy/dx into the chain rule of differentiation, which states that (dy)/(dt) = (dy)/(dx) * (dx)/(dt).

In this case, (dy)/(dx) is 2x - 6 and (dx)/(dt) is 2t. Therefore, we have (dy)/(dt) = (2x - 6) * (2t) = 4xt - 12t.

Since x = t^2 + 4, we substitute this value into the expression to get (dy)/(dt) = 4(t^2 + 4)t - 12t = 4t^3 + 16t - 12t = 4t^3 + 4t.

Hence, (dy)/(dt) for the given pair of functions is (dy)/(dt) = 2t - 6.

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Answer:

24.5 so 24 and a half .....

The depth of water in tank A is modeled by a differentiable and increasing function h.

This means that the function h describes how the depth of water changes as time passes.

The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.

This makes sense since water is constantly being added to the tank.

Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.

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The approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

Depreciation is to decrease in the value of a product in a period of time. This can be given as,

\(FV=P\left(1-\dfrac{r}{100}\right)^n\)

Here, (P) is the price of the product, (r) is the rate of annual depreciation and (n) is the number of years.

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.

Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is \(n_1\). Thus, by the above formula for the first car,

\(0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}\)

Take log both the sides as,

\(\log 0.6=\log (0.9)^{n_1}\\\log 0.6={n_1}\log (0.9)\\n_1=\dfrac{\log 0.6}{\log 0.9}\\n_1\approx4.85\)

Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.

Thus, the depreciation price of the car is 0.6y. Let the number of year is \(n_2\). Thus, by the above formula for the second car,

\(0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}\)

Take log both the sides as,

\(\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14\)

The difference in the ages of the two cars is,

\(d=4.85-3.14\\d=1.71\rm years\)

Thus, the approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

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Answer:

1:2

Step-by-step explanation:

Its just like fractions

You can simplify it.

Answer:

see below

Step-by-step explanation:

1) Length of side OQ can be solved by using Pythagorean

OQ² = 3² + 4²

        = √25

        = 5

2)  Length of side PQ can be solved by using Pythagorean

13² = 5² + PQ²

PQ² = 13² - 5²

       = √144

       = 12

3) Length of side RS and SQ can be solved by using Pythagorean

RS² = 13² - 6²

       = √133

       = 11.5

SQ² = 8² - 6²      

       = √28

       = 5.3

9514 1404 393

Answer:

Step-by-step explanation:

A tangent meets the radius at right angles at the point of tangency. The triangles here are all right triangles, so the Pythagorean theorem can be used to find the missing side lengths.

__

1. a² = 3² +4² = 25

  a = √25 = 5 = OQ

__

2. 5² +a² = 13²

  a² = 13² -5² = 144

  a = √144 = 12 = PQ

__

3. a = √(13² -6²) = √133 ≈ 11.5 = RS

  b = √(8² -6²) = √28 ≈ 5.3 = SQ

Answer:

Hi! The correct answer is 16!

Step-by-step explanation:

~Use the formula (b/2)^2 in order to create a new term to complete the square~

Answer:

the answer is option : c 16

Answer:

F) No solutions

Step-by-step explanation:

Since both lines are parallel they have no solutions as both the lines will never intersect each other because they have the same slope

The ship is 16.4 mi from the port.

The ship's bearing from port is 90.0°.

To determine the ship's distance from the port and its bearing, we can break down the problem into two steps.

Initial Movement

The ship leaves the port on a bearing of 45.0° and travels 13.9 mi. This movement forms a right triangle with the port as the starting point, the distance traveled as the hypotenuse, and the eastward movement as one of the legs. Using basic trigonometry, we can find the distance traveled eastward:

Eastward distance = hypotenuse * cos(angle)

Eastward distance = 13.9 mi * cos(45.0°)

Eastward distance ≈ 9.83 mi

Final Movement

After turning due east, the ship travels an additional 3.3 mi. Since the ship is now moving directly eastward, there is no northward or southward component to consider.

Calculating the total distance from the port:

Total distance = eastward distance + additional distance

Total distance = 9.83 mi + 3.3 mi

Total distance ≈ 13.13 mi

Calculating the bearing from the port:

The ship is traveling eastward, so the bearing from the port is 90.0°.

Therefore, the ship is approximately 16.4 mi from the port, and its bearing from the port is 90.0°.

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Answer:

4 lines of reflective symmetry, 1 center of rotational symmetry.

To determine if two hexadecimal numbers can be consecutive in gray code, you need to convert them to binary and then compare their corresponding bits.

Gray code is a binary numeral system where two consecutive numbers differ by only one bit. Therefore, if two hexadecimal numbers can be consecutive in gray code, their binary representations must differ by only one bit as well. To convert a hexadecimal number to binary, simply convert each hexadecimal digit to its corresponding 4-bit binary representation. For example, the hexadecimal number 3A would be converted to 0011 1010 in binary.

Here is a step-by-step guide to determine if two hexadecimal numbers can be consecutive in gray code:
1. Convert the first hexadecimal number to binary. For example, if the first hexadecimal number is 3A, convert it to 0011 1010 in binary.
2. Convert the second hexadecimal number to binary using the same method as step 1.
3. Compare the corresponding bits of the two binary numbers. If there is only one bit that differs between the two binary numbers, then the original hexadecimal numbers can be consecutive in gray code.
4. If there is more than one bit that differs between the two binary numbers, then the original hexadecimal numbers cannot be consecutive in gray code.

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The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90  angle.

To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.

Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.

Without this information, no concrete calculations can be made.

Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.

Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.

Round your answer to the nearest tenth as specified.

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Answer:

Step-by-step explanation:

To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:

yz + x²

Substituting the given values, we get:

(6.1 * 0.2) + (3.2^2)

This simplifies to:

1.22 + 10.24

Therefore, the value of the expression is approximately 11.46.

11.46

gimme brainlyest gang

We have to find the slope and the y-intercept of the linear function shown.

For doing so, we will take two points that pass through the line and we will use the formula:

for finding the slope. In this case, two of those points could be:

Using them, and replacing onto the slope formula we get:

This is, the slope is - 3/4.

For the y-intercept, we see that the function passes through the point:

and then, when x=0, y=3. This means that the y-intercept is 3.

The 99th percentile for the mean height of a random sample of 20 adult women is approximately 68.7 inches, which is 3.7 inches above the mean of 65 inches.

The 99th percentile for the mean height of a random sample of 20 adult women can be calculated using the normal distribution. The normal distribution is a bell-shaped curve that describes the probability of a given event occurring. In this case, the mean and standard deviation of the height of adult women is used to calculate the probability of the mean height of a sample of 20 adult women being a certain value. For the 99th percentile, this means that the probability of the mean of the sample of 20 adult women being equal to or less than the value of 68.7 inches is 99%. This value is 3.7 inches above the mean of 65 inches, which is the expected mean height of adult women.

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Answer:

It is 22.524

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

The sample mean versus desired mean is not a type of comparison one would anticipate for a two-sample test to be performed. Therefore, the option C holds true.

A sample test can be referred to or considered as the test that includes the conducting of an activity to determine the nearest possible outcome of a much larger set of observations. The purpose of conducting such a test is testing that two population means are the same in a set of observations. If the means are same, it means that the test is successful.

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Answer:

28 feet

Step-by-step explanation:

thank you the same as the guy above me

Answer: 80

Step-by-step explanation: The answer is 80 because there are 16 ounces in 1 pound and when you multiply 5x16 you get 80. Hope this helped!

Answer:

80

Step-by-step explanation:

Answer: 12, 18, 24

Step-by-step explanation:

An order of 660 units should be placed at the start of Week 2 to meet the demand requirement of 500 units at the start of Week 5.

We have,

To determine when and how large of an order should be placed to meet the demand requirement of 500 units of Item X at the start of Week 5, we need to consider the lead time and the planned receipts.

Given:

Demand requirement: 500 units at the start of Week 5

Lead time: 3 weeks

Planned receipts: 120 units in Week 1, 120 units in Week 3, and 100 units in Week 4

We can calculate the available inventory at the start of Week 5 by considering the planned receipts and deducting the units used during the lead time:

Available inventory at the start of Week 5

= Planned receipts in Week 1 + Planned receipts in Week 3 + Planned receipts in Week 4 - Units used during the lead time

Available inventory at the start of Week 5 = 120 + 120 + 100 - 500 = -160

The available inventory is negative, indicating a shortage of 160 units at the start of Week 5.

To meet the demand requirement, an order should be placed. Since the lead time is 3 weeks, the order should be placed 3 weeks before the start of Week 5, which is at the start of Week 2.

The order quantity should be the difference between the demand requirement and the available inventory, considering the shortage:

Order quantity = Demand requirement - Available inventory

= 500 - (-160)

= 660 units

Therefore,

An order of 660 units should be placed at the start of Week 2 to meet the demand requirement of 500 units at the start of Week 5.

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Answer:

The mean is 128.7

There is no mode

The median is 9

The range is 11.5

Step-by-step explanation: