How far up the tree is the cat ?

The lengths of the sides and angles of the triangles, obtained using Pythagorean Theorem and trigonometric ratios are;

D. 19.2

C. 5.3

F. 2·√5

G. √3

H. 8·√3

K. 18.9

O. 15.5

N. 14.5

M. 41.4°

I. 74.1°

The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the triangle.

D. x = √(15² + 12²) ≈ 19.2

C. x = √(10² - 8.5²) ≈ 5.3

F. x = 2·√(5) (Special triangles)

G. tan (60°) = 30/x = √3

x = 30/√3 = 10·√3

H. x/16 = (√3)/2

x = 16 × (√3)/2 = 8·√3

x = 8·√3

K. tan(34°) = x/28

x = 28 × tan(34°) ≈ 18.9

O. cos(55°) = x/27

x = 27 × cos(55) ≈ 15.5

N. sin(16°) = 4/x

x = 4/(sin(16°) ≈ 14.5

M. x = arccos(9/12) ≈ 41.4°

I. x = arcsin(25/26) ≈ 74.1°

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The electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.

What is an electric field?

An electric field is a region in which an electric charge experiences a force. It is created by an electric charge or a changing magnetic field. Electric fields exist everywhere in nature and are vital to the functioning of many electronic devices. Electric fields are also used to describe the motion of electrons in a conductor and the behavior of electric currents.

The electric field at the origin (x=0, y=0) can be calculated using the equation of electric field,

E = k(q1/r1² + q2/r2²)

Where k is the Coulomb's constant, q1 and q2 are the charges and r1 and r2 are the distances from the charges to the origin.

The electric field at the origin can be calculated by substituting the given values in the equation.

The distance from the charge at y = 4.0 cm to the origin is 5 cm and the distance from the charge at y = -4.0 cm to the origin is also 5 cm.

E = 8.988 X 10⁹ (3.8 X 10⁻⁹/25 + 3.8 X 10⁻⁹/25)

E = 8.99 X 10⁹ (3.8 X 10⁻⁹/25)

E = 1.05 X 10⁷ N/C

Therefore, the electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.

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Right Question:-

Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y, Find electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm?

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

I just answered this.

in short : we rotate each vertex on a circle arc. the center of that circle being P.

so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.

therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.

that is starting at

360/5 = 72°

and then every additional 72°

144°

216°

288°

360°

so, A, D and E are correct

Answer:

5:20 to 9:20

Step-by-step explanation:

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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Answer:

\(\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2\)

Step-by-step explanation:

We want to find the linear function given that:

\(f^{-1}(2) = -1\text{ and } f^{-1} (-9) = 3\)

Recall that by the definition of inverse functions:

\(\displaystyle \text{If } f(a) = b\text{ then } f^{-1}(b) = a\)

In other words, f(-1) = 2 and f(3) = -9.

This yields two points: (-1, 2) and (3, -9).

Find the slope of the linear function:

\(\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(-9) - (2)}{(3) -(-1)} = -\frac{11}{4}\)

From point-slope form:

\(\displaystyle y - (2) = -\frac{11}{4}( x- (-1))\)

Hence:

\(\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2\)

We can simplify if desired:

\(\displaystyle f(x) = -\frac{11}{4}x -\frac{3}{4}\)

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

VIII or 8

Step-by-step explanation:

XLII converts to 42

XXXIV converts to 34

42-34 = 8 or VIII

Answer:

Choice A

Step-by-step explanation:

Answer:

F is -5, 4

G is 0, 1

H is 0, 4

I hope this is right and if it is not then I'm sorry.

Answer:

\(2 \frac{3}{8} \)

Step-by-step explanation:

\(9 \frac{1}{2} \times \frac{1}{4} \\ \frac{19}{2} \times \frac{1}{4} \\ = \frac{19}{8} \\ = 2 \frac{3}{8} \)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

2 3/8

Hope this helps :)

Answer:

11%

Step-by-step explanation:

If you assume this is out of 100 you can do 98/100 - 87/100, or 98% - 87%, which equals 11%

Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

\(\frac{125}{5} = 25 mpg\\\)

2. Divide miles you want to travel by the mileage per gallon you got on the first step

\(\frac{400}{25} = 16 gallons\)

Answer:

option 1

Step-by-step explanation:

Answer:no

Step-by-step explanation:

Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Step-by-step explanation:

please mark me as brainlest

Answer:

The quantities that would be used to determine the total cost for Joey to derive to work using the highway are:

A. 0.5 hours

C. $1.25 per car

D. $3.05 per gallon

F. 35 miles per gallon

H. 54 miles per hour

Step-by-step explanation:

Cost of a gallon of gas = $3.05

Distance travelled per gallon on the highway = 35 miles

Distance travelled per gallon in the city = 27 miles

Joey's average speed using the highway = 54 miles per hour

Number of hours to get to work using the highway = 0.5 hours

Toll on the highway = $1.25

Joey's average speed using the city street route = 36 miles per hour

Number of hours to get to work using the city street route = 1 hour

Relevant data for highway driving total costs:

Cost of a gallon of gas = $3.05

Distance travelled per gallon on the highway = 35 miles

Joey's average speed using the highway = 54 miles per hour

Number of hours to get to work using the highway = 0.5 hours

Toll on the highway = $1.25

Total costs for using the highway = $1.25 + ($3.05/35 * 54 * 0.5) = $3.60

Answer:

A, B, D, F, H

Step-by-step explanation:

The lowest score for the normally distribution with mean 72 and standard deviation 8 is equal to 82.

Mean of the normally distributed data 'μ' = 72

Standard deviation 'σ ' = 8

Lowest score with 10% ( 90percentile )

z = InvNorm(0.90)

 = 1.28

Let 'X' be the lowest score for the normal distribution

z = ( X - μ ) / σ

Substitute the values we get,

⇒ 1.28 = ( X - 72 ) / 8

⇒ X - 72 = 1.28 × 8

⇒ X = 10.24 + 72

⇒ X = 82.24

⇒ X = 82 ( round to an integer )

Therefore, the lowest score for normally distribution which will place manage on 90th percentile with given mean and standard deviation is equal to 82.

The above question is incomplete, the complete question is:

Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.we want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. Your answer is Please round to an integer number.

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There are 45697600 number of different license plates can be manufactured for this state.

The combination is a mathematical technique that is the number of ways to arrange the n number of collections where the order of selection does not matter.

ⁿCₐ= n!/(n-a)!a!

Here given in the question is,

On the license plate, there are 4 letters and 2 numbers.

Since, There are 26 alphabets in English from A to Z for which at position 1, there are 26 possibilities of alphabets at every position by,

²⁶C₁ = 26!/(26-1)!1!

       = 26!/25!1!

       = 26!/25!

        = 26

So, for 4 different positions of letters,

Then, The number of ways is,

⇒ 26×26×26×26 = 26⁴= 456976

And, There are 10 numbers in math for which at position 1, there are 10 possibilities of numbers at every position by,

¹⁰C₁ = 10!/(10-1)!1!

       = 10!/9!1!

       = 10!/9!

        = 10

So, for 2 different positions of numbers, the number of ways is,

= 10×10 = 10²= 100

Thus, The total number of ways the license can be manufactured = 456976 × 100= 45697600

Therefore, 45697600 different license plates can be manufactured for this state.

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Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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You got 85% of the problems on Test #1 correct, ¾ of the problems on Test #2 correct, and 0.95 of the problems on Test #3 correct. On which test did you get the most problems correct?

we have that

test 1

85%

test 2

3/4=0.75 ----> convert to percentage (multiply by 100) -----> 75%

test 3

0.95 -----> convert to percentage (multiply by 100) -----> 95%

therefore

Compare

95% > 85%> 75%

x=5

steps

they are vertical angles

they are equal

4x+90=110

4x=20

x=5

Answer:

Step-by-step explanation:

9900

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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If m∠ 1=(3 x) degrees and m ∠2=(x+48) degrees

The equation to solve the value of x is

3x = x+48

The value of x = 33

The angle 1 = 99 degrees

The angle 2 = 81 degrees

The measure of angle 1 = 3x degrees

The measure of angle 2 = x + 48 degrees

The sum of the angles on a straight line is add up to 180 degrees. Therefore angle 1 and angle 2 are supplementary angles.

∠1 + ∠2 = 180 degrees

Substitute the values in the equation

3x + x + 48 = 180

4x + 48 = 180

4x = 180 - 48

4x = 132

x = 132/4

x = 33

Part b

Then the measure of angle 1 = 3x

= 3 × 33

= 99 degrees

The measure of angle 2 = x + 48

= 33 + 48

= 81 degrees

Therefore, the equation to solve x is 3x = x + 48 and the measure of angles 1 and 2 is 99 degrees and 81 degrees respectively

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The pairs ∠2 and ∠8, ∠8 and ∠1, and ∠3 and ∠5 are not alternate Interior angles.

The pairs of alternate interior angles, we need to identify angles that are on opposite sides of the transversal and between the parallel lines.

From the given information:

Angles 5 and 4 are on opposite sides of the transversal and between the parallel lines, so they are alternate interior angles.

Angles 6 and 5 are also on opposite sides of the transversal and between the parallel lines, so they are alternate interior angles.

Angles 2 and 8 are not on opposite sides of the transversal, so they are not alternate interior angles.

Angles 8 and 1 are not on opposite sides of the transversal, so they are not alternate interior angles.

Angles 3 and 5 are not on opposite sides of the transversal, so they are not alternate interior angles.

Therefore, the pairs of alternate interior angles are:

- ∠5 and ∠4

- ∠6 and ∠5

The pairs ∠2 and ∠8, ∠8 and ∠1, and ∠3 and ∠5 are not alternate interior angles.

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You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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