in an isosceles triangle, one base angle measures 60 degrees. what is the measure of the third angle?

The measures of the angles of the triangles are

m∠1 = 55°

m∠2 = 125°

m∠3 = 35°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔCDE

And ∠BAC = m∠1

And , ∠CDE = m∠3

Now , from the triangle ΔABC

∠ABC = 180° - 110° ( Angle of a straight line is 180° )

So , the measure of angle ∠ABC = 70°

The sides of the triangle AC and BC are similar

So , The angles of the triangle are = 70° + x + x = 180°

On simplifying the equation , we get

70° + m∠1 + m∠1 = 180°

Subtracting 70° on both sides of the equation , we get

2m∠1 = 110°

Divide by 2 on both sides of the equation , we get

m∠1 = 55° = ∠ACB

And , ∠ACB and m∠2 are on a straight line

So , m∠2 = 180° - 55°

On simplifying the equation , we get

m∠2 = 125°

The triangle ΔCDE is a right triangle with ∠DCE = m∠1 ( vertically opposite angles )

So , the angles of the triangle are = 90° + 55° + m∠3 = 180°

On simplifying the equation , we get

145° + m∠3 = 180°

Subtracting 145° on both sides of the equation , we get

m∠3 = 35°

Hence , the measures of the angles of the triangles are are m∠1 = 55° , m∠2 = 125° , m∠3 = 35°

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Explanation:

Let 'y' be the total charge for the trip and let 'x' be the number of miles.

When the number of miles x is 0, the taxicab charges $5.00, so y = 5 at first.

Then for each mile x they charge $1.50.

The algebraic expression is:

To evaluate the expression for traveling 20 miles, we have to replace x for 20 in the expression above:

Answer:

The expression:

The charge for traveling 20 miles is $35

We are told tha our sample consists of n=1100 polls, out if which 542 said yes.

The 90% confidence level is not used to calculate the point estimate of the population proportion p.

The best point estimate of the population proportion p is obtained by simply calculating the the proportion among the sample. That is

which rounded to three decimal places is

Answer:

64, 65, 66

Step-by-step explanation:

16 x 4 = 64

13 x 5 = 65

6 x 11 = 66

^^

Answer:

40/30

Step-by-step explanation:

\( \tan(c) = \frac{40}{30} = \frac{4}{3} \)

Step-by-step explanation:

The answer will be-+ 11376

Answer:

√{5688×5688×4}=√{5688²×2²)==±11376

(a) Out of a population of 1 million, we can expect 1000 people to have this form of cancer, as the rate of the disease is 0.001 (0.1% of the population) multiplied by 1 million.
(b) Out of a population of 1 million, 5000 people would test positive for this form of cancer, as the false positive rate is 0.005 (0.5% of the population) multiplied by 1 million.
(c) The probability that a person who tested positive actually has this form of cancer is 16.69%.

(a) Out of a population of 1 million, how many people are expected to have this form of cancer?

To calculate this, we'll multiply the population by the rate of cancer occurrence:
1,000,000 (population) × 0.001 (rate) = 1,000 people with cancer.

(b) Out of a population of 1 million, how many people would test positive for this form of cancer?

First, we need to find out how many false positives there would be:
1,000,000 (population) × 0.005 (false positive rate) = 5,000 false positives.

Next, since the test has a perfect detection rate (1) for individuals with cancer, all 1,000 people with cancer would test positive.

Total positive tests = 1,000 (true positives) + 5,000 (false positives) = 6,000 positive tests.

(c) Bayes' theorem. The probability of having the disease given a positive test result can be calculated as follows:

P(A|B) = P(B|A) * P(A) / P(B)

where A is the event of having the disease, B is the event of testing positive, P(A) is the prior probability of having the disease (0.001), P(B|A) is the probability of testing positive given that you have the disease (1), and P(B) is the probability of testing positive, which can be calculated as the sum of the true positive and false positive rates:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
P(B) = 1 * 0.001 + 0.005 * 0.999
P(B) = 0.005995

Now we can plug in the values and solve:

P(A|B) = 1 * 0.001 / 0.005995
P(A|B) = 0.1669

So the probability that a person who tested positive actually has this form of cancer is 16.69%.

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Answer:

y= -4x + 3

Step-by-step explanation:

Because the slope is -4/1 which is the same as 4 and 3 is the y-intercept.

Here's the work;

We can just use the first two coordinates which are (0,3) and (1,-1) to get from the x-value 0 to 1 we add 1. and to get from the y-value 3 to -1 we subtract 4. Therefore the slope is -4 and the y- intercept (when x is zero) is 3. Pop that into slope intercept form to get y=-4x +3

Hope that helps and have a great day!

Step-by-step explanation:

the slope of the line is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

x changes by -22 (from 19 to -3)

y changes by +13 (from -4 to 9)

the slope is +13/-22 = -13/22

To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

To find the particular solution to a differential equation, we need to know the specific form of the differential equation. Without this information, it is not possible to determine the particular solution.

A differential equation is an equation that relates a function and its derivatives. The form of the differential equation determines the method used to solve it and find the particular solution.

For example, a simple linear first-order ordinary differential equation has the form:

\(\frac{dy}{dx} = f(x)\).

To find the particular solution, we need additional information such as the initial condition \(y(x_0) = y_0\), where \(x_0\) and \(y_0\) are known values.

The method of solution depends on the specific type of differential equation, which can include linear equations, separable equations, exact equations, etc. Each type of equation requires different techniques to find the particular solution.If you provide the specific form of the equation you want to solve or any additional information or context, I can guide you through the process of finding the particular solution. Otherwise, without the differential equation, it is not possible to determine the particular solution.

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Answer:

8x + x^2

Step-by-step explanation:

See attached image

The necessary preprocessor directive to enable the use of functions like sqrt and sin

#include <math.h>

Generally, A preprocessor directive is a command that is processed by the preprocessor in a programming language before the actual compilation of the source code begins.

Preprocessor directives are used to give instructions to the preprocessor, which is a program that performs text substitution on

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Answer:

40000

Step-by-step explanation:

it is the nearast 10000

Answer:

The smallest integer is 8

Step-by-step explanation:

2( x + 4 ) < 4x - 6

4x - 6 > 2x + 8

2x > 14

x > 7

The smallest integer is 8

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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The coefficient of static friction is typically larger than the coefficient of kinetic friction. This is because static friction needs to be overcome to initiate motion, while kinetic friction acts during the motion, which usually requires less force to maintain.

1. Difference between static and kinetic friction: -

Static friction occurs when two surfaces are not moving relative to each other. It opposes the force that is trying to make the objects move. -

Kinetic friction, on the other hand, occurs when two surfaces are moving relative to each other. It acts against the direction of motion.

2. Normal force: - The normal force is a perpendicular force exerted by a surface on an object resting on it. It acts perpendicular to the contact surface and balances the weight of the object.

3. Relationship between friction and normal force: - The frictional force (both static and kinetic) is directly proportional to the normal force acting on an object.

Mathematically, F_friction = μ * F_normal, where F_friction is the frictional force, μ is the coefficient of friction, and F_normal is the normal force.

4. Wheel friction type: - A wheel experiences static friction at the point of contact with the surface because there's no relative motion between the wheel's contact point and the surface. The rest of the wheel experiences kinetic friction as it moves in relation to the surface.

5. Comparison between coefficients of static and kinetic friction: - The coefficient of static friction is typically larger than the coefficient of kinetic friction. This is because static friction needs to be overcome to initiate motion, while kinetic friction acts during the motion, which usually requires less force to maintain.

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To organize the information about summer jobs available for college students in my area, I could use a spreadsheet as my data set.

(a) The cases would be each job opportunity available for college students in the area.

(b) The variables would include:
- Job Title
- Company Name
- Job Description
- Pay Rate
- Location
- Required Skills/Qualifications

The possible values for each variable would depend on the specific jobs available.

(c) The variables "Job Title," "Company Name," "Location," and "Required Skills/Qualifications" would be categorical variables, as they involve categories or labels. The variables "Job Description" and "Pay Rate" would be quantitative variables, as they involve numerical values.

(d) I would label this data set as "Summer Jobs for College Students in [Name of Area]." I chose this label to clearly indicate the focus of the data set.

(e) The key characteristics of this data set would include the job title, company name, job description, pay rate, location, and required skills/qualifications for each summer job available for college students in the area. By organizing this information, students can compare and contrast job opportunities to find the best fit for their skills and needs.

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Dean can obtain a sample that is most representative of the entire student body and obtain accurate results about the percentage of students interested in painting

To obtain a representative sample of students for the interview, Dean could use a random sampling method. He could randomly select students from different grades, genders to ensure that the sample is diverse and represents the entire student body. He could also distribute the survey in different areas of the school, such as the cafeteria, the library, or the student center, to ensure that all students have an equal chance of being included in the sample. It is important that Dean ensures that the sample size is large enough to get accurate results. For example, if Dean wants to know the percentage of students interested in painting with a margin of error of 5% and a confidence level of 95%, he would need a sample size of approximately 385 students (based on a total population of 1000 students). By using a random sampling method, Dean can obtain a sample that is most representative of the entire student body and obtain accurate results about the percentage of students interested in painting

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Answer:

This is a combination problem, where order doesn't matter.

We want to find the number of ways to choose 3 exercises from a list of 25, which is denoted as 25C3.

This is also equal to (252423) / (321) which is equal to 2300.

Therefore, there are 2300 different groups of 3 exercises the fitness coach can choose from the list of 25 exercises.

Step-by-step explanation:

Answer:

the hypotenuse is 68 yards

Step-by-step explanation:

A^2+B^2 then square rooted equals C

32^2+60^2

1,024+3,600=4,624

4,624 square rooted is 68

68 yd is your answer

The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer:

11.75$

Step-by-step explanation:

do 94 divided by 8. You get 11.75, so each ticket costs 11 dollors and 75 cents

Answer: x = 1/2

Step-by-step explanation:

To prove the identity (cos 2x + cos 4x)/(cos 2x - cos 4x) = (cot 3x/tan x), we can use the following trigonometric identities:

1. cos 2x = 2cos^2 x - 1

2. cos 4x = 8cos^4 x - 8cos^2 x + 1

3. cot 3x = (3cos^2 x - 1)/(3sin x cos x)

4. tan x = sin x/cos x

Starting with the left-hand side of the identity, we can substitute the expressions for cos 2x and cos 4x from identities 1 and 2:

(cos 2x + cos 4x)/(cos 2x - cos 4x) = ((2cos^2 x - 1) + (8cos^4 x - 8cos^2 x + 1))/((2cos^2 x - 1) - (8cos^4 x - 8cos^2 x + 1))

Simplifying this expression gives:

(cos 2x + cos 4x)/(cos 2x - cos 4x) = (6cos^2 x)/(2cos^2 x) = 3

Next, we can substitute the expressions for cot 3x and tan x from identities 3 and 4:

(cot 3x/tan x) = ((3cos^2 x - 1)/(3sin x cos x))/(sin x/cos x)

Simplifying this expression gives:

(cot 3x/tan x) = (3cos^2 x - 1)/sin x = 3cos^2 x/cos x = 3cos x

Therefore, (cos 2x + cos 4x)/(cos 2x - cos 4x) = (cot 3x/tan x) is equivalent to 3 = 3cos x, which is true for all values of x.

So, the identity is proven.

Answer:

8

Step-by-step explanation:

4 doubled and added to 12 gives 20.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11

Given

Let number be x

2x + 12 = 20

2x = 20-12 = 8

2x = 8

x = 8/2 = 4

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Step-by-step explanation:

I'm assuming this question is multiple choice, as there are several answers. y=x-18 is one, if that's an option. if you gave me the rest of the question, I might be able to help more :)

The answers are explained in the solution.

Part A:

To calculate how much fabric is needed to make 3 aprons, we need to multiply the amount of fabric needed for one apron by 3.1 apron requires 1 1/2 yards of fabric for the front and 1/8 yards of fabric for the tie.1 1/2 yards + 1/8 yards = 15/8 yards.

Now we can multiply the total fabric needed for one apron by 3 to get the fabric needed for 3 aprons:

3 x 15/8 yards = 45/8 yards

So, the total fabric needed to make 3 aprons = 45/8 yards.

Part B:

If Susan originally has 7 yards of fabric and she uses 45/8 yards to make 3 aprons, we can subtract the amount used from the original amount to find out how much fabric is left over.

7 yards - 45/8 yards = 56/8 yards - 45/8 yards

= 11/8 yards

So, after making the aprons, Susan will have 11/8 yards of fabric left over.

Part C:

To determine if Susan has enough fabric left to make another apron, we need to compare the amount of fabric left (11/8 yards) with the amount of fabric needed for one apron (1 1/2 yards + 1/8 yards = 15/8 yards).

Since 15/8 yards is greater than 11/8 yards, Susan does not have enough fabric left to make another apron.

She is short by 4/8 yards (or 1/2 yard) of fabric.

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The correct answer is d. emergent.

An emergent leader is an individual who grows into the leadership role naturally, often due to circumstances or necessity. They are not appointed or assigned to the position of leadership but rather emerge from the group or organization based on their skills, qualities, or actions.

Emergent leaders may possess certain qualities or demonstrate their competence and ability to guide and influence others. They gain recognition and respect from their peers, leading to their emergence as leaders within the group or organization.

This type of leadership often occurs in situations where formal leadership structures may be absent or ineffective, and individuals step up to take charge based on their capabilities and the needs of the group.

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The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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