HELP ASAP PLEASE !!?!

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

A perpendicular bisector can be defined as a type of line that bisects (divides) a line segment exactly into two (2) halves and forms an angle of 90 degrees at the point of intersection.

In this scenario, we can reasonably infer that to divide the triangles into these regions, you should construct the perpendicular bisector of each segment. These perpendicular bisectors intersect and divide each triangle into three regions. The points in each region are those closest to the vertex in that region.

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Part a

\(\frac{\pi}{3} > \frac{\pi}{4} \implies f(\pi/3)=\sin(\pi/3)=\boxed{\frac{\sqrt{3}}{2}}\)

Part b

\(\frac{\pi}{6} \leq \frac{\pi}{4} \implies f(\pi/6)=2+\cos(\pi/6)=\boxed{2+\frac{\sqrt{3}}{2}}\)

Part c

\(\frac{\pi}{4} \leq \frac{\pi}{4} \implies f(\pi/4)=2+\cos(\pi/4)=\boxed{2+\frac{1}{\sqrt{2}}}\)

Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability.

The term "experiment" in the context of probability refers to a process or activity that involves observing or measuring an outcome that is subject to chance or uncertainty. The outcome of an experiment is not necessarily predictable with certainty, and it may depend on various factors such as the conditions under which the experiment is conducted and the randomness inherent in the process.

Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability. An experiment is essentially a process that leads to one of several possible outcomes, and the probability of each outcome can be calculated or estimated based on the underlying assumptions and factors involved. Examples of experiments in probability include rolling a die, tossing a coin, drawing a card from a deck, or conducting a clinical trial to test a new drug.

Option b) is not an appropriate definition of an experiment because it suggests that the outcome can be predicted with certainty based on mathematical analysis, which is not always the case in experiments involving chance or uncertainty.

Option c) is also not an appropriate definition of an experiment because it suggests that an experiment is conducted to confirm a hypothesis, which may or may not be true. While experiments can be used to test hypotheses and provide evidence to support or refute them, the primary goal of an experiment in the context of probability is to observe or measure the outcome and calculate the probability of each possible outcome.

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The standard deviation of the population of all sample means is approximately 0.577 times less than the standard deviation of the population of individual measurements σ.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

The standard deviation of the sampling distribution of sample means is smaller than the standard deviation of the population of individual measurements (σ) by a factor of 1/√n, where n is the sample size.

This is known as the standard error of the mean (SE) and is calculated as SE = σ/√n.

So, in this case, where n = 3, the standard deviation of the sampling distribution of sample means will be σ/√3, which is approximately 0.577 times σ.

Therefore, the standard deviation of the population of all sample means is approximately 0.577 times less than the standard deviation of the population of individual measurements σ.

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Answer: B

Step-by-step explanation:

hope this helps x have a great friday :)

Answer:

2

Step-by-step explanation:

145 - 75 = 70

70 divided by 35 = 2

2 hours

Answer:

2 hours

Step-by-step explanation:

x is how meany hours he worked and we know that

145=45x+75 is true and when you put 2 in place for x you get 90+75 = 145 and 145=145

Answer:

green= 7

purple=5

Step-by-step explanation:

we already know the trapezoid is 5 so 12-5=7

then since we know the green cresent is seven do 12- 7= purple = 5

Hope this helps

Answer:

the answer will be B. a baker uses 4 cups of flour. she uses 1/4 cup to flour the counters and the rest to make 8 identical muffins.

Answer:

3.16666667 tons

Step-by-step explanation:

hope this helps have a good evening

Answer:

1450 residents

Step-by-step explanation:

Number of residents who live in Harris

= 5800 pounds ÷ 4 pounds

= 1450 residents

The probability that a student scores between 450 and 600 on the SAT math section is approximately 0.4147 or 41.47%.

To find the probability that a student scores between 450 and 600 on the SAT math section, we need to use the properties of the normal distribution. We know that the mean is 511 and the standard deviation is 110.

First, we need to standardize the values of 450 and 600 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For 450:

z = (450 - 511) / 110 = -0.55

For 600:

z = (600 - 511) / 110 = 0.81

Next, we need to find the area under the normal curve between these two standardized values. We can use a table or a calculator to find that the area between z = -0.55 and z = 0.81 is approximately 0.4147.

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Therefore, the volume of the solid generated by revolving the shaded region about the x-axis is (20π/3) cubic units.

To find the volume of the solid generated by revolving the shaded region about the x-axis, we can use the method of cylindrical shells.

The region bounded by the curves y = 6 - 3x, y = 0, and x = 0 forms a triangular region in the first quadrant. Let's find the limits of integration for x.

The line y = 0 intersects with the curve y = 6 - 3x at x = 2. Therefore, the limits of integration for x will be from x = 0 to x = 2.

Now, let's consider a vertical strip at a specific x-value within this region. The height of this strip is given by the difference between the curves y = 6 - 3x and y = 0, which is (6 - 3x) - 0 = 6 - 3x.

The width of the strip is dx.

The circumference of the shell is the distance traveled by revolving the strip around the x-axis, which is given by 2πx.

The volume of the shell is then given by the product of the circumference and the height, which is (2πx) * (6 - 3x) * dx.

Integrating this expression from x = 0 to x = 2 will give us the total volume of the solid:

V = ∫[0 to 2] (2πx) * (6 - 3x) dx.

Simplifying and evaluating the integral, we get:

V = 2π ∫[0 to 2] \((6x - 3x^2) dx.\)

V = 2π \([3x^2/2 - x^3/3]\) evaluated from 0 to 2.

V = 2π \([(3(2)^2/2 - (2)^3/3) - (3(0)^2/2 - (0)^3/3)]\)

V = 2π [(3(4)/2 - (8)/3) - 0].

V = 2π [(6 - 8/3)].

V = 2π [(18/3 - 8/3)].

V = 2π (10/3).

V = (20π/3) cubic units

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9514 1404 393

Answer:

  115 square units

Step-by-step explanation:

The area of a parallelogram is the product of base length and height. The height is the perpendicular distance between the bases.

  A = bh

  A = (23)(5) = 115 . . . . square units

Answer:

The current of the circuit at t = 0 is equal to 0.

If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:

\(\displaystyle (cu)' = cu'\)

Derivative Property [Addition/Subtraction]:

\(\displaystyle (u + v)' = u' + v'\)

Derivative Rule [Basic Power Rule]:

Slope Fields

Integration

Integration Rule [Reverse Power Rule]:

\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Rule [Fundamental Theorem of Calculus 1]:

\(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:

\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Method: U-Substitution

Electricity

Ohm's Law: V = IR

Circuits

Step-by-step explanation:

*Note:

In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.

Step 1: Define

Identify given.

\(\displaystyle L \frac{dI}{dt} + RI = V\)

[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.

Step 2: Find Current Expression Pt. 1

Step 3: Find Current Expression Pt. 2

Identify variables for u-substitution.

Step 4: Find Current Expression Pt. 3

Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.

Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.

Step 5: Solve

If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:

\(\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}\)

If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:

\(\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}\)

∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.

---

Topic: AP Physics C - EMAG

Unit: Induction

Answer:

-1  1/5

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

Multiply to remove 1 decimal places. Here, you multiply top and bottom by 101 = 10

Find the Greatest Common Factor (GCF) of 12 and 10, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 2,

Simplify the improper fraction

-1 1/5

The vertex and axis of symmetry of the graph is shown in image.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Now,

Since, The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Hence, The points corresponds to x = - 2 and - 4 are;

For x = - 2;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-2 + 6)² - 5

⇒ f (x) = 1/4 (4)² - 5

⇒ f (x) = 4 - 5

⇒ f (x) = - 1

For x = - 4;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-4 + 6)² - 5

⇒ f (x) = 1/4 (2)² - 5

⇒ f (x) = 1 - 5

⇒ f (x) = - 4

Thus, The points are;

⇒ (- 2, - 1) , (- 4, - 4)

And, The vertex of the function is,

⇒ ( - 6, - 5 )

And, The axis of symmetry of the graph is,

⇒ x = - 6

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The correct interpretation of this confidence interval is that, based on the random sample of 351 diamonds taken from AwesomeGems.com on July 28, 2005, with a confidence level of 95%, the true population mean cost per carat of diamonds purchased from the website is estimated to fall between $5938.42 and $6546.32.

This means that if we were to repeat the sampling process many times and construct confidence intervals using the same method, about 95% of these intervals would contain the true population mean cost per carat. It is important to note that this statement is about the population mean, not any particular diamond's cost, and that this interval only applies to diamonds purchased from AwesomeGems.com on July 28, 2005.

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Answer:

Step-by-step explanation:

The system has infinitely many solutions if the two equations are equivalent.

We can analyze the given systems to see:

A)

Different slopes, there is one solution

B)

Different slopes, there is one solution

C)

Same lines, infinitely many solutions

D)

Different slopes, there is one solution

Solution:

When two equations are equivalent, it is infinitely many solutions because the two lines overlap each other.

Option A - 2x + 7x + y = 6 and y = 9x + 6

Option B - y = 5x + 7 and y = 2x + 8

Option C - y = x + 4 and 2y = 2x + 8

Option D - 7x - y = 10 and y = 6x + 8

Hence, Option C is correct.

There are 6 possible results for each roll: 1, 2, 3, 4, 5 or 6. Each result has a probability of 1 in 6 or 1/6. The probability of rolling a 3 is 1/6. After 3000 rolls, you would likely reach theoretical probability of 1/6 and therefore 1/6x3000 = 500 rolls would be a 3, so p(3) = 1/6.

Answer:

c)  124.96

Step-by-step explanation:

Geometric series:  100 + 20 + ... + 0.16

First we need to find which term 0.16 is.

General form of a geometric sequence: \(a_n=ar^{n-1}\)

(where a is the first term and r is the common ratio)

To find the common ratio r, divide one term by the previous term:

\(\implies r=\dfrac{a_2}{a_1}=\dfrac{20}{100}=0.2\)

Therefore, \(a_n=100(0.2)^{n-1}\)

Substitute \(a_n=0.16\) into the equation and solve for n:

\(\implies 100(0.2)^{n-1}=0.16\)

\(\implies (0.2)^{n-1}=0.0016\)

\(\implies \ln(0.2)^{n-1}=\ln0.0016\)

\(\implies (n-1)\ln(0.2)=\ln0.0016\)

\(\implies n-1=\dfrac{\ln0.0016}{\ln(0.2)}\)

\(\implies n=\dfrac{\ln0.0016}{\ln(0.2)}+1\)

\(\implies n=5\)

Therefore, we need to find the sum of the first 5 terms.

Sum of the first n terms of a geometric series:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

Therefore, sum of the first 5 terms:

\(\implies S_5=\dfrac{100(1-0.2^5)}{1-0.2}\)

\(\implies S_5=124.96\)

Answer:

1: (4,1) x=4 y=1

2: (1,10) x=1 y=10

3: (-25/4,5) x= -25/4 y=5

Step-by-step explanation:

It would be a lot to explain all three so if you really need it just ask

We now have three equations, so we can solve them.

Let's define the length of the 3 boards in terms of x:

F=x

S=2x-3

T=2

F+S+T =26

x+2x-3+2 =26

3x =26+1=27

x =27/3 = 9 feet for First section

2x-3 =18-3 = 16 feet = Second

2 = Third

9+16+2 = 27

27 is the length of the shortest piece.

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The number of visitors that we must sample to construct a 95% confidence interval is (b) 1,030 visitors.

In order to construct the 95% confidence interval with a margin of error of  ±3%, we need to find the sample size that will give us a margin of error of 0.03 or less.

The formula used to find desired sample-size is :

⇒ n = (Z² × p × (1-p)) / (E²)

Where, n = required sample size

Z = Z-score for required level of confidence (1.96 for 95% confidence)

p = proportion of visitors who favor proposal;

E = margin of error = (0.03);

We don't know the value of p, So, we use the sample proportion as an estimate:

⇒ p' = 89/150 = 0.5933;

Substituting the values,

we get,

⇒ n = (1.96² × 0.5933 × (1-0.5933)) / (0.03²)
⇒ 1029.67 ≈ 1030.

Therefore, the number of visitors to sample is (b) 1,030 visitors.

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The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.

A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.

When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.

So that we can find real solution of quadratic equation by finding discriminant of given equation.

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Answer:

4 books

Step-by-step explanation:

15-3=12

12/3=4

In general, two congruent segments have the same measure. Since no more information about the figure is given, we would need to estimate the measurement of each of its segments.

A) Notice that

B)

C)

D)

E)

Answer:

> that is the answer I have to make it 20 character

The required comparison is √180 > √128,which is the required inequality.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given numbers are, one hundred eighty and one hundred two eighths which are 180 and 128

Now square roots of one hundred eighty and one hundred two eighths will be,

√180

√128

Converting them to decimals we get,

√180 = 13.416

√128 = 11.313

Here we can see that

13.416 > 11.313

Therefore, √180 > √128

which is the required inequality.

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Supercomputers are the most powerful computers at any given time, but are built especially for assignments that require arithmetic speed.

The supercomputers, which are the most advanced and high-performance computers available, are specifically constructed to handle assignments that demand rapid arithmetic processing.

These machines are optimized for executing complex mathematical operations and simulations, enabling them to tackle problems that require immense computational power.

By harnessing parallel processing, massive memory capacities, and specialized architectures, supercomputers excel in solving scientific, engineering, and research challenges that necessitate exceptional arithmetic speed.

Their capabilities contribute to advancements in various fields, including weather forecasting, molecular modeling, astrophysics, and cryptography.

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Answer:

- 7/1 is the simplified fraction for 14/2.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

do 14/2 in a calculator! (dividing)