Rewrite the equation y=−3|x−1|−3 as two linear functions f and g with restricted domains

Answer:

Question 37:

B) 21

Step-by-step explanation:

How I found the radius:

radius= 132/ 2 x π  

r=132 / 6.2831853071796

r=21.0084525

Divide 132 by 6.2831853071796

π = 3.1415926535898

Note: Hope this Helps!

-kiniwih426

Answer: 6.68

To calculate the number of years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash, we can use the formula for compound interest.

A = P (1 + r/n) ^ nt

where

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time in years

Given:

P = $49 million

r = 10.5%

n = 1 (annual compounding)

A = $90 million

We need to find t. Let's plug in the given values in the formula and solve for t.

A = P (1 + r/n) ^ nt

90 = 49(1 + 0.105/1) ^ t

Dividing both sides by 49, we get:

1.8367 = (1 + 0.105) ^ t

Taking the logarithm of both sides, we get:

t log (1.105) = log (1.8367)

Dividing both sides by log (1.105), we get:

t = log (1.8367) / log (1.105)

Using a calculator, we get:

t ≈ 6.68

Therefore, it will take approximately 6.68 years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash.

Answer:

ok ok ima solve it

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

The perimeter of ABCDE is equal to AB + BC + CD + DE + AE.

AB = 10 - 2 = 8 (The x values of A and B are the same, therefore the distance between them is the difference between their y values.)

BC = 7 - 4 = 3 (The y values of B and C are the same, therefore the distance between them is the difference between their x values.)

CD =  \(\sqrt{(X_D - X_C)^2 + (Y_D - Y_c)^2} = \sqrt{(15 - 7)^2 + (4 - 10)^2} = \sqrt{8^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10\)

DE = \(\sqrt{(X_E - X_D)^2 + (Y_E - Y_D)^2} = \sqrt{(7 - 15)^2 + (-2 - 4)^2} = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10\)

AE =

\(\sqrt{(X_E - X_A)^2 + (Y_E - Y_A)^2} = \sqrt{(7 - 4)^2 + (-2 - 2)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\)

\(\Delta \text{ABCDE} = \text{AB} + \text{BC} + \text{CD} + \text{DE} + \text{AE} = 8 + 3 + 10 + 10 + 5 = 36\)

Answer:

7

Step-by-step explanation:

3x- 1/9y = 18

value of x when y is 27

3x- 1/9*27 = 18

3x- 3 = 18

3x = 18 + 3

3x = 21

x= 21/3

x = 7

Hope this helps you!

Answer:

x = 7

Step-by-step explanation:

3x-1/9(27) = 18

x = 21/3

=7

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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Answer:

(3,7π/6),(3,11π/6)

Step-by-step explanation:

You let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

My english is not well,but my math is good

Answer:

D and E

Step-by-step explanation:

Edge 2020

Answer:

(4 + 11x)(4 - 11x)

Step-by-step explanation:

To factor the expression 16 - 121x^2 completely, we need to recognize it as a difference of squares. The difference of squares formula states that:

a^2 - b^2 = (a + b)(a - b)

In this case, we have 16 as a perfect square (4^2) and 121x^2 as a perfect square (11x)^2. Applying the formula, we can rewrite the expression as:

16 - 121x^2 = (4)^2 - (11x)^2

Using the difference of squares formula, we have:

= (4 + 11x)(4 - 11x)

Answer:

107

Step-by-step explanation:

6x + 3x + 5x + 6x

9x + 11x

When solving the multiplication of fractions by whole numbers, it's important to remember that a fraction is a number that represents the division of two quantities, and a whole number is a non-negative integer.

To multiply a fraction by a whole number, you need to multiply the numerator (the top number of the fraction) by the whole number and leave the denominator (the bottom number of the fraction) unchanged. For example, if you have the fraction 3/4 and you want to multiply it by 2, you would get 3/4 * 2 = 6/4 = 3/2.

Another way to think about it is that when multiplying a whole number by a fraction, you are essentially adding the fraction to itself that many times. For example, if you have 3/4 * 2, you can think of it as 3/4 + 3/4 = 3/2

It's important to note that when multiplying a fraction by a whole number, you are not changing the value of the fraction, you are only changing its representation.

It's also important to simplify the result if possible, check if both the numerator and denominator have a common factor, if they do, you can divide both by that factor. For example, if you have the fraction 6/8, you can simplify it to 3/4.

In summary, to multiply a fraction by a whole number, you need to multiply the numerator by the whole number and leave the denominator unchanged, and then simplify the result if possible. It's a simple operation but it is important to understand the concept behind it before solving the problem.

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The answer is D. None of the above, the long-term DPMO is 25137, which is equivalent to a Z-value of 3.46. The short-term Z-value is usually 1.5 to 2 times the long-term Z-value,

so it would be between 5.19 and 6.92. However, these values are not listed as answer choices. The Z-value is a measure of how many standard deviations a particular point is away from the mean. In the case of DPMO, the mean is 6686. So, a Z-value of 3.46 means that the long-term defect rate is 3.46 standard deviations away from the mean.

The short-term Z-value is usually 1.5 to 2 times the long-term Z-value. This is because the short-term process is more variable than the long-term process. So, the short-term Z-value would be between 5.19 and 6.92.

However, none of these values are listed as answer choices. Therefore, the correct answer is D. None of the above.

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False.
The Precautionary Principle is a guiding principle in decision-making when there is scientific uncertainty about potential harm.

Science is a process of investigation and discovery that aims to understand the natural world. It relies on evidence, experimentation, and observation to develop theories and explanations for phenomena. However, science does not claim to achieve 100% absolute proof. Scientific theories are constantly subject to revision and refinement based on new evidence and observations.

The Precautionary Principle is a guiding principle in decision-making when there is scientific uncertainty about potential harm. It suggests taking preventative measures to avoid potential risks, even if scientific evidence is not yet conclusive. Based on this principle, the situations in which it may be applied are:

- The FDA is determining a safe dose for a new diabetes medication.
- The EPA sets a new standard for a contaminant in public drinking water.

In these scenarios, there is a need to assess the potential risks associated with the medication and the contaminant in public drinking water. The Precautionary Principle encourages taking precautions to ensure public safety and minimize harm until more conclusive scientific evidence is available.

It's important to note that the Precautionary Principle may also be applied in other contexts, depending on the specific circumstances and the level of uncertainty involved. For example, if a car manufacturer discovers a potential safety issue with a new car's interior color, they may choose to apply the Precautionary Principle and investigate further before releasing the product. However, this specific scenario was not listed among the options provided. Similarly, the architect designing elevators for a skyscraper in New York City or the engineer ordering a new painting for their office may consider safety factors, but the Precautionary Principle may not necessarily be the primary guiding principle in those cases.

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Given the subtotal of $55.97, apply taxes as shown below (remember that 6.75%=6.75/100=0.0675)

Now, apply the discount (20%=20/100=0.20)

The answer is approximately $47.8 (taxes first, then discount)

Based on the information that has been provided, it is not possible to conclude whether there are a greater number of philosophers or mathematicians.

The statement only provides information regarding the proportion of mathematicians to philosophers and vice versa; it does not provide information regarding the total number of people working in either subject. It is possible that there are a greater number of philosophers, a greater number of mathematicians, or an equal number of both. We would need further information, such as the overall number of people in the fields, in order to accurately establish the number of persons who are present in each field specifically.

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Answer:

The number 1/3 is a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.

1/3 is not a natural number, whole number, or integer. Natural numbers are the set of positive integers (1, 2, 3, …). Whole numbers are the set of non-negative integers (0, 1, 2, 3, …). Integers are the set of whole numbers and their additive inverses (-3, -2, -1, 0, 1, 2, 3, …).

Step-by-step explanation:

The standard deviation of the value of the variable at the end of 3 years is 3√3.

a) To find the expected value of the variable x after 3 years, we can use the properties of the Wiener process. The expected value of the variable at any given time t is given by:

E[x(t)] = x(0) + a * t

Given that x(0) = 10 and a = 2, we can substitute these values into the equation:

E[x(3)] = 10 + 2 * 3 = 10 + 6 = 16

Therefore, the expected value of the variable x after 3 years is 16.

b) The standard deviation of the value of the variable at the end of 3 years can be calculated using the formula:

σ = √(b^2 * t)

Given that b = 3 and t = 3, we can substitute these values into the formula:

σ = √(3^2 * 3) = √(9 * 3) = √27 = 3√3

Therefore, the standard deviation of the value of the variable at the end of 3 years is 3√3.

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The image of the patient is located approximately 28.9 cm from the convex mirror.

To locate the image of a patient using a convex spherical mirror, we can use the mirror equation.

Equation:

1/f = 1/do + 1/di

where:

f is the focal length of the mirror,

do is the object distance (distance of the patient from the mirror), and

di is the image distance (distance of the image from the mirror).

Given:

The magnitude of the mirror's radius of curvature:

0.562 m (since it's a convex mirror, the radius of curvature is positive).

The object distance (distance of the patient from the mirror): do = 10.2 m.

To solve for the image distance, we need to find the focal length.

For a convex mirror, the focal length is half the magnitude of the radius of curvature, so f = 0.562 m / 2

= 0.281 m.

Now we can substitute the values into the mirror equation:

1/f = 1/do + 1/di

1/0.281 = 1/10.2 + 1/di

Simplifying the equation:

3.559 = 0.098 + 1/di

Subtracting 0.098 from both sides:

3.461 = 1/di

To find the image distance, we take the reciprocal:

di = 1/3.461

= 0.289 m

The image of the patient is located at a distance of 0.289 m from the mirror. Since the image distance is positive, it indicates that the image formed by the convex mirror is a virtual image.

Converting the image distance to centimeters, we have:

di = 0.289 m × 100 cm/m

= 28.9 cm

Therefore, the image of the patient is located approximately 28.9 cm from the convex mirror.

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The answer is expression \($\sqrt{7!}$\) simplifies to \($12\sqrt{35}$\).

What is the factorial?

Factorial is a function that is used to find the number of possible ways in which a selected number of objects can be arranged among themselves.

We can simplify\($\sqrt{7!}$\) by dissecting it into its component components thanks to the property that the square root of a product is equal to the product of the square roots of the factors.

We can simplify the expression \($\sqrt{7!}$\) by first evaluating\($7!$\), which is:

\(7! &= 7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1 \&= 5040\)

Therefore, \($\sqrt{7!}$\) = \(\sqrt{5040}$\) We can further simplify this expression by factoring 5040 into its prime factors:

\(5040 &= 2^4 \cdot 3^2 \cdot 5 \cdot 7\)

Taking the square root of 5040, we get:

\(\sqrt{5040} &= \sqrt{2^4 \cdot 3^2 \cdot 5 \cdot 7} \&= \sqrt{2^4} \cdot \sqrt{3^2} \cdot \sqrt{5} \cdot \sqrt{7} \&= 2^2 \cdot 3 \cdot \sqrt{5} \cdot \sqrt{7} \&= 12\sqrt{35}\)

Therefore, The answer is expression \($\sqrt{7!}$\) simplifies to \($12\sqrt{35}$\).

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If the null hypothesis is true and there is no treatment effect, the expected value on average for the F-ratio would be 1.00. The correct answer is option (b) 1.00

In hypothesis testing using the F-test, the F-ratio is calculated by dividing the variance between groups (treatment effect) by the variance within groups (random variation). When the null hypothesis is true and there is no treatment effect, the numerator (variance between groups) and the denominator (variance within groups) would be similar, resulting in an F-ratio close to 1.

Therefore, the correct answer is b. 1.00, as the expected value for the F-ratio would be around 1 when the null hypothesis is true and there is no treatment effect.

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The extended ring R[a], obtained by adjoining an element a to a ring R, is indeed a ring isomorphic to R. This is demonstrated by showing that R[a] satisfies the properties of a ring and by constructing an isomorphism between R[a] and R.

To prove that adjoining an element a to a ring R gives a ring isomorphic to R, we need to show that the extended ring R[a] satisfies the definition of a ring and that there exists an isomorphism between R[a] and R.

First, let's define the extended ring R[a]. The elements of R[a] are represented as polynomials in a with coefficients from R. An element in R[a] can be written as:

R[a] = {r₀ + r₁a + r₂a² + ... + rₙaⁿ | r₀, r₁, r₂, ..., rₙ ∈ R}

where n is a non-negative integer and r₀, r₁, r₂, ..., rₙ are coefficients from R.

Now, let's prove the two main properties of a ring for R[a]:

Closure under addition and multiplication:

For any two elements (polynomials) p = r₀ + r₁a + r₂a² + ... + rₙaⁿ and q = s₀ + s₁a + s₂a² + ... + sₘaᵐ in R[a], the sum p + q and product p * q are also elements of R[a]. This can be proven by applying the distributive property and associativity of addition and multiplication.

Existence of additive and multiplicative identities:

The additive identity in R[a] is the polynomial 0, and the multiplicative identity is the polynomial 1. These identities satisfy the properties of an additive and multiplicative identity, respectively, when added or multiplied with any element in R[a].

Next, we need to show that there exists an isomorphism between R[a] and R, which means there is a bijective map that preserves the ring structure.

Consider the function φ: R[a] → R defined as φ(r₀ + r₁a + r₂a² + ... + rₙaⁿ) = r₀. This function maps each polynomial in R[a] to its constant term.

We can prove that φ is an isomorphism by verifying the following:

a) φ preserves addition: φ(p + q) = φ(p) + φ(q) for any p, q in R[a].

b) φ preserves multiplication: φ(p * q) = φ(p) * φ(q) for any p, q in R[a].

c) φ is bijective: φ is both injective and surjective.

The proofs for these properties involve applying the distributive property and associativity of addition and multiplication, and considering the coefficients of the polynomials.

Hence, we have shown that adjoining an element a to a ring R gives a ring isomorphic to R, denoted as R[a] ∼ R.

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Answer:

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The time they arrive at the destination is 9:24 am the next day

How to determine the time they arrive at the destination.

From the question, we have the following parameters that can be used in our computation:

Time = 4 pm

Distance = 64 km

Start by calculating time taken for the father to ride the horse and son to walk the first 32 km:

Time = Distance / (Difference between rates of father and son)

Time = 32 km / (8 km/h - 3 km/h)

Time = 32 km / 5 km/h

Time = 6.4 hours

Calculate time taken for the son to ride the horse and father to walk the remaining 32 km:

Time = Distance / (Difference in Speed)

Time = 32 km / (8 km/h - 4 km/h)

Time = 32 km / 4 km/h

Time = 8 hours

So, we have

Total time = 6.4 hours + 8 hours + 3 hours break + 4 pm

Evaluate

Total time = 9:24 am the next day.

Dilating the triangle TRW would change the size of the triangle

The ordered pair that best represents the location of point R′ is (nRx,nRy)

The coordinates of the point R would be represented as:

R = (Rx,Ry)

The scale of dilation (k) is given as:

k = n

Given that the center of dilation is the origin, the location of point R' would be:

R' =R * k

So, we have:

R' = (Rx,Ry) * n

Evaluate the product

R' = (nRx,nRy)

Hence, the ordered pair that best represents the location of point R′ is (nRx,nRy)

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Answer:  (−3n, −5n)

I did the test

Answer:

Tristemente, no podemos ayudar pero the recomiendo que lo intentes tú mismo

The Equation of circle is (x-2)² +(y+ 8)² = 7²

The standard form of a circle with center (h, k) and radius r is given by the equation:

(x-h)²  + (y-k)² = r²

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

In this case, the center of the circle is (2, -8) and the radius is 7.

Plugging these values into the equation, we have:

(x- 2)² + (y- (-8))² = 7²

Simplifying further:

(x-2)² +(y+ 8)² = 7²

So, the equation in standard form for the circle with center (2, -8) and radius 7 is:

(x-2)² +(y+ 8)² = 7²

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The probability that at least 75 rolls are necessary to exceed a total sum of 275 is approximately 0.293.

Let X be the random variable denoting the total number of rolls required to exceed 275. We want to calculate P(X >= 75). The probability of rolling a number greater than 5 is 1/3, and the probability of rolling a number less than or equal to 5 is 2/3. Therefore, the expected value of a single roll is

The variance of a single roll is

Using the properties of the geometric distribution, we can calculate the probability that it takes at least 75 rolls to achieve a sum greater than 275:

P(X >= 75) = (1 - P(X < 75)) = (1 - (1 - (275/3.67)/75\()^{(75)}\)) = 0.293.

Therefore, the probability that at least 75 rolls are required is approximately 0.293.

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The probability that 4 students arrive during a randomly selected office hour is 0.134, or about 13.4%.

To find the probability that 4 students arrive during a randomly selected office hour, we need to use the Poisson distribution formula.

The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space.

The formula for the Poisson distribution is:

P(X = x) = (e^-λ * λ^x) / x!

Where X is the number of events, λ is the average number of events per interval, and e is the mathematical constant e.

In this case, λ = 2.5, since the average number of students who arrive during an office hour is 2.5. So, we can plug in λ and x = 4 into the formula:

P(X = 4) = (e^-2.5 * 2.5^4) / 4!

P(X = 4) = (0.082 * 39.0625) / 24

P(X = 4) = 0.134

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Answer:

M + 20 cookies.

Step-by-step explanation:

The number of cookies that Chandler has can be represented by the expression M + 20, where M is the number of cookies that Monica has. This is because it is given that Chandler has 20 more cookies than Monica, so we need to add 20 to Monica's number of cookies to get Chandler's number of cookies. Therefore, if Monica has M cookies, then Chandler has M + 20 cookies.

Answer:

Step 3

Step-by-step explanation:

Given

\((5 - 2)^ 2 + 23 * 4\)

Required:

Determine the first step where she made mistake

Her Step 1:

\((3)^ 2 + 23 * 4\) --- This is correct because she solved the bracket first

Her Step 2:

\(9 + 23 * 4\) --- This is correct because she solved 3^2 as 9

Her Step 3:

\(9 + 9 * 4\) --- This is incorrect because 23 * 4 is not equivalent to 9 * 4

Hence, her first mistake is in step 3.

The correct expression would have been

\(9 + 92\)

Then

\(= 101\)

He equation that rightly shows the Commutative Property of addition is

10 x3/10 = 3/10 x 10

The Commutative Property of Multiplication states that changing the order of the factors doesn't change the product. In other words, when you multiply two figures, it doesn't count which number comes first. The equation 10 x3/10 = 3/10 x 10 is an illustration of this property, as both sides of the equation represent the same value, indeed though the order of the factors is different.

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