What are the domain and range of the function below?

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

\( \longrightarrow \tt5x + 10 = 3x + 3x\)

\( \longrightarrow \tt \: 5x + 10= 6x\)

\( \longrightarrow \tt10 = 6x - 5x\)

\( \longrightarrow \tt \: 10 = x\)

Replacing value :

✯\( \tt m \: \angle \: \: BCD = 5 \times 10 + 10 = \boxed{ \tt{60}} \)

-------------- HappY LearninG <3 -------

A 95% confidence interval for the percentage of obese U.S. adults aged 20 years and over was found to be 22.4% to 23.5%. To determine the sample size, additional information is needed.

To determine the sample size based on a confidence interval, we need to know the margin of error and the desired level of confidence. The margin of error represents the maximum allowable difference between the sample estimate and the true population parameter. In this case, the confidence interval provided (22.4% to 23.5%) gives us the range of plausible values for the true percentage of obese U.S. adults. However, the sample size cannot be determined solely from this information.

To calculate the sample size needed to estimate the population percentage with a given margin of error and confidence level, we would require additional information such as the margin of error or the desired level of confidence. For example, if we assume a margin of error of 1% and a 95% confidence level, we can calculate the sample size using appropriate statistical formulas. The sample size calculation involves factors such as the estimated population proportion, the desired level of confidence, the margin of error, and the variability of the population. Without this information, it is not possible to determine the sample size based solely on the provided confidence interval.

In summary, the sample size cannot be determined solely from the provided confidence interval (22.4% to 23.5%). Additional information, such as the margin of error or the desired level of confidence, is needed to calculate the sample size accurately.

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Answer:

Area of the circle=π×(radius)²

→3.14×(0.3)²=3.14×0.09=0.28yd²

0.28yd² is the right answer.

To find the reference angle of a negative angle, follow these steps:

Determine the positive equivalent: Add 360 degrees (or 2π radians) to the negative angle to find its positive equivalent. This step is necessary because reference angles are always positive.

Subtract from 180 degrees (or π radians): Once you have the positive equivalent, subtract it from 180 degrees (or π radians). This step helps us find the angle that is closest to the x-axis (or the positive x-axis) while still maintaining the same trigonometric ratios.

For example, let's say we have a negative angle of -120 degrees. To find its reference angle:

Positive equivalent: -120 + 360 = 240 degrees

Subtract from 180: 180 - 240 = -60 degrees

Therefore, the reference angle of -120 degrees is 60 degrees.

In summary, to find the reference angle of a negative angle, first, determine the positive equivalent by adding 360 degrees (or 2π radians). Then, subtract the positive equivalent from 180 degrees (or π radians) to obtain the reference angle.

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The formula for the midpoint is as follows:

Let:

Substitute the coordinates into the formula and then simplify.

Answer:181/250

Step-by-step explanation:

The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.9476

To determine the probability

The given parameters are:

True proportion and the mean (p) = 0.06

The samples size (n) = 235

Start by calculating the standard deviation using

\(\sigma = \sqrt{\frac{p(1-p)}{n} }\)

This gives

\(\sigma = \sqrt{\frac{0.06\;*\;(1-0.06)}{235} }\)

\(\sigma = \sqrt{\frac{0.06\;*\;(0.94)}{235} }\)

\(\sigma = \sqrt{\frac{0.0564}{235} }\)

\(\sigma = \sqrt{0.00024 }\)

\(\sigma = 0.01549\)

Next, we calculate the x values

\(x = x_{1} \pm x_{2}\)

where x₁ = 0.06 and x₂ = 0.03

x = x₁ + x₂ , x₁ - x₂

x = 0.06 + 0.03, 0.06 - 0.03

x = 0.09, 0.03

Calculate the z score for both x values

\(z = \frac{x\; - \; \mu}{\sigma}\)

\(z = \frac{0.09\; - \; 0.06}{0.01549}, \frac{0.03\; - \; 0.06}{0.01549}\)

\(z = \frac{0.03}{0.01549}, \frac{-0.03}{0.01549}\)

\(z = 1.94, -1.94\)

The p values at the z scores are:

p = 0.9738, 0.0262

Note: refer to z tables to find the p values

Calculate the difference

p = 0.9738 - 0.0262

p = 0.9476

Hence, the probability that the sample proportion will differ from the population proportion by less than 0.03 is 0.9476

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Answer:

-8x+8

Step-by-step explanation:

8x-7x=x-9x=-8x

5+3=8

true - searching for a value in a binary search tree takes O(log n) time.

a binary search tree is a data structure where each node has at most two children, and the left child is always smaller than the parent while the right child is always larger. This structure allows for efficient searching, as we can compare the value we are searching for with the value of the current node and traverse either the left or right subtree accordingly. By doing so, we can eliminate half of the remaining nodes with each comparison, leading to a time complexity of O(log n).

searching for a value in a binary search tree takes O(log n) time, which is a relatively efficient algorithmic complexity. However, it's important to note that this assumes the tree is balanced and does not take into account worst-case scenarios where the tree may be heavily skewed.

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The frequency of 1 is option (d) 973

Reselecting cases means selecting a subset of data that meets specific criteria. In this case, you will need to identify which cases to keep based on certain conditions. After reselecting cases, the next step is to define the variable TX + Y. This means that you will perform an operation on two existing variables, T and Y, and create a new variable that is the sum of T and Y. The result will be a numerical variable.

To summarize, you will need to follow these steps:

Reselect cases based on specific criteria.

Define the variable TX + Y as the sum of T and Y.

Recode the numerical variable into a categorical variable with two categories: G-1 İFT <= 10 and G=0 if T>10.

Calculate the frequency of category 1 in the new variable G.

Finally, to answer the question, you will need to calculate the frequency of category 1 in the variable G. This means that there are 973 cases where the value of TX + Y is less than or equal to 10.

The correct answer is option d. 973.

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Value of is in the plane spanned will be -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].

If y is on the plane covered by v1 and v2, v1 and v2 can be combined linearly to form y.

Y is equal to av1 plus bv2, where a and b are constants.

[4,-1,h] = a[1,2,-1] + b[-2,-1,1]

According to the laws of vector addition and multiplication, [4,-1,h] = [a - 2b,2a - b, -a + b]. A vector is equal if each of its components is equal.

4 = a - 2b

-1 = 2a - b

h = -a + b

From the first two equations, we can solve for a and b to obtain h:

a = -2

b = -3

h = -1

As we can see, -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].

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Full Question:

For what value of h is y in the plane spanned by v1 and v2?

11/20 of the 200 video game players voted for Unknown Kingdom, which is 11/20 * 200 = 110 players.

Survey means to gather information or data by asking questions to a group of people. A survey can be conducted in various forms such as through interviews, questionnaires.

To write 55% as a rate per 100,

we write it as 55/100 = 55%.

To find an equivalent ratio where the number of players surveyed is 200, we need to multiply the ratio by 200.

So, the equivalent ratio becomes 55/100 * 200 = 110/200 = 11/20.

Therefore, 11/20 of the 200 video game players voted for Unknown Kingdom, which is 11/20 * 200 = 110 players.

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Answer:

I don't think there is a way the values can be determined...

If a and b are in different triangles then the true option is that values of a and b can't be determined.

A triangle is a two dimensional figure having three sides and three angles.

Sum of angles of a triangle is equal to 180° whether it is a right angled or not.

In first triangle one angle is x°, second is 75° and third one is a° and in second triangle one angle is 60°, second is y°, third one is b°.

Sum of angles in first triangle is x+75+a=180

Sum of angles in second triangle is y+60+b=180

because any relationship between x and y is not given in the questions so values of a and b cannot be determined.

Hence the correct option is D which is that values of a and b cannot be determined.

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Answer:

D

Step-by-step explanation:

They're not similar because the angle lengths are different.

After 40 hours the population of bacteria will be equals to 318 hours.

We can calculate the total population growth using the following equation:

A(t)= A₀× 2ᵗ/¹⁵

Where, A(t) --> the total population

A₀ --> the initial population

t --> the time in hours

From the statement we know that the population of bacterias doubles every 15 hours, so, using the formula we have: A(15) = A₀ × 2ᵗ/¹⁵

The initial population is = 50 , then

A(15) = 50×2¹⁵/¹⁵ = 100

It shows that every 15 hours, the population of bacterias doubles it size. We are asked to calculate the popualation after 40 hours, so:

A(40) = 50 × 2⁴⁰/¹⁵

= 6.35 × 50 = 317.5 ~ 318

So, after 40hours the population of bacteria will be 318.

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Answer:

1/-7x

Step-by-step explanation:

All you have to do is find the distance between both points.

Answer: A polygon that does not have all sides equal and all angles equal.

Step-by-step explanation:A polygon that does not have all sides equal and all angles equal. (A polygon is "regular" only when all angles are equal and all sides are equal, otherwise it is irregular.)

Answer:

\(\boxed{x = -31}\)

\(\boxed{y = -62}\)

\(\boxed{z = -6}}\)

Step-by-step explanation:

There are a couple of properties of parallelograms that can help solve for the unknowns

Using property 1 that opposite angles are equal we have:
-4x - 5 = 119

⇒  -4x = 119 + 5

⇒ -4x = 124

⇒ x = 124/-4

⇒ x = -31

Using property 2 that consecutive angles are supplementary on angles
(-y - 1)° and 119°:

(- y - 1) + 119 = 180

⇒ - y - 1 + 119 = 180

⇒ - y + 118 = 180

⇒ - y = 180 - 118

⇒ - y = 62

⇒ y = -62

Using property 2 for angles (-10z - 1)° and 119°
(-10z + 1) + 119 = 180

- 10z + 1 + 119 = 180

⇒ - 10z + 120 = 180

⇒ -10z = 180 - 120

⇒ -10z = 60

⇒ z = 60/-10

⇒ z = -6

\(e^{-5 \lambda}\) is the probability that we have to wait for more than 5 min for the bus to arrive.

So, \(f_X(x)=\lambda e^{-\lambda x}, x \geq 0\) ⇒ \(P(x \geq 5)=\int_5^{\infty} f_X(x) d x\)

Now, solving the above function as follows:

\(\begin{aligned}&P(x \geq 5)=\int_5^{\infty} f_X(x) d x \\&=\int_5^{\infty} \lambda e^{-\lambda x} d x \\&=\left.\right|_5 ^{\infty} \frac{\lambda e^{-\lambda x}}{-\lambda} \\&=\left.\right|_5 ^{\infty}-e^{-\lambda x} \\&=e^{-5 \lambda}\end{aligned}\)

Therefore, the probability that we have to wait for more than 5 min for the bus to arrive is \(e^{-5 \lambda}\).

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The correct question is given below:
Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable with probability density function  \(f_X(x)=\lambda e^{-\lambda x}, x \geq 0\). Suppose you arrive at the bus stop precisely at noon. Find the probability that you have to wait for more than 5 min for the bus to arrive

Answer:

y+1-1x

Step-by-step explanation:

.................

In order to answer the above question, we may thus state that the type of statistical inference in this scenario is null hypothesis testing.

A type of statistical hypothesis known as a null hypothesis claims that a particular collection of observations has no significance in statistics. The viability of theories is evaluated using sample data. Occasionally referred to as "zero," and represented by H0. The assumption made by researchers is that there may be a relationship between the factors. The null hypothesis, on the other hand, asserts that such a relationship does not exist. Although it might not seem significant, the null hypothesis is an important part of study.

The type of statistical inference in this scenario is hypothesis testing.

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The approximate probability that the pH measurement of a randomly selected water specimen is between 7.5 and 8.2 is approximately 0.7011 or 70.11%.

To find the approximate probability that the pH measurement of a randomly selected water specimen is between 7.5 and 8.2, we can use the properties of the normal distribution.

Given:

Mean (μ) = 8

Standard deviation (σ) = 0.3

We need to find the probability of the pH measurement falling between 7.5 and 8.2. Let's denote this as P(7.5 < X < 8.2), where X represents the pH measurement.

To calculate this probability, we can standardize the values using the z-score formula:

z1 = (7.5 - 8) / 0.3

z2 = (8.2 - 8) / 0.3

Calculating the z-scores:

z1 ≈ -1.67

z2 ≈ 0.67

Now, we can look up the z-scores in the standard normal distribution table or use a calculator to find the corresponding probabilities.

Using a standard normal distribution table or calculator, we can find:

P(Z < z1) ≈ P(Z < -1.67) ≈ 0.0475 (approximately)

P(Z < z2) ≈ P(Z < 0.67) ≈ 0.7486 (approximately)

To find the probability between 7.5 and 8.2, we subtract the lower probability from the upper probability:

P(7.5 < X < 8.2) ≈ P(Z < z2) - P(Z < z1)

≈ 0.7486 - 0.0475

≈ 0.7011

Therefore, the approximate probability that the pH measurement of a randomly selected water specimen is between 7.5 and 8.2 is approximately 0.7011 or 70.11%.

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Answer:

14 days

Step-by-step explanation:

you divide the total distance, 35, by the amount of miles ran per day, 2.5, to get 35/2.5=14.

Answer:

15 whole hours.

Step-by-step explanation:

The growth factor is 1.30 / hour.

(a) After 4 hours there are 20000*(1.30)4

= 57,122.

(b) 1,000,000 = 20000(1.30)^x   where x = number of hours

(1.30)^x =  1,000,000 / 20000

(1.30)^x =  50

x log 1.30 = log 50

x = log50 / log 1.30

x = 14.91

So the number is greater than 1 million at 15 hours to nearest hour.

Answer:

D

Step-by-step explanation:

13-(-14)=13+14

          =27

Answer:

y = -0.5x - 3.5

Explanation:

Take two points: (1, -4), (3, -5)

Find slope:

\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

\(\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}\)

Equation:

\(\sf y- y_1 = m (x - x_1)\)

\(\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)\)

\(\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}\)

\(\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4\)

\(\rightarrow \sf y = -0.5 x -3.5\)

The formula of a line is:

\(f(x) = kx + b\)

k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.

We can see 2 points:
A (1, -4)
B (3, -5)

We can make a system of equations:

\(k*1+b=-4\\k*3+b=-5\\\)

From second equation:

\(b = -5 - 3k\)

Let's put b in first equation:

\(k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}\)

Now we can find b:

\(b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5\)

The answer is:
-0.5x -3.5

Answer:

No Mason is not correct you would use fractions and find a common denominator such as 12 and 2/3 would be 8/12 and 3/4 would be 9/12 therefore the two ratios are not equivelent

No, the statement is not correct.

Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b

The example given here is not relevant.

This is because if 2:3 is added by 1/1

gives 3/4 or 3:4

but  3:4 cannot be more simplified.

So, let us make the equivalent denominator for both

2/3*4*4= 8/12

3/4*3/3=9/12

So, 2:3 ≠3:4

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