Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 125 and a​ y-intercept of negative 400. Complete parts​ (a) and​ (b) below. a. What is the equation of the regression​ line? Select the correct choice below and fill in the answer boxes to complete your choice.

Answer:

2 1/6 lbs. of chicken left

Step-by-step explanation:

4 1/2 - 2 1/3

9/2 - 7/3

27/6 - 14/6

13/6 = 2 1/6

Answer:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

Step-by-step explanation:

Given vector equation:

\(\textbf{r} = \textbf{i} - 5\textbf{j} + 4\textbf{k} + \lambda(3\textbf{i} + \textbf{j} - 2\textbf{k}) + \mu(-\textbf{i} + 2\textbf{j} + \textbf{k})\)

The vector 3i + j - 2k is perpendicular to n.

The vector -i + 2j + k is perpendicular to n.

\(\textsf{So}\;\;\textbf{n}=\left|\begin{array}{ccc}\textbf{i}&\textbf{j}&\textbf{k}\\3&1&-2\\-1&2&1\end{array}\right|\)

        \(=\textbf{i}\left|\begin{array}{rr}1&-2\\2&1\end{array}\right|-\textbf{j}\left|\begin{array}{rr}3&-2\\-1&1\end{array}\right|+\textbf{k}\left|\begin{array}{rr}3&1\\-1&2\end{array}\right|\)

        \(=\textbf{i}(1 \cdot 1 - (-2) \cdot 2)-\textbf{j}(3 \cdot 1-(-2) \cdot (-1))+\textbf{k}(3 \cdot 2-1 \cdot (-1))\)

        \(=\textbf{i}(1 +4)-\textbf{j}(3-2)+\textbf{k}(6+1)\)

        \(=5\textbf{i}-\textbf{j}+7\textbf{k}\)

So the equation of the plane written in Cartesian form is:

\(5x-y+7z+d=0\)

Substituting (1, -5, 4) gives:

\(5(1)-(-5)+7(4)+d=0\)

\(5+5+28+d=0\)

\(38+d=0\)

\(d=-38\)

Therefore, the given vector equation in Cartesian form is:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

Step-by-step explanation:

let

(-7,-8) =(x1, y1)

and (-6,7)=(x2, y2)

by the formula

d=√(y2-y1) ²+(x2-x1) ²

=√(7+8)²+(-6+7)²

=√15²+1²

= √225+1

= √226

The mean should be calculated for data sets A, B, C, and D.

It is useful to take into account the nature of the data and any potential outliers when deciding whether to choose the mean or the median as the measure of center in a data set.

When the data is symmetrically distributed with no major outliers, the mean is usually a better choice. It affects extreme values and gives an indication of the average value.

The median, on the other hand, is often preferred when the data is skewed or contains outliers. It represents the middle value when the data is ordered, and it is less affected by extreme values.

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Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

The third side must be greater than 9 and less than 17.

9 < x < 17

Step-by-step explanation:

The Triangle Inequality Theorem says that if you know two sides of a triangle, and you subtract them and you add them (get two separate numbers), the third side will be in between those numbers. So if you have 4 and 13 as the two sides.

13 - 4 is 9. The third side has to be bigger than 9.

Then, 13 + 4 is 17. The third side has to be smaller than 17.

9 < x < 17

The probability that the next person to purchase this car will request at least one automatic transmission or built-in GPS is 43%.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.

We solve this question by treating these probabilities as Venn sets.

Event A: Requesting automatic transmission

Event B: Requesting built-in GPS

70% of all buyers request an automatic transmission

This means that

55% of all buyers request built-in GPS

This means that

77% of all buyers request both automatic transmission and built-in GPS.

The next person to purchase this car will request at least one automatic transmission or built-in GPS

P(AUB) = P(A) + P(B) - P(\(\cap\)B)

P(AUB) = 0.7 + 0.55 - 0.77

P(AUB)  = 0.43 or 43%

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Answer:

9

Step-by-step explanation:

Answer:

P = 0.309

Step-by-step explanation:

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

I think that the answer is 2.07

Step-by-step explanation:

Answer:

15 smukeroos

Step-by-step explanation:

The cost of an entrance ticket on the trip to Spring Shot trampoline park is equal to $ \(16\frac{1}{2}\).

What do you mean by algebraic expressions ?

Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.

It is given that the total cost of trip for Lorenzo and his friends is $68.

Let's assume the cost of the entrance ticket be x.

The cost of entrance ticket for all of them = 4x

The fee added to entrance ticket is $2.

So , the algebraic expression can be written as :

2 + 4x = 68

reordering the like terms :

4x = 68 - 2

4x = 66

Dividing by 2 on both sides :

2x = 33

or

x = \(\frac{33}{2}\)

or

x = \(16\frac{1}{2}\)

Therefore , the cost of an entrance ticket on the trip to Spring Shot trampoline park is equal to $ \(16\frac{1}{2}\).

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Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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It’s true for all right triangles.

Answer:

A- \(5.12*10^{-4}\)

Step-by-step explanation:

1.6* 3.2

add the exponents so 10 to the -4

Answer:

2a squared - 4a

Step-by-step explanation:

12 a^2 - 3a - 10a^2 - a

12 - 10 = 2

-3 - 1 = -4

2a^2 - 4 a

Answer:

b. 2/3

Explanation:

Given the fraction:

We can write each of the numbers as a product below:

Next, cancel the common number, 9:

The simplified form of the fraction is 2/3.

Option B is correct.

Therefore, the simplified result of the expression (1/10x − 23) - (4/5x − 16) is (137x - 3)/10x.

A fraction is considered to be in its simplest form when the top and bottom can both be whole numbers and not smaller. To simplify a fraction, multiply the top and bottom by the biggest number that divides both values exactly (they must stay whole numbers).

To subtract the fractions (1/10x − 23) - (4/5x − 16), we first need to find a common denominator. The least common multiple of the denominators 10x and 5x is 10x, so we can rewrite the fractions as follows:

1/10x - 23 = (1/10x)(5/5) - (23/1)(10x/10x) = 5/50x - 230x/10x

4/5x - 16 = (4/5x)(2/2) - (16/1)(10x/10x) = 8/10x - 160x/10x

Now we can combine the fractions by subtracting the numerators:

(1/10x − 23) - (4/5x − 16) = (5/50x - 230x/10x) - (8/10x - 160x/10x)

= (5 - 23x)/10x - (8 - 160x)/10x

= (137x - 3)/10x

Therefore, the simplified result of the expression (1/10x − 23) - (4/5x − 16) is (137x - 3)/10x.

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Therefore, the simplified result of the expression (1/10x − 23) - (4/5x − 16) is (137x - 3)/10x.

When both the top and bottom can be whole numbers and are not smaller, a fraction is said to be in its simplest form. The top and bottom of a fraction can be multiplied by the largest number that divides both values equally to simplify the fraction (they must stay whole numbers).

To subtract the fractions (1/10x − 23) - (4/5x − 16), we first need to find a common denominator. The least common multiple of the denominators 10x and 5x is 10x, so we can rewrite the fractions as follows:

1/10x - 23 = (1/10x)(5/5) - (23/1)(10x/10x) = 5/50x - 230x/10x

4/5x - 16 = (4/5x)(2/2) - (16/1)(10x/10x) = 8/10x - 160x/10x

Now we can combine the fractions by subtracting the numerators:

(1/10x − 23) - (4/5x − 16) = (5/50x - 230x/10x) - (8/10x - 160x/10x)

= (5 - 23x)/10x - (8 - 160x)/10x

= (137x - 3)/10x

Therefore, the simplified result of the expression (1/10x − 23) - (4/5x − 16) is (137x - 3)/10x.

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The quadratic equation written in vertex form is:

y = (x + 1)^2 - 9

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

On the graph we can see that the vertex is at (-1, -9), then we have:

y = a*(x + 1)^2 - 9

Now we also can see that the y-intercept is y = -8, then evaluating in zero we should get:

-8 = a*(0 + 1)^2 - 9

-8 = a - 9

-8 + 9 = a = 1

The quadratic equation is:

y = (x + 1)^2 - 9

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Answer:

Probability distribution

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. Alternative hypothesis is a statement which we accept or reject based on the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

The answer is $3.91 hope it is help you

Not all linear transformations have a matrix representation. A counter-example is a linear transformation that changes the dimension of the vector space.

What is Linear transformation?

The function g(x) is a linear transformation if each term of each component of g(x) is a number times one of the variables.

For example, consider the linear transformation T: R^2 -> R^3 defined by:

T(x, y) = (x, y, 0)

This transformation maps each point in the xy-plane to a point in the x,y,z-space with z-coordinate 0. It is a linear transformation, since it preserves addition and scalar multiplication. However, it cannot be represented by a matrix, since it changes the dimension of the vector space.

The theorem that establishes the existence of a matrix representation for every linear transformation is known as the matrix representation theorem. It states that every linear transformation from a finite-dimensional vector space to another finite-dimensional vector space can be represented by a matrix with respect to suitable bases of the vector spaces. However, it does not apply to linear transformations that change the dimension of the vector space.

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Answer:

x = -12

Step-by-step explanation:

=> 1/2 (x-4) = -8

=> x-4 = -8 × 2

=> x-4 = -16

=> x = -16+4

=> x = -12

The statement that "an estimated regression coefficient is statistically significant if it is statistically different from 1" is false.

When we say that an estimated regression coefficient is statistically significant, we mean that it is statistically different from zero, not from 1.

The reason for this is that the null hypothesis in a hypothesis test for a regression coefficient is typically that the true value of the coefficient is zero. Therefore, if we reject the null hypothesis and find that the estimated coefficient is statistically significant, we conclude that there is evidence to suggest that the coefficient is not equal to zero and therefore has a non-zero effect on the response variable.

In some cases, we may be interested in testing whether a regression coefficient is equal to a specific value, such as 1. However, this would be a different hypothesis test with a different null hypothesis, and the result of this test would not necessarily be related to whether the coefficient is statistically significant or not.

Therefore, the statement that "an estimated regression coefficient is statistically significant if it is statistically different from 1" is not accurate.

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Answer:

7,009

Step-by-step explanation:

The reasonable domain for the function is (b) x > 0

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

The function f(x) = 75x + 100

Where x is the number of hours

f(x) is the total cost.

In this case, the number of hours cannot be negative or 0

This means that the values of x in the function would be x > 0

These values of x are the domain

So, the reasonable domain for the function os (b) x > 0

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