How much is 50% of 10 liters of milk?
How far is 50% of a 2,000-kilometer trip?
How long is 50% of a 24-hour day?
How can you find 50% of any number?

In summary, the difference between these two regression equations is mainly in the notation used to represent the regression coefficients, with lowercase letters used in simple linear regression models and uppercase letters used in multiple linear regression models.

In mathematics, an equation is a statement that asserts that two mathematical expressions are equal to each other. It usually contains one or more variables, which are placeholders for values that can vary. Equations are used to describe mathematical relationships and to solve problems. They can take many forms, such as linear equations, quadratic equations, polynomial equations, exponential equations, and so on. The specific form of an equation depends on the type of problem being solved and the mathematical relationships involved.

Here,

Both the regression equations ^y = b0 + b1x and Y = B0 + B1x are used to model the relationship between a dependent variable (y or Y) and an independent variable (x). However, the key difference between these two equations lies in the notation used to represent the regression coefficients.

In the first equation ^y = b0 + b1x, the regression coefficients are represented with lowercase letters (b0 and b1). This notation is typically used in simple linear regression models where there is only one independent variable. The hat symbol (^) over the y indicates that this is an estimated value of y based on the model.

In the second equation Y = B0 + B1x, the regression coefficients are represented with uppercase letters (B0 and B1). This notation is typically used in multiple linear regression models where there are two or more independent variables. The capitalization of the letters helps to distinguish them from the coefficients in the simple linear regression model.

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Answer:

what table

Step-by-step explanation:

Answer:

x

≥

−

1

Step-by-step explanation:

Answer:

The x,y that start with 1,4

Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Here,

Given :

customer uses 390 minutes , the monthly cost will be $178.

customer uses 940 minutes, the monthly cost will be $398.

To find an equation ,

where x is number of monthly minutes

and y is total monthly of splint plan.

So , equation is :

=> y =mx +b

For first case :

=> 178 = 390x + b

Second case :

=> 398 = 940x + b

Solve for x:

=> 178 - 390x = 398 - 940x

=> -200x = - 550

=> x = 550/200

=>x = 55/20

=>x = 11/4

=> x = 2.75

For value of b

=>  178 = 390(2.75) + b

=> 178 - 1072.5 = b

=> -894.5 = b

B)

=> y = 866(2.75) - 894.5

=> y = 2381.5 - 894.5

=> y = 1487

Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.

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The equation of the graph g(x)  is \(3^{x-6}\)

What is a graph ?

A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;

In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.

The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)

If the graph of the function  f(x) = 3^x is translated 6 units to the right , then the function becomes

g(x) = f(x - 6)

     = \(3^{x-6}\)

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Answer:

40

Step-by-step explanation:

angles QPR and RPS are complimentary, so they equal 90, or angle QPS, so you can set up the equations like so:

7x - 9 + 4x + 22 = 90

Combine like terms:

11x + 13 = 90

Subtract 13 from each side:

11x = 77

Divide each side by 11:

x=7

Then use this value in the angle that you are finding:

7(7) - 9

49 - 9

40

40 is your answer

Hope this helps!

\( \sf \: 70 \times 20\)

\(\sf \longmapsto1400\)

OR the question can also be written as

\( \sf \: 70 (20)\)

\(\sf \longmapsto1400\)

Answer:

cost when 400 miles is driven is $143.

Step-by-step explanation:

Model for cost calculation: C=0.32m + 15

We have to find cost when no. of miles driven is 400.

To find that cost we need to plug 400 in place of m.

C=0.32m + 15

=> c = 0.32*400 + 15

=> c = 128 + 15 = 143

Thus, cost when 400 miles is driven is $143.

Answer:

The C-intercept, 15, means that if Janelle drove 0 miles on a particular day it would cost her 15 dollars to rent the car for that day.

Given:

Vertices of a square are A(-4,6), B(5,6) C(4,-2), and D(-5,-2).

To find:

The intersection of the diagonals of square ABCD.

Solution:

We know that diagonals of a square always bisect each other. It means intersection of the diagonals of square is the midpoint of diagonals.

In the square ABCD, AC and BD are two diagonals. So, intersection of the diagonals is the midpoint of both AC and BD.

We can find midpoint of either AC or BD because both will result the same.

Midpoint of A(-4,6) and C(4,-2) is

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

\(Midpoint=\left(\dfrac{-4+4}{2},\dfrac{6+(-2)}{2}\right)\)

\(Midpoint=\left(\dfrac{0}{2},\dfrac{6-2}{2}\right)\)

\(Midpoint=\left(\dfrac{0}{2},\dfrac{4}{2}\right)\)

\(Midpoint=\left(0,2\right)\)

Therefore, the intersection of the diagonals of square ABCD is (0,2).

Answer:

Explained below.

Step-by-step explanation:

A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.

While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.

A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.

Answer:

3) 8^10

Step-by-step explanation:

Use formula: (same base)

a^m × a^n = a^m+n

So,

8^3 × 8^7 = 8^3+7

= 8^10

Answer: 1.3

Step-by-step explanation: Ok, let's make a number line...

0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6

From the number line, the only number that fits is 1.3

I hope this helps!

Answer:

1.3

Step-by-step explanation:

Hope this helps have a wonderful day

Answer:

5.6556 or round it to 6

Step-by-step explanation:

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

????????????????????????

Answer:

\(y = 2.25x \\ \boxed{y = \frac{9}{4} x}\)

Coordinates :---

• (x, y)

→(-2, -9/2)

→(-1, -9/4)

→(0, 0)

→(1, 9/4)

→(2, 9/2)

By using the given information we can infer the domains of the function, and we will see that the piecewise function is:

c(x) = $15*x   if  0 ≤ x ≤ 4

c(x) = $60 + 9*(x - 4)   if x > 4.

We know that the print charges $15 for each of the first four lines on an add, and $9 for each additional line.

Then we will have one piece for x between 0 and 4, and another piece for x larger than 4. The function will be:

c(x) = $15*x   if  0 ≤ x ≤ 4

c(x) = $60 + 9*(x - 4)   if x > 4.

Where the y-intercept on the second part is equal to the cost for the first four lines of the add.

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The calculated value of the side length of ​ QR is 60 mm

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

6 mm      24 mm

5 mm      20 mm

15 mm

The above means that

Scale factor = 24/6

So, we have

Scale factor = 4

This means that

Length QR = 4 * 15 mm

Evaluate

QR = 60 mm

Hence, the side length QR is 60 mm

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By solving a linear equation we will see that there were 6 hours of labor.

We know that the total cost is composed by a fixed amount of $365 plus $89 per hour of labor, so if there are x hours of labor, the total cost will be:

c(x) =  $365 + x*$89

We know that the total cost is $899, then we can write the linear equation:

$899 = $365 + x*$89

$899 - $365 = x*$89

($899 - $365)/$89 = x = 6

So there were 6 hours of labor.

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Answer:

Step-by-step explanation:

(0,0)

i hope this helps

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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Answer:

since .45 times 1 = .45 plus  __ zeros bascially move the decimal ____ times (the amount of zeros)

Step-by-step explanation:

weebs rule

Since .45 times 1 = .45 plus 2 zeros basically move the decimal 4 times

Answer:

Step-by-step explanation:

We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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Answer:

0.001967 per gallon

Step-by-step explanation:

19.67/10000 = 0.001967

Answer:

see the attachment photo!

Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

1. We are given the following premises:

  - p ⟹ ¬q (Premise 1)

  - q V r (Premise 2)

  - p V u (Premise 3)

  - ¬r (Premise 4)

2. To prove the conclusion, u, we need to use the premises and apply inference rules.

3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.

4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.

5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.

6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.

7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.

8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.

9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.

10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

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Answer:

Step-by-step explanation:

.................8908989