If a least-squares regression line fits the data well, what characteristic should the residual plot exhibit?

Answer: If the army regiment had 400 soldiers with provisions for 80 days, the food would last each soldier for 80 days / 400 soldiers = 0.2 days per soldier.

If 80 soldiers moved out, the number of soldiers remaining in the regiment would be 400 soldiers - 80 soldiers = 320 soldiers.

Since the amount of provisions has not changed, the food would last for 80 days / 320 soldiers = 0.25 days per soldier.

Therefore, the food would last the 320 soldiers for 0.25 days * 320 soldiers = 80 days.

Step-by-step explanation:

The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

[tex]\rm 4 \times (10^{-3x})=18[/tex]

Simplify the equation, then we have

[tex]\begin{aligned} \rm 4 \times (10^{-3x}) &=18\\\\\rm (10^{-3x}) &=4.5 \end{aligned}[/tex]

Take a log with base 10 on both sides, then we have

- 3x log₁₀ 10 = log₁₀ 4.5

- 3x = 0.6532

x = -0.2177

The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.

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Answer:Rewrite the equation in vertex form.

Tap for more steps...

y

=

4

(

x

−

1

)

2

−

9

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of

a

,

h

, and

k

.

a

=

4

h

=

1

k

=

−

9

Since the value of

a

is positive, the parabola opens up.

Opens Up

Find the vertex

(

h

,

k

)

.

(

1

,

−

9

)

Find

p

, the distance from the vertex to the focus.

Tap for more steps...

1

16

Find the focus.

Tap for more steps...

(

1

,

−

143

16

)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x

=

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

no idea sorry :/

The length of the altitude CH is 17.234.

Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.

The figure for the triangle is given below.

Here the area of a triangle can be found in two ways.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

Consider the triangle ABC given below.

Area of the triangle when considered base as BC and altitude as AC is,

Area, A = [tex]\frac{1}{2}[/tex] × BC × AC

BC = AB Sin (50) = 35 sin(50)

AC = AB Sin (40) = 35 sin(40)

A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))

Area of the triangle when considered base as AB and altitude as CH is,

Area, A = [tex]\frac{1}{2}[/tex] × AB × CH

A = [tex]\frac{1}{2}[/tex] × 35 × CH  

Area of the same triangle will be equal when find in different ways.

[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH  

Cancelling the terms which are on both sides,

CH = 35 sin(50) sin(40)

CH = 35 × 0.766 × 0.643

CH = 17.234

Hence the length of the altitude is 17.234.

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x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1

x = -1, y = 6, z = 1 is the solution.

Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]

the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]

we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.

operating R₂→R₂-R₁ , R₃→R₃-R₁

[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]

operating, R₃→R₃-3R₃

~  [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]

which is the row echelon, form of the matrix [A:B]

we have rank of [A:B] = the number of the non zero rows in echelon form = 2

also by the same elementary transformation we get,

A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]

∴ rank of A = 2

since rank A = rank  [A:B] = 2 < number of unknowns

therefore, the given equation are consistent and will have an infinite number of solutions.

We see that the given system of equations is equivalent to the matrix equation

[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]  =  [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]

which gives the equations x + y + z = 6 ........(1)

and y + 2z = 8 .......(2)

from (2), y = 8 - 2z, putting the value of y in (1) we get,

x = 6 - y - z = 6 (8 - 2z) z = z - 2

taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,

if k = 1

x = -1, y = 6, z = 1 is the solution.

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Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To find out how much Leo Gandolfi saves by paying off the loan early, we need to first calculate how much interest he would pay if he were to continue making payments for the full 6-month term of the loan.

The total interest on the loan for the full 6 months can be calculated as:

Total interest = Total payments - Loan amount

We know the loan amount is $1,800, and the monthly payment is $310.50, so the total payments for the full 6 months would be:

Total payments = Monthly payment x Number of payments

Total payments = $310.50 x 6 = $1,863

Therefore, the total interest paid over the 6-month term of the loan would be:

Total interest = $1,863 - $1,800 = $63

Now, we need to calculate how much interest Leo Gandolfi would pay if he were to pay off the loan after making 4 payments.

The remaining balance on the loan after 4 payments is $612.34, so if Leo were to make one more payment, the remaining balance would be:

Remaining balance = $612.34 - $310.50 = $301.84

To calculate the interest paid on this remaining balance, we need to calculate the interest for one month:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 12% / 12 = 1%

Monthly interest = Monthly interest rate x Remaining balance

Monthly interest = 1% x $301.84 = $3.02

Therefore, if Leo were to make one more payment, he would pay $310.50, which includes both the principal and the interest. So, the amount of interest he would pay if he were to pay off the loan after 4 payments is:

Interest paid = Total payment - Remaining balance

Interest paid = $310.50 - $301.84 = $8.66

So, by paying off the loan early, Leo Gandolfi would save:

Savings = Total interest - Interest paid

Savings = $63 - $8.66 = $54.34

Therefore, Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.

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The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.

So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:

f(0) = 57(3.2)(0)

f(0) = 0

So the y-intercept of this function is (0,0).

From power rules, the value of n is 4.

The main power rules are presented below.

For solving this question, you should convert the given text into a math expression. See below.

7^7 multiplied by 7^5 equals (7^n)^4 over 7^4 =  [tex]7^7 * 7^5 =\frac{ (7^n)^4 }{7^4}[/tex]

After that, you should apply the power rules. Using the rule for the multiplication with the same base, you have: [tex]7^{12} =\frac{ (7^n)^4 }{7^4}[/tex].

Next step, you should apply the rule Power, then: [tex]7^{12} =\frac{ (7^{4n})}{7^4}[/tex].  One more time, you should apply the rule for the multiplication with the same base, and you will have:

[tex]7^{12} =\frac{ (7^{4n})}{7^4}\\ \\ 7^{16}=7^{4n}[/tex]

Thus,

16=4n

n=16/4

n=4

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Answer:

Step-by-step explanation:

The equation that represent the graph is C = 1.5m + 200.

A moving company charges a one time fee and cost per miles of it service. Therefore, the relationship is between the total cost and the number of miles.

Therefore, let's use equation to represent the relationship between the total cost C and number of miles travelled, m.

Hence, using slope intercept form

y = mx + b

where

Hence,

using (0, 200) (200, 500)

m = 500 - 200 / 200 - 0

m = 300 / 200

m = 1.5

Hence,

y-intercept = 200

Therefore, the equation is C = 1.5m + 200

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Answer:

Step-by-step explanation:

A square is a 4 sided polygon in which all of its side lengths are equal and the diagonals are also be

The number of times a variable appears in a data set is Known as Frequency.

Frequency

The frequency of a particular data is the number of times the data value appears. Denote the frequency of a data value by f. For example, if 5 students got an A in science, the frequency of an A score is considered to be 5.

Frequency distributions are used to tabulate the collected data. Data can be scores given by students, temperatures in different cities, scores scored in volleyball matches, and so on. After data is collected, it needs to be presented in a meaningful way for better understanding. Organize your data so that all characteristics are summarized in a table. This is called a frequency distribution.

Types of Frequency distribution:

1. Group frequency distribution: Use group frequency distribution tables to organize large numbers of observations or data. By doing so, we create class intervals to calculate the frequency of data belonging to a particular class interval.

2. Ungrouped Frequency Distribution:  In an ungrouped frequency distribution table, we record the exact frequency of individual data without classifying them.

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A new image that is formed after a transformation is called reflection.

A sort of symmetry known as reflective symmetry occurs when one half of an object mirrors the other half. For instance, both the left and right sides of a human face are typically the same. Most butterflies have identical wings on their left and right sides.

From the question, it is asked what we call a new image that is formed after a transformation. Reflection is the name given to the new picture that results from a change.

Therefore, the new image will be called a reflection after transformation.

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To find a polynomial function of degree 3 such that f(10) = 17 and the zeros of f are 0, 5, and 8, we can use the factored form of the polynomial. The polynomial can be written as f(x) = (17/20)x(x - 5)(x - 8).

If the zeros of a polynomial function are 0, 5, and 8, then the factored form of the polynomial can be written as: f(x) = k(x - 0)(x - 5)(x - 8)

To find a polynomial function of degree 3 such that f(10) = 17 and the zeros of f are 0, 5, and 8, we can use the factored form of a polynomial. The factored form of a polynomial is the product of its factors, which are its linear binomials that correspond to its zeros.

For example, if a polynomial has zeros of 1, 2, and 3, then its factored form can be written as (x - 1)(x - 2)(x - 3). We can use this concept to find the factored form of the polynomial with zeros of 0, 5, and 8, which is:

f(x) = k(x - 0)(x - 5)(x - 8)

where k is a constant coefficient that we need to determine. We can use the given condition that f(10) = 17 to solve for k. When we plug in x = 10, we get:

f(10) = k(10 - 0)(10 - 5)(10 - 8) = 2k * 5 * 2 = 20k

Since f(10) = 17, we can set 20k = 17 and solve for k:

k = 17/20

Therefore, the polynomial function of degree 3 with the given conditions is:f(x) = (17/20)x(x - 5)(x - 8)

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Answer: My guess is 90 degrees if we're looking at the uppercase C

Step-by-step explanation: Because of the square in the corner

Answer:

In 1 hour run:

4 4/5 miles

Step-by-step explanation:

2 4/5 = 2 + 4/5 = 10/5 + 4/5 = (10+4)/5 = 14/5

Proportions:

14/5 miles ⇒ 7/12 hour

A miles ⇒ 1 hour

A = (14/5 miles)(1hour) / (7/12 hour)

A = (14/5)/(7/12)

A = (14*12) / (5*7)

A = 168 / 35

A =  140/35 + 28/35

A = 4 + 28/35

A = 4 + 4/5

A = 4 4/5 Miles

The algebraic expression is,

⇒ 5 (6 - n)

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 expression is,

⇒ five times the difference between six less than a number.

Now, Let a number = n

Hence, We can formulate;

⇒ 5 (6 - n)

Thus, The value of expression is,

⇒ 5 (6 - n)

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The solution to the algebraic expression w² + 2 + 48 ÷ 28 is 2.68

w² + 2 + 48 ÷ 28

Where,

w=5

X=3

Y=4

Z=8

w² + 2 + 48 ÷ 28

substitute w = 5 into the expression

= 5² + 2 + 48 ÷ 28

= 25 + 2 + 48 ÷ 28

Add

= 75 ÷ 28

divide

= 2.678571428571428

Approximately,

2.68

In conclusion, 2.68 is the solution to the given expression.

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Answer:

99

Step-by-step explanation:

We can set up and solve this equation:

X + X - 50 = X + 49

X = 99

The points are plotted on the graph below.

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

Given a coordinate plane.

We have to plot the points given.

(0, 1/2) is a point on the Y axis, since the x coordinate is zero. y coordinate will be in the middle of 0 and 1.

(1, 1 1/2) is a point at a distance of 1 to the right from the origin and at a distance of 1 1/2 to the up from the origin.

(2, 2 1/2) is a point at a distance of 2 to the right from the origin and at a distance of 2 1/2 to the up from the origin.

These points are plotted in the graph below.

Hence the graph is shown below.

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The length of BD in the triangle is 24 units.

The triangles are similar by angle bisector theorem. The angle bisector theorem states that the angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.

Therefore, let's find BD.

Hence, using the proportion,

12  / 20 = x / x + 6

cross multiply

12(x + 6) = 20x

12x + 72 = 20x

72 = 20x - 12x

72 = 8x

divide both sides by 8

x = 72  /8

x = 9

Therefore,

BD = x + x + 6 = 2x + 6

BD = 2(9) + 6

BD = 18 + 6

BD = 24 units

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Considering AB=BC, the matrices A, B, and C are square matrices such that matrix B is invertible.

Now, post-multiply both sides of 

[tex]AB=BC by  {B}^{−1} [/tex]

[tex] {ABB}^{−1} = {BCB}^{−1} [/tex]

Solving the obtained equation for A by using the properties

[tex]AI= {BCB}^{−1} \\ A= {BCB}^{−1} [/tex]

Therefore, the required matrix A is BCB−1

A matrix, also known as matrices, is a rectangular array or table of letters, numbers, or other symbols arranged in rows and columns that is used to represent a mathematical object or a characteristic of one.

In linear algebra, matrices represent linear maps and enable explicit computations. Since most properties and operations of abstract linear algebra can be expressed in terms of matrices, the study of matrices constitutes a significant portion of linear algebra.

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With given features we can definably say that Both triangles are congruent under ASA Criteria.

A triangle is a closed polygon made up of three line segments that intersect at three different angles.

If the sides and angles of two triangles are the same length, the triangles are said to be congruent. As a result, two triangles can be superimposed side by side and angle by angle. Congruence is the term used to describe the relationship between an object and its mirror image. When two objects or shapes superimpose on one another, they are said to be congruent. They are identical in terms of shape and size. Line segments of the same length and angles of the same measure are congruent in the context of geometric figures.

Given far opposites angle are same = 25°

Given intersected line makes equal line

Intersecting angles are equal due to vertically opposite angle theorem.

Then we have,

Angle = Angle

Side = Side

Angle = Angle

With this features we can definably say that Both triangles are congruent under ASA Criteria.

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Based on the information in the graph, it can be stated that the median test score of period 2 was less than the median test score of period 1.

The median is identified by locating the value that lies in the middle, in the case of a whisker plot, the median corresponds to the value shown by the vertical line.

The median for period 1: 84

The median for period 2: 82

Based on this information, it can be stated that the median test score of period 2 was less than the median test score of period 1.

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We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix

Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.

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Using the concept of proportion, Gianna will have enough yards to make 18 bows

To solve this problem, we need to apply the concept of proportions.

In order to make 1 bow, she needs 1/5 yard of ribbon

Representing this in an equation form will be;

1 bow = 1/5 yard

18 bow = x yard

cross multiply both sides and solve for x

x * 1 = 18 * (1/5)

x = 3.6 yards

From the above, there will be enough yards to make 18 bows.

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The equation shows how to find the length of each piece is L = R / N and the length of each piece is 1.5 feet.

To find the length of each piece, we can use the following equation:

Length of each piece = Total length of the ribbon / Number of pieces

In mathematical terms, we can represent this equation as:

L = R / N

Where,

L is the length of each piece

R is the total length of the ribbon (66 feet in this case)

N is the number of pieces (44 in this case)

In this problem, we are given a 66-foot ribbon and we are asked to cut it into 44 equal pieces. We need to find out the length of each piece.

Using this equation, we can easily find the length of each piece:

L = 66 / 44

L = 1.5 feet

Therefore, each piece of the ribbon is 1.5 feet long.

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The two consecutive integers whose squares have a difference of 279 is 140 and 139.

The uninterrupted series of integers is represented by consecutive meaning in mathematics. It implies that the numbers are continuously following one another in a series. First, we must comprehend the idea of predecessors and successors in order to comprehend the consecutive meaning of consecutive numbers in mathematics. The number that is written immediately before the number is referred to as the predecessor. As opposed to successors, which refer to the number that follows the number. Think about the range 4, 5, 6, and 7. In this case, 4 comes before 5, while 6 comes after 5.

Let us suppose a number = x.

The consecutive number is given as (x - 1)

Two consecutive integers whose squares have a difference of 279, is given as:

x² - (x - 1)² = 279

x² - x² + 2x - 1 = 279

2x - 1 = 279

2x = 280

x = 140

x - 1 = 140 - 1 = 139

Hence, the two consecutive integers whose squares have a difference of 279 is 140 and 139.

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