Write the equation of the line in slope-intercept form (y=mx+b):

The day that Cardi B paid back the loan is given as follows:

June 3rd.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

The parameter values for this problem are given as follows:

A = 17873.97, P = 17500, r = 0.065.

Hence the time in years is obtained as follows:

17873.97 = 17500(1 + 0.065t)

1 + 0.065t = 17873.97/17500

1 + 0.065t = 1.02136971429

t = (1.02136971429 - 1)/0.065

t = 0.32876483523

A year is composed by 365 days, hence the time in days is given as follows:

0.32876483523 x 365 = 120 days.

120 days after February 3rd is June 3rd.

More can be learned about simple interest at https://brainly.com/question/20690803

#SPJ1

The required probabilities = 0.16

The required probabilities = 0.68

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.

As given that,

μ = 36.2

σ = 10

As per empirical Rule:

μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%

μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%

μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%

less than 26.2:

13.5% + 2.35% + 0.15% = 0.16

between 26.2 and 36.2:

68% = 0.68

The required probabilities = 0.16

The required probabilities = 0.68

To know more about probabilities refer to:

https://brainly.com/question/24756209

#SPJ4

When the slope of the line is 3 the equation of the line using point slope formula is

D. у - 8 = 3 (x - 6)

Point slope formula is giving by (y - y₁) = m (x - x₁)

where

m = slope

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

For slope of 3, equation passing through point (5, 8)

(y - y₁) = m (x - x₁)

y - 8 = 3 (x - 6)

y - 8 = 3x - 18

y = 3x - 18 + 8

y = 3x - 10

Learn more about linear function at:

https://brainly.com/question/30125370

#SPJ1

Last week, Toby bought 11 book and 8 movie for a total of $207. Today, Toby bought 16 book and 9 movie for a total of $280 the cost of book is 13$.

Toby bought 11 book and 8 movie for a total of $207 so,

11B + 8M = 207

Today, Toby bought 16 book and 9 movie for a total of $280 so,

16B + 9M = 280

Solving equations simultaneously we get,

11B + 8M = 207

16B + 9M = 280

99B = 1863

B = $13

So, the cost of a book in dollar is $13.

Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.

Lear more about Cost related problem :

https://brainly.com/question/12912968

#SPJ4

The dot product of a.b is 20.

What is the dot product?

The dot product (also called scalar product or inner product) of two vectors a and b in a Euclidean space is a scalar value that represents the projection of one vector onto the other and the cosine of the angle between them. The dot product of two vectors a and b is defined as:

a · b = ||a||||b||cos(θ) = a1b1 + a2b2 + ... + anbn

where a = (a1, a2, ..., an) and b = (b1, b2, ..., bn) are the components of the vectors and θ is the angle between the vectors.

Finding a · b:

Given a = (4, 1, 1) and b = (8, -3, -9), we can calculate the dot product as:

a · b = 4 * 8 + 1 * -3 + 1 * -9 = 32 - 3 - 9 = 20

Hence, the dot product of a.b is 20.

To learn more about the dot product, visit:

https://brainly.com/question/26726614

#SPJ4

Answer:

Step-by-step explanation:

The answer will be the third one because 2/3 * (3/10 X 1) is the same as 2/3 already being multiplied to 3/10.

If you use a calculator and put 2/3 * (3/10 X 1), you will get 0.2 and if you put (2/3 * 3/10) x 1 you will also 0.2.

So (2/3 * 3/10) x 1 is equal to 2/3 * (3/10 X 1)

The evaluation of obtuse angle ∠AOC is 124°.

Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

3x + 94 + x + 30 + 2x - 4 = 180

Sum of angle in a triangle

6x + 120° = 180°

6x = 180° - 120°

6x = 60°

x = 10°

Now, ∠AOC = 3x + 94

3 × 10 + 94

30 + 94

124°

To know more about obtuse angle visit:-

https://brainly.com/question/29077542

#SPJ1

The system of equations has a unique solution. The solution is (0,-5.5).

What is the system of equations?

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.

The system of equations is

4x - 4y = 22 ....(i)

y = -5.5  ...(ii)

Putting x = 0 in 4x - 4y = 22:

4 × 0 - 4y = 22

- 4y = 22

y = -5.5

Putting x = 1 in 4x - 4y = 22:

4 × 1 - 4y = 22

- 4y = 18

y = -4.5

The points on equation (i) are (0,-5.5) and (1, -4.5).

The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).

Plot the points and join them.

The intersection point is the solution of the system of equations.

The solution is x = 0 and y = -5.5

To learn more about the graphing solutions, click on the below link:

https://brainly.com/question/13677313

#SPJ1

The length of the new line is twice the length of the old line and total length is given by the equation L = (3/8 ) of an inch

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the length of the old line be A

Now , the value of A = 1/8 of an inch

Let the length of the new line be B

Now , the value of B = 1/4 of an inch

So , the equation will be

The number of times the new line is greater than old line is given by

B / A = x

Substituting the values in the equation , we get

x = ( 1/4 ) / ( 1/8 )

x = 8/4

x = 2 times

So , the total length of the line = A + B

Substituting the values in the equation , we get

The total length of the line L = ( 1/4 ) + ( 1/8 )

The total length of the line L = 3/8 of an inch

Hence , the equation is L = (3/8 ) of an inch

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

When 65 inches are converted to feet, the result is 5.41667 feet.

To learn more about inches refer to :

brainly.com/question/30403115

#SPJ4

The probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16

Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A statistical function known as a probability distribution explains all the potential values and probabilities for a random variable within a certain range.

The uniform probability distribution is a distribution composed by two bounds, given by a and b, in which each possible outcome within these two bounds is equally as likely.

The probability that a call is made in the first quarter is 15/60

Now the probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16

Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1

To learn more about Probability refer to :

https://brainly.com/question/29483317

#SPJ4

Answer:

11.55m², 181.12mm²,11ft,

Step-by-step explanation:

Simplify the expression.

and multiply A=1/2bh

The value for (1.0x10³) / 2.0x[tex]10^5[/tex] is 0.005.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

(1.0x10^3) and 2.0x10^5

We don't have any sign so we proceed with operation division

(1.0x10³) ÷ 2.0x[tex]10^5[/tex]

= (1.0x10³) / 2.0x[tex]10^5[/tex]

Suing exponents

[tex]a^m/ a^n= a^{m-n[/tex]

= 1/2 x [tex]10^{3-5[/tex]

= 0.5 x [tex]10^{-2[/tex]

= 0.5 / 10²

= 0.5 /100

= 0.005

Learn more about Exponent and power here:

https://brainly.com/question/15722035

#SPJ1

In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

2. AD = BC due to the congruence of a rectangle's opposite sides.

3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.

4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).

5. Since they form right angles and all right angles are congruent, ADC=BCD.

6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).

7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).

Statement                                    Reason

1. Rectangle ABCD                         Given

2. AD=BC                                        Opposite sides of a rectangle are congruent

3. DC=DC                                        Reflexive Property of Congruence

4. <ADC and <BCD are                  Definition of rectangle

  right angles

5.  <ADC=<BCD                              All right angles are congruent

6. ∆ADC=∆BCD                              SAS Congruence Postulate

7. AC=BD                                        CPCTC  

To learn more about Reflexive Property refer to:

https://brainly.com/question/8741371

#SPJ1

Every molecule has a unique molecular formula.

A molecular formula is a chemical formula that represents a molecule and gives information about the number and type of atoms present in the molecule. This formula is unique to each molecule and distinguishes one molecule from another, even if they have the same number and type of atoms arranged in a different way.

For example, the molecular formula for glucose (C6H12O6) is different from that of fructose (C6H12O6), even though they have the same number and type of atoms. The molecular formula represents the actual number of atoms present in the molecule and their chemical makeup, which in turn determines the chemical properties and behavior of the molecule.

Thus, for a given number of domains, the characteristic that is common to every molecule is their unique molecular formula.

To learn more about molecule, visit:

https://brainly.com/question/19922822#

#SPJ11

The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).

(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).

(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).

(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).

(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).

(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).

The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

Learn more about measurement here:

https://brainly.com/question/29178095

#SPJ4

Using the inscribed angle theorem:

7. m<A = 79°

8. m<B = 90°

9. m(BC) = 152°

The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.

Applying the inscribed angle theorem, we have:

7. m<A = 1/2(158)

m<A = 79°

8. m<B = 1/2(180)

m<B = 90°

9. m(BC) = 2(76)

m(BC) = 152°

Learn more about the inscribed angle theorem on:

https://brainly.com/question/3538263

#SPJ1

The angle has a measure of 0° and is in standard position with its vertex at the origin. On the terminal side of lies the point (-2, 3).

The vertex of an angle in standard position on a coordinate plane is at the plane's origin. The angle's terminal side is rotated anticlockwise from the starting side while the angle's initial side is on the positive x-axis. The number of degrees the terminal side has travelled away from the initial side anticlockwise is how an angle is measured in standard position. This signifies that the terminal side is exactly on the same line as the initial side because the angle has the smallest positive measure of 0°. Since the line segment from the origin to the point (-2,3) is on the terminal side of, the point (-2,3) is on that side as well.

Learn more about angle here

https://brainly.com/question/28451077

#SPJ4

The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.

The probability of both events happening is the product of the individual probabilities:

P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196

So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

To learn more about probability visit : brainly.com/question/30034780

#SPJ4

The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.

The probability of both events happening is the product of the individual probabilities:

P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196

So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

To learn more about probability

brainly.com/question/30034780

#SPJ4

An argument that supports Argument A is given below:

Geometric figures play a crucial role in many areas of mathematics and science, including engineering, architecture, physics, and computer graphics.

Being able to construct these figures accurately and efficiently is therefore an important skill for students to have. By using only a compass and straightedge, students can explore and understand the properties of different shapes and their relationships with one another.

This helps them develop their spatial reasoning abilities and improves their understanding of mathematical concepts such as congruence, similarity, and symmetry.

Furthermore, this skill can be applied to solving real-world problems, such as determining the dimensions of a building or designing a circuit board.

In conclusion, the ability to construct geometric figures using a compass and straightedge is essential for students' mathematical and scientific development and should be taught as part of their education.

Read more about geometric figures here:

https://brainly.com/question/8430622

#SPJ1

The length of AG which is the diagonal of the cuboid is; 8.5 cm

A cuboid is defined as a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.

A diagonal in geometry is defined as a line segment that connects two polygonal vertices when they are not on the same edge.

The parameters are;

A, B, C, D, E, F, G & H form a cuboid. AB= 3.2 cm, BC = 1.6 cm & CG = 7.7 cm. That is l=3.2 cm, b=1.6 cm, h=7.7 cm.

A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is;

Diagonal length = √(l² + b² + h²) units.

Thus lugging in the relevant values;

Diagonal length = √(3.2² + 1.6² + 7.7²)

Diagonal Length = 8.49 cm

≈ 8.5 cm

Read more about Cuboid Diagonal at; https://brainly.com/question/29446615

#SPJ1

If a 4x7 coefficient matrix has four pivot columns, the system is consistent and has exactly one solution.

A coefficient matrix is a matrix that represents a system of linear equations. In the case of a 4x7 coefficient matrix, the matrix has 4 rows and 7 columns.

When it comes to determining the consistency of a system of linear equations, the presence of pivot columns is a key factor.

A pivot column is a column that contains a leading 1 in the row reduced echelon form of the matrix. If a system has four pivot columns, this means that the system has 4 linearly independent equations, meaning that there is exactly one solution to the system.

Therefore, the system is considered consistent.

However, if the number of pivot columns is less than the number of unknowns, then the system is considered inconsistent, meaning that there is either no solution or an infinite number of solutions.

To know more about matrix here.

https://brainly.com/question/28180105

#SPJ4

To find the second derivative of y(t) at t = 0, we can use the chain rule. We can write the given equation as dy/dt = f(y), where f(y) = (4-3y)/(5+2y).

Then the second derivative of y at t = 0 can be calculated as: d2y/dt2 (0) = f'(y) * dy/dt (0) = f'(0)f(0) = [-3/(5+20)](4-30)/(5+2*0) = -3/5.

A differential equation is an equation that relates one or more unknown functions and their derivatives. It is mainly used in the fields of biology, physics, engineering, economics, and other sciences.

A differential equation states how a rate of change (a "differential") in one variable is related to other variables. For example, the Single Spring simulation involves a differential equation that describes the displacement of a spring in response to a force.

Learn more about differential equation:

https://brainly.com/question/1164377

#SPJ4

The relation between the number of ide, edge, and vertice in each shape Euler’s Formula for Polyhedron.

Polyhedron Euler's Formula

One of the most significant mathematical theorems, the Euler theorem is named Leonhard Euler and is widely recognized as such.

The link between a polyhedron's face, vertex, and edge counts is stated in the theorem.

F + V = E + 2 is the formula for Euler's equation, where F is the number of faces, V is the number of vertices, and E is the number of edges.

According to Euler's formula, many solid shapes have a number of faces plus vertices plus vertices minus vertices equal to two.

Know more about Euler’s Formula for Polyhedron

https://brainly.com/question/27782111

#SPJ4

After 6 hours, Anderson and Addison will be 126 miles apart.

Let's call the time they have been traveling "t" (in hours).

Anderson will have traveled 15t miles and Addison will have traveled 6t miles. The total distance between them is 15t + 6t = 21t miles.

We know that they need to be 126 miles apart, so we can set up the equation:

21t = 126

Now we can solve for t:

t = 126 / 21

t = 6

So after 6 hours, they both will be 126 miles apart.

You can learn more about distance at

https://brainly.com/question/26550516

#SPJ4

Answer:

Step-by-step explanation:

3/6

There are 5 inches between the two picnic areas on the map. Therefore, option A is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, a map of a national forest has a scale in which 1 inch represents 3 miles.

If two picnic areas in the national forest are actually located 15 miles apart, then on map it is 15/3 =5 inches

Therefore, option A is the correct answer.

To learn more about the scale factor visit:

https://brainly.com/question/22312172.

#SPJ1

A function equation in slope-intercept form to model the situation are as follows;

Slope: 3.

Y-intercept: 48.

Equation: y = 3x + 48.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the liquid started at a temperature of 48 degrees and drops 3 degrees per minute, an equation that model the situation is given by:

y = mx + c

y = 3x + 48

Next, we would fill in the table as follows. At x = 0, the temperature of liquid (y) is given by:

y = 3(0) + 48

y = 48.

At x = 1, the temperature of liquid (y) is given by:

y = 3(1) + 48

y = 51.

At x = 2, the temperature of liquid (y) is given by:

y = 3(2) + 48

y = 54.

At x = 3, the temperature of liquid (y) is given by:

y = 3(3) + 48

y = 57.

At x = 4, the temperature of liquid (y) is given by:

y = 3(4) + 48

y = 60.

At x = 5, the temperature of liquid (y) is given by:

y = 3(5) + 48

y = 63.

At x = 6, the temperature of liquid (y) is given by:

y = 3(6) + 48

y = 66.

At x = 7, the temperature of liquid (y) is given by:

y = 3(7) + 48

y = 69.

At x = 8, the temperature of liquid (y) is given by:

y = 3(8) + 48

y = 72.

Read more on slope here: brainly.com/question/20354825

#SPJ1

Answer:

[tex]\frac{51}{8} \:or \: 6\frac{3}{8}[/tex]

Step-by-step explanation:

solution given:

[tex]\frac{3}{4} *8\frac{1}{2}[/tex]

let make mixed fraction to normal fraction

[tex]8\frac{1}{2} =\frac{8*2+1}{2} =\frac{17}{2}[/tex]

replace [tex]\frac{17}{2}[/tex]

we have

[tex]\frac{3}{4} *\frac{17}{2}[/tex]

in multplication fraction, we multiply numerator to numerator and denominator to denominator.

[tex]\frac{3}{4} *\frac{17}{2}=\frac{3*17}{4*2} =\frac{51}{8}[/tex]

again

in mixed fraction =[tex]6\frac{3}{8}[/tex]