Jo borrowed ​$6,650 for 8 months from a bank. The bank discounted the loan at 8.5% .
a. How much interest did Jo pay the bank for the use of its​ money?
b. How much did he receive from the​ bank?
c. What was the actual rate of interest he​ paid?
Round interest amount to nearest cent.

m = -2, 0.  The function y = xm is a solution when m = -2 or 0.

For the differential equation xy'' + 2y' = 0, the function y = xm is a solution if m = -2 or 0. This can be seen by substitution and solving the resulting equation. When m = -2, the equation simplifies to 0 = 0, which is true. When m = 0, the equation simplifies to 0 = 2y', which is true when y' = 0. Therefore, the function y = xm is a solution when m = -2 or 0.

To solve for m, first substitute the function y = xm into the differential equation, giving xm'' + 2mx' = 0. Then move all terms containing m to one side of the equation, leaving 0 on the other side. This gives m'' + 2m' = 0, which is a second-order linear differential equation. This equation can be solved using the characteristic equation, which is found by setting the discriminant of the equation equal to 0. The discriminant for this equation is 4 - 4(1)(0) = 4, which is greater than 0. Thus, the equation has two distinct real solutions, which are m = -2 and m = 0. Therefore, the function y = xm is a solution when m = -2 or 0.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

a. The vector equation for the given line is (x,y,z) = (1,0,7) + t(1,3,1) and the parametric equations are x = 1+t, y = 3t, z = 6+t.

b. The vector equation for the given line is

(3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k and the parametric equation is

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t.

What is a parametric equation?

A series of equations known as a parametric equation specifies a point's location in the xy plane in terms of a third variable, which is typically referred to as a parameter.

a. We are given that a line passes through the point (1,0,7) and is perpendicular to the plane x + 3y + z = 2.

Now, since the line is perpendicular to the plane, the normal vector (1,3,1) for the plane is parallel to the line.

So the vector equation for the line is

(x,y,z) = (1,0,7) + t(1,3,1)

The parametric equations for the line are

x = 1+t, y = 3t, z = 6+t

b.  We are given that a line passes through the point (3, 2.3, 3.6) and parallel to the vector 3i + 3j - k.

So the vector equation "r" for the line is

r = (3i + 2.3j + 3.6k) + t(3i + 3j - k)

r = (3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k

The parametric equations for the line are

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t

Hence, the required vector and parametric equations have been obtained.

Learn more about parametric equation from the given link

https://brainly.com/question/30451972

#SPJ4

In the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

Row echelon form suggests that: Each row's leading (first) entry must be

Each following row's first entry must be on a new column to the right.

All rows with zero entries are listed below rows with non-zero items.

If the leading entry in each column is the only nonzero element in that column, reduced echelon form also results from echelon form conditions.

According to the definitions we see that, in the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

Learn more about matrix here:

https://brainly.com/question/28180105

#SPJ4

Checks, debit cards, and electronic payments are considered forms of cashless payments because they allow for the transfer of funds between individuals or businesses without the need for physical currency, such as bills and coins.

Checks are considered cash because they are legal tender and can be deposited into a bank account, allowing the funds to be transferred between parties. Debit cards and electronic payments work in a similar way by deducting funds directly from a bank account or transferring funds electronically. While these forms of payment may not involve physical currency, they represent a transfer of value and can be used to purchase goods and services in the same way as cash.

In summary, checks, debit cards, and electronic payments are considered forms of cash because they facilitate the transfer of value between parties, even though they do not involve physical currency.

Answer:

Debit cards account for 28% of all payments, and credit cards account for 23% of all payments. For these payments, payment details are entered manually during a checkout process, or the physical card is processed at a point of sale (POS) system. There’s usually a debit or credit card processing fee, which the business owner needs to pay.

Step-by-step explanation:

pls tell me if wrong thank you have a great night or day

The sample size that required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (0.073) is 120.

As per the data given:

The makers of skittles claim that 20% of skittles candies are orange.

20 % = 0.20

Select a random sample of 30 skittles from a large bag.

[tex]\hat p[/tex] = the proportion of orange skittles in the sample.

The standard deviation of the sampling distribution of [tex]\hat p[/tex] = 0.073

The Standard deviation of the Sampling distribution was reduced to [tex]$= \frac{1}{2} \sigma_{\hat{p}}$[/tex].

[tex]$ \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=0.073$[/tex]

Divide both sides by 2

We get:

[tex]$\sqrt{\frac{p(1-p)}{n}}=\frac{0.073}{2}[/tex]............... (1)

Now it should become be one - half.

Let [tex]$n_1[/tex] be the new sample size.

[tex]$\sqrt{\frac{p(1-p)}{n_1}}=\frac{0.073}{2}[/tex] ..................2

From (1) and (2) RHS of both equations is equal.

Then equate both equations

[tex]$\frac{1}{2} \sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{p(1-p)}{n_1}}$[/tex]

Squaring on both sides

We get:

[tex]$\Rightarrow\left(\frac{1}{2}\right)^2 \frac{p(1-p)}{n}=\frac{p(1-p)}{n_1}\end{aligned}$[/tex]

[tex]$\Rightarrow \frac{1}{4 n}=\frac{1}{n_1}$[/tex]

[tex]$\Rightarrow n_1=4 n$[/tex]

[tex]$n_1-[/tex] The new sample size required = 4n

n-The old sample size.

The sample size that required = 4n

= 4 (30)

= 120

For more questions on random sample

https://brainly.com/question/5431978

#SPJ4

The makers of skittles claim that 20% of skittles candies are orange. Suppose this claim is true. You select a random sample of 30 skittles from a large bag. Let p-hat = the proportion of orange skittles in the sample. The standard deviation of the sampling distribution of p-hat = .073

What sample size would be required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (.073)

The value of the last one is 18.

The solution of the diagram can be modelled with an equation. Therefore, let's find the last value.

we will use variable to represent the fruit names.

Hence,

yellow fruit = x

red fruit = y

green fruit = z

Therefore,

x + y + z = 29

2y + z = 26

2z + y = 25

Using substitution,

y = 25 - 2z

2(25 - 2z) + z = 26

50 - 4z + z = 26

50 - 3z = 26

-3z = 26 - 50

-3z = -24

z = 8

y = 25 - 2(8)

y = 25 - 16

y = 9

Therefore,

x + 9 + 8 = 29

x = 29 - 17

x = 12

Finally,

x + 1 / 2x  = 12 + 1 / 2(12) = 12 + 6 = 18

learn more on equation here: https://brainly.com/question/30066982

#SPJ1

Δ BAD and Δ CAD are congruent by SAS rule.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given that, in a Δ BAC, AD bisects ∠ BAC, AB = AC,

We need to prove, BD = DC

         STATEMENT                                                     REASON

1) AD bisects ∠ BAC                                                      given

2) ∠ 1 = ∠ 2                                                           definition of angle bisector

3) AB = AC                                                                      given

4) AD = AD                                                             Reflexive property

5) Δ BAD ≅ Δ CAD                                                       SAS rule

Hence, Δ BAD and Δ CAD are congruent by SAS rule.

Learn more about congruency, click;

https://brainly.com/question/7888063

#SPJ1

Do u have a screen protector cuz if u do thats probably why

Step-by-step explanation:

Answer:

light diffraction and a dirty phone screen.

Using the principle of alternate angles we can say that the value of x will be 120°.

The intersection of two parallel lines by a transversal produces alternate angles.

The alternate angles are equivalent when a transversal cuts two parallel lines.

The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Alternate interior angles for non-parallel lines don't have any special characteristics.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

So, do not observe the given image:
We know that it is the pair of alternate angles that is equal.

Then, x = 120°.

Therefore, using the principle of alternate angles we can say that the value of x will be 120°.

Know more about Alternate angles here:

https://brainly.com/question/26167358

#SPJ1

Answer:

Step-by-step explanation:

We can use similar triangles to find the function that models the length of the woman's shadow. If the woman is standing at a distance d from the base of the lamp, the length of her shadow will be proportional to her height, so the ratio of the shadow length to the height will be equal to the ratio of the distance from the base of the lamp to the height of the lamp.

So, if h is the woman's height and L is the length of her shadow, we have:

L/h = d/13

And since h = 6 feet, we can write:

L = (d/13) * 6

So the function that models the length of the woman's shadow in terms of her distance from the base of the lamp is:

L = (d/13) * 6

The value of the x is 19.9.

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.

Given:

The angle C is 98°.

Applying law of cosines:

c² = a² + b² -2ab cosC.

Substituting the values,

c² = (17)² + (13)² -2(17)(13) cos98°.

c² = 458 -  (-0.13917)442

c² = 396.48686

c = 19.9

Hence, x = 19.9.

To learn more about the law of cosines;

https://brainly.com/question/17289163

#SPJ1

The cost per kg of clay is $0.7 and cost per kg of wood is $ 8.

Linear Equation in two variables:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Now according to the given question,

Let cost per kg of clay be x and cost per kg of wood be y.

Then according to the given information in  table, we can get two equations,

5x + 4y = 35.50                                   .....(1)

3.5x + 6y = 50.45                               .....(2)

Now multiply equation (1) by 3 and equation (2) by 2, we get,

15x + 12y = 106.50                               ......(3)

7x + 12y = 100.90                                 ......(4)

Now subtract equation (4) by equation (3), we get,

8x = 5.60

x = 0.7

Now put this value of x in (1),

we get,

5(0.7) + 4y = 35.5

3.5 + 4y = 35.5

subtracting both sides by 3.5, we get

4y = 32

by dividing both sides by 4, we have

y = 8

Therefore, cost per kg of clay is $0.7

and cost per kg of wood is $ 8.

To know more about linear equation , visit:

https://brainly.com/question/29739212

#SPJ1

The ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

Given that, two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post, we need to find where should the stake be laced to use the least amount of rope,

Let rope of the 16 ft high pole be at x ft and that of 24 ft high pole at (30-x)

The structure of rope and poles are making a set of similar triangles, (refer to figure attached)

We know that, the corresponding sides of the similar triangle are in same ratio,

Therefore,

16 / x = 24 / (30-x)

2 / x = 3 / (30-x)

60 - 2x = 3x

5x = 60

x = 12

30-12 = 18

Hence, the ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

Learn more about similar triangles, click;

https://brainly.com/question/29731302

#SPJ1

The solution that works for both the equations is (-4, 5) and the two lines intersect at this point.

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."

The given equation are:

y = -1/2x + 3

y = 5

Substitute the value of y in first equation:

5 = -1/2x + 3

5 = -x + 6 / 2

10 = -x + 6

10 - 6 = -x

x = -4

The solution that works for both the equations is (-4, 5) and the two lines intersect at this point.

Learn more about system of equations here:

https://brainly.com/question/90105

#SPJ1

Answer:

The player has an annual salary of $305,000, and they have decided to donate 1/8 of their salary to charity. To calculate this, we simply divide their salary by 8.

305,000 / 8 = $38,125

So, the player is donating $38,125 to charity every year. This is calculated by taking 1/8 of their annual salary.

The fraction 1/8 represents one out of eight equal parts of the player's salary, and when this fraction is multiplied by the player's salary, it gives the exact amount that they are donating to charity.

The costs of 5 oranges and 15 oranges are R15 and R45

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

Six oranges cost R18,00

This means that the unit rate is

Unit rate = R18,00/6 = R3.00

For 5 oranges, we have

Cost = 5 * R3.00 = R15.00

For 15 oranges, we have

Cost = 15 * R3.00 = R45.00

So, the costs are R15.00 and R45.00

Read more about unit rate at

https://brainly.com/question/19493296

#SPJ1

Answer:

(8,-5)

x=8

y=-5

Step-by-step explanation:

Ha:mu<10  is the appropriate alternative hypothesis that the consumer group wishes to test .

How would you define hypothesis?

An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.

                               In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

Ha:mu<10

Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.

Learn more about hypothesis

brainly.com/question/29519577

#SPJ4

The proceeds (discounted value) on the third-party discount note are $4,116.90.

The discounted value of a note is a value that is less than the maturity value.

The maturity value is the face value of the note plus the accumulated interest.

Face value of the note receivable = $4,000

Annual interest rate = 12%

Note issuance date = March 16

Note due date = November 14

The total number of days = 243 days

Discount date = June 11

Discount rate = 11%

March 16 to June 11 = 87 days

Interest on the note = $320 ($4,000 x 243/365 x 0.12)

Maturity value = $4,320 ($4,000 + $320)

Discount period = 156 days (243 - 87)

Discount on the note = $203.10 ($4,320 x 156/365 x 11%)

Discounted value = $4,116.90 ($4,320 - $203.10)

Thus, the man, who holds a note of $4,000 at 12% interest but sells it at a discount rate of 11%, will receive $4,116.90.

Learn more about discounted notes at https://brainly.com/question/13161668.

#SPJ1

Answer: First, let's calculate Jason's weekly earnings:

Jason's weekly tips = $2100 * 18% = $378

Jason's total weekly earnings = $2100 + $378 = $2478

Next, let's calculate David's weekly earnings:

David's weekly commission = $3500 * 6% = $210

David's total weekly earnings = $185 + $210 = $395

To find the monthly earnings, we need to multiply their weekly earnings by 4 (since there are 4 weeks in a month):

Jason's monthly earnings = $2478 * 4 = $9912

David's monthly earnings = $395 * 4 = $1580

So, Jason makes more money in one month, earning approximately $9912, compared to David's $1580.

Step-by-step explanation:

The individual who makes more money in a month between Jason and David is David.

Jason's weekly tips = 18% of $2100

= $378

David weekly salary= $185

David's weekly tips = 6% of $3400

= $210

Total weekly salary of David = $185 + $210

= $395

Total monthly salary of Jason= $378 × 4

= $1,512

Total monthly salary of David= $395 × 4

= $1,580

Therefore, David makes more money than Jason in a week.

Read more on earnings:

https://brainly.com/question/29018756

#SPJ1

La condición para convertir una fracción impropia en una fracción mixta es que el denominador sea menor que el numerador. de modo que en esta pregunta solo (4) se puede cambiar a una fracción mixta.

El número 4 se cambia a una fracción mixta se convierte en:

1 372/1000

Una Fracción Ordinaria cuyo cuantificador es menor que el denominador no se puede convertir en una Fracción Mixta.

Entonces, de los números 1-5, solo el número 4 se puede convertir en una fracción mixta.

4)

Convertido a fracciones comunes se convierte en 1371/1000

Convertido a un número mixto se convierte en 1 371/1000

léase uno - trescientos setenta y uno - por mil.

Learn more about fraction at https://brainly.com/question/10354322

#SPJ1

As stated in the preceding statement When 4 points are given in one method for calculating grade point averages (GPA), the resulting mean grade rating is 3.41.

Average While calculating the arithmetic mean, a group of integers is added, their count is divided, and the result is then taken. For instance, the average of 2, 3, 5, 7, and 10 is 5, this is the result of 30 reduced by 6.

The quality points by each grade every course must first be calculated before being added together to determine the GPA.

3 credit hours times 4 points for A equals 12 quality points.

B - ( 3 points x 2 credit hours ) x 2 (because there are 2 courses) = 18 quality points

C - 2 points x 4 credits = 8 quality points

D - 1 point x 3 credits = 3 quality points

Now add up all the quality points = 12 + 18 + 8 + 3 = 41

Add the credit hours as well = 3 + 2 + 4 + 3 = 12

Divide the total kit by total semester credit to calculate the GPA = 41/12 = 3.41

To know more about Average visit:

https://brainly.com/question/20118982

#SPJ1

Answer: Let's call the bill before the tip "x".

The tip was 20.7% of the bill, so the amount of the tip can be expressed as:

tip = 0.207 * x

The total bill, including the tip, was $31.09, so we can write an equation to represent this:

x + tip = 31.09

Substituting the expression for the tip into this equation, we get:

x + 0.207x = 31.09

Expanding and solving for x, we get:

1.207x = 31.09

x = 31.09 / 1.207

x = 25.76

So the bill before adding the tip was $25.76.

Step-by-step explanation:

The steps that an accountant generally follows to prepare a bank reconciliation statement will be:

A company's prepared bank reconciliation statement demonstrates that the balance of its recorded bank account matches the balance the bank lists.

This report comprises every transaction from a specific time period, including deposits and withdrawals.

Learn more about bank on;

https://brainly.com/question/25664180

#SPJ1

According to the information, it can be inferred that US President Nixon's visit to China proved that the communist world was not a single entity and had many different positions.

The visit of the President of the United States Richard Nixon to the People's Republic of China is an important event in the political and foreign relations sphere of the United States because it was a way to establish a formal relationship between the United States and the People's Republic of China.

This was significant because it was the first time a US President had visited the PRC, who at the time considered the US one of his main enemies. Additionally, this allowed him to verify to the other states that there were different ways of proposing communism. In this case, Chinese communist thought was moderated, so the relationship with the United States was allowed.

Learn more about China in: https://brainly.com/question/9695945

#SPJ1

Answer:

Yes

Step-by-step explanation:

Dilations shrink or expand a figure.  If the scale factor is one, the two figures will be identical.