Find the principal needed now to get the given amount; that is, find the present value. to get $110 after 1 1/4 years at 4% compounded continuously The present value of $110 is $?. (Round to the nearest cent as needed.)​

The distance between the points (7,-2) and (3, 1) is √(13).

Since, the distance between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula,

d = √((x₂ - x₁)² + (y₂ - y₁)²),

where, d is the distance between the points (x₁, y₁) and (x₂, y₂).

To find the distance between the points (7,-2) and (3, 1) .

Thus the distance between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula,

d = √((x₂ - x₁)² + (y₂ - y₁)²),

d = √((1 - (-2))² + (3 - 1)²),

or, d = √((3)² + 2²),

or, d = √((9+ 4),

or, d = √(13),

Learn more about the distance formula at;

brainly.com/question/7243416

#SPJ1

The measure of angle x is 57 degrees.

Remember that the sum of the measures of two adjacent angles is always equal to 180°.

Here we can see that the angle x° and 123° are adjacent, then we can write the linear equation:

x + 123° = 180°

Solving the equation for x, we will get.

x = 180° - 123°

x = 57°

That is the value of x.

Learn more about angles at:

https://brainly.com/question/25716982

#SPJ1

The journal entries for to record the issuance of the convertible bond on 1st July 2008 are Cash 475,000,000, Discount on Bonds Payable 25,000,000, Bonds Payable 500,000,000.

To record the issuance of the convertible bond on 1st July 2008

Cash (0.95*500,000,000) 475,000,000

Discount on Bonds Payable 25,000,000

Bonds Payable 500,000,000

(Note: The discount on bonds payable is calculated as the difference between the cash proceeds and the face value of the bond, and it represents the portion of the bond discount that is attributable to the conversion feature.)

To record the interest expense and coupon payment on 30th June 2009

Interest Expense 30,000,000

Discount on Bonds Payable 15,000,000

Cash 45,000,000

(Note: The interest expense is calculated as 6% of the face value of the bond, and the discount on bonds payable is amortized over the life of the bond using the effective interest rate method.)

To record the interest expense and coupon payment on 30th June 2010

Interest Expense 30,000,000

Discount on Bonds Payable 12,750,000

Cash 42,750,000

To record the interest expense and coupon payment on 30th June 2011

Interest Expense 30,000,000

Discount on Bonds Payable 10,088,750

Cash 40,088,750

To record the redemption of the bond on 30th June 2012

Bonds Payable 500,000,000

Premium on Bonds Payable 25,000,000

Cash 525,000,000

(Note: The premium on bonds payable is calculated as the difference between the redemption price and the face value of the bond, and it represents the portion of the bond premium that is attributable to the conversion feature.)

To know more about journal entries here

https://brainly.com/question/23857927

#SPJ1

Answer:

[tex]39ft^{2}[/tex]

Step-by-step explanation:

Area of a Trapezoid - 1/2 x (base1+base2) x h

1/2(2+5)4

1/2(7)4

1/2(28)

28/2=14

So, the Trapezoid area is 14

Are of a Square - base x height

5(5)=25

14+25=39

So, the total area is [tex]39ft^{2}[/tex]

The area of a sector TOP is 89.019 square meter.

Given that, radius of the sector is r=9 m and measure of arc TP = 126°.

Here, ∠TOP =measure of arc TP = 126°.

We know that, area of a sector = θ/360° ×πr²

= 126°/360° ×3.14×9²

= 0.35×3.14×81

= 89.019 square meter

Therefore, the area of a sector TOP is 89.019 square meter.

Learn more about the area of a sector here:

brainly.com/question/7512468.

#SPJ1

Answer:

16.03% increase.

Step-by-step explanation:

4.264+25%+6.396 = 16.03% increase.

Answer:

A)

Step-by-step explanation:

original height- h

We are gonna add 5 to it cuz it's taller but if it was shorter we would have subtracted 5.

We are gonna add 5 to it cuz it's taller but if it was shorter we would have subtracted 5.or if it was 5 times taller we would have multiplied.

In this case it is mentioned taller so the expression would be h+5

Answer:

1

Hope this helps

please mark me Brainliest

The value of z is (15±5i√7)/4

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Solving x²/5 +5 = 3z/2

multiplying all terms by 10

2z²+50 = 15z

2z²-15z +50= 0

using formula method

z = -b ±√ b²-4ac)/2a

a = 2, b = -15, c = 50

(-(-15 )± √ 15²-4×2×50)/2× 2

z = 15±√225-400)/4

z = 15±√-175)/4

z = 15±√-25×7)/4

z= (15±5i√7)/4

therefore the value of z is (15±5i√7)/4

learn more about quadratic equation from

https://brainly.com/question/1214333

#SPJ1

The correct statement is,

⇒ The values below the X-axis are negative values of y

We have to given that;

To find true statement for the Cartesian coordinate system.

Now, We know that;

the values below the X-axis are negative values of y

And, the values above the X-axis are positive values of y.

Thus, The correct statement is,

⇒ The values below the X-axis are negative values of y

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

We can first start off by getting from 5 cups of water to 1 cup of water. We can do this by dividing 5 by 5 to get 1. Since we did this to the water, we need to do the same thing with the sugar. 1 cup of sugar divided by 5 is equivalent to 0.2 cups of sugar.

The answer is 0.2 cups of sugar.

Answer:

the rectangular coordinates of the point (9, 150°) are approximately (-4.5, 7.794).

Step-by-step explanation:

To convert from polar coordinates to rectangular coordinates, we use the following formulas:

x = r cos θ

y = r sin θ

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point, measured counterclockwise.

In this case, r = 9 and θ = 150°. However, we need to convert θ to radians before we can use the formulas. We know that 180° = π radians, so:

150° = (5/6)π radians

Now we can use the formulas:

x = r cos θ = 9 cos (5/6)π ≈ -4.5

y = r sin θ = 9 sin (5/6)π ≈ 7.794

Therefore, the rectangular coordinates of the point (9, 150°) are approximately (-4.5, 7.794).

Answer:

14:09 (5 hours and 9 minutes later)

Step-by-step explanation:

To determine the time the truck will arrive in Kimberley if it left Johannesburg at 09:00, we can use the formula:

time = distance/speed

where the distance is 505.5 km and the speed is 98 km/h.

Substituting these values into the formula gives:

time = 505.5 / 98 = 5.15 hours

Therefore, if the truck left Johannesburg at 09:00, it will arrive in Kimberley at approximately 14:09 (5 hours and 9 minutes later) to the nearest minute.

Hope this helps

please mark me Brainliest

The distance between the two points plotted is 10 units.

In geometry, the distance between two points is the length of the shortest path connecting them. It is the measure of the length of a straight line segment connecting two points in space.

To find the distance between two points, we can use the distance formula, which is based on the Pythagorean theorem. The formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]

In this problem, the two points plotted are (-6, 4) and (-6, -6). Using the distance formula, we can calculate the distance between these two points as:

D = √((-6 - (-6))² + (-6 - 4)²)

D = √(0² + (-10)²)

D= √(100)

D= 10

Therefore, the distance between the two points plotted is 10 units.

To know more about coordinate geometry follow

https://brainly.com/question/31719714

#SPJ1

Answer:

10 units

Step-by-step explanation:

i did in class

The value of arc CD is determined as 60⁰.

option A.

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

arc BD = 2 x m∠BED

From the diagram, we have, m∠BED = 62⁰

The value of arc BD is calculated as follows;

arc BD = 2 x 62⁰

arc BD = 124⁰

arc BD = arc BC + arc CD

arc CD = 124 - 64

arc CD = 60⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Explanation:

Let's find the roots aka x intercepts.

Plug in y = 0 and solve for x.

y=(x+3)(x-7)

(x+3)(x-7) = 0

x+3 = 0 or x-7 = 0

x = -3 or x = 7 are the two roots.

Now find the midpoint of those roots.

Add them up and divide in half.

(-3+7)/2 = 4/2 = 2

The midpoint happens at x = 2, which is the x coordinate of the vertex. This is the axis of symmetry where the vertex is located.

The vertex in this case is the lowest point on the parabola. It's the turning point where it goes from decreasing to increasing.

Plug x = 2 back into the original equation to find its paired y value.

y=(x+3)(x-7)

y=(2+3)(2-7)

y=(5)(-5)

y=-25

Therefore, the vertex is located at (2, -25) as indicated in the graph below. I used GeoGebra to make the graph. Desmos is another good choice.

An equation of the line in point-slope form is y + 40 = -2(x - 70).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 100)/(50 - 0)

Slope (m) = -100/50

Slope (m) = -2

At point (70, -40) and a slope of -2, an equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 40 = -2(x - 70)

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

JKLMN is a regular polygon inscribed in a circle. The radius of the polygon is 5 units.

What is regular polygon?

Every polygon with equal side lengths and interior angles is said to be regular. A regular polygon's circumradius, also known as its radius, is the constant distance from the center to any of its vertices. It holds true for every vertex in the polygon. Therefore, PM = radius = 5 units.

As a result, the circumradius acts as a fundamental geometric characteristic of a regular polygon, describing both the size of the circle that completely encloses the polygon and the equal distance between its center and vertices. Therefore, the radius of the polygon is 5 units.

Know more about radius of the polygon,

https://brainly.com/question/31283390

#SPJ1

The cash discount is $38.40

The rate of cash discount is 4%.

The invoice price is $960, and the cash price is $921.60. The cash discount is the difference between these two price :

Cash discount = Invoice price - Cash price

Cash discount = $960 - $921.60

Cash discount = $38.40

The cash discount is $38.40.

The proportion of the cash discount in relation to the invoice price is necessary to calculate the cash discount rate. By dividing the cash discount by the invoice price, then multiplying the result by 100, we can determine this:

Rate of cash discount = (Cash discount / Invoice price) x 100%

Rate of cash discount = ($38.40 / $960) x 100%

Rate of cash discount = 0.04 x 100%

Rate of cash discount = 4%

Therefore, the rate of cash discount is 4%.

Learn more about multiplying here : brainly.com/question/28768606

#SPJ1

While finding with similar volumes, which might be volumes of figures that are similar in shape and proportion, we can find the ratio of their volumes by using the ratio of their linear dimensions.

The linear dimensions refer to the measurements of the duration, width, and height of the figures. If two comparable figures have corresponding linear dimensions inside the ratio of a:b, then their volumes could be in the ratio of [tex]a^3:b^3.[/tex] that is because the volume of a 3-dimensional determine is decided by way of multiplying its duration, width, and top collectively.

For example, if we have cubes which are similar in shape and proportion & the period of one cube is two times the period of the other dice, then the ratio in their linear dimensions is 2:1. therefore, the ratio in their volumes can be [tex](2^3):(1^3)[/tex], which simplifies to 8:1. which means the larger dice has 8 times the volume of the sm

Learn more about  linear dimensions:-

https://brainly.com/question/30556861

#SPJ1

The volume of the Canada post mailbox is given as follows:

1,152,115.5 cm³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

Hence the volume of the rectangular bottom is given as follows:

V = 180 x 70 x 85.5

V = 1,077,300 cm³.

The triangular top has a height of 25 cm, hence the volume is obtained as follows:

V = 0.5 x 25 x 70 x 85.5 (multiply by 0.5 as it is a triangle).

V = 74812.5.

Hence the volume is given as follows:

1077300 + 74812.5 = 1,152,115.5 cm³.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

The reduction in reserve requirements led to an increase of $79 billion in both excess reserves and the lending capacity of Chinese banks.

According to the news accounts from March 2020, the reduction in the reserve requirement ratio (RRR) by the People's Bank of China increased the lending capacity of Chinese banks by approximately US$79 billion

(a) The excess reserves in China increased by $79 billion.

(b) As a result of the reduction in the reserve requirement, the lending capacity of Chinese banks increased by $79 billion.

This means that Chinese banks had an additional $79 billion available for lending purposes, which aimed to stimulate economic growth and support the country's economy. By lowering the reserve requirement, commercial banks were able to hold a smaller portion of their deposits as reserves, thus freeing up more funds that could be utilized for lending to businesses and individuals.

In summary, the reduction in reserve requirements led to an increase of $79 billion in both excess reserves and the lending capacity of Chinese banks.

To learn more about : reduction

https://brainly.com/question/13107448

#SPJ11

An equation for the wheel if the center of the wheel is on the​ y-axis and y represents the height above the ground is x² + (y - 169)² = 22500.

In order to write an equation of the circle, we need two major components: the radius of the circle and the coordinates of its center. We can then express the equation in the form (x - a)² + (y - b)² = r², where r is the radius and (a, b) is the center.

Let's start by first finding the radius of the Ferris wheel. We know that the diameter of the wheel is 300 ft, and that the radius of a circle is half of the diameter. So, we have d = 300,

r = d/2

r = 300/2

r = 150 ft

Now that we know the radius, we can save that for later and move on to finding the center point.

We are told that the center of the wheel is on the y-axis; this means that the x-coordinate of our center point is a = 0.

Next, to find the y-coordinate, we can note that even though the diameter of the wheel is 300 ft, the maximum height of the wheel is actually 319 ft. That means that there must be a structure below the wheel that holds it up 19 ft above the ground (319- 300= 19).

Therefore, we must add this 19 ft to the radius of 150 ft straight up to find the center point of the circle, which is 169 ft above the ground. Thus, the y-coordinate of our center point is b = 169.

We can then plug in our radius and center point (0, 169) into our equation for a circle and simplify to get our final answer

(x - (0))² + (y - (169))² = 150²

x² + (y - 169)² = 22500

Therefore, an equation for the wheel if the center of the wheel is on the​ y-axis and y represents the height above the ground is x² + (y - 169)² = 22500.

To learn more about an equation of a circle visit:

https://brainly.com/question/23799314.

#SPJ1

The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

There are 33,800 different four-letter passcodes that can be formed if the first letter must be an S or a T, and the last letter must not be a Z.

The English alphabet consists of 26 letters. Because the initial letter must be a S or a T, there are only two options.

There are 26 options for each letter in the second and third letters because there are no constraints. As a result, the second and third letters have a total of 26 26 = 676 potential combinations.

We have 25 options for the fourth letter (which cannot be a Z).

As a result, the total number of possible four-letter passcode combinations is:

2 × 676 × 25 = 33,800

So, if the first letter is a S or a T and the last letter is not a Z, there are 33,800 possible four-letter passcodes that may be constructed.

learn more about combinations at https://brainly.com/question/4658834

#SPJ1

The unit vector that has the same direction as v is u = v/|v| = (2i - 5j)/√(29)

To find the unit vector that has the same direction as the vector v, we need to divide the vector v by its magnitude. The magnitude of a vector is the square root of the sum of the squares of its components. In other words, if v = (a,b), then the magnitude of v is given by:

|v| = √(a² + b²)

Using this formula, we can find the magnitude of the vector v as:

|v| = √(2² + (-5)²) = √(29)

Now, to find the unit vector that has the same direction as v, we divide v by its magnitude:

u = v/|v| = (2i - 5j)/√(29)

This is the unit vector in the same direction as v. It has a magnitude of 1, which means that it is a vector of length 1. By dividing v by its magnitude, we have scaled v so that its length is 1, but its direction is still the same as the original vector v.

In summary, to find the unit vector that has the same direction as the vector v, we divide v by its magnitude. This gives us a vector of length 1 in the same direction as v.

To learn more about vector click on,

https://brainly.com/question/31590170

#SPJ1

The value of cosβ is 4/5.

The value of sinβ is 3/5.

The value of tanβ is 3/4

The value of angle α is 53.1⁰.

The basic trigonometric ratios for β is calculated as follows;

The length of AC is calculated as follows;

AC² = AB² - BC²

AC² = 15² - 12²

AC² = 81

AC = √ (81)

AC = 9

The value of cosβ is calculated as;

cosβ = 12/15 = 4/5

The value of sinβ is calculated as;

sinβ = 9/15 = 3/5

The value of tanβ is calculated as;

tanβ = 9/12 = 3/4

The value of angle α is calculated as follows;

sinα = 12/15 = 4/5

sinα = 0.8

α = arc sin (0.8)

α = 53.1⁰

Learn more about trigonometry ratios here: https://brainly.com/question/10417664

#SPJ1

The requreid line plot displays a data set with an outlier given below.

The line plot with the outlier is the second one that displays the values as dots above the corresponding values on the number line. The data set has a clear outlier with one dot above the number 5, while the rest of the data points cluster around the values of 6 to 13. The other line plots do not display any clear outliers.

Learn more about line plot here:

https://brainly.com/question/29573088

#SPJ1