Is it possible to have a polygon with the degrees of 10, 15, and 155 ?

Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.

(1)

(a) The relationship between D, o, and S can be expressed as follows:

DoS (D divided by o multiplied by S) = D / (35 * S)

(b) To find the value of S when D is 176, we can substitute D = 176 into the equation from part (a):

DoS = 176 / (35 * S)

Since the relationship between DoS is not specified further, we cannot determine a specific value of S without additional information. We need more context or a specific equation to solve for the value of S.

Let's denote the amount Alfa gets as x Naira. According to the given information, Aisha gets twice as much as Alfa, so Aisha receives 2x Naira.

The sum of the amounts they receive is 210 Naira, so we can set up the equation:

x + 2x = 210

Combining like terms:

3x = 210

Dividing both sides by 3:

x = 70

Therefore, Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.

In summary, Alfa receives 70 Naira, while Aisha receives 140 Naira.

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Answer:

Let's assume that the length of the rectangle is "x" units.

According to the problem, the width of the rectangle is 1 unit less than the length. Therefore, the width can be represented as (x-1) units.

We know that the area of a rectangle is equal to its length multiplied by its width. So, the area of this rectangle is given as 56 square units.

Using the formula for the area of a rectangle, we can write:

Length x Width = Area

x(x-1) = 56

Expanding the left side of the equation, we get:

x^2 - x = 56

Rearranging the terms, we get a quadratic equation:

x^2 - x - 56 = 0

Now we can solve for x by factoring the quadratic equation:

(x-8)(x+7) = 0

This gives us two possible values for x: x=8 and x=-7.

Since length cannot be negative, we reject x=-7 and conclude that the length of the rectangle is 8 units.

Therefore, the length of the rectangle is 8 units and the width is (8-1) = 7 units.

Step-by-step explanation:

The dimension of section 1 is

15 ft by 3 ft

The dimension of section 2 is

3 ft by 3 ft

The dimension of section 3 is

10 ft by 3 ft

Option A is the correct answer.

From the figure given below,

We have,

Section 1: 15 ft by 3 ft

Section 2: 3 ft by 3 ft

Section 3: 10 ft by 3 ft

The perimeter of all these sections.

= 15 + 3 + 15 + 3 + 3 + 10 + 3 + 10

= 62 feet

Thus,

The dimensions of each section are:

Section 1: 15 ft by 3 ft

Section 2: 3 ft by 3 ft

Section 3: 10 ft by 3 ft

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Answer:

[tex] \frac{\pi( {4}^{2}) }{\pi( {8}^{2}) } = \frac{16}{64} = \frac{1}{4} = .25[/tex]

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.

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The measure of the angle S is 54 degrees

Using the Pythagorean theorem, we have that;

r² = t² + s²

Subsitute the values

s² = 24² - 14²

Find the square values

s² = 576 - 196

s² = 380

find the square root value

s = 19. 5

Then, using the law of sines, we have that;

sin R/r = sin S/s

Substitute the values, we get;

sin 98/24 = sin S/19.5

cross multiply the values

sin S = 19.3/24

Divide the values

sin S = 0. 8045

S = 54 degrees

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The probability of getting a 6 on a biased dice is 0.4. The P(X ≤ 2) is 0.936.

The probability of rolling a 6 is 0.4 and the probability of not rolling a 6 is 0.6. The probability mass function for X is given in the table. To find P(X ≤ 2), we need to sum the probabilities for X = 0, 1, and 2.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.216 + 0.432 + 0.288

= 0.936

Therefore, the probability of rolling a 6 two or fewer times in three trials is 0.936 (rounded to 3 decimal places).

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Answer:0.432

Step-by-step explanation:

edge

The new budget for each category would be:

Housing: $19,680

Food: $8,856

Transportation: $8,856

Other goods and services: $11,808

After the government mandate, the average individual's salary would be reduced by 40%:

New annual salary = $82,000 - (40% x $82,000) = $49,200

Similarly, the prices of all goods and services would be reduced by 40%. Therefore, the new amounts spent on each category would be:

Housing: $32,800 - (40% x $32,800) = $19,680

Food: $14,760 - (40% x $14,760) = $8,856

Transportation: $14,760 - (40% x $14,760) = $8,856

Other goods and services: $19,680 - (40% x $19,680) = $11,808

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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.)

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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

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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.

The equation of the circle in the form (x - h)² + (y - k)² = r² is (x + 7)² + 7(y - 33/7)² = 49.

The equation of a circle is given by the standard form:

(x - h)² + (y - k)² = r²

where

h = center of the circle

r = radius of the circle.

To find the center and radius of the circle in the given equation:

x² + 14x + y - 8y = -16

we need to rewrite the equation in standard form

(x - h)² + (y - k)² = r²

First, let's group the x-terms and y-terms separately:

x² + 14x + y - 8y = -16

Decompose the equation on the left

x² + 14x = (x + 7)² - 49

y - 8y = -7y

Substituting the above expressions back into the original equation, we get:

(x + 7) - 49 - 7y = -16

Simplifying the equation:

(x + 7)^2 + 7y = 33

Now, we can rewrite the equation in standard form by completing the square again, this time for y:

(x + 7)² + 7(y - 33/7)² = 49

Comparing this with the standard form (x - h)² + (y - k)² = r², we have:

centre of the circle = (-7, 33/7)

radius = 7.

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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.

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 total cost of the fabric that Christine needs for the tablecloths is $90.0.

A rectangle is a figure which has four sides of which opposite sides have equal length.

The area of a rectangle is the amount of space to be covered by the figure in a 2 dimensional plane.

Area of a rectangle = length x width

In the information given, we have;

area of the tablecloth = length x width

                      = 6 x 5/2

                      = 3 x 5

                      = 15

The area of the tablecloth is 15 sq. ft.

But Christine plans to make 1 tablecloth for each 4 seasons of the year.

So that;

total area of tablecloth needed for the year = 15 x 4

                            = 60 sq. ft

Then the fabric costs $1.50 per square foot,

total cost of fabric needed = 60 x $1.5

                                             = $90.0

The total cost of the fabric that Christine needed for the tablecloth is $90.0

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A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?

The resultant force acting on the block is 47.6N.

The acceleration of the block will be 23.8 m/s².

The speed of the block after 5 seconds of movement is 119 m/s.

In this question, we need to make use of Newton's second law, hence:

resultant force = mass × acceleration

So, for question a. The value of the resultant force  will be obtained by adding the two forces together:

resultant force = F₁ + F₂

                       = 25N + 22.6N

                        = 47.6N

b.  Its acceleration will be:

acceleration = resultant force / mass

                  = 47.6N / 2kg

                  = 23.8 m/s²

c. The speed of the block after 5 seconds of movement will be:

Velocity  (v) = u + at

velocity = initial velocity + acceleration x time

Based on the block was initially at rest, the initial velocity is 0.

Hence:

V = acceleration x time

    = 23.8 m/s² x 5s

     = 119 m/s

Hence the speed of the block after 5 seconds of movement will be: 119 m/s.

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See full text below

The block in the figure is at rest when the forces begin to act.

F₁ = 25N

F, = 22.6 N

m = 2kg

to. Find the value of the resultant force.

b. Determine its acceleration.

C. Calculate the speed of the block after 5 seconds of movement.

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.

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Answer:

To solve for y in the equation:

3y - 1/3 = 5

First, we need to isolate the term containing y by adding 1/3 to both sides of the equation:

3y - 1/3 + 1/3 = 5 + 1/3

Simplifying the left-hand side:

3y = 5 + 1/3

Next, we need to isolate y by dividing both sides of the equation by 3:

3y/3 = (5 + 1/3)/3

Simplifying the right-hand side by finding a common denominator:

3y/3 = (15/3 + 1/3)/3

3y/3 = 16/3

Simplifying the left-hand side:

y = 16/9

Therefore, the solution to the equation 3y - 1/3 = 5 is y = 16/9.

Step-by-step explanation:

The calculated value of the  length of the arc JK is 35π/12

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

central angle = 75 degrees

Radius = 7

Using the above as a guide, we have the following:

Arc JK = central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

JK = 75/360 * 2 * π * 7

Evaluate

JK = 35π/12

Hence, the length of the arc JK is 35π/12

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Complete question

Find the indicated measure. Length of JK

See attachment

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%.

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The possible values lx + 5| = 6 of x in the equation are x = -11 or x = 1

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

lx + 5= 6

Express properly

So, we have

lx + 5| = 6

The above equation is an absolute value equation

When the above equation is expanded, we abe

x + 5 = -6 or x + 5 = 6

Solving for x in the equations. we have

x = -11 or x = 1

This means that the values of x in the equation are x = -11 or x = 1

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The requried position of point B on the number line is 1/4 or 0.25.

Since point B represents the number 0.25 on the number line, its position can be described as 0.25 units to the right of 0 or as 0.25 units to the left of 0.5.

Alternatively, we can describe its position as a fraction or mixed number using the length of the number line as the denominator. If the number line extends from 0 to 1, then the position of point B can be expressed as:

B = 0 + 0.25 = 1/4

Therefore, the position of point B on the number line is 1/4 or 0.25.

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The equation in each case will be 5(x - 2) = x + 7, 2x - 4 > 10, and 2x - 2 = x + 5 and their solution will be 4.25, more than 7, and 7, respectively.

1. Let the number be x. Then the equation can be written as,

5(x - 2) = x + 7

5x - 10 = x + 7

4x = 17

x = 4.25

2. Let the number be x. Then the equation can be written as,

2x - 4 > 10

2x > 14

x > 7

3. Let the number be x. Then the equation can be written as,

2x - 2 = x + 5

x = 7

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The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).

Given expression is,

[15 / (x - 6)] + [7 / (x + 6)]

Cross multiplying the two fractional expressions,

= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]

= [15x + 90 + 7x - 42] / [x² - 6²]

= (22x + 48) / (x² - 36)

Hence the equivalent expression is D.

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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.

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Answer:

4 months

Step-by-step explanation:

This question is just asking you to construct a system of equations!

The amount that they will start with will be the y-intercept, because that's the amount in the bank account when no time has passed (aka since no additional deposits were made).

Chrisitiana: 10x + 50 = y

Marlena: 15x + 30 = y

Y in this case is going to be the amount of money in the bank account when x amount of months have passed. We want both y values to be the same.

10x + 50 = y = 15x + 30

Cut out the y as a middleman and we have

10x + 50 = 15x + 30

-10x

50 = 5x + 30

-30

20 = 5x

/5

4 = x

They will have the same amount of money in their accounts after 4 months.