Use the original price and the markdown to find the retail price. Original price: $100; Markdown: 28%. What is retail price ?​

The yield to maturity on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time is 37.14%.

Yield to maturity (YTM) is the total return anticipated on a bond or other fixed-interest security if the security is held until it matures. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In this problem, the present value (PV) of the simple loan is $1,500, the future value (FV) is $7,500, the time to maturity is five years, and the interest rate is the yield to maturity (YTM).

Now we will calculate the yield to maturity (YTM) using the formula for the future value of a lump sum:

FV = PV(1 + YTM)n,

where,

FV is the future value,

PV is the present value,

YTM is the yield to maturity, and

n is the number of periods.

Plugging in the given values, we get:

$7,500 = $1,500(1 + YTM)5

Simplifying this equation, we get:

5 = (1 + YTM)5/1,500

Multiplying both sides by 1,500 and taking the fifth root, we get:

1 + YTM = (5/1,500)1/5

Adding -1 to both sides, we get:

YTM = (5/1,500)1/5 - 1

Calculating this value, we get:

YTM = 0.3714 or 37.14%

Therefore, the yield to maturity on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time is 37.14%.

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Answer:

10.) x = 29

11.) x = 144

Hope this helps!

The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

a) 60.4

b)2.4×10^6

c)1.47×10^-3

Step-by-step explanation:

here is the answer

Step-by-step explanation:

take any two points of the line and find .

Answer:

17*

Step-by-step explanation:

180*-163*=17*

Answer:

3
4
2
5
1

Step-by-step explanation:

(4.3 x 10^6)*(9.8 x 10^-4)=4.214x10^3
(2.9 x 10^7)*(1.6 x 10^-9)=4.64x10^-2
(4.7 x 10^3)*(8.6 x 10^-7)=4.042x10^-3
(3.8 x 10^-4)*(6.1 x 10^2)=2.318x10^-1
(4.042x10^-3)/(2.318x10^-1)=1.74x10^-2
(4.9 x 10^3)*(7.4 x 10^-6)=3.626x10^-2
(3.9 x 10^5)*(8.7 x 10^-3)=3.393x10^3
(3.7 x 10^-5)*(2.9 x 10^8)=1.073x10^4
(3.393x10^3)/(1.073x10^4)=3.16x10^-1
sorry took a while but hope that helps

Answer:

1) Event A = 2/3

   Event B = 1/2

2) 1/2

Step-by-step explanation:

1)

Event A :

No. we need on dice = 4

Total numbers on dice = 6

Hence sample space of the event = 6

P( getting 4) = 4/6 = 2/3

Event B :

A coin has a head & a tail.

Hence sample space of the event = 2

But as we need tail only ,

P ( getting Tail ) = 1/2   [ if only tossed once ]

2)

Total numbers on a die = 6

Total no. of odd numbers on die = 3 (∵ 1 , 3 & 5 are odd )

Sample space of this event = 6

P (getting an odd number) = 3/6 = 1/2

(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Solution

By definition of similar figures:

Similar figures are two figures having the same shape

The polygons that are similar to poly gone 1 are

Polygon 3 and Polygon 4

Answer: 360 miles

Step-by-step explanation: 640/16=40. 40x9=360.

The value of the fifth term (a₅) is 96.

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the value of the fifth term (a₅) as follows;

a₅ = -2a₅₋₁

a₅ = -2a₄

a₅ = -2 (-2a₄₋₁)

a₅ = 4a₃

a₅ = 4 (-2a₃₋₁)

a₅ = -8a₂

a₅ = -8 (-2a₂₋₁)

a₅ = 16 a₁

a₅ = 16 × 6

a₅ = 96

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Answer:

3. from right to left is: -1.9, -.6, .4, 1.1

4. C

5. B

Answer:

3) -1.9, -.6, -.4, 1.1

4) C

5) A

Step-by-step explanation:

3) -1.9, -.6, -.4, 1.1

4) C

18-6=12

12/3=4

-6/3=-2

18-2=16

4<16

5) A

24/4=6

6+2(4)=14

x+2x=3x

3(4)=12

24/12=2

12>2

Answer:

10 Km/h

Step-by-step explanation:

Let the speed of the container ship be y

The speed of the aircraft = y + 5

Next, we shall determine the time taken by the aircraft to travel 450 Km. This can be obtained as follow:

Speed of aircraft (Sₐ) = y + 5

Distance travelled (dₐ) = 450 Km

Time for aircraft (tₐ) =?

Speed = distance / time

Sₐ = dₐ / tₐ

y + 5 = 450 / tₐ

Cross multiply

(y + 5) × tₐ = 450

Divide both side by (y + 5)

tₐ = 450 / (y + 5)

Finally, we shall determine the speed of the carrier. This can be obtained as follow:

Speed of container ship (S꜀) = y

Distance travelled (d꜀) = 300 Km

Time for container ship (t꜀) = Time for aircraft (tₐ)

Time for aircraft (tₐ) = 450 / (y + 5)

t꜀ = tₐ

t꜀ = 450 / (y + 5)

Speed = distance / time

S꜀ = d꜀ / t꜀

y = 300 ÷ 450 / (y + 5)

y = 300 × (y + 5) / 450

y = (300y + 1500) / 450

Cross multiply

450y = 300y + 1500

Collect like terms

450y – 300y = 1500

150y = 1500

Divide both side by 150

y = 1500 / 150

y = 10 Km/h

Thus, the speed of the container ship is 10 Km/h.

Answer: C.

Step-by-step explanation:

Step-by-step explanation:

\( = \lim \limits_{x \to0}x \cot(2x) \)

\( = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \)

\( = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \times \frac{2x}{2x} \)

\( = \lim \limits_{x \to0} \frac{2x}{ \tan(2x) } \times \lim \limits_{x \to0} \frac{x}{2x} \)

\( = \lim \limits_{u \to0} \frac{u}{ \tan(u) } \times \frac{1}{2} \)

\( = \frac{1}{2} \)

Answer:

12

Step-by-step explanation:

2a + 2b is 2 times a + b

Therefor, the answer will be 2 times the sum of a+b

6x2 = 12

Answer:

weeks..................... 4 3 2 1

amount in dollar..28 21 14 7

The correlation coefficient will provide a numerical value that quantifies the strength and direction of the relationship, allowing the teacher to evaluate the association.

In this case, since the teacher wants to investigate the relationship between being on time or late for class and exam performance, an appropriate single statistic to examine the relationship would be the correlation coefficient.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this scenario, the two variables of interest are being on time or late for class (categorical variable) and exam performance (quantitative variable).

By calculating the correlation coefficient, the teacher can determine whether there is a statistically significant relationship between being late to class and exam performance. The correlation coefficient can range from -1 to +1, where a value close to +1 indicates a strong positive correlation (as being late increases, exam performance tends to increase), a value close to -1 indicates a strong negative correlation (as being late increases, exam performance tends to decrease), and a value close to 0 indicates no significant correlation.

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The answer of the question based on population growth is , the estimated population after one year is approximately 34 deer.

To estimate the population after one year, we can use the formula for exponential growth:

P = P0 * (1 + r)^t.

P0 represents the initial population (20 deer in this case), r represents the growth rate (70% or 0.7 as a decimal), and t represents the time period in years (1 year in this case).

Using these values, we can calculate the population after one year as follows:

P = 20 * (1 + 0.7)¹
P = 20 * 1.7
P ≈ 34

Therefore, the estimated population after one year is approximately 34 deer.

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We have explained the ASA rule of congruency of the triangle

What is an ASA congruency of triangles?

ASA Congruence. Angle-Side-Angle. If two angles in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.

If a triangle PQR is congruent to a triangle ABC, we write it as ∆ PQR ≅ ∆ ABC.

Note that when ∆ PQR ≅ ∆ ABC, then sides of ∆ PQR fall on corresponding equal sides of ∆ ABC and so is the case for the angles.

This means that PQ covers AB, QR covers BC, and RP covers CA;

∠P, ∠Q, and ∠R cover ∠A, ∠B, and ∠C respectively.

Also, between the vertices, there is an existence of one-one correspondence.

That is, P corresponds to A, Q corresponds to B, R corresponds to C and it is written as

P↔A, Q↔B, R↔C

Under this condition, the correspondence ∆ PQR ≅ ∆ ABC is true but is not correct for the correspondence ∆QRP ≅ ∆ ABC.

Hence, we have explained the ASA rule of congruency of the triangle

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Answer:

n+14

Step-by-step explanation:

you just add 14 to n and since you can't put the n and the 14 together it's just n+14

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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The height of the  building which casts a 103-foot shadow is 95.5 foot.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow

We need to find the height of the building.

Let us consider x be the height of building.

Form a proportional equation.

x/103=32/34.5

Apply cross multiplication

34.5x=32×103

34.5x=3296

Divide both sides by 34.5

x=3296/34.5

x=95.5

Hence, 95.5 foot be the height of the  building which casts a 103-foot shadow.

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Answer:

Option B

Step-by-step explanation:

We have to solve this system of equations by using the Substitution method so here goes,

\(Equation\ 1\\\\\y=x^2+5x+3\\\\Equation\ 2\\\\\ y=\sqrt{2x+5}\\\)

We insert equation 2 in equation 1 since both equations are equal to y so we equate both of them,

\(\sqrt{2x+5}=x^2+5x+3\\Square\ both\ sides\\\\\2x+5=(x^2+5x+3)^2 \\\)

To square the right hand side suppose

\(a=x^2+5x\\b=3\\(a+b)^2=a^2+2ab+b^2\\(x^2+5x)^2+2(x^2+5x)(3)+(3)^2\\\\((x^2)^2+2(x^2)(5x)+(5x)^2)+6(x^2+5x)+9\\x^4+10x^3+25x^2+6x^2+30x+9\\x^4+10x^3+31x^2+30x+9\\\)

Now,

\(2x+5=x^4+10x^3+31x^2+30x+9\\x^4+10x^3+31x^2+30x-2x+9-5=0\\x^4+10x^3+31x^2+28x+4=0\\\)

Apply Newton-Raphson method to quickly determine the approximate solution of the polynomial we get the values of x to be,

x ≈ -0.175 and x ≈ -1.22

now insert these values into equation 1 or 2 to get the values of y

we use the first value ,

\(y=x^2+5x+3\\y=(-0.175)^2+5(-0.175)+3\\y=2.155\\\)

now for the second value of x,

\(y=x^2+5x+3\\y=(-1.22)^2+5(-1.22)+3\\y=-1.612\)

now since the second set of values are not in the options we ignore the second set of values which are ( -1.22 , -1.612)

we use the first set of values which are (-0.175 , 2.155) which rounded off lead to (-0.2 , 2.1), so Option B is your answer

I also attached a graphical representation so you can verify the answer yourself , The approximate solution of this system of equation is the point of intersection between both the graphs which is marked on the image.