Calculate the area of the figure below using the following information:

Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units

The future value (A) is approximately 5610.2 for the given investment and annu $4000 for 5 years at 7% compounded annually

To find the compound amount and compound interest rate for the given investment, we can use the formula for compound interest:

(a) The compound amount in the account after 5 years can be calculated using the formula:

A = P(1 + r/n)^(nt)

Where A is the compound amount, P is the principal (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal (P) is $4000, the interest rate ® is 7%, and the interest is compounded annually (n = 1), and the investment is for 5 years (t = 5), we can plug these values into the formula:

A = 4000(1 + 0.07/1)^(1*5)

A = 4000(1 + 0.07/1)^(1*5)

= 4000(1 + 0.07)^(5)

= 4000(1.07)^(5)

≈ 4000(1.402551)

≈ 5610.20

Therefore, the future value (A) is approximately 5610.2

Calculating this expression will give us the compound amount after 5 years.

(b) The compound interest earned can be calculated by subtracting the principal from the compound amount:

Compound interest = Compound amount – Principa

This will give us the total interest earned over the 5-year period.

By evaluating the expressions in (a) and (b), we can determine the compound amount and the compound interest earned for the given investment.

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The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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For the given system of equation, the value of x = 4 and the value of y = -1

From the question, we are to solve the given system of equations

-7x + 4y = -32 -------- (1)

9x - 2y = 38   -------- (2)

From equation (2)

9x - 2y = 38

2y = 9x - 38

y = 4.5x - 19 -------- (3)

Substitute this into equation (1)

-7x + 4y = -32

-7x + 4(4.5x -19) = -32

-7x + 18x - 76 = -32

-7x + 18x = -32 + 76

11x = 44

x = 44/11

x = 4

Substitute the value of x into equation (3)

y = 4.5x - 19

y = 4.5(4) - 19

y = 18 - 19

y = -1

Hence, the value of x = 4 and the value of y = -1

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Answer:

I think it's true

Step-by-step explanation:

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

because the given graph is linear...when the graph is linear the given relationship is always linear.

Answer:

the first one is 14 45

second one is 3 hours

lastly its 260km  

Step-by-step explanation:

1 becuase u add 2 to 12 u get 14

2  u could do the same thing and minus them by each other to get the answer

and lastly u can multiply 65 by 4 and get the km

Answer:

8

Step-by-step explanation:

In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.

The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:

\(56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3\)·\(7\)

\(72=(24)(3)=8(3)(3)=2^3\)·\(3^2\)

Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the \(2^3\).

Thus, \(2^3=8\) is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.

Answer:

yeah sure

Step-by-step explanation:

all I can say if you wanna find the starting point of a quadratic graph use the rule (-b/2a).

use that rule to find x or h then substitute in your quadratic equation , and with the that you found out using rule.

then you will find the y or k then make a table of values and put the vertex of the x and y that you found.

then add two values that are less than x and add two values that are more than x then you substitute with the new values in order to find their y.

then point all the points you found and finally draw the graph you will find it like a u shaped graph or called a parabola.

hope this helps

The equivalent equation for a two-input XOR gate is y = ab’ + a’b.

A two-input XOR gate is a logic gate that outputs a high or 1 signal only when the two inputs are different. In other words, the output of an XOR gate is 1 when one input is 0 and the other input is 1, and vice versa.

To represent an XOR gate with an equation, we can use Boolean algebra. The Boolean expression for an XOR gate is y = ab’ + a’b, where y is the output, a and b are the two inputs, and a' and b' represent the complement (or NOT) of a and b, respectively.

This equation can be derived using the laws of Boolean algebra. For example, we know that the product of a variable and its complement is always 0, i.e., a a' = 0. Using this property, we can simplify the equation y = ab’ + a’b as follows:

y = ab’ + a’b
 = ab’ + ab’’ + a’b     (adding a' and b')
 = ab’ + a’b + ab’’    (rearranging terms)
 = ab’(1) + a’b(1)     (using a a' = 0 and b b' = 0)
 = ab’ + a’b            (simplifying)

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By using function, it can be concluded that-

The predictor variables are bed, bath, floor

What is function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

In a function y = f(x), x is the independent variable and y is the dependent variable.

The price of an apartment is dependent on the number of bedrooms, bathrooms and the floor of the apartment

So the required function is p = f(bed, bath, floor) where p is the price of the apartment

The predictor variables are bed, bath, floor

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The required z-intercept is 2 and the distance between the skew lines is 0.80.

Given equation of plane is [x. y. 2] = [-1,-1, 1] + s[1, 0, 1] + [0, 1, 2].

We are to find the z-intercept of the plane.

So we know that the z-intercept occurs when x = 0 and y = 0.

Therefore, substituting these values into the equation of the plane, we get:

[0,0,2] = [-1,-1,1] + s[1,0,1] + [0,1,2]2

= 1 + 2s

So, s = 1/2

Substituting s in the equation of plane, we get:

[x, y, 2] = [-1,-1,1] + 1/2[1,0,1] + [0,1,2][x, y, 2]

= [-1/2,-1,3/2] + [0,1,2]

So, the z-intercept of the plane is 2.

Given two skew lines [x, y, 2] = [1,-1, 1] + [3.0, 4] ,

and [x, y, z] [1, 0, 1] + [3, 0, -1]

We are to find the distance between the skew lines:

Let the direction vector of the line 1 be d1 = [3, 0, 4] and that of line 2 be d2 = [3, 0, -1].

The vector which is perpendicular to both the direction vectors is given by cross product d1 × d2 = i[0 + 4] - j[(-1) × 3] + k[0 + 0]

= 4i + 3k

So, a = 4, b = 0, c = 3.

The given point on line 1 is [1, -1, 1] and that on line 2 is [1, 0, 1].

So, the required distance is [1, -1, 1] - [1, 0, 1])· (4i + 0j + 3k) / √(4² + 0² + 3²)

= (-4/5)

So, the required distance is 0.80 (approx).

Therefore, the required z-intercept is 2 and the distance between the skew lines is 0.80.

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Answer:

6

Step-by-step explanation:

Answer:

∠ N = 10° , arc RS = 134°

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc.

(5)

∠ N is an inscribed angle and we require arc LM

the measure of the arcs in a circle = 360°

note LN is the diameter so arc LN = 180°

Then

LM + MN + LN = 360°

LM + 160° + 180° = 360°

LM + 340° = 360° ( subtract 340° from both sides )

LM = 20°

then

∠ N = \(\frac{1}{2}\) LM = \(\frac{1}{2}\) × 20° = 10°

(6)

∠ Q is an inscribed angle so its intercepted arc is twice its measure

arc RS = 2 × 67° = 134°

The picture shown, shows the first step in the construction of B. Inscribed Square.

The steps to construct an inscribed square from a circle are:

So this picture shows the first step of that process.

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The first step that is being represented here is done during construction of inscribed square. That is option B

Answer:

2.9032

Step-by-step explanation:

Hi.

Hope it helps.

Please mark as brainliest.

Have a good day.

Answer:

2/3 of 27/4÷(14/5-5/4)

=(14/5-5/4)

=56-25/20

=31/20

2/3 of 27/4

=9/2

9/2÷31/20

=90/31

Answer:

Step-by-step explanation:

0

Answer:

Theradius is 16 + 9 = 5. The equation of thecircle is2 2( x− 4) + ( y− 3) = 25. 53.54.x2 + y2 – 4 x ...

A linear model for the situation below passes through the origin. A manufacturer can produce 4,200 gears in 8 hours. How many gears can be made in 1 hour? values of the following algebraic expressions : L 3c2; 72/3; 5a&; ... 2x^-x^-3x-^ by 2 x'^ - 3 x~^ - x-^ ; a" - 1 + ft- " by a^ + ft~i ...

Step-by-step explanation:

A less character after a greater in10 = X. creases its value, as XI X+I, ... the root of each and set one above the other; as, % is the square root of 3X.180 / 90 / 15 lm | 12 VDC | 3 W module | 16 Wh battery | white | ... 48 VDC | PV 23,6 kW | 4 x VE SmartSolar MPPT 25 / 100-TR | 3x VE .

Answer:

  (0, -2)

Step-by-step explanation:

The solution to a system of equations is the point on the graph where the lines intersect.

Here, both lines have a y-intercept of -2, so intersect there. The solution is ...

  (x, y) = (0, -2)

We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.

Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.

The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."

Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.

We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.

Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.

Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.

Hence, 2e >= 3v.

Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.

Since e >= 6, it follows that G is not planar.

Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.

For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.

Let G be a planar graph with n vertices.

By part (a), there exists a vertex v of G with degree <= 5.

We remove v and all its edges from G to get a new graph G' with n - 1 vertices.

By the induction hypothesis, we can color G' with 6 (or less) colors.

We add back v and its edges to G.

Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.

We use a new color for v.

Thus, G can be colored with 6 (or less) colors.

Therefore, by induction, the statement is true for all planar graphs.

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Triangle ADC and ΔBDC are congruent.     then DE ≅ CE

What do you mean by congruent?

Given,

        AD ≅ BC

      ∠BCD ≅ ∠ADC

In triangle ADC and ΔBDC

                    AD ≅ BC    ( GIVEN )

      ∠BCD ≅ ∠ADC          ( GIVEN )

             DC = DC             ( Common line)

so  triangle ADC and ΔBDC are congruent.

             then DE ≅ CE

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There is only one way to pick a president from 1000 number of professors, and that is to select one of the professors.

1. There are 1000 number of professors to choose from

2. The board of trustees can only pick one of the 1000 professors

3. Therefore, there is only one way to pick a president - select one of the professors.

The board of trustees can pick a president from the 1000 professors by considering their qualifications, experience, and other criteria. They can also take into account the opinion of the faculty and students of the college. If applicable, the board may also take into account any applicable legal requirements. Finally, they can make their selection by majority vote.

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Answer:

3.1

Step-by-step explanation:

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

x = - 1

Step-by-step explanation:

Answer:

The axis of symmetry is the line x=1, , and the vertex is the point (1, -1).

Step-by-step explanation:

The standard form of a quadratic function is y= ax^2 + bx + c The formula for finding the equation of the axis of symmetry is x= -b/2a The x-coordinate of the vertex is also -b/2a  and the y-coordinate of the vertex is given by substituting the x-coordinate of the vertex into the original function.

For y= 2x^2 - 4x +1, a= 2,b= -4, and c=1

The axis of symmetry is:

x= -1  ⋅ -4/ 2⋅2

   x=4/4

    x=1

The x-coordinate of the vertex is also 1. The y-coordinate of the vertex is found by:

y= 2(1)^2   -4(1)+1

y=2(1) -4+1

y=2-3

y= -1

So, the vertex is the point (1, -1).

Hope this helps please let me know if I'm wrong.

Without specific table structures and dependencies provided, it is not possible to determine the 1NF, 2NF, and 3NF of the bookorder tables.

To determine the 1NF, 2NF, and 3NF of the bookorder tables, we need to consider the normalization process and identify any dependencies among the attributes. Without the specific table structures and dependencies provided, it is not possible to provide a specific answer. However, in general, the normalization process aims to eliminate data redundancy and update anomalies by organizing data into separate tables based on functional dependencies. In 1NF, each attribute should hold atomic values. In 2NF, non-key attributes should depend on the entire key. In 3NF, non-key attributes should depend only on the key, not on other non-key attributes. The specific normalization steps depend on the specific attributes and dependencies in the given tables.

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Answer:

8 3/4 is a mixed number

Step-by-step explanation:

I don know how to explain

The true statement is t = 2 years.

What is simple interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Here, we have

Given: suppose you deposited $400 in a saving account 2 years ago.

The simple interest rate is 2.5%. The interest you earned in those 2 years is $18.40.

We have to find the true statement.

We concluded that

I = 2.5%

P = $400

t = 2 years

Hence, the true statement is t = 2 years.

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the main answer is that the mean value of the activity time is 21.67. This is calculated using the formula (optimistic + 4 * most likely + pessimistic) / 6.

To find the mean value of the activity time, we can use the three estimates provided: optimistic, most likely, and pessimistic time.

1. The optimistic time is the shortest possible time for completing the activity, which is 11 units.
2. The most likely time is the time that is most likely to be taken to complete the activity, which is 21 units.
3. The pessimistic time is the longest possible time for completing the activity, which is 35 units.

To calculate the mean value, we can use the following formula:
Mean value = (optimistic + 4 * most likely + pessimistic) / 6

Substituting the given values, we get:
Mean value = (11 + 4 * 21 + 35) / 6

Calculating the numerator first:
11 + 4 * 21 + 35 = 11 + 84 + 35 = 130

Now, we can calculate the mean value:
Mean value = 130 / 6

Dividing 130 by 6, we get:
Mean value = 21.67 (rounded to two decimal places)

Therefore, the mean value of the activity time is 21.67.

the main answer is that the mean value of the activity time is 21.67. This is calculated using the formula (optimistic + 4 * most likely + pessimistic) / 6.

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Answer:

x=1/25

Step-by-step explanation:

Answer: -25

Step-by-step explanation:

You would have to divide both sides by 3/5 which is the same as multiplying by 5/3.

x = -15*5/3

x = -75/3 = -25