Suppose A = {2, 5, 7, 9, 13, 25, 26}.
(a) Find n(A).
n(A) =

(b) T/F: 20 A
True
False

The actual distance between towns on the map is 350km

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given;

The scale on the map is 1:5,000,000

Which implies that 1 cm on the map represent 5,000,000 cm in the actual;

Remember that;

1km = 1000m

1m= 100cm

1km= 100000cm

Convert cm to Km;

Divide by 100,000

5,000,000cm= 5,000,000/100,000= 50km

Now 1:5,000,000= 1cm/50km

That means

1 cm on the map represent 50 Km in the actual

So, 7 cm apart on the map

Multiply by 50

7 x 50= 350km

Hence, the answer to this question in kilometers is 350km

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Answer:105

Step-by-step explanation:

let the number is x

Then 15% of x = 0.15x = 45 .

x= 45/0.15

x = 300

now 50 % of x = 0.5x =150

x = 150/0.5

x= 300 (crosscheck correct)

now 35% of 300 = 0.35 ×3000

= 105

The displacement of the particle from time t = 0 and t = 5, with the velocity function, v(t) = arctan(t² + t - 1), using numerical integration which is the difference in the values of the indefinite integral at t = 0 and t = 5, we get option B

B. 5.504

The indefinite integral of a function is the antiderivative of the function, which does not have limits.

The function for the velocity is; v(t) = arctan(t² + t -1)

The position of the particle at time t = 0 is x = 0.085

The duration of the required displacement (between time t = 0 and t = 5)

The displacement = The area under the velocity time graph, therefore;

Displacement = ∫v(t)

Using substitution method, which is the similar to the inverse of chain rule, we get;

[tex]\int\limits {arctan(t^2+t-1)} \, dt = t\cdot arctan(t^2+t-1)-\int\limits {\frac{t\cdot (2\cdot t+1)}{(t^2+t-1)^2+1} } \, dt[/tex]

The value of ∫v(t), using manual steps on an online calculator, is a large expression, however, using numerical integration, we get;

[tex]\int\limits^5_0 {arctan(t^2+t-1)} \, dt \approx 5.504[/tex]

The displacement of the particle from time t = 0 to time t = 5 is about 5.504. The correct option is therefore;

B. 5.504

The displacement is the change in the position of the particle, and is the shortest distance between the particle's current position and the initial position of the particle

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The value of the investment will be lesser by $26325.30 $25657.08 $668.22 $26325.30 −$25657.08 = $668.22 if the interest is compounded daily rather than annually.

What's composite interest?

The investment compounded annually will be worth $16,640 after 16 years, while the investment compounded periodically with 4 interest periods per year will be worth $16,383.84.

To calculate the investment compounded annually, we can use the formula:

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

where:

A = the future value of the investment

P = the principal amount (i.e., the initial deposit)

r = the annual interest rate as a decimal

n = the number of times the interest is compounded per year

t = the number of years the money is invested for

So for this example, we would have:

A = $10,000 * (1 + 0.04)^(16) = $16,640

For the investment compounded periodically, the formula is a little different:

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

where:

A = the future value of the investment

P = the principal amount (i.e., the initial deposit)

r = the annual interest rate as a decimal

n = the number of times the interest is compounded per year

t = the number of years the money is invested for

So for this example, we would have:

A = $10,000 * (1 + 0.04/4)^(4 * 16) = $16,383.84

As you can see, the investment compounded annually is worth slightly more than the investment compounded periodically with 4 interest periods per year.

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Answer: x+y=7, x+3=y

Step-by-step explanation:

For 1, since the exponential decay formula is a*(1-r)^x, a is still the same as the base value and r would replace 1-r with r being the decay rate, so r would be 1-the decay rate.

For 2, applying that formula, getting 52500*(1-2.5%)^10 (because it's for 10 years and compounded annually). Since 100% is 1, 2.5% is 0.025, and

1-0.025=0.975. Putting that in, we get 52500*(0.975)^10=around 40757 people.

For inverse functions, what we do is have y=2x+1, so we switch x and y and solve for y, so in x=2y+1 we subtract one from both sides to get x-1=2y. Next, dividing both sides by 2, we get (x-1)/2=y as our inverse. Since we want positive integers less than 10, (x-1) has to be even and therefore x has to be odd. Hence, we get that x can be 9 while y can be 4 for (9, 4)

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Answer:

Step-by-step explanation:

Sure

Answer:

7v^10

Step-by-step explanation:

The graph does not represent a function, because is is possible to draw a vertical line that intersects the graph more than once.

An infinite number of nodes or vertices and the connecting edges make up a graph, which is a type of non-linear data structure. When dealing with real-world issues, graphs in data structures are used because they model the issue as a network, similar to social networks, telephone networks, and circuit networks.

In a telephone network, for instance, it might depict a single user as nodes or vertices, with the telephone line connecting them as edges.

The non-linear type of data structure known as a graph is composed of nodes, also known as vertices and edges. In a graph, the nodes, which are also referred to as vertices, are connected by edges.

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Answer:

2 * 1 ==> 1st option

Step-by-step explanation:

Matrix dimensions are:

number of rows by number of columns

The number of rows is 2   :   ( 2 and 12 are the rows)

The number of columns is 1   :  ( 2      

                                                    12 )    

Hence, the dimensions is 2 * 1.

Answer:

To the nearest dollar, Savannah would have $8,007 more in her account than Lincoln.

Step-by-step explanation:

To find out how much more money Savannah would have in her account than Lincoln after 20 years, we need to calculate the future value of both investments using the appropriate interest rate and compounding period.

For Lincoln's investment:

Future value = $6,500 * (1 + (3^3/4/100) / 4)^(4*20) = $6,500 * (1 + 0.046875)^80 = $6,500 * 2.611 = $16,917.50

For Savannah's investment:

Future value = $6,500 * e^(0.041875*20) = $6,500 * 3.843 = $24,924.50

To find the difference between the two investments, we can subtract Lincoln's future value from Savannah's:

$24,924.50 - $16,917.50 = $8,007

To the nearest dollar, Savannah would have $8,007 more in her account than Lincoln.

Answer: The result of the exercise is BRL 15.00

Step by step explanation:

To find the total value, simply multiply the number of sheets and the price per copy.

[tex]\sf{ \bold{30 * 0.50} ={\boxed{\bold{15 \: \: real}}} }[/tex]

Rpt: The result of the exercise is BRL 15.00

Answer:

360 kilometres

Step-by-step explanation:

To find the distance a car would have to cover if it has been traveling for four and a half hours, you can use the formula:

distance = speed x time

In this case,

distance = 80 km/hour x 4.5 hours

To calculate the distance in kilometers, we multiply the speed in kilometers per hour by the time in hours.

distance = 80 x 4.5

distance = 360 kilometers

So, the car would have to cover 360 kilometers if it has been traveling for four and a half hours at 80 km/hour.

The boat and the whale are about 218.5 miles apart.

Using the Pythagorean theorem to calculate the distance between the boat and the whale.

Let's call the distance between the boat and the whale "d" and the time they moved apart "t".

1st movement:

d = 45t

2nd movement:

d = (45t + 25(t+35))²

To calculate the final distance, we need to square d from the second movement and add the result from the first movement.

d² = (45t)² + (25(t+35))²

We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.

d² = (4535)² + (2560)²

Taking the square root of the result and get the final distance between the boat and the whale.

d =  ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])

d ≈ 218.5 miles

Hence, the boat and the whale are about 218.5 miles apart.

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Answer:

Step-by-step explanation:

?

|z|^2 = |z|*|z| = (|z|)^2

Since the argument of z is pi/4, z can be written as z=r*(cos(pi/4)+i*sin(pi/4)) where r is the magnitude of z.

We also know that |x-w| =sqrt(5).

This means that |z-w| = sqrt(5).

Substituting the expression for z, we get:

|r*(cos(pi/4)+i*sin(pi/4))-w| = sqrt(5)

Simplifying this equation, we get:

|r-2-i| = sqrt(5)

Squaring both sides, we get:

(r-2-i)(r-2+i) = 5

Simplifying, we get:

r^2-4+i(2r-2)=5

Equating the real and the imaginary parts, we get:

r^2-4 = 5

and

2r-2=0

Solving these equations simultaneously, we get:

r = sqrt(9)

Therefore,

|z| = sqrt(9)

Hence,

|z|^2 = (sqrt(9))^2 = 9

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{b + b + b + b + b}\\\mathsf{= 1b + 1b + 1b + 1b + 1b}\\\mathsf{= 2b + 2b + 1b}\\\mathsf{= 4b + 1b}\\\mathsf{= 5b}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{5b}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

b+b+b+b+b is 5b

[tex]\vec A = \left[\begin{array}{cccc}- 3&- 14&7 &18\\-13&-2&-5 & -6\end{array}\right][/tex]

In this problem we find a matrix as result of the addition of two matrices. According to linear algebra, matrix addition is performed between matrices with same number of rows and columns. There, matrix A must have two rows and two columns to make addition operation possible, that is:

[tex]\vec A + \left[\begin{array}{cccc}3&9&-1 &-8\\16&- 2&3 & 13\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}3 + a_{11}&9+a_{12}&-1+a_{13} &-8+a_{14}\\16+a_{21}&- 2+a_{22}&3+a_{23} & 13+a_{24}\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]

And we shall solve the following equations:

First row

3 + a₁₁ = 0

9 + a₁₂ = - 5

- 1 + a₁₃ = 6

- 8 + a₁₄ = 10

Second row

16 + a₂₁ = 3

2 + a₂₂ = 0

3 + a₂₃ = - 2

13 + a₂₄ = 7

The solutions to the equations are: a₁₁ = - 3, a₁₂ = - 14, a₁₃ = 7, a₁₄ = 18, a₂₁ = - 13, a₂₂ = - 2, a₂₃ = - 5, a₂₄ = - 6.

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Answers:

(a)    $1092.03

(b)    $1093.08

===========================================

Work shown for part (a)

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.09/2)^(2*1)

A = 1000*(1+0.045)^(2)

A = 1000*(1.045)^(2)

A = 1000*1.092025

A = 1092.025

A = 1092.03

Don't forget to round to the nearest penny, aka nearest hundredth.

-----------------------------------

Work shown for part (b)

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.09/4)^(4*1)

A = 1000*(1+0.0225)^(4)

A = 1000*(1.0225)^(4)

A = 1000*1.09308331878906

A = 1093.08331878906

A = 1093.08

The triangles  ΔPQR ≈ ΔXYZ are similar by Angle-Angle Similarity.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are items that feature more than two figures that are the same shape but different sizes.

Given two triangles, ΔPQR and ΔXYZ

both the triangles are right triangles,

∠P = ∠Z = 90°

and given ∠R = ∠Y = 62°

A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.

From the above-described figure

ΔPQR ≈ ΔXYZ

so triangles are similar to Angle-Angle Similarity.

Hence the triangles are similar.

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The solution of the equation (x - 5)² + 3(x - 5) + 9 = 0 is x = -7 ± √35/2. Option B

From the information given, we have the equation as;

(x - 5)² + 3(x - 5) + 9 = 0

To solve the equation, take the following steps;

(x -5)(x-5) + 3x - 15 + 9 = 0

x² - 5x - 5x + 25 + 3x - 15 + 9 = 0

Now, collect like terms

x² - 5x - 5x + 3x + 25 - 15 + 9 = 0

add or subtract the like terms

x² - 7x + 21 = 0

The quadratic formula is is given as;

x =[tex]-b[/tex] ± [tex]\frac{\sqrt{b^2 - 4ac} }{2a}[/tex]

substitute the values

x = -(7) ± [tex]\frac{(-7)^2 - 4(1)(21)}{2(1)}[/tex]

expand the bracket

x = -7 ± [tex]\sqrt{\frac{49 - 84}2} }[/tex]

x = -7 ± √35/2

Hence, the value is x = -7 ± √35/2

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Usain's speed in miles per hour is 22.72 mph.

Speed = Distance/Time

Distance = Speed X Time

Time = Distance / Speed

Given:

Usain run 100 yards in 9 sec.

So, he can 1760 yards in

= 9/100  x 1760

= 158.4 sec

As, his speed in yards/ sec= 100/9

So, 1760 yard= 1 mile and 3600 sec = 1 hour

Now, the speed in miles per hour

= 100/ 9 x 3600/1760

= 100/9 x 2.045

= 22.72 mph

Hence, the speed is 22.72 mph.

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Answer:

Step-by-step explanation:

volume  of cylinder is

[tex]V = \pi r^{2}h[/tex]

In your cylinder, r = 20 and h =20

V = 3.14 x 20^2 x 20

   =25 120.00 ft^3

Please note: The numbers in the question seem wrong if your teacher wants you to round to the nearest hundredth.  Double check if the information.  They might have said " 0.1 times" instead of 1 times or they meant the nearest hundred instead of the nearest hundredth.  Please check.

The equation of the line that passes through the points ( − 1 , − 5 ) and (1, 3) is y = 4x - 1

The slope, m of the linear function is calculated using the points on the graph (-1, -5) and  (1, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-5 - 3) / (-1 - 1)

m = (-8) / (-2)

m = 4

equation passing through point (1, 3)

(y - y₁) = m (x - x₁)

plugging in the points

y - 3 = 4 * (x - 1)

y - 3 = 4x - 4

y = 4x - 4 + 3

y = 4x - 1

The equation of the line passing through points  (-1, -5) and  (1, 3) is written as y = 4x - 1

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Answer:

2× radius of the circle

Step-by-step explanation:

The line segment joining two points on the circle and passing through the centre is the diameter.

The single fraction is 7x/20

A fraction can be defined as the part of a whole variable, number or element.

The different types of fractions are;

Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.

They are made of operations such as multiplication, addition, subtraction, division, etc

Given the expression;

3/4x - 2/5x

Find the LCM

15x - 8x/20

7x/20

Thus, the value is 7x/20

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Considering the properties of the angles of the given triangle, the required prove is explained below.

When it can be observed that two sides and measure on internal angles of a given triangle are equal, then it can be inferred that it is an isosceles triangle. Thus the measure of the internal angles that are opposite to the equal sides are the congruent angles.

Considering the given isosceles triangle, the properties of angles required for the prove are:

             STATEMENT                                   REASON

1. LO ≅ NO                                 Congruent sides of isosceles triangle.

2. <LOM ≅ <NOM                      Angle bisector property.

3. LM ≅ NM                                Definition of midpoint.

4. <LMO ≅ <NMO                      Definition of a perpendicular bisector.

5. <OLM ≅ <ONM                      Congruent angles of an isosceles triangle.

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Answer:

me I would guess

Step-by-step explanation:

like break it down step by step or just buy answers

The value of the specified finite sum is -15.

The correct option is D.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The finite sum,

[tex]\sum^n_{k=1}{a_k = 5[/tex],

and [tex]\sum^n_{k=1}{b_k = 10[/tex].

Now,

[tex]\sum^n_{k=1}{a_k -2b_k = \sum^n_{k=1}{a_k -2\sum^n_{k=1}{b_k[/tex]

Substituting the values,

[tex]\sum^n_{k=1}{a_k -2b_k[/tex] = 5 - 20

                      = -15

Therefore, the value is -15.

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Answer:

\frac{27}{17}+\frac{28}{17}i

Step-by-step explanation: