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In 5 years after depositing 3500, the bank account will have 3850

It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.

The formula for simple interest and procedure we will use to solve this exercise is:

S.I.= (P*R*T)/100

Where:

Information about the problem:

Applying the simple interest formula, we get:

S.I.= (P*R*T)/100

S.I.= (3500*2*5)/100

S.I.= 350

Calculating the total amount that would be in my savings account, we get:

Total amount = P + S.I.

Total amount = 3500 + 350

Total amount = 3850

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The measures of angles α and β and the side lengths h, k, and r, found using trigonometric ratios and the Pythagorean Theorem are;
α = 60°, β = 30°, h = √3, k = 3, r = 2·√3

Pythagorean Theorem states that the square of the length of the hypotenuse side is equivalent to the sum of the squares of the lengths of the legs of a right triangle.

The triangle formed by the sides h, k, and r, is a right triangle

The hypotenuse side of the right triangle = r

The legs of the right triangle are h and k

The measure of arctan(√(3)/3) = β...(1)

The tangent of angle β = h/k

Therefore; arctan(h/k) = β...(2)

Comparison the equations (1) and (2), we get;

h/k = (√3)/3

When h = √3, k = 3

Arctan(√3)/3 = 30°

Therefore;

Angle α and angle β are complementary angles, therefore;

α + β = 90° (definition of complementary angles)

α = 90° - β

α = 90° - 30° = 60°

Pythagorean Theorem indicates that we get;

r² = h² + k²

Therefore; r² = (√3)² + 3² = 3 + 9 = 12

r = √(12) = 2·√3

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Answer:

To find the probability of selecting a green or black marble, we need to add the number of green marbles (16) to the number of black marbles (9) and divide by the total number of marbles (7 + 8 + 16 + 9 = 40). So the probability is:

(16 + 9) / 40 = 0.625 or 62.5% in decimal form.

In mathematics, a combination is a decision taken from a set of independent elements when the order of the choices is unimportant.

A combination is a choice made from a set of separate elements in mathematics when the order of the choices is irrelevant.

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

Combination and permutation are two alternative strategies to divide up a collection of elements into subsets in mathematics. The components of the subset may be arranged in any order when combined. The subset's components are listed in a permutation in a certain order.

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Total number of combinations formed equals 10, She will have a total of 4 winning combinations.

In mathematics, a combination is a decision taken from a set of independent elements when the order of the choices is unimportant.

Combinations are mathematical procedures that count the number of possible configurations from a set of things, where the order of the selection of the elements is not important. You can select any set of items in any arrangement.

In mathematics, there are two additional methods for dividing a set of components into subsets: combination and permutation. When merged, the subset's elements can be put in any order. The elements of the subset are listed in a permutation in a certain sequence.

Given,

There are total 4 number of cubes in the box,

She will win if she chooses cube of same color,

Total number of combinations = [tex]\frac{n!}{r!(n-r)!}[/tex]

where n = total number of items [tex]\frac{4!}{2!(2!)}[/tex],

r = 2

Putting the values in the above formula,

⇒ combinations = [tex]\frac{4 \times 3 \times 2 \times 1}{2 \times 2}[/tex]

⇒ 6

With repetition,

she will have 4 more combinations of same color,

Total combinations = 6 + 4

Total winning combinations will be = Red Red, Blue Blue, Yellow Yellow, Green Green = 4

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The quantity of possible outcomes is known as probability.All events that could possibly occur.

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The required volume of the gas that can fit in the cylindrical tank is given as 6154.4 cubic feet.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,

Radius = 14/2 = 7 feet
The volume of the cylinder is given as,
= πr²h
= 3.14 × 7 ² × 40
= 6154.4 cubic feet

Thus, the required volume of the gas that can fit in the cylindrical tank is given as 6154.4 cubic feet.

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Points T''(x, y) = (10, - 15), U''(x, y) = (10, 0) and V''(x, y) = (25, - 5) are the images of vertices T(x, y) = (- 1, - 1), U(x, y) = (- 1, 2) and V(x, y) = (2, 1).

In this problem we need to make use of rigid transformations on a triangle, rigid transformations are transformations applied on geometric locus such that Euclidean distance is conserved in every site of the locus. We need to make use of the following two operations:

Translation

P'(x, y) = P(x, y) + T(x, y)

Dilation

P'(x, y) = k · P(x, y)  

Where:

First, write the three vertices of the triangle:

T(x, y) = (- 1, - 1), U(x, y) = (- 1, 2), V(x, y) = (2, 1)

Second, apply translation on every vertex:

T'(x, y) = (- 1, -1) + (3, - 2)

T'(x, y) = (2, - 3)

U'(x, y) = (- 1, 2) + (3, - 2)

U'(x, y) = (2, 0)

V'(x, y) = (2, 1) + (3, - 2)

V'(x, y) = (5, - 1)

Third, apply dilation on every image:

T''(x, y) = 5 · (2, - 3)

T''(x, y) = (10, - 15)

U''(x, y) = 5 · (2, 0)

U''(x, y) = (10, 0)

V''(x, y) = 5 · (5, - 1)

V''(x, y) = (25, - 5)

Vertices T(x, y) = (- 1, - 1), U(x, y) = (- 1, 2) and V(x, y) = (2, 1) have the following images T''(x, y) = (10, - 15), U''(x, y) = (10, 0) and V''(x, y) = (25, - 5), respectively.

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The two given triangles are not similar. The correct option is D.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that there are two triangles one triangle has sides 20 and 24. The second triangle has sides 36 and 42.

If the ratio of the two lines should be equal to the other two lines then the triangle will be similar.

( 20 / 36) = ( 24 / 42 )

4 / 9 = 6 / 7

Hence, the two triangles will not be similar.

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On Solving the initial value problem y(t)  , e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0  , we get the solution is y² = e^(2t) - 2t - 1 .

The function is : e⁻²¹ dy/dt =y⁻¹(1-e⁻²t) ;

⇒ e^(-2t)dy/dt = (1/y)(1-e⁻²t)   ..because y⁻¹ = 1/y ;

⇒ ydy = e^(2t)[1-e^(-2t)) dt ;

⇒ ydy = (e^(2t) - 1)dt ;

now integrating both sides of the problem ;

⇒ y²/2 = [e^(2t)/2 - t]+c ;

Now we know that initial value : y(0) = 0 ;

Substituting y(0)= 0 , we get ;

⇒ 0²/2 = [e⁰/2 - 0]+c ;

⇒ c = -1/2 ;

So , the solution is  y²/2 = [e^(2t)/2 - t] - 1/2 .

it can be written as : y² = e^(2t) - 2t - 1 .

Therefore , the solution of the initial value problem is y² = e^(2t) - 2t - 1 .

Solve the following initial value problems for y(t) by antidifferentiation or by aseparation of variables :  e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0  .

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No, the point (2, 3) is not a solution to the linear inequality y < 2x-3, since 3 is not less than 2*2-3, which is 1.

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The solution for different cases of positive integers by using the initial condition y(0) = 1.

A differential equation is an equation that relates an unknown function y to its derivatives, represented by symbols such as y' or y". On the other hand, a positive integer is a whole number greater than zero. For example, 1, 2, 3, and so on are positive integers.

Here we need to  to solve a differential equation where y' is equal to y". In this exercise, we will consider different cases where n is a positive integer.

In the given equation,

=> y' = y", y(0) = 1,

we are trying to find the value of y at any given time a. To solve this equation, we need to use the initial condition y(0) = 1.

By using this condition, we can find the solution for different cases of positive integers.

For the first case, if n = 1, then y(t) = eᵃ.

For the second case, if n = 2, then y(t) = (1 + a²)/2.

Then the solution for different cases of positive integers by using the initial condition y(0) = 1.

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The page where the number 110 appears will be 37.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

An arithmetic sequence 2, 5, 8, 11, 14,... is written in the order in a book. Then the first term is 2 and the common difference is 3. Then the number of terms if the nth term is 110. Then we have

110 = 2 + (n - 1) x 3

108 = (n - 1) x 3

n - 1 = 36

n = 37

The page where the number 110 appears will be 37.

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To find out how many bags of each color should be made, we need to first find the total ratio of bags, which is 3+4+5+8=20.

Next, we find the number of bags in each color by dividing the color's ratio by the total ratio and multiplying by the total number of bags to be made (2000):

   Red bags: (3/20) * 2000 = 300 bags

   White bags: (4/20) * 2000 = 400 bags

   Yellow bags: (5/20) * 2000 = 500 bags

   Black bags: (8/20) * 2000 = 800 bags

So the factory should produce 300 red bags, 400 white bags, 500 yellow bags, and 800 black bags.

For a randomly chosen deceased person from this population in  a certain population,

Probability can be defined as the rate of the number of favorable issues to the total number of issues of an event. For an trial having 'n' number of issues, the number of favorable issues can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability of car accidents was 1.2% i,e 12/10 → 6/5

Probability of deaths due to sharks are 0.0005% → 1/2000

If a person is a surfer then,

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As the alternate hypothesis is a two-tailed test the p-value for this hypothesis test is 0.0512.

Here the null hypothesis, H₀, is μ₁ =μ₂

    Alternate hypothesis,  H₁ , is  μ₁ ≠ μ₂

The statistical test is said to be a two-tailed test. So the critical area of of distributions are on both sides of the range.

Here t test-ind method for spicy module is used.

The output is given as (-1.99 , 0.0512)

In such an output the first value is the test statistic value and second value is the p-value.

So the test statistic value = -1.99

p-value = 0.0512.

So the p-value is 0.0512.

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Answer:

(A). 5,-25,125,-625

Answer:

Step-by-step explanation:

To find the value of P, we need to use the information that the median of the data is 19. The median is the middle value in a set of data when it is arranged in numerical order. The first step is to arrange the data in numerical order which is 6-12 12-18 18-24 24-30 30-36 36-42.

We know that n = 4+3+3+4+10+P = 24+P, where P is the number of students in the age group 36-42.

Since the median is 19, half of the total number of students (n) will have ages less than 19. Therefore, we need to find the number of students whose ages are less than 19. Since 4+3+3 = 10, we know that 10 students are less than 19 years old.

To find P, we need to subtract the number of students whose ages are less than 19 from n, which is 24+P.

n = 24+P

10 = 24+P

P = -14

The value of P cannot be negative, so the given data is not correct. There is missing information that is needed to solve this problem.

Depending on the two coefficients, the confidence sets are either rectangles, trapezoids, squares, or ellipses.

When a confidence set contains two coefficients, the coefficients determine the shape of the confidence set. Depending on the two coefficients, the confidence sets are either rectangles, trapezoids, squares, or ellipses. When the coefficients are the same, as in a linear regression, rectangles are created. When the coefficients are different, as they are in a quadratic regression, trapezoids are created. When the coefficients are inversely connected, squares are created. Finally, ellipses are created when the coefficients, as in a cubic regression, are both distinct. The resulting confidence set can therefore take any of the four previously described shapes depending on the coefficients.

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Two unit squares share the same center. the overlapping region of the two squares is an octagon with perimeter 10/3. The area of the octagon is 0.833 square unit.

Let the octagon's eight successive vertices be A, B, C, D, E, F, G, and H.

Connect the squares' vertices to the shared center O by drawing the segments OA, OB, OC, OD, OE, OF, OG, and OH.

The octagon is divided into 8 triangles by the segments.

The bases of these triangles are AB, BC, CD, DE, EF, FG, GH, and HA; each triangle's height equals 1/2 of a unit.

Consequently, the octagon's surface area is

Area = (1/2) × (1/2) × (AB + BC + CD + DE + EF + FG + GH + HA)

Area = (1/4) × Perimeter of the octagon

Perimeter of the octagon = 10/3

Area = (1/4) × (10/3)

Area = 10/12

Area = 0.833 square unit.

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The number of years will be 5 years, will it take for the amount of money in the account to double.

Here, we have,

The number of years will be computed using the excel formula as:

=N per(rate,pmt,pv,fv,type)

where

N per is number of years

rate is 4%

But is compounded quarterly,

So,

rate = 4% × 4

rate = 16%

pmt is $0

pv is Present value which is -$1,000

fv is future value which is $2,000 (as it will get doubled)

Putting the values above:

=N per(4%× 4,0,-1000,2000,0)

= 4.67 years or 5 years

Therefore, the amount will get double in 5 years will it take for the amount of money in the account to double.

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Answer:

Answer: 80

Step-by-step explanation:

Solution:

salary of A: yA = 12.5x+500

suppose salary of B: YB= kx+ b

5455 = 3446

= Sk= It

500=10kth

b=350

YB = 15x + 350

When

X=28

УA = 830

48=770

УА -43 = 80

:)

Answer:

x = 33/2

Step-by-step explanation:

2x-7/4 = x+3/3

By cross multiplication we get

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

6x - 21 = 4x + 12

6x - 4x = 12 + 21

2x = 33

x = 33/2

Answer:

[tex]x=16.5[/tex] [tex]or[/tex] [tex]\frac{33}{2}[/tex]

Step-by-step explanation:

[tex]\frac{2x-7}{4}=\frac{x+3}{3}[/tex]

In this situation, you can cross-multiply:

[tex](2x-7)3[/tex] [tex]=[/tex] [tex](x+3)4[/tex]

[tex]6x-21 = 4x+12[/tex]

   [tex]+21[/tex]           [tex]+21[/tex]

[tex]6x=4x+33[/tex]

[tex]-4x[/tex] [tex]-4x[/tex]

[tex]2x=33[/tex]

[tex]\frac{2x}{2}=\frac{33}{2}[/tex]

[tex]x=16.5[/tex] [tex]or[/tex] [tex]\frac{33}{2}[/tex]

Answer:

Step-by-step explanation:

As you move from left to right along the graph, each y-value gets larger and larger.  Therefore the y value is always increasing.  The correct answer is D.

The landing speed of the F/A 18 aircraft in mph and ft/sec is 184 mph and 270.2488 ft/sec, respectively. The landing speed in km/h and m/sec is 298.72 km/h and 81.82752 m/sec, respectively.

What is speed ?

The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.

1 knot = 1.15078 miles per hour (mph)

1 knot = 1.68781 feet per second (ft/sec)

1 knot = 1.852 km per hour (km/h)

1 knot = 0.51444 meter per second (m/sec)

Given that the F/A 18 aircraft lands at approximately 160 knots, we can convert its landing speed to different units:

a. mph and ft/sec:

160 knots x 1.15078 mph/knot = 184 mph

160 knots x 1.68781 ft/sec/knot = 270.2488 ft/sec

b. km/h and m/sec:

160 knots x 1.852 km/h/knot = 298.72 km/h

160 knots x 0.51444 m/sec/knot = 81.82752 m/sec

Therefore, the landing speed of the F/A 18 aircraft in mph and ft/sec is 184 mph and 270.2488 ft/sec, respectively. The landing speed in km/h and m/sec is 298.72 km/h and 81.82752 m/sec, respectively.

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Factor the Greatest Common Factors out and then we are left with the expression 3(3c+10d).

Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression.

The terms are the numbers or the variables added together, factors are the numbers or the variables that are multiplied together and the coefficient is the number multiplied to the variable.

The numbers or variables that are multiplied to form a term are called its factors. For example, 5xy is a term with factors 5, x and y. The factors cannot be further factorized.

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The graph of g(x) = 5x+9 can be obtained from the graph of f(x) by shifting the graph of f(x) up by 9 units.

A graph is a visual representation of data points or connections between them. It is a mathematical structure used to represent relationships among data points. Graphs are used in various fields, such as mathematics, physics, engineering, computer science, and economics. They are also used to visualize complex information and to make it easier to understand. Graphs can be used to show relationships between two or more variables, to show how different variables are connected, and to illustrate trends in data.

This is because the equation of g(x) is the same as f(x) but with an added constant of 9. This addition of 9 causes the graph of g(x) to be shifted up by 9 units compared to the graph of f(x).

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The value of QS is 56 ft if Point Q is the midpoint of PS. And PQ = 56 ft

What is mid point  ?

A midpoint is a factor mendacity among points and is within the middle of the line joining the 2 factors. If a line is drawn becoming a member of the two points, then the midpoint is a factor on the middle of the line and is equidistant from the two factors.

Given any factors, say A and C, the midpoint is a factor B that is located halfway among points A and C. therefore, to calculate the midpoint, we are able to truly degree the duration of the line section and divide through 2.

Given ,

Point Q is the midpoint of PS.

And PQ = 56 ft; so we have to find the value of QS.

Midpoint means that Q is between the points of P and S. Meaning the line QP and QS would be equal.

So the answer would be 56 ft,

Hence, The value of QS is 56 ft if Point Q is the midpoint of PS. And

PQ = 56 ft

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To prove that secθ + 1 / tanθ = tanθ / secθ−1, we can use trigonometric identities.

First, we will define secθ as 1/cosθ and tanθ as sinθ/cosθ.

Now, we can substitute these definitions into the equation to get:

secθ + 1 / tanθ = (1/cosθ) + 1 / (sinθ/cosθ)

And, tanθ / secθ−1 = (sinθ/cosθ) / (1/cosθ) - 1

Expanding both sides using basic algebraic manipulations, we get:

(1/cosθ) + 1 / (sinθ/cosθ) = (1/cosθ) * ((sinθ/cosθ) + cosθ/cosθ)

= (sinθ/cosθ) / (1/cosθ) - 1

= (sinθ/cosθ) * (cosθ/1) - 1

= (sinθ) / 1 - 1

= sinθ.

Therefore, secθ + 1 / tanθ = tanθ / secθ−1 has been proven.

The amounts needed of brown and green material for 52 gallons of compost are

Brown material: 39 gallons.

Green material: 13 gallons.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

On the first column of the table, the total amount is:

12.75 + 4.25 = 17 gallons.

The fractions of each material are given as follows:

Brown material: 12.75/17 = 0.75

Green material: 4.25/17 = 0.22.

Thus, the amount of brown material needed with 52 gallons is:

0.75 x 52 = 39 gallons.

and, the amount of green material needed with 52 gallons is:

0.25 x 52 = 13 gallons.

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Answer:

Brown material: 39 gallons

Green material: 13 gallons.

Step-by-step explanation: