Use the Simple Interest formula to find the simple interest. (l=prt)

Answer:

39.4°

Step-by-step explanation:

complementary angles add up to 90

therefore, the complementary angle to 50.6 is:

90 - 50.6 = 39.4

Answer:

Slope is [tex]\frac{7}{-9}[/tex]

Step-by-step explanation:

For this problem we must use the slope formula:

[tex]\frac{change* in *y}{change*in*x}[/tex]

Our 2 y coords are: 3, -4

To find the change in y, we must subtract.

3 - ( -4 ) = 7

Our 2 x coords are: -2, 7

-2 - 7 = -9

Therfore, our answer is

[tex]\frac{7}{-9}[/tex]

The quantity 8 to the power of x end quantity over 16

In mathematics, two expressions are said to be equivalent if they have the same value for all possible values of the variables involved. In other words, equivalent expressions represent the same mathematical object or concept, but they may be expressed in different forms or notations.

Equivalent expressions are expressions that have the same value for all possible values of the variables involved, and they can be used to simplify or manipulate algebraic expressions.

Then we have;

8^x/16

= 2^3(x)/2^4

Then we use the laws of exponents;

2^3x - 4

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The total amount that Rahul will have is 108,006.20.

Compound interest is a type of interest where the interest earned on a principal amount is added to the principal, and the new total amount becomes the basis for calculating interest in the next period.

In other words, the interest is earned not only on the principal amount but also on the accumulated interest.

The formula for compound interest is:

Here we have, Rahul's plans to invest $25,000 in a retirement account that compounds 6% monthly.

From the data,

The principal amount, P = 25000

Rate of interest, r = 6% = 6/100 = 0.06

Time period, t = 25 years  

Number of compounds, n = 12  [ Since compounded annually ]

By using the formula, A = P (1 + r/n)^(n×t)  

A = 25000 [ 1 + 0.6/12]⁽¹²ˣ²⁵⁾

A = 25000 [ 1 + 0.005]⁽³⁰⁰⁾

A = 25000 [1.005]⁽³⁰⁰⁾  

A = 108,006.20 (rounded to the nearest cent)  

Therefore,

The total amount that Rahul will have is 108,006.20.

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The cost of framing for the masterpiece is $46.73.

To calculate the cost, we need to first determine the perimeter of the artwork.

Given the dimensions of the artwork, the perimeter is 100 + 100 + 70 + 70 = 340 inches.

The cost of framing is $4.95 per yard, so we need to convert the perimeter to yards.

To do this, we divide the perimeter by 36 inches since 1 yard equals 36 inches.

Thus, 340 inches divided by 36 inches equals 9.44 yards.

Therefore, the cost of framing the artwork will be 9.44 yards multiplied by $4.95 per yard, which equals $46.73.

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The triangle will have a perimeter of 19 units.

Triangle perimeter: The circumference of any two-dimensional figure is referred to as its perimeter. By adding the lengths of the sides, we can determine the perimeter of any closed shape. You will first learn what the perimeter is in this article.

For a triangle, the perimeter is the sum of all the sides of the triangle. To calculate the perimeter add all the sides of the triangle as below,

Perimeter = 4 + 6 + 9

Perimeter = 19 units

Therefore, the perimeter of the triangle is 19 units.

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The complete question is given below.

The sides lengths 4, 6, and 9 can be used to form the size of a triangle. Find the perimeter of the triangle.

Answer:

C

Step-by-step explanation:

the perimeter means to go along all 4 sides and sum up the distance.

so, we have

x + 12 + x + 12 + 2x + 2x

we combine all similar terms (the ones with a variable and the constants without a variable)

x + x + 2x + 2x + 12 + 12 = 6x + 24

why do you think the sum of x + x + 2x + 2x is 4x ?

and 12 + 12 is 28 ?

do you need any further explanation, or is this now clear ?

Therefore , the solution of the given problem of equation comes out to be  the system of equations has an answer of x = -20 and y = 10.

The same letter is frequently used in mathematical formulas to attempt to enforce variable uniformity among two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.

Here,

The set of linear equations can be used to find the values of x and y:

144x + 288y = 1440 \s28x + 84y = 280

By dividing both parts of the second equation by 28, we can begin by making it simpler:

x + 3y = 10

Then, by separating x, we can use this equation to solve for x in terms of y:

x = 10 - 3y

In order to simplify the first problem, we can use this expression in place of x:

=>  144(10 - 3y) + 288y = 1440

=>  1440 - 432y + 288y = 1440

=>  -144y = -1440

=>  y = 10

Given that y = 10, we can solve for x by substituting this number into the equation x + 3y = 10:

=>  x + 3(10) = 10

=>  x + 30 = 10

=> x = -20

As a result, the system of equations has an answer of x = -20 and y = 10.

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The e values that satisfy the inequality 3e ≤ 6, are e = 1 and e = 2.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

To determine which values of e satisfy the inequality 3e ≤ 6, we can divide both sides by 3 -

3e/3 ≤ 6/3

e ≤ 2

Therefore, any value of e that is less than or equal to 2 will satisfy the inequality.

Out of the given choices, e = 1 and e = 2 satisfy the inequality, but e = 3 does not, because 3 is greater than 2.

Therefore, the correct answers are -

e = 1 and e = 2

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Create four angles by drawing a straight line that meets another straight line at an angle. To keep track of the angles, assign letters to each one. Make a note of the angles' measurements using a protractor.

A right angle is created when two perpendicular lines cross at an exact 90-degree angle. Four 90-degree right angles are formed by intersecting perpendicular lines.

A right angle is a right angle if one of the four angles created by two intersecting lines is a right angle. Straight lines that are perpendicular to one another intersect at a 90° angle.

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Answer:

-csc^2 θ = dθ/dt = 1/5 (dx/dt)

or

3.49 km/min

Step-by-step explanation:

dx/dt

- 5cosec^2 θ * (rate of change of angle of elevation)

- 5 cosec^2 (π/3) * (-π/6)

(5π/6) * (4/3)

= 10π/9 km/min. = 3.49 km/min

Answer:

The median of the given data is 20. To find the median, arrange the data in numerical order, and then take the middle value. In this case, the data is arranged in numerical order as 0, 5, 10, 10, 12, 15, 15, 20, 25, 30, 30, 35, 35, 45, 60. The middle value is 20, which is the median.

Answer:

17.5

Step-by-step explanation:

To find the median of a set of numbers, we need to arrange the numbers in order from smallest to largest and then find the middle value.

In this case, the numbers in the set arranged in ascending order are:

0, 5, 10, 10, 12, 15, 15, 20, 25, 30, 30, 35, 35, 45, 60

There are 15 numbers in the set, which means that the middle value is the eighth number. Since there are two numbers in the middle (15 and 20), we take the average of these two numbers to find the median:

median = (15 + 20) / 2 = 17.5

Therefore, the median of the set of numbers is 17.5.

The numbers 4 and 12  are not the best factors to use because they do not fully simplify the expression

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

Square root of 48

This can be expressed as

√48

Using Letty's solution, we have

√48 = √(4 * 12)

This gives

√48 = 2√12

So, we simplify again

√48 = 2√(4 * 3)

This gives

√48 = 4√3

Hence, the factors are not the best

Instead, she can use 16 and 3

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The relation given is a function since each of the input value only maps to a single output value.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are set of coordinate values of a relation.

We have to determine whether the relation is function or not.

The points are,

{(-3, -8), (3, 6), (5, -5), (7,-6), (10, 6)}

Domain of the relation are {-3, 3, 5, 7, 10}

Range of the relation are {-8, 6, -5, -6, 6}

We can see that each of the input value only maps to a single output value.

So the relation is a function.

Hence the relation is a function.

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Answer:

y = 3/5x - 3

Step-by-step explanation:

slope (m) of line perpendicular to y = -5/3x is 3/5, the negative reciprocal of -5/3

use the point (5, 0) and the point-slope form to find b, the y-intercept:  

y - 0 = 3/5(x - 5)

y = 3/5x - 15/5

y = 3/5x - 3   equation is now in the slope-intercept form

Answer:

7.75 ; 7.81 ; 7.77 ; 7.84

The common factor of the trinomials x² - 7x - 18 and x² + 14x + 24 is (x + 2).

The above polynomials are trinomials. A trinomial is a polynomial with three terms. Let's factor the trinomials and find what they have in common.

Hence,

James factors x² - 7x - 18.

x² - 7x - 18

x² + 2x - 9x - 18

x(x + 2) - 9(x + 2)

(x - 9)(x + 2)

Kaitlin factors x² + 14x + 24.

Hence,

x² + 14x + 24

x² + 2x + 12x + 24

x(x + 2)+ 12(x + 2)

(x +2)(x + 12)

Therefore, the common factor is (x + 2)

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The key features of the graph are

If the graph has a local maximum

From the given graph, we can see that:

The graph has a maximum (momentarily) at x = 1

This means that "yes", the function has a local maximum at x = 1

The local maximum

In (a), we have

x = 1

The y coordinates at this point is

y = 1

So, the local maximum is y = 1

The decreasing interval

From the graph, we can see that the y values decrease from -∝ till x = -1 and also decrease from x = 1 till ∝

The function type

Based on the appearance of the graph, the function is an odd function

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The coordinates of the fourth vertex are (0, -4).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;

Midpoint = [(3 - 6)/2, (6 - 6)/2]

Midpoint = [-3/2, 0/2]

Midpoint = (-1.5, 0).

For the fourth vertex, we have:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(-1.5, 0) = [(-3 + x₂)/2, (4 + y₂)/2]

-3 + x₂ = 2(-1.5)

x₂ = -3 + 3

x₂ = 0.

4 + y₂ = 0

y₂ = -4.

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The inequality for this graph is given as follows:

y < 2.

The four inequality symbols, along with their meaning, are presented as follows:

For the graph in this problem, the inequality is composed by the values that are below y = 2, with an open interval as the line is dashed and not solid, hence it is defined as follows:

y < 2.

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The answer of the given question based on to determine that the quadrilateral must be a parallelogram the answer is given below.

A parallelogram is  type of quadrilateral ( polygon with four sides) with two pairs of parallel sides. This means that the opposite sides of parallelogram are parallel and congruent.

Yes, we can determine that the given quadrilateral is a parallelogram based on the information given.

We are told that opposite sides of the quadrilateral are congruent (that is, AB is congruent to CD, and BC is congruent to DA), which is a property of parallelograms. We are also told that opposite angles of the quadrilateral are congruent (that is, angle A is congruent to angle C, and angle B is congruent to angle D), which is another property of parallelograms.

Therefore, based on these two pieces of information, we can conclude that the quadrilateral must be a parallelogram. This is because these properties are unique to parallelograms and do not apply to other types of quadrilaterals, such as rectangles, rhombuses, or trapezoids.

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Answer: 18 boxes per hour

Step-by-step explanation:

72 divided by 4 is 18

Answer: I believe the answer would be 53.85%

Step-by-step explanation:

6+8=14

14+7+5=26

14/26=.53846

Move decimal and round up.

Answer:

x is greater than or equal to 3

Step-by-step explanation:

I'm gonna assume you meant 3x-8

Treat it as an equation

3x-8 =1, 3x=9, x=3

If its x^3 -8

x^3 -8 =1, x^3=9, x is greater than or equal to the cubed root of 9

Answer:

B. 15.2 inches.

Answer: b = 8

Step-by-step explanation:

From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.

Let's factor the equation and set each factor equal to zero:

x²(x+3)(x - b) = 0

x = 0 or x + 3 = 0 or x - b = 0

Solving for x in each case, we get:

x = 0 or x = -3 or x = b

Since the sum of the solutions is 5, we can write:

0 + (-3) + b = 5

Simplifying, we get:

b - 3 = 5

Adding 3 to both sides, we get:

b = 8

Therefore, the value of b is 8.

The probability of F P(F) = 0.33 and the conditional probability of F given G P(F|G) = 0.24. F and G is associated since they are not independent.

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome. The conditional probability P(A|B) occur only in the case of dependent events. It gives the conditional probability of A given that B has occurred.

P(F|G) = P(F∩G) / P(G)

P(F∩G) = Probability of happening of both F and G

P(F) = 199/600 = 0.3317

P(F∩G) = 79/600 = 0.1317

P(G) = 330/600 = 0.55

P(F|G) = 0.1317/0.55

P(F|G) = 0.2394.

Two events say A and B are independent if the probability of occurrence of one of them is not affected by the occurrence of the other, mathematical expressed as P(A ∩ B) = P(A) × P(B)

P(F) × P(G) = 0.3317 × 0.55

P(F) × P(G) = 0.1824

P(F∩G) is not equal to P(F) × P(G) from the data given.

Therefore, the probability of F P(F) = 0.33 and the conditional probability of F given G P(F|G) = 0.24. F and G is associated since they are not independent.

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Answer:

The answer that you are looking for is 70º

Step-by-step explanation:

Usually, in three-sided figures, there is a total of 3 angles all adding up to 180º.

So in turn, since most quadrilaterals are made up of 2 triangles all the sides have to equal to 360º.

We can use the equation 360 = 110×2+q2

To find the value of q.

The First step to do is to simplify all terms with 110×2 being equal to 220 and q2 staying the same.

We then use the opposite symbol to remove 220 leaving q2 by itself while 360 is subtracted by 220 and turned into 140.

The only thing left to do is to do the opposite operation of multiplying, which is dividing and dividing both sides by 2 leaving q = 70.

You can find the equation below:
360 =  110×2+q2
360 =  220 + q2
-220 = -220 + q2
 140 = q2
  ÷2 = ÷2
  70 = q

I hope this was helpful!

Answer:

Step-by-step explanation:

(a) Since the current entering and leaving the intersection of wires must be equal, we have:

x + y = 18 (current entering the top intersection)

z + w = 18 (current leaving the top intersection)

x + z = 9 (current entering the bottom intersection)

y + w = 9 (current leaving the bottom intersection)

We can solve this system of equations using substitution or elimination. For example, we can eliminate w by adding the first two equations and subtracting the last two equations:

2x + 2y + 2z = 36

2y + 2z - 2x = 0

2z - 2x = 9

Solving for z in terms of x, we get:

z = (x + 9/2)

Substituting this into the first equation, we get:

x + y = 18

Substituting z in terms of x into the second equation, we get:

w = (18 - z) = (18 - x - 9/2) = (27/2 - x)

Therefore, the solution in terms of x, y, z, and w is:

(x, y, z, w) = (x, 18 - x, x + 9/2, 27/2 - x)

(b) To know all of the currents exactly, we need to measure the current in any one wire that is not already determined by the system of equations. From part (a), we see that w is determined in terms of x, y, and z. Therefore, we should measure the current in wire x or y to know all of the currents exactly.