Jacob invests a sum of money in a savings account with an interest rate of 9% compounded
continuously. After 6 years, the balance reaches $11,303.34. What was the amount of the initial
investment?

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x = 6 \:\: units[/tex]

[tex]{\qquad \tt \rightarrow \: y = 20° } [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Two sides and their opposite angles of a Triangle are given equal.

[tex]\large \textsf{ For x :} [/tex]

[tex]\qquad \tt \rightarrow \: 2x - 1 = x + 5[/tex]

[tex]\qquad \tt \rightarrow \: 2x - x = 5 + 1[/tex]

[tex]\qquad \tt \rightarrow \: x = 6 \: \: units[/tex]

[tex] \large\textsf{For y :} [/tex]

[tex]\qquad \tt \rightarrow \: 3y - 10 = y + 30 [/tex]

[tex]\qquad \tt \rightarrow \: 3y - y = 30 + 10[/tex]

[tex]\qquad \tt \rightarrow \: 2y = 40[/tex]

[tex]\qquad \tt \rightarrow \: y = 20 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The count of patients needing a blood transfusion can be modelled as a continuous distribution.

A continuous distribution is a distribution that can take on an infinite number of possible values. A continuous distribution is not defined at specific values. The number of patients can be 1 or 10 or 50 or even 0.

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The area of the sector, to 4 decimal places, is: 78.6794 cm².

Area of sector = ∅/360 × πr².

Given the following:

Area of sector = 46/360 × π(14²)

Area of sector ≈ 78.6794 cm²

The area of the sector is approximately 78.6794 cm².

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Answer:

slope == -1

Step-by-step explanation:

y-2 = -(x+1)

; y-2 = -x-1 expanding the bracket

; y = -x-1+2

; y = 1-x

hence slope equals -1

Answer:

219,221

Step-by-step explanation:

the second number can be represented by the equation n1+2=n2

adding these expressions together you get

(n+2)+n=440

youre going to think of n now as just your first number because the equation solves for n1

with that you will get a number valued at 219

you then solve the first equation n1+2=n2 because we now know the value of n1

219+2=221

so the second numbers value is 221

Answer: Length = 13 ft. , Width = 9 ft.

Step-by-step explanation:

Rectangle area = Length x width

Area = 117 ft.

Length = x + 4

Width = x

To solve

(x)(x + 4) = 117

x^2 + 4x = 117

x^2 + 4x - 117 = 0

(x - 9)(x + 13)

x = 9, -13

x = 9 (measurement cannot be negative)

Length

x + 4

9 + 4 = 13

Answer:

The correct linear inequality is y<2/3x+3

Step-by-step explanation:

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols

In the graph, the grey region corresponds to the region non-allowed by inequality. We see that for x=0, y is allowed to be only less than 3: this means that the correct inequality must be in the form y<mx+3, so only the 1st option or the 4th option.

In order to choose the correct option, we should find the value of m, the slope of the line in the graph. This slope can be found by calculating the variation of y divided by the variation of x:

m=dy/dx

Choosing for example the points x=0 (which corresponds to y=3) and x=3 , we find

So, the equation of the line is y=2/3x+3

and so the correct inequality is

y<2/3x+3

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The number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

28.6% of city employees ride the bus to work. Last year,29.7% of city employees rode the bus to work.

The relative change will be calculated as follows:-

Relative change =  Present year data - Last year's data

Relative change = 28.6 - 29.7

Relative change  = -1.1%

Therefore the number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.

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The concentration could not be 59.

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.

Given:

solutions one of 45% concentration

other of 55% concentration.

The concentration should lie between 45 % to 55 %.

This is because it is not possible to get a mixture concentration which is lower than the lower concentrated acid or higher than the higher concentration acid.

Hence, Mixture concentration must be between 45% and 55%.

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Answer:

The answer will be A. 6 or fewer.

The probability that during a given 10 minutes the number of smokers passing will be 6 or fewer.

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

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Example

Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The following terms in probability help in a better understanding of the concepts of probability.

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

Given:

There are 5 smokers who passes by in every 10 minutes.

So, the probability that during a given 10 minutes the number of smokers passing will be approx 5 or less.

i.e., 6 or fewer.

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Answer:

4 kg

Step-by-step explanation:

........................

Answer:

4 kg

Explanation:

Let the mass of tank be 't' and water 'w'

First equation :              (when it is 1/4 filled with water)

Second equation :        (when it is filled fully with water)

Insert second equation into first equation :

[tex]\rightarrow \sf t + \dfrac{1}{4} (10.4 - t) = 5.6[/tex]

[tex]\rightarrow \sf t - \dfrac{1}{4} t + 2.6 = 5.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 5.6 - 2.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 3[/tex]

[tex]\rightarrow \sf t = 4[/tex]

The tank weights 4 kg when it is empty.

The expression are; [tex](h - g) (x) = 3x^{3} -x^{2}[/tex], [tex](h + g) (x) = 3x^{3} +x^{2}[/tex] , [tex](h.g) (-1) = -3[/tex].

The function is a type of relation, or rule, that maps one input to specific single output.

Given function;

g(x) = [tex]x^{2}[/tex]

h(x) = [tex]3x^{3}[/tex]

The expression;

[tex](h - g) (x) = 3x^{3} -x^{2}[/tex]

[tex](h + g) (x) = 3x^{3} +x^{2}[/tex]

[tex](h.g) (-1) = x^{2} .3x^{3} \\\\(h.g) (-1) = 3x^5\\\\(h.g) (-1) = 3(-1)^5\\\\(h.g) (-1) = -3[/tex]

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Answer:

6.708.

Step-by-step explanation:

hope this helps

The expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

Expression is a mathematical statement consisting of variables , constants and mathematical operators .

It is given in the question to solve the expression

[tex]\rm \dfrac{4x}{7} + \dfrac{5}{4x^2}[/tex]

Taking LCM , LCM = 28x²

[tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

Therefore the expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

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Answer:

Step-by-step explanation:

Answer: The graph shown

Step-by-step explanation:

Another graph of the function is attached in this answer.

Answer:

So, the answer is 20

Step-by-step explanation:

[tex]f(x) = \frac{1}{2} x + 10 = = = > \\ f(x) - 10 = \frac{1}{2} x = = = > \\ 2f(x) - 20 = x = = = > \\ {f}^{ - 1} (y) = 2y - 20 = = = > {f}^{ - 1} (x) = 2x - 20[/tex]

The missing value of the inverse function is 20.

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To find the inverse of a function, we usually replace f(x) with y, then solve for x in terms of y, and finally replace y with the inverse function notation h(x).

So let's do that with the given function:

f(x) = (1/2)x + 10

y = (1/2)x + 10

2y = x + 20 (multiply both sides by 2 to isolate x)

x = 2y - 20 (subtract 20 from both sides)

Now we can replace x with h(x) and y with x to get the inverse function:

h(x) = 2x - 20

Thus,

The missing value is 20.

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Answer:

  (√5)/2

Step-by-step explanation:

To simplify the root, we remove perfect squares.

__

Factors that are the same in numerator and denominator cancel. A square under the radical can have its root brought out of the radical.

  [tex]\sqrt{\dfrac{405}{324}}=\sqrt{\dfrac{9^2\cdot5}{9^2\cdot2^2}}=\boxed{\dfrac{\sqrt{5}}{2}}[/tex]

The value of TC(10) is 5300 Dollars

Given function is TC(Q) = 500Q +300 dollars

We need to calculate the value for TC (10)

As we know that the equation given is TC(Q) = 500Q + 300 dollars

Q is the number of TVs produced

Therefore, The value of Q is 10 for TC(10)

Substituting the value of Q

in the total cost of flatiron TVs given by function TC(Q) = 500Q + 300 dollars That Q= 100,

TC(10) = 500(10)+300 dollars

∴ TC (10) = 5000+300 dollars

∴ TC (10) = 5300 dollars

Hence the value of TC(10) is 5300 Dollars

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The amount of pounds of his weight is made up of fat is 28.7lbs

Given the following parameters

Total weight of body = 164lbs

Percentage fat = 17.5%

Determine the amount made up of fat

Fat amount = 17.5% of 164

Fat amount = 0.175 * 164

Fat amount = 28.7lbs

Hence the amount of pounds of his weight is made up of fat is 28.7lbs

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Answer:

The standard deviation is about 2.915

Step-by-step explanation:

Answer:

=  2.9154759474227

Step-by-step explanation:

Answer:

1/4 + x = (-5)/4

x = -5/4 - 1/4

x = (-5)-1 /4

x = (-6)/4

Two (2) lines are considered to be parallel if their slopes are the same (equal) and they do not intersect.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

In conclusion, two (2) parallel lines are shown in the image attached below for more understanding,

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None of the options is true.

Three Different, Regular tessellation is formed 1. if we join regular polygons of side 3, called equilateral triangle,2. Regular polygon of side 4, called Square, and 3. Regular polygon of side,6 called hexagon,

to form a pattern.

A polygon is said to be regular if all interior angles and all sides are equal.

The regular polygon of side 3, when joined together can be named: 3.3.3.

The regular polygon of side 4, when joined together can be named 4.4.4.

The regular polygon of side 6, when joined together can be named 6.6.6.

So, a regular tessellation is formed, from a regular polygon having,3,4, and 6 Sides.

None of the sides of the polygon, which is given in the option, can be used to form a regular tessellation.

None of the options is true.

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The one which is not part of the solution is option D. Using the commutative property.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

5(2x-8)= 20

By Using the distributive property

10x-40-20 = 0

Combining like terms

10x-40+40-20 + 40 = 0

Dividing both sides by 10 to isolate the variable

10x = 60

x = 6

Thus, we can see that all the options are included except option D.

So, the one which is not part of the solution is option D. Using the commutative property.

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Answer:

y = - 1/4 x + 1

Step-by-step explanation:

Find two convenient integer coordinates like   -4,2 and  4, 0

  use these points to  calculate the slope to be -1/4

   intercept is b = 1

y = -1/4 x + 1