Find the principal which amounts to $918 in 1 year at a simple interest
of 2% per annum

Answer:

4

Step-by-step explanation:

→ We go up the y axis to 6 and read of the x coordinate which is 4. This is because an inverse function does the the opposite i.e.  if f ( x ) = y

f⁻¹ ( y ) = x.

See below for the solution to the inverse function and the rational equation

Create functions f(x) and g(x)

The functions are given as:

f(x) = x + a/b

g(x) = cx − d

Let a = 4 and b = 2.

So, we have:

f(x) = x + 4/2

Rewrite as:

y = x + 2

Swap x and y

x = y + 2

Make y the subject

y = x - 2

So, we have:

g(x) = x - 2

So, the functions are:

f(x) = x + a/b ⇒ f(x) = x + 4/2

g(x) = cx − d ⇒ g(x) = x - 2

Show that the functions are inverse functions

In (a), we have:

f(x) = x + 4/2

g(x)= x - 2

If the functions are inverse functions, then:

f(g(x)) = x

We have:

f(x) = x + 4/2

This gives

f(g(x)) = g(x) + 4/2

This gives

f(g(x)) = x - 2 + 4/2

Evaluate

f(g(x)) = x

Evaluate g(f(x))

In (a), we have:

f(x) = x + 4/2

g(x)= x - 2

We have:

g(x)= x - 2

This gives

g(f(x)) = f(x) - 2

This gives

g(f(x)) = x + 4/2 - 2

Evaluate

g(f(x)) = x

Graph the functions

See attachment for the graph

The table of values is:

x    f(x)    g(x)

0    2     -2

1     3      -1

2    4       0

3    5      1

4    6      2

Create the equations

The form of the equations is given as:

[tex]a\sqrt{x + b} + c= d[/tex]

So, we have:

[tex]\sqrt{4x + 5} + 1 = 0[/tex] --- has extraneous solution

[tex]2\sqrt{3x - 1} + 2 = 8[/tex] --- has no extraneous solution

The equation solution

Equation 1 with extraneous solution

[tex]\sqrt{4x + 5} + 1 = 0[/tex]

Subtract 1 from both sides

[tex]\sqrt{4x + 5} = -1[/tex]

Square both sides

4x + 5 = 1

Evaluate the like terms

4x = -4

Divide by 4

x = -1

Substitute x = -1 in [tex]\sqrt{4x + 5} + 1 = 0[/tex] to check

[tex]\sqrt{4(-1) + 5} + 1 = 0[/tex]

[tex]\sqrt{-4 + 5} + 1 = 0[/tex]

[tex]\sqrt{1} + 1 = 0[/tex]

Evaluate the root

[tex]1 + 1 = 0[/tex]

[tex]2= 0[/tex] --- false

Equation 2 without extraneous solution

[tex]2\sqrt{3x - 1} + 2 = 8[/tex]

Subtract 2 from both sides

[tex]2\sqrt{3x - 1} = 6[/tex]

Divide by 2

[tex]\sqrt{3x - 1} = 3[/tex]

Square both sides

3x - 1 = 9

Evaluate the like terms

3x = 10

Divide by 3

x = 10/3

Substitute x = x = 10/3 in [tex]2\sqrt{3x - 1} + 2 = 8[/tex] to check

[tex]2\sqrt{3 * \frac{10}{3} - 1} + 2 = 8[/tex]

[tex]2\sqrt{10 - 1} + 2 = 8[/tex]

[tex]2\sqrt{9} + 2 = 8[/tex]

Evaluate the root

[tex]2*3 + 2 = 8[/tex]

[tex]8 = 8[/tex] --- true

Why the equations have (or do not have) an extraneous solution

The first equation has an extraneous solution because the solution is false for the original equation and the second does not have an extraneous solution because the solution is true for the original equation

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The question asks for the probability that a marble is NOT YELLOW

Total Marbles: orange+yellow+blue=7+3+2=12

We need to count all marbles except yellow:

orange+blue=7+2=9

Now to find the probability that is NOT YELLOW:

[tex]\frac{All Marbles Except Yellow}{Total Marbles}[/tex]= [tex]\frac{9}{12} = \frac{3}{4}[/tex]

Answer is 3/4

Hope it helps!

The probability that exactly 6 out of them are women is 0.176

According to the statement

Number of selected pet owner randomly is 9. So, Here in this case n=9.(number of randomly selected owners).

Number for which have to find the probability is 6. So, Here in this case x=6.

Find the probability by a use of BINOMIAL THEOREM

So, n!/((n-x)!*x!) = 9!/((9-6)!*6!) = 84

Now, find out the probability of success p and probability of failure (1-p)=q.

From here we get p = 0.8 and q= 0.2

Now, use  p^x = (0.8)^6 = 0.2621

Then use q^(n-x) = (0.2)^(9-6) = 0.008

Now, Multiply the results obtained to get the probability is

84*0.2621*0.008 = 0.176

So, The probability that exactly 6 out of them are women is 0.176

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The system of equations used to find roots of the equation is y=12x³-5x and y=2x²+x+6.

Given the equation is 12x³-5x=2x²+x+6.

A set of equations containing one or more variables is called a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.

Firstly, separate the given equation into two parts by equating the left-hand side and right-hand side with 0, we get

12x³-5x=0

2x²+x+6=0

Now, to make a system of equations replace 0 with y as we know that system of equations contains two variables, we get

12x³-5x=y

2x²+x+6=y

Hence, the system of equations used to find the roots of the equation 12x³-5x=2x²+x+6 is y=12x³-5x and y=2x²+x+6.

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If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then the probability of observing at least one car during any 5-minute time interval is 609/2500

Given The probability of observing at least one car on a highway during any 20 minute time interval is 609/625.

We have to find the probability of observing at least one car during any 5 minute time interval.

Probability is the likeliness of happening an event among all the events possible. It is calculated as number/ total number. Its value lies between 0 and 1.

Probability during 20 minutes interval=609/625

Probability during 1 minute interval=609/625*20

=609/12500

Probability during 5 minute interval=(609/12500)*5

=609/2500

Hence the probability of observing at least one car during any 5 minute time interval is 609/2500.

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The measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have shown the rhombus in the picture.

As we know the diagonals bisect at a 90-degree angle.

So angle 2 = 90 degree

angle 1 = angle 3

angle 1 = 54 degrees

angle 1 + angle 2 + angle 5 = 180

54 + 90 + angle 5 = 180

angle 5 = 36 degrees

angle 5 = angle 4 = 36 degrees

Thus, the measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.

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Answer:

m = 2

Step-by-step explanation:

m - 2 = 2 - m

2m = 4

m = 2

Hello,

Answer: m = 2

Step-by-step explanation:

       m - 2 = 2 - m

⇔ m - 2 + m = 2 - m + m

⇔ 2m - 2 = 2

⇔ 2m - 2 + 2 = 2 + 2

⇔ 2m = 4

⇔ 2m/2 = 4/2

⇔ m = 2

The probability that the train will be there when Alex arrives is 5/18

If Alex arrives at any time after 1.20pm the chances that train will  be there is 1/3.

However  if alex arrives at 1.00pm exactly there is no chance the train will be arrive there.

The probability that the train will be there increase linearly to 1/3 as alex's arrival time moves from 1.00pm to 1.20pm.

By arranging the probabilities over the first 20 minutes to get a 1/6 chance the train will be there if alex arrives between 1.00pm to 1.20pm

we get the final answer by

=1/3( 1/6 + 1/3 + 1/3)

=5/18

So, the probability that the train will be there when Alex arrives is 5/18

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Answer:

D

Step-by-step explanation:

As you can observe from the pattern, the numerator gets multiplied by 4 every increase in the sequence.

So , clearly, the 5th term will be = [tex]\frac{64*4}{5} =\frac{256}{5}[/tex]

and the 6th term will be = [tex]\frac{256*4}{5} =\frac{1024}{5}[/tex]

Therefore , D will be the answer.

For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.

The one-repetition maximum test, also called a one-rep max or 1RM, is used to find out the heaviest weight you can lift just once.

If Maximal strength is desired, it is best achieved by performing  repetitions at  85 to 100 % of the one-repetition maximum (1RM).

Formula to find the repetition is

weight used x (reps done x 0.33 + 1) =  1RM

so,

Reps done = {{1RM/weight used} - 1}/ 0.33

By this find the no of reps are recommended for maximum strength.

The maximum strength is achieved by doing the number of reps by 85 to 100% of the value of 1 RM.

So,

For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.

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Answer:

4 units to the left and 2 units up.

Step-by-step explanation:

The equation in slope-intercept form of the line containing the points (3,-1) and (6, 7) is; y = ⁸/₃x - 7

We are given the coordinates of two points as;

(3,-1) and (6, 7).

Now, the formula for the equation of the line containing the two points in slope intercept form is;

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

Thus, we have;

(y + 1)/(x - 3) = (7 + 1)/(6 - 3)

(y + 1)/(x - 3) = = 8/3

y + 1 = (8/3)(x - 3)

y + 1 = ⁸/₃x - 8

y = ⁸/₃x - 7

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The proportional graph that corresponds to M = 3n is: Graph C.

The constant of proportionality, k, of a proportional graph is given as, y/x. The graph is expressed by the equation, y = kx.

The equation given, M = 3n, represents a proportional relationship where k = 3.

Using a point on graph C, (400, 1,200):

k = 1,200/400

k = 3

Therefore, the graph that corresponds to the situation is: C.

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The material needed to make the hat is 3840 cm³.

The hat occupies the whole volume of the rectangular box. Therefore, the material needed to make the hat is the volume of the rectangular box it occupies.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

l = 16 cm

w = 16 cm

h = 15 cm

volume of a rectangular prism = 16 × 15 × 16

volume of a rectangular prism = 3840 cm³

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Answer: e= x + y = 10

Step-by-step explanation :
check out the attachment for the answer

We got the value of [tex]e=\frac{78}{7}[/tex] by solving the given equations [tex]3x+2y=26[/tex] and [tex]5x+y=26[/tex] by reduction method.

The reduction or elimination approach includes using arithmetic operations between equations to produce equivalent equations with fewer unknowns that are simpler to analyze and evaluate.

Given equations are

[tex]3x+2y=26[/tex] .........(1)

[tex]5x+y=26[/tex] ...........(2)

We need to find the value of [tex]e=x+y[/tex]

Simplifying the given equation (2) and we get

[tex]5x+y=26\\\Rightarrow y=26-5x[/tex]................(3)

Now, substitute the equation (3) in equation (1) and we get

[tex]3x+2(26-5x)=26\\\Rightarrow 3x+52-10x=26\\\Rightarrow -7x+52=26\\\Rightarrow -7x=26-52\\\Rightarrow -7x=-26\\\Rightarrow x=\frac{26}{7}[/tex]

Substitute the value of x in equation (3), we get

[tex]y=26-5\frac{26}{7} \\\Rightarrow y=26-\frac{110}{7}\\\Rightarrow y=\frac{162-110}{7}\\\Rightarrow y=\frac{52}{7}\\[/tex]

Now adding the values of x and y, we get

[tex]\therefore e=\frac{26}{7}+\frac{52}{7}\\\Rightarrow e=-{[\frac{26+52}{7}]\\\Rightarrow e={[\frac{78}{7}][/tex]

Therefore, the value of [tex]e=\frac{78}{7}[/tex].

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The equation which best models the data in the scatterplot is: D. y = -16743x² + 19.76x + 745.73.

By critically observing the scatter plot shown in the image attached below, we can logically deduce that it's data are best modelled by a quadratic equation (parabolic curve).

Mathematically, the equation of a quadratic equation (parabolic curve) is given by:

y = ax² + bx + c

Since the parabolic curve opens downward, we have:

a < 0, c > 0, x = 0 and y > 0;

y = -16743x² + 19.76x + 745.73.

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The domain is (-2, 3) and the range is (-3, 4]

The domain

This is the possible x values

From the graph, we have the following highlights:

The endpoints at these intervals is a open circle

Hence, the domain is (-2, 3)

The range

This is the possible y values

From the graph, we have the following highlights:

The endpoint at the minimum is a open circle, while the maximum is a closed circle

Hence, the range is (-3, 4]

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The proportion of defective corks produced by this machine through z test comes out is 0.320.

Given mean of 2 cm and standard deviation of 0.1 cm, The diameter is between 1.9 and 2.1 cm.

We have to find the proportion of defective corks that are produced by machine.

In this problem we have to first find z score and then we will be able to find the probability of defective corks produced by the machine.

Z=(X-μ)/σ

μ=2 cm and σ=0.1 cm.

Z value corresponding to X=1.9.

Z=(1.9-2)/0.1

=-0.1/0.1

=-1

Z value corresponding to X=2.1.

Z=(2.1-2)/0.1

=0.1/0.1

=1

P value of P(-1<Z<1)=2*0.3410=0.6820

Proportion of corks which are not defective=0.6820.

Proportion of corks which are defective=1-0.680.

=0.320

Hence the proportion of defective corks produced by machine is 0.320.

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If f(x) is an odd function, the greatest number of points that can lie in Quadrant II is 1

The given parameters are:

Function f(x) = Odd function

Points in quadrant IV

The number of points in the upper quadrants is:

Upper = 14/2

This gives

Upper = 7

The upper quadrants are I and II

This means that:

I + II = 7

So, we have:

6 + II = 7

Subtract 6 from both sides

II  = 1

Hence, the greatest number of points that can lie in Quadrant II is 1

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Answer:

[tex]3x^{2} -2x+3x-3[/tex]

Step-by-step explanation:

This is one of the easier things to do so definitely learn how to do it.

You just start by taking the first number in each parenthesis (F) and then multiply. 2x by x is 3x^2

Then take the outer (O) number from both problems, so the leftmost and rightmost number. 2x times -1 is -2x

Then take the two inner (I) numbers, 3 and x. Multiply and get 3x

Then take the last number in each parentheses (L) which is 3 and -1, get -3

Answer:

a) 7

b) -1

c) 9

Step-by-step explanation:

a) Substitute -1 into the x's of the function.

f(-1) = -5(-1) + 2

f(-1) = 5 + 2

f(-1) = 7

b) f^-1(7) means: find the inverse of the function with 7 substituted as x.

Let y = f(x)

y = -5x + 2

5x = 2 - y

x = 2 - y / 5

f^-1(x) = 2 - x / 5

f^-1(7) = 2 - 7 / 5

f^-1(7) = -5/5

f^-1(7) = -1

c) We have already found the inverse of the- original function. Substitute -43 into the x's of the inverse function.

f^-1(-43) = 2 - (-43) / 5

f^-1(-43) = 2 + 43 / 5

f^-1(-43) = 45/5

f^-1(-43) = 9

Because the cosine and sine must be negative when evaluated in theta, the angle lies on the third quadrant.

We know that if:

Here we know that:

sec(θ) < 0

And we know that:

sec(θ)  = 1/cos(θ)

Then we have cos(θ) < 0

We also have that:

sec(θ)*csc(θ) > 0

Because sec(θ) < 0, we must have that csc(θ) < 0.

Remember: csc(θ) = 1/sen(θ)

Then sen(θ) < 0.

Then we have the two conditions:

sen(θ) < 0

cos(θ) < 0

The only quadrant where both are negative is the third quadrant, so that is the correct option.

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Answer:

I believe the answer is C

Step-by-step explanation:

Hope this helps!!!

Because the lines drawn are straight.

Explanation:

When the straight lines join together, the original point from where the first line started, becomes a right angle (90°)

The solution to the graph given is 7/16.

It should be noted that a graph is used to show the relationship between the variables illustrated.

Here, the successive approximation is used to solve equations.

This is done by the comparison to the sequence of the known quantities.

Here, the equation given is 4(-)x + 5 = 3^x + 4. solution to the graph given is 7/16. This is based on the graph given.

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Answer:

c and d, because they both have 2 squares

Answer:

4230.14

Step-by-step explanation:

2040/1700=1.2

2448x1.2=2937.6

2937.6x1.2=3525.12

3525.12x1.2=4230.144

round to the nearest hundredth

4230.14

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