4. The simple interest on a savings account is directly proportional to the amount of the investment.
A savings account with $6,000 earns $75.00 after 1 year. Find a mathematical model that gives the
interest Nafter 1 year in terms of the amount invested P, then calculate the simple interest after
saving an amount of $10,500.

Answer:

1.87

Step-by-step explanation:

The first step in this problem is to get rid of the percent by making it a number. The way you do this is divide by 100.

11%/100=0.11

The "of" after 11% means multiply, so you multiply 0.11 and 17

0.11*17=1.87

Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations

3x+2y−z=4

82x+2z=4

−4x+3y=4

(3x+2y−z=4)*2

6x+4y−2z=8 ==> add this equation

82x+2z=4 ==> add this equation

88x+4y=12 ==> add the top 2 equations

(−4x+3y=4)*4

-16x+12y=16

(88x+4y=12)*3   ==> multiply by 3 to get 12y

264x+12y=36

-16x+12y=16

264x-(-16x)=36-16

264x+16x=20

280x=20

280x/280=20/280

x=1/14

−4x+3y=4

−4(1/14)+3y=4

-4/14 + 3y=4

-2/7 + 3y=4

(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions

-2+21y=28

21y=30

y=30/21

y=10/7

3x+2y−z=4

3(1/14)+2(10/7)−z=4

3/14 + 20/7 - z=4

(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions

3 + 20*14/7 - 14z=56

3 + 280/7 - 14z=56

3+40-14z=56

43-14z=56

43-43-14z=56-43

-14z=13

z=-13/14

Answer: (1/14, 10/7, -13/14)

If you earn a manager point every 30 minutes, then the number of minutes you would need to work for 50 manager points is equal to 1500.

The number of minutes needed to work for 50 manager points can be calculated using multiplication. Multiplication is one of the arithmetic parts and is thought to be the opposite of division. It represents the basic idea of the repeated addition of groups of equal sizes.

As,

one manager point = 30 minutes

50 manager points = x

Here x represents the number of minutes required to earn 50 manager points

Cross multiplying,

30 × 50 = x

x = 1500

Hence the number of minutes required to earn 50 manager points if a manager point is earned every 30 minutes is calculated to be 1500 minutes.

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The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.

time is calculated using the formula

[tex]Time=\frac{Distance}{Speed}[/tex]

In the given question

driver drove 50 miles at slower speed.

Let the slower speed be x miles per hour.

So the time taken to cover 50 miles at slower speed = [tex]\frac{50}{x}[/tex]    ...(i)

driver drove 300 miles at faster speed.

given speed is 20 miles per hour faster i.e. speed = (x+20) miles per hour So the time taken to cover 300 miles at (x+20) mph speed = [tex]\frac{300}{(x+20)}[/tex]....(ii)

According to the question

the time spent driving at the faster speed was thrice that spent driving at the slower​ speed.

From equation (i) and (ii) we get

[tex]3*(\frac{50}{x} )=\frac{300}{x+20}[/tex]

[tex]\frac{150}{x} =\frac{300}{x+20}[/tex]

Cross Multiplying we get

[tex]150(x+20)=300x\\ \\ 150x+3000=300x\\ \\ 300x-150x=3000\\ \\ 150x=3000\\ \\ x=20[/tex]

Slower speed = x = 20mph.

Faster speed = (x+20) = 20+20 = 40mph.

Therefore , The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.

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The solution for x in the compound inequality is 18 < x ≤ 3

The compound inequality is given as

6x − 10 ≤ 8 or 1/3x + 6 > 12

Add or subtract the constant to both sides of the compound inequality

So, we have

6x ≤ 18 or 1/3x > 6

Divide both sides of the compound inequality by the coefficient of x

So, we have

x ≤ 3 or x > 18

Rewrite as

x > 18 or x ≤ 3

Combine both inequalities

18 < x ≤ 3

Hence, the solution for x in the compound inequality is 18 < x ≤ 3

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The sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.

The continuous compounding formula is as follows:

So,

According to the first point, we know that atr = 0.02,  and t = 1.

Thus for advantage > 1$ we need is as follows:

According to the second point, we got that:

Then,

Now we hold that r > 0.04439:

According to the third point, we got to know that:

Now 2nd equation holds t > 4.621.

Therefore, the sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.

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The correct answer of the question is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .

The given quadratic equation is 3 x²+ 9 x=27

To begin, we must transform the equation in the form

ax² + bx + c = 0, then apply the quadratic formula i.e.

x = {-b±√(b²- 4ac)}/ 2a .

Now,

3 x²+ 9 x=27

⇒ 3 x²+ 9 x - 27 = 0

⇒  3(x²+ 3 x - 9 )= 0

⇒  x²+ 3 x - 9 = 0

Here, a = 1, b = 3 and c = --9

Now, applying quadratic formula

{-b±√(b²- 4ac)}/ 2a

= {-3±√(3²- 4 × 1 × -9)}/ (2 × 1)

= {-3±√(9 + 36)}/ 2

= {-3±√45}/ 2

= {-3±3√5}/ 2

= 3{-1 ±√5}/ 2

= 3{-1+√5}/ 2 or 3{-1-√5}/ 2

Therefore, the ultimate answer to the given equation is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .

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Answer:

10812

Step-by-step explanation:

books sold=106

number of pages=102

106 × 102=10812

Answer:

106^102

Step-by-step explanation:

Because there are 106 copies of the book and each book has 102 pages

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

|-5|+|7|

|-5|=5

|7|=7

=5+7

=12

hope this helps u ; )

The result of simplifying each number (-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃  using the exponent rules is -3

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

(-3)¹/₃⁺ ¹/₃ ⁺ ¹/₃

(-3)³/₃

(-3)¹

-3

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:1,816

2,013 minus 197 equals 1,816

Answer:

[tex]x=\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{30x^1}{3}=1[/tex]

Multiply both sides by 3

[tex]\frac{3\cdot \:30x^1}{3}=1\cdot \:3[/tex]

Simplify

[tex]30x=3[/tex]

divide both sides by 30

[tex]\frac{30x}{30}=\frac{3}{30}[/tex]

Simplify

[tex]x=\frac{1}{10}[/tex]

Answer: 53412

Step-by-step explanation:

17

6.5−1−21

−(−5)2−

Cinematic layout lead, Technical Assistant, Game Artist, 2D Artist, and Game Producer are the best anime jobs that use geometry.

There are many opportunities for animators to get anime jobs that use geometry as well. In order to demonstrate how an object is rotated or shifted to be made larger or smaller—for the process of producing movement—animators must comprehend the geometrical characteristics of figures and apply linear algebra.

Due to their work with moving and changing objects, animators frequently use a number of mathematical techniques, including geometry, linear algebra, and others. The ability to utilize linear algebra to demonstrate how a certain figure or object is shifted or rotated with the intention of making it smaller or larger is crucial for animators. Movement is produced by this mechanism.

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.

Answer: hello frawn

Step-by-step explanation:

free point dootie head

Answer:

the length is 19

the width is 13

Step-by-step explanation:

well since a rectangle has two even sides the width have to be the same and the lengths have to be the same

perimeter is all the sides added together

since the length is the bigger size choose a sensible number (for example 15) and add another 15 to get the length and since it's 6cm smaller take 6 away from 15 which is 9 and add the two 9s together but 15+15+9+9 isn't 64 so you try again with a higher number until you each a total of 64

[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{Answer:-}}}[/tex]

To solve this problem, let's denote the width of the rectangle as $w$ (in cm).

According to the given information, the length of the rectangle is 6 cm more than the width, so the length can be represented as $w + 6$ (in cm).

The perimeter of a rectangle is given by the formula:

$$\text{{Perimeter}} = 2(\text{{length}} + \text{{width}})$$

Substituting the values, we have:

$64 = 2((w + 6) + w)$

Now, let's solve for $(w)$:

$64 = 2(2w + 6)$

$64 = 4w + 12$

$4w = 64 - 12$

$4w = 52$

Dividing both sides of the equation by 4, we get:

$w = \frac{{52}}{{4}}$

$w = 13$

So, the width of the rectangle is 13 cm.

Substituting the value of $w$ back into the expression for the length:

$$\text{{Length}} = w + 6 = 13 + 6 = 19$$

Therefore, the dimensions of the rectangle are 13 cm (width) and 19 cm (length).

Answer:

AB has the slope of 4/3

CD has the slope of 3/2

Step-by-step explanation:

CD I chose the points (0,2) and (3,0)

[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 2}{3 - 0} \\ m = \frac{ - 2}{3} [/tex]

AB I chose the points (0,6) and (8,0)

[tex] \frac{y2 - y1}{x2 - x1} \\ \frac{0 - 6}{8 - 0} \\ m = \frac{ - 3}{4} [/tex]

It should be noted that in order to measure the value, the measurement has to be in the same unit.

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

Measurement is crucial in establishing connections across different branches of mathematics. For instance, it gives the use of math abilities and spatial concepts a rich and meaningful context. Measurement also establishes connections between mathematics and other academic disciplines.

From the information, it was illustrated that the boys all had measurements of trees taken. Therefore, it should be noted that since they are in different units, it cannot be done.

In this case, the reason is that in order to measure the value, the measurement has to be in the same unit. This will make it easier to do the calculation.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

now we also know that

the height in that triangle is twice its baseline.

so,

height = 2×baseline

so, for the given area we have

49 = baseline × 2 × baseline / 2 = baseline²

baseline = 7 ft.

therefore,

height = 2×baseline = 2×7 = 14 ft.

and now we run into a problem. as we don't have any further information about the triangle, the lengths of the sides cannot be determined.

the reason is that the height can be placed anywhere on the baseline (from the left end point all the way over to the right end point). all these triangles created by the moving height have the same area (49 ft²), but different lengths of the legs.

the lengths of the legs are calculated via Pythagoras, because the height splits the main triangle into 2 smaller right-angled triangles.

so, if I assume e.g. an isoceles triangle (both legs are equally long), then I know that the height splits the triangle into 2 equal triangles and the baseline in half.

then I can calculate :

leg² = (baseline/2)² + height² = 3.5² + 14² =

= 12.25 + 196 = 208.25

(each) leg = 14.43086969... ft

if I assume the height is at an endpoint of the baseline then the whole triangle is by itself a right-angled triangle.

and the height is one leg and the other leg is again via Pythagoras

leg² = baseline² + height² = 7² + 14² = 49 + 196 = 245

leg = 15.65247584... ft

all the possible solutions for the leg lengths are between 14 ft (the height) and 15.65247584... ft.

Answer:

[tex]\frac{1}{8b^6 a^12}[/tex]

Step-by-step explanation:

Hope this helps you :))

The answer to the following listed algebra questions are below:

6 = a/4 + 2

substract 2 from both sides

6 - 2 = a/4

4 = a/4

cross product

4 × 4 = a

a = 16

-6 + x/4 = -5

x/4 = -5 + 6

x/4 = 1

x = 4 × 1

x = 4

9x - 7 = -7

Add 7 to both sides

9x = -7 + 7

9x = 0

x = 0/9

0 = 4 + n/5

0 - 4 = n/5

-4 = n/5

-4 × 5 = n

-20 = n

-4 = r/20 - 5

-4 + 5 = r/20

1 = r/20

1 × 20 = r

r = 20

-1 = (5+x) / 6

-1 × 6 = (5 + x)

-6 = 5 + x

-6 - 5 = x

x = -11

(v+9)/3 = 8

v + 9 = 8 × 3

v +9 = 24

v = 24 - 9

v = 15

2(n + 5) = -2

2n + 10 = -2

2n = -2 - 10

2n = -12

n = -12/2

n = -6

-9x + 1 = -80

-9x = -80 - 1

-9x = -81

x = -81/-9

x = 9

-6 = n/2 - 10

-6 + 10 = n/2

4 = n/2

4 × 2 = n

n = 8

-2 = 2 + v/4

-2 - 2 = v/4

-4 = v/4

-4 × 4 = v

-16 = v

144 = -12(x + 5)

144 = -12x - 60

144 + 60 = -12x

204 = -12x

x = 204 / -12

x = 17

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Answer:

It looks like the chart says time and hours.

Step-by-step explanation:

Using the axis title we found that the time is the measurement represented on the x- axis  and and time is measured in hours

The axis title is a title in the form of words or numbers that describes the  entire axis . The title that describes that what quantity varies along x-axis is called x-axis title and the title which describes what quantity varies along y- axis is called y- axis title.

Some times units of the quantities measured along the respective axis  is also mentioned in the title of the axis in a bracket.

From the Given graph in the question we can see that a Distance vs Time graph is given

And the title of the x- axis is Time (hours )

Therefore , the measurement along the x- axis is of time and unit of time is hours.

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The value of the quadratic equation 2x^2 - 10x + 13 when x = 2 is 1

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

2x^2 - 10x + 13

When the value of x is 2, the quadratic equation becomes

2x^2 - 10x + 13 = 2 x 2^2 - 10 x 2 + 13

Evaluate the exponent

So, we have

2x^2 - 10x + 13 = 2 x 4 - 10 x 2 + 13

Evaluate the product

So, we have

2x^2 - 10x + 13 = 8 - 20 + 13

Evaluate the difference

So, we have

2x^2 - 10x + 13 = -12 + 13

Evaluate the sum

So, we have

2x^2 - 10x + 13 = 1

Hence, the value of the quadratic equation 2x^2 - 10x + 13 when x = 2 is 1

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Complete question

What is the value of 2x^2-10x+13 when x = 2

The statements are true regarding the area of circles and sectors are:

1). The area of a sector depends on the ratio of the central angle to the entire circle.

2) The area of the entire circle can be used to find the area of a sector.

3)The area of a sector can be used to find the area of a circle.

Option (B) ,(D) and (E) is correct.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

Given:

The statements are true regarding the area of circles and sectors.

According to given question we have

WE know that

Area of a circle= π[tex]r^{2}[/tex]

So, area is dependent only on the radius.

The area of a sector depends on the ratio of the central angle to the entire circle is   1: 5.

The area of the sector of a circle is /360° *([tex]r^{2}[/tex]) where r is the radius of the circle and is the angle of the sector,.

Therefore, statements are true regarding the area of circles and sectors are:

1). The area of a sector depends on the ratio of the central angle to the entire circle.

2) The area of the entire circle can be used to find the area of a sector.

3)The area of a sector can be used to find the area of a circle.

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The probability that a boy selected at random is a Junior is 0.23 and the probability of randomly choosing a student who is a Junior and a boy is 0.14

The probability of an event is the chance or the likelihood that the event would occur.

Note that the chance or the likelihood is represented as a numerical value

The table that completes the question is added as an attachment

From the table, we have the following values

n(Boys and Junior) = 65

n(Boys) = 285

So, the probability that a boy selected at random is a Junior is

P = n(Boys and Junior)/n(Boys)

This gives

P = 65/285

Evaluate

P = 0.23

From the table, we have the following values

n(Boys and Junior) = 65

Total = 465

So, the probability of randomly choosing a student who is a Junior and a boy is

P = n(Boys and Junior)/Total

This gives

P = 65/465

Evaluate

P = 0.14

Hence, the probability of randomly choosing a student who is a Junior and a boy is 0.14

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Answer:

2.97%

Step-by-step explanation:

Answer:

2.72807     (aprox)

Step-by-step explanation:

14% = 14/100 = 0.14

100% = 100/100 = 1

It was a increase

then 14% = 100% + 14% = 1 + 0.14 = 1.14

3.11 / 1.14 = 2.72807    (aprox)

Check:

2,72807 + (2.72807*0.14) = 2.72807 + 0.38193 = 3.11

The order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is: A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

Generally, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In conclusion, we can reasonably and logically deduce that the order of transformation which best describes how the graph of h(x) = ∛1 - x should be sketched is to start by plotting the graph of the basic function y = ∛x, and then horizontally shift the graph of function y = ∛x to the left one​ unit, and then reflect the graph about the​ y-axis.

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Complete Question:

Which of the following order of transformations best describes how to sketch the graph of h(x) = ∛1 - x?

A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

B. Starting with the graph of the basic function y = ∛x, vertically shift the graph up one​ unit, and then reflect the graph about the​ y-axis.

C. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ x-axis.

D. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the right one​ unit, and then reflect the graph about the​ y-axis.

The college bookstore paid $44.4 for the book

A college store marks up the price it pays the publisher for a book by 35%

The selling price of the book is $60.00

Therefore the amount paid by the bookstore can be calculated as follows

( 35/100 + 1) x = 60

0.35+1x= 60

1.35x= 60

Divide both sides by the coefficient of x which is 1.35

x= 60/1.35

x= 44.4

Hence the book store will pay $44.4 for the book

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