pls help quick. this was due a while ago. my math teacher doesnt teach and tells us to “read from the book.”

The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.

Answer:

19.2 ft

Step-by-step explanation:

Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.

To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).

by the question.

a. x-3.5>6.9

x>6.9+3.5

x>10.4

b. 6.4>x+3.1

x[tex]\geq 32[/tex]

c. x/4≤8

x≤32

d. 2/3x≤-10

x≤-15

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Answer:

Step-by-step explanation:

(x+3)^2=49

x+3=√(49)

x+3=√(7^2)

x+3=7

x+3-3=7-3

x+3=-√(49)

x+3=-7

x+3-3=-7-3

x = 4,-10

Answer:

32.67 square meters

Step-by-step explanation:

finding the area of the shaded region.

area of sector = (θ/360°) x πr²

where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.

Substituting the given values into the formula, we get:

area of sector = (60°/360°) x π(14m)²

area of sector = (1/6) x 3.14 x 196m²

area of sector = 32.67m² (rounded to two decimal places)

Therefore, the area of the section is 32.67 square meters

The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

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Answer:

0.9973 or 364/365

Step-by-step explanation:

Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.

Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:

P(not on 1st day) = 1 - P(on 1st day)

P(not on 1st day) = 1 - 1/365

P(not on 1st day) = 364/365

So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.

The volume of the solid is approximately 0.558 cubic units.

To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.

We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:

d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2

The radius of each semi-circle is half of the diameter, which is:

r(a) = (ln(a) - a + 2) / 2

The area of each semi-circle is π times the square of its radius, which is:

[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]

To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:

V = ∫[e,2] A(a) da

V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]

V ≈ 0.558 (rounded to the nearest thousandth)

Therefore, the volume of the solid is approximately 0.558 cubic units.

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The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.

When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).

Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.

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10³•10⁵•10³

Step-by-step explanation:

10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110

Answer:

x is first angle

y is second angle

and z is third angle

Step-by-step explanation:

This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.

the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.

To find the pressure at a depth of 66 ft in a liquid, we can use the formula:

pressure = density x gravity x depth

Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².

First, we need to convert 66 ft to meters:

66 ft x 0.3048 m/ft = 20.1168 m

Then, we can find the pressure at this depth:

pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa

To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:

P₁V₁ = P₂V₂

where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.

We can rearrange this equation to solve for V₂:

V₂ = (P₁ x V₁) / P₂

Substituting the values, we get:

V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L

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Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

The correct answer is (d) No, quadrilaterals LMNO and PQRS are not similar because their corresponding sides are not proportional.

A quadrilateral is a geometric shape with four sides and four corners.

To be classified as a quadrilateral, its shape must be a closed figure with four straight sides and four interior angles. 

To determine quadrilaterals are similar, we need to check if corresponding angles are congruent and corresponding sides are proportional.

Checking corresponding angles are congruent:

∠ L  to ∠P.

∠M  to ∠Q.

∠ N  to ∠ R.

∠O  to ∠S.

All corresponding angles are congruent. Therefore, quadrilaterals have the same shape.

Check if corresponding sides are proportional.

LM =√((-1 - (-2))² + (4 - 2)²) = √(2² + 2²) = 2√2

MN = √((3 - (-1))² + (4 - 4)²) = √(4²) = 4

NO = √((4 - 3)² + (2 - 4)²) = √(2² + 2²) = 2√(2)

OL = √((-2 - 4)² + (2 - (-6))²) = √(6² + 8²) = 10

PQ = √((4 - 2)² + (-2 - (-6))²) = √(2² + 4²) = 2√5

QR = √((12 - 4)² + (-2 - (-2))²) = √(8²) = 8

RS = √((15 - 12)² + (-6 - (-2))²) = √(3² + 4²) = 5

SP = √((2 - 15)² + (-6 - (-6))²) = √(13²) = 13

LM / PQ = (2√2) / (2√5) = √(8/5)

MN / QR = 4 / 8 = 1/2

NO / RS = (2√(2)) / 5√(1) = (2/5)√(2)

OL / SP = 10 / 13

The corresponding sides are not proportional because they are not all equal or proportional to each other. Therefore, we can conclude that the quadrilaterals LMNO and PQRS are not similar.

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The variance of the number of citizens favoring the supermarket is 6.

To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:

Variance = n × p × (1 - p)

where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.

Plugging in the values, we get:

Variance = 25 × 0.6 × (1 - 0.6)

Variance = 25 × 0.6 × 0.4

Variance = 6

The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.

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The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

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Step-by-step explanation:

lol sorry for untidy work

Answer:

y = 5/6x + 1/6

Step-by-step explanation:

m = 5/6, x = 7, y = 6

y = mx + b

6 = 5/6(7) + b

b = 6 - 35/6

b = 36/6 - 35/6 = 1/6

y = 5/6x + 1/6

Answer:

Below

Step-by-step explanation:

Here is another way:

 Start with point ( 7,6)   slope ( m= 5/6)  form :

    (y-6) = 5/6 ( x-7)     expand

    y-6 = 5/6 x -  35/6     add 6 to both sides

       y = 5/6 x + 1/6     Done.

The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.

Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:

BSA = √(H x M) / 3600

We can rearrange the equation to solve for M:

M = (BSA^2 x 3600) / H

Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:

M = (2.0^2 x 3600) / 165

M = (4 x 3600) / 165

M = 87.27 kg

The above question is in response to the full question as seen in the image;

A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less

than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?

The equation for BSA is BSA = √(H x M)/3600

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A) The completed table is given as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

B) the graph is attached accordingly.

C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.

We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.

D(L) = ceil(L/6)

Using this formula, we can complete the table as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).

b) The graph is attached.

c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.

So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.

In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

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Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.

given

If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.

You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:

1000 x 67% = 670

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

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The complete question is :-  

Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?

Possible Answers:

3,700

57,000

67

None of the given answers

670

A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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Therefore , the solution of the given problem of angles comes out to be  M∠R measured at 45.4 degrees, to the closest tenth.

The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.

Here,

To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:

=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)

=>  cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)

=>  cos(R) = 0.6960917

When we calculate the inverse cosine of both sides, we obtain:

=>  R = cos⁻¹(0.6960917)

=>  R equals 45.4 degrees

Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.

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