0.1067 as a fraction

Derek must give the bank approximately $26,695.78 to pay off his car loan after 11 months. To calculate how much Derek must give the bank to pay off his car loan after 11 months, we need to consider the principal amount borrowed, the interest rate, the loan term, and the number of payments made.

Derek borrows $30,924.00 to buy a car, and he will make monthly payments for 6 years. The interest rate is 5.89%.

First, we need to calculate the monthly interest rate. We divide the annual interest rate by 12 (number of months in a year) and convert it to a decimal:

Monthly interest rate = 5.89% / 12 = 0.4908%

Next, we calculate the number of payments made up to the point when Derek decides to pay off the loan. In this case, he makes payments for 11 months.

Now, let's calculate the remaining balance on the car loan using the formula for the remaining balance on an amortizing loan:

Remaining balance = Principal * [(1 + r)^n - (1 + r)^p] / [(1 + r)^n - 1]

Where:

Principal = $30,924.00 (initial loan amount)

r = Monthly interest rate (0.004908)

n = Total number of payments (6 years * 12 months per year = 72 payments)

p = Payments made (11 payments already)

Substituting the values into the formula, we have:

Remaining balance = $30,924.00 * [(1 + 0.004908)^72 - (1 + 0.004908)^11] / [(1 + 0.004908)^72 - 1]

Using a calculator, we can evaluate this expression:

Remaining balance ≈ $30,924.00 * [1.4042 - 1.0552] / [1.4042 - 1] ≈ $30,924.00 * 0.3490 / 0.4042 ≈ $26,695.78

Therefore, Derek must give the bank approximately $26,695.78 to pay off his car loan after 11 months.

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Answer:

\(12 = 12 \\ 12 - 12 = 12 - 12 \\ 0 = 0\)

Answer:

40 feet

Step-by-step explanation:

24^2+32^2=x^2

solve for x

x=40 feet

For the given information, the value of the test statistic is -1.724 and its associated p-value is 0.0426.

In order to calculate the p value of students with GPA of 3.00 or below, the standard score (z -score or test statistic) must be determined first. In statistics, the standard score refers to the number of standard deviations by which the scores differs from the mean value of the observed or measured data. Scores above the mean have positive standard scores, while those below the mean have negative standard scores.

In a sample of 190 graduates, 28 students have a GPA of 3.00 or below, x = 28/190 = 0.15

The standard deviation = √(p(1 – p)/n) = √(0.2(1-0.2)/190) = 0.029 (where p is the probability of success and n is the total number of data)

The z-score = (x - µ)/σ = (0.15 – 0.2)/0.029 = - 1.724

From the table,

The P (z < -1.724) = 0.0426 or 4.26%.

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Answer:

30 J

Step-by-step explanation:

Given : -

Height ( h ) = 3m

Weight ( W ) = 10 N

To find : GPE = ?

Note : -

GPE is Gravitational Potential Energy.

It is expressed in Joules ( J ).

Formula : -

W = mg

mg = 10 N

Formula : -

GPE = mgh

GPE = 10 x 3

GPE = 30 J

Therefore,

A bird weighs 10 N and is standing 3 m, it's

GPE is 30 J.

Answer:

The answer is GPE = 300 Nm (Newton meters)

Step-by-step explanation:

The bird's mass weighs to 10 Newtons.

Presuming this took place on Earth, the gravitational force is 10 Newtons.

The bird is standing 3 meters above the ground.

Using the GPE formula (GPE = mgw,) the answer should be 300 Newton metres.

Answer:

At 4 meters, the potential energy is 800 Joules

At 3 meters, the potential energy is 600 Joules

At 2 meters, the potential energy is 400 Joules

At 1 meter, the potential energy is 200 Joules

Step-by-step explanation:

The given mass of the object = 20 kg

The Potential Energy of an object at a height is. P.E. = m × g × h

Where;

m = The mass of the object

g = The acceleration due to gravity taken as 10 m/s²

h = The height of the object

The potential energy if the height is 4 meters is given as follows;

P.E. = 20 kg × 10 m/s² × 4 m = 800 Joules

The potential energy if the height is 3 meters is given as follows;

P.E. = 20 kg × 10 m/s² × 3 m = 600 Joules

The potential energy if the height is 2 meters is given as follows;

P.E. = 20 kg × 10 m/s² × 2 m = 400 Joules

The potential energy if the height is 1 meter is given as follows;

P.E. = 20 kg × 10 m/s² × 1 m = 200 Joules.

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Answer:

the product of the two integers is -80

Answer:

-80

Explanation:

it was on a mathcounts competition

The period of a trigonometric function is the distance between each repetition of the function.

In this case, we have:

As we can see in the graph of the function, the distance between each repetition is 2π.

Therefore, the period of f(x) = csc(x) is 2π.

She works for 3 hours each day.

The art project takes Misty 4 hours to complete

Let's call x to the number of days she needs to complete the project

The next equation model the situation

3x = 4

Solving for x:

x = 4/3 days

The amount remaning is 38.59 grams rounded to 2 decimal place.

The exponential function, y = ab^t can be used to find the amount remaining after 41 hours, where 'a' is the initial amount, 't' is time and 'b' is the growth or decay factor.

A growth factor is used if the amount is increasing with time whereas a decay factor is used if the amount is decreasing with time.In this problem, the amount of radioactive substance is decreasing. Hence we use a decay factor.

So, the exponential function is given by y = ab^-kt, where k is a constant to be determined.

To find the value of k, we use the given information that the mass of the radioactive substance decreased by 9% after 3 hours.

Therefore, the proportion remaining after 3 hours = 100% - 9% = 91%.

Hence, we have (91/100) = 77(b^-3k)

Multiplying both sides by (10/91) we get (10/91)(91/100) = (10/100) = 0.1.

Hence, 0.1 = 77(b^-3k)

Taking the natural logarithm of both sides, we get ln(0.1) = ln 77 - 3k

ln b`Substituting the value of ln b, we get

ln(0.1) = ln 77 - 3k ln 0.91

k = (ln 77 - ln 0.1) / (3 ln 0.91) = 0.00175

Therefore, the exponential function becomes

y = 77e^(-0.00175t)

At t = 41, the amount remaining is given by y = 77e^(-0.00175 × 41) = 38.59.

Therefore, the amount remaining after 41 hours is 38.59 grams (rounded to 2 decimal places).

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The translation rule of the tile floor is T -3,2 (x,y)

From the complete question, the tile floor is shifted left by 3 units, and shifted up by 2 units.

This is represented as:

(x,y) -> (x - 3, y + 2)

This can also be written as:

T -3,2 (x,y)

Hence, the translation rule is T -3,2 (x,y)

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Answer:

A: T-3, 2(x, y)

Step-by-step explanation:

The function that fits the points (-1, 21) (3, 45) (4, 81) is 6x²-6x+9.

Quadratic Regression is a method according to which we can make an equation of a quadratic curve from given no. of x and y data points

Quadratic Regression Equation(y) = a + b x + c x^2

The formula for its coefficients is,

c = { [ Σ x2 y * Σ xx ] - [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }

b = { [ Σ xy * Σ x2x2 ] - [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }

a = [ Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x 2 / n ] }

Where,

Σ x x = [ Σ x 2 ] - [ ( Σ x )2 / n ]

Σ x y = [ Σ x y ] - [ ( Σ x * Σ y ) / n ]

Σ x x2 = [ Σ x 3 ] - [ ( Σ x 2 * Σ x ) / n ]

Σ x2 y = [ Σ x 2 y] - [ ( Σ x 2 * Σ y ) / n ]

Σ x2 x2 = [ Σ x 4 ] - [ ( Σ x 2 )2 / n ]

x and y are the Variables.

a, b, and c is the Coefficients of the Quadratic Equation

n = Number of Values or Elements

Σ x= Sum of First Scores

Σ y = Sum of Second Scores

Σ x2 = Sum of the square of the First Scores

Σ x 3 = Sum of Cube of First Scores

Σ x 4 = Sum of Power Four of First Scores

Σ xy= Sum of the Product of First and Second Scores

Σ x2y = Sum of Square of First Scores and Second Scores

when we input the points (-1,21),(3,45),(4,81)

we get the equation 6x²-6x+9

which looks like this (The image has been attached),

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Answer:

y = (-3/7)x + 2

Step-by-step explanation:

slope-intercept form is y = mx + b, where m = slope and b = y-intercept.

all you need to do is plug the values into the equation! :)

since your slope is (-3/7), plug that in for m.

y = mx + b ⇒ y = (-3/7)x + b

and since your y-intercept is 2, plug that in for b.

y = (-3/7)x + b ⇒ y = (-3/7)x + 2

therefore, the line's equation in slope-intercept form is y = (-3/7)x + 2.

don't worry about the parentheses, i only put them in there to separate the 7 in -3/7 from x. i'm not good at putting equations in here on brainly lol i just wanted to make sure you didn't think that it was -3 over 7x.

i hope this helps! have a lovely day <3

Answer:

6/9

Step-by-step explanation:

Answer: 0.66666666666667

The scaling factor from the triangle ABC to triangle A'B'C' is 4/3.

Scale factor:

Scaling factor refers number that is multiplied by the original value to find the dilation of the figure.

Given,

Here we have the two triangles, now we have to identify the scale factor between these triangle.

While we looking into the given triangle, we have identified that the side of triangle ABC is 3 inch and side of triangle A'B'C' is 4 inch.

Now, we have to Determine the scale factor for triangle ABC to triangle A'B'C' as,

Scaling factor = new side/old side

Therefore, the scaling factor is,

Scaling factor = 4/3

Therefore, Scaling factor is 4/3 for triangle ABC to triangle A'B'C'.

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Step-by-step explanation:

the given  function: \(c(x) = 0.5x+70.\)

Where C = cost (in dollars) and x is the number of miles you drive the truck.

when we compare the given function by slope- the intercept form y=mx+b, what we get  is

Slope m = 0.5 whose fraction can be written as \(\frac{1}{2}\)

And y-intercept b =70.

for us to be able to graph it, we need to plot y-intercept from 70  and then plot some more points by applying or increasing the points by \(\frac{1}{2}\)

the shaded lines on the graph indicates the given function.

cost is at $70 for 0 number of miles. travelled.

Thus;

the Domain: x≥0 and Range :  \(C(x)\)≥\(70\)

Answer:

a

Step-by-step explanation:

368

Answer:

answer is 54. Since angleABD - angleCBD = angleABC

THEREFORE,. 90-36

By evaluating the expression, the value is -10.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator). An expression is a mathematical term that combines variables, operators, and numbers to show the value of something.

Given that 8 - 2x² when x = -3

= 8 - 2(-3)²

= 8 - 2(9)

= 8 - 18

= -10

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The complete question is,

Evaluate the expression 8 - 2x² when x = -3

Answer:

1) 100+10+10 = 120

2) 120 : 2 = 60

1 block — 60

Answer:

Below

Step-by-step explanation:

In areas that require building, such as carpentry or architecture, the Pythagorean Theorem can be used to find unknown side lengths in order to determine the lengths of building material needed to complete the triangle- a shape often used in construction due to its more durable nature.

Answer:

The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. … The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal

Step-by-step explanation:

Answer:

Explanation:

Recall that the slope-intercept form of the equation of a line is generally given as;

where m = slope of the line

b = y-intercept of the line

Given the slope(m) of the line as 2, let's go ahead and determine the y-intercept(b) of the line using the point (-3, -4) where x = -3 and y = -4 as seen below;

Since b = 2 and m = 2, we can now go ahead and write the equation of the line in slope-intercept form as;

Answer:

c

Step-by-step explanation:

when there is subtraction you add the number with the variable on each side to get it by it's self

+515=y-5+5

20=y

Answer:

A. 10=y

B.-5=y

C.0=5y

D.15=20y

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

A triangle's angles must add up to 180 degrees, so 180 = 40 + 12 + x which is the same as 180 - 40 - 12 = x

x = 128

Answer: 128 degrees

Step-by-step explanation:

Answer:

a. Yes

b. 3x+7

c. 105 cm

Step-by-step explanation:

a. a(1)+b=10

   a(2)+b=13

when you solve this by elimination or simultaneously: a=3 and b=7

∴ f(x)=3x+7

b. f(x)=3x+7

c. 3(35)+7=112 cm

The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.

A combination is a grouping of items where order does not matter. The formula of combination is

\(_{n}C_{r} = \frac{n!} {r! (n-r)!}\)

Where

Given the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.

What is the probability that no two adjacent people will stand?

First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.

The number of arrangements according to the number of people standing.

Case 1: 0 people standing = 1 arrangement.

Case 2: 1 people standing = \(_{8}C_{1}\) = \(\frac{8!} {1! 7!}\) = 8 arrangements.

Case3: 2 people standing = \(_{8}C_{2}\) = \(\frac{8!} {2! 6!}\) = \(\frac{7 \times 8} {2}\) = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.

Case 4: 3 people standing = \(_{8}C_{3}\) = \(\frac{8!} {3! 5!}\) = \(\frac{6 \times 7 \times 8} {6}\) = 56 arrangements. In this case, three people standing are next to each other = \(_{8}C_{1}\) = 8 arrangements. Two people standing are next to each other and the third person is not = \(_{8}C_{1} \times _{4}C_{1}\) = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.

Case 5: 4 people standing but no two adjacent people = 2 arrangements.

The number of arrangements that no two adjacent people will stand.

n(A) = 1 + 8 + 20 + 16 + 2 = 47

The probability that no two adjacent people will stand is

P(A) = n(A)/n(S)

P(A) = 47/256

Hence, the probability that no two adjacent people will stand is 47/256.

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The standard equation of the line is:

\(3x - 4y = 20\), option B.

------------------------------

In slope-intercept form, the equation of a line is given by:

\(y = mx + b\)

In which:

In standard form, the equation of the line is:

\(y - mx = b\)

Without fractions.

In this problem:

Thus, the equation is:

\(y = mx + b\)

\(y = \frac{3}{4}x - 5\)

Multiplying everything by 4:

\(4y = 3x - 20\)

\(4y - 3x = -20\)

\(3x - 4y = 20\), option B.

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