Ryan's total payment for his loan was $47,292. What was his monthly payment if hepaid it off after making 57 payments? Round answer to a whole number.

Answer:

\(-\frac{1}{8\\}\)

Step-by-step explanation:

Break the equation into 2 pieces:

(-1/2)•(-1/2) = 1/4

1/4 •  (-1/2) = -1/8

Answer:

-0.125

Step-by-step explanation:

A mean is an arithmetic average of a set of observations. The correct option is B.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

The average pay does not differ significantly since the average wage for subpopulations is not significant. As a result,  the subpopulations of mechanical and civil engineers are Not earning different salaries.

Hence, the correct option is B.

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Answer:

B

Step-by-step explanation:

Answer:

5( cos(- 0.64)+\(i\) sin(-0.64))

Step-by-step explanation:

Given:

z = -4+3i

\(r=\sqrt{(-4)^2+3^2}= 5\)

θ=\(tan^-^1(\frac{3}{-4} ) = -0.64\)

Polar form=r(cosθ+\(i\) sinθ)=> 5( cos(- 0.64)+\(i\) sin(-0.64))

Answer:

Step-by-step explanation:

The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line, we need to find the slope, which can be calculated using the formula:

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.

In this case, the coordinates are:

P = (-3, 2) and Q = (5, 7)

So, the slope is:

m = (7 - 2) / (5 - (-3)) = 5 / 8

Next, we can use either of the points to find the y-intercept. Let's use point P:

b = y - mx, where y and x are the y and x coordinate of the point, respectively.

In this case,

b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8

So, the equation of the line joining the points P and Q is:

y = (5/8)x + 89/8

Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.

So, we have:

0 = (5/8)x + 89/8

Solving for x, we get:

x = -(89/8) / (5/8) = -89 / 5

This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.

Let's call the point of intersection with the y-axis R. The distances are then:

PR = (3, 2) and QR = (5 - (-89/5), 7)

The ratio of the distances is then:

PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47

So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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You're looking for a solution of the form

\(\displaystyle y = \sum_{n=0}^\infty a_n x^n\)

Differentiating twice yields

\(\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n\)

\(\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n\)

Substitute these series into the DE:

\(\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0\)

\(\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0\)

\(\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0\)

Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:

\(\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0\)

which indicates that the coefficients in the series solution are governed by the recurrence,

\(\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}\)

Use the recurrence to get the first few coefficients:

\(\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}\)

You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,

-7 = -7/0!

-7/2 = -7/2!

-7/6 = -7/3!

and so on, with only the coefficient in the n = 1 position being the odd one out. So we have

\(\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots\)

which looks a lot like the power series expansion for -7eˣ.

Fortunately, we can rewrite the linear term as

3x = 10x - 7x = 10x - 7/1! x

and in doing so, we can condense this solution to

\(\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}\)

Just to confirm this solution is valid: we have

y = 10x - 7eˣ   ==>   y (0) = 0 - 7 = -7

y' = 10 - 7eˣ   ==>   y' (0) = 10 - 7 = 3

y'' = -7eˣ

and substituting into the DE gives

-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0

as required.

The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.

We have,

Let's start by assigning variables to unknown quantities.

Let m be the time it takes for Mike to wash the car alone (in minutes).

We know that Stephanie takes 17 minutes to wash the car alone, so her rate of work is 1/17 car per minute.

Working together, their combined rate of work is 1/8.24 car per minute.

Using the formula:

(rate of work) = (amount of work) / (time)

we can set up the following equation to represent the work they do together:

1/8.24 = (1 car) / t

where t is the time it takes them to wash the car together.

We can also set up a similar equation for Stephanie's work alone:

1/17 = (1 car) / (t + x)

where x is the extra time it takes Mike to wash the car alone.

Since they are working on the same car, the amount of work done in both cases is the same, so we can set the two equations equal to each other and solve for x:

1/8.24 = 1/(t + x) + 1/17

Multiplying both sides by the least common multiple of the denominators (8.2417(t+x)).

17*(t+x) + 8.24*(t+x) = 8.24*17

Simplifying.

25.24t + 17x = 139.68

We also know that Mike's rate of work is 1/m car per minute.

Since we know the combined rate of work when they work together, we can set up another equation:

1/m + 1/17 = 1/8.24

Multiplying both sides by the least common multiple of the denominators (8.2417m).

178.24m + 8.2417m = 8.2417m + m8.24m

Simplifying.

141.08m = 139.68

Solving for m.

m = 0.989

Therefore,

It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.

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Answer:

A2 + B2 = C2, so 4 squared + 19 squared = C2, 16 + 361 = 377. 377's square root is 19.4.

Step-by-step explanation:

The measure of the hypotenuse is 19.4 cm.

Given that, one of the legs of a right triangle measures 4 cm and the other leg measures 19 cm.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Let the measure of the hypotenuse be x.

Using Pythagoras theorem,

x² = 4² + 19²

⇒ x² = 16 + 361

⇒ x² = 377

⇒ x = √377

⇒ x = 19.4 cm

Therefore, the measure of the hypotenuse is 19.4 cm.

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Answer: C

Step-by-step explanation:

The closed circle on the left denotes "or equal to," and the open circle on the right denotes "less than."

So, it cannot be A, B, or D because they do not have \(\leq\) on the left and < on the right.

Only C has that option.

The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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The required parameters is as follows:

Equation: y = 10x + 12.

Slope: 10.

Y-intercept: 12.

Given the slope of the line and the intercept it forms with the y-axis, the slope intercept form in mathematics is one of the forms used to determine the equation of a straight line. Y = mx + b is the slope intercept form, where m is the slope of the straight line and b is the y-intercept.

The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope. The slope is the ratio of the change in the y values over the change in the x values, or the rise over run, and the point form is written as (x,y).

This mathematical formula gives the equation of a straight line in slope-intercept form;

y = mx + c

Where, m represents the slope or rate of change

x and y are the points

c represents the y-intercept or initial value.

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Answer:

The Answer Will Be D

Step-by-step explanation:
The fuel economy of a car is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour.We need to find the fuel economy of the car when it travels at an average of 20 miles an hour.f(20) = -0.009(20)² +0.699(20) +12f(20) = -0.009(400) +13.98f(20) = 9.6The fuel economy of the car when it travels at an average of 20 miles an hour is 9.6 miles per gallon.Therefore, the answer is option D. 22.38 miles per gallon.

Answer:

18-16=2

Step-by-step explanation:

hence she missed to football games

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have a great day ahead.!.

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

\(H_0\) : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

\(H_1:\mu < 25\)

The test statistic is given by:

\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)

The parameters are:

the values of the parameters are:

x = 23.5 , \(\mu=25\) , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Step-by-step explanation:

Commutative means a + b = b + a

So, 4x + 3 = 3 + x

Associative means a + (b + c) = (a + b) + c

So, 6 + (9 + 7) = (6 + 9) + 7

Distributive means expand the bracket a * (b + c) = a*b + a*c

So, (4x + 3y + 2z) * 7 = 4x*7 + 3y*7 + 2z*7

Commutative is a + b = b + a

So, 15a + 15b = 15b + 15a

The commutative property states that we can sum the terms in different orders and the result will be the same:

a+b=b+a

So for the expression 4x + 3, we can write:

4x+3=3+4x

The associative property states that we can group the operations of sum and subtraction in different orders and the result is the same:

a+(b+c)=(a+b)+c

So for 6 + (9 + 7) we have:

6+(9+7)=(6+9)+7

The distributive property states the following:

a⋅(b+c)=a⋅b+a⋅c

So for (4x + 3y + 2z) * 7, we have:

(4x+3y+2z)⋅7=28x+21y+14z

Using the commutative property for 5a + 15b, we have:

5a+15b=15b+5a

As given by the question:

There are given the expression;

(a):

Hence, the value of the expression is 1.96.

Now,

(b):

Hence, the value of the given expression is 6.

(B):

Hence, the value of the given expression is shown below:

Answer:

(x+6)^2+(y-7)^2= 29

Step-by-step explanation:

general exqn-> (x-h)^2+(y-k)^2=(r)^2

here, h= -6 and k=7

r= √ 29

Therefore, exqn of circle=

(x+6)^2+(y-7)^2= 29

Answer:

(x + 6)² + (y - 7)² = 29

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 6, 7 ) and r = \(\sqrt{29}\) , then

(x - (- 6) )² + (y - 7)² = (\(\sqrt{29}\) )² , that is

(x + 6 )² + (y - 7 )² = 29

Answer:

Step-by-step explanation:

The revenue can be modeled by the polynomial function

R

(

t

)

=

−

0.037

t

4

+

1.414

t

3

−

19.777

t

2

+

118.696

t

−

205.332

where R represents the revenue in millions of dollars and t represents the year, with t = 6 corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.

Multiplicity and Turning Points

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Suppose, for example, we graph the function

f

(

x

)

=

(

x

+

3

)

(

x

−

2

)

2

(

x

+

1

)

3

.

Notice in the figure below that the behavior of the function at each of the x-intercepts is different.

Graph of h(x)=x^3+4x^2+x-6.

The behavior of a graph at an x-intercept can be determined by examining the multiplicity of the zero.

The x-intercept

x

=

−

3

is the solution to the equation

(

x

+

3

)

=

0

. The graph passes directly through the x-intercept at

x

=

−

3

. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.

The x-intercept x=2

is the repeated solution to the equation  (x−2)2=0

. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.

(x−2)2=(x−2)(x−2)

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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Answer:

74 handkerchief

Step-by-step explanation:

Let the number of Thomas' and Randy's handkerchief be T and R respectively.

Thomas

blue ----- ¼T

yellow ----- 1T -¼T= ¾T

Randy

blue ----- \( \frac{3}{7} \)R

yellow ----- \( \frac{4}{7} \)R

Since they have the same number of yellow handkerchiefs,

¾T= 4/7 R

Multiply by 28 on both sides,

(since 28 is the lowest common multiple of 4 and 7)

21T= 16R -----(1)

From this we can see that R is greater than T.

Hence, given that the difference between R and T is 10,

R= T +10 -----(2)

Subst. (2) into (1):

21T= 16 (T +10)

21T= 16T +160 (expand)

21T -16T= 160

5T= 160 (simplify)

T= 160 ÷5 (÷5 on both sides)

T= 32

Subst. into (2):

R= 32 +10

R= 42

Thus, total number of handkerchief

= 32 +42

= 74

Answer:

The original price would be $75

Step-by-step explanation:

I just used a calculator

The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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The margin of error is defined as follows:

M = 1.9z/sqrt(n).

In which:

The bounds of the confidence interval are given as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is then given as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The problem is incomplete, hence the general procedure to obtain the sample size was presented.

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Answer:

30 mph

Step-by-step explanation:

Distance travelled=300 miles

Time travelled=10hours

At a constant rate,k

Let distance travelled=d

Time travelled=t

Then,

d=kt

300=k*10

300=10k

k=300/10

=30

k=30mph

30 miles per hour

30 MPH                                                                                       ............................................................................................................

Answer:

<1 and <3 equal 29 degrees

<2 ans <4 equal 151 degrees

Step-by-step explanation:

instructions in pic :)

Answer:

y=2/5x

Step-by-step explanation:

The equation of the line containing the points (5,2), (10,4), and

(15, 6) are,

⇒ y = 2/5x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (5, 2) and (10, 4).

Now,

Since, The equation of line passes through the points (5, 2) and (10, 4).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 2) / (10 - 5)

m = 2 / 5

Thus, The equation of line with slope 2/5 is,

⇒ y - 2 = 2/5 (x - 5)

⇒ y - 2 = 2/5x - 2

⇒ y = 2/5x

Therefore, the equation of the line containing the points (5,2), (10,4), and

(15, 6) are,

⇒ y = 2/5x

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The answer is X=165 lbs (or) 74.84 kg.

Solution:

Given,

1kg/2.2lbs = X/165lbs,

So we get 1kg×165lbs= 2.2lbs×X,

By converting kg to lbs ∵ 1 kg= 2.2 lbs,

X=165 lbs.

∴ Hence X=165 lbs