A borrower has been approved for a loan of $5,000 at 8% interest. The loan will be repaid in nine months. What amount will be repaid at that time?

Answer:

Step-by-step explanation:

To convert degrees to radians: [tex]n(\frac{\pi }{180})[/tex] where n is degrees.

For n = 13

[tex]13(\frac{\pi}{180} ) = 0.229 radians[/tex] when rounded to the nearest thousandth

[tex]\text{Given that,}\\\\\theta =\tan^{-1} \left(\dfrac y x \right)\\\\\\\dfrac{\partial \theta}{\partial x} = \dfrac{\partial }{\partial x} \tan^{-1} \left(\dfrac yx \right)\\ \\\\~~~~~~=\dfrac{1}{1 +\tfrac{y^2}{x^2}} \cdot y \dfrac{\partial }{\partial x} \left(\dfrac 1x \right)\\\\\\~~~~~~=\dfrac{yx^2}{x^2 +y^2} \cdot (-1)x^{-2}\\ \\\\~~~~~~=-\dfrac{yx^2}{x^2(x^2 +y^2)}\\\\\\~~~~~~=- \dfrac{y}{x^2 +y^2}\\\\\\[/tex]

[tex]\dfrac{\partial^2\theta}{ \partial x^2} = -\dfrac{\partial }{ \partial x} \left( \dfrac{y}{x^2+y^2} \right)\\\\\\~~~~~~=-y\dfrac{\partial}{\partial x} \left(\dfrac 1{x^2 +y^2} \right)\\\\\\~~~~~~=y (-1)(-1) (x^2 +y^2)^{-2} \dfrac{\partial }{\partial x}(x^2 +y^2)\\\\\\~~~~~~=\dfrac{y}{(x^2 +y^2)^2} \cdot (2x+0)\\\\\\~~~~~~=\dfrac{2xy}{(x^2 +y^2)^2}[/tex]

[tex]\text{Similarly,}~~\\ \\\dfrac{\partial \theta}{\partial y }= \dfrac{x}{x^2 +y^2}\\\\\\\dfrac{\partial^2 \theta}{\partial y^2 } = -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\\text{Now,}\\\\\dfrac{\partial^2 \theta}{\partial x^2 }+\dfrac{\partial^2 \theta}{\partial y^2 }\\\\\\=\dfrac{2xy}{(x^2 +y^2)^2} -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\=0[/tex]

Answer:

[tex]\green{ \rule{500pt}{999999pt}}[/tex]

Answer: 3 coupons

Step-by-step explanation:

       We will divide the total amount of money spent by the amount of money needed to spend to receive a coupon.

$600 / $200 = 3

         Sarah would get 3 coupons.

If the length of UP = 7, then the length of UQ will also be = 7 units.

A perpendicular bisector is a line that cuts a straight line into two both anteriorly and posteriorly.

From the given information:

If the length of UP = 7 units, then the length of UQ will also be = 7 units.

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Answer:

The factorisation of 405

405 = 5x3x3x3x3

Answer:

405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5

Step-by-step explanation:

I'll factor 405 with the Factor Tree Method.

Step 1: Place the number 405 on top of the factor tree.

Step 2: Notice that 405 can be divided by 5 -> 405 = 5 x 81. The two branches from 405 become 5 and 81.

Step 3: Continue factorizing other numbers in the tree until you are left only with the prime factors, which you cannot further factorize.

Step 4: Write the number as the product of prime factors you got.

405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5

Answer:

160 m

Step-by-step explanation:

Length of running track = Total Length of straight sections + Total length of curved sections

Solving :

⇒ 400 m = 2 x 120 m + Total Length of curved sections

⇒ Total Length of curved sections = 400 m - 240 m

⇒ Total Length of curved sections = 160 m

Answer:

1.75

Step-by-step explanation:

Finding average rate of change :

The average rate of change for P between 1992 and 2000 is -1.025.

The average rate at which one quantity changes in relation to another is known as the average rate of change function.

It can be determined by dividing the amount of one quantity's change by the amount of another quantity's change.

Average rate of change for a function 'f' in the interval [a, b] is,

A = f(b) - f(a) / (b-a)

So, the Average rate of change

= P(2000) - P(1992) / (2000 - 1992)

= (34.5 - 42.7) /(2000 - 1992)

= -8.2 / 8

= -1.025

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Find shift

f(x-6)

So

x is decreased 6 units

So

The graph will shift 6 units right

Graph attached

Answer:

shifted right

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:  [tex]f(x)=x^2[/tex]

Translated 6 units to the right:  [tex]f(x-6)=(x-6)^2[/tex]

Answer:

106

Step-by-step explanation:

Answer: 1333.(3)

Step-by-step explanation:

Let her monthly income be x. Then,

(1/10)x + (1/8)x = 300

(4/40)x + (5/40)x = 300

(9/40)x = 300

x = 300 / (9/40)

x = 300*40/9

x = 12000/9

x = 1333 1/3 = 1333.(3)

Answer:

4522mm³

Step-by-step explanation:

7×50×9 + 28×7×7 = 4522

Answer:

4522 mm^3.4522 mm^3.

Step-by-step explanation:

Splitting this up into 2 prisms, one vertical and the other horizontal:

Volume of each prism = length * width * height:

Volume of the figure =

Horizontal + vertical prism

= 7 * 9 * 50 + 7* 7* 28

= 3150 + 1372

= 4522 mm^3

Answer:

B

Step-by-step explanation:

Median value = 14    ( the number in the middle of the ascending-order list)

2 quartile   25% are below 11

3 quartile    25% are above 18

min 9       max = 20

Answer:

i think it's b

Step-by-step explanation:

Answer:

C. $16.95

Step-by-step explanation:

Median is putting the numbers in numerical order and finding the middle by  listing a number on each side off.

As there would need to be bigger numbers in order for the $17.99 to be in the middle, the smallest number would mess the order up.

Answer:  0.3 feet

Work Shown:

(1 ft)/(150 ft) = (x ft)/(40 ft)

1/150 = x/40

1*40 = 150*x

40 = 150x

x = 40/150

x = 4/15

x = 0.2667 approximately

x = 0.3

Note: 0.3 ft = 0.3*12 = 3.6 inches

Answer:

the square root of 99

6pi-6

pi^3

Step-by-step explanation:

The square root of 99 is approximately 9.9.

6pi-6 is approximately 12.8

pi^3 is approximately 12.8

Answer:

C

Step-by-step explanation:

In the unit circle

cos x corresponds with x

sin x corresponds with y.

Here, they are both negative so the angles lies in the third quadrant because both x and y is negative in the third quadrant

Step-by-step explanation:

the other answer we is correct.

here a few words about why :

the quadrants in a circle start in the right top corner. so, right top is number I.

left top is number II.

left bottom is number III.

right bottom is number IV.

simply because this goes with the growing angle. the angle starts at 0° at the right center. and then it grows counterclockwise and goes all around the circle until reaching 360° being equal to 0° again.

Answer:

1st horizontal lines is 2,5,8=15

2nd horizontal line 4,5,6

vertical line 5,5,5

Answer:

See below ~

Step-by-step explanation:

The density of the material that this figurine was made from in pounds/inch³ is 0.183 lb/in³

To answer the question, we need to know what density is

Density is the mass per unit volume of a material.

It is given by ρ = m/v where

Now, given that the toy is dropped into a basin filled with water and found to displace 125.4 mL of water. It's volume is v = 125.4 mL

= 125.4 × 1 mL

= 125.4 × 0.0610237 in³

= 7.65237198 in³

Also, given that the figurine is then put on a scale and found to be 1.4 pounds in weight. It's mass is m = 1.4 lb

So, the density of the material ρ = m/v

ρ = 1.4 lb/7.65237198 in³

ρ =  0.183 lb/in³

So, the density of the material that this figurine was made from in pounds/inch³ is 0.183 lb/in³

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Answer:

E (10, 15)

Step-by-step explanation:

Plotting the points on a graph : (Check attachment)

On plotting the points, and joining a line that connects all points except one, it becomes evident that the point not on the line is :

Answer:

E

Step-by-step explanation:

Answer:

The quotient of seven and p

7 / p

Answer:

Everything is in the picture

Using it's concept, it is found that the period of the function graphed is of 2.244 seconds.

The period of a function is given by the distance between it's repetitions.

In this graph, one example is that the value of 6 repeats at t = 1.87 and at t = 4.114, hence the period in seconds is given by:

P = 4.114 - 1.87 = 2.224.

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Answer:

√5 is the answer

Answer:

x plus y

Step-by-step explanation:

because if lawns is y and earnings are $35 per lawn, then y (lawn) plus $40 per car(x) is y plus x... Hope it helped??

Answer:

1. Yes, all sides are congruent

2. Yes, the opposite sides are parallel

3. Yes, adjacent sides are perpendicular

Answer:

P(Not a 3)=0.85. This is option C.

Step-by-step explanation:

P(Not a 3) would include values 1,2 and 4.

Therefore, P(Not a 3) would be the combined totals of the probabilities of P(1), P(2) and P(4).

P(Not a 3)= P(1)+P(2)+P(4)

P(Not a 3)= 0.30+0.40+0.15

P(Not a 3)=0.85

Alternate method

P(Not a 3) is the same as 1-P(3)

P(Not a 3)=1-P(3)

P(Not a 3)= 1-0.15

P(Not a 3)=0.85

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

          what is the value of 7x-3y-1 for x = -2 and y = 4?

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Replace x with -2 and y with 4:-

[tex]\sf{7(-2)-3(4)-1}[/tex]

On simplification,

[tex]\sf{-14-12-1}[/tex]

On further simplification,

[tex]\sf{-27}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

Step-by-step explanation:

Question 3

Question 4

Question 5