James borrows $4,200 to pay his college tuition. He signs a 5-year simple interest loan. Lf the monthly payments are $78. 40, what is the interest rate on the loan?.

Answer:

Given that:

[tex]\longmapsto{ \large{ \rm{y = \sin \:x \degree}}}[/tex]

We know that,

[tex] \dashrightarrow{ \boxed{ \red{ \rm{1 \degree = \left ( \frac{\pi}{100} \right)^{c} }}}}[/tex]

So, using this, above given can be written as,

[tex]{ \large{ \longrightarrow{ \rm{y = \sin \left( \frac{\pi x}{180} \right) }}}}[/tex]

On differentiating both sides w.r.t. x, we get:

[tex]{ \large { \longrightarrow{ \rm{ \frac{d}{dx}y = \frac{d}{dx} \sin \left( \frac{\pi x}{180} \right) }}}}[/tex]

We know that,

[tex]{ \dashrightarrow{ \boxed{ \red{ \rm{ \frac{d}{dx} \sin x = \cos x }}}}}[/tex]

So, using the result, we get:

[tex]{ \large{ \longrightarrow{ \rm{ \frac{d}{dx} = \cos \left( \frac{\pi \: x}{180} \: \right) \frac{d}{dx} \left( \frac{\pi \: x}{180} \right) }}}}[/tex]

We know that,

[tex]{ \dashrightarrow{ \boxed{ \red{ \rm{ \frac{d}{dx}k \: f(x) = k \frac{d}{dx} \: f(x)}}}}}[/tex]

So, using this, we get:

[tex]{ \large{ \longrightarrow{ \rm{ \frac{dy}{dx} = \cos \left( \frac{\pi \: x}{180} \right) \: \times \: \left( \frac{\pi}{180} \right) \frac{d}{dx} x}}}}[/tex]

We know that,

[tex]{ \dashrightarrow{ \boxed{ \red{ \rm{ \frac{d}{dx} x= 1 }}}}}[/tex]

So, using this, we get:

[tex]{ \large{ \longrightarrow{ \rm{ \frac{dy}{dx} = \left( \frac{\pi}{180} \right) \: \cos \left( \frac{\pi \: x}{180} \right ) \times 1}}}}[/tex]

Hence:

[tex]{ \large{ \leadsto{ \green{ \rm{ \frac{dy}{dx} = \left( \frac{\pi}{180} \right) \cos \left( \frac{\pi \: x}{180} \right) }}}}}[/tex]

[tex]{ \large{ \leadsto{ \green{ \rm{ \frac{dy}{dx} = \left( \frac{\pi}{180} \right) \cos \: x \degree }}}}}[/tex]

[tex] \: \: [/tex]

Learn More:

[tex] \boxed{\begin{array}{c|c}\bf f(x)&\bf\dfrac{d}{dx}f(x)\\ \\ \frac{\qquad\qquad}{}&\frac{\qquad\qquad}{}\\ \sf k&\sf0\\ \\ \sf sin(x)&\sf cos(x)\\ \\ \sf cos(x)&\sf-sin(x)\\ \\ \sf tan(x)&\sf{sec}^{2}(x)\\ \\ \sf cot(x)&\sf-{cosec}^{2}(x)\\ \\ \sf sec(x)&\sf sec(x)tan(x)\\ \\ \sf cosec(x)&\sf-cosec(x)cot(x)\\ \\ \sf\sqrt{x}&\sf\dfrac{1}{2\sqrt{x}}\\ \\ \sf log(x)&\sf\dfrac{1}{x}\\ \\ \sf{e}^{x}&\sf{e}^{x}\end{array}}[/tex]

Answer:

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

Answer:

I'm pretty sure the answer is C.

Step-by-step explanation:

Because I'm smart.

Answer:

Step-by-step explanation:

In the given arithmetic series,

To find the sum of the series, we need to find the number of terms (n) at first. So,

[tex]a_{n} = a + (n - 1)d\\38 = 6 + (n - 1) 4\\38 - 6 = 4n - 4\\32 = 4n - 4\\32 + 4 = 4n\\36 = 4n\\36 \div 4 = n\\\boxed{9 = n}[/tex]

Now, let's find the sum of the arithmetic series (Sₙ).

[tex]S_{n} = \frac{n}{2} [2a + (n - 1)d]\\S_{n} = \frac{9}{2} [2*6 + (9 -1)4]\\S_{n} = \frac{9}{2} [12+ (8*4)]\\S_{n} = \frac{9}{2} [12+ 32]\\S_{n} = \frac{9}{2} (44)\\S_{n} = 9*22\\\boxed{S_{n} = 198}[/tex]

_______________

Hope it helps!

[tex]\mathfrak{Lucazz}[/tex]

Answer:

x = 7

Step-by-step explanation:

5x - 1 + 8x + 5 = 95

13x + 4 = 95

13x = 91

x = 7

Triangle in 95° so x is

»8x + 5° + 5x - 1° = 95°

»13x + 4° = 95°

»13x = 91°

»x = 91°/13

»x = 7°✅

Answer:

(-6,9)

Step-by-step explanation:

x + y = 3

0 + y = 9

We can subtract the two equations.

(x-0) + (y-y) = (3-9)

x=-6

y=9

(-6,9)

Answer:

a) i) y = - 5/3

  ii) y = 4/3

b) i) x = 1

   ii) x = -3/4

Step-by-step explanation:

[tex]y=\dfrac23x +\dfrac13[/tex]

a) i) [tex]x=-3[/tex]

[tex]\implies y=\dfrac23(-3) +\dfrac13\\\\\\\implies y=\dfrac{-6}{3} +\dfrac13\\\\\\\implies y=\dfrac{1-6}{3} \\\\\\\implies y=-\dfrac53[/tex]

ii) [tex]x=1\frac12=\dfrac32[/tex]

[tex]\implies y=\dfrac23\left(\dfrac32\right) +\dfrac13\\\\\\\implies y=\dfrac{6}{6}+\dfrac13\\\\\\\implies y=\dfrac{3}{3}+\dfrac13\\\\\\\implies y=\dfrac{3+1}{3}\\\\\\\implies y=\dfrac43[/tex]

b) i) [tex]y=1[/tex]

[tex]\implies \dfrac23x +\dfrac13=1\\\\\\\implies \dfrac23x =1-\dfrac13\\\\\\\implies \dfrac23x =\dfrac23\\\\\\\implies x =1[/tex]

ii) [tex]y=-\dfrac16[/tex]

[tex]\implies \dfrac23x +\dfrac13=-\dfrac16\\\\\\\implies \dfrac23x =-\dfrac12\\\\\\\implies x =-\dfrac12 \div \dfrac23=-\dfrac12 \times\dfrac32=-\dfrac34[/tex]

Answer:

1st statement

Step-by-step explanation:

The line inside the box is the median.
Since in Class A the median line is on around 80 whilst Class B's median is 75.

So Median of

Class A > Class B

Answer:

(8, 63)

Step-by-step explanation:

Substitute 63 for y and solve for x. x =8.

Answer:

see below

Step-by-step explanation:

7. 4=2^2, 9=3^2, 9*4=36, lcm =36

8. 3=3, 6=3*2, 3*2=6, lcm=6

9. 8=2^3, 10=2*5, 2^3*5=40, lcm = 40

10. 3=3, 5=5, 3*5=15, lcm = 15

11. 12=2^2*3, 5=5, 12*5=60, lcm = 60

12. 4=2^2, 11=11, 4*11=44, lcm =44

Answer:

its the first second and third ones:)

Step-by-step explanation:

I just took the test and got a 100%

I hope this helps:) <3

Figure A, B, D have point symmetry.

Point Symmetry is when every part has a matching part the same distance from the central point but in the opposite direction. It looks the same when viewed from opposite directions (180° rotation).

Try imagining how each of the figure will look after rotating it for 180°.  If it looks exactly same as the original figure, it has point symmetry.

Learn more about point symmetry here

https://brainly.com/question/1593820

#SPJ2

Answer:

The answer is $27

Step-by-step explanation:

540 x .05 = 27

Take the commission rate and move the decimal over to the left twice.

Then you multiply it by the sale price.

Answer:

1-3 are perpendicular ones and the 4th one is parallel

Step-by-step explanation:

Answer:

348in

Step-by-step explanation:

29×12=348

hope this helps

Answer:

$30.48

Step-by-step explanation:

Meals tax = 25.30 x 1.06

= 26.50

Tip = 1.15 x 26.50

= 30.475

after rounding = $30.48

The meal cost $30.48 in total.

Answer:

Is letter B the correct one.

Step-by-step explanation:

If you take that 12 and then multiply it x1, x2, x3, x4, x5, x6, x7 and x8 you will get the numbers in the Chart.

answer:

the answer is 12 pounds

Step-by-step explanation:

Amount of Bananas that Johnny has= 2.6 pounds

Amount of grapes that Johnny has=3.1 pounds

Amount of apples that Johnny has = 6.3 pounds

Total weight of the fruits= 2.6+3.1+6.3=12 pounds

Answer:

First, let's just pick an arbitrary number as an example 7.031.

the 1 is in the thousandth place, so we can represent this as [tex]7\frac{31}{1000}[/tex].

This is so because determining what denominator of a decimal number is can be known through what non-zero digits is on the right-most side of the number.

Step-by-step explanation:

Answer:

The third digit after a decimal point is in the "thousandth" place.

Therefore, to convert a decimal that terminates after three decimal places to a fraction, simply write the digits (without leading zeros) as the numerator and 1000 as the denominator.

For example:

[tex]12.345=\dfrac{12345}{1000}[/tex]

[tex]0.932=\dfrac{932}{1000}[/tex]

Answer:

2x+5=31

2x=31-5

2x/2=26/2

x=13

Answer:

X = 13

Step-by-step explanation:

[tex]2x+5=31 \\ 2x = 31 - 5 \\ x = \frac{31 - 5}{2} \\ x = \frac{26}{2} \\ x = 13[/tex]

Answer:

Mark will save $20 in 17 weeks, but there is no equation for Jen.

Step-by-step explanation:

y = x + 3

1) replace y with $20

20 = x + 3

2) subtract 3 from both sides

17 = x

Answer:

The original mixture contains 41.4 ounces of glycol. for this to be 30 percent of the mixture, the total mixture must be 138 ounces, so 46 ounces of water must be added.

Answer:

1/3 because 1 is 2 less than 3 and the denominator which is the bottom of a fraction is 2 more so the answer again is 1/3

Step-by-step explanation:

Hope this helped.

A brainliest is always appreciated.

Answer:

C

since volume of rectangular prism is given by V=wlh

the volume of the small cubic blocks is (1/5)^3= 1/125

hence we need 4 of the small cubic blocks.

Answer:

13 : 46

Step-by-step explanation:

First, find amount of sugar.

= 100 - 41 - 13

= 100 - 54

= 46

Blackberries : Sugar

= 13 : 46

Answer:

13 : 46

Step-by-step explanation:

amount of sugar required = 100 - 41 - 13 = 100 - 54 = 46 g

ratio of blackberries : sugar = 13 : 46

The second image is larger so the scale needs to be larger than 1.

to find the scale divide the larger k own side by the smaller similar side:

1.5/0.6 = 2.5

The scale factor is 2.5

Answer:

[tex]\frac{34}{12}[/tex] , [tex]\frac{51}{18}[/tex] , [tex]\frac{68}{24}[/tex] , [tex]\frac{85}{30}[/tex]

some equivalent fraction examples of [tex]\frac{17}{6}[/tex]:

Therefore the equivalent fractions are [tex]\frac{34}{12}[/tex] , [tex]\frac{51}{18}[/tex] , [tex]\frac{68}{24}[/tex] , [tex]\frac{85}{30}[/tex]

[tex]{\pmb{\bf{Refer \: to \: the \: attachment \: :D}}}[/tex]