Janet paid for her prescriptions costing $37.13. She paid with a $50 bill. How much change did Janet get back? (Show your work)

Recall some identities:

sin²(x) + cos²(x) = 1

cos(2x) = cos²(x) - sin²(x)

and from the first identity, you can establish that

cos(2x) = 2 cos²(x) - 1

So, rewrite the integrand as much as possible in terms of cos(x) :

[tex]\sin^3(x) \cos(2x) = \sin(x) \sin^2(x) (\cos^2(x)-\sin^2(x)) \\\\ \sin^3(x) \cos(2x) = \sin(x) (1-\cos^2(x)) (2\cos^2(x) - 1)[/tex]

Then in the integral, substitute u = cos(x) and du = -sin(x) dx. With some rewriting, you end up with

[tex]\displaystyle \int_1^2 \sin^3(x) \cos(2x) \,\mathrm dx = -\int_{x=1}^{x=2} (1-\cos^2(x))(2\cos^2(x)-1) (-\sin(x)\,\mathrm dx) \\\\ = -\int_{u=\cos(1)}^{u=\cos(2)} (1-u^2)(2u^2-1)\,\mathrm du \\\\ = \int_{\cos(1)}^{\cos(2)} (1-3u^2+2u^4) \,\mathrm du \\\\ = \left(u-u^3+\frac25u^5\right)\bigg|_{\cos(1)}^{\cos(2)} \\\\ = \left(\cos(2)-\cos^3(2)+\frac25\cos^5(2)\right) - \left(\cos(1)-\cos^3(1)+\frac25\cos^5(1)\right) \\\\ = \boxed{\cos(2) - \cos^3(2) + \frac 25 \cos^5(2) - \cos(1) + \cos^3(1) - \frac25 \cos^5(1)}[/tex]

Answer:

Step-by-step explanation:

The figure is divided into a rectangle and a right-triangle.

The area of the figure is the sum of the individual areas of the rectangle and triangle

Area of rectangle = Length x Width = 10 ft x 8 ft = 80 ft²

Area of triangle = 1/2 x Base X Height = 1/2 x 6 ft x 8 ft =24ft²

Hence, the area of the figure is:

80 ft²+ 24ft² = 104 ft²

Answer:

104 ft^2

Step-by-step explanation:

The figure consist a rectangle and a triangle

to calculate triangle's area we multiply height and base then divide it  by two

the height of the triangle is 8 ft (the given is a special right triangle)

8*6/2 = 24 ft^2

to calculate the area of the rectangle we multiply width and length

8*10 = 80 ft^2 the total area of the figure is :

24 + 80 = 104 ft^2

Answer:

64

Step-by-step explanation:

Since each student must get the same amount of chips and water, the ratio of the number of chips to water received by each student is 1:1.

Hence, a maximum of 64 students can be invited to the party, as the bags of chips is lower than that of the number of bottles of water, and we take it as a 64.

Answer:

0.189x1000=189

1.75x1000=1750

189÷1750 = 0.108

The value of the required expression (x- 3 ) using the given equation -5(3x - 9) = -15 is equal to 1.

Let's solve for the value of "x" in the given equation:

-5(3x - 9) = -15

First, distribute the -5 on the left side of the equation:

-15x + 45 = -15

Now, subtract 45 from both sides to isolate the term with "x":

-15x = -60

Divide both sides by -15 to solve for "x":

x = 4

Now that we have the value of "x," we can find the value of (x - 3):

x - 3

= 4 - 3

= 1

Therefore, the value of (x - 3) is 1.

learn more about value here

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Answer:

610023626728387383838

Answer:

use cymath

Step-by-step explanation:

Answer:

the cost of the bench is $806

Step-by-step explanation:

853 minus 47 is 806

Answer:

17 1/2

Step-by-step explanation:

19+7÷2-5

Solve using PEMDAS

Divide first

19 + 7/2 -5

Then add and subtract from left to right

Getting a common denominator

38/2 + 7/2 - 10/2

45/2 - 10/2

35/2

17 1/2

Answer:

3.   15

6.   4

Step-by-step explanation:

Put  3 instead of x

3.    5x

     = 5 × 3

    = 15

6.   12 ÷ x

     = 12 ÷ 3

     = 4

Answer:

When X is 3 it will be

5(3)=15

Then for the second one it will be 12/3

The answer is 4

Hope I helped

Answer:

8/5 = x

Step-by-step explanation:

6 = 5x - 2

~Add 2 to both sides

8 = 5x

~Divide 5 to both sides

8/5 = x

Best of Luck!

9514 1404 393

Answer:

  (c)  -0.5

Step-by-step explanation:

Starting from standard form ...

  ax +by = c

and solving for y, we get the slope-intercept form ...

  y = (-a/b)x +c/b

The coefficient of x is the slope: -a/b.

For your equation x+2y=16, the slope is -1/2 = -0.5.

Answer:

Sorry about that, I did not see the decimal. As liamly said, it is positive but is not a natural number because of the decimal.

Step-by-step explanation:

Answer:

[tex]volume \: of \: rectangular \: prism = base \: area \: \times height \\ \\ = length \times width \times height[/tex]

Answer:

188 units cubed

Step-by-step explanation:

General Arithmetic Terms

[tex] \displaystyle \large{a_n = a_1 + (n - 1)d}[/tex]

We want to find a8; we know:

Substitute in the formula.

[tex] \displaystyle \large{a_n = 9 + (n - 1)4} \\ \displaystyle \large{a_n = 9 + 4n - 4} \\ \displaystyle \large{a_n = 4n + 5}[/tex]

To find a8, substitute n = 8

[tex] \displaystyle \large{a_8= 4(8) + 5} \\ \displaystyle \large{a_8= 32 + 5} \\ \displaystyle \large{a_8= 37}[/tex]

Hence, the 8th term of sequence is 37

Answer:

-21b + 180 / 5

Step-by-step explanation:

Hey there!

b^3 - 21/5b + 9

= 3^3 - 21/5(3) + 9

= 27 - 63/5 + 9

= 72/5 + 9

= 117/5

Answer: 117/5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

9514 1404 393

Answer:

  m = (5x -6)/(43y -4)

Step-by-step explanation:

Subtract 4m+6 to separate m-terms from other terms.

  5x +4m -(4m +6) = 43my +6 -(4m +6)

  5x -6 = 43my -4m

  5x -6 = m(43y -4) . . . . factor out m

 (5x -6)/(43y -4) = m . . . . divide by the coefficient of m

Answer:

[tex]2 {b}^{2} - 5b - 63[/tex]

Step-by-step explanation:

[tex](b - 7) \times (2b + 9)[/tex]

[tex]b \times 2b + 9b - 7 \times 2b - 7 \times 9[/tex]

[tex]2 {b}^{2} + 9b - 14b - 63[/tex]

[tex]2 {b}^{2} - 5b - 63[/tex]

Answer:

For option A she would receive $1,690. For house B, she would receive $2,070 for a weeks worth of pay.

Step-by-step explanation:

Please mark Brainliest if this helped :)

Answer:

The answer above me is correct!

Step-by-step explanation:

Give them BRAINLIEST! have a good day<3 :)

Answer:

The  Measure of Central Tendency are

1. Mean

2. Median and Quartiles

3. Mode

4. Geometric Mean

5. Harmonic Mean

→When all the five Measure of Dispersion are Same, it means the two data sets have Identical Variate.

→Now consider the two data sets,

A=3,4,4,5

B=1,4,4,7

Both the Data set have , same mean, median, and Mode,which is equal to 4.

→When you will consider, First three as Measure of central tendency ,then it becomes incorrect statement ,that Data Set are same.

Step-by-step explanation:

A measure of central tendency is a descriptive statistic

The correct response to the question is as follows;

Yes; A data having two modes can have two points of central tendency

The reason a dataset having two modes can have two points of central tendency is as follows:

A dataset having two modes is said to be bimodal

A dataset having three modes is said to be trimodal

A dataset having more than three modes is said to be multimodal

A measure of central tendency is a type of summary statistics that is a

single value representing the center point, or average of a set of data

thereby providing a description of the data by telling the middle value, the

average or the most common value which is the mode

As can be seen from the given example, by having two modes, a bimodal

data set describes a data that has two points of central tendency, thereby

giving a description of the data type, which for example may a collection

of the height of individuals, male and female, that have two most common

height values for each gender

Therefore, the correct response is yes, a dataset having two modes can

have two points of central tendency because the mode is a measure of

central tendency which is a descriptive statistics

Learn more about the measures of central tendency here:

https://brainly.com/question/17762288

https://brainly.com/question/16964486

Answer:

x=10

Step-by-step explanation:

10 a 8 son dos, entonces 14 ax es 4

Answer:

La explicación sería:

//////////////////////////

=> 9 * 2 + 4/2 = 20

=> 18 +2 =20

=> 20 =20

//////////////////////////

=> 5*2 + 8/2 = 14

=> 10 +4 =14

=> 14 =14

//////////////////////////

=> 3*2 + 10/2 = x

=> 6 + 5 = x

=> 11 = x

Answer:

8x-6=14

Step-by-step explanation:

Whenever you see less next to a number, you know it's gonna be -6. If it said 6 minus 8x though, then you would do 6-8x etc. Hope this helped.

Step-by-step explanation:

[tex]4x - 2 = 18x + 5[/tex]

Collect like terms and simplify

[tex] - 2 - 5 = 18x - 4x \\ - 7 = 14x[/tex]

Divide both sides of the equation by 14

[tex] \frac{ - 7}{14} = \frac{14x}{14} \\ - \frac{1}{2} = x[/tex]

Answer:

x = -1/2

Step-by-step explanation:

4x-2=18x+5

-2-5=18x-4x

-7=14x

-7/14=14/14x

-1/2=x

Answer:

Step-by-step explanation:

The question is not totally clear. I will assume that the spinner has 2 colors, red and blue.

Your chances of rolling a 3 are 1 in 6 = 1/6

Your chance of getting blue is 1/2

Your chances are 1/2 * 1/6 = 1/12

As a decimal that is 0.0833333

As a % it is 8.3333 %

Answer:

135

Step-by-step explanation:

250 x 54%=135

Answer:

[tex]243 {x}^{2} {y}^{5} [/tex]

Step-by-step explanation:

[tex] \frac{(3xy {)}^{5} }{ {x}^{3} } [/tex]

[tex] \frac{243 {x}^{5} {y}^{5} }{ {x}^{3} } [/tex]

simplify:

[tex]243 {x}^{2} {y}^{5} [/tex] ✅

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{-8 (3r - 4) - 6}[/tex]

[tex]\huge\text{= -8(3r) + (-8)(-4) - 6}[/tex]

[tex]\huge\text{= -24r + 32 - 6}[/tex]

[tex]\huge\boxed{\textsf{COMBINE the LIKE TERMS}}[/tex]

[tex]\huge\text{= -24r + 6}[/tex]

[tex]\huge\boxed{\mathsf{Answer: {= -24r + 6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]