• Riley and her sister collect stickers. Riley has 220 stickers
in her sticker collection. Her sister has 55 stickers in her
collection. Riley has how many times as many stickers as
her sister? Use mental math or the guess, check, and
revise strategy to solve the equation 55x = 220.

Answer:

  sin(8w)/1024 -sin(4w)/128 +3w/128

Step-by-step explanation:

No doubt there are a variety of formulas and identities that can be used. Absent knowledge of those, I found it convenient to rewrite the integrand using Euler's formula. It tells you ...

  [tex]\sin(x)=\dfrac{e^{ix}-e^{-ix}}{2i},\quad\cos(x)=\dfrac{e^{ix}+e^{-ix}}{2}[/tex]

After some only slightly messy algebra, we find ...

  [tex]\cos^4(w)\sin^4(w)=\dfrac{\cos(8w)-4\cos(4w)+3}{128}[/tex]

Then the integral becomes straightforward:

  [tex]\displaystyle \int{\cos^4(w)\sin^4(w)}\,dw=\int{\dfrac{\cos(8w)}{128}}\,dw-\int{\dfrac{\cos(4w)}{32}}\,dw+\dfrac{3}{128}\int{}\,dw\\\\=\boxed{\dfrac{\sin(8w)}{1024}-\dfrac{\sin(4w)}{128}+\dfrac{3w}{128}}[/tex]

__

Additional comment

The slightly messy algebra involves the identities ...

  (a+b)(a-b) = a² -b²

  (a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

This means the given integrand is equivalent to

cos⁴(w) sin⁴(w) = (cos(w) sin(w))⁴ = (1/2 sin(2w))⁴ = 1/16 sin⁴(2w)

Also recall the half-angle identities for sine and cosine:

cos²(x) = 1/2 (1 + cos(2x))

sin²(x) = 1/2 (1 - cos(2x))

Then we can rewrite further as

1/16 sin⁴(2w) = 1/16 (sin²(2w))²

… = 1/16 (1/2 (1 - cos(4w)))²

… = 1/16 (1/4 (1 - 2 cos(4w) + cos²(4w))

… = 1/64 (1 - 2 cos(4w) + 1/2 (1 + cos(8w)))

… = 1/128 (3 - 4 cos(4w) + cos(8w))

You'll end up with the same solution as in the other answer:

[tex]\displaystyle \int \cos^4(w)\sin^4(w) \, dw = \frac1{128} \int (3 - 4\cos(4w) + \cos(8w)) \, dw \\\\ = \frac{3w-\sin(4w)+\frac18\sin(8w)}{128} + C \\\\ = \boxed{\frac{24w-8\sin(4w)+\sin(8w)}{1024} + C}[/tex]

Answer:

8t - 5 ≤ 91

8t ≤ 96

t ≤ 12

Christine can spend up to 12 hours in the boat.

Answer:

The area of the trapezoid is 40 ft

Step-by-step explanation:

11ft + 14ft + 15ft = 40 ft

*please help with my 1st question *

Answer:

please follow me and take thanks

The data for the assist forms the possible x-values, while the data for the

points represent the y-values of the scatter plot.

Response:

The given table is presented as follows;

[tex]\begin{tabular}{|c|c|c}Assist&Points\\22&28\\16&18\\46&72\\19&29\\13&26\\9&13\\16&22\\8&18\\12&13\\12&17\\37&50\\7&12\\17&34\\27&58\\18&34\end{array}\right][/tex]

A scatter plot of the above data can be created using MS Excel, by

entering the values into cells as presented above, selecting all values,

and selecting Insert then Scatter from the Chart sub-menu.

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Answer:

what? I don't understand what your trying to say

Answer:

2

Step-by-step explanation:

every rectangular prism has 6 faces, 2 will be congruent together and thw other 4 will be congruent to each other

Answer:

The answer is 2 and 1

Step-by-step explanation:

Sum means to add, so you are looking for two numbers that add up to equal 3.

2+1=3

Quotient means to divide, So secondly you would for two numbers that when divided equals 2

2 divided by 1 =2

hope this helps mark brainliest please :)

Answer:

ahem...

the answer you are looking for is.....

91! :)

Answer:

take the common between dy and y

do similarly also with x .and make a equation

[tex]5x+40 = 5(x+8)[/tex]

Answer:

12 cupcakes were sold

11 brownies were sold

Step-by-step explanation:

Let c = number of cupcakes sold

Let b = number of brownies sold

Total number of items sold = 23

⇒ b + c = 23

cupcake = $1.50 each

brownie = $1.25 each

Total money made = $31.75

⇒ 1.5c + 1.25b = 31.75

Rewrite  b + c = 23  to make b the subject, substitute into 1.5c + 1.25b = 31.75 and solve for c:

⇒ b = 23 - c

⇒ 1.5c + 1.25(23 - c) = 31.75

⇒ 1.5c + 28.75 - 1.25c = 31.75

⇒ 0.25c + 28.75 = 31.75

⇒ 0.25c = 3

⇒ c = 12

So 12 cupcakes were sold

Substitute found value for c into  b + c = 23  and solve for b:

⇒ b + 12 = 23

⇒ b = 11

So 11 brownies were sold

The radius of the circle is a line from the center of the circle to its circumference

The radius of the circle with the same vertex as a center is 10.16 units

From the question, we understand that:

Start by calculating the area of the triangle using:

[tex]Area = 0.5ab\sin C[/tex]

So, we have:

[tex]Area = 0.5 * 12 * 12\sqrt 3 *\sin (60)[/tex]

This gives

[tex]Area = 0.5 * 12 * 12\sqrt 3 * \frac{\sqrt 3}{2}[/tex]

[tex]Area = 108[/tex]

The arc divides the triangle into two equal regions.

So, the area of the arc is:

[tex]Arc = 0.5 * Area = 0.5 * 108[/tex]

[tex]Arc = 54[/tex]

Also, the area of the arc is:

[tex]Arc = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]Arc = \frac{60}{360} *3.14 * r^2[/tex]

Simplify

[tex]Arc = 0.523 * r^2[/tex]

This gives

[tex]0.523 * r^2 = 54[/tex]

Divide both sides by 0.523

[tex]r^2 = 103.25[/tex]

Take the square roots of  both sides

[tex]r = 10.16[/tex]

Hence, the radius of the circle with the same vertex as a center is 10.16 units

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#a

#b

#c

#d

#e

#f

Same like f(2)

#g

The only option for which the limit exist is option f, while for the other options the DNE.

"If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist. If the graph has a hole at the x value c, then the two-sided limit does exist and will be the y-coordinate of the hole."

Let's check the values of the given quantity exist or not. Therefore, we can write,

(a) f(-2) = DNE

(b) [tex]\lim_{x \to \--2} f(x)[/tex] = DNE

(c) f(0) = DNE because hole are exist

(d) [tex]\lim_{x \to \-0} f(x)[/tex] = DNE

(e) f(2) = DNE

(f) [tex]\lim_{x \to \-2} f(x)[/tex] = 0.5 (exist)

(g) f(4) = DNE

(h) [tex]\lim_{X \to \-4} f(x)[/tex] = DNE

Hence, the only option for which the limit exist is option f.

Learn more about Limit Existence here:

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#SPJ2

Answer:

$25

Step-by-step explanation:

$20 = 80%

100% to 80% = x 0.8 ( you have to do inverse)

$20/ 0.8 = $25

Answer:

-see link below for graph

-slope- 6/270

Step-by-step explanation:

link in comments

Answer:

1.5

Step-by-step explanation:

Answer:

(x , y)=(0 , -2)

Step-by-step explanation:

Answer:

A) Compare and contrast texts demonstrate the similarities and differences between two or more topics

Step-by-step explanation:

Compare and Contrast is a text structure (or pattern of organization) where the similarities and differences of two or more things is discussed/explored.

Answer:

100 heavy on the way the calculations and the way solution of equipment and the questions

V(t)=100-4t so at the beginning of the experiment t=0

so you substitute to the given formula

V(0)=100-4(0)

=100litres .

Answer:

90$

Step-by-step explanation:

You multiply the number by 0.10 for your answer.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (900)(0.10)(1)\implies I=90[/tex]

Answer:

A

Step-by-step explanation:

Let x = speed of the faster car, y = speed of the slower car

after t = 5 hours, distance of slower car = 275 = 5 * y, so y = 275/5 = 55 mph

distance of faster car = 275 + 40 = 315 miles

then x = 315/5 = 63 mph

Answer: A

The monthly rent of the apartment in the 10th year is  $1041.67.

The first step is to determine the yearly rent in the first year of living in the apartment.

Yearly rent = $900 x 12 = $10,800

The second step is to determine the yearly rent in the 10th year

$10,800 + (170 x 10) = $12,500

The third step is to determine the monthly rent

Monthly rent = $12500 / 12 = $1041.67

To learn more about division, please check: https://brainly.com/question/13281206

Answer:

243

Step-by-step explanation:

Answer :

2 hours 36 minutes

Step-by-step explanation :

speed = distance / time

Distance = 150 km

time = 1 hour 30 minutes

= 1,5 hours

[tex]speed = \frac{150 \: km}{1.5 \: hours} [/tex]

[tex] speed = 100 \: km/hour[/tex]

How long will it take the car to cover a distance of 260 km at the same average speed ?

Time = Distance/Speed

= 260 km / 100 km/hour

= 2,6 hours

____________________

to convert hours to hours and minutes we can multiply by 60.

2, 6 hours

2 hours and 0,6 hours

0,6 = 3/5

3/5 × 60

60 ÷ 5 × 3

36 minutes

2,6 hours = 2 hours 36 minutes

251.20 50 I think is the answer maybe not but at least try

Answer:

s²+2s-80

Step-by-step explanation:

First (first in each parentheses)

Outside (the two terms on the outside of the expression)

Inside (the two terms in the inside of the expression)

Last (last in each parentheses)

An example:

(a+b)(c+d)=ac+ad+bc+bd

Therefore...

(s+10)(s-8)=(s)(s)+(s)(-8)+(10)(s)+(10)(-8)=s²-8s+10s-80=s²+2s-80

All below;

Green question mark = 10

50 (longer opposite side) - 40 = 10

Red question mark = 20

30 (longer opposite side) - 10 = 20

Perimeter = 160

30 + 50 + 10 + 40 + 20 + 10 = 160

Area = 700

30 * 50 = 1500; (Total area if it were fully a rectangle)

40 * 20 = 800; (Chunk of rectangle that is missing)

1500 - 800 = 700 (Total area - missing space)

Green question mark = 14

Opposite of the other side

Red question mark = 20

35 (longer opposite side) - 15 = 20

Perimeter = 152

35 + 22 + 20 + 14 + 10 + 14 + 15 + 22 = 152

Area = 630

35 * 22 = 770; (Total area if it were fully a rectangle)

14 * 10 = 140; (Chunk of rectangle that is missing)

770 - 140 = 630 (Total area - missing space)