A sample of 40 11th graders were asked to select a favorite pattern out of 6 choices. The following display shows what their favorite color patterns were. The counts have been recorded in the accompanying table according to pattern and the number of students who chose that pattern.

Answer:

(-1,4)

Step-by-step explanation:

Answer:

Your process is indeed correct!

The full solution is:

[tex]\displaystyle \int\frac{\sin ^3 x}{\sqrt{\cos x}}\, dx= \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]

Step-by-step explanation:

We want to evaluate the integral:

[tex]\displaystyle \int \frac{\sin^3(x)}{\sqrt{\cos(x)}}\, dx[/tex]

As you had done, we can rewrite our integral as:

[tex]\displaystyle =\int \frac{\sin(x)(\sin^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]

Using the Pythagorean Identity, this is:

[tex]\displaystyle =\int \frac{\sin(x)(1-\cos^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]

Now, we can make a substitution. Let u = cos(x). Then:

[tex]\displaystyle du = - \sin x \, dx[/tex]

Substitute:

[tex]\displaystyle = \int\frac{1-u^2}{\sqrt{u}} \, \left(- du\right)[/tex]

Simplify:

[tex]\displaystyle = -\int \frac{1}{\sqrt{u}} - \frac{u^2}{\sqrt{u}}\, du[/tex]

Rewrite:

[tex]\displaystyle = -\int u^{{}^{-1}\!/\!{}_{2}} - u^{{}^{3}\!/\!{}_{2}}\, du[/tex]

By the Reverse Power Rule:

[tex]\displaystyle = -\left(2u^{{}^{1}\!/\!{}_{2}} - \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}\right) + C[/tex]

Simplify:

[tex]\displaystyle = \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}-2u^{{}^{1}\!/\!{}_{2}} + C[/tex]

Back-substitute:

[tex]\displaystyle = \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]

Answer:

=  - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x)  + C

                          5

Step-by-step explanation:

∫ sin³ (x)    dx

  [tex]\sqrt{cos(x)}[/tex]

= ∫ sin² (x) sin (x)    dx

   [tex]\sqrt{cos(x)}[/tex]

= ∫ (1 - cos² (x) sin (x)  dx

   [tex]\sqrt{cos(x)}[/tex]

= ∫ - 1 - u²   du

        √u

= ∫ -   1    +  u³/₂   du

        √u

= - ∫   1    du  +  ∫ u³/₂   du

        √u

substitute it back

=  - 2 √u + 2 cos⁵/₂ (x)

                 5

add constant, therefore

=  - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x)  + C

                         5

Answer:

0.3

Step-by-step explanation:

There are:

Total marbles:

Then:

Answer is: the probability of not draw a blue marble is 0.3

Answer:

10x

Step-by-step explanation:

3x + 7x

= 10x

Answer:

Hope it helped u if yes mark me BRAINLIEST pzllzllzl

Answer:

238,900 miles away

Answer:

238,900

Step-by-step explanation:

Light travels at a speed of 186,282 miles per second, you multiply this number by 1.25 you get your answer.

Answer: x=4

Step-by-step explanation:

 -8-x=x-4x

  -8-x=-3x

-x+3x=8

    2x=8

      x=4

Answer:

34

Step-by-step explanation:

The dead bodies are still in the room.

Answer:

[tex]5x^5+5xyz+7xy+8x[/tex]

Step-by-step explanation:

When putting an equation in standard form, you always prioritize the term with the most variables - unless terms have a greater exponent.

The prioritization order is:

Exponents

Amount of variables

Value of coefficient

So, [tex]5x^5[/tex] is the only term with an exponent in this expression, so it will go first.

Next up, we have to choose between [tex]8x[/tex], [tex]5xyz[/tex], and [tex]7xy[/tex]. We know that [tex]5xyz[/tex] has more variables than the other ones, so it goes next.

Now we're left with [tex]7xy[/tex] and [tex]8x[/tex]. [tex]7xy[/tex] has more variables than [tex]8x[/tex], so it goes next.

This leaves [tex]8x[/tex] last.

So, the expression becomes [tex]5x^5+5xyz+7xy+8x[/tex].

Hope this helped!

Answer:

4 1/8hours ÷ 2 3/4

Step-by-step explanation:

Answer:

2²⁰ bytes

Step-by-step explanation:

Given

[tex]Phone\ Storage = 2^{20}\ bytes[/tex]

[tex]App\ Storage = 4^4\ megabytes[/tex] of phone storage space

Required

Determine the storage space of the app in bytes

To answer this, we simply multiply the app storage by the phone storage

This gives:

[tex]Total = 2^{20} * 4 ^4[/tex]

Express 4 as 2²

[tex]Total = 2^{20} * 2^2^* ^4[/tex]

[tex]Total = 2^{20} * 2^8[/tex]

Apply Laws of Indices

[tex]Total = 2^{20+8}[/tex]

[tex]Total = 2^{28}[/tex]

Hence, the storage space of the app is 2²⁰ bytes

Answer:

  33, 11, 24 feet

Step-by-step explanation:

Let s represent the length of the second side. Then the length of the first side is 3s and the length of the third side is s+13. The perimeter is the sum of side lengths:

  (3s) +(s) +(s +13) = 68

  5s = 55 . . . . . subtract 13

  s = 11 . . . . . . . divide by 5

The side lengths are ...

  33, 11, 24 feet

(2x+8)/6=1/3(x+4)

3(2x+8)=6(x+4)

6x+24=6x+24.

0=0.

∴There are no real solutions.

Step-by-step explanation:

sin(2A)

Use double angle formula:

= 2 sin(A) cos(A)

Use Pythagorean identity.  0 ≤ A ≤ π/2, so cos(A) > 0.

= 2 sin(A) √(1 − sin²(A))

Substitute and simplify.

= 2 (¼) √(1 − (¼)²)

= ½ √(¹⁵/₁₆)

= ⅛ √15

Answer:

b=8

Step-by-step explanation:

Solution steps:

-7b=-56

b=-56 / -57

b=8

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ b = 8}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 7b = - 56}[/tex]

divide both sides of the equation by -7

[tex] \sf{ \dashrightarrow\frac{ - 7b}{ - 7} = \frac{ - 56}{ - 7} }[/tex]

Calculate

[tex] \dashrightarrow \sf{b = 8}[/tex]

Hope I helped!

Best regards! :D

Answer:

The angle from the centre of Ann's slice is 60 degrees.

Step-by-step explanation:

If the size of the slices is proportional to the ages of the children eating the cake, then the sum of their ages equal to 360 degrees (since the cake is a circle).

So to work out the angle of Ann's portion, we find a fraction for Ann's age over the total of all of their ages. So:

5/(5 + 10 + 15) = 5/30

Now since we know their ages are proportional to the slices of cake, we can find the same value for the fraction 5/30 that is out of 360 to work out the angle. Let's call the angle representing Ann's slice x. So know we can create an equation:

5/30 = x/ 360

5/30 * 360 = x

x = 60

Answer:

60 degrees.

Step-by-step explanation:

Answer:

158

Step-by-step explanation:

10.89-2.99 = 7.90

.5/7.90=158

Answer:

158 songs

Step-by-step explanation:

Monthly membership = 2.99

Each song cost = .05

Total Amount spent after 1 month = 10.89

S = Songs purchased

=> 2.99 + .05S = 10.89

=> 2.99 - 2.99 + .05S = 10.89 - 2.99

=> .05S = 7.9

=> .05S / .05 = 7.9 / .05

=> S = 158

So, she purchased 158 songs that month.

Answer:

Angle ABC is bisected by BD

BC =Half AC

2 mangle DBC =mangle ABC

Answer:

  a² = b² -w² +2wx

Step-by-step explanation:

The algebra is pretty straightforward. Expand the expression in parentheses and add x².

  b² -(w -x)² = e² = a² -x²

  b² -(w² -2wx +x²) = a² -x² . . . . . expand the square

  b² -w² +2wx -x² = a² -x² . . . . . . distribute the minus sign

  b² -w² +2wx = a² . . . . . . . . . . . . add x²

Answer:

-3, 0, 3

Step-by-step explanation:

Given, [tex] y = -\frac{4}{3}x + 2 [/tex], the set of x values that will make Kayda not to get y values that are not fraction are -3, 0, 3.

This is so, because,

when x = -3, [tex] y = -\frac{4}{3}(-3) + 2 = \frac{12}{3} + 2 = 4 + 2 = 6 [/tex]

when x = 0, [tex] y = -\frac{4}{3}(0) + 2 = -0 + 2 = 2 [/tex]

when x = 3, [tex] y = -\frac{4}{3}(3) + 2 = \frac{-12}{3} + 2 = -4 + 2 = -2 [/tex]

The correct response is -3, 0, 3

Answer:

D

Step-by-step explanation:

If the number is positive, the absolute value is the same as the number. If the number is negative, the absolute value is just a positive version of that number. So the absolute value of 0 is 0, -18 is 18, -31 is 31, and -44 is 44. Out if these, D has the greatest absolute value, so it would be D

Answer:

D. -44.

Step-by-step explanation:

Absolute value of -44:

= |-44| = 44

Answer:

B < -76

Step-by-step explanation:

You start out with writing out the equation

8-1/4b> 27

Then, you subtract 8 from each side, so the -1/4b can be by itself

-1/4b>27-8

-1/4b>19

After that, you want to get rid of that -1/4, so you multiply both sides by -4

This makes the > sign flip to <

So, this makes:

b < -76

Answer:

y = 8x-40

Step-by-step explanation:

The slope intercept form of a line is

y= mx+b  where m is the slope and b is the y intercept

We know the slope is 8 and the x intercept is 5 ( 5,0)

y = 8x +b

Substitute the point into the equation

0 = 8(5)+b

0 = 40+b

b=-40

The equation is

y = 8x-40

Answer:

4

Step-by-step explanation:

0</x/<5

0</1, 2, 3, 4/>5

(1,2,3,4) there are 4 numbers that are greater than 0 and less than 5.

Answer:

8

Step-by-step explanation:

All possible answers are 1,2,3,4,-1,-2,-3, and -4. Since we are using the absolute value here, the opposites of the positive values are also included.

Answer:

$1 for one tube

Step-by-step explanation:

Ratio is 10:10

if you keep on reducing it

you will eventually get to 1:1

Therefore, the answer is $1 for one tube

Answer:

a)

{FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV,VVFV,FVVF,FFVF,VFVF,VVVF,FVFF,FFFF,VFFF,VVFF}

b)

{FFFV,FFVF,FVFF,VFFF}

c)

{FFFF,VVVV}

d)

{FFFV,FFVF,FVFF,FFFF,VFFF}

e)

{FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}

{FFFF}

f)

{FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}

{ }

Step-by-step explanation:

a)

The 16 outcomes for a sample of four home mortgages classified as fixed and variable rate are

Sr.No Outcomes

1          FVVV

2         FFVV

3         VFVV

4         VVVV

5         FVFV

6         FFFV

7         VFFV

8         VVFV

9         FVVF

10        FFVF

11         VFVF

12        VVVF

13        FVFF

14        FFFF

15        VFFF

16        VVFF

b)

Let A be the event that exactly three are fixed rate. Thus, event A consists of following outcomes

A={FFFV,FFVF,FVFF,VFFF}

c)

Let B be the event that all four are of same type. The event B consists of either all fixed rate or all variable rate. Thus, event B consists of following outcomes

B={FFFF,VVVV}

d)

Let C be the event that at most one of four is variable rate. The event C consists of less than and equal to one variable rate. Thus, event C consists of following outcomes

C={FFFV,FFVF,FVFF,FFFF,VFFF}

e)

Let union of part(c) and part(d) can be represented as BUC. The union represents all the outcomes in event B and event C.

B∪C={FFFF,VVVV}∪{FFFV,FFVF,FVFF,FFFF,VFFF}

B∪C={FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}

Let intersection of part(c) and part(d) can be represented as B∩C. The intersection represents the common outcomes in event B and event C.

B∩C={FFFF,VVVV}∩{FFFV,FFVF,FVFF,FFFF,VFFF}

B∩C={FFFF}

f)

Let union of part(b) and part(c) can be represented as AUB. The union represents all the outcomes in event A and event B.

A∪B={FFFV,FFVF,FVFF,VFFF}∪{FFFF,VVVV}

A∪B={FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}

Let intersection of part(b) and part(c) can be represented as A∩B. The intersection represents the common outcomes in event A and event B.

A∩B={FFFV,FFVF,FVFF,VFFF}∩{FFFF,VVVV}

A∩B={ }

So intersection of part(b) and part(c) is an empty set as there is no common outcome in these two sets.

Sample of four homes.

The sample of 4 homes is on a mortgage and has been classified as a fixed rate of F and a variable rate of V. The mortgage is thus an agreement between the lender of the money and the borrower. The lender has the right to take away the property.

Thus answer is given below.

Learn more about the sample of four homes.

brainly.com/question/14565659.

Answer:

y= -1/2(x) +8

gradient= -1/2

Intercept= 8

Step-by-step explanation:

Let's transform the equation to y -intercept form first

6x - 3y - 15= 0

-3y= -6x+15

Y= -6/-3(x) +(15/-3)

Y= 2x -5

Intercept c= -5

Gradient m =2

Rule of perpendicularity

mm'= -1

m'= -1/m

m' = -1/2

Equation of line of the point (4, 6)

(Y-Y1)/(x-x1)=m'

(Y-6)/(x-4)= -1/2

2(y-6)= -1(x-4)

2y -12 = -x +4

2y= -x +4+12

2y= -x+16

y= -1/2(x) +8

gradient= -1/2

Intercept= 8