Divide
(3x⁴ +7x³-20x²-30x+25) ÷ (x²+x−6)

⚘Refer to the attachment for solution!!~

The sample to be taken in each organization such as 2.6 in the taekwondo club, 5.3 in the math club, 8 in the drama club, and 4 in the science club.

Total members of taekwondo club = 20

Total members of math club = 40

Total members of drama club = 60

Total members of science club = 30

The researchers want to get 20 respondents out of these organizations.

The stratified sampling method is the process of dividing members of data into homogenous subgroups before sampling.

The total number of members = 150

For taekwondo club

= Total members of taekwondo club /total number of members × 20    

= 20/150 × 20    

= 2.6

For math club

= Total members of math club/total number of members×20

= 40/150 × 20  

= 5.3

For drama club

= Total members of drama club/total number of members × 20

=  60/150 × 20  

= 8

For science club

= Total members of the science club/total number of members × 20

= 30/150 × 20  

= 4

Therefore, The sample to be taken in each organization such as 2.6 in the taekwondo club, 5.3 in the math club, 8 in the drama club, and 4 in the science club.

Learn more about the stratified sampling method;

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Answer:

Step-by-step explanation:

2)Cos²x - Sin² x = √2/2

Cos²x - Sin² x = Cos 2x

⇒ Cos 2x = √2/2

General solution for Cos 2x = √2/2 is

[tex]2x = \dfrac{\pi }{4}+2\pi n \ ; 2x=\dfrac{7\pi }{4}+2\pi n\\\\\\x = \dfrac{\pi }{2*4}+\dfrac{2\pi n }{2} \ ; \ x=\dfrac{7\pi }{4*2}+\dfrac{2\pi n}{2}\\\\\\x =\dfrac{\pi }{8}+\pi n ; \ x=\dfrac{7\pi }{8}+\pi n[/tex]

Option A

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

[tex]f(x)=5sin(\frac{x}{12})+14.5\\\\17=5sin(\frac{x}{12})+14.5\\ \\2.5=5sin(\frac{x}{12})\\ \\0.5=sin(\frac{x}{12})\\ \\\frac{x}{12}=\frac{\pi}{6}+2\pi n,\frac{5\pi}{6}+2\pi n\\ \\x=2\pi+24\pi n,10\pi+24\pi n[/tex]

Therefore, the fourth option is correct.

Problem 2

[tex]cos^2x-sin^2x=\frac{\sqrt{2}}{2}\\ \\cos(2x)=\frac{\sqrt{2}}{2}\\\\2x=\frac{\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n\\ \\x=\frac{\pi}{8}+\pi n,\frac{7\pi}{8}+\pi n[/tex]

Therefore, the first option is correct.

Answer:

The answer to the nearest CENT is A= 11699.69

Step-by-step explanation: round to the nearest cent

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4700\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ t=years\dotfill &19 \end{cases} \\\\\\ A=4700e^{0.048\cdot 19}\implies A=4700e^{0.912}\implies A\approx 11699.69[/tex]

Answer:

D)  P - 3

Step-by-step explanation:

"fewer than" a number means "less than" a number.  So "3 fewer than" means "subtract 3" from the number.

⇒ P - 3

Answer:

OPTION B

Step-by-step explanation:

3sin(2x)=5cos(x)

3×(2sinxcosx)=5cos(x)

6sin(x)cos(x)=5cos(x)

6sin(x)cos(x)-5cos(x)=0 Factor out a cos(x)

cosx(6sinx-5)=0

Answer:

red is 50% blue is 25%

Step-by-step explanation:

red is half the circle so it would be 50% and blue is half of a half so 25%

Answer:

21

Step-by-step explanation:16+20/t, T=4 so its 16 + 20/4, 20/4 is 5, 16+5 = 21.

Answer:

812/1 = 1624/2 = 2436/3

= 3248/4 = 4060/5 = 4872/6

= 5684/7 = 6496/8 = 7308/9

= 8120/10 = 8932/11 = 9744/12

= 10556/13 = 11368/14 = 12180/15

= 12992/16 = 13804/17 = 14616/18

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

The list tends to be much bigger.

Hope this helps!

Answer:

Step-by-step explanation:

Fractions equivalent to 8/12:

There is an infinite amount, but this is how far I can get.

The square root of 61 is about 7.81, so it lies in between the numbers 7 and 8.

Hope that helps!

Answer: So for Choice A 30% off $25 is $7.50 off or $17.50 which is 70% of the original price and you save 7.50 dollars.

Then for Choice B 25% off $32 is $8 off or $24 which is 75% of the original price and you save 8 dollars.

Therefor the better choice is Choice B.

Step-by-step explanation:

hope it helps

Answer:

x = 1/2

Step-by-step explanation:

10^-3x * 10^x = 10^-2x = 10^-1

Answer: the awnser will be 17.55$

Step-by-step explanation: cause you multiply 6.5 x 2.70

Answer:

D. (0,-4)

Step-by-step explanation:

When you plug in 0 into the x and -4 into the y variable you get 2(0)-4(-4)>15.

Then you solve and get 0+16>15.

then you at and get 16>15.

16 is greater than 15 which makes D correct

Answer:

a) acute triangle

b) obtuse triangle

c) right-angled triangle

d) equilateral

e) isosceles, right-angled triangle

Step-by-step explanation:

Hope this helps!

Angles are the measures between two intersecting lines or rays

The relationship between angle QRS and angle SRT is the two angles are adjacent.

The given parameter is:

The sum of angle QRS and angle SRT = 90 degrees.

Complementary angles have a sum of 90 degrees.

This means that, angles QRS and SRT are complementary angles, and that can be adjacent angles

Read more about angles at:

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Answer:

Step-by-step explanation:

it's a

Answer:

y=2.5x^2+102x+15.4

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

420/12 is 35

540/20 is 27

35-27=8

The set of equation that models the point of intersection of the arrow

and the target is the option; y = -0.004·x² + 0.25·x + 8 and y = 0.22·x

The given parameters are;

Point of intersection of the line and the parabola is the point (48.63, 10.7)

Therefore, the point (48.63, 10.7) satisfies both the equation of the

parabola and the equation of the line, which by plugging in the value x =

48.67 in the different parabolas, we have;

The first set;

The linear function in the first set should be excluded, given y ≠ x in the

ordered pair.

In third set, y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7, while, from the

ordered pair, we have;

y = C·x

10.7 = 48.63·x

[tex]C = \dfrac{10.7}{48.63} \approx \mathbf{0.22}[/tex]

Therefore;

y ≈ 0.22·x

The set of equations that best models the point of intersection of the arrow and target are therefore;

Learn more about the equation of a parabola here:

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Answer:

x = 0 ; x = -1 ; x = 5

Step-by-step explanation:

3x^3-12x^2-15x=0

-> 3x(x+1)(x-5)=0

-> 3x = 0 or x+1=0 or x-5=0

-> x = 0; x = -1 ; x = 5

Answer:

20

Step-by-step explanation:

If 5 is 1/4, then multiply 5 by 4 to get 20

Hope this helps! :)
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A toy company produces rubber balls that have a radius of 1.7 cm.

What is the volume of one rubber ball? Round to the

nearest hundredth of a centimeter.

20.58 cm3

If the price of the rubber needed to produce a ball is

$0.0045/cm3, what is the cost of producing one ball?

Round to the nearest cent.

If the company sells a ball for $0.50, how much profit

will it make on each ball?

$1.7 cm

20.58 cm^3, $0.09, $0.41

Hope this helps

Answer:

250 stickers

Step-by-step explanation:

125 plus 125 is 250

Answer:

250 stickers because 125x2=250

Answer:

∠V = 12.68°

Step-by-step explanation:

In this question, we are tasked with calculating the value of the sine of ∠V to the nearest hundredth

Kindly note that since one of the angles in the triangle equals 90°, then we are dealing with a right-angled triangle.

PLEASE VIEW ATTACHMENT TO SEE THE DIAGRAM OF THE SHAPE

Mathematically, to calculate the sine of an angle in a triangle, the ratio to use is

Sine of an angle = length of side facing angle/length of hypotenuse = opposite/Hypotenuse

From the diagram, we can see that the length of the opposite is 9 while the length of the hypotenuse is 41

Sine V = 9/41

V = arcsin (9/41)

V = arcsin (0.2195)

V = 12.68° to the nearest hundredth

The value of the cosine of ∠V is 0.98

The given parameters are:

The cosine of V is calculated using:

cos(V) = WV/VU

So, the equation becomes

cos(V) = 40/41

Evaluate

cos(V) = 0.98

Hence, the value of the cosine of ∠V is 0.98

Read more about right triangles at:

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Answer:

$12,938.26

Step-by-step explanation:

The equation for solving this is:

A = P(1+r/n)^nt

P = 4600

^ initial amount/principal

R = 0.09

^ rate (9% converted to a decimal)

n = 1

^ how often it is compounded (yearly, so it is 1)

t = 12

^ how long the investment is for (in years)

A = 4600(1.09)^12

A = 12,938.26

^ rounded to the nearest hundred, because when dealing with money it has to be rounded to the nearest hundred. Un-rounded the answer is 12938.2579962.

The investment will be worth $12,938.26 after 12 years.

Answer:

x = 29/8

Step-by-step explanation:

7 - 5(2x - 9) = -(-6x + 10) + 4

7 - 10x + 45 = (6x - 10) + 4

-10x + 52 = 6x - 10 + 4

-10x + 52 = 6x - 6

52 + 6 = 6x + 10x

58 = 16x

x = 58/16 = 29/8

Answer:

B is the answer

Step-by-step explanation:

it goes downward if viewed left-right

Answer:

If I directly give you the answers they won't help you...so I've shown you how to do the questions instead

Step-by-step explanation:

8/9 + 5/6 (make them have the same denominator)

= 48/54 + 45/54

= 93/54 (make it a mixed fraction)

1 and 39/54

(The second and third one are done the same way... make them have the same denominator by using their equivalent fractions (e.g 1/2 = 2/4), add the numerators ONLY... simplify the result)

1 and 6/9 divided by 5/6

(make the first number an improper fraction)

1 x 9 + 6 = 15 (this is the numerator...the denominator remains the same)

15/9 divided by 5/6 (reciprocate the number after the division sign and then change the division sign to a multiplication sign)

15/9 x 6/5

(Then simplify. e.g the 5 in 6/5 can be divided by the 15 in 15/9)

3/9 x 6/1

(The 6 in 6/1 and the 9 in 3/9 have a common factor... 3)

3/3 x 2/1

(3/3 = 1)

1 x 2

=2

(The other questions are done in the same way... Make the mixed fraction an improper fraction(This means the denominator is larger than the numerator)... reciprocate the number after the division sign (This means flipping it (e.g 2/3 becomes 3/2) then change the division sign to a multiplication sign and either directly multiply the result or simplify it first by dividing numerators with denominators (e.g instead of 9/3 x 12/4 = 108/12 = 9, you could say 1 divided 3 = 4 thus 9/1 x 4/4 (which is = 1) thus 9 x 1 = 9). Either way you should get the same answer whichever way you choose.

PS: YOU COULD ALSO USE A CALCULATOR TO CONFIRM YOUR ANSWER

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#4

#5

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]

c. The inverse image of h(x) is h⁻¹(x) = x + 9

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So,  the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

The inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y =  ln(x)

Taking exponents of both sides, we have

[tex]e^{y} = e^{lnx} \\e^{y} = x[/tex]

Replacing x with y, we have

[tex]y = e^{x}[/tex]

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]

The inverse image of h(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of h(x) is h⁻¹(x) = x + 9

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