LESSON 3
WHATS MORE
Translate each English phrase/sentance into Mathematical phrase/sentance
1. The sum of 4 and number________
2. Six less than a number_________
3. The product of 8 and a number______
4. The quotient of x and 7 ______
5. Five more than a number is equal to 15_____ ​

Answer:

  266

Step-by-step explanation:

There are (3 ft)^3 = 27 ft^3 in 1 cubic yard. Then 9.83 cubic yards will be ...

  (9.83 yd^3)(27 ft^3/yd^3) = 265.41 ft^3

265 sacks will not be enough. 266 sacks must be ordered.

Answer:

Step-by-step explanation:

There are 4 tens.

There are 48 cards that are not a 10. The probability of drawing 1 of the 48 is

P(~10) = 48/52 which is quite high as you might imagine.

Answer:

1/52

Step-by-step explanation:

A deck has 52 cards and the probability of picking a specific one is 1/52, or 1.92%

If you are looking for the probability of a diamond, it is 1/4, or 25%

This is the same as typing in 0.5x^7

Other equivalent forms are (1/2)x^7 or (x^7)/2

=====================================================

Work Shown:

[tex]\frac{d}{dx}\left[f(x^2)\right] = x^8\\\\f'(x^2)*\frac{d}{dx}(x^2) = x^8\\\\f'(x^2)*2x = x^8\\\\f'(x^2) = \frac{x^8}{2x}\\\\f'(x^2) = \frac{x^7}{2}\\\\f'(x^2) = \frac{1}{2}x^7\\\\f'(x^2) = \boldsymbol{0.5x^7}\\\\[/tex]

I used the chain rule on the second step. The chain rule will apply the derivative to the outer function f(x^2). Then we also apply the derivative to the inner function x^2 to get 2x, which is multiplied with f ' (x^2). From that point, we isolate f ' (x^2).

Side note: When applying the first derivative, it might help to think of f(x^2) as simply f(x) on a temporary basis.

Given nth term of an AP = 7-4n

Put n = 1 then t1 = 7-4(1) = 7-4 = 3

Put n = 2 then t2 =7-4(2) = 7-8 = -1

Common difference = t2-t1 = -1-3 = -4

Answer:

Step-by-step explanation:

You can easily convert 3 minutes into seconds using each unit definition:

Minutes

minute = 60 s = 60 s

Seconds

1 s

= 1 sec / 60 = 0.01667 min

With this information, you can calculate the quantity of seconds 3 minutes is equal to.

In 3 min there are 180 s.

Which is the same to say that 3 minutes is 180 seconds.

Answer:

a = 11

Step-by-step explanation:

As all angles on a straight line must add up to 180°:

(9a + 6) + 75 = 180

9a + 6 + 75 = 180

9a + 81 = 180

Subtract 81 from both sides of the equation:

9a + 81 - 81 = 180 - 81

9a = 99

Divide both sides by 9 to isolate a:

9a ÷ 9 = 99 ÷ 9

a = 11

Hope this helps!

Answer:

[tex]a=11[/tex]

Step-by-step explanation:

These are supplementary angles, meaning they together make up the whole measure of the angle of a straight line. A straight line is 180°, so the sum of these has to be 180° too:

[tex](9a+6)+75=180[/tex]

Then just solve for a:

[tex]9a+6+75=180\\9a+81=180\\9a=99\\a=11[/tex]

Explanation:

The general template of a sine function is

y = Asin(B(x-C))+D

The value of B is the only thing that determines the period T. We ignore every other term.

It turns out that T = 2pi/B which can be solved to B = 2pi/T

Plug in the given period of T = 8pi and compute to get

B = 2pi/T

B = (2pi)/(8pi)

B = 2/8

B = 1/4

This means that the term out front of the x is 1/4 and the equation must be [tex]y = \sin\left(\frac{1}{4}x\right)[/tex] which matches with answer choice B.

Answer:

112 in.³

Step-by-step explanation:

This box is a combination of two rectangular prisms:

bottom - 9 in. by 2 in. by 4 in.

top - 5 in. by 2 in. by 4 in.

total volume = 9 in. × 2 in. × 4 in. + 5 in. × 2 in. × 4 in.

total volume = 112 in.³

Answer:

its 112

Step-by-step explanation:

first see how it looks like 2 boxes on top of each other, break it into major parts then multiply depth by wighth by highth

Answer:

good day of school and➕➕ I have a great day of school and I have a great day☀☀☀ of school and➕➕ I

Answer:

Angle 5

Step-by-step explanation:

Building a probability distribution, it is found that the expected value for both players is of 0.25 points.

In this problem, the four possible outcomes, considering Player A - Player B, are:

H - H

T - H

H - T

T - T

That is, considering a success as the number of heads, the distribution is:

[tex]P(X = 0) = 0.25[/tex]

[tex]P(X = 1) = 0.5[/tex]

[tex]P(X = 2) = 0.25[/tex]

For Player A, the earnings of each outcome are: -1, 0 and 2

Hence, the expected value is:

[tex]E_A(x) = -1(0.25) + 0(0.5) + 2(0.25) = 0.25[/tex]

For Player B, the earning of each outcome are: 2, 0 and -1.

Hence:

[tex]E_B(x) = 2(0.25) + 0(0.5) - 1(0.25) = 0.25[/tex]

The expected value for both players is of 0.25 points.

You can learn about expected value at https://brainly.com/question/24855677

Answer:

a) 32km

b) 40 miles

Step-by-step explanation:

Answer: The simplified ratio is 4:3

Step-by-step explanation:

To find the ratio of the number of girls to the number of boys, we can divide the number of girls (28) by the number of boys (21) to get:

28 ÷ 21 = [tex]\frac{28}{21}[/tex]

Next, we can simplify the fraction further to get [tex]\frac{4}{3}[/tex], which equals 4:3.

[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]

The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).

"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".

For the given situation,

z1= 3+3i and

z2= 7(cos(5π/9) + i sin (5π/9))

To divide the complex numbers, both should be in same form.

Convert z1 in polar form.

z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]

⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]

⇒[tex]r=\sqrt{18}[/tex]

θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]

⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]

⇒[tex]tan^{-1}(1)[/tex]

⇒[tex]45[/tex]°

The polar form is of the form, z= r (cosθ + i sinθ),

⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)

The formula for dividing complex number is

z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)

⇒ z1/z2 = r(cosθ + isinθ)

where, r = r1/r2 and θ = (θ1 - θ2)

z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)

⇒ r = [tex]\sqrt{18}[/tex] / 7 and

θ = (π/4 - 5π/9 )

⇒ θ = (-11π/36)

cos(-θ) = cos θ

⇒cos( -11π/36 ) = cos ( 11π/36 )

sin(-θ) = -sin θ

⇒ sin ( -11π/36 ) = -sin ( 11π/36 )

Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))

Hence we can conclude that the value of z1/z2 is

√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).

Learn more about complex number here

https://brainly.com/question/19612663

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Answer:

4060

Step-by-step explanation:

Answer:4060

Step-by-step explanation:

Answer: c

Step-by-step explanation: I JUST ANSWERED BOTH PARTs

Answer:

Step-by-step explanation:

The conjugate of the given is:

Find their product:

Answer:  40 ounces or 0.3125 of a gallon

i didnt quite understand what you were asking but here is it broken down. :)

Answer:

x=7,4

Step-by-step explanation:

all real numbers except the 90 and 270 because of cosx

Answer:

The value of the 5 in 50.89 is 100 times the value of the 5 in 261.58

Step-by-step explanation:

The 5 in 50.89 is in the 10's place

The 5 in 261.58 is in the 1/10's place

1/10(100) = 10

Check the picture below.

btw, when Pythagoras said the square of this equals that and so on, he really meant the square or square area.

Answer:

the answer is

1. 11.33

2. 5.9

3. 8.1

Answer:

1)B 4 x 4 x 4 x 4

2)B 8292

Step-by-step explanation: