Ryan drove 480 miles and used 20 gallons of gas. How many miles did Ryan’s car get per gallon? Write an equation that would solve this problem.

Answer:

B

Step-by-step explanation:

did the course

The equivalent complex expression of [tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5[/tex] is

[tex]\frac{1}{32} (cos(\pi)+i~sin(\pi))[/tex]

The correct answer is an option (b)

"The number of the form a + ib, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"

"This theorem gives a formula for computing powers of complex numbers.

[tex](r(cos\theta+i~sin\theta))^n=r^n~(cos(n\theta)+i~sin(n\theta))[/tex] "

For given question,

We have been given a complex expression [tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5[/tex]

Using the DeMoivre's theorem,

[tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5\\\\=(\frac{1}{2})^5~((cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5\\\\=\frac{1}{32} (cos(\frac{5\pi}{5} )+i~sin(\frac{5\pi}{5} )) )\\\\= \frac{1}{32} (cos(\pi)+i~sin(\pi))[/tex]

Therefore, the equivalent complex expression of [tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5[/tex] is

[tex]\frac{1}{32} (cos(\pi)+i~sin(\pi))[/tex]

The correct answer is an option (b)

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Answer:

The answer is 2/5.

Step-by-step explanation:

First, use the stay-switch-flip method. Keep 1/5 the same, switch the division sign into a multiplication sign, and flip the numerator and the denominator of 1/2 to get 1/5 x 2/1. Multiply the numerators. 1 x 2 = 2. Now, multiply the denominators. 5 x 1 = 5. Therefore, you're answer is 2/5.

Hope this helps! Please mark Brainliest.

Step-by-step explanation:

-17z - 12 + 15z = -12 - 2z

-2z - 12 = -2z - 12

-12 = -12

Since this statement is always true for all real values of z, there are infinitely many solutions.

Answer:

3.19 m

Step-by-step explanation:

L = 2.5

W x 25/16 = 2.5

w = 2.5 x 16 / 25 = 1.6

LWH = V

H = V / LW = (12 3/4) / (2.5 x 1.6) = 3.19

Answer:

as for the other stuff you need to update my 45=44

Answer:

7

Step-by-step explanation:

This is a Poisson distribution problem with the formula;

P(x;μ) = (e^(-μ)) × (μ^(x))/x!

We are told that the grocer sells three of a certain article per week. Thus;

μ = 3

Now, we want to find out How many of these should he have in stock so that the chance of his running out within a week is less than 0.01.

This means;

P(X > k) < 0.01

This can be rewritten as;

P(X ≤ k) < 0.99

Let's try x = 8

P(8;3) = (e^(-3)) × (3^(8))/8!

P(8;3) = 0.008

But; P(X ≤ 8) = 1 - 0.008 = 0.992

This is more than 0.99 and thus is not the answer

Let's try x = 7

P(7;3) = (e^(-3)) × (3^(7))/7!

P(7;3) = 0.022

But; P(X ≤ 7) = 1 - 0.022 = 0.978

Thus is less than 0.99.

Thus, stock should be 7

Answer:

I belive the equation would be...

Step-by-step explanation:

8x+$35=$167.00

Hope it helps??

Answer

they worked 16.5 hours that week.

Step-by-step explanation:

You first subtract the tip by the total cost and that gives you $132.00. and from that cost you divide by $8 which they get paid by the hour... and then you get the 16.5 and that means they worked 16.5 hours that week.

Answer:

-113 and 113

Step-by-step explanation:

I'm not sure exactly what you mean by -1 13, so I'll assume you mean -113.

It's opposite would be 113.

If what you mean is -1 1/3 then it would be -4/3

Hope I helped

Answer:

d. y = -2×

Step-by-step explanation:

First to solve find the slope using the formula, [tex]\frac{10+10}{-5-5}[/tex]. The slope equals 20/-10 or -2. Then plug the slope and point, (-5,10), into slope-point form. y-10=-2(x+5), then solve for y. This gives you y=-2x+0 or y=-2x.

Ms Patel bought 4 pliers, 2 wrenches and 1 plier set.

        4:2:1

        PLIERS: 4 × 17.50 = $70

        WRENCHES: 2 × 21.50 = $43

        CHISEL SETS: 1 x 28 = $28

        TOTAL = $70 + $43 + $28 = $141

Mrs Patel purchased 2 wrenches, 4 pliers, and 1 chisel set for her shop.

I hoped this helped!

Answer:

[tex]\mathrm{Domain\:of\:}\:4\sqrt{t}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:t\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]

The graph is also attached below.

Step-by-step explanation:

Given the expression

[tex]f\left(t\right)=\sqrt{t}\:+3\sqrt{t}[/tex]

We know that the domain of a function is the set of inputs or argument values for which the function is real and defined.

We know that we can not have a negative value of 't' inside the radicals because if we put any negative number inside the radical expression, it would make the function undefined.

In other words,  the value of t ≥ 0.

Therefore, the function domain is:

[tex]\mathrm{Domain\:of\:}\:4\sqrt{t}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:t\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]

The graph is also attached below.

Answer:$2.98

Step-by-step explanation:

Answer:

3.125

Step-by-step explanation:

Answer:

25/8 in a decimal form is

Step-by-step explanation:

3.125

Answer:

14

Step-by-step explanation:

Answer:

Step-by-step explanation:

I hope this helps !!

Answer:

92.3% are not vacationing

Step-by-step explanation:

482 - 37 = 445

445 * 100 / 482 = 92.3

9514 1404 393

Answer:

Step-by-step explanation:

There is some disagreement over whether the "imaginary part" includes the factor "i" or not. Here, we assume it is simply the coefficient of i.

  Re(z) = -19 . . . . the part that does not have a factor of i

  Im(z) = -24 . . . . the coefficient of i

Answer:

T5 = 512

Step-by-step explanation:

Given the sequence

2,8, 32, 128,...

The sequence is a geometric progression

nth term of a geometric progression is expressed as:

Tn = ar^n-1

a is the first term = 2

n is the number of terms = 5 (next term is the 5th term)

r is the common ratio = 8/2 = 32/8 = 4

Substitute and get the fifth term

T5 = 2(4)^5-1

T5 = 2(4)^4

T5 = 2*256

T5 = 512

Hence the next term is 512

Answer: Henrik grew 147 more potatoes than Derek

Step-by-step explanation:

Answer:

[tex]u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}[/tex]

Step-by-step explanation:

From the question we are told that

Temperature is given [tex]T ( x, y, z) = x + yz.[/tex]\

A fly is at (1,2,1)

Generally the direction of fly is given by

      [tex]\triangleT(x,y,z) =(1,z,y)\\[/tex]

       [tex]v= \triangleT(1,2,1)\\v=(1,1,2)[/tex]

Mathematically solving for the vector direction

       [tex]|v|=\sqrt{1^2+1^2+2^2}[/tex]

       [tex]|v|=\sqrt{6}[/tex]

       [tex]u=- \frac{v}{|v|}[/tex]

       [tex]u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}[/tex]

Therefore this the direction which should be taken to cool down soonest

Answer:

Benson has 5,120 bottle caps.

Step-by-step explanation:

160x32

Answer:

v = 80 cubic units

Step-by-step explanation:

The formula for a rectangular prism is: v = lwh

l = length

w = width

h = height

v = 8 x 2 x 5

v = 16 x 5

v = 80

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

Plane RTS

Step-by-step explanation:

Answer: Choice D) Plane PQY

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

Explanation:

By definition, a plane is formed by 3 non-collinear points. The three points cannot all be on the same line. If you had 3 points on the same line, then infinitely many planes are possible. Imagine the plane spins around the line as a sort of fan blade.

Choice A can be ruled out because points R, T, and S are all on the same line. They are collinear points. Using these three points is not enough to properly identity/label this plane, since infinitely many other planes could result.

Choices B and C can also be ruled out for similar reasons.

Choice D is correct because points P, Q, and Y are all in plane M, and also because they are not all on the same line.

Side note: another way to phrase "a plane is formed by 3 non-collinear points" is to say "a plane is formed by 3 points that form a triangle".

Answer:

x = 11.4715

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Angle θ = 35°

Opposite Leg = x

Hypotenuse = 20

Step 2: Solve for x

9514 1404 393

Answer:

  y ≈ 12.3

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationship between trig functions and side of a right triangle. In particular, when the adjacent side and hypotenuse are involved, the desired relation is ...

  Cos = Adjacent/Hypotenuse

  cos(35°) = y/15

  y = 15·cos(35°)

  y ≈ 12.3

it ain't possible.

unless Either X's value is given for u to get y.

All pairs such that x is > 4 and y = 6 are solutions.

It is given that ordered pair is a solution to the inequality 7x-3y>10.

What is inequality?

The definition of inequality is a difference in size, amount, quality, social position or other factor.

Now, characterize these solutions

if 7x - 3y > 10 then

7x > 10 +3y

Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6

then by substitution

7  must be > 10+ 3*6

or 7x must be > 28

or x must be > 4

So, all pairs such that x is > 4 and y = 6 are solutions.

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