what are the values Of p and q ?​

w-z can be expressed in ploar form as √2∠(7π/4)

Sometimes the expression A(cos(α)+i·sin(α)) is written as A·cis(α). I prefer the notation A∠α, because it is more compact.

 Given: w = √2∠(π/4)

 z = 2∠(π/2)

And you are asked to find the difference w-z in polar form.

In rectangular form, ...

 w = √2∠(π/4) = √2(1/√2 +i/√2) = 1 +i

 z = 2∠(π/2) = 2(0 +i·1) = 2i

Then the difference is ...

 w -z = (1 +i) -(2i) = 1 -i

You may notice this is the conjugate of w, so will have the opposite angle:

w - z = w* = √2∠(-π/4) = √2∠(7π/4)

In the terms used by the problem statement, ...

 w -z = √2(cos(7π/4) +i·sin(7π/4))

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Answer:

Step-by-step explanation:

Surface Area Formula

SA = 2lw + 2lh + 2hw

2 * 2 * 5 + 2 * 2 * 3 + 2 * 3 * 5 =

62cm²

Answer:

x=-7

Step-by-step explanation:

0.3(8-2x) - 1.2(2-3x) < -21

2.4 - 0.6x - 2.4 + 3.6x < -21

3x < -21

x < -7

Answer: [tex]x=-2 \pm \sqrt{29/5}[/tex]

Step-by-step explanation:

[tex]5x^2 + 20x=9\\\\5(x^2 + 4x)=9\\\\5\left((x+2)^2 -4 \right)=9\\\\5(x+2)^2 - 20=9\\\\5(x+2)^2 = 29\\\\(x+2)^2 = \frac{29}{5}\\\\x+2 =\pm \sqrt{29/5}\\\\x=-2 \pm \sqrt{29/5}[/tex]

Answer:

[tex]\huge\boxed{\sf 37 }[/tex]

Step-by-step explanation:

Highest weight = 116 g

Lowest weight = 79 g

= 116 g - 79 g

= 37

[tex]\rule[225]{225}{2}[/tex]

Answer:

$497

Step-by-step explanation:

Added all three purchases (154.18 + 122.79 + 219.54) will give you $496.51. Rounded to the nearest dollar, you get $497.

Answer: A translation 1 unit to the left

Step-by-step explanation:

See attached image.

Answer:

Step-by-step explanation:

(-41.8 + 32.2)² =

(-9.6)² =

92.16

Answer:

92.16

Step-by-step explanation:

solving the brackets first, -41..8 + 32..2 equals -9.6 in total. The bracket has a square around it so our answer would be the square of wat ever we get in the bracket meaning (-9.6)^2 which gives us 92.16

x is 3 that is the number of hits

e = 2.71828 is the Euler number

μ is the mean in the given interval = 0.967

There is 5.72% probability that a randomly selected region had exactly three hits.

Let X be the random variable denoting the number of bombs hitting the selected sample.

The following formula determines the likelihood that x in a Poisson distribution corresponds to the number of successes of a random variable.

P(X = x) = e^₋μ × μˣ / (x)!

Here, X is the random variable denoting the number of bombs hitting the selected sample.

μ is the mean number of hits per region.

e is the constant value.

Since 535 bombs struck a total of 553 regions, the ratio of strikes per region to the total number of regions is 535 to 553.

μ = 535 / 553

μ = 0.967

Assume that we want to find the probability that a randomly selected region had exactly 3 hits.

which means, P(X = 3)

P(X = x) = e^₋μ × μˣ / (x)!

P(X = 3) = e^₋0.967 × (0.967)³/ (3)!

             = 0.057

There is approximately 5.72% probability that a randomly selected region had exactly three hits.

Your question was incomplete. Please find the missing content here.

In analyzing hits by certain bombs in a​ war, an area was partitioned into ​553 regions, each with an area of 0.95 km². A total of 535 bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly 3 hits.In applying the Poisson probability distribution formula,  P(X) = e^₋μ × μˣ / (x)!, identify the values of μ, x and e. Also , briefly describe what each of those symbols represent.

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The information given about the proof does that Daniel made an error on line 2.

Given:

1. AB = 3x +2;  BC = 4x + 8;  AC = 38

2. AB + BC = AC      incorrect (not an angle angle addition postulate)

3. 3x+2 + 4x + 8 = 38         correct

4. 7x + 10 = 38                    correct

5. 7x = 28                           correct

6. x = 4

Daniel made an error on line 2.

Here is the complete question:

Daniel wrote the following two-column proof for the given information. Given: AB = 3x + 2; BC = 4x + 8; AC = 38 Prove: x = 4 Statements Reason 1. AB = 3x + 2; BC = 4x + 8; AC = 38 1. Given 2. AB + BC = AC 2. Angle Addition Postulate 3. 3x + 2 + 4x + 8 = 38 3. Substitution Property of Equality 4. 7x + 10 = 38 4. Combining Like Terms 5. 7x = 28 5. Subtraction Property of Equality 6. x = 4 6. Division Property of Equality On which line, did Daniel make his error? line 2 line 3 line 4 line 5

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Answer: [tex]4\pi r^{2}[/tex]

Step-by-step explanation:

Area of a circle is pi r squared

The points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)

Given the following function

f(x) = - 0.5x + 2

g(x) = x^3 - 5x^2 + 3

The point of intersection is the point where f(x) = g(x)

x^3 - 5x^2 + 3 = - 0.5x + 2

x^3 - 5x^2 + 3 + 0.5x - 2 = 0

x^3 - 5x^2 + 0.5x + 1 = 0

Factorize and determine the value of x

x = 0.53 and 4.85

If x = 0.53

f(0.53) = -0.5(0.53) + 2

f(0.53) = -0.265 + 2

f(0.53) = 1.375

If x = 4.85

f(4.85) = -0.5(4.85) + 2

f(4.85) = -2.425 + 2

f(4.85) = -0.245

Hence the points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)

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Answer:

13)x=59 answer is d 14)x=24

Step-by-step explanation:

180-116(angles on a striaght line sum to 180)180-116=64

angle in a triangle sum to 180

64+x=180

64+57=121

180-121=59

x=59

question 14 answer is 24

90+66=156

sum of a triangle is 180

180-156=24

Simplify the LHS by using the identities above to get the RHS:

Proved

The estimated probability for P(H) is 0.17.

Probability is the stream in mathematics that studies about the likeliness of an event to happen.

It is given that

Total number of times coin is flipped = 30

Total number of times the coin gave heads = 5

Total number of times the coin gave tails=25

The P(H) = Total no. of Heads /  Total outcomes

P(H) = 5 / 30

= 1/6

= 0.1666

≈ 0.17

Therefore the estimated probability for P(H) is 0.17.

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The probability that it is less than 11.9 inches long will be 0.11304.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

A manufacturer knows that their items have a normally distributed length, with a mean of 14.2 inches, and standard deviation of 1.9 inches.

If one item is chosen at random.

Then the probability that it is less than 11.9 inches long will be

Then the z-score will be

z = (11.9 – 14.2) / 1.9

z = –1.21

Then the probability will be

P(x < 11.9) = P(z < –1.21)

P(x < 11.9) = 0.11304

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The equations will be solved by putting the values of the variables in the bracket.

1. (b + a) = 4; use a = 1 and b = 3

( 1 + 3) = 4

2) c(b + b); use b = 1 and c = 5

5(1 + 1)

= 5 × 2 = 10

3) 4+ pm; use m = 4 and p =3

= 4 + (4 × 3)

= 4 + 12

= 16

4) 5+ pm; use m = 4 and p = 2

= 5 + (2 × 4)

= 5 + 8

= 13

5) m(p + 2); use m = 5 and p = 2

= 5(2 + 2)

= 5 × 4

= 20

6) h+j²; use h = 1 and j = 4

= 1 + 4²

= 17

7) y-(x - 5); use x = 5 and y = 6

= 6 - (5 - 5)

= 6 - 0

= 6

8) 4xy; use x = 5 and y = 2

= 4 × 5 × 2

= 40

9) n(p + 3); use n = 2 and p = 2

= 2(2 + 3)

= 10

10) y +x+x; use x = 3 and y=5

= 5 + 3 + 3

= 11

11) 6+ a-b; use a = 4 and b = 4

= 6 + 4 - 4

= 6

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Answer:

100 times stronger

Step-by-step explanation:

The Richter scale is a measurement system for the strength of Earthquakes. The most powerful Earthquakes are at 5-10, while the least powerful ones stay from 1-4.

This is how the Richter scale works:

An earthquake with a magnitude of 2 is 10 times more powerful than an earthquake with a magnitude of 1. Each number is 10 times more powerful than the last.

So, simple math tells us that Magnitude six is 10 times more powerful than magnitude five, and magnitude seven is 100 times more powerful than magnitude 5..

The amount of dose is 10.5oz

The dosage is given as:

1/2oz 3x day for 7 days

This means that:

The patient will use 1/2 oz  3 times daily for 7 days

So, the dose is

Dose = 1/2 oz * 3 * 7

Evaluate the product

Dose = 10.5oz

Hence, the amount of dose is 10.5oz

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The value of w is -1 and -5.

The correct option is (B)

A mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Given:

2w² + 12w + 10 = 0

First, divide through by 2

2w²/2 + 12w /2 + 10/2 =0/2

w² + 6w + 5 = 0

now, Take half of the w term and add - subtract the square of it

w² + 6w + 5 + 3² - 3² = 0

w² + 2*3w + 3² + 5 - 9 = 0

(w+3)² = 4

w+3 = ±2

w = +2 - 3, -2-2

w= -1 and -5.

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Step-by-step explanation:

√3x+31=x+7

√3x=+7-31

DBS by√3

√3x/√3=7-31/√3

x=−12.12435565298

x=12.1

Answer:

-2n + 28

Step-by-step explanation:

-5(n-5) + 3(n+1)

Let's distribute!

-5n + 25 + 3n + 3

Now we can add the like terms (n's with n's and numbers with numbers)

-2n + 28

Answer: -2n+28

Step-by-step explanation:

We can use the distributive property to solve this problem.

-5n+25+3n+3

-2n+28

Answer:

f(x) = x^(1/2) + 3

Step-by-step explanation:

Translating to the right 3 units would change these:

0^(1/2) = 0 /// 3 units to the right would be (0,3)

1^(1/2) = 1 //// 3 units to the right would be (1,4)

4^(1/2) = 2 //// 3 units to the right would be (4,5) etc

Answer:

1654.9

Step-by-step explanation

1/0.1273 = 13000/x

x=1654.9

Answer:

A. 1, 2, 3, 4, 6, 8, 12, 24

Using the normal distribution, it is found that due to the greater z-score, Stewart caught the longer fish relative to the same specie.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

To find who caught the longer fish relative to the same specie, we need to find out who had the higher z-score.

Stewart caught a bluefish with a length of 322 mm, hence the parameters are as follows:

[tex]X = 322, \mu = 267, \sigma = 39[/tex]

The z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{322 - 267}{39}[/tex]

Z = 1.41

Gina caught a pompano with a length of 176 mm, hence the parameters are as follows:

[tex]X = 176, \mu = 155, \sigma = 28[/tex]

The z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{176 - 155}{28}[/tex]

Z = 0.75.

Hence Stewart caught the longer fish relative to the same specie.

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Answer: 76.5 meters

Step-by-step explanation:

To find the side lengths you use trig ratios for 30,60,90 triangles. The ratio is n (attached to the opposite side of the 30-degree angle, or the smallest leg), n[tex]\sqrt{3}[/tex] (attached to the opposite side of the 60-degree angle, or the longest leg), 2n (attached to the hypotenuse). Using the inner triangle you can use 2n=28 to find the side opposite the 30-degree angle, 14. Then you plug 14 into every n and add the sides. the full answer is 76.4974226 but this problem said to round making your final answer 76.5 meters. always remember to give proper units.  

Answer:

  -S = 15

Step-by-step explanation:

You are asked to find the opposite of the given value.

The opposite of an integer value is obtained by changing its sign.

  S = -15

  -S = -(-15) = 15

__

Additional comment

Equivalently, you are multiplying by -1. The product of an even number of minus signs is a plus sign. We usually don't write the plus sign for a numerical value.

Step-by-step explanation:

Just plug in -2 anywhere you see an a

[tex]f(a)=2a^3+3a^2+5\\f(-2)=2(-2)^3+3(-2)^2+5\\f(-2)=2(-8)+12+5\\f(-2)=-16+12+5\\f(-2)=1[/tex]

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Answer [tex]\curvearrowright[/tex] [tex]\\[/tex]

f(-2)=1

Step-by-step explanation [tex]\curvearrowright[/tex]

Given,

To find,

                                           All work is shown here. :))

[tex]\Large\begin{gathered} \boldsymbol{\sf{Plug \ in \ the \ number \ for \ a, \ which \ is \ -2 (it's \ given \ to \ us). Then}}\\ \boldsymbol{\sf{evaluate,}} \\ \curvearrowright\\\boldsymbol{\sf{Now \ substitute \ -2}} \\\curvearrowright\\\sf{2(-2)^3+3(-2)^2+5}\\\sf{2*(-8)+3*4+5}\\\sf{}-16+12+5=-4+5}\\\underline{\boxed{\sf{f(-2)=1}}}\end{gathered}[/tex]

Done !!

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[tex]\tiny\pmb{CALLIGRAPHY}[/tex]