What is the volume of the prism? __ in.³.

equation: (x + 14)² + (y + 5)² = 149

Given:

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

Formula's:

Find the radius:

[tex]\rightarrow \sf \sqrt{(-7-(-14))^2 + (5-(-5))^2}[/tex]

[tex]\sf \rightarrow \sqrt{\left(-7+14\right)^2+\left(5+5\right)^2}[/tex]

[tex]\sf \rightarrow \sqrt{149}[/tex]

Equation of circle:

Graph for clarification:

Answer:

[tex]\sf (x+14)^2+(y+5)^2=149[/tex]

Step-by-step explanation:

Standard equation of a circle:  [tex]\sf (x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

[tex]\sf \implies (x-(-14))^2+(y-(-5))^2=r^2[/tex]

[tex]\sf \implies (x+14)^2+(y+5)^2=r^2[/tex]

Now substitute the point (-7, 5) into the equation to find r²:

[tex]\sf \implies ((-7)+14)^2+(5+5)^2=r^2[/tex]

[tex]\sf \implies (7)^2+(10)^2=r^2[/tex]

[tex]\sf \implies 149=r^2[/tex]

Final equation:

[tex]\sf (x+14)^2+(y+5)^2=149[/tex]

The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5.

Let be two numbers of the form z = a + i · b, where i = √-1, the product of two of these numbers in rectangular form is described by the following formula:

z₁ · z₂ = (a + i · b) · (c + i · d) = (a · c - b · d) + i · (a · d + b · c)   (1)

If we know that a = 3 · cos 14π/15, b = 3 · sin 14π/15, c = 3√3 · cos 11π/15, d = 3√3 · sin 11π/15, then the result in rectangular form is:

z₁ · z₂ = 7.794 - i · 13.5

The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5. [tex]\blacksquare[/tex]

The statement presents typing mistakes and is poorly formatted, the correct form is introduced below:

Given the complex number z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15), express the result of z₁ · z₂ in rectangular form with fully simplified fractions and radicals.

To learn more on complex numbers, we kindly invite to check this verified question: https://brainly.com/question/10251853

Answer:

-8.5

Step-by-step explanation:

no step involved just trace 2 out from y-axis

Answer:

B

Step-by-step explanation:

-½(10+¼)

-½*10 + -½*¼

-5 + -⅛

-5-⅛

Don't forget a positive and negative makes a negative

Answer:

8 hours

Step-by-step explanation:

11 hours = $176

⇒ 1 hour = $176 ÷ 11 = $16

To determine how many hours she would have to work to make $128, divide $128 by $16:

⇒ number of hours = $128 ÷ $16

                                = 8 hours

___________________________________________________

[tex]\frac{128\times11}{176}[/tex]

___________________________________________________

[tex]\frac{8\times11}{11}\\ 8[/tex]

I hope this helps you

:)

Step-by-step explanation:

If u casually solve the given equation by putting 115 instead of 'F' u will get the value of 'X' which is 43 and i guess it's the answer

Answer:

372

Step-by-step explanation:

This is because the formula is a+b/2 x h and 7 is a 24 is b and the other 24 is h so 7 + 24 = 31/2 x 24 is 312

Answer:

Step-by-step explanation:

Answer:

(2 , 2) is the solution

Step-by-step explanation:

7x - 4y = 6

-6x + 7y = 2

49x - 28y = 42

-24x + 28y = 8

25x = 50

therefore

x = 2

7x - 4y = 6

7×2 - 4y = 6

14 - 4y = 6

14 - 6 = 4y

8 = 4y

8 ÷ 4 = 4y ÷ 4

2 = y

therefore

x = 2

y = 2

hope this will helpful to you....

Answer:

324

Step-by-step explanation:

21 + h = 345

group like terms

h = 345 - 21

h = 324

Answer:

h=324

Step-by-step explanation:

21+h = 345

(Substituting the equation)

h=345 - 21

h= 324

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Answer:

this is your answer hope u like it

Answer:

17,060$

Step-by-step explanation:

#CarryOnLearning Free to ask

Answer:

14-18 minutes

Step-by-step explanation:

Part a is 32 inches per minute

part b is 252 inches per minute

The question asks the change in elevation fastest, in part b 252 is greater than 32 so 14-18 minutes is the answer.

Answer:

14-18 minutes

Step-by-step explanation:

Part a is 32 inches per minute and part b is 252 inches per minute

this question asks the change in elevation fastest, in part b 252 is greater than 32 so 14-18 minutes is the answer.

Answer:

Q = 2

Step-by-step explanation:

6-3(2) = 0

0 ≤ 1

Answer:

[tex]8.6\times 10^{-3}=0.0086[/tex]

Step-by-step explanation:

Answer:

(0,-2)

Step-by-step explanation:

one way to solve...

3x - y = 2 --> *4

-2x + 4y = -8

multiply the first equation by 4

12x - 4y = 8

-2x + 4y = -8

-----------------

10x = 0

x = 0

y = -2

this method is called elimination

another way to solve...

3x - y = 2 simplify for y to get y = 3x - 2

-2x + 4y = -8 substitute y into this equation to solve for x

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

-2x + 12x - 8 = -8

10x = 0

x = 0

y = -2

substitution

alsoo if there are options, just plug in the numbers to the correct variables

Answer:

3xy=2 2x4y=8

3x2=6x8=48x8

Answer:

may not be exact

1- surveying every fifth student who walks in

2-randomly selected people of both genders

3-asking 8 random students from each second period

4-asking 4 girls and 4 boys from each~~

5-randomly choosing a page and counting the words

Step-by-step explanation:

1-explanation; the first one is skewed two 7th graders, the third one is skewed to volleyball players, the fourth one is skewed to eight graders

Answer:

Bart 95   bill 30

Step-by-step explanation:

Bill=b

Bart = (3b+5)  

b+ (3b+5) = 125

4b=120

b=30     Bill sold 30 refrigerators

3(30)+5 = 95 (Bart sold 95 refrigerators)

95+30=125

Answer:

31.63495408

Step-by-step explanation:

Find area of trinagles and semicurucles and then add up

Answer:

Step-by-step explanation:

The figure comprises of two semicircles and a triangle.

The two semicircles add to one full circle with the diameter of 5 ft.

Area of circle

Area of triangle

Total area

Answer:

Circumference ≈ 50.27

Area ≈ 201.06

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex] while the area of the circle [tex]\pi r^{2}[/tex]

Since the diameter is the radius multiplied by 2, the radius of the circle is 8. So substituting 8 for r, the circumference is 2 × [tex]\pi[/tex] × 8, which is approximately 50.27 (rounded to the nearest hundredth) and the area of the circle would be [tex]\pi[/tex] × 8². 8² is 64 so 64 times pi is approximately 201.06 (rounded to the nearest hundredth)

Using the binomial distribution, it is found that Sam should have expected 5 people to say yes.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The expected value is given by:

E(X) = np.

In this problem:

Hence, the expected value for the number of people that say yes is given by:

E(X) = np = 15 x 0.32 = 5.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

Answer:

25.86

Step-by-step explanation:

22 * 5 = 110

50 * 3 = 150

17 * 6 = 102

110 + 150 + 102 = 362

362 / 14 = 25.86

Answer:

A, C, D

All 3 of those simplfiy to 4√5

Step-by-step explanation:

1) if the initial figure ABCD, then the figure A'B'C'D' is reduction of the initial one.

2) the scale factor is 0.5: the ratio of all the corresponded coordinates is 2:1 [D(8;4) - D'(4;2); C(4;0)-C'(2;0); B(0;-2)-B'(0;-1) and A(-4;4)-A'(-2;2)].

Mark the quadrilaterals ABcD and A'B'C'D'

The image is reduced in size hence it's reduction

Take 2 sides two calculate scale factor

Scale factor:-

Answer:

$1.50

Step-by-step explanation:

There are 4 3-month periods in a year.

$45,000 per 3 months period × 4 = $180,000 cost

$180,000 ÷ 120,000 subscribers = $1.50

The banner ad costs about $1.50 per subscriber

Answer:

  $6,160

Step-by-step explanation:

The total amount of dividend received is the product of the number of shares and the dividend per share:

  (2000 shares) × ($3.08/share) = $6,160.00 . . . dividend received

In a parallelogram, opposite sides are of equal measure.

QR = TS

find x

1)

2)

Find value of y:

3)

QT:

4)

if x = 5

means the diagram is enlarged.

then y will be:

We need x and y

Opposite sides of a parallelogram are equal

And

Hence

#3

Segment QT is 4

so

Another way

So

scale factor:-

Find y

Answer:

0.437

Step-by-step explanation:

Decimals are read the same as whole numbers, starting with the first digit, which is the largest, to the right. So, to find the larger decimal you need to look at the first digit. If this digit is the same then continue to the right until there is a difference in the number. In this case, the first digit is different. Therefore, whichever has the larger first digit must be the greater one. Since 4 > 3, 0.437 must be greater than 0.347.

[tex]6i~~ + ~~2\sqrt{3}j\implies < \stackrel{a}{6}~~,~~\stackrel{b}{2\sqrt{3}} > \\\\[-0.35em] ~\dotfill\\\\ \stackrel{magnitude}{\sqrt{a^2+b^2}}\implies \sqrt{6^2+(2\sqrt{3})^2}\implies \sqrt{36+(2^2\cdot 3)}\implies \sqrt{36+12}\implies \sqrt{48} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{direction}{tan^{-1}\left( \cfrac{b}{a}\right)}\implies tan^{-1}\left( \cfrac{2\sqrt{3}}{6} \right)\implies tan^{-1}\left( \cfrac{\sqrt{3}}{3} \right) \\\\\\ tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies 30^o[/tex]

Using the expected value of a discrete distribution, it is found that:

a) His expected value is of -$2.5.

b) The fair price of a ticket is of $0.5.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the distribution for the net value of the ticket is:

Item a:

The expected value is given by:

[tex]E(X) = 497\frac{1}{1000} - 3\frac{999}{1000} = -2.5[/tex]

His expected value is of -$2.5.

Item b:

With an unknown ticket price, the distribution is:

The game is fair if E(X) = 0, hence:

[tex]\frac{500 - x}{1000} - \frac{999x}{1000} = 0[/tex]

0.5 - x = 0

x = 0.

The fair price of a ticket is of $0.5.

More can be learned about the expected value of a discrete distribution at https://brainly.com/question/24855677