2. A penguin is setting on an iceberg 157 feet above the water? If a walrus is in the water 312 feet from the base of the iceberg, what is the angle of depression from the penguin to the walrus?

Two urns contains different numbers of different colour balls. Two balls are randomly chosen from both of urns. The probability that two red balls are choosen is 1/3..

We have given that

First Urn, u₁ contains 3 Red( labelled r₁,r₂,r₃) ; 1 blue ball ,(labelled b₁).

Total number of balls in urn, u₁ = 4 balls

Second Urn, u₂ contains 2 red (labelled r₄,r₅) and 2 blue (labelled b₂, b₃) .

Total number of balls in urn, u₂ = 4 balls

Assume , A = first urn , u₁ is selected

Assume, B = Second urn u₂ is selected

Assume , R = selected balls are red

Case 1 : Urn u₁ is choose and two balls without replacement are withdraw.

Probability to choose the first urn, P(A) = 1/2

Probability that the two withdraw without replacement balls are red in colour, P(A/R)

= 3/4 × 2/3 = 1/2

Case 2 : Urn u₂ is choose and two balls without replacement are withdraw.

Probability to choose the second urn, P(B) = 1/2

Probability that the two without replacement withdraw balls are red in colour, P(B/R)

= 2/4 × 1/3 = 1/6

The required probability= P(A) P(A/R) + P(B)P(B/R) = 1/2(1/2) + 1/2(1/6) = 1/4 + 1/12

= 4/12 = 1/3

Hence, the required probability is 1/3..

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Complete question:

One urn u1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn u2 contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. Probability that two red balls are choosen.

Answer: -5/3

Down -5

right 3

Step-by-step explanation: count the distance between the 2 dots looking from the y axis (up and down)and from the x axis (left to right)

The simplest form of [(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)] is 3p/ (p - 3).

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given expression is

[(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)]

Now factories p²- 4p -12, p²-9p+18, and 6p + 12:

p²- 4p -12

= p²- (6 - 2)p -12

= p²- 6p + 2p -12

= p(p - 6) + 2(p - 6)

=(p - 6)(p + 2)

p²- 9p + 18

= p²- (6 + 3)p + 18

= p²- 6p -3p + 18

= p(p - 6) -3(p -6)

=(p - 6)(p - 3)

6p + 12

=6(p+2)

Now putting p²- 4p -12 = (p - 6)(p + 2); p²- 9p + 18 = (p - 6)(p - 3); 6p + 12 = 6(p+2) in the given expression:

[ (p - 6)(p + 2)/6(p+2)] × [18p/(p - 6)(p - 3)]

Multiply the denominator with denominator and numerator with numerator:

= 18p (p - 6)(p + 2)/ 6(p+2)(p - 6)(p - 3)

Now cancel out (p+2)(p - 6) from denominator and numerator:

= 18p/ 6(p - 3)

Divide denominator and numerator by 6:

= 3p/ (p - 3)

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Answer:

-48 ft.

Step-by-step explanation:

-76+28= -48

Hope this helps! Had this on one of my quizzes

Answer:

-48 espero te sirva perdon por llegar tarde

The sum of both accounts' expression in its most basic form is 55w + 145.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the instructions given in the question,

Amount in savings account = 10w + 120

Amount in checking account = 45w + 25

Then, total money shaved each week will be,

(10w + 120) + (45w + 25)

10w + 45w + 120 + 25

= 55w + 145

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Any line perpendicular to line C must have a slope equal to -3/2.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two linear equations are perpendicular if the product between the slopes is -1, then if the slope of the line perpendicular to line C is x, then we can write:

x*(2/3) = -1

Solving for x we get:

x = -3/2

That is the slope of the perpendicular line.

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The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

What is Acceleration ?

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Given,

Velocity  v= x² − 5x + 4

now, the acceleration

a = dv/dt

​a = 2x (dx/dt) - 5x(dx/dt)

​

given that, v= dx/dt =0

so, a = 2x*0−5*0

a=0 m/sec²

so, the acceleration is zero ,when the velocity is zero.

Hence ,The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

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The like terms to make a simpler expression is   19 x^2-6 x+9 n-6

Group like terms

What is simpler expression?

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.

[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]

[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]

[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$3 n+6 n=9 n$[/tex]

[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]

Add the numbers: [tex]$-7+1+5-5=-6$[/tex]

[tex]=19 x^2-7 x+9 n-6[/tex]

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Answer:

A:Infinite solutions

Step-by-step explanation:

1.2 ( 3x + 5 ) = 3.6x + 6

1.2 ( 3x ) + 1.2 ( 5 ) = 3.6x + 6

3.6x + 6 = 3.6x + 6

Answer: A

Step-by-step explanation:

im not sure if you made a mistake and meant hundredths or not but if you are adding hundreds it would be 59.031 but if you adding hundredths is would be 0.621.

Answer:  C. The width of the bar representing dogs is more than the widths of the other bars.

Step-by-step explanation: The following statements describes how this Bar Chart misrepresents the data.

The volume of the solid you (the region) create by spinning about the x-axis is V = 225units³

Depends whether it is a solid with sides, height, and depth. In this case it is the multiplicarion of the three to get the volume.

If it is an irregular shaped object it is done by water displacement. Fill a container with a known amount of water, immerse the object, and the difference in volume in the water is the volume of the object.

Break the volume down into prisms and pyramids that you can calculate the volume of and sum the pieces up to get the total volume. If the shape has curved surfaces, it gets much more complicated.

This gives a y = 15

                   x = 3

The straight line equation will be y = 5x

The volume of a pyramid is given by the following equation:

where r = radius of the base

          h= height of the cone

from the graph, roating about the x - axis gives h = 3, r = 15

Volume =

            = 225  units³

Volume of cone formed is 225  units³.

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The perimeter of the figure with side length of 5 units is 50 units

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Answer:

point

vertex

one

face

face

circular

length

area

volume

Answer:

D

Step-by-step explanation:

slope of the given line :

(-4-2)/(-1-4)

-6/-5

6/5

slope of a perpendicular line : -5/6

y-7 = -5/6 (x-(-3)

y -7 = -5/6 (x+3)

y -7 = -5/6 x - 5/2

5/6 x + y - 7 + 5/2 = 0

5/6 x + y + (-14 + 5)/2 = 0

5/6 x + y - 9/2 = 0

5x + 6y - 27= 0

5x + 6y = 27

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )

m = [tex]\frac{2-(-4)}{4-(-1)}[/tex] = [tex]\frac{2+4}{4+1}[/tex] = [tex]\frac{6}{5}[/tex] ← slope of graphed line

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{6}{5} }[/tex] = - [tex]\frac{5}{6}[/tex] , then

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (- 3, 7 ) into the partial equation

7 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 7 - [tex]\frac{5}{2}[/tex] = [tex]\frac{14}{2}[/tex] - [tex]\frac{5}{2}[/tex] = [tex]\frac{9}{2}[/tex]

y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{9}{2}[/tex] ← equation in slope- intercept form

multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions

6y = - 5x + 27 ( add 5x to both sides )

5x + 6y = 27 ← equation of perpendicular line in standard form

Answer:

Yes, your answer would be correct.

Step-by-step explanation:

That graph intersects at (0, 2), is a solid line, and the slope is -2.

Answer:

2, 13, 103

Step-by-step explanation:

These prime numbers are the ones.

2678 = 2 * 13 * 103

A prime number is a natural number that is greater than one and is not a product of smaller natural numbers. For example,  3 is a prime number and we can write it as a product, 1 * 3 or 3 * 1, which involves 3 itself.

So, prime numbers are those numbers that have only two factors, which are 1 and the number itself.

A natural number that is greater than 1 and is not a prime number, is called a composite number. Every natural number which is greater than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order.

The answer is -

    2678 = 2 * 13 * 103

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Step-by-step explanation:

whenever you see a variable ( a letter )  without a number in front of it, add a 1 ! It means the same thing...

y is the same as 1y

1). 3y + y = ?

Add that 1!

3y + 1y = ?

This problem is the same as 3 + 1

3y + 1y = 4y

2). b + b = ?

Add those 1's !

1b + 1b = ?

this is the same as 1 + 1

1b + 1b = 2b

Remember to keep the variable !

Part B is like a puzzle and the instructions give us hints.

It is telling us, when we see an r, we replace it with the number 3

and when we see t , we replace it with the number 9

Let's solve these puzzles!

8). [tex]\frac{r}{t} = ?[/tex]

We see and r and a t, let's plug in 3 and 9

Now we have ...

[tex]\frac{3}{9} = ?[/tex]

Divide using a calculator!

We get ....

[tex]\frac{3}{9} = \frac{1}{3}[/tex] or 0.33

9). [tex]rt = ?[/tex]

When variables are right next to each other, this means they are being MULTIPLIED!

Let's replace r and t with 3 and 9 and multiply them together!

[tex]rt =[/tex] 3 × 9

3 × 9 = 27

We do similar things for Part C

12). [tex]ab = ?[/tex]

It tells us a = 5 and b = -4

Let's plug it in

[tex]ab =[/tex]  5 × -4

5 × - 4 = -20

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There is an effective change of 50% in the school.

What is Percentage?

A percentage is a relative figure that represents the hundredth part of any amount. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Solution:

To find the net/effective change we can the use the formula:

(a + b + ab/100)

here a and b are the rate of change

a = 25% and b = 20%

Net change = (25 +20 + 500/100) = 45 + 5 = 50%

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Answer:

x = 3.66

Step-by-step explanation:

Area of a rectangle = length * width

In this case:

(x+10)x = 50

x*x + x*10 = 50

x² + 10x - 50 = 0

x = {-10±√((10²) -(4*1*-50))} / (2*1)

x = {-10±√(10² + 200)} / 2

x = {-10±√(100+200)} / 2

x = {-10±√300} / 2

x = {-10±17.321} /2        aprox,

It is a geometric figure so only the positive value is taken.

x = {-10+17.321} / 2

x = 7.321/2

x = 3.66

Check:

3.66(3.66+10) = 50

3.66*13.66 = 50

Answer:

84

Step-by-step explanation:

EFD is an iscosilies triangle therefore angle F = angle D = 48

and therefore angle E= 180-48-48=84

Answer:

29 is the correct answer

Answer:

Z

Step-by-step explanation:

Angle V is congruent to angle z because they have the same placement in the letter order.

Answer:

Below

Step-by-step explanation:

6139 * x * 3 = 798

x = 798/(3*6139) = .0433= 4.33%

Answer:

D

Step-by-step explanation:

D. If it's not D, C. It's a negative slope with a negative y-intercept of -1

The ordered pairs to the system of linear inequality are (-1, 5), (0, 4), (-6, 7)

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the problem given;

x + 5y > 8 ...eq(i)

4x - y < 6 ...eq(ii)

From eq(i)

x + 5y > 8

x > 8 - 5y ...eq(iii)

however, this can easily be solved using a graph.

Plotting the inequality in a graph line;

The ordered pairs are (-1, 5), (0, 4), (-6, 7)

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In the given figure QT is of 16 units.

A line segment has two end points unlike a line which can extend indefinitely in both the directions.

According to the given question S is between Q and T and R is the midpoint of QS. RS=4 And RT= 12 we have to find QT.

As R is the midpoint of QS It will be twice of RS which

= 8 units.

And if RS is 4 units then QR is also 4 unit as R is the midpoint.

QT = QR + RT.

QT = 4 + 12

QT = 16 units.

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Answer:

684.

Step-by-step explanation:

If you are given an equation of a line and a set of points, you should determine the slope of the equation that is perpendicular to the given equation of line. Lastly, you should use the set of points to write an equation for the perpendicular line.

Mathematically, the slope-intercept or standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:

m₁ × m₂ = -1

Assuming the given equation of a line is y = 2x, the slope of the equation that is perpendicular to this line would be calculated as follows;

m₁ × m₂ = -1

2 × m₂ = -1

Slope, m₂ = -1/2.

In conclusion, you will use the newly calculated slope alongside the set of points to determine the equation for the perpendicular line either by using the slope-intercept form or point-slope form.

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