I need help with the solution

I Need Help With The Solution

Answers

Answer 1

The answer is Pedro.


Related Questions

A shipping company charged $15 to ship a package and 5% to insure the package.What was the total cost to ship this particular item?

Answers

Answer:

5% of 15 is 0.75 i think

Step-by-step explanation:

15/5% is 0.75

$15.75

First we need to calculate how much the company charges in insurance. 5% is the same as 0.05, so we multiply $15 by 0.05 to find the 5% of the package cost it takes to insure the package. This gets us $0.75. We then have to add this new insurance price of $0.75 to the initial shipping cost of $15 to get the total cost to ship this item. This gets us a total of $15.75.

$15 x 0.05 = $0.75
$15 + $0.75 = $15.75

P = √mx_ £x MX t make x the subject
[tex]p = \sqrt{ \frac{mx}{t} } - t {}^{2}x \: \: make \: x \: the \: subject [/tex]

Answers

So, making x subject of the formula, x = [m - 2pt³ ±√(m²  - 4pt²m)]/{2t⁵}

How to make x subject of the formula?

Since p = √(mx/t) - t²x

So, p + t²x = √(mx/t)

Squaring both sides, we have

(p + t²x)² = [√(mx/t)]²

p² + 2pt²x + t⁴x² = mx/t

Multiplying through by t,we have

(p² + 2pt²x + t⁴x²)t = mx/t × t

p²t + 2pt³x + t⁵x² = mx

p²t + 2pt³x + t⁵x² - mx = 0

t⁵x² + 2pt³x - mx + p²t = 0

t⁵x² + (2pt³ - m)x + p²t = 0

Using the quadratic formula, we find x.

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]

where

a = t⁵, b = (2pt³ - m) and c =  p²t

Substituting the values of the variables into the equation, we have

[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

So, making x subject of the formula,  [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

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Lamar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $10, and paint and canvas for each painting costs $45; he will sell each painting for $50. Once Lamar sells a certain number of his paintings, he will be breaking even. How many paintings will that be?

Answers

Answer:

2

Step-by-step explanation:

If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.

50x = 45x + 105x = 10x = 2

The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.

What is breakeven?

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."

Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.

Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,

Total cost of x painting = $10 + $45(x)

Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,

Revenue generated = $50(x)

Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,

Total cost of x painting = Revenue generated

$10 + $45(x) = $50(x)

10 + 45x = 50x

10 = 50x - 45x

10 = 5x

x = 10/5

x = 2

Hence, For breakeven Lamar needs to sell 2 paintings.

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A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 45% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answers

The gallons of the first brand of antifreeze should be 60 gallons.

The gallons of the second brand of antifreeze should be 90 gallons.

What are the linear equations that represent the question?

0.2f + 0.45s = 52.50 (0.35 x 150) equation 1

f + s = 150  equation 2

Where:

f = gallons of the first antifreezes =  gallons of the second antifreeze

how many gallons of each brand of antifreeze must be used?

Multiply equation 2 by 0.2

0.2f + 0.2s = 30 equation 3

Subtract equation 3 from equation 2

0.25s = 22.50

s = 22.50 / 0.25

s = 90

f = 150 - 90 = 60 gallons

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HELPPPP PLSSSSSSSSS!!!!!!!!??!

Answers

Answer:

(3+3) x (3+1)

Step-by-step explanation:

nice

Given :

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

Solution :

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

Given angle YMC = 170 degrees, find the measure of angle AMC.

Answers

Answer:

i think 10 because in triangle there is 180 and 180-170 = 10

Answer:

Step-by-step explanation:

hjhj

A baker uses 3 cups (c) of flour to bake 2 loaves of bread. If 1 pound (lb) of flour is equivalent to 3 c, how many loaves of bread can the baker make with a 10 lb-bag of flour? 3 (Round the answer to the nearest whole number.)​

Answers

The number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

Number of loaves

Ratio of flour to loaves of bread = 3 cups : 2 loaves

1 pound (lb) of flour = 3 cups of flour

10 pounds (lb) of flour = 30 cups of flour

Number of loaves of bread can the baker make with a 10 lb-bag of flour

Equate the ratio of flour to loaves of bread

3 : 2 = 30 : x

3/2 = 30/x

3 × x = 2 × 30

3x = 60

x = 60/3

x = 20 loaves of bread

Therefore, the number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

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One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is

Answers


Answer: 5 is the smaller number and 21 is the larger number

Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.

A teacher records the number of students present in her 1st period class each day. This count is a ___________ random variable.
A. Discrete
B. Countable
C. Continuous
D. Finite

Answers

This count is a discrete random variable (option A).

What is a discrete random variable?

A discrete random variable is a variable that contains integers that can only be a limited number of possible values.  A discrete random variable is can contain only a finite set of numbers .

An example of discrete random variable is the number of students in the first period class. It is impossible for the number of students in the class to go on indefinitely.

Discrete random variable has the following properties:

It is finiteIt is numericIt is countableIt contains non-negative integers.

A continous random variable is a variable that has an infinite number.

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find all the zeros in y=x^2+2x-24

Answers

Answer:

x = 4 and x = 6

Step-by-step explanation:

Allison went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 20 grams of sugar. Allison purchased a total of 11 bottles of juice and soda which collectively contain 445 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system.

Answers

Using a system of equations, it is found that Allison bought 2 bottles of juice and 9 bottles of soda.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are:

Variable x: bottles of juice purchased.Variable y: bottles of soda purchased.

Allison purchased a total of 11 bottles of juice, hence:

x + y = 11 -> x = 11 - y.

These 11 bottles contain 445 grams of sugar, hence, considering the amounts of each bottle, we have that:

20x + 45y = 445

Since x = 11 - y:

20(11 - y) + 45y = 445

25y = 225

y = 225/25

y = 9.

x = 11 - y = 11 - 9 = 2.

She bought 2 bottles of juice and 9 bottles of soda.

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Please help I need to turn this in by Monday!

Answers

Answer: Rational, Irrational, Rational, Natural, Natural, Integer

Step-by-step explanation:

-4.2 is a rational number as it can be converted into a fraction

3√5 is an irrational number as it can't be converted into a fraction

5/3 is a rational number as it is a fraction

9 is a natural number as it is a positive whole number

√16 is a natural number as despite the square root, √16 is 4 which is a natural number

-8/2 is an integer as -8/2 is -4 which is a negative whole number

The two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company.

Text
Message Instant
Message Phone Call Email Total
0 to 7 years 36 49 8 21 114
8 or more years 12 22 19 43 96
Total 48 71 27 64 210

What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication?

A.
48.84%
B.
20.48%
C.
67.19%
D.
44.79%

Answers

Using it's concept, the percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is:

D. 44.79%.

What is a percentage?

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, there are 96 employees with 8 or more years of experience, of which 43 prefer email, hence the percentage is:

P = 43/96 x 100% = 44.79%.

Hence option D is correct.

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Ashlee sells lunches for $7.00 and drinks for $2.25. One busy Saturday, Ashlee sold $440.00 worth of lunches and drinks. Which equation represents the relation between the number of lunches sold, x, the number of drinks sold, y, and the amount in dollars that Ashlee sold that day?
Group of answer choices

Answers

Answer:

7x + 2.25y = 440

Step-by-step explanation:

Ashlee sells lunches for $7.00 and drinks for $2.25.

One busy Saturday, Ashlee sold $440.00 worth of lunches and drinks.

The number of lunches sold is x.

The number of drinks sold is y.

The appropriate equation will be:

= (7 × x) + (2.25 × y)

7x + 2.25y = 440

Someone help me with this question !,

Answers

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The side opposite to the largest angle is the longest side of a triangle.

[tex] \qquad \large \sf {Conclusion} : [/tex]

hence, we can conclude that longest side is e

( since it's opposite angle is the largest, i.e 86° )

2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?

Answers

Answer:

no solution

Step-by-step explanation:

16x - 32y = 27 → (1)

8x - 16 = 16y ( subtract 16y from both sides )

8x - 16 - 16y = 0 ( add 16 to both sides )

8x - 16y = 16 → (2)

multiply (2) by - 2 and add to (1)

- 16x + 32y = - 32 → (3)

add (1) and (3) term by term

0 + 0 = - 5

0 = - 5 ← not possible

this indicates the system has no solution

(b)

the solution to a system is the point of intersection of the 2 lines

since there is no solution, no point of intersection, then

this indicates the lines are parallel and never intersect

Answer:

a) no solution

b) the two lines never intersect

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]

Part (a)

To solve by linear combination (elimination):

Step 1

Write both equations in standard form: Ax + By = C

[tex]\implies 16x-32y=27[/tex]

[tex]\implies 8x-16y=16[/tex]

Step 2

Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:

[tex]\implies 16x-32y=27[/tex]

[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]

Step 3

Subtract one of the equations from the other to eliminate one of the variables:

[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]

Therefore, as 0 ≠ 5, there is no solution to this system of equations.

Part (b)

The solution to a system of equations is the point(s) of intersection.

As there is no solution to the given system of equations, this tells us that the two lines never intersect.

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the equation of a circle given the center (–4, 4) and raduis r = 5.

Answers

Answer:

x² + y² + 8x - 8y + 7 = 0

Step-by-step explanation:

Formula: (x - a)² + (y - b)²= r²

where,

a = -4

b = 4

Substitute a and b

( x - (-4))² + (y - 4)² = 5²

(x + 4)² + (y - 4)² = 25

Open Bracket( )

(x + 4) (x + 4) = x² + 4x + 4x + 16

(y - 4) (y - 4) = y² - 4y - 4y + 16

x² + 4x + 4x + 16 + y² - 4y - 4y + 16= 25

Collect Like Terms

x² + y² + 8x - 8y + 16 + 16 - 25 = 0

x² + y² + 8x - 8y + 7 = 0

Therefore,

x² + y² + 8x - 8y + 7 = 0

Is The Equation Of The Given Circle.

IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each

Answers

In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.

About the Central Angle:

An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.

Since BD is the diameter of the circle,

∠BAC + CAD = 180°

It is given that ∠BAC = 100°

⇒ ∠CAD = 180° - 100°

⇒ ∠CAD = 80°

About Major Arc:

The arc which subtends an angle greater than 180° at the center, is called a major arc.

Angle subtended by arc BEC = 360° - m(arc CD)

= 360° - 80°

= 280° > 180°

Arc BEC is the major arc

About Minor Arc:

The arc which subtends an angle less than 180° at the center, is called a minor arc.

Arc CD is the minor arc.

Calculating arc BEC and arc BC:

Let us assume the radius of the circle is r.

Then, the formula of the measure of an arc is given by,

θ × (π/180) × r

Here, θ is the angle ( in degrees) subtended by the arc at the center.

Arc BEC = 260 × (π/180)r  ......... [Put π = 3.14]

= 2.27r

Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]

= 0.87r

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A rectangular park had a dirt path across its diagonal that was yards long. The diagonal and the long side of the park formed an angle that measured . A person walked along the sidewalks outside the park, from the start to the end of the path, as shown by the arrows. The diagonal dirt path that cuts across the rectangular park and the sidewalks outside the park form a right triangle. The dirt path is the hypotenuse and it is labeled 100 yards. The start of the sidewalk is adjacent to the 30-degree angle, and it is labeled X. The end of the path is opposite the 30-degree angle, and it is labeled Y. Which expression shows the distance that he walked?

Answers

Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles.

The expression that shows the distance that he walked = x + y + 100

                                                                 = 87 + 50 + 100

                                                                 = 237 yards

Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles. The required function may be a sine function, a cosine function, or a tangent function.

Such that;

Sin θ = [tex]\frac{Opposite}{Hypotenuse}[/tex]Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]

The given question can be solved by applying the appropriate trigonometric function.

So that to determine the value of x, we have:

Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Cos 30 = [tex]\frac{x}{100}[/tex]

⇒ x = 100 cos 30

      = 100 x 0.866

x = 86.60

Thus, the start of the sidewalk is approximately 87 yards.

To determine the value of sidewalk y, we have:

Sin θ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

Sin 30 = [tex]\frac{y}{100}[/tex]

⇒ y = 100 x Sin 30

      = 100 x 0.5

   y = 50

Thus the sidewalk which represents the end of the path is 50 yards.

Therefore, the total distance that he walked = 100 + 87 + 50

                                                                 = 237 yards

The expression that shows the distance that he walked = x + y + 100

                                                                 = 87 + 50 + 100

                                                                 = 237 yards

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PLEASE HELP ME .IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each

Answers

Answer: [tex]\frac{10\pi}{3}[/tex] m

Step-by-step explanation:

[tex](2)(\pi)(4) \left(\frac{150}{360} \right)=\frac{10\pi}{3}[/tex]

Find the measures of angles a and b when 0=47

Answers

Answer:

b = 133, a = 47

Step-by-step explanation:

If the two lines are parallel, then angle b is equal to 180-47 = 133 (same side interior angles), and angle is equal to angle 0 (alternate interior angles)

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

a = 47°

b = 133°

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:a = \theta[/tex]

( by Alternate interior angle pair )

[tex]\qquad \therefore\: \sf \:a = 47 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \:b = 180 - \theta[/tex]

( by co - interior angle pair )

[tex]\qquad❖ \: \sf \:b = 180 - 47[/tex]

[tex]\qquad \therefore \: \sf \:b = 133 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \:a = 47 \degree[/tex]

and

[tex]\qquad❖ \: \sf \:b = 133 \degree[/tex]

Will mark brainliest!

Answers

Answer:

Area under the graph = 6 sq.units

I've shown the complete calculation over the attached page

Questions are in the pictures

Answers

The values of h and r to maximize the volume are r = 4 and h = 2

The formula for h in terms of r

From the question, we have the following equation

2r + 2h = 12

Divide through by 2

r + h = 6

Subtract r from both sides of the equation

h = 6 - r

Hence, the formula for h in terms of r is h = 6 - r

Formulate a function V(r)

The volume of a cylinder is

V = πr²h

Substitute h = 6 - r in the above equation

V = πr²(6 - r)

Hence, the function V(r) is V = πr²(6 - r)

The single critical point

V = πr²(6 - r)

Expand

V = 6πr² - πr³

Integrate

V' = 12πr - 3πr²

Set to 0

12πr - 3πr² = 0

Divide through by 3π

4r - r² = 0

Factor out r

r(4 - r) = 0

Divide through by 4

4 - r = 0

Solve for r

r = 4

Hence, the single critical point on the interval [0. 6] is r = 4

Prove that the critical point is a global maximum

We have:

V = πr²(6 - r)

and

V' = 12πr - 3πr²

Determine the second derivative

V'' = 12π - 6πr

Set r = 4

V'' = 12π - 6π* 4

Evaluate the product

V'' = 12π - 24π

Evaluate the difference

V'' = -12π

Because V'' is negative, then the single critical point is a global maximum

The values of h and r to maximize the volume

We have

r = 4  and h = 6 - r

Substitute r = 4  in h = 6 - r

h = 6 - 4

Evaluate

h = 2

Hence, the values of h and r to maximize the volume are r = 4 and h = 2

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Solve the equation: (4x - 5)^4 = 81.​

Answers

hope this helps

by

aman10we

The value of x after solving this equation is 2

What is a polynomial?

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, the equation as : (4x - 5)^4 = 81.​

(4x - 5)^4 = 3⁴.​

4x - 5    = 3

      x     = 2

Hence, the value of x is equal to 2

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A chemist has three different acid solutions. The first acid solution contains
20
%
acid, the second contains
30
%
and the third contains
60
%
. They want to use all three solutions to obtain a mixture of
72
liters containing
35
%
acid, using
2
times as much of the
60
%
solution as the
30
%
solution. How many liters of each solution should be used?

Answers

Let [tex]x,y,z[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% solutions used in the mixture, respectively.

The chemist wants to end up with 72 L of solution, so

[tex]x+y+z=72[/tex]

while using twice as much of the 60% solution as the 30% solution, so

[tex]z = 2y[/tex]

The mixture needs to have a concentration of 35%, so that it contains 0.35•75 = 26.25 L of pure acid. For each liter of acid solution with concentration [tex]c\%[/tex], there is a contribution of [tex]\frac c{100}[/tex] liters of pure acid. This means

[tex]0.20x + 0.30y + 0.60z = 26.25[/tex]

Substitute [tex]z=2y[/tex] into the total volume and acid volume equations.

[tex]\begin{cases}x+3y = 72 \\ 0.20x + 1.50y = 26.25\end{cases}[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. Multiply both sides of the second equation by 5 to get

[tex]\begin{cases}x+3y = 72 \\ x + 7.50y = 131.25\end{cases}[/tex]

By elimination,

[tex](x+3y) - (x+7.50y) = 72 - 131.25 \implies -4.50y = -59.25 \implies \boxed{y=\dfrac{79}6} \approx 13.17[/tex]

so that

[tex]x+3\cdot\dfrac{79}6 = 72 \implies x = \boxed{\dfrac{65}2} = 32.5[/tex]

and

[tex]z=2\cdot\dfrac{79}6 = \boxed{\dfrac{79}3} \approx 26.33[/tex]

Evaluate 3|12−x|−4 when x=15

Answers

Answer:

5

Step-by-step explanation:

3 x |12 - x| - 4

3 x |12 - 15| - 4

3 x 3 - 4

9 - 4

5

From the top of the Eiffel tower, which is 984 feet tall, you look down and see your friend at a 60°
angle of depression. How far is your friend from the foot of the tower?

Answers

The answer is 492 feet.

If we picture the scenario as a right triangle, using trigonometric ratios, this problem can be solved.

cos 60° = x / 984

1/2 = x/984

x = 984/2

x = 492 feet

Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y= cos 2 (x+y/2) cos (x-y/2) .

Answers

The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

Substituting a = x + y/2 and b = x - y/2 in this, we get:

cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],

or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],

or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:

cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.

Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

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The provided question is incorrect. The correct question is:

"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."

A box contains 13 green marbles and 13 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

[tex]\textbf{Answer:\ \ \large\boxed{\frac{12}{25} }\ or\ 0.4800}[/tex]

Step-by-step explanation:

[tex]\large\boxed{13\ green\ marbles\ and\ 13\ white\ marbles}[/tex]

After a white marble is chosen:

[tex]\large\boxed{13\ green\ marbles\ and\ 12\ white\ marbles}[/tex]

Now there are 25 (13 + 12) total marbles.

Without replacing the white marble we chose already, what is the probability of choosing another white marble?

Well, now there are 12 white marbles to choose from, out of a total of 25 marbles. This means our probability is:

[tex]\large\boxed{\frac{12}{25} }[/tex]

This in decimal form is:

0.4800

A) AB and BC
B) AC and BD

tell if each pair of segments is congruent

Answers

a. Line AB and line BC are not congruent because their distance of separation are not equal

b. Line AC and line BD are not congruent because their distance of separation are not equal

How to proof the statement

From the number line drawn, we have the following deductions;

Line AB = -5 to -2 = 3

Line BC = -2 to 0 = 2

Line AC = -5 to 0 = 5

Line AD = -5 to 5 = 10

Line BD = -2 to 5 = 7

We can see that;

a. Line AB and line BC are not congruent because their distance of separation are not equal

b. Line AC and line BD are not congruent because their distance of separation are not equal

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