You have $5$ red shirts, $5$ green shirts, $6$ pairs of pants, $8$ green hats and $8$ red hats, all of which are distinct. How many outfits can you make consisting of one shirt, one pair of pants, and one hat without having the same color of shirts and hats

The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by

y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].

To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is

1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is

-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.

1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]

=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].

When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.

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Answer:

Probability of one hit in 4 in a row = 42% = 42/100

Probability of 4 hits in a row = 3.1% = 31/1000

Step-by-step explanation:

Since all throws are independent events;

If 4 hits in a row

You can make a fraction and square by the amount of hits so if the questions asking 4/4 hits see below or change to the amount of hits you need.

(42/100)^4 = 0.03111696

This is 3.1%

42/100^1 stays 42% = 42/`100

42/100^2 becomes 17.64% = 441/2500

42/100^3 becomes  7.4% = 37/500

The probability that the baseball player will get a hit in 4 at-bats in a row is 0.0313 or about 3.13%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Assuming each at bat is independent of the others.

The probability of getting a hit in any one at bat = 0.42

The probability of not getting a hit = 0.58.

The probability of getting a hit in 4 at bats in a row is the product of the probabilities of getting a hit in each of the 4 at bats.

= P(hit in 4 at bats)

= 0.42 × 0.42 × 0.42 × 0.42

= 0.0313

Therefore,

The probability that the baseball player will get a hit in 4 at-bats in a row is 0.0313 or about 3.13%.

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The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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In this case I believe you would add 25 to both sides. The -25 +25 would cancel out and then +25 would be on the right.

Answer:

x = -4

y = 29

Step-by-step explanation:

Let's take our two equations and turn the decimals into fractions for simplicity's sake. We get:

x/4 + 5y/100 = 9    x + y = 25

Simplifying a bit gives us:

x/4 + y/20 = 9       x + y = 25

Now, we will take the first equation and multiply it by 20 to get rid of the fractions. We get:

5x + y = 9

We will rearrange numbers to give us an answer to y that we can substitute in. we get:

y = 9 - 5x

Then, we will plug this into our second equation giving us:

x + 9 - 5x = 25

Combining like terms and subtracting 9 from both sides gives us:

-4x = 16

Dividing by -4 gives us:

x = -4

Then, we can substitute this into our second equation giving us:

-4 + y = 25

We will add 4 to both sides giving us:

y = 29

Hope this helped!

Answer:

1 ) 597

2 ) 346

Step-by-step explanation:

1 )

A.P : - 15, - 7, 1, ...

Here,

a = - 15

d = - 7 - ( - 15 )

= - 7 + 15

d = 8

65th term is t65.

t65 = a + ( 65 - 1 )d

= a + 64 d

= - 15 + 64 ( 8 )

= - 15 + 512

t65 = 597

Therefore,

65th term = 597

2 )

A.P = 3, 10, 17, 24, ...

Here,

a = 3

d = 10 - 3 = 7

50th term is t50.

t50 = a + ( 50 - 1 )d

= a + 49d

= 3 + 49 ( 7 )

= 3 + 343

t50 = 346

Therefore,

50th term = 346

Answer:

65ᵗʰ Term of the sequence is 479

50ᵗʰ Term of the sequence is 346

Step-by-step explanation:

Here,

First Term = a₁ = 3

Second Term = a₂ = 10

Third Term = a₃ = 17

Now,

Common Difference (d)

d = a₂ - a₁ = (-7) - (-15) = -7 + 15 = 8

d = a₃ - a₂ = 1 - (-7) = 1 + 7 = 8

Here, Common Difference is same everywhere

Now, For 65ᵗʰ term, n = 65

aₙ = a + (n - 1)d

a₆₅ = (-15) + (65 - 1) × 8

a₆₅ = (-15) + 64 × 8

a₆₅ = (-15) + 512

a₆₅ = 479

Thus, 65ᵗʰ Term of the sequence is 479

Here,

First Term = a₁ = -15

Second Term = a₂ = -7

Third Term = a₃ = 1

Now,

Common Difference (d)

d = a₂ - a₁ = 10 - 3 = 7

d = a₃ - a₂ = 17 - 10 = 7

Here, Common Difference is same everywhere

Now, For 50ᵗʰ term, n = 50

aₙ = a + (n - 1)d

a₅₀ = 3 + (50 - 1) × 7

a₅₀ = 3 + 49 × 7

a₅₀ = 3 + 343

a₅₀ = 346

Thus, 50ᵗʰ Term of the sequence is 346

-TheUnknownScientist

The volume of the composite solid round to the nearest tenth is 83.7 inches³.

Volume of a three dimensional shape is the space occupied by the shape.

There are 2 hemispheres and a cylinder in the given composite solid.

Volume of hemisphere =  [tex]\frac{2}{3}[/tex] π r³, where r is the radius.

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Here r = 2 inches and

h = 8 - 4 = 4 inches

Volume of hemisphere = [tex]\frac{2}{3}[/tex] π × 2³

                                      = [tex]\frac{16}{3}[/tex] π

There are two hemispheres.

Volume of two hemispheres = 2 × [tex]\frac{16}{3}[/tex] π =  [tex]\frac{32}{3}[/tex] π

Volume of the cylinder = π r² h

                                      = π × 2² × 4

                                      = 16 π

Volume of the composite Solid = [tex]\frac{32}{3}[/tex] π + 16 π

                                                    = [tex]\frac{80}{3}[/tex] π

                                                    = 83.7 inches³

Hence the volume of the composite solid is 83.7 inches³.

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Step-by-step explanation:

u vector components:

x-comp = 8 - (-17) = 25

x-comp = -11 - 4 = -15

Therefore, we can write vector u as

u = 25i - 15j

v = 14i - 4j

u - v = 11i - 11j

Therefore,

2(u - v) = 22i - 22j

Answer:

a) $12

b) $2.99

Explanation:

for both questions, the amount saved would be the original price × discounted percentage, since that is the amount that does not have to be paid due to the discount.

as such:

a) $150 × 8% = $12

b) $23.95 × 12.5% = $2.99 (to 2 decimal places)

i hope this helps! :D feel free to comment if you need to clarify anything

Answer:

24.36m²

Step-by-step explanation:

area = ½×(8.9+2.7)×4.2= ½×48.72=24.36m²

The total number of students on the honor roll increased by 20%.

Given that, 75 boys and 50 girls on the honor roll

=> boys increased by 24% =  75*24/100  = 18

So, the number of boys is increased by 18.

=> girls increased by 14% =  50*14/100  = 7

So, the number of girls is increased by 7.

After the increment, the number of boys and girls on the honor roll is 93 and 57, respectively.

Thus, the total number of students increased = 18+7 = 25

Therefore, the percentage increment in total = 25 / 125 * 100 = 20%

Hence, The total number of students on the honor roll increased by 20%.

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Answer:

supplementary angles

Step-by-step explanation:

for instance, 50 + 130 = 180.

Answer:

3.975 square inches

Step-by-step explanation:

Step 1

We find the length of the triangle

We solve using Pythagoras Theorem

Diagonal² = Length² + Width²

Diagonal = 4 inches

Width = 3 inches

Length² = Diagonal² - Width²

Length = √Diagonal² - Width²

Length = √4² - 3²

Length = √16 - 9

Length = √(7)

Length = 2.6457513111 inches

Length = 2.65 inches

Step 2

Area of Triangle = 1/2 × Base × Height

Base = Length = 2.65 inches

Height = Width = 3 inches

=1/2 × 2.65 inches × 3 inches

= 3.975 square inches

Therefore, the area of one of the triangles that are formed is 3.975 square inches

Answer:

I believe the correct answer is D

= (7⁵ × 7ⁿ)⁴ = (7¹⁶/7ⁿ)³

= (7²⁰ × 7⁴ⁿ) = (7¹⁶ × 7-ⁿ)³

= 7²⁰⁺ ⁴ⁿ = 7⁴⁸ ⁻ ³ⁿ

= 20 + 4n = 48 - 3n

= 20 - 48 = -3n - 4n

= -28 = -7n

= -28/-7 = n

= 4 = n

_____________

If you have any doubt,let me know in comments :D

For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .

The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .

The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;

On differentiating both sides of the curve with respect to "x"  ,

we get ;

the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;

Now for the  x- intercepts , the value [tex]y = 0 ,[/tex]

On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,

we get ;

[tex]x^{2} +x(0)+0^{2} =27[/tex]

On simplifying further ,

we get ;

[tex]x=\pm 3\sqrt{3}[/tex] ;

So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;

to find the slopes , we substitute the values in the slope equation .

On substituting the values in the slope equation ,

we get ;

[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex]  and

[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].

we see that the slope at both the intercepts is same ,

Therefore , the lines tangents of the curve at the x intercepts are parallel .

The given question is incomplete , the complete question is

Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .

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Answer:

A

Step-by-step explanation:

each text message is .17 text messages are x the total bill is 28.45. the service charges are 24.20.

.17x + 24.50 = 28.45

Answer:

7.5

Step-by-step explanation:

Answer:

[tex]y=0[/tex]

Step-by-step explanation:

[tex]y+25=25 \\ \\ y=25-25 \\ \\ y=0[/tex]

Answer:

[tex] \sf \: y = 0[/tex]

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.

Answer: Is this completing a a square?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perfect square identity is:

Apply to the given equation to complete the square:

Required number is 9/4

Logarithmic Functions

In mathematics, the logarithmic function is an inverse function to exponentiation

Domain and range of logarithmic functions

We know that is defined only when >0. So the domain is the set of all positive real numbers. We can see that can be either a positive or negative real number (or) it can be zero as well. Thus,  can take the value of any real number.

Note:

The domain of function = is >0 (or) (0,∞).

The range of any log function is the set of all real numbers ().

Logarithmic graph

We know that exponentials and functions are inversely proportional to each other, and so their graphs are symmetric concerning the line =. Also, note that =0 when =0 as =(1)=0 for any . Thus, all such functions have an -intercept of (1,0).  A logarithmic function doesn’t have a -intercept as 0 is not defined.

Properties of logarithmic graph

>0 and ≠1.

The logarithmic graph increases when >1 and decreases when 0<<1.

The domain is obtained by setting the argument of the function greater than 0.

The range is the set of all real numbers.

Graphing logarithmic functions

Before plotting the log function, just have an idea of whether you get an increasing curve or decreasing curve as the answer. If the >1 then the curve is increasing, and if 0<<1, then the curve is decreasing.

Here are the steps for graphing logarithmic functions:

Find the domain and range.

Find the vertical asymptote by setting the argument equal to 0. Note that a  function doesn’t have any horizontal asymptote.

Substitute some value that makes the argument equal to 1 and use the property (1)=0. This gives us the -intercept.

Substitute some value that makes the argument equal to the base and use the property ()=1 This would give us a point on the graph.

Connect the two points (from the last two steps) and extend the curve on both sides relative to the vertical asymptote.

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3.) x = 15.25 or 15 1/4 ( not sure if you'll need to round your answer )

4.) x =6

5.) x = 10

6.) x = 9

Explanation:

1.) write your equation down 8x + 9 = 131

2.) Subtract +9 from 131. you'll get 122

3.) divide 8x and 122.

4.) Then there's your answer 15.25

you'll do the same thing throughout each equation. write down your equation but with the 22x and 23x you're going to subtract 22x from 23x. and you'll get 1x then continue on the same way as with the last equation.

Answer:

-17h-36 is your answer

Step-by-step explanation:

3(-7h-4) +4 (h-6)

-21h-12+4h-24

-17h-36

The stem plot for the given data is 3 4 5 6.

A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

Arranging the given data in ascending order,

30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68

The stem plot = 3 4 5 6

Calculated Statistics:

Minimum:30

Maximum:68

Range:38

Count:30

Sum:1365

Mean:45.5

Median:43

Mode:43

Standard Deviation:9.616

Variance:92.47

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Answer:

C

Step-by-step explanation:

The volume is (6*12*5 1/4). Since 6*12 is 72, this is equal to 72*(5 1/4).

17²-8²=225

√225= 15

therefore both x and y are 15 ft

Answer:

Im not sure but I think its x and y both equal 14.7ft

Step-by-step explanation:

Take this with a grain of salt I dont know if its correct but i hope it helps

a) The data on the y-axis: the numbers of people in each salary category.

b) The data on the x-axis: salaries

c) The distribution of salaries is skewed to the right.

We know that a histogram is a graph in which the x-axis is a quantitative variable split into bins, and the y-axis is the frequency.

For given distribution of salaries for individuals, the Y-axis would have the frequency i.e., the numbers of people in each salary category.

And x-axis would have income, because this is out quantitative variable of interest.

consider the following histogram.

We can observe that the graph of distribution of salaries is skewed to the right, because most income data are positively skewed. There would be a substantial number of individuals at or near the lowest salary level, but some people make a tremendously high salary.

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The two step equations are used to represent the equations and solve real life problems .

What is Two Step Equations ?

The Equations that can be solved in exactly two steps are called as Two Step Equations .

We can use the two-step equations to represent and solve real-world problems by translating the problem into an algebraic equation, and solving equation, and then interpreting the solution of equation.

An example of the two step equation is : If a rental car costs $40 plus extra 10 cents for every mile driven, then how many miles can be driven for $50 ?

Translating The problem into equation we get  [tex]40 + 0.1m = 50[/tex] where m is  number of miles driven.

Step(i) we Subtract 20 from both sides

we get , [tex]0.1m = 10[/tex].

Step(ii) We Divide both sides by 0.1 ;

we get , [tex]m = 100[/tex].

Therefore , the problem to find the number of miles is solved in exactly two steps .

The given question is incomplete , the complete question is

What is the two step equation used for ?

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Answer:

Since your diameter is 8,

half of that is 4.

We are going to find the area now of both the bottom and the top.

4^4 = 16

16 x 3.14 = 50.24

Now we multiply by two since there are two circles  (bottom and top) we only got one circle's area.

50.24 x 2 = 100.48

Now we need to find the round curved area.

In order to do that we need to find the circumference them multiply by the height:

2 x 3.14 x 4 = 25.12(circumference)

25.12 x 19Height) = 477.28

Now we need to add both the areas(surface area):

477.28 + 100.48 = 577.76 yard2 is your answer.