What is the length of leg s of the triangle below?

Answer:

+ 0.26

Step-by-step explanation:

[tex]~~~~~~\tan^{-1}(xy) = \sin^{-1}(4x+4y)\\\\\\\implies \dfrac d{dx} \left[ \tan^{-1}(xy)\right] = \dfrac d{dx} \sin^{-1}\left( 4x+4y\right)\\ \\\\\implies \dfrac{1}{1+(xy)^2} \left[ \dfrac{d}{dx} (xy)\right] = \dfrac{1}{\sqrt{1-(4x+4y)^2}} \cdot \dfrac{d}{dx}(4x+4y)\\\\\\\implies \dfrac{1}{1+x^2 y^2} \left(x\dfrac{dy}{dx}+y \right)=\dfrac{1}{\sqrt{1-(4x+4y)^2}} \left(4+ 4 \dfrac{dy}{dx} \right)\\\\\\\\[/tex]

[tex]\implies \left(\dfrac{x}{1+x^2y^2} \right) \dfrac{dy}{dx} + \dfrac{y}{1+x^2y^2}=\dfrac{1}{\sqrt{1-(4x+4y)^2}} \left(4+ 4 \dfrac{dy}{dx} \right)\\[/tex]

[tex]\\\\\implies 0 \cdot \dfrac{dy}{dx} +0 = \dfrac{1}{\sqrt{1 -0}} \left(4+4 \dfrac{dy}{dx} \right) ~~~~~~~~~;\left[ \text{at}~~ (0,0) \right]\\\\\\\implies 4+4 \dfrac{dy}{dx} = 0\\\\\\\implies \dfrac{dy}{dx} = -\dfrac 44\\\\\\\implies \dfrac{dy}{dx} = -1\\\\\text{So, the slope of the tangent line at (0,0) is}~ -1\\ \\\\\text{The equation of tangent line,}\\\\~~~~~~y-0 = -1(x-0)\\\\\implies y=-x[/tex]

Answer:

4.4 degrees C.

Step-by-step explanation:

C = 5/9 (F - 32)

When F = 40:

C = 5/9( 40 - 32)

= 5/9 * 8

= 40/9

= 4.4 degrees C,

Answer:

So you must first get the total of all the birds, which is going be a fraction of course , that being 14/14 birds in total, since there are only 3 black birds the probability of me getting a black one 3/14 because there are fourteen in total, and the probability for the green birds is 6/14.

The combined probability that the first bird is black and the second is green is 0.0918

Probability is the likeliness of an event to happen.

Total Blue birds = 5

Total Green birds = 6

Total Black birds = 3

Total birds = 14

The probability of selecting two birds such that the first bird is black and the second is green.

Probability = ( No. of the desired outcome )/( Total outcomes)

The probability of selecting black bird is 3/14

The probability of selecting green bird is 6/14

Therefore, the combined probability that the first bird is black and the second is green is

= (3/14) * (6/14)

= 18/196

= 0.0918

To know more about Probability

https://brainly.com/question/11234923

#SPJ2

Answer:

$3600

Step-by-step explanation:

900/5=180

180*20=3600

Answer:

$3600

Step-by-step explanation:

Since they are being sold 5 at a time, divide 900 by 5 first to get 180. Then, since every 5 are worth 20$, multiply 20 by 180 to get $3600.

Answer:

Exactly 1 solution

Step-by-step explanation:

The equations are both in slope intercept form: y=mx+b We can use the y-intercept and slope to identify points on each line.

The line given by the first equation y= 1x+1 has a y-intercept of (0, 1) and a slope of 1, so another point on that line is (0 + 1, 1 + 1)= (1, 2).

Now we have two points to graph this line. In a similar manner, we will find that the line given by y=2x-5 passes through (0, -5) and (0 + 1, -5 + 2)= (1, -3). We can use those lines to graph the points.

Upon graphing our system of equations, we see that the lines intersect exactly once.

Since the lines intersect exactly once, the system has exactly one solution.

The system of equation has exactly one solution.

Simultaneous equations are any equations with the same number of unknowns that may be solved at the same time. The system of equations is a simultaneous equation.

Given, the system of equation;

y = x+1                { equation 1}

y = 2x-5              { equation 2}

Subtracting equation 2 to equation 1;

2x-x = 5+1

x = 6

And y = 7

The solution set is (6,7).

Therefore, the system of equation has unique solution.

To learn more about the system of equation;

brainly.com/question/13729904

#SPJ2

Answer:

All three sides and angles are different in measurement.

Step-by-step explanation:

Answer:

The mean is 77.

Step-by-step explanation:

Step one: add all the numbers

Step two: Divide the sum by the number of values you added

(example: 1,5,8,12,13. You would add them together, since we have 5 numbers, we will divide the sum by 5, then we have the mean)

462 divided by 6 is 77

Hope this helps!

Answer: 5km

Step-by-step explanation: 2cm=1 km

10cm divided by 2 is 5km

Answer:

44 servings are in the bottle

Answer:

44

Step-by-step explanation:

One trick for dividing fractions is:

1. Keep the first fraction. 22/1 divided by 1/2

2. Change division into multiplication. 22/1 times 1/2

3. Flip the second fraction. 22/1 times 2/1

22*2 is 44

1*1 is 1

The final answer should be 44/1

Answer:

Jake has 144 cookies.

Step-by-step explanation:
Let's say Clementine is x.

Clementine: x
Jake: 2x

Now, let's substitute x with 72 since the number is given.

This means that Jake has 72 * 2 cookies which are 144.

Answer:

translate down 6 units and left 3 units

Answer:

X=-1 or x=1/3

Step-by-step explanation:

That is the explanation in the photo

Answer:

Step-by-step explanation:

Given

y = x^2 + 10x + 21

Complete the square

y = x^2 + 10x + 21                           Put brackets around the first 2 terms

y = (x^2 + 10x) + 21                         Take 1/2(10) and square it. Add inside the brackets.

y = (x^2 + 10x + 5^2) + 21                 Subtract 5^2 after 21

y = (x^2 + 10x + 25) + 21 - 25          Make  (x^2 + 10x + 25) into a perfect square.

y = (x + 5)^2 - 4

Answer: (x + 5)^2 - 4

Answer:

$1,100

Step-by-step Explanation:

Dee Wallace's salary in 2006 = $61,000 Dee Wallace's salary in 2009 = $64,300

The salary increased in => 2009 - 2006 = 3yrs

The amount of salary increased = 64,300-61000 = $3,300

The annual change of salary = 3,300/3 = $1,100

Answer:

Therefore, area is 50.24

Step-by-step explanation:

⇒ Area = [tex] \sf \pi {r}^2 [/tex]

Radius = 4

⇒Area = 3.14 × 4²

⇒Area = 50.24

​

The answer:= 12π

​

I got this on khan academy.

Answer:

First, let's find how many students there are in total:

11 girls + 9 boys

= 20 students.

Out of those 20 students, we are trying to find the probability if Natalia will be selected first.

There is only one Natalia.

So, out of those students, the probability of selecting Natalia is a:

1/20 probability

(if wanted to convert into a percentage):

1/20 x 100

= 5% probability

Since we already know there are 28 given pens in total and 4 of them are red pens, there is a:

4/28 chance of selecting a red pen which can be simplified to a 1/7 probability.

(if wanted to convert into a percentage):

1/7 x 100

= 14% probability

Since we already know there are 24 jelly beans in total and 9 of them are cherry beans, there is a:

9/24 chance/probability of selecting a cherry jelly bean.

(if wanted to convert into a percentage):

9/24 x 100

= 37.5% probability

Let's first figure out how many marbles there are in total.

2 + 3 + 7

= 12 marbles in total.

Now let's exclude the marbles that are blue and yellow, leaving us with 7 orange marbles.

So the probability of selecting a marble that isn't blue/yellow is a:

7/12 probability

(if wanted to convert into a percentage)

7/12 x 100

= 58% probability

Answer:

B

Step-by-step explanation:

As stated in the problem x is the number of hours that he works.

x = 6y

All of the other answers establish y as 6, but B is the only answer that has 6 Infront of y (Pretty much multiplying it)

If you were to plug 6 into Y you would get 6(6)

6 times 6 equals thirty six.

x ≠ 36

Answer:

[tex]165[/tex].

Step-by-step explanation:

Since repetition isn't allowed, there would be [tex]11[/tex] choices for the first donut, [tex](11 - 1) = 10[/tex] choices for the second donut, and [tex](11 - 2) = 9[/tex] choices for the third donut. If the order in which donuts are placed in the bag matters, there would be [tex]11 \times 10 \times 9[/tex] unique ways to choose a bag of these donuts.

In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type [tex]3 \times 2 \times 1 = 6[/tex] times.

For example, if a bag includes donut of type [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex], the count [tex]11 \times 10 \times 9[/tex] would include the following [tex]3 \times 2 \times 1[/tex] arrangements:

Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count [tex]11 \times 10 \times 9[/tex] by [tex]3 \times 2 \times 1 = 6[/tex] to find the actual number of donut combinations:

[tex]\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].

Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of [tex]3[/tex] objects from a set of [tex]11[/tex] distinct objects:

[tex]\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].

Answer:

The last one {14,15,16,20,22,25, and 51}

Step-by-step explanation:

This set shows an outlier because 51 is a huge jump from 25 which causes it to be the outlier.

The data set {14,15,16,20,22,25,51} contains an outlier. So, option D is correct.

Option A:

{30, 31, 31, 32, 34, 37}

There is an even number of data points.

Diving into 2 groups- {30,31,31} and {32,34,37}

So, [tex]Q_1[/tex]=31 and [tex]Q_3[/tex]=34

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=34-31=3

Then 1.5×3=4.5

[tex]Q_1[/tex]-4.5=31-4.5=26.5

[tex]Q_3[/tex]+4.5=34+4.5=38.5

So, for this data set, there are no outliers either below or above.

Option B:

{11,12,12,12,13,13,14,14}

There is an even number of data points.

Diving into 2 groups- {11,12,12,12} and {13,13,14,14}

So, [tex]Q_1[/tex]=[tex]\frac{12+12}{2}=12[/tex] and [tex]Q_3[/tex]=[tex]\frac{13+14}{2}=13.5[/tex]

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=13.5-12=1.5

Then 1.5×1.5=2.25

[tex]Q_1[/tex]-2.25=12-2.25=9.75

[tex]Q_3[/tex]+2.25=13.5+2.25=15.75

So, for this data set, there are no outliers either below or above.

Option C:

{6.1,6.8,7.3,8,9.1,9.5}

There is an even number of data points.

Diving into 2 groups- {6.1,6.8,7.3} and {8,9.1,9.5}

So, [tex]Q_1[/tex]=6.8 and [tex]Q_3[/tex]=9.1

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=9.1-6.8=2.3

Then 1.5×2.3=3.45

[tex]Q_1[/tex]-3.45=6.8-3.45=3.35

[tex]Q_3[/tex]+3.45=9.1+3.45=12.55

So, for this data set, there are no outliers either below or above.

Option D:

{14,15,16,20,22,25,51}

There is an odd number of data points.

Diving into 2 groups- {14,15,16,20} and {20,22,25,51}

So, [tex]Q_1[/tex]=[tex]\frac{15+16}{2}=15.5[/tex] and [tex]Q_3[/tex]=[tex]\frac{22+25}{2}=23.5[/tex]

Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=23.5-15.5=8

Then 1.5×8=12

[tex]Q_1[/tex]-8=15.5-8=3.5

[tex]Q_3[/tex]+8=23.5+8=35.5

In this data set, some values are above the value of 35.5 (35.5<51).

So, this data set is said to have outliers.

Therefore, Option D is correct.

The required data set is {14,15,16,20,22,25,51}.

Learn more about outliers here:

https://brainly.com/question/24195133

#SPJ2

Answer:

lim x - 3 + f ( x ) - As 3 approaches 3 from the right, the value of f ( x ) approaches 0. lim x - 3 f ( x ) - Since the value of f ( x ) as x approaches 3 from the left does not equal the value as x approaches 3 from the right, this limit does not exist.

The type of toy the kids enjoyed the most is the doll.

The total number of kids evaluated = 80

The percentage of kids that like train = 30%

The percentage of kids that like doll = 70%

30% of 80 = 30/100×80

= 2400/100

= 24

70% of 80 = 70/100×80

= 5600/100

= 56

Therefore, the type of toy the kids enjoyed the most is the doll.

Learn more about percentage here:

https://brainly.com/question/24304697

#SPJ1

The volume of the rectangular prism is the number of cubes in it

The calculated volumes of the rectangular prisms are 32 and 36 unit cubes, respectively.

The volume of a rectangular prism is:

Volume = Length * Width * Height

From the question, we have the following prisms:

So, the volumes are:

Volume= 4 * 4 * 2

Volume= 32

Volume= 3 * 4 * 3

Volume= 36

Hence, the volumes of the rectangular prisms are 32 and 36 unit cubes, respectively.

Read more about volumes at:

https://brainly.com/question/1972490

Answer:

  f(3) = -20

Step-by-step explanation:

To find the value of a function, substitute the number for the variable and do the arithmetic.

  f(x) = -2x^2 +x -5 . . . . . . given

  f(3) = -2(3^2) +(3) -5 . . . . function value for x = 3

  f(3) = -2(9) +3 -5 = -18 +3 -5

  f(3) = -20

Answer:

0.065 units ³

Step-by-step explanation:

Volume of sphere = 4/3 π r³

=> 4/3 × 22/7 × 1/4 × 1/4 × 1/4

=> 0.065 units³

Answer:

[tex]\frac{1}{48}[/tex] π units³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex] πr³ ( r is the radius ) , then

V = [tex]\frac{4}{3}[/tex] π × ( [tex]\frac{1}{4}[/tex] )³

  = [tex]\frac{4}{3}[/tex] π × [tex]\frac{1}{64}[/tex] ( cancel 4 and 64 on numerator/ denominator by 4 )

  = [tex]\frac{1}{3}[/tex] π × [tex]\frac{1}{16}[/tex]

  = [tex]\frac{1}{48}[/tex] π units³