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Therefore , the solution of the given problem of probability comes out to be precisely five of them is black is 33.04 percent.

Mathematics' field of probability theory is concerned with estimating the possibility that a claim is true or that a certain event will take place. Any number between 0 and 1, where 1 denotes certainty and 0 typically conveys possibility, may be employed to denote chance. A probability diagram displays the possibility that a specific event will occur. The numerals 0 and 1, ratios that range from 0% to 100%.

Here,

The number of intended results divided by the total number of outcomes is the definition of probability.

It is not crucial which buttons are selected in what order. Therefore, to answer this question, we apply the combinations formula.

Combinations formula: The number of distinct combinations of x items from the a set of n items, denoted by nCr, is determined by the formula below.

The desired results are: D= 10C5 * 6C4 = 3780.

Five of a total of ten black buttons

4 of a total of 6 brown buttons are available.

Overall results

=> T = 16C9 = 11440

nine of the total of sixteen buttons.

Probability: => P=3780/11440 =>P=0.3304

Probability that precisely five of them is black is 33.04 percent.

Therefore , the solution of the given problem of probability comes out to be precisely five of them is black is 33.04 percent.

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The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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Let

R ----> resistance in ohms

L ---> the length of the wire in ft

D ---> the diameter of the wire in mm

In this problem, the equation is of the form

we have

L=432 ft

D=4 mm

R=1.26 ohms

so

Find out the value of K (constant of proportionality)

substitute the given values

Part 2

The formula is

For

R=1.41 ohms

D=5 mm

substitute in the formula above

Both the gongs will strike together at 3 pm.

Given,

Two gongs strike at intervals 90 and 60 minutes respectively.

Use LCM to find at what time they will strike together

Using prime factorization:

LCM of (60,90)=\(2^2*3^2*5=4*9*5=180\)

They will strike together after 180 minutes i.e. 3 hours

Hence, if they start simultaneously at 12 noon then they will strike together again at 3 pm

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30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

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Answer:

  37.4 ft^2

Step-by-step explanation:

The area of the parallelogram is given by ...

  A = bh = (8 ft)(7 ft) = 56 ft^2

The area of the right triangle is given by ...

  A = (1/2)bh = (1/2)(3 ft)(4 ft) = 6 ft^2

The area of the circle is given by ...

  A = πr^2 = π(2 ft)^2 = 4π ft^2 ≈ 12.6 ft^2

__

The shaded area is the area of the parallelogram less the areas of the unshaded triangle and circle:

  (56 ft^2) -(6 ft^2) -(12.6 ft^2) = 37.4 ft^2 . . . . shaded area

Answer:

560

Step-by-step explanation:

8000x.07

Answer:

B. xy(y - x) (y + x)

Step-by-step explanation:

Answer:

g(x) = 2x² - 10

Step-by-step explanation:

g(x) = f(x) - 2

so

g(x) = 2x² - 8 - 2

g(x) = 2x² - 10

This is a paraola: y = 1 is the directrix (it is perpendicular to the axis of symmetry); the focus is (0, 3)

The vertex of the parabola (which must also be on the parabola) is at (0, 1) because it is at a distance of 1 away; it is the nearest point to the point y = 1 & is at a distance 1 away from (0, 3)

The distance of the point (x,y) from the point (0,3) is gotten by using the formula for distance between two points (Pythagoras theorem):

Answer: She had 27.2% correct.

Step-by-step explanation: To find the percent, we can divide the part and whole then multiply the quotient by 100. After that we'll need to convert the percent to a decimal. In mathematical terms, the formula will be,

\(\frac{part}{whole}=quotient*100\)

40% will be the part and 68% will be the whole.

Step 1.

Convert 40 into a decimal by dividing it by 100.

40 ÷ 100 = 0.4

Step 2.

Multiply 0.4 by 68.

0.4 × 68 = 27.2

Hence, she had 27.2% correct.

The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

6/5

Step-by-step explanation:

The reciprocal of 5/6 means flip it

6/5

Answer:

6/5

Step-by-step explanation:

The reciprocal of a fraction is switching the numerator with denominator.

5/6 ⇒ 6/5

Answer:

Step-by-step explanation:

We would substitute in 3 for r and 5 for h

s = 2\(\pi\)(3 + 5)

s = 2\(\pi\)8

2 = 16\(\pi\)

Answer:

1 hour

Step-by-step explanation:

1/2 hour:1/2 pool

1/2x2 hour:1/2x2 pool

1 hour: 1pool

Answer:

448

Step-by-step explanation:

\((p1)(q1)^2=p2(q2)^2\\p1(2)^2=28(8)^2\\p1=(4)=28(64)\\4p1=1792/4\\p1=448\)

Value of \(\boldsymbol{pp}\) is \(\boldsymbol{\frac{112}{9}}\)

\(pp\) is inversely proportional to the square of \(qq\)

So,

\(\boldsymbol{pp=\frac{(qq)^2}{k}}\) where \(k\) is a constant.

Put \(pp=28,qq=3\)

\(28=\frac{3^2}{k}\\28=\frac{9}{k}\)

\(\boldsymbol{k=\frac{9}{28}}\)

So,

\(pp=\frac{28}{9}(qq)^2\)

Put \(qq=2\)

\(pp=\frac{28}{9}(2)^2\\ pp=\frac{112}{9}\)

So, value of \(\boldsymbol{pp}\) is \(\boldsymbol{\frac{112}{9}}\)

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Answer:

\(\frac{4}{5}\)

0.8

Step-by-step explanation:

Happy to help:)

Answer:

4x + (-2) = -2x+6

Step-by-step explanation:

im not gonna explain a diagram but it won't let me submit.

Answer:

Surface Area: 184cm^2

Volume: 120cm^2

Step-by-step explanation:

Answer:

I and II are the correct answer

pls follow me on brainly for further help ☺️

The statements that are true about congruent triangles :

I. Each of the three pairs of corresponding sides are of equal length.

II. Each of the three pairs of corresponding angles are of equal measure.

"Two triangles are congruent if and only if it obeys following two conditions.

- three corresponding sides are equal  

- all the three corresponding angles are equal in measure"

For given example,

Consider two triangles ABC and PQR.

If i) ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R

  ii) Also, AB = PQ, BC = QR and AC = PR

then ΔABC and ΔPQR are congruent triangles and it is written as ΔABC ≅ ΔPQR

Therefore, the statements that are true about congruent triangles :

I. Each of the three pairs of corresponding sides are of equal length.

II. Each of the three pairs of corresponding angles are of equal measure.

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Answer:

25000

Step-by-step explanation:

The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Answer:

draw all 100 of two colors to be assured

Step-by-step explanation:

if wrong plz tell me i can help on other things if wrong

Answer:

132.12

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the value of,

\(\longrightarrow \cos\theta=\dfrac{3}{\sqrt{22}} \\\)

And we know that cosine is the ratio of base and hypotenuse. Therefore,

\(\longrightarrow \cos\theta =\dfrac{b}{h} \\\)

So we can also say that,

\(\longrightarrow \cos\theta = \dfrac{b}{h}=\dfrac{3}{\sqrt{22}}\\\)

Let us take the given ratio to be 3x:√22x . Now we may find out the value of perpendicular using Pythagoras theorem . The Pythagoras theorem is ,

Pythagoras theorem:-

Mathematically,

\(\longrightarrow \boxed{ \boldsymbol{p^2+b^2=h^2}} \\\)

where the symbols have their usual meaning.

On substituting the respective values, we have;

\(\longrightarrow p^2+(3x)^2=(\sqrt{22}x)^2 \\\)

\(\longrightarrow p^2 = 22x^2-9x^2\\\)

\(\longrightarrow p^2=13x^2 \\\)

\(\longrightarrow \boldsymbol{ p = \sqrt{13}x} \\\)

Now again , we know that, tangent is defined as the ratio of perpendicular and base. Therefore,

\(\longrightarrow \tan\theta = \dfrac{p}{b} \\\)

\(\longrightarrow \tan\theta = \dfrac{\sqrt{13}x}{3x}\\\)

\(\longrightarrow \boldsymbol{ \tan\theta = \dfrac{\sqrt{13}}{3}}\\\)

Now we may use a identity which is ,

\(\longrightarrow\boxed{ \boldsymbol{ \tan (2x)= \dfrac{2\tan x}{1-\tan^2 x}}}\\\)

On substituting the respective values, we have;

\(\longrightarrow \tan2\theta = \dfrac{ 2\tan\theta}{1- \tan^2\theta}\\\)

\(\longrightarrow \tan2\theta = \dfrac{2\bigg(\dfrac{\sqrt{13}}{3}\bigg)}{1-\bigg(\dfrac{\sqrt{13}}{3}\bigg)^2 } \\\)

\(\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{1-\dfrac{13}{9}} \\\)

\(\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{9-13}{9}} \\\)

\(\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{-4}{9}} \\\)

\(\longrightarrow \tan2\theta = -\dfrac{2\sqrt{13}\cdot 9}{3\cdot 4 } \\\)

\(\longrightarrow \boxed{\boldsymbol{ \tan2\theta = -\dfrac{3\sqrt{13}}{2}}} \\\)

This is the required answer .

The first step to be performed in the following mathematical expression, Σx² is; Square each score

In statistic, we know that;

Mean = Σx/n

where

Σx is sum of all data

n is the sample size of the data

Now, there are other expressions such as mean deviation, variation, standard deviation e.t.c

However, when we see the expression Σx², it means the sum of the square of each score. Thus, the first step to get it is to square all the scores.

Thus, we conclude that the first step to be performed in the following mathematical expression, Σx² is; Square the scores

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Answer:

160mm2 is the correct answer

Step-by-step explanation: