you run an experiment in which you flip 3 coins, and each one lands heads or tails. your sample space can be written: {hhh, hht, hth, htt, thh, tht, tth, ttt}. assume all outcomes have equal probability.

The missing side of problems using sine and cosine is 9.

The formula for calculating the triangle's side is: c = [a2 + b2 - 2ab cos C] where the triangle's sides are a, b, and c.

According to the Cosine Rule, the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them. Law of cosines and Cosine Formula are other names for the cosine rule.

a2 = b2 + c2 – 2bc cos ∠x

b2 = a2 + c2 – 2ac cos ∠y

c2 = a2 + b2 – 2ab cos ∠z

6^2 + 7^2 = X

x = 9^2

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The marks of the pupil who was recently added is 3.

Given is that overall mark for english test for 15 pupils is 82. If one more pupil being added, the overall mark become 85.

For 15 peoples, the overall mark for english is 82. When one more person is added, the overall mark become 85. Then, the marks of the pupil who recently added was -

85 - 82

3

Therefore, the marks of the pupil who was recently added is 3.

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The Mean is 350 and Median is 383.3

The first step in calculating the mean of grouped data is to establish the midpoint (also known as a class mark) of each interval or class. The frequencies of the relevant classes must then be multiplied by these midpoints. The mean value is determined by dividing the total number of values by the sum of the products.

Given:

 CI                  F        x        d       Fd        cf

100 - 200 2 150     -2       4   2  

200 - 300 2 250     -1       -2   4  

300 - 400 3 350      0       0   7  

400 - 500 6 450       1       6   13

                     n= 13                              

Mean = 350+ 0/13 x 100

Mean = 350+0

Mean = 350

Hence, the Mean is 350 and Median is 383.3

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The numeric value of the function f(x) = 4x² + 2x + 2 at x = x + 2 is given as follows:

f(x + 2) = 4x² + 20x + 22.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 4x² + 2x + 2

To obtain the numeric value at x = x + 2, we replace the two instances of x by x + 2, hence:

f(x + 2) = 4(x + 2)²  + 2(x + 2) + 2

f(x + 2) = 4(x² + 4x + 4) + 4x + 4 + 2

f(x + 2) = 4x² + 16x + 16 + 4x + 6

f(x + 2) = 4x² + 20x + 22.

The problem asks for the numeric value of the function f(x) = 4x² + 2x + 2 at x = x + 2.

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The value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.

Let us solve this problem step by step.

For the given equation: y' + 2y = e^{-x}

We have the solution as: y = ce^{-2x} + e^{-x}

We have to find the value of c for which the solution satisfies the initial condition y(2)= 9.

Substituting x = 2 in the above equation, we get:

9 = c + e^{-2}.

Therefore, we can solve for c as:

c = 9 - e^{-2}

Hence, the value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.

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The inequalities that are equivalent to the inequality $x<3$ are:

$x<3-b$

$x-b<3$

Note that $x-b-3.0$ and $x-b-3<0$ are not equivalent to $x<3$

and -3 is not an inequality.

Answer:

you have to do this by formula in the copy try this by l×b or b×h

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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The range of the function shown on the graph is, y ≥ 2.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The graph of function is shown in figure.

Now, We know that;

The range is the set of possible outputs values, which are shown on the y - axis.

Hence, By the graph;

The range of function is,

⇒ y ≥ 2

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Statistic is a measure that describes a characteristic of the whole population.

Estimate  is a measure that describes a sample.

A statistic is a measure of a characteristic of an entire population. This means that it is a measure that describes the entire population, such as the average age, number of people, etc.

An estimate is a measure of a characteristic of a sample. This means that it is a measure that describes a portion of the population, such as the average age of a group of people, number of people in a certain area, etc.

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The extent of a square prism is given by V = l × w × h, so that you can quantity without the hollow would be 18×22×77=30,492cm³

Determine the most intensity to which the container can be packed with water so that when the water freezes, the ice does not move above the top of the container.?

The surface region is:

A = 2 × (l × w + w × h + h × l)

= 2×(18×22+22×77+77×18)

=4862cm³

Now cut a cylindrical hollow through the middle … however in what route??? because the orientation of the hole isn't given, the valuable axis of the cylindrical hole might be parallel to any individual of the three most important axes of the square prism!

[Note: a ‘round’ hole in any other direction – not parallel to a major axis – would have either elliptical ends, or (worse) cut through vertices or even corners.]

Therefore, The extent of a square prism is given by V = l × w × h, so that you can quantity without the hollow would be 18×22×77=30,492cm³

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The carrying capacity K for this equation be 33.33.

To determine how many people an ecosystem can support, carrying capacity is crucial. Without significant setbacks from environmental degradation, this is essential for sustainable growth.

The greatest population that may be supported in a given environment under a variety of restrictions is known as the carrying capacity. In the population vs. time graph, it is at the value K that the graph asymptotically approaches the graph y=K.

The population growth model is given by [tex]$\frac{d P}{d t}=0.01 P-0.0003 P^2$[/tex]

The population model can be re-written as:

[tex]$$\begin{aligned}\frac{d P}{d t} & =0.01 P-0.0003 P^2 \\& =0.01 P(1-0.03 P) \\& =\frac{1}{100} P\left(1-\frac{3 P}{100}\right)\end{aligned}$$[/tex]

Carrying capacity of the equation be

[tex]$$\begin{aligned}K & =\frac{P}{1-\frac{1}{r P} \frac{d P}{d t}} \\& =\frac{P}{1-\frac{100}{P} \cdot \frac{P}{100}\left(1-\frac{3 P}{100}\right)} \\& =\frac{P}{\frac{3 P}{100}} \\& =\frac{100}{3}=33.33\end{aligned}$$[/tex]

The complete question is:

Suppose that a population of bacteria grows according to the logistic differential equation [tex]$\mathrm{dP} / \mathrm{dt}=0.01 \mathrm{P}-0.0003 \mathrm{P}^2$[/tex] where P is the population measured in thousands and t is time measured in days.

a) Calculate the carrying capacity K for this equation? (You must justify your answer by showing how you derived K.)

b) What does the carrying capacity represent?

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Answer:

A = 44º

[tex]b \approx 28.99[/tex]

[tex]c \approx 40.31[/tex]

Step-by-step explanation:

In this problem we are tasked with "solving the triangle," which means we need to solve for each of the triangle's non-given dimensions.

We can first solve for angle A, since we are given the other two interior angles of the triangle (90º and 46º), and we know that the measures of the interior angles of a triangle add to 180º.

A + 90º + 46º = 180º

A = 180º - 90º - 46º

A = 44º

Now that we have angle A, we can use the Law of Sines to solve for side length b.

[tex]\dfrac{a}{\sin(A)} = \dfrac{b}{\sin(B)}[/tex]

[tex]\dfrac{28}{\sin(44\textdegree)} = \dfrac{b}{\sin(46\textdegree)}[/tex]

[tex]b = \dfrac{28\sin(46\textdegree)}{\sin(44\textdegree)}[/tex]

[tex]b \approx 28.99[/tex]

Finally, we can solve for c using the Pythagorean Theorem.

a² + b² = c²

28² + 28.99² ≈ c²

[tex]c \approx \sqrt{1624.70}[/tex]

[tex]c \approx 40.31[/tex]

Answer: five and six hundred-twenty-five

Step-by-step explanation:

the decimal point represents the and, and all you need to do is write out the numbers, then you are good to go

Answer:

15

Step-by-step explanation:

35/k=7/3

7k=35*3

7k=105

k=15

Answer:

5.8%

Step-by-step explanation:

To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.

First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.

So the amount invested in mutual funds is 40/100 * $100 = $40

The amount invested in real estate is 40/100 * $100 = $40

The amount invested in stocks is 20/100 * $100 = $20

Then we can calculate the growth of each investment using the percentages provided:

The growth of mutual funds is 2/100 * $40 = $0.80

The growth of real estate is 7/100 * $40 = $2.80

The growth of stocks is 11/100 * $20 = $2.20

Now we can add up the growth of each investment and divide it by the total investment to find the average growth:

($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%

So the average growth on Alexandra's total investment is 5.8%.

Answer:

  f(x) = (x +6)(x -5)  or  f(x) = x² +x -30

Step-by-step explanation:

You want a quadratic function whose zeros are -6 and +5.

If p is a zero of the polynomial f(x), then (x-p) is a factor. The two given zeros meant that the factors are ...

  f(x) = (x -(-6))·(x -5)

  f(x) = (x +6)(x -5) . . . . . . . . simplify a bit

This can be put in standard form by multiplying the factors:

  f(x) = x(x -5) +6(x -5) = x² -5x +6x -30

  f(x) = x² +x -30 . . . . . . . . simplified quadratic function

The quadratic function of the zeros is f(x) = [tex]x^2+x-30[/tex].

What is quadratic function?

A polynomial function that has one or more variables and a variable having a maximum exponent of two is said to be quadratic. A polynomial of degree 2 is referred to as such because the greatest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. It is a mathematical function.

Here the zeros of the function is -6 and 5.

We know that if zeros of the function is a then the factor is (x-a).

Then,

=> f(x) = (x-(-6))(x-5)

=> f(x) = (x+6)(x-5)

=> f(x) = [tex]x^2+6x-5x-30[/tex]

=> f(x) = [tex]x^2+x-30[/tex]

Hence the quadradic function is f(x) = [tex]x^2+x-30[/tex].

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To find the intersection point of Runways AB and CD, we need to find the point where the two lines intersect. The two lines can be described as follows:

What exactly is a math graph?

A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.

Line AB: y = mx + b, where m = (9-(-24))/(6-(-5)) = 33/11 and b = -24 - (33/11)(-5) = -24 + 165/11 = 141/11

Line CD: 2x + y - 11 = 0

Now we can substitute the equation of the line AB into the equation of the line CD:

2x + (33/11)x + 141/11 -11 = 0

Combining like terms we get:

(33/11+2)x + (141/11 - 11) = 0

35/11x + 130/11 = 0

35/11x = -130/11

x = -130/35 = -26/7

Now we can use this value of x to find the corresponding y value using the equation of the line AB

y = (33/11)x + 141/11 = (33/11)(-26/7) + 141/11 = -86/11

So the point of intersection of the two lines is (-26/7, -86/11)

So the intersection point of Runways AB and CD is (-26/7, -86/11)

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The explicit formula of the arithmetic sequence in this problem is given as follows:

[tex]a_n = 40 - 7n[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The explicit formula of an arithmetic sequence is given as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

From the recursive formula, each term is the previous term subtracted by 7, hence the common difference is given as follows:

d = 7.

The first term of the sequence is given as follows:

[tex]a_1 = 33[/tex]

Hence the explicit formula is obtained as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

[tex]a_n = 33 - 7(n - 1)[/tex]

[tex]a_n = 40 - 7n[/tex]

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The linear equations in slope-intercept form are  y=2x+3 ,  y=-1x-2 , y=-3x+4 and y = 3x .

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

We have to write linear equations in slope intercept form.

So,

An equation in the slope-intercept form is written as

y = mx + b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

So, from given graphs we can say that

y - 3 = 2x

y=2x+3

y + 2 = -x

y=-1x-2

y - 4 = -3x

y=-3x+4

y - 0 = 3x

y=3x+0

y = 3x

Therefore, The linear equations in slope-intercept form are  y=2x+3 ,  y=-1x-2 , y=-3x+4 and y = 3x .

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Answer:

x=3

Step-by-step explanation:

-4(x-2)=2-2x

-4x+8=2-2x

-4x+8=-2x+2

-4x=-2x+2-8

-4x=2x-6

-2x=-6

x=3

Let's solve your equation step-by-step.

-4(x-2)=2-2x

Step 1: Simplify both sides of the

equation.

-4(x-2)=2-2x

Simplify:

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

(Distribute)

-4x+8=2+ -2x

-4x+8=-2x+2

Step 2: Add 2x to both sides.

-4x+8 + 2x = -2x+2+2x

-2x+8=2

Step 3: Subtract 8 from both sides.

-2x+8-82-8

-2x=-6

Step 4: Divide both sides by -2.

-2x -6 = -2 -2

x=3

Answer:

[tex]x \approx 31.6\textdegree[/tex]

Step-by-step explanation:

Apply the Law of Sines.

[tex]\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b}[/tex]

↓ plug in given side lengths and angle measures

[tex]\dfrac{\sin(74\textdegree)}{22} = \dfrac{\sin(x)}{12}[/tex]

↓ multiply both sides by 12

[tex]\dfrac{12\sin(74\textdegree)}{22} = \sin(x)[/tex]

↓ take the inverse sine of both sides

[tex]\sin^{-1}\left(\dfrac{6\sin(74\textdegree)}{11}\right) = x[/tex]

↓ evaluate using a calculator and round to tenths place

[tex]x \approx 31.6\textdegree[/tex]

Answer:

44

Step-by-step explanation:

Because of similar triangles we have

VN/UN = VL/UM

11/8 = VL/24

Cross multiply.

8VL = 11 × 24

VL = 11 × 3

VL = 33

LN = VL + VN

LN = 33 + 11

LN = 44

According to mathematics, a regular hexagon's area A is  288 sq units option -A is correct answer.

How to Locate a Hexagon's Area

A regular hexagon's side length can be determined in step 1.

Step 2: Calculate the area using the formula for the area of a hexagon (3√3 s²)/2, where s is the length of the hexagon's sides.

A regular hexagon whose side length is 8 in.

and the apothem is 12 in.

The equation for the area,

A=(3√3)/2 × a²

Therefore

A = 6×(0.5×8×12)

A = 288 sq units

In conclusion, a regular hexagon's surface area A is 288 square feet.

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Answer:

Your answer is A) [tex]288in^{2}[/tex]

Step-by-step explanation:

To calculate y, we use the sum() function with an argument of x < 5 to count the number of entries in x that are strictly less than 5. To calculate z, we use the sum() function with an argument of (x > -5) & (x < 5) to count the number of entries in x that are both greater than -5 and less than 5.

y = sum(x < 5)

z = sum((x > -5) & (x < 5))

y = sum(x < 5)

 = sum(TRUE, FALSE, FALSE, TRUE, FALSE, FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, FALSE)

 = 5

z = sum((x > -5) & (x < 5))

 = sum(TRUE, FALSE, FALSE, TRUE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, TRUE, FALSE)

 = 4

The first variable, y, is the number of entries of x that are strictly less than 5. To calculate y, we can use the sum() function with an argument of x < 5. This will count the number of entries in x that are less than 5. For example, if

x <- c(-5, 7, 9, 3, 14, 9, 5, 10, 2, -2, 0, 12), then y will be equal to 6 because there are 6 entries in x that are strictly less than 5.

The second variable, z, is the number of entries of x that are strictly between -5 and 5. To calculate z, we can use the sum() function with an argument of (x > -5) & (x < 5). This will count the number of entries in x that are both greater than -5 and less than 5. For our example, z will be equal to 4 because there are 4 entries in x that are strictly between -5 and 5.

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Answer:

15,910

Step-by-step explanation:

(390*26)+5770=15910

On solving the provided question, we cans ay that in the equation 390t + 5770, In the year 2021, the total average credit card debt for a U.S.

household will be 5,910 dollars.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

in the equation 390t + 5770

t = 26

In the year 2021, the total average credit card debt for a U.S.

household will be 5,910 dollars.

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The number of games played is 6 and the number of rides is 2.

Here it is given that the number of games played was 3 times the number of rides. So, by this, we get the value of both is the ratio.

That is $15,

number of games played: number of rides = 3: 1

Let x be the common ratio. So, we have

Number of games played = 3x, and number of rides = x

It is given that the cost of each game is $1.50 and cost of each ride is $3 and the total cost is $15.

By this, we get an equation,

1.50 × 3x + 3 × x = 15

4.5x + 3x = 15

7.5x = 15

x = 2

Therefore the number of games= 3x = 3×2 = 6 and the number of rides = x = 2.

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Answer: x = 57°

Step-by-step explanation:

63 + x + 2x + 183 - x = 360 (exterior ∡s of a polygon adds up to 360°)

                  x + 2x - x = 360 - 63 - 183

                             2x = 114

                                x = 57°

The value of x in the given diagram is 57° .

We know that the sum of internal angles of a triangle is equal to 180°.

But here we are given the external angles of the triangle:

Angle 1 : 63 + x

Angle 2 : 2x

Angle 3 : 183 - x

Now , changing the given angles into internal angles , we get:

Angle 1 : 180 - ( 63 + x ) = 117 - x

Angle 2 : 180 -2x

Angle 3: 180 -(183-x) = x-3

Now,

(117-x) + (180 -2x) + (x-3) =180

114 - 2x = 180

x = 114/2=57

Therefore, The value of x in the given diagram is 57° .

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Therefore , the solution of the given problem of expression comes out to be 4x -2y is the sum of given expression.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

expressions are : 3x,x,2y and y-5y

To find the sum of the expression ,

We add them:

=> 3x+ x+2y+y-5y

=> 4x+3y-5y

=>4x -2y

Therefore , the solution of the given problem of expression comes out to be 4x -2y is the sum of given expression.

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Answer:

Answer in attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note that t(u) is different from t·u, t(u) is multiplying vectors together, while t·u is the dot product of 2 vectors.