There are 9 five-minute segments in_____________________.

The largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].

It is given to us that -

The rectangle has the base on x-axis

The rectangle has its upper vertices on the curve [tex]y = 8 -x^{2}[/tex] ----- (1)

We have to find out the largest possible area for the rectangle with given specifications.

We know that the area of a rectangle can be represented as -

[tex]A = xy[/tex] ---- (2)

where,

[tex]x =[/tex] length of the base of the rectangle

[tex]y =[/tex] vertices of the curve = width of the rectangle

Since it is given to us that the rectangle has it base on the x-axis, therefore the length of the base of the rectangle = [tex]2x[/tex] ---- (3)

Substituting equations (1) and (3) in equation (2), we have

[tex]A = xy\\= > A = (2x)(8-x^{2}) \\= > A = 16x-2x^{3}[/tex]----- (4)

For the largest possible area, we know that -

[tex]\frac{dA}{dx}=0[/tex] ---- (5)

Substituting equation (4) in equation (5), we have

[tex]\frac{dA}{dx}=0\\= > \frac{d}{dx}(16x-2x^{3}) =0\\ = > \frac{d}{dx}(16x)-\frac{d}{dx}(2x^{3} )=0\\= > 16-6x^{2} =0\\= > 6x^{2} =16\\= > x^{2} =\frac{16}{6} \\= > x=\frac{4}{\sqrt{6} }[/tex]------ (6)

To find out the largest possible area, we have to put the value of x from equation (6) in the area of the rectangle in equation (4). So, we have

[tex]A = 16x-2x^{3}\\= > A = (16*\frac{4}{\sqrt{6} }) -[2(\frac{4}{\sqrt{6} } )^{3} ]\\= > A = \frac{16*4}{\sqrt{6} } -\frac{2*4*4*4}{\sqrt{6}*\sqrt{6}*\sqrt{6} } \\= > A = \frac{64\sqrt{6} }{9}[/tex]

Therefore, the largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].

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The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.

What is cost?

A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.

Let, a game consists of drawing three cards at random from a deck of playing cards.

You win $3 for each red card that is drawn.

It costs $2 to play.

After deducting the cost of pay the amount will start from -$2.

For first red card drawn you win $3.

So, the amount becomes, -$2 + $3 = $1.

For second red card drawn you again win $3.

So, the next amount becomes $1 + $3 = $4.

For third red card drawn the amount becomes,

$4 + $3 = $7.

Hence, the sample space S for the net amount you win is

S = {-$2, $1, $4, $7}.

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Answer:

376

Step-by-step explanation:

The domain of the function is{x | −4 < x < 6}.

A function's domain is the set of all potential inputs.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

What is range?

The statistical difference between the highest and lowest values for a given data collection is called the range.

For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. It is possible to think of the range as the distance between the highest and lowest observation as a result.

the domain of the function is{x | −4 < x < 6} because

there is no restriction on x domain and range both are the set of real numbers.

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The average rate of change in median age per year from 1950 to 1990 is 0.085 years of age per year.

The median is the mid-value in a set of data. to find it we first arrange the data set from smallest to largest, then pick the middle value which divides the data set in half.

From the given table,

The median age at the time of the first marriage in 1950 = 22.8 years,

While the median age in 1990 = 26.1 years,

Hence, the average rate of change in median age per year from 1950 to 1990

= (22.8-26.1)/(1950-1990)

= (-3.3)/(-40)

= 0.0825 years of age per year.

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The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.

What is linear equation?

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

Given, the equation y = 2x -4

Which is linear function and have y a dependent variable and x be the independent variable,

because value of y depends upon the value of x.

Hence, a is the correct answer.

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Answer: A

Step-by-step explanation: Trust me

The equation of the line in slope-intercept form is: y = 5/2x.

If the value of the slope of the line is represented by m, and y-intercept of the line is b, therefore, the equation of the line in slope-intercept form can be written as: y = mx + b.

The slope of the line (m) = rise/run = 5/2

m = 5/2

The line intercepts the y-axis at 0. The y-intercept therefore is b = 0.

To write the equation of the line, substitute m = 5/2 and b = 0 into y = mx + b:

y = 5/2x + 0

y = 5/2x

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The solution to the equation represented by One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x is (b) x = negative 4

The statement in the question is given as

One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x

Mathematically, this statement can be represented as

1/4x - 1/8 = 7/8 + 1/2x

Multiply through the equation by 8

So, we have:

2x - 1 = 7 + 4x

Collect the like terms

4x - 2x = -1 - 7

Evaluate the like terms

2x = -8

Divide both sides by 2

x = -4

Hence, the solution is -4

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Time intervals = 14/7 = 2

Final Amount = 40(1/2)² = 10

Answer:

4.33

Step-by-step explanation:

See picture attachment.

The weighted average of points is M = 5.4

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the weighted average be represented as M

Now , the value of M is

The points A, B, and C, shown on the number line, have weights 1, 1,

and 3 respectively.

A = 2 , B = 4 and C = 7

To find the weighted average of points A, B, and C with the given weights, we need to use the formula:

The weighted average M = (weight of A * value of A + weight of B * value of B + weight of C * value of C) / (total weight)

Plugging in the given values, we get:

The weighted average M = (1 * 2 + 1 * 4 + 3 * 7) / (1 + 1 + 3)

The weighted average M = (2 + 4 + 21) / 5

The weighted average M = 27 / 5

The weighted average M = 5.4 (rounded to one decimal place)

Hence , the weighted average of points A, B, and C with the given weights is 5.4

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Answer:

one number is 8 and other is 4

Step-by-step explanation:

So we can say x+y=12.

And 3x+5y=44

For x+y=12, we can subtract x to get: y=12-x

Plug that in to get 3x+5(12-x)=44

3x+60-5x=44

Subtract 44: -2x+16=0

2x=16

x=8

12-8=4.

The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides

A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.

The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;

S = 180·(n - 2)

Where;

n = The number of sides the polygon has

The sum of the interior angles in the specified polygon = 1,260°

The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;

When S = 1.260°, we get;

1,260 = 180·(n - 2)

Which indicates;

n - 2 = 1,260 ÷ 180 = 7

Therefore; n - 2 + 2 = 7 + 2 = 9

n = 9

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Answer:

23

Step-by-step explanation:

Taking an algebraic approach

let the number be n, then (n - 17) is 17 subtracted from the number, and -2(n - 17) = - 12 ( divide both sides by - 2 )n - 17 = 6 ( add 17 to both sides ) which is n=23

Using PEMDAS to solve the mathematical expression, the result is -637.947

The mathematical operation refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.

In this kind of problem, we need to use the PEDMAS rule which is

Parenthesis, Exponents, Division, Multiplication, Addition and Subtraction.

The order in which this must be prioritized is from parenthesis and the least is subtraction.

Applying PEMDAS to this mathematical operation, we would have

19.42 - 34.89(19.3) + 10.23 + 5.78

Using a calculator which follows this rule, we would have;

19.42 - 34.89(19.3) + 10.23 + 5.78 = -637.947

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Probability of people less than 19 year old = 0.5343

Probability of people greater than 10 year old = 0.8116

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.

People under age 10 = 253

People between the age of 10-18 = 466

People between the age of 19-30 = 174

People above the age of 30 = 450

Total no. of people = 1343

a) people less than 19 years old = 253+466 = 719

probability of people<19 year old = P(age<19) = 719/1343 = 0.5354

b) people of age greater than 10 = 466+174+450 = 1090

probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116

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Answer:

75÷50

Step-by-step explanation:

1.5 or 3÷2 is the correct answer

Answer:

P = 16w - 4

Step-by-step explanation:

P = (5w-2 + 3w)2

P = (8w-2)2

P = 16w - 4

Answer: $21.33

Step-by-step explanation: 50 - 28.67 = 21.33

The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.

We have,

i] f(x) = 8x  and
g(x) = (2x+8)

(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16

(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) =  8x.
(f ∘ g) (x) = 8(2x+8)  
= 16x + 64

ii]  f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2  
= 6x - 28

g [f(3)] = (6x + 2 ) - 5
= -30x - 10

Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

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The initial value of the function obtained from the table of values for the linear function is; 7

A linear function is a function that when plotted, produces a straight line on the coordinate plane.

The initial value of a function is the value of the function, when the input value is 0.

The initial value indicates the point where the graph intersects the y-axis, which is the y-intercept. It the point the graph enters quadrant I, where the x and y-values are positive.

From the initial value, and to the right of the x-axis, the input variable (x) is positive, such that the values of the function for natural value input, such as time can be found, and the initial value then represents the start of the measurement of the output values of the function.

The data in the table indicates that when the input variable x = 0, the output variable, y = 7

Therefore:

Which indicates that at the initial point of the positive value inputs of the function, the output is 7

Question details are:

Please find the table of the linear function, which is to be examined, presented as follows:

[tex]\begin{array}{|c|c|}In put (x) & Out put (y)\\-3 &14 \\0 & 7 \\3 & 0 \\6 & -7 \\\end{vmatrix}[/tex]

The initial value of the function that the above table represents is required.

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Answer:19/12 or 1 7/12

Step-by-step explanation:

51/12 - 32/12=19/12

1 7/12

Answer:

1 7/12

Step-by-step explanation:

4 3/12 - 2 8/12

First, subtract the integers:

2 3/12 - 8/12

Since 3/12 cannot subtract 8/12, we can take 1 from the 2 and turn it to 12/12 to add to our 3/12:

1 15/12 - 8/12

Simplify:

1 7/12

The volume of this cone is 83.7 cubic meters and the given height 5m then diameter 3.99 m.

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).

Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

Given that ;

volume of cone = [tex]\pi r^{2} \frac{h}{3}[/tex]

volume of cone = 83.7 [tex]m^3[/tex]

height = 5m

to find diameter :
[tex]d = \sqrt{\frac{3\times V}{\pi \times h} }[/tex]

[tex]d=\sqrt{\frac{3\times 83.7}{3.14\times 5} }[/tex]

[tex]d = \sqrt{\frac{251.1}{15.7} }[/tex]

[tex]d = \sqrt{15.993}[/tex]

d = 3.99 m

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The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.

To find equivalent expression we can simplify the expression.

Therefore,

(6x² - 9x) - (2x -3)

open the brackets

6x² - 9x - 2x + 3

combine like terms

Therefore,

(6x² - 9x) - (2x -3) = 6x² - 11x + 3

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The rational equation with the desired asymptotes and intercepts is given by: f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

Vertical asymptotes are x values that are outside the domain and, in a fraction, are the denominator zeroes.

As long as this value differs from infinity, the horizontal asymptote is the value of f(x) as x approaches infinity.

The vertical asymptotes are related to the denominator roots, so:

f(x) = a / ( x + 5)( x + 2 )

f(x) = a / ( x² + 7x + 10 )

The x-intercepts are related to the function's numerator, so:

f(x) = [a( x + 1 )( x - 6) ] / [x² + 7x  + 10 ]

The y-intercept is to find a, hence, when x = 0, y = 5, thus:

4 = a(-6)/ 10

a = (-40/6)

a = -20 / 3

The equation will be written as,

f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

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X=pi/2 only in the interval 0 to 4 . We have the maximum value of f(x) = sinx = 1

What is  function interval ?

If the value of the function f (x) grows with an increase in the value of x, the function interval is said to be positive.

                         The function interval, on the other hand, is said to be negative if the value of the function f (x) decreases as the value of x increases.

First of all to apply the extreme value theorem function must be countions at the interval 0 to 4.

F(x)=(x^2-16)/(x^2+x-20) is countinious int the given interval .

Now we find

F'(x)= d(F(x))/dx=1/(x+5)^2 so here we don't have in critical point therefore this choice is incorrect

Similarly if we take

F(x)= sinx

F'(x) = cosx

For critical point ,

Cosx =0

X=pi/2 only in the interval 0 to 4

And this point we have the maximum value of f(x) = sinx = 1

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The maximum average BAC during the first 6 hours is about 0.177 mg/ml.

What is average ?

The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.                                  

                                          When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

The maximum is found where the derivative of C(t) is zero.

 dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0

Solving for t gives ...

 t = 1/2.802

So, the maximum C(t) is ...

 C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL

The maximum average BAC during the first 6 hours is about 0.177 mg/mL.

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Reject H0 if the test statistic is less than  -1.321  or greater than  1.321  .

What is a hypothesis simple definition?

A tested assertion regarding the relationship between two or more variables .

                  a theory put out to explain an observed occurrence is referred to as a hypothesis (plural: hypotheses) in a scientific context.      

Reject H0 if the test statistic is less than  -1.321  or greater than  1.321  .

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The result of the following Boolean expression, if x equals 5, y equals 3, and z equals 8 not (x < y or z > x) and y < z will be false.

It is defined as the combination of constants and variables with mathematical operators.

Finally, keep in mind that two negatives add up to a positive. This would print that the compound expression is False because it contains one negative The first step, and one positive expression 2-4 as a whole.

Expression 1 is False because (x=5) (y=3)

The value must now be reversed according to the first step. the current value is true (-) False

Both sub-expressions 1 and 2) must be true for the AND= operator #3. The sub-expression 2 in (y=3) (z=8) is true.

Thus, the result of the following Boolean expression, if x equals 5, y equals 3, and z equals 8 not (x < y or z > x) and y < z will be false.

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50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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