is the statement a valid null hypothesis?

Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

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 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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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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The perimeter of the quadrilateral is 46 units, so the correct option is d.

The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.

Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:

L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)

The length between the first two vertices: (−6, −2), (0, −10)

L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10

The length between the second two vertices:  (0, −10), (5, 2)

L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13

The length between the third two vertices:  (5, 2), (−1, 10)

L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10

The length between the fourth two vertices:  (−1, 10), (−6, −2)

L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13

Then the perimeter is:

P = 10 + 13 + 10 + 13 = 46

The correct option is D.

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The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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The best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

In the given question,

The best fitting line is one where the intercept of the regression equation:

As we know that;

The slope of the line of best fit is the coefficient in a simple regression with a single independent variable. The slope is a mixture of the two coefficients in this example and in any regression with two independent variables. The y-intercept of the line of best fit is constant C.

So, the best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

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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:

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.

[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]

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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According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

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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 perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, perimeter =2(x-2+5)

= 2(x+3)

= 2x+6 units

Area of a rectangle =length × width

= (x-2) × 5

= 5x-10 square units

Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

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The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(x) = 4x² - 1. and g(x) = 2x - 1.

Now, g(f(2)) is the output of f(2) is the input of g(x).

∴ f(2) = 4(2)² - 1.

f(2) = 15.

Now, g(f(2)) = 2(15) - 1.

g(f(2)) = 29.

Also given,

f(x) = x² and g(x) = x - 1.

Now, 2.f(g(x)).

2.f(g(x)) = 2.f(x- 1).

2.f(g(x)) = 2(x - 1)².

2.f(g(x)) = 2(x² - 2x + 1).

2.f(g(x)) = 2x² - 4x + 2.

2.f(g(x)) = 2x² - 2x - 2x + 2.

2.f(g(x)) = 2x(x - 1) - 2(x - 1).

2.f(g(x)) = (x - 1)(2x - 2).

There is no restriction to the domain of this quadratic function.

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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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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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The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)

From the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.

The given expression is

18 + 24

First, we will determine the greatest common factor of 18 and 24

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Thus,

The greatest common factor is 2 × 3 = 6

Now, we will write the expression using the greatest common factor and the distributive property

18 + 24

6(3 + 4)

Hence, the expression is 6(3 + 4)

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Answer: $21.33

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

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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The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7

A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle

angle Z = 180-(90+51)

angle Z= 180- 141= 39°

using trigonometry ratio

tan51 = 27/XY

XY= 27/tan51

XY= 27/1.2

XY= 21.9

using Pythagoras theorem

XZ²= 21.9²+27²

XZ²= 1208.6

XZ= √1208.6

XZ= 34.7

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1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

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Answer: Yes

Step-by-step explanation:

y=4x+1
(2,9) 2 is x, 9 is y
9=4(2)+1
9=8+1
9=9

The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)

In this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:

cos 3x / (sin x · cos x)

Second, use trigonometric formulas:

cos (x + 2x) / (sin x · cos x)

(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)

cos 2x / sin x - sin 2x / cos x

csc x · cos 2x - sec x · sin 2x

The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.

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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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Brody reads 8 books each month.

The slope of a line indicates the direction and the steepness of the line. The formula for the slope of a line passing through the points (x₁,y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁).

Give the graph of the line.

The graph of the line passes through points (0,15) and (5,55)

To find the number of books Brody read each month, find the slope of the line.

The slope of the line is:

m  = (55 - 15)/ (5 - 0)

m = 8

Hence, Brody reads 8 books each month.

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Answer:

75÷50

Step-by-step explanation:

1.5 or 3÷2 is the correct answer

The number of runs up and runs down for the preceding data is 5.

Runs up refers to the number of observations that are higher than the number of observations before them.

Runs down refers to the number of observations that are lower than the number of observations before them.

As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.

Therefore,

Runs up = 2nd + 4th + 6th observations

             = 3

As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down

Therefore,

Runs down= 3rd +5th observations

                 =2

Therefore,

Runs up + Runs down  =3+2

                                        =5

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Answer:

p=45-2.5f

Step-by-step explanation:

5f+2p=90

We have to isolate p in one side

5f+2p=90

-5f. -5f

2p=90-5f

/2. /2. /2

p=45-2.5f

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