What proportion of the data points in a data set are expected to be within one standard deviation of the mean.

Step-by-step explanation:

the law of intersecting lines : the angles between both lines are the same on both sides of either line, just left-right mirrored.

that's why the angles are while going around the intersection point (starting with the known 37° angle) :

37° - supplementary angle - 37° - supplementary angle

and again from the start.

"supplementary" angles are pairs of angles that together are 180°. just like 2 neighboring angles at intersecting lines.

so, 37° = 7x - 5

example 4

116° is the supplementary angle of 4x.

that means

180 = 116 + 4x

64 = 4x

x = 64/4 = 16

The larger acute angle in the right triangle is 60°

A triangle with at least one angle a right angle, is called a right triangle.

Given that, In a right triangle, cos (9x) = sin (6x - 10)°.

We know that, sine and cosine of an angle are supplementary.

Therefore,

9x+6x-10 = 90

15x = 100

x = 20 / 3

Therefore, sin(6(20/3)-10)°

= sin(30)°

And also,

cos(9(20/3)

= cos(60)°

Hence, the larger angle is in the triangle is 60°

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The graph shows that the domain and range of the line segment were [-5, 1] & [-4, 7, correspondingly.

A function's domain is the set of values that it can accept. These figures represent a function like f's x-values (x). The domain of a function is the set of possible values on which it can operate. This set is the value which the return type after the x value has been entered. Y = f is a function where x is an independent variable and y is a dependent variable (x). If a value of x can be successfully utilized to produce a single value of y using a value of f, then that value is said to be within the domain of that function.

Here,

The domain denotes all conceivable possibilities for x, whereas the range denotes all possible values of y.

The graph shows that the domain and range of the line segment is [-5, 1] & [-4, 7, respectively.

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The students that have both a Netflix and Hulu account is 12.

We can use the principle of inclusion-exclusion to solve this problem. The principle states that if we want to know how many students have either a Netflix or a Hulu account (or both), we can add the number of students who have a Netflix account to the number of students who have a Hulu account and then subtract the number of students who have both.

So, using the information given:

Netflix or Hulu = Netflix + Hulu - (Netflix and Hulu)

87 = 53 + 46 - (Netflix and Hulu)

To find the number of students who have both a Netflix and Hulu account we can solve for (Netflix and Hulu) :

(Netflix and Hulu) = Netflix + Hulu - 87

(Netflix and Hulu) = 53 + 46 - 87

(Netflix and Hulu) = 12

So, 12 students have both a Netflix and Hulu account.

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Answer:

---------------------------------

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

An integer which can be used to represent a diver's elevation if the diver is 40 feet below sea level is -40.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

On the other hand (conversely), a negative integer simply refers to a whole number that is less than zero (0), but do not include decimals or fractions.

In this context, we can reasonably infer and logically deduce that an integer which can be used for representing a diver's elevation when he or she is 40 feet below sea level would be the negative integer -40.

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Answer:

a) 7x

b) 8x-1

c) 6x=12

d) 3x+4

e) 13x-7

Step-by-step explanation:

To collect the like terms, you combine similar terms. e.g- 4x+3x would be 7x because there are 7 x's.

x = 3y perendicular to l

y = -3x parallel to l

y = 3x + 2 neither

A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks.

One approach for determining a line's slope from a graph is to use the formula immediately after knowing the coordinates of two points that are on the line. Let's assume that the coordinate values for the two spots are unknown. Therefore, we also have another way to determine the slope of the line. This approach entails attempting to determine the tangent of the angle formed by the line and the x-axis.

The line is y = -3x -1

slope is -3 by slope intercept form

The line x = 3y

or y = (1/3)*x

slope is 1/3

we know for a line perpendicular to a given line slope should be -1/m so the slope will be  (1/3)

so, x = 3y  is perpendicular

y = -3x have slope -3 so it is parallel

y = 3x + 2  slope is 3 so neither

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The expression that is equivalent to (1/16)^-4 is 16^4. Option B

Index form of a number is mathematically described as the number that is written as an exponential expression or that is raised to a variable or another number.

The exponent of an expression explains the multiple times in which the base replicates itself to evaluate the expression.

It is also called the scientific notation or standard form of a number.

From the information given, we have that;

(1/16)^-4

Using the indices rule;

(a^-n) is same as (1/a)^n

So, if we have (1/16)^-4, it is equivalent to;

16^4

Hence, the value is 16^4

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Complete question:

Which expression is equivalent to (1/16)^-4?

The answer choices are

A) (-16)^4

B) 16^4

C) 4 square root 1/16

D) -(1/16)^-4

Water and ocean are two closely related words, as the ocean is the largest source of water on the planet.

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The value of x in degrees will be 6° and 11° using properties of parallel lines.

They are typically equal-distance, parallel straight lines. The lines here are parallel. They never come together no matter how far you extend them in any one way.

Pairs of equal-sized angles that are both obtuse or acute and are generated on the same side of the transversal are known as corresponding angles. Each pair of comparable angles on the same side of the crossing transversal is equal to the other.

The alternative angle theorem states that alternate interior angles or alternate exterior angles that come from cutting two parallel lines are congruent.

In the above figure,

8x + 7 = 55

8x  = 55 - 7

x = 6

Measure of the angle will be 8 × 6 + 7 = 49

In 11)

10x + 10 = 9x + 21 (by using first corresponding angles and then alternate angles)

⇒x = 11

The value of x in degrees will be = 11° using properties of parallel lines.

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Answer:

it is, in fact, i

Step-by-step explanation:

first of all, let's remember that

[tex]i^{0} = 1 \\ {i}^1 = i \\ {i}^{2} = - 1 \\ {i}^{3} = - i[/tex]

and follow up powers follow the same pattern. at this point let's look at the exponent: you should know that if a number is a multiple of 4, his last two digits are a multiple of 4. in our case,

[tex]5689 = 5688 + 1 = 4k + 1[/tex]

and honesly, we do not care about what k is. rest is playing with power rules

[tex] {i}^{5689} = {i}^{5688 + 1} = {i }^{4k + 1} = { ({i}^{4}) }^{k} \times i = i[/tex]

Answer: 21 new children have come.

Data :

We simply have to subtract the number of children playing from the number of children who arrived after a while:

[tex]\bf \: 43 - 22 = 21[/tex]

We check:

[tex]\bf \: 22 + 21 = 43[/tex]

Rpt: 21 new children have come.

The angles which measure 20 degrees are∠1 ,∠5 ,∠7 ,∠9 ,∠11 ,∠14 ,∠16. The solution has been obtained using the properties of parallel lines.

Parallel lines are any two or more lines that lie in the same plane, are equally spaced apart, and never cross one another.

We are given t || x and k || w and m∠3 = 20°

Using the properties of parallel lines, we get -

∠3 = ∠1            (As these are vertically opposite angles)

∠3 = ∠5           (As these are alternate interior angles)                

∠3 = ∠7             (As these are corresponding angles )

Now,

∠4 = 180 - ∠3                     (As they form a linear pair)

∠10 = 180 - ∠9                    (As they form a linear pair)

Also,

∠10 = ∠4                            (Parallelogram's opposite angles are same)

So,

180 - ∠9 = 180 - ∠3

∠3 = ∠9                                                       .... [ii]

∠9 = ∠11               (As these are vertically opposite angles)

∠3 = ∠11               ( from [ii] )                                           .... [iii]

∠11 = ∠14               (As these are alternate interior angles)

∠3 = ∠14               ( from [iii] )                                               .... [iv]

∠14 = ∠16               (As these are vertically opposite angles)

∠3 = ∠16               ( from [iv] )    

Hence, the angles which measure 20 degrees are

∠1 ,∠5 ,∠7 ,∠9 ,∠11 ,∠14 ,∠16.

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The statistical measure which would best represent the average temperature as required is; Mean.

It follows from the task content that the measure of central tendency which best represents the average temperature is to be determined.

On this note, although the mean and median are statistical measures of the central tendency, the mean is a more accurate measure of the average temperature as in this context.

The mode on the other hand, is a statistical measure of spread.

Ultimately, while checking the average temperature in different locations, it follows that the average temperatures in each of the locations is reported as a mean.

This follows from the fact that the mean is a representative of all temperatures recorded in any one location.

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The arithmetic mean of the set of data 6, 1, 5, 8 and 10 is calculated to be 6

The simplest and most popular way to measure a mean or average is with the arithmetic mean. It simply entails adding up a collection of numbers, then dividing that total by the total number of numbers in the series.

Adding up the numbers

= 6 + 1 + 5 + 8 + 10

= 30

The total number of items in the data is = 5

The arithmetic mean calculation

arithmetic mean = sum of numbers / number of items

arithmetic mean = 30 / 5

arithmetic mean = 6

The arithmetic mean is 6

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The corresponding letters based on the signs in their correct order that makes the numbers and operators a true equation is as follows;

((12 B E 16) C 17) D 62 F 1/2

The order of operation which indicates the proper sequence of the operations on the numbers in the equation, (PEMDAS), is as follows;

P; Parenthesis first(), then E; Exponents, followed by M or D, Multiplication or Division (Left to Right), and A or S; Addition or Subtraction.

The specified numbers are; 12, 16, 17, 62, and 1/2

The operators are; +, ×, √, -, ÷, and =

The number that is a perfect square is 16 = 4²

Applying the square root to 16, and multiplying the result to 12, we get;

12 × √(16) = 48

Subtracting 17 from the above result, we get;

48 - 17 = 31

Dividing the above result of 31 by 62, we get;

31/62 = 1/2

The operations on the numbers that make the set of numbers and operators an equation are therefore;

(12 × √(16)) - 17) ÷ 62 = 1/2

The corresponding letters from the set of letters and operators, that can make this a true equation is therefore;

B = '×', E = '√', C = '-', D = '÷', F = '='

12 B E 16 C 17 D 61 F 1/2

Applying the bracket symbol that indicates the order of operations, we get;

((12 B E 16) C 17) D 61 F 1/2

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The  spherical water tank can not hold enough water to fill up the swimming pool, given the length, width, and constant depth of the water.

The amount of water that the spherical tank can hold is the volume of the spherical tank. This volume can be found by the formula:

= 4 / 3 x Pi x radius ³

The volume of this spherical tank is therefore :

= 4 / 3 x Pi x 25 feet

= 65, 450 feet ³

Then, to see if it can hold enough water for a swimming pool 50 meters long, 25 meters wide with a constant depth of 2 meters, find the volume of the swimming pool as:

= Length x Width x Depth

= 50 x 25 x 2

= 2, 500 meters ³

1 m³ to feet ³ is 35.3147 so the volume in feet is:

= 2, 500 x 35.3147

= 88, 287 feet ³

The water tank can not hold enough water for the swimming pool.

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Answer:

x= -3

Step-by-step explanation:

Answer: The symbol ⊕ is known as the XOR (Exclusive Or) operator.

Step-by-step explanation:

The symbol ⊕ is known as the XOR (Exclusive Or) operator. It is a logical operator that compares two binary digits or bits and returns a 1 if one of the bits is 1 but not both. It returns 0 if both bits are the same (either 0 or 1). It is commonly used in digital logic and computer science, particularly in the field of cryptography. In simple terms, it compares two bits and returns 1 if they are different and 0 if they are the same.

The equation which having the solution n = -4 is,

11/4n + 2 = -3 + 3/2n.

What is solution of an equation?

Any value of the variable that satisfies the equality, that is, makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal, is a solution of the equation. Finding an equation's solution or solutions is known as solving the equation.

Consider, the given equation  -5n + 31 = -14n -5

Solving this equation,

14n - 5n = -5 - 31

       9n = -36

          n = -4

We have to find the equation which having the solution n = -4.

Consider, the first equation

-1 - 22n = -20n - 9

Solving this, we get

n = 4

Consider, the second equation

3 - 6n + 3n = -3 + 4 - 4n

Solving this, we get

n = -2

Consider, the third equation

1 = 0.75n + 3.25

Solving this, we get

n = 3

Consider, the fourth equation

11/4n + 2 = -3 + 3/2n

Solving this, we get

n = -4

Hence, the equation which having the solution n = -4 is,

11/4n + 2 = -3 + 3/2n.

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Each girl scored 9 points

Each boy scored 7 points

Step-by-step explanation:

Let the number of points each girl scored = a

Let the number of points each boy scored = b

7 girls and 6 boys scored a total of 105 points.

7a + 6b = 105......... Equation 1

The difference between the number of points scored by the 7 girls and the number of points scored by the 6 boys is 21

7a - 6b = 21........... Equation 2

7a + 6b = 105......... Equation 1

7a - 6b = 21........... Equation 2

Subtract Equation 2 from Equation 1

12b = 84

b = 84/12

b = 7

Therefore, each boy scored 7 points

7a + 6b = 105......... Equation 1

b = 7

7a+ 6b = 105

7a + 6(7) = 105

7a + 42 = 105

7a = 105 - 42

7a = 63

a = 63/7

a = 9

Therefore, each girl scored 9 points.

The width of the table top is 132 cm and 1.32 in metres.

The shorter distance of an object or a figure is its width, which indicates how broad or wide the given figure is. Additionally, width is measured in linear units such as metres, centimetres, inches, and so forth.

Length: Length is used to calculate the separation between two points. The longest dimension of a figure, length, indicates how long an object or figure is. It is measured in linear units like metres, centimetres, inches, and so forth.

Width of hand = 8cm

No of hands = 16.5 hands

Width of tabletop = Width of hand * No. of hands = 8cm × 16.5 = 132cm = 1.32m

The width of the table top is 132 cm and 1.32 in metres

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Answer:

5 people per 42 square feet.

Step-by-step explanation:

The area of the rectangle is 7 x 12 = 84 square feet.

The ratio of the number of people to the area of the rectangle is:

10 people : 84 square feet

You can simplify this ratio by dividing both sides by 2:

10/2 people : 84/2 square feet

Which can be written as

5 people : 42 square feet

Answer:

The ratio of the number of people to the rectangle's area is 10 people : 84 square feet.

Step-by-step explanation:

The ratio of the number of people to the rectangle's area is 10 people : 84 square feet.

It is important to note that this ratio represents the maximum number of people that can fit comfortably in the 7 x 12 feet square. The actual number of people that can fit in the space will depend on various factors such as the size and layout of the room, the presence of furniture, and the size of the people.

Answer:

15p + 10

Step-by-step explanation:

5 (3p+2)

15p + 10

Answer: 12.60

Step-by-step explanation: A = B^2. If B is multiplied by 3.55, then A = (3.55B)^2. That gives us A = 12.6025B. Round 12.6025 to hundredth and you get 12.60

The required fence to be built around the perimeter of the park should be 453 m long.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,
A City Park is in the Shape of a triangle where the sides have Lengths of 163 m, 145m, and 145m.
The perimeter of the triangle  = sum of all sides
                                                 = 163 + 145 + 145
                                                 = 453 m

Thus, the required fence to be built around the perimeter of the park should be 453 m long.

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The range of values of x for the given expression (x - 12)(x + 5)/(x - 3)³≤0 is ,

( -∞ , -15] and [3, 12]

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given expression,

(x - 12)(x + 5)/(x - 3)³ ≤0

by using wavy curve method it can be state that,

function hold negative value,

1. when x is less than -15

⇒  x ≤15

2.  when x is in between

⇒   3≤ x ≤12

Hence, range of x is ( -∞ , -15] and [3, 12]

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