The average amount of money spent for lunch per person in the college cafeteria is $5. 97 and the standard deviation is $2. 25. Suppose that 46 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.


What is the distribution of X? X~ N(_______,_______)


What is the distribution of ¯x? ¯x~ N(______,_____)


For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6. 4225 and $6. 5884.


For the group of 46 patrons, find the probability that the average lunch cost is between $6. 4225 and $6. 5884

a. The trigonometric ratio tanθ = -√(sec²θ - 1)

b. The trigonometric ratio secθ = -1/√(1 - sin²θ)

Trigonometric ratios are the following mathematical expressions sinθ, cosθ, tanθ,secθ,cosecθ and cotθ.

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

tan²θ + 1 = sec²θ

Making tanθ subject of the formula, we have that

tan²θ = sec²θ - 1

tanθ = ±√(sec²θ - 1)

Since in Quadrant II, tanθ is negative, we choose the negative answer.

So, tanθ = -√(sec²θ - 1)

Since we want to express tanθ in terms of secθ in the second quadrant,using the trigonometric identity

secθ = 1/cosθ and

sin²θ + cos²θ = 1

Making cosθ subject of the formula, we have that

cos²θ = 1 - sin²θ

cosθ = ±√(1 - sin²θ)

So, secθ = 1/cosθ

= ±1/√(1 - sin²θ)

Since in Quadrant III, secθ is positive, we choose the positive answer.

So, secθ = -1/√(1 - sin²θ)

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The value of c will be 0.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

m = y2 - y1 / x2 - x1

where m = 0

y2 = c

y1 = 0

x1 = -2

x2 = -8

0 = c - 0 / -8 - -(2)

0 = c - 0 / -8 + 2

0 = c - 0 / -6

c - 0 = -6(0)

c - 0 = 0

c = 0

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Answer:

  36.9°

Step-by-step explanation:

You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.

The tangent of an angle is the ratio of the side opposite to the side adjacent:

  Tan = Opposite/Adjacent

The tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:

  tan(α) = (6 in)/(8 in) = 3/4

The angle is found using the inverse tangent function.

  α = arctan(3/4) ≈ 36.9°

__

Additional comment

You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.

Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".

The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.

Answer:

0.75 tangent 0.75

Step-by-step explanation:

The slope of linear eqution of two variables x and y, i.e., 2x+3y = 6 is -2/3 and intercept is 2 .

The slope-intercept form expression of a linear equation is y = mx + c --------->(1)

Where m --> slope of the straight line and

c --> the x - intercept .

The expression for slope is represented as :

m = (y₂ - y₁) / (x₂ - x₁) ------>(2)

where (x₁, y₁) and (x₂, y₂) are any two points lying on the straight line. Once the slope m is determined then the general equation of the straight line can be determined easily.

Now we have , the equation in the problem statement is 2x + 3y = 6. firstly , we can rewrite it in the slope-intercept form as :

3y = 6 - 2x

=> y = 6/3 - 2x/3

=> y = -2x/3 + 6/3

=> y = (-2/3)x + 2

comparing the above eqution with eqution(1) we get , m = -2/3 and c = 2. So, slope and intercept of eqution 2x + 3y = 6 are -2/3 and 2 respectively.

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Answer: 8-4+5

Step-by-step explanation: Best I could do

Multiplying the  second equation by -4 eliminates the x terms when adding the first equation.The second equation is 4x + 5y = -8

In order to eliminate the x terms when adding the first equation, you need to multiply the second equation by -4. The formula and calculation steps are as follows:

Formula:

Equation 1 + (-4 x Equation 2)

4x + 5y = -8

-4(4x + 5y) = -4(-8)

-16x -20y = 32

Adding the two equations together gives:

0x + 25y = 24

Therefore, multiplying the second equation by -4 eliminates the x terms when adding the first equation.

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On solving the provided question, we can say that - by fraction we karime walks = 3/4 so, 3/4  X 5 = 15/4

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

karime walks = 3/4

for = 5 days

so, 3/4  X 5 = 15/4

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Answer:

4/8
3/8 + 1/8 = 4/8

Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

y = x+5

2.When x = 10,y = x+5 = 10+5 = 15

3.When x =15,y = x+5 = 15+5 = 20

4.When x = 20,y = x+5 = 20+5 = 25

Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.

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Using basic concept of proportion value and percentage from the total, The answer is there are 15 students in the club.

A percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, 50% means 50/100 or 0.50. It is commonly used to express rates and proportions. Percentages can be used to express a variety of information, such as discounts, increases, and proportions. For example, if a product is on sale for 20% off, that means the price has been reduced by 20/100 or 0.20 times the original price. If a company's profits have increased by 10%, that means they have gone up by 10/100 or 0.10 times the original amount.

A proportion is a mathematical relationship between two values that indicates that they are in a specific ratio to each other. Proportions can be expressed in a variety of ways, but one common way is to use the symbol ":" to separate the two values. In statistics, it is common to use proportions to express the relationship between different groups or categories in a population. In physics, proportions can be used to calculate different quantities in systems.

total = x

40% of x =6

40/100 * x =6

x=6*100/40

=15

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Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.

f(x)=ax3+bx2+cx+d, where  0 and the coefficients a, b, c, and d are complex numbers, and where the variable x has real values. In other words, it is both a three-degree polynomial function and a real function.

Here,

Our role in this situation is:

y = ∛(x - 5) (x - 5)

so the cubic root is given.

In this case, we see that when x = 0, we have:

The y-intercept is y = -5.

And if x = 5, we get:

Because of the sign change, the x-intercept and inflection point are both equal to  y = ∛0 = 0 

Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.

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The graph of y is a straight line parallel to the x−axis through the point (0,-2)

Now, According to the question:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The given equation is Y = -2

y = -2 is a line in which all points have the y-value -2. The line has a slope of 0 (horizontal line) since the y-value does not change for any value of x.

The point-intercept form for the equation of a line is:

y = mx + b

We can write y = -2

As y = 0x - 2;

slope = 0, y-intercept = -2

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The value of x is 18.45°.

The value of y is 2.5 units.

The measure of the angle TOQ is 128.15°.

The measure of the angle QRS is 90°.

The perimeter of QRST is 36 units.

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

Given,  m∠ROS = 7x - 1, m∠STO= 4x - 22.

We know the sum of linear pair of angles is 180°.

Therefore,

7x - 1 + 4x - 22 = 180.

11x = 203.

x = 203/11.

x = 18.45°.

Also given that line segment QT = 4y + 2 and ST = 8y - 8.

We know the sides of a rhombus are of equal length.

Therefore,

4y + 2 = 8y - 8.

- 4y = - 10.

4y = 10.

y = 10/4.

y = 2.5.

We know vertically opposite angles are equal hence m∠ROS = m∠TOQ.

= 7(18.45) - 1.

= 128.15°.

m∠QRS is 90° as all four interior angles of a rhombus are right angles.

The perimeter of QRST is 4×(QT).

= 4×(10 + 2).

= 4×12.

= 36 units.

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The percentage markup the store made before selling those speakers

are 136.33%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A store bought a set of speakers for $82.86 and sold them for

$195.82.

So, The amount of profit is $(195.82 - 82.86).

= $112.96.

Now, The markup percentage can be obtained by the concept of the percentage change.

Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,

= (112.96/82.86)×100%.

= 136.33%.

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The number of concrete masonry units needed to construct a foundation wall is 102.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, a foundation wall 104" high with a 120" perimeter.

Since, perimeter of square =  4 * side

120 = 4 * side

side  = 30"

Hence area of the foundation wall = side²

area of the foundation wall = 30² = 900

volume of the foundation wall  = area * height

the volume of the foundation wall  = 104 * 900 = 93,600"

The volume of the concrete masonry whose length, width, and depth are 16, 8, and 8 respectively is

Volume of masonry = 8 * 8 * 16

The volume of masonry = 1024

since 10 % of masonry goes to waste.

Thus the effective volume of the masonry  = 1024*0.9 = 921.6

total masonry required = 93600/ 921.6 = 101.56

therefore, To build a foundation wall, 102 concrete masonry units are required.

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Answer: Solve one equation for one of the variables.

Step-by-step explanation:

A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.

In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,

Let us say that n number of five ounces glasses are required to equate 12 ounce glass.

Now, we can write the relation,

using simple algebra,

n(Five ounces glasses) = 1 Ounce alcohol content

n = 12/5

n = 2.4

But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.

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The property of congruence illustrated in the statement is the transitive property.

The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.

here,

In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.

The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.

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Answer:

46

Step-by-step explanation:

You multiply 23×2 and that is how I got my answer.

this is a question of arithmetic and the solution is as follows,

The expression 8x + 12y represents the sum of harry and mike’s total monthly wages.

Generally the equation for the  The Distributive property is mathematically given as,

a x (b +c) = a x b+ b x c.

Where

8x+12y

Therefore,

= 4 x 2x + 4 x 3x

= 4 x( 2x + 3x)

= 4( 2x + 3x)

Arithmetic

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division.

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No, the sides of a right triangle do not include 8, 15, and 17. The sides of a right triangle must follow the Pythagorean theorem, so the sum of the squares of the two shorter sides must equal the square of the longest side. 8² + 15² does not equal 1

8² + 15² = 64 + 225 = 289

17² = 289

Therefore, 8, 15, and 17 are not the sides of a right triangle.

The Pythagorean theorem is an important mathematical concept used to determine if three numbers form the sides of a right triangle. This theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. In the case of 8, 15, and 17, 8² + 15² does not equal 17², so it is not a right triangle. To test this, we can calculate 8² + 15² = 289, and then 17² = 289. Since the two values are not equal, we can conclude that 8, 15, and 17 are not the sides of a right triangle.

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Answer: 26

Step-by-step explanation:

In the picture, we are given a right triangle. Based on that, we can use the Pythagorean Theorem, which helps us find the missing side length with the formula [tex]a^2+b^2=c^2[/tex].

a and b represent the legs, and c is the hypotenuse. The hypotenuse is the longest side of the right triangle. It is also the side that is diagonal from the right angle.

In the picture, we are presented with the legs. So, we can plug in the legs into a and b to solve for c.

[tex]a^2+b^2=c^2[/tex]               [plug in a and b]

[tex]10^2+24^2=c^2[/tex]            [exponent]

[tex]100+576=c^2[/tex]            [add]

[tex]676=c^2[/tex]                      [square root both sides]

[tex]c=26[/tex]

This tells us that the length of the third side is 26.

Br₂ does not equal to Avogadro's number. Since bromine is a diatomic element.

What is a diatomic element?

Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).

Each bromine molecule consists of 2 atoms of bromine. Br₂ consists of two moles. One mole of bromine consists of 6.02214076 × 10²³ atoms. Thus 2 moles of bromine consist of 2 × 6.02214076 × 10²³ = atoms. Thus Br₂ does not equal to Avogadro's number.

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Answer:

5

Step-by-step explanation:

4x-3=17

+3 on both sides = 4x=20

divide 20 by 4 and your answer is 5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{4x - 3 = 17}[/tex]

[tex]\text{ADD 3 to BOTH SIDES}[/tex]

[tex]\mathsf{4x - 3 + 3 = 17 + 3}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{4x = 17 + 3}[/tex]

[tex]\mathsf{4x = 20}[/tex]

[tex]\text{DIVIDE 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{20}{4}}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{x = \dfrac{20}{4}}[/tex]

[tex]\mathsf{x = 5}[/tex]

[tex]{\huge\text{Therefore, your answer should be:}[/tex][tex]\huge\boxed{\mathsf{x = 5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Based on the table, an equation of the linear relationship in slope-intercept form include the following: A. y = 2x − 8

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of the data points in this table as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-6 - (-8))/(1 - 0)

Slope, m = 2/1

Slope, m = 2.

At point (0, -8), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept is equal to -8.

y = mx + c

y = 2x + (-8)

y = 2x - 8.

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Answer:

A. y = 2x − 8

Step-by-step explanation:

On observing the provided question we can say that - the function f(x) = a^x is Range : (−∞,∞) or all real numbers

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the number and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The answer to the question is that all real numbers or (−∞,∞)

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Answer: Shift right 20 units

Answer:

It's B, -2, v/5 4, and 3².

Answer: The relationship between the x-coordinates of the first and second bus stop is that the x-coordinate of the second bus stop is 4 units greater than the x-coordinate of the first bus stop.

The relationship between the y-coordinates of the first and second bus stop is that the y-coordinate of the second bus stop is 2 units greater than the y-coordinate of the first bus stop.

Step-by-step explanation: