Devn's friend anthony spent $7.45 on trail mix. the trail mix costs $1.75 per pound. how many pounds of trail mix did anthony buy? round your answer to the nearest hundredth of a pound.

The mean age for peak performance of Olympic and professional athletes in various sports has been increasing over time due to advancements in training, technology, specialization and professionalization of sports.

The mean age for peak performance of Olympic and professional athletes in various sports has been increasing over time due to various factors. Advancements in training techniques and technology have allowed athletes to maintain peak performance for longer periods of time. Additionally, increased specialization and professionalization of sports has also led to older athletes being able to compete at a high level.

The average age of athletes participating in the Olympic Games has also been increasing over time. This trend can be observed across a variety of sports including track and field, gymnastics, swimming and many more. Furthermore, the trend is not limited to a specific gender, both men and women athletes are getting older and still performing at elite level.

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Let's consider what the question asks for:

 --> domain and range, x-intercept, y-intercept of the equation

Let's find the domain:

 --> the only range of x-values that will make this equation 'untrue'

      --> is when the function inside the square root becomes negative

         --> as a square root cannot have a negative value inside it

                [tex]x+8\geq 0\\x\geq -8\\\\\text{Our domain is therefore [-8}[/tex],∞)

Let's find our range:

 --> the function doesn't have any limitations vertically

               [tex]\text{Our range is therefore}[/tex]  (-∞,∞)

Our x-intercept

 --> is when the y-value is zero

      [tex]0=-2\sqrt{x+8} \\\sqrt{x+8} =0\\x+8=0\\x=-8[/tex]

                [tex]\text{Our x-intercept is therefore -8}[/tex]

Our y-intercept:

 --> is when the x-value is zero

    [tex]y=-2\sqrt{x+8} \\y=-2\sqrt{0+8} \\y=-2\sqrt{8} \\y=-2*2\sqrt{2} \\y=-4\sqrt{2}[/tex]

                [tex]\text{Our y-intercept is therefore }-4\sqrt{2}[/tex]

Answer:

  Domain: [-8, ∞)

  Range: {-∞,∞)

  X-intercept is -8

  Y-intercept is [tex]-4\sqrt{2}[/tex]

Answer: Using the absolute value function, the value that is the opposite of being short $3.96 is: x + 3.96.

Step-by-step explanation:

The absolute function is defined by:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin, that is, |2| = |-2| = 2.

For this problem, the number is of $3.96, that is:

|x| = 3.96.

Hence:

Short of $3.96 means that x = -3.96.

The opposite is the other solution, of x = 3.96.

By applying permutation theory, it can be concluded that there are 6840 different orders of 1st, 2nd, and 3rd place winners

Permutation is rearranging a collection of objects in a different order from the original order. In permutations, order matters.

If an object can be selected more than once then the number of permutations is:

P = [tex]n^{r}[/tex]

Otherwise, If an object can only be selected once, then the number of permutations is:

P = n! / (n-r)!

where n is the number of total objects and r is the number of the selected objects to arrange. Hence. n cannot be less than r.

We are given information that there are 20 runners competing in a marathon.

We are asked to find how many different orders could the 1st, 2nd, and 3rd place medals are received. It means that the order matters and they can only be selected once, so we use the second permutation formula, where n = 20 and r = 3.

P = n! / (n-r)!

  = 20! / (20-3)!

  = 20! / 17!

  = 10 * 19 * 18

  = 6840

Thus, there are 6840 different orders of 1st, 2nd, and 3rd place winners.

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Answer: To find the value of c in the expression n² + 38n + c, we need additional information. Without any additional information, it is not possible to determine the value of c.

In general, c is the constant term in a polynomial equation, it is the coefficient of the term x^0. In this case, c is the coefficient of the term n^0.

However, when c is not given a specific value, it can be any real number, and therefore it cannot be determined without more information.

Step-by-step explanation:

Lisa will have 12 books and Joe will have 22 books.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that Joe has 10 more books than Lisa Lisa has 1 more book than Felix Felix has 11 books.

The equations can be written as:-

J = L + 10

L = F + 1

F = 11

Lisa's number of books,

L = F + 1

L = 11 + 1

L = 12

Joe's number of books will be,

J = L + 10

J = 12 + 10

J = 22 books

Therefore, Lisa will have 12 books and Joe will have 22 books.

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The question for the daily use of algebra is given below,

Joe has 10 more books than Lisa Lisa has 1 more book than Felix Felix has 11 books. How many books does Lisa have?

Answer:

7/3

Step-by-step explanation:

Suppose x of 1/3=7/9

           so, 1/3x=7/9

                     x=7/9*3/1

                     x=7/3

The solutions of equation x² + 12 = 7x are x = 3 and x = 4

Consider given equation x² + 12 = 7x

x² + 12 = 7x

x² + 12 - 7x = 7x - 7x                 .......(subtract 7x from both the sides)

x² -7x + 12 = 0

Now we find the two factors such that their sum is -7 and the product is 12

x² - 4x - 3x + 12 = 0            .............(splitting the middle term)

x(x - 4) - 3(x - 4) = 0        

(x - 4) (x - 3) = 0                  ............(seperate out like terms)

(x - 4) = 0  OR  (x - 3) = 0

this means, (x - 4) and (x - 3) are factors of equation x² + 12 = 7x

for (x - 4) = 0

⇒ x = 4

and for (x - 3) = 0

⇒ x = 3

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It is a good idea to scale the number line when making a dot plot when the range of data values is large.

Scaling the number line allows you to fit all the data points on the plot, making it easier to read and interpret. When the range of data values is small, you do not need to scale the number line, but if the range is large, you may need to compress or expand the scale of the number line to fit all the data points.

Additionally, when dealing with large numbers or decimal numbers, scaling the number line can make the dot plot more readable and easy to compare. It can also be useful when you want to compare different data sets that have different ranges, you can use the same scale on both dot plots, which makes it easier to compare the data.

Finally, you may also need to scale the number line when the data contains outliers, this will help to see the distribution of the data better.

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The surface area of pyramid is 229.6 [tex]m^2[/tex] and volume is  164.26 [tex]m^3[/tex].

What is surface area and volume?

The total of a regular pyramid's lateral face areas makes up the lateral surface area. A regular pyramid's total surface area is the sum of the surfaces of its lateral sides and base. The area of a pyramid's base is multiplied by the pyramid's height to determine its volume, which is then divided by 3.

Here Length a = 8 m , Height b = 11.2 m and slant height s= 11m.

Now using surface area of the Pyramid = [tex]\frac{1}{2} (ab)+\frac{3}{2} (bs)[/tex] square unit

=> Surface area = [tex]\frac{1}{2}(8\times 11.2)+\frac{3}{2}(11.2\times 11)[/tex]

=> Surface area = (4×11.2)+(3×5.6×11)

=> surface area = 44.8+184.8 = 229.6 [tex]m^2[/tex]

Now volume of the pyramid =[tex]\frac{1}{3}[/tex] base area ×Height cubic unit

=> volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{2}[/tex]×8×11×11.2 = 164.26 [tex]m^3[/tex]

Hence the surface area of pyramid is 229.6 [tex]m^2[/tex] and volume is  164.26 [tex]m^3[/tex].

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There are 136 solutions to the equation:

X1 + X2 + X3 = 15

where X1, X2, and X3 are non-negative integers. I'm not gonna list them all, but, it starts off with:

01. 0, 0, 15.

02. 0, 1, 14.

03. 0, 2, 13.

134.14, 0, 1.

135.14, 1, 0.

136.15, 0, 0.

The constraint of:

1<X1<6

implies X1 either equals 1, or is greater than 1.

So, there are 65 solutions where X1 equals 1, or is greater than 1, and less than 6!

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The percentage of students are boys = 51.5% and The percentage of students always wear glasses = 21.3%

What is percentage ?

percentage can be defined as the product of ratio of given value , total value and hundred.

Given ,

A principal of a school with 484 students collected information about how many of the students wear glasses complete the two way frequency table

So, the number of boys always wears glasses are 40

the number of boys sometimes wears glasses are 48

the number of boys never wear glasses are 161 .

Total number of boys = 249

the number of girls always wears glasses are 36

the number of girls sometimes wears glasses are 55

the number of girls never wear glasses are 144.

Total number of girls = 235

Total number of students always wears glasses = 76

Total number of students sometimes wears glasses = 103

Total number of students never wear glasses = 305 .

Total number of students = 484 .

The percentage of students are boys = 51.5%

The percentage of students always wear glasses = 21.3%

Hence, The percentage of students are boys = 51.5% and The percentage of students always wear glasses = 21.3%

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Answer:

0.115

Step-by-step explanation:

Answer: 0

Also could you mark my answer as brainliest? It helps and doesnt hurt a bit

Answer:

3.1

Step-by-step explanation:

Answer: 180

Step-by-step explanation:

The angle, in degrees, of the compass direction of a line connecting will be 53.9 degrees

Your entire distance from the beginning location is your hypotenuse.

We employ the hypotenuse formula because...

The Pythagoras theorem can be used to determine the length of the hypotenuse in a right triangle. According to the theory, the hypotenuse's square is equal to the sum of its two other sides' squares.

R2=A2+B2

R2=17.52+242R2

=306.25+576

R=√882.25

=29.7 meters

However, the assertion that R=A + B is incorrect (the assertion on the figure is FALSE!).

Your direction is northwest.

Now use trigonometry:

sinθ=B/R

sinθ=24/29.70

=0.808

θ=53.9 degrees. This is your angle.

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Answer: 0.89

Step-by-step explanation:

Stocks will be worth $1180 in 2024 due to a 10% percent annual decline in value.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Steve bought $2,000 worth of stocks in 2019. The value of the stocks has been decreasing by 10 percent each year

thus the value of stocks becomes 90 percent or 0.9 times each year

After 5 years Value of stocks = 2000 * (0.9)⁵

After 5 years Value of stocks = 1180.98

Therefore the value of stocks in 2024 will be $1180 as stock decreases by 10% every year.

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GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

Okay in this question, we're looking at the g mat and g p, a looking at like students who are applying to be in an m b a program. You can see that our answers are down here and we're going to be looking at the g mat and the g p a so like. Let'S keep track of how many people have good, just only good g p, only a good g mat and not a good g p, both good, so i'm just going to put a check for a good bath good or both bad. Those are our categories, so i'm going to put an x both bad, so we're just going to count up these people. We know a total there's going to be 10 in the sample, so a good g p. A! U was just refreshed. I think a good g p, a was 9.0 and a good g mat was 600 point, so first person, 599 and 9.6, not a good g mat, even though its really close had to be above 600 but g p, a 9.6. That'S a good g p. So we have 1 person in this category of good g p, but not a good g mat then 689 and 8.8. That is a good g mat, but not a good g p. So then, 58410 good g p now to go at 6317.4. Good g mat bad g, p, 5949.8, good g p, a bad g mat 6439.2 that is going to be both good 6569.6, both good 594 poi 8.4. That'S both bad 71011.2, both good and 611 point okay. So that's a good g, math, 7.6 bad g p. So, just a good g mat now to calculate the relative frequency which, since you see decimals here, we know that's what that means. You just take the number and divide by 10 because 10 is your total sample size you're, trying to figure out like relative to the whole group? What percent had each of these 3 divided by 10? Point? That'S a .33 divided by 10.3 .3. These should always add up to 1 and .1. So, let's see what matches with that its going to be option d down here : (values from 0 to 12) and their gmat score (values range from 200 to 800) are listed below: gmat gpa 5999.6 6898.8 58410.0 6317.4 5947.8 6439.2 6569.6 5948.4 71011.2 6117.6

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

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GMAT greater than 600, less than or equal to 600, GPA greater than 9.0, 0.2, and 0.3, and less than or equal to 9.0, 0.4, and 0.1 Hence the correct table is Table 4.

In this question, we're going to be looking at the GMAT and the GPA, as well as people who are applying to be in an MBA school. We'll be looking at the GMAT and the GPA, as you can see from our answers, which are located down below. To keep track of how many people have good, just a good GMAT and not a good GPA, both good, and only a good GMAT, I'm just going to write a check for a good bath good or both horrible. These are our categories, so I'm going to mark both with an x, and we'll just add up these folks . The sample will have a total of 10, therefore that is a good general probability. A! You had just refilled. A good g mat, in my opinion, had to be above 600 points, so first person, 599 and 9.6, even though it's pretty near, isn't a good g mat. However, a good GPS 9.6 was. That's a decent g p. In this category of good GPA there is only one person who is not a good GMAT, followed by 689 and 8.8. That is an excellent g mat, but a poor GPA. 58410 nice GPA is now ready to depart at 6317.4, so. 5949.8, excellent g mat terrible g, p, good g p,  a bad g mat 6439.2 that is going to be both good 6569.6, both good 594 poi 8.4.

Both are awful. 71011.2, good and 611 points are acceptable. So, 7.6 terrible g p, decent g in math. Simply use a decent g mat to determine the relative frequency, which is what that indicates since decimals are included. You just divide the number by 10, since that is the overall sample size you are attempting to determine relative to the entire group. How much of each of these three when multiplied by ten? Point? 10.3 divided by.33 equals a. The sum should always be 1 plus.1. Let's see whether this matches option d down here, then: Below is a list of the applicants' (ranging from 0 to 12) and GMAT scores (200 to 800): GMAT GPA: 5999.6, 6898.8, 58410.0, 6317.4, 5947.8, 6439.2, 6569.6, 5948, and 71011.2, respectively.

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

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The complete question is:

Graduate Management Admission Test is required of students applying to MBA schools (GMAT). One of the most important indicators of how well a student would likely perform in the MBA program is the GMAT score, which is used by university admissions committees. A sample of 10 graduates was chosen to assess how well the GMAT score predicts MBA achievement. Below are their GMAT scores (which range from 200 to 800) and grade point averages (ranging from 0 to 12) for the MBA program (See Picture).

Suppose that university admissions committees consider a GMAT score higher than 600 as an indicator of a good candidate, and a GPA higher than 9.0 as a good performance. find the probability distribution table that correctly summarizes the data.

The perimeter of its varignon parallelogram is 30 units.

Diagonal of varignon parallelogram cross at right angle i.e., 90°.

This makes the parallelogram a rhombus.

now, all sides of the rhombus are equal.

When you cut a trapezium into three pieces it is made up of a central rectangle of height 4 units and 2 congruent right-angled triangles whose hypotenuse is 13 units and side is 5 units.

Using Pythagoras theorem,

Another side = √13∧2-5∧2

=√144

=12

Hence the height of the triangle= 12 units.

Now, consider one of the congruent triangles

Half part of the base is included in the other diagonal but the other half is not.

Since the base is 5 so other diagonal is 2.5.

But there are two right triangles so 2.5*2=5 units from the base are not in the other diagonal.

So the diagonal is 14-5=9 units

Hence the diagonal of the rhombus is 12,9 units

and half of the diagonal is 6 and 4.4 respectively

Again, using Pythagoras theorem,

side of the rhombus is equal to 7.5

Hence perimeter = 4x7.5

perimeter = 30

Therefore, The perimeter of its varignon parallelogram is 30 units.

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To write a given function in the factored form from a given graph is expressed as f (x) = A ( x - t )( x - q ).

As given in the question,

Let us consider a equation representing the graph of a function :

2x² - 4x - 30

Simplify this into factored form

= 2 ( x² - 2x - 15 )

= 2 ( x² - 5x + 3x -15 )

= 2 ( x ( x - 5 ) + 3 ( x - 5 ) )

= 2 ( x - 5 ) ( x + 3 )

In standard form if the function is f(x) = Ax² + Bx + C

Then its factored form is  f (x) = A ( x - t )( x - q ).

Therefore, the function can be written in factored form from a graph in the following way :  f (x) = A ( x - t )( x - q ).

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The variance is 13.84. Variance is a measure of dispersion that considers the spread of all data points in a data collection, in contrast to range and interquartile range.

The following data set's variance should be calculated: 2, 7, 3, 12, and 9.

The mean must be calculated first. There are 5 data points and the total is 33. The mean is therefore 33 x 5 = 6.6. The next step is to take each data point in the set, subtract the mean, and square the result. For the first value, as an illustration:

(2 - 6.6)2 = 21.16

All values' squared differences are added.

21.16 + 0.16 + 12.96 + 29.16 + 5.76 = 69.20

Next, divide the total by the number of data points:

69.20 ÷5 = 13.84

It varies by 13.84. You must calculate the square root of the variance, which is 3.72, to obtain the standard deviation.

The complete question is,

calculate the variance of the follow data set: 2, 7, 3, 12, 9.

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To find the pay/hour that makes traveling on the plane and bus travel equally attractive, we can use the concept of "opportunity cost" by comparing the cost of the plane ticket with the cost of the bus ticket plus the pay/hour.

One way to do this is to use the concept of "opportunity cost," which is the cost of foregone opportunities. In this case, the opportunity cost of traveling by plane is the cost of the plane ticket, while the opportunity cost of traveling by bus is the cost of the bus ticket.

To find the pay/hour that would make traveling by plane and bus equally attractive, we can set up an equation where the opportunity cost of the plane ticket equals the opportunity cost of the bus ticket plus the pay/hour. This equation can be written as:

Plane ticket cost = Bus ticket cost + Pay/hour

To find the pay/hour, we will have to know the costs of the plane and bus tickets and solve the equation for Pay/hour.

Pay/hour = Plane ticket cost - Bus ticket cost

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The expression that represents the number of inches the plant grew this week is,

⇒ 8 - x

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

A plant measured x inches tall last week, and 8 inches tall this week.

Here, We have;

A plant measured x inches tall last week, and 8 inches tall this week.

Hence, The number of inches the plant grew this week is,

⇒ 8 - x

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We can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}    and    f{x} = - {x + 17}/{3}

Given is the expression as -

f{x} = - {1/3}x - {17/3}

We can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}

and

f{x} = - {x + 17}/{3}

Therefore, we can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}    and    f{x} = - {x + 17}/{3}

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The value for Tan 2a = Cot ( a - 70) gives a= 53.33

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Tan 2a = Cot ( a - 70)

As, tan a= cot (90 - a)

So, cot (90- 2a) = Cot (a-70)

Now, comparing the angles we get

90 -2a = a - 70

90 + 70 = a + 2a

3a = 160

a = 160/3

a = 53.33

Hence, the value of a is 53.33.

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The total number of solutions to a polynomial equation can be determined by analyzing its degree and the number of times that the variable equals to zero. A polynomial equation of degree n will have at most n solutions.

Here is the general rules for finding the number of solutions to a polynomial equation:

If the polynomial is a degree-n equation and has n distinct roots, then it will have n solutions.

For example, the polynomial 5x^3 - x +2 has 3 solutions as it is third-degree polynomial.

It's worth noting that these rules are based on the assumptions that the polynomial is defined over the field of complex numbers, which means that the solutions can be complex numbers, and not just real numbers.

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