Mathematics: What is a mean

The statement correctly represents the situation is "Paul runs 5/8 mile for every one mile that John runs".

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.

The ratio of the number of runs that John and Paul do is 5:8, which means that for every 5 runs that John does, Paul does 8 runs.

Let J and P number of miles John and Paul run respectively. We can write:

P : J = 5 : 8

P / J = 5 / 8

P = (5/8)J

Therefore, Paul runs 5/8 mile for every one mile that John runs

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Complete Question

John and Paul both run on the same track each morning. The ratio of the number of  John runs to the number of  Paul runs is 5:8 Which statement correctly represents the situation?

A. Paul runs 5/8 mile for every one mile that John runs

B. Paul runs 8/13 mile for every one mile that John runs.

C. John  runs 5/8 mile for every one mile that Paul runs.

D. John runs 8/13 mile for every one mile that Paul runs.

Measure of angle B is 36.87°.

Trigonometric functions are defined as the real functions or the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given is a right angled triangle.

We have to find measure of angle B.

Cosine of an angle in a right angled triangle is equal to the ratio of it's adjacent side to the hypotenuse.

Hypotenuse = AB = 5

Adjacent side to B = CB = 4

Cos B = 4/5

∠B = Cos⁻¹ (4/5)

     = 0.6435 radians

     = 36.87°

Hence the measure of the angle B is 36.87°.

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Answer: 5,840,000

Step-by-step explanation:

96/24=4

365,000x2x2x2x2=5,840,000
or
365,000 x 2^4=5,840,000

Answer: x = y

Step-by-step explanation:

x and y are angles with vertical sides, and angles with vertical sides are always equal

The total surface area of this cone is equal to 735.1 square meters.

Mathematically, the total surface area (TSA) of a cone can be calculated by using this mathematical expression:

Total surface area (TSA) of a cone = πr(l + r)

Where:

Substituting the given parameters into the total surface area (TSA) (SA) of a cone formula, we have the following;

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)

Total surface area (TSA) of a cone = 3.142 × 6 × (39)

Total surface area (TSA) of a cone = 735.1 square meters.

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The values in the table are 7, 11, 15, and 19.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We are assuming the table to be:

x             value

2            2x2 + 3 = 7

4           4x2 + 3 = 11

6           6x2 + 3 = 15

8           8x2 + 3 = 19

Thus,

The values in the table are 7, 11, 15, and 19.

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A polynomial term is an expression composed of constants, variables, and exponents.

A polynomial term is an expression composed of constants, variables, and exponents. Constants are the numerical values that don't change, while variables are values that can change. Exponents are numbers that indicate how many times a number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 8. A polynomial term is an expression that combines constants, variables, and exponents, such as 6x^2 - 3x + 5. In this expression, 6, -3, and 5 are constants, x is a variable, and 2 and 1 are exponents. A polynomial term can also contain fractions, such as (2x + 1)/3. In this case, 2, 1, and 3 are constants, and x is a variable. Polynomial terms are the building blocks of polynomials, which are equations that consist of multiple polynomial terms.

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Answer:

304

Step-by-step explanation

it was on my quiz

Answer:

The number 304 is exactly halfway between 61 and 547.

Step-by-step explanation:

To find the halfway point between two given numbers we can simply add them together then divide them by 2.

Note:

let [tex]N[/tex] be the number that is halfway

[tex]N=\frac{547+61}{2}[/tex]

[tex]N=\frac{608}{2}[/tex]

[tex]N=304[/tex]

Answer:

216 in^3

Step-by-step explanation:

Volume = 6 in. * 4 in. * 9 in. = 216 in^3

a.) The equation for g(x) is g(x) = 6((x+5)/2)³and output is 384.

b.) The inverse machine, g¹(a), we need to undo each of the four steps in reverse order is g¹(a) = [tex]((a/6)^{(1/3)})*[/tex]2 - 5

c.) To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result is  3.

What is Function?

A function is a mathematical rule that takes one or more inputs (also called independent variables or arguments) and produces a single output (also called a dependent variable or function value). In other words, a function is a relationship between the inputs and the output, where each input produces a unique output.

Functions can take many different forms and can be used to describe a wide variety of mathematical and real-world phenomena.

a. The equation for g(x) is:

g(x) = 6((x+5)/2)³

When 3 is put in for x, the output is:

g(3) = 6((3+5)/2)³= 6(4)³ = 384

b. To find the inverse machine, g¹(a), we need to undo each of the four steps in reverse order:

Putting this in equation form, we get:

g¹(a) = [tex]((a/6)^{(1/3)})[/tex]*2 - 5

c. To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result:

g¹(384) =[tex]((384/6)^{(1/3)})[/tex]*2 - 5 =[tex](64^{(1/3)})[/tex]2 - 5 = 42 - 5 = 3

Since the output of g¹(a) is 3 when we input the output of g(x), we can conclude that g¹(a) correctly undoes the output of g(x).

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Answer: 0.1 decimal 1/9 fraction

Step-by-step explanation:

Answer:

0.1 or 1/9 i think so but I am sure

The equation that represents this situation is $6t - $450 ≥ $1000.

The number of tickets that should be sold is 242.

The form of the equation is:

total revenue - total cost ≥ $1000

(cost of one ticket x number of tickets sold) -  cost of pizza and drinks ≥ $1000

($6 x t) - ($200 + $250) ≥ $1000

$6t - $450 ≥ $1000

$6t ≥ $1000 + $450

$6t ≥ $1450

t ≥ $1450 / 6t

t ≥ 242

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Answer:

W when c = 4 is 0.128.

Step-by-step explanation:

The relationship between A, C and W can be represented by the following equations:

A = k√c

W = m/a^3

Where k and m are constant of proportionality.

Since A is directly proportional to the square root of c, we can write k = A/√c. Substituting the values of A and C when c = 49, we have:

k = 35/√49 = 35/7

Since W is inversely proportional to a^3, we can write m = W * a^3. Substituting the values of W and A when a = 2, we have:

m = 16 * 2^3 = 128

Now we have both k and m, we can find the value of W when c = 4.

A = k * √c = 35/7 * √4 = 10

W = m/a^3 = 128/10^3 = 0.128

So, the value of W when c = 4 is 0.128.

In a density curve, the proportion of data is represented by the area under the curve. So option B is correct.

The probability that an observation chosen at random falls within a given interval is represented by the area under a density curve, which is a smooth representation of a probability distribution. As a result, the area under the curve between the respective points is proportional to the percentage of data that falls inside a given range.

The area under the curve that directly represents the proportion of data. The intervals of values on the vertical and horizontal axes are used to plot the curve and are important for interpreting the graph, but they do not directly represent the proportion of data. The length of the curve is not relevant for determining the proportion of data, as it can vary depending on the scaling of the graph.

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There 144 four digit numbers are made up of four consecutive numbers from 1 to 9

We can approach this problem by counting the number of ways we can choose four consecutive numbers from 1-9 and then arranging them in a four-digit number.

Here we have to use combination

There are 6 possible sets of four consecutive numbers in the range 1-9

= {1,2,3,4}, {2,3,4,5}, {3,4,5,6}, {4,5,6,7}, {5,6,7,8}, and {6,7,8,9}.

For each set, there are 4! = 24 ways to arrange the four numbers into a four-digit number.

So the total number of four-digit numbers made up of four consecutive numbers from 1-9 is:

6 sets × 24 arrangements per set = 144

Therefore, there are 144 such four-digit numbers.

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A quadratic equation with -1 and 5 as its roots is x^2 - 4x - 5 = 0 by multiplying the terms.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

Derive factor from the roots

x = -1    and    x = 5

x + 1 = 0  and  x - 5 = 0

Now, (x+1)(x-5) = 0

 x(x - 5) + 1(x - 5) = 0

x^2 - 5x + x - 5 = 0

 x^2 - 4x - 5 = 0

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Answer: 37

Step-by-step explanation:

let x be the number of students who pass "fante". Then the number of students who passed "Ga" will be x + 6.

with the added information that 8 students passed both we can say:

(x + x + 6) - 8 = 60

2x + 6 = 68

2x = 62

x = 31

.: x + 6 = "only Ga pass" = 37

The question does not make it clear if it is asking for students who *only* passed Ga, or students who passed Ga + those who passed both. I'll assume the former though. Otherwise the answer would be 37 + 8 = 45 students

The resulting expression of the algebraic expression  is 13r²(2rs + 4r³ - 3s⁴).

option C.

The resulting expression of the algebraic expression given as

26r³s + 52r^(5) - 39r²s⁴

can be determined by finding the highest common factor here and factorize out.

The highest common factor of the letters is r²

Factors of 26 = 1, 2, 13, 26

Factors of 39 = 1, 3, 13, 39

Factors of 52 = 1, 2, 4, 13, 26, 52

The highest common factor for the 3 numbers is 13.

Thus, in total, the highest common factor for the algebraic expression is 13r².

Finally, we have;

13r²(2rs + 4r³ - 3s⁴)

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The complete question is below:

Factor  26r³s + 52r^(5) - 39r²s⁴

To get 77 marks on a quiz the student has to spend approximately 3 hrs.

The expected quiz score if a student spends no time on homework is 55.

What is meant by a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."

It is given that y = 7.2x + 55

where y is the expected quiz score.

x is the number of hours spent on homework that week.

If the value of y=77

77=7.2x+55

22=7.2x

x is approximately 3 hrs.

If the student spends no time on their homework:

x=0

y=0+55

y=55.

Therefore to get 77 marks on a quiz the student has to spend approximately 3 hrs.

The expected quiz score if the student spends no time on home work is 55.

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The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In this context, an equation that models the situation is given by:

y = mx + c

340 = 28x + 102

28x = 340 - 102

28x = 238

x = 238/28

x = 8.5 gallons of gasoline.

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Answer:

-16

Step-by-step explanation:

[tex]h\left(x\right)=\frac{1}{2}x-14\\h\left(-4\right)=-4/2-14=-2-14=-16[/tex]

a) Formula that gives the total yearly expense as a linear function of the number of dairy cows is E = 21,000 + 2,000C.

b) Formula that gives I as a linear function of C is I = 7,000C. The smallest number of cows the dairy needs to break even is 5.

(a) Let's call the number of dairy cows "C".

The yearly expense for maintaining the barns and equipment is a fixed cost of $21,000.

The yearly expense for feeding and caring for each dairy cow is $2,000.

To find the total yearly expense, we can add the fixed cost of maintaining the barns and equipment to the variable cost of caring for the cows:

E = 21,000 + 2,000C

This is a linear equation that gives the total yearly expense as a function of the number of dairy cows.

(b) Each dairy cow produces 3,500 gallons of milk per year.

The dairy sells milk for $2.00 per gallon.

To find the yearly income for the dairy, we can multiply the number of gallons of milk produced by the price per gallon:

I = 2.00(3,500)C = 7,000C

This is a linear equation that gives the yearly income as a function of the number of dairy cows.

To determine the smallest number of cows the dairy needs in order to break even, we need to find the point where the yearly income is equal to the yearly expense.

Setting I = E, we get:

7,000C = 21,000 + 2,000C

Simplifying and solving for C, we get:

5,000C = 21,000

C = 4.2

Since we cannot have a fraction of a cow, we round up to the nearest whole number.

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Answer:

x = 4

The missing angle is 28°

Step-by-step explanation:

7x + 62 = 90  These angles are complementary which means that they add to 90°

7x + 62 = 90  Subtract 62 from both sides of the equation

7x = 28  Divide both sides by 7

x = 4

The total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

The cost of each cement ring is given as RS. 2500. Since there are 28 cement rings used in the water well, the total cost of the cement rings can be calculated as follows:

Total cost of cement rings = Cost of each cement ring x Number of cement rings used

Total cost of cement rings = 28 x 2500 = RS. 70,000

Volume of the well = [tex]\mathrm{ \pi r^2h = \pi (0.7)^2(5.6) = 9.768m^3 }[/tex]

Cost of digging out the well = 500 x 9.798 = RS. 4,899

Total cost of the well = RS. 74,899

Total cost of cement rings = 2500 x 28 = RS. 70,000

Therefore, the total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

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An appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Since the data represents the average time employees spent online, the y-axis of the bar graph should represent time in minutes.

To choose an appropriate scale for the y-axis.

we need to consider the range of values in the data set.

The lowest value is 15 minutes

and the highest value is 60 minutes

Range of values is 60 - 15 = 45 minutes.

It's best to choose a scale that divides the range of values into equal intervals.

One possible option is to use a scale where each unit represents 5 minutes of time. This would allow us to represent the data accurately without making the bars too small or too large.

Therefore, an appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.

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Answer:

Step-by-step explanation:

well if there are 5 pepperoni pizzas that means that he eats 2 meaning he has 3 pepperoni slices of pizza.

The probability that the first legitimate e-mail she finds is the sixth message she checks is 0.0656.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: according to internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate.

For each message, we have the following probabilities:

90% probability it is spam.

10% probability it is legitimate.

Compute the probability that the first legitimate e-mail she finds is the fifth message she checks:

The first four are all spam, each with a 90% probability.

The fifth is legitimate, with a 10% probability.

P = (0.9)⁴×0.1

P = 0.0656

Hence, the probability that the first legitimate e-mail she finds is the sixth message she checks is 0.0656.

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The height of the hill in the painting 3 inches from the left side of the picture is 30 Inches. Option C

From the information given, we have that;

We also have that the function is;

h(x) =-(x)(x-13)

Given that the distance is 3 inches

Substitute the values, we have;

h(3)= -(3)(3-13)

substract the values

h(3) = (-3)(-10)

multiply the values

h(3) = 30 inches

Hence, the value is 30 inches

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I know, I answer quick. What do you expect I'm Johnny Sins to help you with your homework. :)

Anyways,

The height of the nth bounce can be calculated using the formula:

h_n = h_1 * 0.68^(n-1)

Where h_1 is the height of the first bounce, h_n is the height of the nth bounce, and 0.68 is the percentage of the height lost with each successive bounce.

Substituting the given values, we have:

h_9 = 5 * 0.68^(9-1)

h_9 = 5 * 0.68^8

h_9 = 5 * 0.265

h_9 = 1.325

So the height of the 9th bounce would be approximately 1.3 feet, rounded to the nearest tenth.

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Tina pays 0.7p more than Amy when buying the coffee.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

Given that,

Amy gets 15p change from £2. The price of the coffee is:

A = 2 - 0.15

A = 1.85

Tina gets £2.45 change from £5. The price of the coffee is:

T = 5 - 2.45

T = 2.55

The difference in the cost of the coffee is:

T - A = 2.55 - 1.85 = 0.7

Hence, Tina pays 0.7p more than Amy when buying the coffee.

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