A blueprint of a concrete patio has a scale of 2 inches=5 feet. Use this to answer parts ​a, b, and c.

Work Shown:

x = length

x-2 = width

area = length*width

area = x(x-2)

x(x-2) = 168

x^2-2x = 168

x^2-2x-168 = 0

Plug a = 1, b = -2, c = -168 into the quadratic formula.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-168)}}{2(1)}\\\\x = \frac{2\pm\sqrt{676}}{2}\\\\x = \frac{2\pm26}{2}\\\\x = \frac{2+26}{2} \ \text{ or } \ x = \frac{2-26}{2}\\\\x = \frac{28}{2} \ \text{ or } \ x = \frac{-24}{2}\\\\x = 14 \ \text{ or } \ x = -12\\\\[/tex]

Ignore x = -12 since we cannot have a negative length.

The only practical solution is x = 14.

If x = 14, then x-2 = 14-2 = 12

The rectangular mirror is 14 inches by 12 inches

Check: area = length*width = 14*12 = 168

The answers are confirmed.

Answer:

Below

Step-by-step explanation:

f(x) =  x^2+ 6x -5     Use Quadratic Formula with a = 1     b = 6      c = -5

to find :

x =  - 3 ± [tex]\sqrt{17}[/tex]

Since 1 lbs is 2.2046 kilogram. Therefore, 193 lbs is 87.5433 kilograms.

Pound:

Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.

Kilogram:

The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.

According to the Question:

We can use the following formula to convert Pounds to kilogram :

X(kg) = y(lb) × 0.45359237

Converting  193 lbs to kilograms:

To convert 193 pound to kilogram:

⇒ X(kg) = 193(lbs) × 0.45359237

             = 87.5433 kilogram

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2.5 is the length of segment AB.

What is  line segment ?

A line segment in geometry has two unique points on the line that define its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.

                                   In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.

          BD ║ AE

 Δ CBD ≈ ΔCAE by AA similarity corresponding sides are proportional .

       CB/CA = CD/DE  ⇒ CB/10 = EC - ED/16

  CB/10 = 16 - 4/16   ⇒  CB/10 = 12/16

  CB = 12 * 10/16  = 7.5

  AB= AC - CB = 10 - 7.5

  AB = 2.5

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The distance between the points J=(-4, 0) and E = (4, 7) In the coordinate plane is, 10.63 units

The distance between two points in the coordinate plane can be calculated using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

The given points

J=(-4, 0) and E = (4, 7),

we have:

x₁ = -4, y₁ = 0

x₂ = 4, y₂ = 7

Plugging in these values into the distance formula, we get:

d = √((4-(-4))² + (7-0)²)

  = √(8² + 7²)

  = √(64 + 49)

  = √113

  = 10.63 (rounded to the nearest hundredth)

So, the distance between points J and E is approximately 10.63 units.

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The best conclusion is:

The bag contains more green Marbles than white marbles.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The bag contains 10 green marbles and 20 white marbles.

The bag contains an equal amount of each color.

The bag contains more green than white marbles.

After 15 trials, Mark has drawn 10 green marbles and 5 white marbles

So, the Probability of Total green Marbles

= (10/15) x 30

= 20

Probability of Total White Marbles

= (5/15) x 30

= 10

So, The bag contains more green Marbles than white marbles.

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The requried area of the shaded region is 4.56 square centimeters.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr²

Here,
A right triangle is inscribed in a circle where the diameter of the circle is the hypotenuse of the right triangle,
So from the figure,
The area of the shaded region is given by the difference between the semi-circle LMN and the area of the right triangle LMN

The diameter of the circle is given by trig ratios,
sin 45 = 4/d

d = 4√2 So the radius will be d = 2√2

Now,
As hypotenuse is the diameter of the circle,
So LM = MN

Now,
Area of shaded region = area of semi-circle - an area of a triangle
Area of shaded region = πr²/2 - 1/2 × base × height

Area of the shaded region = 3.14 × [2√2]²/2 - 1/2 × 4 × 4
Area of shaded region = 4.56 cm²

Thus, the requried area of the shaded region is 4.56 square centimeters.

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You should multiply the top equation by 3 to be able to add the equations and eliminate the x-values in this system.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

2x + 5y = 5                .........equation 1.

-6x + 7y = -37                .........equation 2.

By multiplying equation 1 by 3, we have:

3(2x + 5y = 5) = 6x + 15y = 15    ......equation 3

By adding equation 2 to equation 3, we have:

6x + 15y = 15

-6x + 7y = -37

22y = -22

y = -22/22

y = -1.

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Answer:

29.5735296 cc = 1 oz

The prime factorization of 56 is the process of breaking 56 down into its prime factors. The prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.

One way to calculate the prime factorization of 56 is to use a factor tree. To begin, find two numbers that multiply together to equal 56. The two factors that multiply together to equal 56 are 8 and 7. Since 8 and 7 are both prime numbers, they can be written as the prime factors of 56: 56 = 8 x 7.In mathematical terms, the prime factorization of 56 can be expressed as 56 = 2 x 2 x 2 x 7, where 2 is multiplied by itself three times and then multiplied by 7. This is because 56 can also be written as 2 x 2 x 2 x 7, which is the same as 8 x 7.The prime factorization of 56 can also be expressed as the product of the prime exponents: 56 = 2^3 x 7^1. Here, 2 is raised to the third power, and 7 is raised to the first power. This expression is equivalent to 8 x 7.In summary, the prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.

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The system of equations are

a) Drama = ( 1/8 )s + 22

b) Baseball = ( 5/8 )s - 24

c) Dance = ( 1/8 )s + 27

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of students be represented as s

a)

For Drama , it is 22 more than one​-eighth of the students

On simplifying the equation , we get

Drama = ( 1/8 )s + 22

b)

For Baseball , it is 24 fewer than five​-eighths of the students

On simplifying the equation , we get

Baseball = ( 5/8 )s - 24

c)

For Dance , it is 27 more than one​-eighth of the students

On simplifying the equation , we get

Dance = ( 1/8 )s + 27

Hence , the equations are solved

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Answer:

[tex]\huge\boxed{\sf 14\ times}[/tex]

Step-by-step explanation:

[tex]\displaystyle Probability = \frac{Possible \ no. \ of\ events}{Total \ number\ of \ events}[/tex]

If we roll a die 1 time, the probability of obtaining a 3 is:

= 1 / 6

Because a die has total 6 faces, out of which 3 is only 1.

But, if we roll it 84 times, it becomes:

= [tex]\displaystyle \frac{1}{6} \times 84[/tex]

= 84/6

[tex]\rule[225]{225}{2}[/tex]

The solution of the system of equations is equal to (2, 3).

In Mathematics, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (2, 3).

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An expression which shows the money spent per test tube is u = 6/3.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would determine the unit rate for one pack of 3 test tubes by using the following mathematical expression;

Unit price = Cost of test tubes/Number of test tubes

Substituting the given parameters into the unit price formula, we have the following;

Unit price = $6/3

Unit price = $2.

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Answer: A Parameter is a value that represents a property of a population. This could be the population mean.A statistic is a value that represents a property of a sample. This could be the sample mean.In the given scenario, the population is the entire 14 teams.

Step-by-step explanation: I hope this helps^^

The p-value he obtains and the general conclusion that can be made at a 99% significance level is 0.01

A p-value is a measure of the evidence against a null hypothesis. In this case, the null hypothesis is that the coin is fair and equally likely to turn up heads or tails.

The coach carries out a significance test to determine if the number of tails in his trial of 100 flips is significantly different from what would be expected if the coin were fair.

The p-value is calculated by comparing the observed number of tails (35) to the expected number of tails (50, if the coin were fair) using a binomial distribution.

This involves finding the probability of observing 35 or fewer tails in 100 flips, assuming the null hypothesis is true. If this probability is low (i.e. if the p-value is small), then it suggests that the coin is not fair and that the observed difference is unlikely to have occurred by chance.

At a 99% significance level, a common threshold used in statistical tests, the p-value needs to be less than 0.01 to reject the null hypothesis and conclude that the coin is not fair.

If the p-value obtained is less than 0.01, then we can conclude with 99% confidence that the coin is biased towards heads. On the other hand, if the p-value is greater than 0.01, then we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the coin is unfair.

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The Answer Is A

Its hard to explain but the answer is A

Answer: 9

Step-by-step explanation:

Find the factors (numbers that the given number can be divided by to make a whole number) of each number:

9: 1,3,9

18: 1,2,3,6,9,18

It's quite easy here because the numbers are small but if you get bigger numbers, it might be helpful to draw out a prime factorization tree. And then multiply together all the common prime numbers. (I haven't explained this in great detail but if you want to know leave a comment :))

Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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The equation of a line perpendicular to line y = 8/3x-5 in slope-intercept form that contains point (-2, -2) is y = -3x/8 - 11/4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

8/3 × m₂ = -1

m₂ = -3/8.

At data point (-2, -2), a linear equation of this line can be calculated in point-slope form as follows:

y - (-2) = -3/8(x - (-2))

y + 2 = -3/8(x + 2)

y = -3x/8 - 3/4 - 2

y = -3x/8 - 11/4

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Answer:

13.6

Step-by-step explanation:

To find the mean number of movies that the students saw, we add up all the reported numbers of movies and then divide by the total number of students (which is 8 in this case).

Adding up the reported numbers of movies:

4 + 17 + 17 + 20 + 13 + 4 + 16 + 18 = 109

Dividing by the number of students:

109/8 = 13.625

Rounding to the nearest tenth:

Mean number of movies seen = 13.6

Therefore, the mean number of movies that the students saw, rounded to the nearest tenth, is 13.6.

Answer: 13.6

Step-by-step explanation:

Your basically finding the average:

(4+17+17+20+13+4+16+18)/8 = 13.6

[tex]A = B^-1 * BC[/tex]

Since B is invertible, it can be used to solve the equation.

1. Calculate the inverse of B, [tex]B^-1[/tex].

2. Multiply[tex]B^-1[/tex] with BC, to obtain A.

Assuming that AB and C are square matrices and B is invertible, the equation AB=BC can be solved for A. To do this, we first need to calculate the inverse of B, [tex]B^-1[/tex]. The inverse of a matrix is defined as the matrix which when multiplied to the original matrix, yields the identity matrix. Once we have the inverse of B, we can use it to solve the equation by multiplying [tex]B^-1[/tex] with BC, which will give us A. This works because when we multiply a matrix by its inverse, the result is always the identity matrix. Hence, by multiplying the inverse of B with BC, we can obtain A.

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In statistics, p hat is used as an estimator of the population proportion (p) of a categorical variable. It is the sample proportion of the variable, which is calculated as the number of occurrences of a particular category in the sample divided by the total sample size.

The reason why p hat is used is that it provides an estimate of the unknown population proportion based on a representative sample. By using p hat, we can draw inferences about the population proportion with a certain level of confidence. This is important in hypothesis testing and confidence interval estimation, where we want to make statements about the population based on the information gathered from a sample.

Using p hat as an estimator of p is also beneficial because it has desirable statistical properties, such as being an unbiased estimator, having a sampling distribution that approaches normality, and having a known standard error.

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Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources

Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.

Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.

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Answer:

Write both linear equations in slope intercept form.

The t statistic table is the t-test table is used to evaluate proportions combined with z-scores.

In Statistics, a t-test, can be expressed similarly as a statistical hypothesis test where the test statistic maintains a student’s t-distribution, if the null hypothesis is set. Hence, we know we can use the t-test table here.

The t-test table is used to evaluate proportions combined with z-scores. This table is used to find the ratio for t-statistics. The t-distribution table displays the probability of t-values from a given value. The acquired probability is the t-curve area between the t-distribution ordinates, i.e., the given value and infinity.

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Answer:

This is a standard problem if GP (Geometric Progression) as the height of the ball is getting reduced by 25% every-time it touches the ground.

Step-by-step explanation:

The average rate of change of f(x) over the interval is 15/7

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table, we have

f(-3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(-3)]/[4 + 3]

Substitute the known values in the above equation, so, we have the following representation

Average rate = (11 + 4)/(4 + 3)

Evaluate

Average rate = 15/7

Hence, the average rate is 15/7

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Complete question

Find the average rate of change on the interval [-3, 4].

X f(x)

-3 -4

4 11

Answer:

Evaluate the function for x = 10 , that is substitute 10 into any x in the function.

f(10) = 102+8=5+8=13

Step-by-step explanation:

I hope it helps you

The value of function f(x) at x= 10 is 13.

The correct option is C.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = x/2 + 8

Now, we have to find the value of function at x= 10.

So, put the value x= 10 the f(x) we get

f(10)= 10/2+ 8

f(10) = 5 + 8

f(10) = 13

Thus, the required value is 13.

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(D) Its mean is equal to its median is NOT a characteristic of a Normal curve.

While it is true that the mean and median are equal in a symmetrical distribution like the Normal curve, not all distributions with equal mean and median are symmetrical and Normal.

In a Normal distribution, the mean, median, and mode are equal and located at the center of the bell-shaped curve. However, in a skewed distribution, the mean and median may still be equal but the distribution will not be symmetrical or bell-shaped.

The most important continuous probability distribution in probability theory and statistics is known as the Normal Distribution, commonly known as the Gaussian Distribution.

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