What is the missing length?

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The 10 expressions in Math are:

Math is a subject that can be intimidating to many, but it is a fundamental part of life that is necessary to understand. It is important to have a basic grasp of different expressions in order to be successful in math. This essay will explore the ten expressions of math and provide insight into their importance.

The first expression is the sum. This is the answer you get when adding two or more numbers together. For example, if you have the numbers 5, 7, and 8, the sum would be 20. Sums can also be used to find the total amount of a group of objects.

The second expression is the difference. This is the answer you get when subtracting two or more numbers. For example, if you have the numbers 8 and 5, the difference would be 3. Differences can also be used to find the difference between two amounts.

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To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Inverse function

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.

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The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.

Given :

Let x represent the length of the garden and y represent the width of the garden.

Perimeter = 2(x + y)

32 = 2(x + y)

x + y = 16

y = 16 - x

Area (A) = length * width

A = xy

A = x(16 - x)

A = 16x - x²

Maximum area is at dA/dx = 0:

dA/dx = 16 - 2x

0 = 16 - 2x

2x = 16

x = 8.0 m

y = 16 - x = 15 - 7.5 = 8.0 m

The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.

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Each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

In mathematics, a dimension is the length or width of an area, region, or space in one direction.

area = length × width

    a = l × w

But, we want to triple than area;

3A = 3 (l × w)

3A = (k × l) (k × w)

k² = 3

k = √3

The new dimensions will be: 6√3 and 3√3

Increased Dimension: 6√3 - 6 and 3√3 - 3

let x is the amount of increase in each side:

(x + 6) (x + 3) = 3(18)

x² + 3x + 6x + 18 = 54

x² + 9x + 18 = 54

x² + 9x - 36 = 0

∵ x = 4

Hence, each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.

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Answer:3

Step-by-step explanation:

One over seventeen raised to the second power is (1/17)².One over seventeen raised to the power of negative two is (1/17)⁻².

In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied. Let's learn more about power and exponent. A power is a phrase that depicts the same component being multiplied repeatedly. For instance, in the number 52, the base is the number 5, and the exponent is the number 2. The base is multiplied by the exponent, which is 2, to get the total number of factors.

Given,

one over seventeen raised to the second power

(1/17)²

one over seventeen raised to the power of negative two

(1/17)⁻²

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Answer:

13. Given below is a graph showing the number of Hindi movies released in the first six months of 2005. Which of the following questions can be answered from this graph?

14. The table below gives the dimensions of some rectangles.

Step-by-step explanation:

Answer + Explanation:

13. A. can be answered - add all the monthly figures using the bar height.

     B. cannot be answered - the graph shows May has the least movies but the graph doesn't tell you WHY it has the least movies, it does not give any reason.

     C. can be answered - look at the highest bar height (it's February)

     D. can be answered - calculate March, April and May figures together.

As such, circle A , C and D.

14.

A. Wrong - perimeter does not change in the table despite increase in area (all the perimeters in the table are the same).

B. Wrong - none have equal areas that have equal perimeters.

C. Wrong - none of the rectangles with equal perimeters have equal areas.

D. Correct - All the rectangles with the equal perimeter do not have equal areas (areas can be different).

So circle only D.

The length of the perpendicular of the right-angle triangle will be 20.4 meters.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The hypotenuse is 30 m and the base is 22 m. Then the length of the perpendicular is given as,

30² = P² + 22²

900 = P² + 484

P² = 900 - 484

P² = 416

P = 20.4 m

The length of the perpendicular of the right-angle triangle will be 20.4 meters.

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The probability that the selected student was the youngest student from Section B is 2/6.

The total number of  students is 18 which include

Section A: 5 students

Section B: 6 students

Section C: 7 students

Given that the selected student was from Section B

Calculate the probability of selecting a student from Section B

P(Section B) = 6/18 = 1/3

Calculate the probability of selecting the youngest student from Section B

Since there are 6 students in Section B, the probability of selecting the youngest student is 1/6.

Calculate the probability of selecting the youngest student from Section B given that the selected student was from Section B

P(Youngest student from Section B|Section B) = P(Youngest student from Section B ∩ Section B) / P(Section B)

= (1/6) / (1/3)

= 2/6

Therefore, the probability that the selected student was the youngest student from Section B is 2/6.

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When data are transformed to ranks and the Pearson correlation is performed, the Spearman correlation is what is obtained as a correlation.

Therefore, the correct answer is A)the Spearman correlation

The complete question is:

What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?

a) the Spearman correlation

b) the point-biserial correlation

c) the phi coefficient

d) it is still called a Pearson correlation

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The value of  p is 20

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Is the mean of the following data is 18.75 then find the value of p?

Xi  10   15   p   25  30

Fi   5    10   7   8     2

We may prepare th frequency table as given below:

mean=(∑Fi *Xi) / ∑Fi

         = (5*10 + 10*15 + 7*p + 8*25 + 2* 30)/ (5 + 10 +7 +8 +2)

        = (460+7p)/ 32

        =18.75

460+7p=(18.75×32)

⇒(460+7p)=600

⇒7p=140

⇒p=20

The value of  p is 20

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If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.

The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.

Probability , p = 0.6 (60%=60/100)

Number of trial,n = 10(selected)

Mean = number of trial ✕ probability

= 10 ✕ 0.6

= 6.0

Mean is 6.0

Standard deviation :

σ = np(1-p)

= 10 ✕ 0.6 ✕(1- 0.6 )

= 2.4

Standard deviation = 1.5492

If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.

Rules of Probability : The first rule of probability used in this essay is the definition of a random sample. A random sample is a set of data taken from a larger population that is chosen by a method that gives each element of the population an equal chance.

The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.

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The number of simulation trials that would be likely to produce results that are  closest to the actual probability is 25. The correct option is C).

The following steps can be used  in order to determine the number of simulations:

Step 1 - Remember the maximum number of trials gives the maximum chance to produce results that are  closest to the actual probability.

Step 2 - Now, check all the options given in the question and choose the largest one.

From the above steps, it can be concluded that the correct option is C) 25.

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Full question :

Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.

A. 10

B. 15

C. 25

D. 20

Answer:

y = - [tex]\frac{1}{4}[/tex] x - 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x - 2 ← is in slope- intercept form

with slope m = 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute (4, - 11 ) into the partial equation

- 11 = - [tex]\frac{1}{4}[/tex] (4) + c = - 1 + c ( add 1 to both sides )

- 10 = c

y = - [tex]\frac{1}{4}[/tex] x + (- 10) , that is

y = - [tex]\frac{1}{4}[/tex] x - 10 ← equation of line

The three consecutive odd numbers of the number 75 are:

77, 79 and 81

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.

In our case we have a specific value and this is the number 75, if we want to know the consecutive numbers immediately we add +1, +2 and so on.

But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:

The consecutive and odd numbers will be 77, 79, 81.

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Answer:

Hi ! the answer is .38!

Step-by-step explanation:

The rate of change is 1 and the y-intercept is 1/2.

How do you find the rate of change on a line graph?

To get the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.

The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.

It is frequently referred to as rate of change when determining the slope of real-world scenarios. "Rate of change" and "slope" have the same meaning. Use the slope formula or create a slope triangle if you are asked to determine the rate of change.

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To see the steps of  sum a column in Excel on a Mac.

Now, According to the question:

1. Click the first empty cell below a column of numbers.

2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click  AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...

3. Press RETURN .

How do you sum cells on a Mac?

Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.

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The value of y is -2.

What is coordinate of point?

The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.

Given points are (0,y) and (2,4)​.

The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of the given line is (4 - y)/(2 - 0) =  (4 - y)/2.

Again given that the slope of the line is 3.

Therefore,

(4 - y)/2 = 3

Multiply both sides by 2

4 - y = 6

Subtract 4 from both sides:

-y = 2

Multiply both sides by -1:

y = -2

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The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10

In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y

If a given number let's say Z is Y less than X then the value of Z will be

Z=X-Y

More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value

So, 3 more than 7 means 7+3 = 10

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Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.

A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).

whole = 0,1,2,3,4,5,6,7,8,9,10,11........….

rational = 12/23,3,3/4,5/6,...…

irrational =  [tex]\sqrt{8}[/tex], [tex]\sqrt{-56}[/tex]etc

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The roots of the quadratic equation 2x^2 + 5x + 3 are the two values of x that make the equation equal to 0. These two values are x = -3 and x = -1/2.

The roots of a quadratic equation are the two values of x that make the equation equal to 0. To find the roots of the equation 2x^2 + 5x + 3, we need to set the equation equal to 0 and solve for x. We can do this by using the Quadratic Formula, which states that the two roots of a quadratic equation ax^2 + bx + c = 0 are x = [-b +/- sqrt(b^2 - 4ac)] / 2a. In this equation, a = 2, b = 5, and c = 3. We can plug these values into the formula to get x = [-5 +/- sqrt(25 - 24)] / 4. Simplifying this expression gives us x = -3 and x = -1/2, which are the two roots of the equation 2x^2 + 5x + 3.

x = [-5 +/- sqrt(25 - 24)] / 4

x = [-5 +/- sqrt(1)] / 4

x = [-5 +/- 1] / 4

x = -3 and x = -1/2

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Using percentage on the population size, the number of infected is 720

Probability sampling is a technique in which the researcher chooses samples from a larger population using a method based on probability theory. For a participant to be considered as a probability sample, he/she must be selected using a random selection.

In this question, we can find the percentage of infected in a sample size of 50.

Percentage of infected = (8 / 50) * 100

Percentage of infected = 0.16 * 100

Percentage of infected = 16%

Using this value, we can further calculate the total number of infected in the population.

16 % of 4500 = ?

16 / 100 = x / 4500

0.16 = x / 4500

x = 4500 * 0.16

x = 720

The number of infected are 720

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By using the concept of depreciation, it can be calculated that

Value of x is 3.6%

What is depreciation?

Depreciation is the exponential decrease in the value of an asset or population or cost of an article at a certain rate over  a certain period of time.

Now opposite of depreciation is growth.

Growth is the exponential increase in the value of an asset or population or cost of an article at a certain rate over  a certain period of time.

Here concept of depreciation has been used

Number of deer in 2005 = 1480

Rate = x%

Time = 7 years

Number of deer after 7 years = 1141

[tex]1141 = 1480(1-\frac{x}{100})^7\\(1 - \frac{x}{100})^7 = \frac{1141}{1480}\\(1-\frac{x}{100}) = (\frac{1141}{1480})^{\frac{1}{7}}\\1 - \frac{x}{100} = 0.964\\\frac{x}{100} = 1 - 0.964\\\frac{x}{100} = 0.036\\x = 0.036 \times 100\\[/tex]

x = 3.6 %

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Answer:

x = 2

Step-by-step explanation:

[tex]\frac{5(x-2)}{3} = -x + 2[/tex]

expand left side:

[tex]\frac{5(x-2)}{3} = -x + 2\\\\\frac{5x-10}{3} = -x + 2[/tex]

multiply both sides by 3:

[tex]3(\frac{5x-10}{3}) = 3(-x + 2)\\\\ =5x - 10 = -3x + 6[/tex]

Add 3x to both sides:

5x - 10 + 3x = -3x + 6 + 3x

8x - 10 = 6

add 10 to both sides:

8x - 10 + 10 = 6 + 10

8x = 16

divide both sides by 8:

8x/8 = 16/8

x = 2

The arrangement of the rooms in increasing order of their areas:

Drawing Room = 72m²

Balcony = 87.5 m²

T.V Room = 156m²

Hallway = 216m²

Bedroom = 225m²

Kitchen = 250m²

What is the area of a shape called?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. Draw a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

We have,

kitchen:

40 feet × 10 feet

bedroom

15 feet × 15 feet

hallway

15 feet

TV room

12 feet × 13 feet

balcony:

5 feet × 12 feet × 12 feet

drawing room:

8 feet × 13 feet

Areas of the various spaces in the house:

Drawing Room = 72m²

Balcony = 87.5 m²

T.V Room = 156m²

Hallway = 216m²

Bedroom = 225m²

Kitchen = 250m²

Hence, the arrangement of the rooms in increasing order of their areas:

Drawing Room = 72m²

Balcony = 87.5 m²

T.V Room = 156m²

Hallway = 216m²

Bedroom = 225m²

Kitchen = 250m²

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Answer:

x=h+2 divided by d x = h+2/d

Step-by-step explanation:

The difference between r and p.  is that r represents the sample correlation coefficient while p represents the p-value

Generally, r represents the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables in a sample of data. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

p represents the p-value, which is a measure of the statistical significance of the sample correlation coefficient. It represents the probability that the observed correlation occurred by chance, assuming that there is no true correlation in the population.

A p-value of less than 0.05 is often used as a threshold for determining statistical significance, meaning that the observed correlation is unlikely to have occurred by chance and is likely to reflect a true correlation in the population.

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The population proportion of women athletes who graduated from the university is more than 67%.

A random sample  of 40 women athletes at the school showed that 23 eventually graduated.

n=40 , X=23 , p0 =67% = 0.67 , alpha = 1% = 0.01

H0: : p0 = 0.67  Vs  H1 : p0 < 0.67

Test statistics = (p-p0) / (square root ((p0(1-p0) / n))

p=X/n

H0::p0=0.67  Vs  H1:p0<0.67

Test statistics = z = (p-p0) / ( square root ((p0(1-p0)/n))

p=X/n=23/40

z = (0.575-0.67) / (square root (0.67(1-0.67)/40))=-1.278

P - value = P(z < -1.278) = 0.1007

Since the p-value is  0.1007 that is less than the level of significance the decision is to reject the null hypothesis. In conclusion, there is a sufficient evidence to support that the population proportion of women athletes who graduated is now more than 67%.

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