The frequency distribution shows the average number of pupils per teacher in some states of the United States. Find the variance and standard deviation for the data. Round your answers to one decimal place.

Answer: To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Step-by-step explanation:

Using the linear function, the monthly cost for 6 HCF is $36.72.

If the monthly water bill is a linear function with a slope of 1.65, it means that for every additional HCF used, the cost increases by $1.65.

Let's denote the monthly cost as C(HCF) and the number of HCF used as HCF. We know that C(12) = $46.62.

Now, to find the monthly cost for 6 HCF (C(6)), we can use the slope information:

C(12) = $46.62

C(12) - C(6) = $46.62 - C(6) = (12 HCF - 6 HCF) * 1.65

C(6) = $46.62 - (6 HCF * 1.65)

Now, let's calculate:

C(6) = $46.62 - (6 * 1.65)

C(6) = $46.62 - 9.90

C(6) = $36.72

So, the monthly cost for 6 HCF is $36.72.

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Answer: 127

Step-by-step explanation:

the image has steps

Answer:

the answer is 127 cm^2 ig

Profit made by each girl Sarah, Lilly and Paula respectivly are R 200 , R 400 and R 600

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. Indicators of proportions include "::" and "=".

The amount of investment done by each girl Sarah, Lily and Paula respectivly is x, 2x and 3x

So, the profit will be

x + 2x + 3x = 1200

⇒6x  =1200

⇒ x = 200

Profit made by each girl respectivly are x = R 200 , 2x = R 400 and 3x = R 600.

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Answer:

A- x+3

Step-by-step explanation:

each number is growing by 3

The pair of equations y = 0 and y = -7 have no solutions.

The pair of equations y = 0 and y = -7 have no solutions because the equations are not equal. The left side of the equation is y = 0, while the right side of the equation is y = -7. Since the two sides of the equation do not have the same value, there is no solution that can satisfy both equations.

The pair of equations y = 0 and y = -7 have no solutions because the two equations are not equal. The left side of the equation is y = 0, while the right side of the equation is y = -7. Since the two sides of the equation do not have the same value, there is no solution that can satisfy both equations simultaneously. This can be confirmed by substituting the value of y on the left side into the equation on the right side. Since the value of y would be 0 on the left side and -7 on the right side, they cannot be equal and thus there is no solution. Therefore, the pair of equations y = 0 and y = -7 have no solutions.

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Significant figures are in this measurement 1.090

In a number, to determine the number of significant figures following three rules are used:  

The digits which are non-zero are always significant.

Any zeros between two digits which are non-zero are significant.

In the decimal portion, trailing zeros are significant.  

Significant figures = Numbers that carry meaning in the measurements of a number.

The number is 1.090, it has two non-zero digits, 1 zero in between two non-zero digit and one trailing zero thus, all of them are significant figures.

Therefore, it has 4 significant figures : 1.090

Significant figures are in this measurement 1.090

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Answer:Volume of Pipe Formula. The pipe volume formula is: Volume = pi x radius² x length. To do piping size calculation, follow these steps: Find the inner diameter and length of the pipe, in inches or millimeters. Calculate the inner diameter of the pipe by measuring

Step-by-step explanation:

The number of doors in one-story building are 8 and the number of doors in two-story building are 12.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, an employee at a construction company is ordering interior doors for some new houses that are being built.

Let the number of doors in one-story houses be x and the number of doors in two-story houses be y.

There are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors.

Here, 6x+2y=72 -------(I)

On the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors.

5x+7y=124 -------(II)

Multiply equation (I) by 7, we get

42x+14y=504  -------(III)

Multiply equation (II) by 2, we get

10x+14y=248 -------(IV)

Subtract equation (IV) from (III), we get

32x=256

x=8

Substitute x=8 in equation (I), we get

48+2y=72

2y=24

y=12

Therefore, the number of doors in one-story building are 8 and the number of doors in two-story building are 12.

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The slope of the line that passes through (-4, 7) and (-6, 5) is 1.

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.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (-4, 7) and (-6, 5).

Now, slope m=(5-7)/(-6+4)

m=-2/(-2)

m=1

Substitute m=1 and (x, y)=(-4, 7) in y=mx+c, we get

7=1(-4)+c

c=11

Substitute m=1 and c=11 in y=mx+c, we get

y=x+11

Therefore, the slope of the line that passes through (-4, 7) and (-6, 5) is 1.

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The number of the books owed by Tara which she has not read would be = 152 books.

Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %..

The number of books owned by Tara = 160 books

The percentage of books read by Tara = 95%

Therefore, 95% of her books = 95/100 × 160

= 15200/100

= 152 books.

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(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.

(b) by noon, the temperature in milwaukee was 3 Fahrenheit.

In mathematics, it deals with numbers of operations according to the statements.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Given that,

    City                Temperature table (°F)

   Montreal                -16

   Atlanta                   68

   Dayton                   36

  milwaukee               -5

   Juneau                   -31

Part A- Temperature difference in Atlanta and Juneau

= (-16) - 68

= -84 F

Part B- temperature in milwaukee raise by 8 F at noon

Temperature in noon = - 5 + 8 = +3 F

Thus,

(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.

(b) by noon, the temperature in milwaukee was 3 Fahrenheit.

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The simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].

What is simplifying an expression?

To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.

Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Consider, the given expression:

[tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3[/tex]

Using the rule:  [tex](\frac{a}{b} )^m = \frac{a^m}{b^m}[/tex]

⇒  [tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3 = (\frac{81x^1^2y^0}{x^-^8})(\frac{y^6x^-^1^2}{125x^3y^2^4} ) = \frac{81y^6}{125x^-^5y^2^4} = \frac{81y^-^1^8}{125x^-^5}= \frac{81x^5}{125y^1^8}[/tex]

Hence, the simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].

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Applying proportions, the amount of money Bob saved is $18.

Proportions can also be used to express a relationship between two or more values in the form of a ratio, such as a:b, where a and b are values being compared.

We can start the problem by using the proportion of saving to earning, which is 9/16.

If for every $16 he earns babysitting, he saves $9, then for $32 that he earned babysitting, he saved:

$9 / (16/32) = $9 * 2 = $18

So Rob saved $18 from the money he earned babysitting on Saturday

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Answer:

You can use the second equation to substitute the value of x in the first equation and solve for y.

x = y - 4

-10(y - 4) + 3y = 5

-10y + 40 + 3y = 5

-7y = 35

y = 5

Now that you have the value of y, you can use the second equation to find the value of x.

x = y - 4

x = 5 - 4

x = 1

So the solution of the system of equations is x = 1 and y = 5

Step-by-step explanation:

1 kilograms is equal to 2.205 pounds, which leads to the conversion factor of 2.205. The conversion factor is based on both the Avoirdupois system of measurement, which is used in the United States and the United Kingdom to measure weight or mass, and the International System of Units (SI).

  The basis for the Avoirdupois system is the pound, which is equal to 0.45359237 kilos. Consequently, 0.45359237 kilograms equal one pound.

  Finding the weight in pounds of 1 kilograms is necessary to convert kilograms to pounds. We can divide 1 kilograms by 0.45359237 kilograms/pound to get this equivalent weight.

1 kg / 0.45359237 kg/lb = 2.20462262 lb

 This is the kilograms to pound conversion factor. The value is rounded to the widely regarded and employed value of 2.205.

 Therefore, to convert kilograms to pounds, we multiply the weight in kilograms by 2.205.

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By solving a linear equation we will see that there are 20 games left.

We know that there is a total of 100 games, and the ratio of wins to loses for the rockets is:

3:2

The ratio for the rangers is:

7:13

We know that if the rockets loses all the remaining games, and the rangers win all the remaining games then both teams will win the same number of games.

Let's define X as the number of games left, the number of games won by the rockets is:

(100 - X)*(3/5)

The number of games won by the rangers is:

(100 - X)*(7/20)

We know that if the rangers win the X games left, they will have the same number of wins than the rockets (if the rockets don't win any more game)

Then we can write the linear equation:

(100 - X)*(7/20) + X = (100 - X)*(3/5)

we can solve this for X.

X = (100 - X)*(3/5) - (100 - X)*(7/20)

X = (100 - X)*(3/5 - 7/20)

X = (100 - X)*(12/20 - 7/20)

X = (100 - X)*(5/20)

(20/5)*X = 100 - X

4*X = 100 - X

4*X + X = 100

5*X = 100

X = 100/5

X = 20

There are 20 games left for the rockets.

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The inequality describing how much she can withdraw is x < 3550

An equation is a expression that shows the relationship between numbers and variables.

Inequalities are used in expression for non equal comparison of variables.

Let x represent the amount of money that can be withdrawn.

Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:

Money remaining = 3800 - 750 = 3050

Tabitha wants to keep a balance greater than $500. Hence:

3050 - x > 500

x < 3550

The inequality is x < 3550

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The monthly payment is $130.50. Therefore, option C is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$2700, rate of interest =8% and time =2 years

Here, SI=(2700×8×2)/100

= 43200/100

= $432

Amount =Principal+Interest

= 2700+432

= $3132

We know that 2 years =24 months

Now, the monthly payment = 3132/24

= $130.50

Therefore, option C is the correct answer.

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(a)- The study was experimental.

(b)- No, the researchers would not be justified in doing so.

(c)- Such a method leads to an incorrect conclusions for justifiable reasons.

This problem involves minute statistical knowledge and assesses the student's ability to differentiate between an experiment and an observation and also his/her potential to make justifiable logics as to draw conclusions for a scientific research. The explainations are-

Part - (a)

The study was not an observation, it was an experiment because the treatments involving D-Cycloserine or placebo were imposed by the researchers on the people with acrophobia.

Part (b) -No, the experiment was designed to compare the D-Cycloserine group with a control group that received a placebo . The researchers can conclude that the D-Cycloserine and two therapy sessions show significantly more improvement than a placebo and two therapy sessions. However, there is no basis for comparison with the other group of people with acrophobia who received eight therapy sessions and no pill.

Part (c)-

We can cite an example that if the therapists were allowed to choose who received a placebo and who received D-Cycloserine, they might assign the people with more severe acrophobia with the other group. Thus, the improvement after only two therapy sessions can be related to the initial severity of the acrophobia rather than to the effects of D-Cycloserine.

Therefore, the answers are -

(a)- The study was experimental.

(b)- No, the researchers would not be justified in doing so.

(c)- Such a method leads to an incorrect conclusions for justifiable reasons.

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Answer:

54 cm^2

Step-by-step explanation:

calculate the area of each of the 2 rectangles and add them .

area of rectangle = l × w

so let the area of the big rectangle be A1 and the area of the small one A2 :

A1 = l × w = 11 × 4 = 44 cm^2

A2 = l × w = 5 × 2 = 10 cm^2

then , the area of the shape is = A1 + A2 = 44 + 10 = 54 cm^2

Answer: The answer is 4

Step-by-step explanation: Firstly you want to convert the whole number into a fraction, the fraction will be 24/1. Then you multiply 1/6 by 24/1 or 1x24/6x1 which equals 26/6. This fractio can be simplified, by finding the greatest common factor. The GCF of 24 and 6 is 6.

24/6 = 4

6/6 = 1

So our full answer is 4/1 which simplifies to 4

Answer:

4

Step-by-step explanation:

take 24 divided by 6 you'll get

Perimeter of rectangular hexagon = 6 × length of side, length of side of given hexagon = 30/6   =5 cm and perimeter of new figure = Number of outer sides × length of each side  =10×5=50 cm

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Perimeter of rectangular hexagon = 6 × length of side

length of side of given hexagon = 30/6   =5 cm

perimeter of new figure = Number of outer sides × length of each side

=10×5=50 cm

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a) The maximum Height of Projectile is 843.75 m

b) The projectile reach its maximum at t= 12.5 sec.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

h(t) = -5t² +120t + 125

a) For the maximum height, h= 0

-5t² +120t + 125 = 0

t²  - 24 t - 25 = 0

t²  - 25t + t - 25 = 0

t( t- 25) + 1(t-25)= 0

(t-25)(t+1)=0

t= 25, -1

So, Max height is reached after half the total flight time, t= 25/2

So, h(25/2 )= -5(25/2)² +120(25/2) + 125

= -5 x 156.25 + 1500+ 125

= 843.75 m

b) The projectile reach its maximum at t= 12.5 sec.

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Answer:

a^n(a+1)

This is just to reach the minimum character limit.

Answer:

4 and 7

Step-by-step explanation:

7-4=3

4x7=28

At point, the parametric curves cross (4, 1, 32).

t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).

It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.

The introduction of the idea of time makes parametric functions the most simple to understand.

Imagine tracing a parabola-like function from left to right as time passes.

Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.

We will investigate functions for which a point exists in this section.

Hence, At point, the parametric curves cross (4, 1, 32).

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each).

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square $abcd$, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each). This can be solved by applying the concept of perimeter.

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square abcd, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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0.1 is probability  in distribution table.

What are examples and probability?

The quantity of success-producing options. the total number of outcomes that could occur.

                             For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

now according to the properties of probability theory we know that sum of probabilities is 1.

so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:

sum of given probabilities =(0.2+0.4+0.3) = 0.9

required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1

hence the complete probability table is

X P(X)

20 0.2

49 0.4

53 0.1

80 0.3

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