Calculate the sample mean and sample variance for the following distribution of heights in centimeters for an 8 year old boy

On solving the provided question, we can say that - the range [tex]|x + 1| = 0[/tex] [tex]x + 1 = 0 = > x = -1[/tex] and [tex]y = 3[/tex]

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

[tex]|x + 1| = 0\\x + 1 = 0\\x = -1[/tex]

[tex]y = |-1 + 1| + 3\\y= 0 + 3\\y = 3[/tex]

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Exact Circumference = 4pi feet

Approximate Circumference = 12.56 feet (when using pi = 3.14)

======================================================

Explanation:

The larger circle has a 3 foot radius.

The inner circle has a 3-1 = 2 foot radius.

Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.

C = 2pi*r

C = 2pi*2

C = 4pi

The exact circumference is 4pi feet. This is the perimeter around the circle.

If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.

The length of x is 6 in simplest radical form.

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given ,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = 3/x

∅ = 30°

⇒ sin30 = 3/x

⇒ 1/2 = 3/x  [ sin30 = /2  ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

Hypotenuse² = Perpendicular² + Base²

6² = 3² + Base²

6² - 3² = Base²

Base² = 25

Base = √25

Base = 5

We can conclude the value of x to be 6.

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Answer:

Steps for How to Transform the Graph of a Cubic Function

Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.

Step-by-step explanation:

Step-by-step explanation:

first we need to identify the lines themselves.

the line from bottom left to top right is simply

y = x

the line is solid, so the points on the line are included.

the dotted line (the points on the line itself are not included) goes through

(0, 2) and (3, 0)

the y-intercept is therefore 2 (the y value when x = 0).

and for the slope

x changes by +3 (from 0 to 3).

y changes by -2 (from 2 to 0).

the slope is -2/+3 = -2/3

and the line is

y = (-2/3)x + 2

we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.

so, the system of inequalities is

y >= x

y > (-2/3)x + 2

On solving the provided question, we can say that - by equation angles will be, x + 5x = 85 => 6x = 85 => x = 14.1666666667

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

let one angle be = x

other angle be 5x

then, x + 5x = 85

6x = 85

x = 14.1666666667

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For 2 weeks tony will spent time for practice basketball is 10 hours.

Given data :

1st week

= Tuesday = 2 hours

= Wednesday = 1 hour

= Friday = 2 hours

same for 2nd week

so total hours = 1st week + 2nd week

                       =  2 + 1 + 2 + 2 + 1 + 2

                       = 10 hours

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Answer:£21.00

Step-by-step explanation:

One pizza: (£35/5) =£7

Three pizza's: (£7x3)=£21

Answer:

9

Step-by-step explanation:

18/5 ÷ 2/5 = 18/5 x 5/2 = 9

Step-by-step explanation:

try this option:

[tex]a) \ log_{15}5+log_{15}3=log_{15}15;\\b) \ log_{1/2}log_{49}7=log_77;\\c) \ log_44=log_22.[/tex]

Answer: Both Rick and Jenny could be correct because we do not know what "x" is.

Step-by-step explanation:

The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.

I hope this helps :)

Answer:

this is in the form of slope intercept. y = mx + b

m is the slope

and b is the y intercept

meaning that -2 is the y intercept

and 1/3 is the slope

(meaning on a graph you go up one, and over 3)

Step-by-step explanation:

The perimeter of the rectangle is 19n + 7.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The perimeter of a rectangle is the sum of the whole sides of the rectangle.

Therefore, let's find the perimeter of the rectangle with width of 6n - 3.5 ft and length of 3.5n + 7 ft. Hence,

perimeter of a rectangle = 2(l + w)

where

Therefore,

w = 6n - 3.5

l = 3.5n + 7

Hence,

perimeter of a rectangle = 2(6n - 3.5 +  3.5n + 7)

perimeter of a rectangle = 2(6n + 3.5n - 3.5 + 7)

perimeter of a rectangle = 2(9.5n + 3.5)

perimeter of a rectangle = 19n + 7

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The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.

Permutations refer to the arrangements of objects in certain order or way.

The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.

The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.

The probability is obtained as 1 / ₉P₃

where;

₉P₃ = 9! / (9 - 3)!

₉P₃ = 9! / 6!

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

6! = 6 * 5 * 4 * 3 * 2 * 1

₉P₃ = 504

Hence, the probability = 1/504

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Answer:

18 songs

Step-by-step explanation:

15 x 1.6 = 24

24 x 0.75 - 18

The number of houses left to be sold is 12

There are 90 new houses built in the neighbourhood

2/5 were sold last month

2/5 × 90

= 18 × 2

= 36

1/3 of the remaining were sold this month

1/3 × 36

=12

Hence there are 12 houses left to be sold

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Answer:

To factor the first expression, "0.7 times square root of 300", we can rewrite it as:

0.7 * sqrt(300)

The prime factorization of 300 is 2 * 2 * 3 * 5 * 5, so we can rewrite the expression as:

0.7 * sqrt(2 * 2 * 3 * 5 * 5)

Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:

0.7 * sqrt(2) * sqrt(2) * sqrt(3) * sqrt(5) * sqrt(5)

Combining like terms, we get:

0.7 * 2 * sqrt(2) * sqrt(3) * sqrt(5)

= 1.4 * sqrt(2) * sqrt(3) * sqrt(5)

This is the fully factored form of the expression "0.7 times square root of 300".

To factor the second expression, "-0.125 times square root of 192", we can rewrite it as:

-0.125 * sqrt(192)

The prime factorization of 192 is 2 * 2 * 2 * 2 * 2 * 2, so we can rewrite the expression as:

-0.125 * sqrt(2 * 2 * 2 * 2 * 2 * 2)

Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:

-0.125 * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2)

Combining like terms, we get:

-0.125 * 6 * sqrt(2)

= -0.75 * sqrt(2)

This is the fully factored form of the expression "-0.125 times square root of 192".

Answer:

for the second one the answer is - square root of 3

Step-by-step explanation:

i could only solve the second one sorry

Except Option - A all satisfy the more appropriate measures of center and spread for the data that is median and IQR.

Given that,

We have to find what are the more appropriate measures of center and spread for data.

We know that,

Mean, median, and mode are the three central tendencies, and median is the more accurate indicator.

This is because

i) Extreme values affect the mean.

ii) If there are more outliers, the mean is in error.

iii) Means that are biassed to the right or left may not accurately reflect the nature of the data.

However, median is preferable to mean because it represents the center entry and is unaffected by extreme items or outliers.

Since extreme items will show higher standard deviation and some outliers may be misleading, IQR is a superior spread measurement tool. However, IQR provides an excellent idea.

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Answer:

Refer to step-by-step

Step-by-step explanation:

Prove the following, [tex]\lim_{x \to \ 2} 2^{x}=4[/tex], [tex]\lim_{z \to \ -1} 3^{x}=\frac{1}{3}[/tex], and [tex]\lim_{x \to \ 1} e^{x-1} = 1[/tex].

For part f:

Plug in the value of the limit, 2,

[tex](2)^{2} =4[/tex]

Thus we proved the limit.

For part g:

Plug in the value of the limit, -1,

[tex]3^{(-1)}[/tex]=>[tex]3^{-1}[/tex]=>[tex]\frac{1}{3^{1} }=\frac{1}{3}[/tex]

Thus we proved the limit.

For part h:

Plug in the value of the limit, 1,

[tex]e^{(1)-1}[/tex]=>[tex]e^{1-1}[/tex]=>[tex]e^{0}=1[/tex]

Thus we proved the limit.

Answer:

There is a root between x=3 and x=5.

Step-by-step explanation:

Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.

The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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The weight of the jar after solving equation simultaneously is w=0.

A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.

A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.

j+w=1.5

2j+w=3

Simultaneously solving gives

w=0

the weight of jar is 0.

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The volume of the parallelopiped is 14 cubic units

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

Given that the parallelopiped has sides

So, we have that

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

So,

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2).

Since (a × b) = (5, -7, -2)

So, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14.

So, the volume is 14 cubic units.

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Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

From the provided figure, it is clear that there are two triangles.

ABC and EFG are the triangles.

AB = EF

AC = FG

BC = EG

As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.

Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

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According to the given cosecant function the value of csc 0 is equal to 6/5.

The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.

It is given that:

[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]

According to trigonometric identity,

[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]

Therefore the value of csc 0 is equal to 6/5.

Complete question;

Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]

find csc 0.

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Answer:

it is not factorable

Step-by-step explanation:

There are no factors of 24 that will make -4, so it is not factorable

Answer: 5

Step-by-step explanation:

1. Since you are told x=35. Plug it into x.

35-25

2. Simplify

35-25=5

Answer: 10

Step-by-step explanation:

x-25

substitute 35 for x

35-25 = 10

Answer:

y-4=-7/4(x+4)

Step-by-step explanation:

Point Slope Form: y-y*sub*1=m(x-x*sub*1)

Parallel lines have the same slope as the line to which they are parallel.

y-4=-7/4(x+4)

Hope this helps :)

Step-by-step explanation:

the tax rate gives us a ratio of tax amount to value.

this ratio (in our case 1.25/100) is constant for any value.

therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.

in other words, we multiply

1.25/100 × f/f

so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.

f = 2000 / 1.25 = 1600

so, we get

1.25/100 × 1600/1600 = 2000 / 160000

so, the value of the condominium is

value = $160,000