Volume of Spheres

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Volume of SpheresVolume of Spheres

The equation to model the maximum and minimum scores is given by |x - 76| = 5

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the student score. All students scored within 5 points of the average, hence:

|x - 76| = 5

The equation to model the maximum and minimum scores is given by |x - 76| = 5

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Answer:

1.1512, 2.1, 2.106, 2.16

Answer:

1.1512, 2.1, 2.106, 2.16

Step-by-step explanation:

1.1512 is the lowest cause it starts with 1

then 2.1 cause it has no more numbers to make it larger than the last two

then 2.106 because there is a 0 separating the 1 and 6 which makes the number smaller

which leaves you with 2.16 as the lasrgest

By using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

What do you mean by arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given:

Total no. of students is  [tex]30[/tex]

Number of students taken English is [tex]15[/tex]

Number of students taken English but not French is [tex]10[/tex]

(i) Number of students taken French = Total no. of students -  Number of students taken English but not French

                                                             [tex]= 30-10\\=20[/tex]

(ii)  Number of students taken French not English = Number of students taken French - Number of students taken English

                                                                         [tex]=20-15\\=5[/tex]

Therefore, by using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

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Answer:

By using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

What do you mean by arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given:

Total no. of students is  

Number of students taken English is

Number of students taken English but not French is

(i) Number of students taken French = Total no. of students -  Number of students taken English but not French

(ii)  Number of students taken French not English = Number of students taken French - Number of students taken English

Therefore, by using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

Answer

14 notebook computers: 3850$

16 desktop computers: 2400$

Step-by-step explanation:

275x14=3850

150x16=2400

The length of the altitude of the equilateral triangle ABC is [tex]\frac{13\sqrt{3} }{2}[/tex].

Equilateral Triangle is defined as the triangle with all the sides equal and all the angles = 60 deg.

Altitude of a Triangle can be defined as the perpendicular drawn from the vertex of a triangle to the opposite side.

According to the question

In the figure given below

In ΔADC

Since ΔADC is a right angle triangle we can apply Pythagoras Theorem.

Let the sides of the equilateral triangle be "a". and "h" be the altitude.

Since the altitude is of equilateral triangle it divides the base i.e. DC=a/2

[tex](AC)^{2} =(AD)^{2}+(DC)^{2}[/tex]

[tex]a^{2} =h^{2}+(\frac{a}{2})^{2}\\ \\ h^{2}=\frac{4a^{2}-a^{2}}{4} \\ \\ h=\sqrt{3} *\frac{1}{2} *a[/tex]

Substituting the value of a=13 we get

Altitude [tex]h=\frac{13\sqrt{3} }{2}[/tex]

Therefore , The length of the altitude of the equilateral ΔABC is [tex]\frac{13\sqrt{3} }{2}[/tex].

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Answer:

Substitution property.

Step-by-step explanation:

The substitution property is just like saying, "If a variable, b, equals c, then b will be substituted for c, and it goes for c being substituted as b, too."

➲ Hope this helps.

Answer:

z = [tex]\sqrt{30}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it) × ( whole hypotenuse) , so

z² =  3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )

z = [tex]\sqrt{30}[/tex]

Amount after 2 years is $44.1

Compound interest formula

[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]

A= Amount after t years.

P= Principal amount.  

r= Interest rate (decimal)

n=Period of compounding

t= Time

So ,

[tex]A=40(1+\frac{0.05}{1}) ^{1*2}\\ =40(1.05) ^{2}\\ = 40*1.1025\\ = 44.1[/tex]

Amount after 2 years is $44.1

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Answer:

24

Step-by-step explanation:

Let x be shirts.

Write an equation.

13x=321

Divide 13 from both sides.

x≈24.69

So, the soccer team can only buy 24 shirts, because it cannot go over the budget.

Hope this helps!

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Answer: 3/10 times 5 equals 15/50

Step-by-step explanation: First you do 3 times 5 which equals 15 and then 10 times 5 to get 50, which together make 15/50 and to make sure it's right check it by finding the greatest common factor they both have.

Answer:

5/5

Step-by-step explanation:

3 will enter 15, 5 times

n 10 will enter 50, 5 times

Based on the definition of vertical angles, m<A = 36°.

Two angles that are vertically opposite to each other are called vertical angles, and they have congruent angle measures. That is, vertical angles are equal.

Angles A and B are vertical angles, then, they are equal to each other.

m<A = (7x + 22)°

m<B = (8x + 20)°

m<A = m<B

Substitute

7x + 22 = 8x + 20

7x - 8x = -22 + 20

-x = -2

x = 2

m<A = 7x + 22

Plug in the value of x

m<A = 7(2) + 22

m<A = 14 + 22

m<A = 36°

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The viables solutions for the given compound inequality are x ∈ (-3, 5).

According to the given question.

The number of pies baked by Rita is x which is limited by ingredients.

Also, the inequalities which represent the situation are

2x - 3 < 7

And, 5 - x < 8

Since, we have to solve the above inequality and find its solutions.

From the given inequality

2x - 3 <7  we can say that,

2x < 7 + 3

⇒ 2x < 10

⇒ x < 5 ..(i)

And, 5 - x < 8

⇒  5 - 8 < x

⇒ - 3 < x

or, x < -3 ..(ii)

From i and ii we can say that the solution of the given compound inequality are the numbers which lies in between  -3 and 5 or x ∈ (-3, 5).

Hence, the viables solutions for the given compound inequality are

x ∈ (-3, 5).

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Based on the definition of complementary angles, the measures are:

m<q = 32°

m<r = 58°

Tow angels are complementary if both angles give a sum of 90 degrees.

The sum of angle q and angle r would give 90 degrees because they are complementary angles. Therefore, we would have the following:

m<r = ?

m<q = m<r - 26

Plug in the values

m<r - 26 + m<r = 90

2(m<r) - 26 = 90

2(m<r) = 90 + 26

2(m<r) = 116

2(m<r)/2 = 116/2

m<r = 58°

m<q = m<r - 26 = 58 - 26

m<q = 32°

Therefore, based on the definition of complementary angles, the measures are:

m<q = 32°

m<r = 58°

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By assuming that one of the two integers is even we will reach an absurd, and in that way, prove the given statement.

Remember that an odd integer number is written as:

A = (2n + 1)

While an even number would be written as:

B = 2n

Where n is a random integer.

Then if x times y is an odd integer we can write:

x*y = (2n + 1)

Where n, m ∈ Z.

Where Z is the set of integer numbers.

Now, let's do find an absurd. Let's suppose that one of the two numbers is even, then we can write:

x = 2m

And y can be even or odd, it does not matter, but it is an integer.

Replacing that we get:

x*y = (2m)*y

We can rewrite that as:

(2m)*y = 2*(m*y)

We know that integer numbers are closed under the product, and here m and y are integers, then m*y is also an integer.

Thus, 2*(m*y) is 2 times an integer, then that is an even number, which is absurd because we know that it should be odd. So, if at least one of the two integers is even, then the product will also be even.

Then if the product is odd, neither of the integers can be even, then we conclude that both of the integers are odd integers.

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Check the picture below, which is just a template for transformations.

so hmmm if we grab f(x) and move it downwards by 8 units, that means that the value for "D" gets a -8 added to it, so let's do that.

[tex]f(x)=3x^2+1\qquad \implies f(x)=\stackrel{A}{3}(\stackrel{B}{1}x+\stackrel{C}{0})^2+\stackrel{D}{1} \\\\\\ g(x)=3(1x+0)^2+1+(-8)\implies {\LARGE \begin{array}{llll} g(x)=3x^2-7 \end{array}}[/tex]

The final answer for this is $36.95.

Now, if we se the explanation

We have, the cost for pizza and pasta for four people is $24.99

and,

the cost of drink for single person is $2.99

Now, if we calculate the cost of drinks for all the four person,

it would be $2.99 × 4 = $11.96.

It is the cost of drinks only for four people.

we have already given the cost of eat I.e. $24.99

total cost for four people to eat and drink is

= $11.96 + $24.99

=  $36.95

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Answer:

243m²

Step-by-step explanation:

work out 18x18=324

work out 9x9=81.

324-81= 243

The calculation for the average water bill for such entire year in sigma notation.

[tex]\bar{x}=\frac{1}{12} \sum_{i=1}^{12} x_i[/tex]

To depict a series in a succinct format, summation or sigma symbols can be employed. The sum is denoted by the Greek capital letter ∑, The series 4+8+12+16+20+24 has the formula 6∑n=14n. As n increases from 1 to 6, the statement is read as the total of 4n.

Summation notation (also known as sigma notation) allows us to express a large sum in a single phrase.

The mean in mathematics and statistics is the average of a set of values. There are several methods for computing the mean, including the simple arithmetic mean, the geometric mean, and the harmonic mean.

 x₁       x₂     x₃     x₄      x₅      x₆      x₇     x₈      x₉     x₁₀     x₁₁     x₁₂

$40   $42  $40  $38  $48   $50  $58  $62  $56  $46   $44   $44

The calculation for the average water bill for such entire year in sigma notation.

[tex]\bar{x}=\frac{1}{12} \sum_{i=1}^{12} x_i[/tex]

  [tex]\bar{x}[/tex] = (40+42+40+38+48+50+58+62+56+46+44+44)/12

     = 568/12

     = 47

The calculation for the average water bill for such entire year in sigma notation.

[tex]\bar{x}=\frac{1}{12} \sum_{i=1}^{12} x_i[/tex]

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The sum of (3x² + 2x + 3) + (x² + 1) will be 4x² + 2x + 4.

The sum of (3x² + 2x + 3) + (x² + 1) will be calculated by simply adding the values.

This will be:

= (3x² + 2x + 3) + (x² + 1)

= 3x² + x² + 2x + 3 + 1

= 4x² + 2x + 4

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No, there is only one outlier at 58 minutes.

An observation that differs abnormally from other values in a population-based random sample is referred to as an outlier. In a way, this definition defers to the analyst's (or a consensus process') judgment as to what constitutes aberrant behavior. It is vital to define typical observations before distinguishing aberrant ones.

A data point is considered an outlier if it is more than 1.5 times the IQR below the first quartile or more than 1.5 times the IQR above the third quartile, according to the general criterion for utilizing it to compute outliers. The first and third quartile percentiles must be known in order to compute the IQR.

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.

9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim?

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136.5 percent chance.

91 percent in one hour

how much percent in 1.5 hour?

we need to find how much percentage is in 0.5 hour

91 divided by 2 = 45.5

91 + 45.5 = 136.5

Am i bad? pls tell

The standard error on the mean of these numbers is 1.08

For given question,

suppose your group measures the following three numbers in some experiment: 12.4,7.8,10.2

Mean of these numbers is:

[tex]\bar x=\frac{ 12.4+7.8+10.2}{3}\\\\ \bar x=10.13[/tex]

So the standard deviation would be,

[tex]\sigma=\sqrt{\frac{(12.4-10.13)^2+(7.8-10.13)^2+(10.2-10.13)^2}{3} }\\\\\sigma=1.88[/tex]

Now we find  the standard error on the mean of these numbers.

[tex]\sigma_M=\frac{\sigma}{\sqrt{N} }[/tex]

where, [tex]\sigma_M[/tex] = standard error of the mean

σ = the standard deviation of the original distribution

N = the sample size

[tex]\sigma_M=\frac{1.88}{\sqrt{3} }\\\\\sigma_M=1.08[/tex]

Therefore, the standard error on the mean of these numbers is 1.08

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Answer:

[tex]2 + 2 + 2 - 2 = 29[/tex]

Volume of a regular Octagon pyramid is = 96.55 [tex]feet^3[/tex]

In the given statement is:

The greenhouse at the right is a regular octagonal pyramid with a height of 5 feet. The base has side lengths of 2 feet.

To find the Volume of the greenhouse

We know that the :

Area of Regular Octagonal Pyramid is [tex]2a^{2}(1+\sqrt{2} )[/tex]

a = side of an octagonal

and, a= 2 feet

Let's find Area of Octagonal :

Now, putting the value of a in above formula:

[tex]2(2^{2} )(1+\sqrt{2} )\\\\8(1+\sqrt{2} )\\\\=19.31 feet^{2}[/tex]

Now, Volume of the green house

Volume of a regular Octagon pyramid is = Area of an Octagon x height

Height = 5 feet

Now,   Volume of a regular Octagon pyramid is = 19.31×5

Volume of a regular Octagon pyramid is = 96.55 [tex]feet^3[/tex]

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Similarly, Q1 is obtained as the median of the lower half as (7+1)/2th = 4th observation i.e 60.

Similarly, Q3 is obtained for the upper half as 79 (4th upper half)

IQR (Interquartile Range) = Q3 - Q1 = 79 - 60 = 19

The interquartile range is a gauge for where a data set's "middle fifty" lies. An interquartile range (IQR) measures where most of the values lay, whereas a range measures where a set's start and finish are. For this reason, it is preferable when reporting things like academic performance or SAT scores over many other measures of spread.

The interquartile range IQR is 19

In ascending order we have: 48,51,57,60,63,65,69,71,72,73,75,79,85,88,97

Also, we get sample size (n) = 15 (odd)

So, Median = Q2 = (n+1)/2th observation

Median = (15+1)/2th term = 8th observation

Median = Q2 = 71

The formula for the interquartile range is the first quartile less the third quartile:

IQR = Q3 - Q1.

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Answer:

1. Not Linear

2. Linear

3. Linear

4. Linear

Step-by-step explanation:

Linear means it follows the form y = mx + b

1. The x value increases by 2 each time, but the y value doubles each time. They are increasing at different rates, so they are not linear.

2. The x value is increasing by 3 each time, and the y value is deceasing by 1 each time. Slope (m) of this line would be -1/3

3. The x value is increasing by 4 each time, the y value is increasing by 3 each time. Slope (m) of this line would be 4/3

4. The x value is increasing by 1 each time, the y value is constantly -3. This means that the line is a horizontal line, which is linear with a slope of 0. So the equation of this line would be y = 0x -3 ---->  y = -3

There of  288 different kinds of  lunch combination .

What is combination ?

The Munchery Restaurant advertises that you can have a different lunch combination every day of the year.

types of soups  =  12

types of sandwich = 4

types of bread = 4

find the number of combinations we multiply all the possible types we have

Number of combinations = 12 × 6 ×  4  =  288

There of  288 different kinds of  lunch combination .

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