Which set of numbers is arranged from least to greatest?

Answer: Rational, integer, whole, natural, real

So basically everything but irrational

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

Explanation:

109 is a rational number because 109 = 109/1. Any rational number is a fraction of two integers. Because of this, it cannot be irrational as "irrational" means "not rational".

An integer is anything that does not have a fractional or decimal part. So it involves the set of positive and negative whole numbers, and zero as well. So we can see that 109 is an integer.

A whole number is very similar to an integer, but we're referring to the set {0, 1, 2, 3, ..} meaning we ignore the negative integers. This makes 109 a whole number as well.

A natural number is from the set {1, 2, 3, ...}. We've kicked 0 out from the set of whole numbers. This is the set of counting numbers. So 109 is also a natural number.

A real number is any number you have encountered so far assuming your teacher has not introduced complex and imaginary numbers yet. Effectively a real number is any number that can be written as decimal. This makes 109 to be a real number.

Answer:

The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs

of crackers

Step-by-step explanation:

IQR of trail mix data = 105 - 90 = 15

The range of cracker data = 100 - 70 = 30.

Therefore, the first option is NOT TRUE.

To check if option 2 is correct, calculate the lower limit to see if 70 is below the lower limit. If 70 is below the lower limit, then it is an outlier in the trail mix data.

Thus, Lower Limit = [tex]Q_1 - 1.5(IQR)[/tex]

Q1 = 90,

IQR = 105 - 90 = 15

Lower Limit = [tex]90 - 1.5(15)[/tex]

Lower Limit = [tex]90 - 22.5 = 67.5[/tex]

70 is not less than the lower limit, therefore, 70 is not an outlier for the trail mix data. The second option is NOT TRUE.

The upper quartile of the trail mix data = 105.

The maximum value of the cracker data = 100.

Therefore, the third option is NOT TRUE.

Range can be used to determine how much variable there is in a data represented on a box plot. The greater the range value, the greater the variation.

Range of trail mix data = 115 - 70 = 45

Range of cracker data = 100 - 70 = 30.

The range value for the number of calories in trail mix is greater than that for cracker, therefore, the number of calories in the packs of trail mix have a greater variation than the number of calories in the packs

of crackers.

The fourth option is TRUE.

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]

Required

Fill in the gaps

Going by the given parameters, we have that

[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]

[tex]x^2 - 9x + 8[/tex], when factorized is [tex](x-1)(x-8)[/tex]

Hence; the expression becomes

[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}[/tex]

Combine Fractions

[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}[/tex]

Simplify the denominators

[tex]4x + 2 = A + B[/tex]

By direct comparison

[tex]A = 4x[/tex]

[tex]B = 2[/tex]

Hence, the complete expression is

[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]

Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)

Answer:

A

Step-by-step explanation:

● first one:

The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.

STP is one of them so this statement is true.

● second one:

If ST and PT were equal this would be a square not a rhombus.

● third one:

If SPQ was a right angle, this woukd be a square.

● fourth one:

Again if the diagonals SQ and PR were equal, this would be a square.

Answer:

(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.

Step-by-step explanation:

The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.

If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.

So the initial weight would occur at (0, 79.5) which is the positive y-intercept.

And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.

Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.

Cheers.

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▹ Answer

1 - 9/7n

▹ Step-by-Step Explanation

1/7 - 3(3/7n - 2/7)

Remove the parentheses (Distribute -3 among the parentheses):

1/7 - 9/7n + 6/7

Calculate:

1 - 9/7n

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1-9/7n

Step-by-step explanation:

[tex]\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7} ) \\=\frac{1}{7}-\frac{9}{7}n +\frac{6}{7} \\=\frac{1-9n+6}{7} \\=\frac{7-9n}{7}\\=1-\frac{9}{7}n[/tex]

Answer:

make a table of values

Step-by-step explanation:

then plot using those values

The required graph has been attached which represents the line y = 4/3x

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We have been given the equation of a line below as:

y = 4/3x

Rewrite in slope-intercept form.

y = (4/3)x

Use the slope-intercept form to discover the slope and y-intercept.

Here the slope is 4/3 and  y-intercept = (0, 0)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,

Hence, the graph represents the line y = 4/3x

Therefore, the required graph of the line y=4/3x will be shown in the as attached file.

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ2

Answer:

Step-by-step explanation:

1. 4/4+4-4=1

2. 4/4+4/4=2

3. 4+4/4-4=3

4. 4 × (4 − 4) + 4=4

5. (4 × 4 + 4) / 4=5

6. 44 / 4 − 4=6

7. 4+4-4/4=7

8. 4+4+4-4=8

9. 4+4+4/9=9

10. 44 / 4.4=10

Answer:

1 = (4 x 4)/(4 x 4) or  (4 + 4)/(4 + 4) or  (4 / 4) x (4 / 4) or  (4 / 4)/(4 / 4)  

2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)

3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4

4 = 4 - (4 - 4)/4

5 = (4 x 4 + 4)/4

6 = 4 + (4 + 4)/4

7 = 4 - (4/4) + 4

8 = 4 + (4 x 4)/4

9 = 4 + 4 + (4/4)

10 - I tried the best. You might need ! or sqrt operator to get 4.

Updated:

I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:

10 = (44 - 4)/4

Answer:

9u^3 + 6u^2 - 7u + 6

Step-by-step explanation:

Answer:

if he needs to walk, we can see that between the street and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.

Now he has a jet-pack, he can ignore the buildings and just travel in the shorter path, so we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.

One of the cathetus is the vertical distance, in this case, is 1km, and the other one is the horizontal distance, also 1km.

So the actual distance is given by the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse, then:

H^2 = 1km^2 + 1km^2

H = (√2)km = 1.41km.

Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, so in this case the distance and the displacement would be the same.

Distance: "how much ground an object has covered"

Displacement: "Difference between the final position and the initial position"

When he walks, the distance is 2km, but the displacement is 1.41km

When he uses the jet-pack, both the distance and the displacement are 1.41km

Answer and Step-by-step explanation:

The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km.  The result of this is a total of 4¨*0.5 km = 2 km.  The second thing is that he must walk 2 kilometers.  On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings.  This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home.  As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km.  The result is that these catheti have a length of 2*0.5 km = 1 km.  The other is the distance of the horizontal line, which is 1 km.  The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2.  Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2.  As well, H = (√2)km = 1.41 km.  Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow.  For this specific situation, the displacement, and the distance would be the exact same.  The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered.  Also, when he walks, the distance is 2 km and the displacement is 1.41 km.  Also, when he utilizes the jet pack, the distance is equal to the displacement.  Both of these are 1.41 km.

Answer:

x > 39 hours

Step-by-step explanation:

Let x be the number of hours she worked.

11x - is how much she would get paid for working for x hours

11x + 20 > 450

11x > 430

x > 39 hours

Hope that helped!!! k

Answer:

Step-by-step explanation:

a) First differences of the f(x) values in the table are ...

  19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162

The second differences are not constant:

  18 -6 = 12, 54 -18 = 36, 162 -54 = 108

But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.

__

b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...

  9, 15, 33, 87, 249

__

c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...

  (x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)

Answer: I think this is it:

The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)

Step-by-step explanation: I got it right on Edmentum!

Answer:

a) 40 dollars

b) 480 dollars

Step-by-step explanation:

Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0

T'(x) = 2(20)x¹ + 40x° + 0

T'(x) = 40x+40

At x = 0,

T'(0) = 40(0)+40

T'(0) = 40

Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).

b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)

Given T(x) =20x²+40x+600

T(4) =20(4)²+40(4)+600

T(4) = 320+160+600

T(4) = 1080 dollars

Also T(0) =20(0)²+40(0)+600

T(0) = 0+0+600

T(0)= 600 dollars

T(4) - T(0) = 1080 - 600

T(4) - T(0) = 480 dollars

Hence, the tax has changed by $480 between 2008 and 2012

Answer:

26.75 units²

Step-by-step explanation:

Cube Area: A = l²

Triangle Area: A = 1/2bh

Step 1: Find area of biggest triangle

A = 1/2(3.5)(2 + 2 + 5)

A = 1.75(9)

A = 15.75

Step 2: Find area of 2nd biggest triangle

A = 1/2(5)(2)

A = 1/2(10)

A = 5

Step 3: Find area of smallest triangle

A = 1/2(2)(2)

A = 1/2(4)

A = 2

Step 4: Find area of cube

A = 2²

A = 4

Step 5: Add all the values together

A = 15.75 + 5 + 2 + 4

A = 20.75 + 2 + 4

A = 22.75 + 4

A = 26.75

Answer:

The correct answer is A

Step-by-step explanation:

Answer:

(-8, -2)

Step-by-step explanation:

y-x = 6

y + x = -10

Add the two equations together to eliminate x

y-x = 6

y + x = -10

--------------------

2y = -4

Divide by 2

2y/2 = -4/2

y = -2

Now find x

y+x = -10

-2+x = -10

x = -8

Answer:

72/n^5r

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

13)

● 2d^3 × c^6 × 8d^5 × c^2

Isolate the similar terms

● (2×8)× (d^3 × d^5)×(c^6×c^2)

● 16 × d^(3+5) × c^(6+2)

● 16 × d^8 × c^8

● 16 × (dc)^8

● 16(dc)^8

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 8n×r^(-4) ×9×n^(-6)×r^3

Isolate the similar terms

● (8×9)× (r^(-4)×r^3) × (n×n^(-6))

● 72 × r^(-4+3) × n^(1-6)

● 72 × r^-1 × n^(-5)

● 72 ×(1/r) × (1/n^5)

● 72/(r×n^5)

Answer:

a. 2

b. x²+10x+26

c. x²+2x+2

Step-by-step explanation:

To find each value, you plug in the x value into the function and solve.

a. 2

f(2)=(2)²-2(2)+2                              [combine like terms]

f(2)=4-4+2

f(2)=2

---------------------------------------------------------------------------------------------------------

b. x²+10x+26

f(x+6)=(x+6)²-2(x+6)+2                  [use FOIL method and distributive property]

f(x+6)=x²+12x+36-2x-12+2            [combine like terms]

f(x+6)=x²+10x+26

---------------------------------------------------------------------------------------------------------

c. x²+2x+2

f(-x)=(-x)²-2(-x)+2                            [combine like terms]

f(-x)=x²+2x+2

Answer:

192 [tex]ft^2[/tex]

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

[tex]\pi[/tex] is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. [tex]Volume =\frac{4}{3}\pi r^3[/tex]

2. [tex]Surface\ Area = 4\pi r^2[/tex]

Given volume is 256 ft³.

[tex]256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}[/tex]

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

[tex]Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}[/tex]

So, approximate surface area of sculpture is 192 [tex]ft^2[/tex].

Answer:

192

Step-by-step explanation:

Answer:

A) Q(t) = 4e^-(0.0079t)

B) t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Step-by-step explanation:

a)

to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.

so given that; half-life of ²³⁸Pu is 87.7 years,

∴ t =  87.7 years , Q(t) = 0.5Q₀

Now we substitute these value in the form  Q(t)= Q₀e⁻^kt

Q(t)= Q₀e⁻^kt

0.5Q₀ = Q₀e^ -(87.7k)

0.5 = e^ -(87.7k)

now we take the natural logarithm of both sides

In(0.5) = Ine^ -(87.7k)

Now using the property logₙnᵃ = a

-87.7k = In(0.5)

k = - In(0.5) / 87.7

k = 0.0079

ALSO it was given that Q₀ = 4.0 kg

Therefore , model quality Q(t) of ²³⁸pu left after t years is:

Q(t) = 4e^-(0.0079t)

b)

to find the time left after 1.6kg of ²³⁸pu

we simple substitute  Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)

so we have

1.6 = 4e^-(0.0079t)

e^-(0.0079t) = 1.6/4

e^-(0.0079t) = 0.4

again we take the natural logarithm of both sides,

Ine^-(0.0079t) = In(0.4)

again using the property logₙnᵃ = a

-0.0079t = In(0.4)

t = - in(0.4) / 0.0079

t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Answer:

The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1

Step-by-step explanation:

Answer:

[tex]\boxed{22,500}[/tex]

Step-by-step explanation:

Hey there!

Well, half of 300 is 150, and 150•150 = 22500

So 150 and 150 are it's highest numbers.

Hope this helps :)

Answer:

Yes, it is invertible

Step-by-step explanation:

We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.

Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!

Then the determinant of this matrix becomes:

[tex]4\,*Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] +0+0+0[/tex]

And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:

[tex]Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] =1 \,(3\,*\,1-0)+4\,(0-0)+6\,(0-0)=3[/tex]

Therefore, the Det of the initial matrix is : 4 * 3 = 12

and then the matrix is invertible

Answer: 200 ways

Step-by-step explanation:

From the given information:

Total number of roads leading from Bluffton to​ Hardeeville = 4

Total number of roads leading from Hardeeville to​ Savannah = 10

Total number of roads leading from Savannah to Macon = 5

We need to find the total number of ways to get from Bluffton to​ Macon.

Total number of ways to get from Bluffton to​ Macon = 4 * 10 * 5

= 200

Therefore, there are 200 required number of ways to get from Bluffton to​ Macon.

Answer:

These are the first 100 digits of pi: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067

Step-by-step explanation:

Pi goes on continuously forever, so this is a reduced version, by including the first 100 digits.

Answer: stratified

Step-by-step explanation:

In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)

In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.

So this would be a "stratified sampling".

X/5 -1/2 = x/6

Find the least common denominator of the 3 denominators:5,2,6

The limited is 30

Multiply all 3 fractions by 30:

6x -15 = 5x

Subtract 6x from both sides:

-15 = -x

Multiply both sides by -1:

X = 15

Answer:

the value of the test statistic is calculated as "T - distribution" with the formula;

t = (x-bar - μ)/(s/√n)

Step-by-step explanation:

We are told that the standard deviation is unknown. But normally, we use a z-distribution if the standard deviation is known.

However, in a hypothesis test for a population mean where the population standard deviation is unknown is still conducted in the same way like we do when we know the population standard deviation. The only difference in this case is that we will use the t-distribution rather than the standard normal z-distribution.

The t-distribution formula used is;

t = (x-bar - μ)/(s/√n)

Full question attached:

Answer and explanation:

A) B2*B10: cell B2 and B10 have the values regular swear costs and number of swears respectively and we need to multiply these two values to get our answer

B) =IF(B10>10,(B10-10)*B3,0): Sam is supposed to pay an extra $2 for swear words over 10 and so we check if his swear words are above 10 and if they are we find out how many they are by subtracting 10 from them and then we multiply the value gotten by the cost for extra swear words($2)

C) =IF(B10<5,B10*B4,0): here we check if swear words are less than 5 and if they are we multiply number of swears words less than by 5 by the cost ($0.50)

D) F10=C10+D10+E10: to calculate total money in jar(F10), we simply add up regular cost(C10), extra cost(D10) and refund(E10)

Answer:

Step-by-step explanation:

notice

The temperature starts off below zero in the early morning and stays cold until the sun comes up. Then it warms rapidly to an above zero temperature that peaks in early afternoon. Once the sun gets lower, the temperature starts cooling off again. (The daily temperature range of 25-27 degrees is pretty typical for partly-cloudy sky conditions and stable weather.)

wonder

We wonder if this isn't a location that is on the east- or north-side of a mountain, or in a mountain valley, where the sun hits it early and is shaded later in the day. (The topo map attached seems to show it is in such a location.)

Answer: $27,279

Step-by-step explanation:

The data is:

Clarissa earned $2,247 per month, in the first 7 months.

After that, she earned $2,310 per month.

What total gross pay did Clarissa  earned in one year?

Ok, a year has 12 months, in the first 7 months she earned $2,247 per month, so 7 times $2,247, this is:

7*$2,247 = $15,729

And in the other 12 - 7 = 5 months, she earned $2,310 per month, so 5 times $2,310.

5*$2,310 = $11,550

Adding those togheter:

Total gross = $15,729 + $11,550  = $27,279