prove that there is a positive integer that equals the sum of the positive integers not exceeding it. is your proof constructive or nonconstructive? proof by cases

A z-score of -2 means that the income of $40,000 is 2 standard deviations below the mean income of $64,000.

The z-score is a standard measure of how many standard deviations a data point is away from the mean. To determine the z-score, we need to use the formula:

z = (x - μ) / σ

Where x is the data point of interest ($40,000), μ is the mean ($64,000), and σ is the standard deviation ($12,000).

Substituting the values:

z = (40000 - 64000) / 12000

z = -2

Therefore, the z-score for someone with an income of $40,000 is -2.

In conclusion, a z-score of -2 means that the income of $40,000 is 2 standard deviations below the mean income of $64,000.

Hence, the correct answer is B.

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--The given question is incorrect; the correct question is

"Consider that in 2019, U.S. household income had a mean of $64,000, a standard deviation of $12,000, and a frequency distribution that was mound-shaped and symmetric. Determine the z-score for someone with an income of $40,000.

A. -3.00

B. -2.00

C. 2.00

D. 3.00"--

The correct compound inequality is:

x - 4 < 9 or x - 4 > -9

We want to find a compound inequality equal to the absolute value one below:

|x - 4| < 9

We can break it into two ones, these are:

x - 4 < 9

x - 4 > -9

Solving these two we will get:

x < 9 + 4 = 13

x > -9 + 4 = -5

Then the compound inequality is:

x < 13

x > -5

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No, blinding was not demonstrated in the experiment because the volunteers knew whether they are drinking purple juice or yellow juice.

Blinding is the process of hiding a participant's group assignment from one or more other participants in a clinical research study, most frequently a randomized controlled trial (RCT).

Although the candy has the same flavour as the drink, participants can tell the difference based on colour. No, because the participants are aware of whether they are consuming yellow or purple juice.

To create a yellow or pink candy, two separate additives that don't affect flavour are added to identical sweets.

In each experiment, group allocations are concealed from data analyzers by blinding or masking. This experiment is not a blinding demonstration since the subject is aware of the juice.

As a result, adolescent volunteers are at random allocated either pink candy or yellow candy, both of whom are aware of the juice.

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The sample size, n is 9 and the sample mean, m is 41.33.

The exam has possible points and the scores for the students in the third classroom are as follows: 30 48 44 32 44 44 32 48 50.

We are asked to determine the sample size(n) and sample mean(m).

Sample size refers to the number of observations included in a study. In this question, the number of observations is equal to the number of scores in the third classroom. Hence, the sample size(n) is equal to n.

Now, the formula of the sample mean(m) is given as  

                m = Sum of all observations/Total Number of observations

          m =  30 + 48 + 44 + 32 + 44 + 44 + 32 + 48 + 50/9

          m = 372/9

          m = 41.33

Hence, the sample mean(m) of the scores for the students in the third classroom is 41.33.

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The calculation for the correlation coefficient for the data graphed was 0.99 which is indicative of a strong positive correlation between smoking rates and lung cancer.

The data graphed showed a positive correlation between smoking rates and lung cancer. The correlation coefficient for the data was 0.99, which is very close to 1. This indicates a strong positive correlation between smoking rates and lung cancer. The formula for calculating the correlation coefficient is r = (NΣxy - (Σx)(Σy)) / √[(NΣx2 - (Σx)2)(NΣy2 - (Σy)2] where r is the correlation coefficient, N is the number of data points, Σx is the sum of all x-values, Σy is the sum of all y-values, Σxy is the sum of the products of the x and y values, and Σx2 and Σy2 are the sums of the squares of the x and y values respectively. The calculation for the correlation coefficient for the data graphed was 0.99 which is indicative of a strong positive correlation between smoking rates and lung cancer.

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The volume of the solid is 16.75 unit³ in the given line x+2y=8 intercseting the x-axis, the y-axis.

What is volumes of Solids?

We shall encounter several solids and their corresponding volumes when discussing the concept of the volume of combination of solids. As is common knowledge, the surface areas and volumes of all three-dimensional shapes depend on their dimensions. As we can see in reality, numerous shapes are created by fusing a variety of shapes. For instance, the combination of a cone and cylinder shapes creates a tent. Similar to how a cone and a hemisphere combine to form an ice cream cone. As a result, the volume of the solids combined will equal the total of the volumes of the individual solids.

The line  x+2y=8.

y = (8-x)/2

Volume will be V = π/2 ∫(r²) dr

So we have 1/3 π * r² * h

Here h = 8, r=2.

So V = 1/3 π * r² * h = 1/3 π * 2² * 8

V = 16.75 unit³

Hence ,the volume of the solid is 16.75 unit³

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El area del rectangulo es 11/3 m²

Longitud = 15/6 m

Ancho=22/15 m

Área = Largo × Ancho

= 15/6 × 22/15

= 22/6

= 11/3 m²

Un rectángulo es una forma plana bidimensional que tiene dos pares de lados paralelos que son paralelos y de la misma longitud, y consta de cuatro ángulos rectos o 90⁰. Esta forma plana también tiene líneas diagonales que tienen la misma longitud.

Para comprender mejor las características de los rectángulos y poder explicar las diferencias con otras formas, es importante que los estudiantes conozcan las propiedades de los rectángulos.

Las propiedades de un rectángulo:

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Answer: There will be 2 players notified in the 1st round of calls,

Those players will then call two players in the 2nd round of calls.

This second round will yield 2 x 2 = 4 players being contacted.

Therefore, 6 players will be contacted after the second round of calls.

Answer: 18 players will be notified during the 2nd round of calls.

Step-by-step explanation: When doing a simple question like this, just follow these steps: First, do 2x3 which equals 6. Then do 6x3, which equals 18. Then 54, then 162, then 486, and so on.

The total square footage (area) of the apartment is 385 square feet.

The total square footage, also known as the area, of an apartment is a measure of how much space the apartment has.

First, let's find the area of the 11ft by 11ft bedroom. To do this, we multiply the length and the width of the room. In mathematical terms, the area of a rectangle is equal to the length times the width. So, for the bedroom, the area is

=> 11ft * 11ft = 121 square feet.

Next, let's find the area of the 4ft by 6ft bathroom. The formula for the area of a rectangle is still the same, so the area of the bathroom is

=> 4ft * 6ft = 24 square feet.

Finally, we'll find the area of the multi-use living room/kitchen, which is 15ft by 16ft. The area of this room is

=> 15ft * 16ft = 240 square feet.

Now that we have the area of each room, we can add them together to find the total area of the apartment. So, the total area is

=> 121 square feet + 24 square feet + 240 square feet = 385 square feet.

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Let's assume that the total amount spent on the movie tickets and snacks is represented by x.

We know that:

The movie ticket costs $13.00

The drinks cost $6.00

Therefore, the equation representing the total amount spent is:

x = 13 + 6 + 4y

where y is the number of snacks purchased.

Let's substitute the given value of x:

23 = 13 + 6 + 4y

Subtracting 13 and 6 from both sides:

4 = 4y

Dividing both sides by 4:

y = 1

So, you purchased 1 snack.

i am 100 percent positivw thw answer is 1 snack

Answer:

C. 11:16

Step-by-step explanation:

It is C, it can't go simpler bcs of 11

Answer: 4) Trapezoid.

Step-by-step explanation:

#1 A rhombus has four equal sides, has opposite angles that are equal, and opposite sides that are parallell.

#2 A rhombus is close to three quadrilaterals that apply to a rhombuses terms, parallel sides, equal sides, equal angles, or opposite angles that are equal are: square, kite, and parallelograms that have the following.

#3 A Trapezoid, however, has four different lengths and different angles. Only one pair of sides from a trapezoid are parallel.

Your welcome, I hope this much information will help you. Good day/night. If the answer incorrect, or there are errors in this explanation, please let me know. Thank you.

Answer:John

Step-by-step explanation: John got 3 shirts each for 25.25

Jayda got 4 shirts each for 27

Answer:

$66.43

Step-by-step explanation:

​47.45$​ divided by 5

9.49*7

=66.43

The solution is (6, 32) and it means that the total cost of 6 kites from 2 different businesses is $32.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph of two lines,

The intersection point is the solution to the two lines system of equations.

Now,

The intersection point = (6, 32)

This means,

x = 6 and y = 32

x = number of kites

y = total cost of the kites

Thus,

The solution is (6, 32).

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The population will be 40 thousnd after 22.5 years,and 60 thousand after 34.4 years.

First, we want to estimate the number of years that takes to reach 40 thousand, to estimate that we need to look at the graph.

We can see that when y = 40, the value of x is between 20 and 25 (almost in the middle)

So here we estimate that the answer is 22.5

b) Now we want to estimate it using the equation

p(x) = 18*e^(0.035*x)

We want to find how many years it takes to reach a population of 60 thousand, then we need to solve:

p(x) = 18*e^(0.035*x) = 60

        e^(0.035*x) = 60/18

Using the natural logarithm in both sides:

ln( e^(0.035*x))  = ln(60/18)

0.035*x =  ln(60/18)

x =  ln(60/18)/0.035 = 34.4

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Answer:

vector

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C, probability is the answer

Answer:

False

Step-by-step explanation:

The number of aluminium balls with a radius of 4.5 in will be 200.

The amount of space that a sphere can occupy is measured by its volume. The three-dimensional shape of a sphere lacks vertices and edges.

Given that Amy's company makes solid balls out of scrap metal for various industrial uses. Her current task is to make a batch of aluminium balls with a radius of 4.5 in. The total volume of the aluminium is 76302 cubic inches.

The number of spheres with a radius of 4.5 inches will be calculated as:-

Number = ( Total volume of aluminium) / ( Volume of the small sphere)

The volume of small sphere = ( 4 / 3 ) πr³

The volume of small sphere = ( 4 / 3 ) π x 4.5³

The volume of the small sphere = 381.7 cubic inches

Number = ( Total volume of aluminium) / ( Volume of the small sphere)

Number = 76302 / 381.7

Number = 200

Hence, the number of spheres will be 200.

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6x³ - 4x² - 16x

To factorize the expression first factor out the GCF out

The GCF in the expression is 2x

2x( 3x² - 2x - 8)

Next, Factorize the terms in the bracket

To factorize write - 2x as a difference

2x( 3x² + 4x - 6x - 8)

Factor out x from the expression

2x [ x( 3x + 4) - 6x - 8 ]

Next factor out - 2 from the expression

2x [ x ( 3x + 4) - 2( 3x + 4) ]

Factor out 3x + 4 from the expression

The final answer : 2x( 3x + 4)( x - 2)

Letter C

When a projectile is at the top of its path, its vertical velocity that is Y direction velocity is 0 m/s. At this point, the projectile has reached its maximum height and is changing direction from moving upward to moving downward.

A vector is a matrix that has only one row or one column. A row vector is a matrix with only one row. Example Because it only contains one row, the matrix is a row vector. A column vector is a matrix with only one column. We can express a vector as a matrix since it is simply a collection of integers. This is why vectors may be written in matrix notation. A vector is a quantity linear array. A matrix is a two-dimensional array of values. Tensors are three-dimensional and higher-dimensional arrays that exist. A matrix may be seen as both a series of column vectors and a sequence of row vectors.

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The new graph would have the same intercept, however it would always assume lesser values than the old graph due to the new slope being less than the old slope.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Hence the two functions are given as follows:

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The common ration between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is ( r,a) = ( 1/7, 12/7)

That means { a/ 1-r} = 2

a^2/1-r^2 = 3

2a/ 1+r = 3

2(2-2r)/ 1+r = 3

4-4r= 3+ 3r

7r + 1

r= 1/7

2a/ 8/7 = 3

7a= 12

a= 12/7

so( r,a) = ( 1/7, 12/7)

What is infinite geometric series?

An infinite geometric series is the sum of an infinite geometric sequence. This series would have no last term. The general form of the infinite geometric series is a1 + a1r + a1r2 + a1r3+…, where a1 is the first term and r is the common ratio.

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Answer:

y = 1/5 x + 5

Step-by-step explanation:

20y- 4x = 100

Slope intercept form is y = mx+b  where m is the slope and b is the y-intercept.

Solving the equation for y

20y = 4x+100

Divide each side by 20

y = 4x/20 + 100/20

y = 1/5 x + 5

The slope is 1/5 and the y-intercept is 5

Answer:

y = 3

x = 5

Step-by-step explanation:

hope it helps.

The secant-tangent rule which is a relationship between a secant and a tangent of a circle indicates that we have;

(a) [tex]\overline{BC}[/tex]² = [tex]\overline{CD}[/tex] × [tex]\overline{CF}[/tex]

(b) The length of the tangent [tex]\overline{BC}[/tex], found based on the secant-tangent rule is 12 inches

A tangent to a curve at a point is the line that touches the curve at the specified point and has the same slope as the curve at the point.

(a) The relationship between the lengths of the segments formed by the secant and the tangent is indicated by the secant-tangent rule which can be presented as follows;

[tex]\overline{BC}[/tex]² = [tex]\overline{CD}[/tex] × [tex]\overline{CF}[/tex]

Therefore, the relationship between the segments is that the square of the length of the tangent is equivalent to the product of the length of the secant and the external segment of the secant

(b) Where the length of the secant (segment) [tex]\overline{CD}[/tex] = 16 inches, and the length of the external segment of the secant, [tex]\overline{CF}[/tex] = 9 inches, therefore, according to the secant-tangent rule, we get;

[tex]\overline{BC}[/tex]² = 16 × 9 = 144

[tex]\overline{BC}[/tex] = √(144) = 12

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The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

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The required simplified value of x for the given similar triangles is given as x = 5.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
From the similar triangle property,
The ratio of sides is equal for similar triangles so,
12/[12-8] = 15/x
12/4 = 15/x
x = 15/3
x = 5

Thus, the required simplified value of x for the given similar triangles is given as x = 5.

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Answer:

480

Step-by-step explanation:

Take 20% of 2400

Answer:

1920

Step-by-step explanation:

20% of 2400 = 480

2400-480= 1920