I need help with this problems i dont understand what they are asking

As reported by the Bureau of Labor Statistics, the inflation rate of CPI for Airfare from 2263 and 22264 is - 0.06198 ( disinflation).

We have given that,

The CPI for Airfare in 2263 = 579.6

The CPI for Airfare in 2262 = 617.9

Base year is 1914 ,

Following the formula which is used to calculate inflation rate of airfare from 2263 to 2263

Inflation= (CPI₂₂₆₃ - CPI₂₂₆₂)/CPI₂₂₆₂

= (579.6 - 617.9)/617.9

= - 153.8/617.9

= - 0.06198

= 6.198%

Since , the inflation is negative this means that the economy is experiencing disinflation of 6.198%.

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The following list has six more terms than the preceding one. What does x+z equal if it is -10?

A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit with in sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.

t1=X\st2=y\st3=Z

t4=7\st5=13

common distinction Since d=6, t4=t3+d 7=t3+6 t3=7-6 t3=1=Z

Z=1\st3=t2+d

X + Z= (-11) + 1 X+Z = -10 because 1 = t2+6 t2= 1-6 t2= -5 = y y= -5 t2= t1+d -5= t1+6 t1= -5 -6 t1= -11 =X X = -11

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Answer:

  D.  70°32'

Step-by-step explanation:

You want the angle represented by arccos(0.333) to the nearest minute.

The attached calculator shows the angle in degrees (70.54903521713) and in degrees, minutes, and seconds (70°32'56.53"). There are 60 seconds in a minute, so the number of seconds being more than 30 means the minutes should be rounded up to ...

  70°33'

The closest answer choice is D. 70°32'.

The real zeros of the quadratic function  f(x) = 2x² - 5x + 1 is between

The given quadratic function is  f(x) = 2x² - 5x + 1

Using a calculator the zeros of the function  f(x) = 2x² - 5x + 1 is solved to be

x = 2.28 OR 0.22

The value 0.22 falls between 0 and 1 = 0 < x < 1

this means greater than 0 and less than 1

The value 2.28 falls between 2 and 3 = 2 < x < 3

this means greater than 2 and less than 3

Therefore the second option is the right choice

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Answer:

After tax = Bill * (1 + rate)

25.30 = x * (1 + 0.08)

25.30 = x * 1.08

25.30 = 1.08x                 (divide 1.08 both side)

x = 23.43

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Step-by-step explanation:

6/8 is an equivalent fraction to 3/4; 2/6 is equivalent to 1/3; 6/9 is equivalent to 2/3; 10/25 is equivalent to 2/5; 4/16 is equivalent to 1/4; the fraction of 1/3 is equivalent to 2/6; 8/16 is an equivalent fraction to 2/4.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. The fractions equivalent to each other have been mentioned above.

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Answer:

y=x^2 + 1

Step-by-step explanation: the second parabola is only raised by 1 unit up, therefore the entire function shifts upwards by 1.

Check the picture below, so that's the triangle hmmmm a bit non-right-triangle or irregular per se, so let's use Heron's formula on this one, so we'll have to first find the length of each side

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ J(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill JK=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill JK=\sqrt{( 2)^2 + ( 2)^2} \implies JK=\sqrt{ 8 }[/tex]

[tex]K(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad L(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill KL=\sqrt{(~~ 3- 0~~)^2 + (~~ -4- 3~~)^2} \\\\\\ ~\hfill KL=\sqrt{( 3)^2 + ( -7)^2} \implies KL=\sqrt{ 58 } \\\\\\ L(\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\qquad J(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill LJ=\sqrt{(~~ -2- 3~~)^2 + (~~ 1- (-4)~~)^2} \\\\\\ ~\hfill LJ=\sqrt{( -5)^2 + (5)^2} \implies LJ=\sqrt{ 50 }[/tex]

now let's use those three lengths for Heron's

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{8}\\ b=\sqrt{58}\\ c=\sqrt{50}\\ s=\frac{\sqrt{8}+\sqrt{58}+\sqrt{50}}{2}\\\\ \qquad \frac{\sqrt{58}+7\sqrt{2}}{2} \end{cases}[/tex]

[tex]A=\sqrt{\frac{\sqrt{58}+7\sqrt{2}}{2}\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{8} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{58} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{50} \right)} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=10 \end{array}}~\hfill[/tex]

Not agree with the Mr. Chin's conjecture, because there may be space for the desk in the room but Mr. Chin not have the actual measurement, it may or may not fit the  desk in room of given length and width.

A good guess or an idea about a pattern is a conjecture. Speculate (about something) We can only speculate about the killer's thoughts. speculate that... He speculated that the population might double within a decade. speculate about something She speculated about the existence of a brand-new species.

A mathematical assertion that has not yet been thoroughly established is known as a conjecture. When one observes a pattern that is consistent across many cases, speculations result. However, just because a pattern applies to a lot of cases does not mean that it applies to all of them. To fully accept the mathematical observation, conjectures must be demonstrated. A theorem is formed when a conjecture is thoroughly demonstrated.

A crucial step in solving a problem is making a guess; It's more than just a tool for professionals in math. It is extremely uncommon for a problem's solution to be immediately apparent in everyday problem solving. Instead, the process of solving problems involves looking at the problem structure, looking at the cases, making a guess about the solution, and then proving that guess.

Hence, not agree with Mr. Chin's conjecture.

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Answer:

1

Step-by-step explanation:

Bc I have calculator

On solving the provided question, In the case of four numbers, 1 and 3 are odd and 2 and 4 are even. As a result, the numbers are odd in half, so the answer is 1/2.

The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:

Probability (event) = positive outcome / overall outcome = x/n

In the case of four numbers, 1 and 3 are odd and 2 and 4 are even. As a result, the numbers are odd in half.

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The greatest common factor of the given term is 26.

What is the greatest common factor?

The greatest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.

The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.

Given, [tex]\frac{52}{78} = \frac{26*2}{26*3}[/tex]

So, the simplest form is [tex]\frac{2}{3}[/tex].

Hence, the greatest common factor is 26.

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The equation of the regression line of the given data is y = 1.28x + 3.69. By using a scatter plot, the required equation is calculated.

A regression line describes the relationship between the dependent and independent variables of a set of data.

It is given by y = mx + b; where m is the estimated slope of the data and b is the estimated y-intercept of the data.

To find the regression line, we need to draw the scatter plot for the given data.

The coordinates paired from the given data are:

(12, 18.11), (7, 14.08), (11, 17.97), (8, 15.55), (13, 17.93), (4, 7.71), (3, 4.93), (5, 10.77), and (9, 16.68).

The scatterplot for these points is shown below:

From the plot, consider any two points on the line.

Such as (x1, y1) = (3.35, 7.99) and (x2, y2) = (9.61, 16.02)

So, the equation of the regression line is

(y - y1) = {(y2 - y1)/(x2 - x1)} (x - x1)

⇒ (y - 7.99) = {(16.02 - 7.99)/(9.61 - 3.35)} (x - 3.35)

⇒ y - 7.99 = (8.03/6.26)(x - 3.35)

⇒ y - 7.99 = 1.282(x - 3.35)

⇒ y - 7.99 = 1.282x - 4.2947

⇒ y = 1.282x + 3.695

When rounded to two decimals, we get

y = 1.28x + 3.69

Therefore, the equation of the regression line of the given data is y = 1.28x + 3.69.

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As per the 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year is (0.1859,0.2133).

Confidence interval:

In statistics, confidence interval is an estimate of an interval in statistics that may contain a population parameter.

Given,

According to a recent pew research center report, many American adults have made money by selling something online. in a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met.

Here we need to construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.

As per the given question, the value of

Confidence interval = 98%

Number of samples = 4579

Reported numbers = 914

Therefore, the number of failure is calculated as,

=> 4579 - 914

=> 3665

Here the sample proportion is the number of successes divided by the sample size:

=> 941/4579

=> 0.1996

Here for confidence level 1 − α = 0.98,

We have to determine zα / 2 ​= z0.01​ using the normal probability table in the appendix, we get

zα/2 ​= 2.33

Then the margin of error is calculated as,

E = 2.33 x √[0.1996 x (1 - 0.1996)]/4579

E = 0.0137

Then the boundaries of the confidence interval are then:

p⁻ˣ = 0.1996−0.0137 = 0.1859

p⁺ˣ = 0.1996+0.0137 = 0.2133

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Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

The exact midpoint between two other plane points needs to be found on occasion. For example, you might seek out a line that splits a particular line segment into two equal halves. This central region is known as the "halfway."

Here,

If you are aware of one endpoint (x1, y1) and the midpoint (a, b), but are unaware of the second endpoint (x2, y 2), you can solve the problem by rewriting the

=> a=[tex]\frac{x1+x2}{2}[/tex]

=> 2a=x1+x2

=>2a-x1=x2

=> b=[tex]\frac{y1+y2}{2}[/tex]

=>2b=y1+y2

=> 2b-y1=y2

So, the unknown endpoint can be found by

(x2,y2)=(2a-x1,2b-y1)

Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

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Answer:

Step-by-step explanation:

You want to know various values of p and q when p varies inversely as the square of q, and p=36 when q=25.

A formula describing the variation of one variable with another will generally have a constant of variation, which we choose to represent here by the letter k.

Since p varies inversely as the square of q, the formula can be written as ...

  [tex]p=\dfrac{k}{q^2}[/tex]

Multiplying by q² gives us a way to find the value of k from known values of p and q:

  k = p·q²

  k = 36·25² = 22500 . . . . . . using the given values of p and q

We can also rearrange the formula to give q as a function of p:

  q = √(k/p)

We are interested in q for p=4, and in p for q=10.

  q = √(22500/4) = 75

  p = 22500/10² = 225

Answer:

$16.67

Step-by-step explanation:

$19.38*14%=$2.71

$19.38-2.71=$16.67

35% of the fuel Capacity did not use on this flight.

Step 1: Calculate the change i.e., subtract old value from the new value

Step 2: Divide that change by the old value.

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

 Percentage change = ((final value - initial value) ÷final value) ×100

Given: Total capacity in a fuel tank of a jet = 200000 liters

Used fuel =130000 liters

% Of fuel which is not used = ((total capacity of fuel tank - used fuel) ÷total capacity of fuel tank) ×100

[tex]=\frac{200000-130000}{200000}*100\\=\frac{70000}{2000}[/tex]

=35%

Therefore, 35% of the fuel capacity did not used in this flight.

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The value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is : -

1.5(x + 4) - 3 = 4.5(x - 2)

Using the distributive property, multiply the terms in the equation.

1.5x + 1.5 × 4 - 3 = 4.5x - 4.5 × 2

1.5x + 6 - 3= 4.5x - 9

Isolate the variable x using transposing method

4.5x - 1.5x = 6 - 3 + 9

3x=15-3

3x = 12

Therefore,  x = 12/3 = 4

The value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is 4.

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The image of two isosceles triangle as per the given information is attached below:

And the proof of AC ⊥ BD is solved below:

A triangle with two equal sides is known as an isosceles triangle in geometry. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as a particular instance.

Statement                                                            Reason

∆ABC and ∆ADC are isosceles triangles              Given

The line segment AC is a common base

to the triangles  ∆ABC and ∆ADC                            Given

BK is the perpendicular bisector of                          Perpendicular bisector

segment AC if K is the

midpoint of segment AC's base.                                           triangle property.

DK is the perpendicular

bisector of line segment AC.                                     perpendicular bisector of                                                                      

                                                                                             triangle property.

This is the proof of  AC ⊥ BD

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The equation of the perpendicular line is y = -5x + 18

From the question, we have the following parameters that can be used in our computation:

y = 1/5x + 3

Also, from the question;

We have the following points

Point = (4, -2) i.e.  (x, y) = (4, -2)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 1/5

This means that the slope is 1/5

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -5

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -5

(x₁, y₁) =  (4, -2)

So, we have

y = -5(x - 4) - 2

Evaluate

y = -5x + 18

Hence, the line has an equation of y = -5x + 18

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The value of a in the diagram is 24°

a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

From the diagram the three angles of the triangle are a + 36, 3a, 2a

a + 36 + 2a + 3a = 180( sum of angles in a triangle is 180°)

6a + 36 = 180

6a = 180 - 36

6a = 144

a = 144/6

a = 24°

In conclusion the value of a is 24°

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From the compound inequality explained below in concept, it has been proven that compound inequality has a solution of all real numbers except 3.5.

We are given the inequalities as;

5x – 3 > 14.5 or (2x + 5)/3 < 4

For the first inequality;

Add 3 to both sides to get;

5x > 17.5

Divide both sides by 5 to get;

x > 3.5

For the second inequality, we have;

(2x + 5)/3 < 4

Multiply both sides by 3 to get;

2x + 5 < 12

Subtract 5 from both sides to get;

2x < 7

Divide both sides by 2 to get;

x < 3.5

The first inequality gives the solution as x > 3.5.

The second inequality gives the solution as x < 3.5.

The solution of an “or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.

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The difference between the numbers 4.7 and 2.3 is 2.4

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

Between 4 and 5 , there are 10 divisions. Each division shows the value 0.1.

So, 4.7 is marked as shown in the figure.

To find the difference 4.7 - 2.3 , reverse the direction by 2.3 units from 4.7, will give us 2.4..

So, the difference between 4.7 and 2.3 is 2.4

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The table with the absolute guessing errors should be completed as follows;

Guess                                  2    15   10   8    12   19   20   5    7    9

Absolute guessing error   12    1      4    6    2     5    6    9    7    5

A graph of the guess and absolute guessing error is shown in the image attached below.

Yes, the absolute guessing error is a function of the guess because every guess (input value) has one absolute guessing error (output value).

In Mathematics, the margin of error (MOE) is sometimes referred to as an absolute guessing error and it can be defined as a measure of the difference that exist between an observed value and a true value of the population parameter.

Mathematically, the absolute guessing error for the guesses made by these group of ten friends with respect to the actual number of 14 as follows;

Absolute guessing error = 14 - 2 = 12

Absolute guessing error = 14 - 15 = 1

Absolute guessing error = 14 - 10 = 4

Absolute guessing error = 14 - 8 = 6

Absolute guessing error = 14 - 12 = 2

Absolute guessing error = 14 - 19 = 5

Absolute guessing error = 14 - 20 = 6

Absolute guessing error = 14 - 5 = 9

Absolute guessing error = 14 - 7 = 7

Absolute guessing error = 14 - 9 = 5

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The probability distribution of rolling a die is

P(1) = 1/6, P(2) = 1/6, P(3) = 1/6, P(4) = 1/6, P(5) = 1/6, P(6) = 1/6

Given that,

Let T be the outcome of a roll with a fair die.

Then

T = {1, 2, 3, 4, 5, 6}

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability of getting 1 P(1) = 1/6

The probability of getting 2 P(2) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 4 P(4) = 1/6

The probability of getting 5 P(5) = 1/6

The probability of getting 6 P(6) = 1/6

Therefore, the probability distribution of rolling a die has been found

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The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1, or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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