The box plot compares the number of events that mrs. Cai’s and mr. Roland’s classes won over the last 10 years on the school’s field day. Based on the data in the box plots, what is the best evidence to show which class has had greater success on field day over the last 10 years? mrs. Cai’s class was more successful because her interquartile range was less spread out. Mrs. Cai’s class was more successful because she had the greater total spread. Mr. Roland’s class was more successful because his class always won at least one event. Mr. Roland’s class was more successful because his class’s lower quartile was the same as mrs. Cai’s class’s upper quartile.

The explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then aₙ = 5 × 2ⁿ⁻¹.

As given in the question,

Given initial terms of the sequence are as follow:

5, 10, 20, 40, 80, 160, 320

a₁ , a₂ , a₃ representing initial terms

a₂ / a₁ = 10 /5

         = 2

a₃ / a₂ = 20 /10

          = 2

a₄ /a₃ = 40 / 20

        = 2

Common ratio 'r ' = 2

First term a₁ = 5

Given sequence is representing the geometric sequence

Explicit formula for nth of the  geometric sequence is given by :

aₙ = a₁ × rⁿ⁻¹

    = 5 × 2ⁿ⁻¹

Therefore, the explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then

aₙ = 5 × 2ⁿ⁻¹.

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The rational root theorem says that if you take all the factors of the constant term in a polynomial and divide by all the factors of the leading coefficient

The rational root theorem is also known as the rational zero theorem (or) the rational zero test (or) rational test theorem and is used to determine the rational roots of a polynomial function.

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Answer:y=-5x-5

Step-by-step explanation:

(0,-5) and (1,-10)

-10-(-5)= -5

1-0=1

-5/1 = -5

Answer:

75

Step-by-step explanation:

1) Divide 5 by 1/3.

Use the rule ---> [tex]a\div\frac{b}{c} =a\times\frac{c}{b} .[/tex]

5 * 3

15

Due to this being a proportional equation, you multiply 15 by 5.

5:(1/3)=75

In order to determine whether this graph shows a proportional relationship, you should determine if the ratios of the two variables plotted on the graph have a constant of proportionality.

In Mathematics, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

In conclusion, the ratio of the two variables plotted on the graph of a proportional relationship is always constant.

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Integers greater than 0 are positive number.

What is rational number?

A rational number could be a number that may be expressed as the quotient or fraction p/q of 2 integers, a dividend p and a non-zero divisor letter.

Main body:

The definition of positive integers in math states that "Integers that are larger than zero are positive integers". Integers may be classified into 3 types: negative integers, zero, and positive integers. examine the quantity line given below to know the position and worth of positive integers.

1 is that the smallest positive whole number and therefore the greatest positive whole number isn't referred to as the list is endless.

Therefore the definition of positive integer is such as.

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Four special two digit numbers exist: 1, 2, 145, and 40585.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits. Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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The equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position is [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex] at x = 0, y = -1.

Here, we have been told that the force has a magnitude of = 8 pounds (i)

It stretches a spring to a length of = 1 foot (ii)

The damping force is 0.8 times the instantaneous velocity. (iii)

We use the differential equation of motion of damping force which is =

= mx₂ +λx₁+kx

Using the formula and the values of (i), (ii), and (iii), we get -

= [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex]

This is the required equation of motion.

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The exact difference from (-4, 2) to (4, 6) is √80 units

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

(-4, 2) to (4, 6)

These points can be rewritten as

(x, y) =  (-4, 2) to (4, 6)

The exact difference can be calculated using the distance formula

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) =  (-4, 2) to (4, 6)

Substitute the known values in the above equation, so, we have the following representation

distance = √[(-4 - 4)² + (2 - 6)²]

Evaluate

distance = √80

Hence, the distance is √80 units

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Answer: 6

Step-by-step explanation:

(P.S.: Everything in italics are numbers.)

So the answer will be 6! You're welcome!

The correct option is that Undergraduate is assigned to the purchaser group.

P ( purchase | Undergraduate ) = [tex]\frac{70}{70 + 30}[/tex] = 70 / 100 = 0.70 ,

                                         ⇒   P ( y = 0 | Undergraduate ) = 0.3

P ( purchase | Graduate ) = [tex]\frac{100}{100 + 110}[/tex] = 0.476

                                         ⇒   P ( y = 0 | Graduate ) = 0.524

Therefore,

    as P ( y = 1 | undergraduate ) = 0.707 >  0.30 and

                                                       0.476  > 0.524,

Undergraduate group is assigned to the purchase group.

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The two column proof for the statemen is as follows

Statement                                         Reason

2(-x + 4) = 3                                      given

-2x + 8 = 3                                         Distributive property of multiplication

-2x = 3 - 8                                          Collection of similar terms

-2x = -5                                              Subtraction property of equality

-2x/-2 = -5/-2                                     Division property of equality

x = 5/2                                               Definition of equality

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

In algebra, we utilize integers with fixed or definite values, such as 2, 13, 0.5, etc. combined with variables like x, y, and z

An instance of algebra is 2( -x + 4) = 3

The distributive property of multiplication is applied when there is multiplication over addition of terms like exemplified here

2(-x + 4)

= -2x + 4

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The value of x is 125.

what angle sum property of hexagon?

The formula for the angle sum property is, S = ( n − 2) × 180°, where 'n' represents the number of sides in the polygon.

The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees. The sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.

Using angle sum property

120+120+120+100+x+x+10=720

2x+470= 720

2x= 720-470

2x= 250

x=125

hence, the value of x is 125.

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The weight that is left when 18759 grams of bricks are removed is 3.241 kg

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

Pile of bricks = 22 kg

The weight removed from the pile = 18759 grams

The remaining weight can be calculated using the following subtraction equation

Remaining weight = Pile of bricks - The weight removed from the pile

Substitute the known values in the above equation, so, we have the following representation

Remaining weight = 22 kg - 18759 grams

Convert grams to kg

This gives

Remaining weight = 22 kg - 18.759 kg

Evaluate the difference in the above equation

Remaining weight = 3.241 kg

Hence, the remaining weight is 3.241 kg

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To avoid any perfect multicollinearity we need to  exclude any one of the binary class variables for all the entities which are independent of whether an given intercept is present across the given equation or not.

Fixed outcomes is a statistical regression version wherein the intercept of the regression version is authorized to differ freely throughout people or groups. It is frequently implemented to panel information with the intention to manage for any individual-unique attributes that don't range throughout time. Use fixed-outcomes (FE) each time you're most effective inquisitive about reading the effect of variables that fluctuate over time.

FE discover the connection among predictor and final results variables inside an entity (country, person, company, etc.). In many packages which includes econometrics and biostatistics a set outcomes version refers to a regression version wherein the organization method are fixed (non-random) instead of a random outcomes version wherein the organization method are a random pattern from a population.

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the test statistic z is 1.7

What is test statistic?

A test statistic may be a datum employed in applied math hypothesis testing. A hypothesis take a look at is often laid out in terms of a test statistic, thought of as a numerical outline of a data-set that reduces the info to at least one worth that may be wont to perform the hypothesis test.

Main body:

Calculate the test statistic using the formula:

z= [tex]p-p'[/tex]/[tex]\frac{p'(p-p')}{n}[/tex]

where:

p = sample proportion,

n = sample size, and

Po =  population proportion under the null hypothesis

Sample size = 34 websites = n

Sample proportion = 0.20 = p'

z = (0.3 - 0.2)/ (0.2*0.1)/34

z = 0.1 *34/0.02

z = 1.7

Hence value of test statistic z is 1.7

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Answer:

12

Step-by-step explanation:

2 * 6

6 + 6 = 12

Answer:

12

Step-by-step explanation:

The equation to represent the hanger diagram is   5x - 2x = 21 - 12 and weight of 1 triangle in the hanger is 3 gram. .

In the question ,

it is given that ,

the the weight of one square is = 2 gram

the weight of one circle is = 3 gram

and the weight of one triangle is is = x gram

When the hanger is balanced , then weight on Left side =  weight on Right side

we see that left side have 2 triangles , 6 squares and 3 circles ,

and the Right side have 2 circle , 3 square and 5 triangle ,

So , the balanced equation for the hanger can be written as

2*x + 6*2 + 3*3 = 2*3 + 3*2 + 5*x

2x + 12 + 9 = 6 + 6 + 5x

2x + 21 = 12 + 5x

5x - 2x = 21 - 12

3x = 9

x = 3

Therefore , the equation is 5x - 2x = 21 - 12  and the weight of triangle is 3 grams .

The given question is incomplete , the complete question is

There is a hanger that is in balance. squares are worth 2 grams and circles are worth 3 grams, and triangles are x grams. write an equation to represent the hanger diagram and find the weight of 1 triangle .

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If the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. The area of the rectangle increasing is:  114 cm2/sec.

Using product rule formula

(dA / dt) = L× (dW / dt) + W × (dL / dt)

Where:

dA/dt = Rate that the area of the rectangle is increasing

dL/dt = 3 cm/s

L = 15 cm

dW/dt = 5 cm/s

W = 13 cm

Let plug in the formula

(dA / dt) = (15) × (5) + (13) × (3)

(dA / dt) = 75 + 39

(dA / dt)  = 114 cm2/sec

Therefore 114 cm2/sec is the area of the rectangular.

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The difference between any two successive integer squares is equal to the total of all these two integers, as demonstrated by the completed proof.

Let x represent any integer to prove algebraically.

This means that x+1 should be the following integer.

The claim demands evidence;

(x+1)² - x² = x+(x+1)

Consider the left hand side;

= x² + x + x + 1² - x²

= 2x+1 (Left Hand Solution)

Similarly, the right side.

= x + (x + 1)

= 2x + 1

Thus, subtracting the difference between two consecutive squared integers equals adding the two integers that since LHS=RHS equality is clear.

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Answer: 39 in

Step-by-step explanation:

Product of first 10 natural numbers is 3628800.

What is natural numbers?

In arithmetic, the natural numbers are those numbers used for enumeration and ordering. Numbers used for enumeration are referred to as cardinal numbers, and numbers used for ordering are referred to as ordinal numbers

Main body:

The first ten natural numbers are 1,2,3,4,5,6,7,8,9,10.

The product is the multiple all numbers.

Product of first 10 natural numbers is given by,

P = 1*2*3*4*5*6*7*8*9*10

P =3628800.

Therefore, Product of first 10 natural numbers is 3628800.

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the average amount of time spent watching television per week has decreased from the previous mean of 20.8 hour then the test is left tailed

In two tailed hypothesis, the alternative hypothesis is when mean can either be lesser or greater than the given value. Usually uses the symbol ≠.

In right tailed, the alternative hypothesis is when the mean is greater than the given value.

In left tailed, the alternative hypothesis is when the mean is lesser than the given value.

In this question, the hypothesis test to be performed is to determine if the average amount of time spent watching television per week has decreased from the given value of 20.8 hours.

Thus, it is left tailed test.

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Answer:

find the tan inverse

[tex] { \tan(?) }^{ - 1} [/tex]

of the value to get the angle.

1d.p = 29.2°

The inequality shown in the diagram is the one in option C.

-2 < x ≤ 7

On the number line we can see that our variable is x, the graph of the solution set of the inequality starts with an open circle at x = -2.

The open circle means that x = -2 is not a solution of the inequality, then we start with:

-2 < x

Then we can see a closed circle at x = 7, a closed cirlce means that the value is a solution, so x can be equal to 7, and the inequality is:

-2 < x ≤ 7

So the correct option is C.

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Answer:

No solution.

Step-by-step explanation:

1. Move terms to the left side

x² - 3x = -8

x² - 3x - (-8) = 0

2. Use the quadratic formula

x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x² - 3x + 8 = 0

a = 1

b = -3

c = 8

x = [tex]\frac{-(-3) + \sqrt{(-3)^2 - 4 * 1 * 8} }{2*1}[/tex]

3. Simplify

After simplifying:

x = [tex]\frac{3 + \sqrt{-23} }{2}[/tex]

4. No real solutions because the discriminant is negative.

The square root of a negative number is not a real number.

d = -23.

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An example of rational roots can be given as:

Let the polynomial be: 4x³ + 3x² + 6x + 9;

Then,

coefficient of the variable with the highest degree = 4

coefficient having the variable with degree 0 = 9

Factors of 4 are: 1, 2;

Factors of 9 are: 1, 3;

The possible rational roots for such an equation will be: 3, 1, 1/2, 3/2, -3, -1, -1/2, -3/2;

Rational roots are the roots or solutions of equations of any polynomial consisting of one variable of any power.

Where all the coefficients are integers.

Let the solution/root of a polynomial be p/q. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q' , and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'

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Answer:

p = 10

Step-by-step explanation:

4 ^ 10 x 4 ^ 5 = 4 ^ 10+5 = 4 ^ 15

p = 10