Determine if the following statement is true or false. To perform a one-way ANOVA, the populations do not need to be normally distributed. This statement is false or true?

The 14th term in the geometric sequence is a₁₄ = 16,384

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the first term of the GP be a = 2

Let the second term of the GP be ar = 4

Now , the common ratio of the GP , r = second term / first term

So , the common ratio r = 2

Now , the 14th term of the GP is a₁₄ = ar¹³

On simplifying , we get

The 14th term of the GP is a₁₄ = 2 ( 2 )¹³

The 14th term of the GP is a₁₄ = 16,384

Hence , the 14th term of the geometric progression is 16,384

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If Eugene calculates how long it will take to earn his first million dollars if he earns an average gross pay of $975.00 per week.: D. Yes, Eugene needs to round the years up to the nearest whole number to show the time required to earn the full million dollars.

To determine if Eugene's answer is viable, we need to find how long it will take him to earn his first million dollars at an average gross pay of $975.00 per week.

$1,000,000 / $975.00 per week

= 1025.64 weeks

So, it will take Eugene approximately 1025.64 weeks or approximately 19.71 years (rounded to the nearest year) to earn his first million dollars.

Therefore the correct option is D.

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The rule for the guided reflection that maps ABC with vertices A(-4,2), B(-2,6), and C(4,4) to A'B'C' with vertices A'(-2,2), B'(0,10), and C'(6,-8) is T(a,b) * R-axis.

Here, T(a,b) represents the translation by the vector (a,b), and R-axis represents the reflection across the x-axis.

To understand the process, let's break it down step by step:

Translation T(a,b):

The vector (a,b) represents the amount and direction of the translation.

The translation moves every point in the original figure by the same amount in the x and y directions.

In this case, the translation is by (2,0), which means shifting every point 2 units to the right and 0 units up or down.

Reflection R-axis:

The reflection across the x-axis flips each point over the x-axis.

The x-coordinate remains the same, but the sign of the y-coordinate is reversed.

In this case, the reflection across the x-axis results in flipping the y-coordinate of each point.

So, applying T(a,b) * R-axis to the original vertices A(-4,2), B(-2,6), and C(4,4), we get the transformed vertices A'(-2,2), B'(0,10), and C'(6,-8).

In summary, the rule for the guided reflection is T(a,b) * R-axis, where T(a,b) represents the translation by (a,b) and R-axis represents the reflection across the x-axis.

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Answer: 15

Step-by-step explanation:

Given

There are x two-wheeled motorcycles

y three-wheeled tricycle

Total no of cycles=43

Total wheels=101

So, we can write

\(x+y=43\quad \ldots(i)\)

For no of tires

\(2x+3y=101\quad \ldots(ii)\)

Solving (i) and (ii)

x=28 and y=15

i.e. they have 15 tricycles

Answer:

We know that lines AB and CD are parallel because if you expand them, we know they will never touch.

Step-by-step explanation:

b. i) The probability of winning all three matches is 1/27.

ii) The probability of winning more times than losing is 3/27.

iii) 7/27

iv) 2/27

c. many factors that can influence the outcome of a match such as the skill of the players, the tactics used by the teams and the condition of the playing surface.

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

a. Tree diagram:

Match 1   | Match 2   | Match 3

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

Win       | Win       | Win

Draw      | Draw      | Draw

Lose      | Lose      | Lose

b. i) The probability of winning all three matches is P(Win, Win, Win) = (1/3) * (1/3) * (1/3) = 1/27

ii) The probability of winning more times than losing is

P(Win, Win, Draw) + P(Win, Draw, Win) + P(Draw, Win, Win)

= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)

= 3/27

iii) The probability of losing at least one match is

P(Lose, Win, Win) + P(Win, Lose, Win) + P(Win, Win, Lose) + P(Lose, Lose, Win) + P(Lose, Win, Lose) + P(Win, Lose, Lose) + P(Lose, Lose, Lose)

= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)

= 7/27

iv) The probability of either drawing or losing all three matches is

P(Draw, Draw, Draw) + P(Lose, Lose, Lose)

= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)

= 2/27

c. It is not very realistic to assume that the outcomes are equally likely in this case because there are many factors that can influence the outcome of a match such as the skill of the players, the tactics used by the teams and the condition of the playing surface.

Therefore, it is unlikely that all outcomes are equally likely as assumed in this case.

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The equation of parabola that open upwards with focus 6 units is x²=24y.

A parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. A parabola is a curve where any point at an equal distance from a fixed point  (the focus) and a fixed straight line (the directrix).

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface is also Parabola.

The general equation of Parabola is given by

y = a(x-h)²+ k

where (h,k) is the vertex of parabola.

And the equation of parabola open upward is,

(x-h)² = 4a(y-k)

where (h,k) is vertex and a is focus unit.

⇒ (x-0)² = 4(6)(y-0)

⇒ x² = 24y

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a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

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Answer:

yes, because the sum of the two smallest sides must be able to be added together to be greater than the largest number, 2, 12, and 13 fit this requirement.

Step-by-step explanation:

12+2=14

14>13

Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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у вас всё правильно вы молодцы

Answer:

16 rows, 8 seedlings left.

Step-by-step explanation:

Divide 200 by 12, since 200 seedlings are going to be split in 12 groups in order to fill the rows.

200 ÷ 12 = 16 with a remainder of 8.

The remainder is basically what is left.

Since 12 seedlings are planted in each row, 8 seedlings is not enough to completely fill the row. So, the answer is 16 rows with 8 seedlings left.

Hope this helped !

The first transformation is a translation one unit up.

The second transformation is a translation of four units left.

The scale factor is 2.5.

According to the transformations above, the circles are similar, they are related with a scale factor of 2.5.

The equation of the preimage is

The equation of the image is

Answer:

34

Step-by-step explanation:

Because to find the diameter simply multiply the radius by 2

17 x 2 = 34

Hope this helps!

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$105000\\ P=\textit{original amount deposited}\dotfill & \$69000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6 \end{cases}\)

\(105000=69000e^{\frac{r}{100}\cdot 6}\implies \cfrac{105000}{69000}=e^{\frac{3r}{50}}\implies \cfrac{7}{46}=e^{\frac{3r}{50}} \\\\\\ \log_e\left( \cfrac{35}{23} \right)=\log_e\left( e^{\frac{3r}{50}} \right)\implies \ln\left( \cfrac{35}{23} \right)=\cfrac{3r}{50}\implies 50\cdot \ln\left( \cfrac{35}{23} \right)=3r \\\\\\ \cfrac{50\cdot \ln\left( \frac{35}{23} \right)}{3}=r\implies 6.9976\approx r\implies \stackrel{\%}{7.00}\approx r\)

Answer:

If the null hypothesis has been rejected when the alternative hypothesis is true, it means that a Type I error has been committed.

Step-by-step explanation:

If the null hypothesis has been rejected when the alternative hypothesis is true, a Type I error has been committed.

A Type I error occurs when the null hypothesis is rejected even though it is actually true. It is also called a false positive error.

The probability of making a Type I error is denoted by alpha (α) and is typically set at a low level (e.g., 0.05 or 0.01) to minimize the chance of making this error.

In hypothesis testing, the Type II error occurs when the null hypothesis is not rejected even though it is false. It is also called a false negative error.

The probability of making a Type II error is denoted by beta (β) and depends on factors such as the sample size, the effect size, and the level of significance.

Therefore, if the null hypothesis has been rejected when the alternative hypothesis is true, it means that a Type I error has been committed.

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Answer:

The Coefficient for the first question is 7

For the Next Question the 55h stands for how many hours Damon has been driving already, and the 125 is how many miles he was driving per hour.

Step-by-step explanation:

Suppose that p and q are statements so that p → q is false.

* p: True

* q: False

The truth values of the following statements are:

* ~p → q: False

* p ∨ q: True

* q → p: True

* p → q is false because p is true and q is false.

* ~p → q is false because the antecedent of the implication is false.

* p ∨ q is true because either p or q is true, or both are true.

* q → p is true because the antecedent of the implication is false, and the consequent is true.

In general, the truth value of an implication depends on the truth values of the antecedent and the consequent. If the antecedent is true and the consequent is false, then the implication is false. If the antecedent is false, then the implication is true regardless of the truth value of the consequent. If both the antecedent and the consequent are true, then the implication is true.

In this case, the antecedent of p → q is true and the consequent is false, so the implication is false. The antecedent of ~p → q is false, so the implication is true. The antecedent of p ∨ q is true, so the implication is true. The antecedent of q → p is false, but the consequent is true, so the implication is true.

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Answer:

x<3 or x> 3/14

Step-by-step explanation:

For the given situation, we can clearly say that the change in one quantity will also cause a change in the second quantity.

Correlation is a relationship between the values ​​of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.

Causality means that one event causes another. Well-designed experiments can only determine causality. In such experiments, similar groups receive different treatments, and the results of each group are examined.

The collected data on the number of miles driven and fuel expenses. we found that number of miles driven tended to be lower when fuel expenses were high, and the number of miles driven tended to be higher when fuel expenses sales were high.

We do not conclude that more fuel expenses mean fewer miles driven. Likely, an Increased in fuel expenses and the number of miles driven may be caused by a third factor, car mileage. So, the present case is a case of negative correlation.

Negative correlation: y decreases as x increases.

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Answer:

Step-by-step explanation: I am sorry but i don't understand a single thing:(

Answer:

2

Step-by-step explanation:

A = P( 1+r/n) ^ (nt)

P is the amount invested

r is the rate

n is the number of times per year the interest is compounded

t is the number of years

every 6 months is twice a year

so n is 2

Answer:

Step-by-step explanation:

10+50+60=500

Answer:

She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume

Step-by-step explanation:

Length = L = 10 inches

Width = W = 6 inches

Suppose x is cut from the 4 corners to make a box.

Dimensions of the Box:

L= 10 - 2x

W = 6 - 2x

H = x

Volume of the Box:

V = (L)(W)(H)

V = (10-2x)(6-2x)(x)

V = 4x³ -  32x² + 60x

For Maximum value:

\(\frac{dV}{dx}=0\)

\(\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0\)

The values of x found are:

x= 4.12 , x = 1.21

If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.

We discard 4.12. Now x=1.21

So,

If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V

Answer:

b is the answer

Step-by-step explanation:

The missing coefficients of x² is 8.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

According to the question we have been given the expression which is :

(15x^2+11y^2+8x)-(7x^2+5y^2+2x)=[blank]x^2+6y^2+6x      

In this we have to find the missing coefficient.

To find the missing coefficients we will solve the L.H.S that is

=  (15x^2+11y^2+8x)-(7x^2+5y^2+2x)    

First we will eliminate the brackets we get

   15x^2+11y^2+8x-7x^2-5y^2-2x

Solving the coefficients of  x² terms , y² terms and x terms we get

       = 8x² + 6y² + 6x

Which is equal to the R.H.S

Combining both the equation we get the coefficient of the x² is 8.

Hence the missing coefficient is 8.

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Answer:

Step-by-step explanation:

262

You’ve done bulk of the work by inserting a straight line through x.

Now, the point at which we have x, has 2 other angles

This makes 3 angles in total which add up to 360( sum of angles at a point)

36 is an alternate angle to one of the angles while 62 is also an alternate angles to one of the angles.

Since alternate angles are equal, the angles are 62 and 36

Thus the angle would be x + 62 + 36 = 360

which makes x = 262

There are several statistics that are robust to outliers: Median, Interquartile range, Winsorized mean and Trimmed mean.

These statistics are more suitable for datasets that contain outliers as they are less influenced by the extreme values and provide more accurate information about the central tendency and variability of the data.

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The one that has the most circles in a group :D

The angle measure of minor arc KM is 41 degrees

From the given diagram, we have the following parameters

mKLM = 82 degrees

Required

arcKM

Since the angle at the vertex is twice that of the intercepted arc, then:

<KLM = 2(arcKM)
arcKM = <KLM/2

arcKM = 82/2

arcKM = 41 degrees

Hence the angle measure of minor arc KM is 41 degrees

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