1/64, 1/16, 1/4, 1... What is the pattern and next term???

Answer:

There is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm

Step-by-step explanation:

From the question we are told that

    The  sample size for each algorithm is [tex]n_1 = n_2 = n = 61[/tex]

     The sample mean  for new algorithm is  [tex]\= x_1 = 14.06 \ hr[/tex]

     The  standard deviation for new algorithm is  [tex]\sigma _1 = 3.004 \ hr[/tex]

     The  sample  mean for  the current algorithm is  [tex]\= x_2 = 16.43 \ hr[/tex]

     The standard deviation for current algorithm is  [tex]\sigma _2 = 4.568[/tex]

     The  level of significance is [tex]\alpha = 0.05[/tex]

The  null hypothesis is  [tex]H_o : \mu_1 = \mu _2[/tex]

The  alternative  hypothesis is [tex]H_a : \mu_1 < \mu_2[/tex]

Here  [tex]\mu _1 \ and \ \mu_2[/tex] are population mean for  new and current algorithm

Generally the test statistics is mathematically represented as

       [tex]Z = \frac{ \= x _1 - \= x_2 }{ \sqrt{\frac{ \sigma_1 ^2 }{n_1} + \frac{\sigma^2_2 }{ n_2}} }[/tex]

=>    [tex]Z = \frac{ 14.06 - 16.43 }{ \sqrt{\frac{ 3.004^2 }{61} + \frac{4.568^2 }{ 61}} }[/tex]

=>    [tex]Z = -3.39[/tex]

Generally the p-value is mathematically represented as

     [tex]p-value = P(Z < -3.39 )[/tex]

From the  z-table  

             [tex]P(Z < -3.39 ) = 0.0003[/tex]

=>    [tex]p-value = P(Z < -3.39 ) = 0.0003[/tex]

From the calculated value  we see that  [tex]p-value < \alpha[/tex]  hence the null hypothesis is rejected

        Hence we can conclude that there is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm

Answer:

-1

Step-by-step explanation:

Simplify the following:

x - 2/2 - x

Hint: | Reduce (-2)/2 to lowest terms. Start by finding the GCD of -2 and 2.

The gcd of -2 and 2 is 2, so (-2)/2 = (2 (-1))/(2×1) = 2/2×-1 = -1:

x + -1 - x

Hint: | Group like terms in x - 1 - x.

Grouping like terms, x - 1 - x = (x - x) - 1:

(x - x) - 1

Hint: | Look for the difference of two identical terms.

x - x = 0:

Answer:  -1

Answer:

-4 and 4

Step-by-step explanation:

Hello!

An absolute value is a number regardless if it is negative or positive

For example, the absolute value of -6 is 6, -3 is 3 and 5 is 5

So numbers that have an absolute value of 4 are 4 and -4

Hope this Helps!

The domain of the function is [tex]\mathbb{R}[/tex] or in set notation [tex](-\infty, \infty)[/tex].

The range of the function is [tex][0, -\infty)[/tex].

Hope this helps.

Answer:

60°, 60°, 60°

Step-by-step explanation:

Since, two side of the given triangle are congruent l. Therefore, measures of both the interior angle will be equal.

By remote interior angle theorem:

120° = x + x

120° = 2x

120°/2 = x

60° = x

Third angle = 180° - 120° = 60°

Hence measure of all the three angles of the triangle are 60°, 60° and 60°

Answer:

4

Step-by-step explanation:

So we know that RT is 36.

Note that RT is the combined length of RS and ST. Therefore:

[tex]RT=RS+ST[/tex]

Substitute. RT is 36, RS is 6x+1 and ST is x+7:

[tex]36=(6x+1)+(x+7)[/tex]

Combine like terms and add:

[tex]36=7x+8[/tex]

Subtract 8 from both sides:

[tex]28=7x[/tex]

Divide by 7:

[tex]x=4[/tex]

So, our answer is 4 :)

Answer:

288π cm³, 904.32 cm³, and 904.778683 cm³

Step-by-step explanation:

The volume of a sphere can be found using the following formula.

[tex]V=\frac{4}{3} \pi r^3[/tex]

We are given the diameter, so we must find the radius.

The radius is half of the diameter.

r= d/2

The diameter is 12 cm.

r= 12 cm/2

r= 6 cm

The radius is 6 centimeters. Let's return to the formula and substitute 6 cm in for r.

[tex]V=\frac{4}{3} \pi (6cm)^3[/tex]

Evaluate the exponent.

[tex](6 cm)^3= 6 cm * 6 cm * 6cm = 36 cm^2 * 6cm= 216 cm^3[/tex]

[tex]V=\frac{4}{3} \pi * 216 cm^3[/tex]

Multiply 4/3 and 216 cm^3

[tex]V= (\frac{4}{3} * 216 cm^3)\pi[/tex]

In terms of pi:

[tex]V= 288\pi cm^3[/tex]

Using 3.14 as pi:

[tex]V= 288 \pi cm^3[/tex]

[tex]V= (288 * 3.14) cm^3[/tex]

[tex]V= 904.32 cm^3[/tex]

Using 3.14159265 as pi:

[tex]V= 288 \pi cm^3[/tex]

[tex]V= (288 * 3.14159265) cm^3[/tex]

[tex]V=904.778683 cm^3[/tex]

The volume of the sphere is 288π cm³, 904.32 cm³, and 904.778683 cm³

Answer:

Volume of sphere by formula is V= 4/3πr^3

Since d= 12

Then r = d/2

Radius = diameter / 2

r = 12/2

r = 6

V = 4/3 x 22/7 x 6^3

V = 1.33 x 3.14 x 216

V = 902.1cm^3....

Thanks

Answer:

12.3 = y

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 35 = y/15

15 cos 35 = y

12.28728066 = y

To the nearest tenth

12.3 = y

Answer:

0.25 of a pound, 1/4

Step-by-step explanation:

3 divided by 12 = 0.25

Answer:

The student must score at least 76 in the third subject

Step-by-step explanation:

Given

Scores in 2 subjects = 77 and 72

Number of subjects = 3

Required

Determine the scores in the third subject to get an average of 75

Represent the score in the third subject with y

Average in 3 scores is calculated as thus;

[tex]Average = \frac{Sum\ of\ 3\ scores}{3}[/tex]

Substitute 75 for Average

[tex]75 = \frac{Sum\ of\ 3\ scores}{3}[/tex]

Multiply both sides by 3

[tex]3 * 75 = \frac{Sum\ of\ 3\ scores}{3} * 3[/tex]

[tex]3 * 75 = Sum\ of\ 3\ scores[/tex]

[tex]225 = Sum\ of\ 3\ scores[/tex]

Substitute (77 + 72 + y) for Sum of 3 scores

[tex]225 = 77 + 72 + y[/tex]

[tex]225 = 149 + y[/tex]

Subtract 149 from both sides

[tex]225 - 149 = 149 - 149 + y[/tex]

[tex]225 - 149 = y[/tex]

[tex]76= y[/tex]

[tex]y = 76[/tex]

Hence, the student must score at least 76 in the third subject

Answer:

9x

Step-by-step explanation:

let's say that x is the number we don't know

the product means multiplication

9*x=9x

so the answer is 9x

Answer:

[tex]\Huge \boxed{9x}[/tex]

Step-by-step explanation:

Let the unknown number be x.

The product of x and 9.

The product refers to multiplication.

[tex]x \times 9[/tex]

Answer:

circumference

Step-by-step explanation:

Going around is the circumference

Answer:

433.6

Step-by-step explanation:

Answer:

x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of 15 multiplied by y to the power of negative 15.

Step-by-step explanation:

Given is expression below to be simplified:

The step in simplifying is the power of the power, which is equal to product of powers: (xᵃ)ᵇ = xᵃᵇ. So, power of  -3 of the whole equals to:

This expression is same as the last option:

So, this is the correct one.

Answer:

other answer was correct

Step-by-step explanation:

The table and the plotted data are in the attachment.

Answer and Step-by-step explanation: A line of best fit is the best approximation of the given data. It is used to show the relation of two variables and it can be determined, more accurately, by the Least Square Method.

To use the method, follow the steps:

1) Calculate the mean of the two variables:

[tex]X = \frac{\Sigma x_{i}}{n}[/tex]

[tex]Y=\frac{\Sigma y_{i}}{n}[/tex]

2) The Slope of the line is given by:

[tex]m=\frac{\Sigma (x_{i}-X)(y_{i}-Y)}{\Sigma (x_{i}-X)^{2}}[/tex]

3) The y-intercept is found by the formula:

[tex]b=Y-mX[/tex]

For the ripening of bananas, the least square method gives the line:

y = -0.142x + 5.56

The rate of change of a line equation is its slope, so

Rate of change = -0.14

The rate of change of ripening time with respect to exposure time is -0.14, which means the more expose the fruit is, the less time it needs to ripe.

Answer:

Step-by-step explanation:

Simplify.

10 x 4000

40000

Unit form.

forty-thousand = four thousands

I'm sorry if I misunderstood.

Please add Brainliest if you'd like, not that it matters.

Multiplication is the process of multiplying. The value of the expression 10 × 4,000 is 40,000.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

In the given expression 10×4000, the symbol of '×' represents that the two digits should be multiplied. Therefore, the value of the multiplication of 10 and 4,000 is,

10 × 4,000 = 40,000

Hence, the value of the expression 10 × 4,000 is 40,000.

Learn more about Multiplication here:

https://brainly.com/question/14059007

#SPJ2

Answer:

GCF= 4

Step-by-step explanation:

A factor is a number that evenly divides into another number.

First, list the factors of 16.

1 , 2, 4, 8, 16

Next, list the factors of 36

1 , 2 , 3, 4, 6, 9, 12, 18, 36

Now, find the GCF, or greatest common factor. The GCF is the largest factor that both numbers share.

16 : 1 , 2, 4, 8, 16

36 : 1 , 2 , 3, 4, 6, 9, 12, 18, 36

When we compare the lists, we see the biggest number that appears in both lists is 4.

The Greatest Common Factor of 16 and 36 is 4.

Answer: 4

Step-by-step explanation: The Greatest Common Factor of two

numbers is the largest factor shared by both numbers.

As a review in case you didn't know, a factor of a

number divides into that number without a remainder.

To find the greatest common factor of 16 and 36,

we begin by finding all of the factors of each number.

Let's start by finding the factors of 16.

16 ÷ 1 = 16

16 ÷ 2 = 8

16 ÷ 4 = 4

We can stop here because if we continue

dividing, we won't find any new factors.

So the factors of 16 are 1, 2, 4, 8, and 16.

Now let's find the factors of 36.

36 ÷ 1 = 36

36 ÷ 2 = 18

36 ÷ 3 = 12

36 ÷ 4 = 9

36 ÷ 6 = 6

So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Now find the largest number shared by the two lists.

In this case, the largest number is 4.

So the greatest common factor of 16 and 36 is 4.

THE answer is 3.173≅3.2(nearest tenth)

Answer:

Step-by-step explanation:

Before we can determine the exact trigonometric ratios for the angle x whose radian measure is given as [tex]\dfrac{3\pi}{4}[/tex], we need to first determine the quadrant the angle falls into.

The angle [tex]\dfrac{3\pi}{4}[/tex] = [tex]\dfrac{3*180}{4} = 135^0[/tex] and it falls in the second quadrant. since the angle is positive, we will use the trigonometry ratio that is positive in the second quadrant. The trigonometry ratio that is positive in the second quadrant is sin(x) while others are negative.

[tex]sin \frac{3\pi}{4} = sin (\pi - \frac{\pi}{4} ) = sin\frac{\pi}{4} = \frac{1}{\sqrt{2} } \\cos \frac{3\pi}{4} =cos (\pi - \frac{\pi}{4} ) = -cos\frac{\pi}{4} = -\frac{1}{\sqrt{2} } \\tan \frac{3\pi}{4} = tan (\pi - \frac{\pi}{4} ) = -tan\frac{\pi}{4} = -1[/tex]

Answer:

The answer is

Step-by-step explanation:

To convert any angle from radians to degrees multiply that angle by

So for the above angle in the question we have

Reduce the fraction with π

That's

We have the final answer as

Hope this helps you

Answer:

2 / 5

Step-by-step explanation:

Fractions are written in the form part/whole, in this case, the part is 18 and the whole is 45 so the fraction would be 18 / 45 which simplifies to 2 / 5.

Answer: [tex]\frac{2}{9}[/tex]

Step-by-step explanation: It is 2/9 because 2/9 converts to 0.222222222...

Hope it helps!

Step-by-step explanation:

Since the above sequence is a geometric sequence

For an nth term in a geometric sequence

That's

[tex]A(n) = a( {r})^{n - 1} [/tex]

where

r is the common ratio

a is the first term

n is the number of terms

From the question

a = 4.05

r = 1.35 / 4.05 = 0.33

Substitute the values into the above formula

We have

[tex]A(n) = 4.05( {0.33})^{n - 1} [/tex]

Hope this helps you

Answer:

The correct option is B.

Step-by-step explanation:

The ANOVA table is as follows:

Source of variation          SS            df             MS                F

   Regression               3177.17         2         1588.584          ___

     Residual                    ___           17          17.71713

        Total                    3478.36       19

The complete table is as follows:

Source of variation          SS                  df             MS                  F

   Regression               3177.17               2         1588.584        89.663

     Residual                   301.1941           17          17.7173

        Total                    3478.36             19

The critical value of F is:

[tex]F_{\alpha, (\eta_{1}, \eta_{2})}=F_{0.05, (2,17)}=3.5915[/tex]

Decision rule:

If the calculated value of the F test statistic is more than or equal to the critical value.

[tex]F=89.663\geq F_{2,17}=3.5915[/tex]

The null hypothesis will be rejected.

Conclusion:

At least one of the predictors is useful in explaining Y.

Thus, the correct option is B.

Answer:

A, B, C, D

Step-by-step explanation:

(A) Checking the Equal Variance Assumption, the appropriate technique to use is:

- The ANOVA (Analysis of Variance) F test

- Plot residuals against fitted values

(B) Checking the Normal Assumption, the appropriate techniques to use are:

- Test for Kurtosis & Skewness

- Kolmogorov-Smirnov Test

- Q-Q Plots (the graphical method) also known as Quantile Plot

- Do not use a histogram; it is not advisable

(C) Checking for Model Misspecification, the appropriate techniques to use are:

- The Ramsey Regression Specification Error Test; also called RESET

- The Davidson & MacKinnon J. Test

(D) Checking for dependent errors, the appropriate technique to use is:

- Plot residuals against time variables

Answer:

75°

105°

Step-by-step explanation:

Two co-interor= 180°

5+7= 12

ratio12= 180°

{find the other ratios, 5 and 7)

12=180°

5×180÷12 = 75°

To find 7, just subtract 180-75= 105°

Smaller t = 2

Larger t = 5

Step-by-step explanation:

Given:

The given function is.

Find the zeros of the function.

Solution:

Simplify the equation above equation.

Now, we first find the root of the above equation.

Use quadratic formula with .

Put a, b and c value in above equation.

For positive sign

t = 2

For negative sign

t = 5

Put t = 2 in given function.

Put t = 5 in given function.

So, the zeros of the function is t = 2 or 5

Therefore, the smaller value of t = 2 and larger value of t = 5.

Answer:

distance = 245 in

Step-by-step explanation:

1 in = 50

distance = 4.9 in x 50

distance = 245 in

Answer: 245 miles

Step-by-step explanation:

fg