What is the missing factor in this factor tree?

To construct a 98% confidence interval for B₁, we can use the t-distribution since the sample size is small (n = 12).

Given the sample mean (B₁ = 46), sample standard deviation (s = 5.7), and sum of squares (SSzz = 57), we can calculate the confidence interval.

The formula for a confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

For a 98% confidence level and n = 12, the critical value is approximately 2.681 (obtained from a t-distribution table).

The standard error is calculated as the sample standard deviation divided by the square root of the sample size (s / √n).

Plugging in the values:

Standard Error = 5.7 / √12 ≈ 1.647

Confidence Interval = 46 ± (2.681 * 1.647)

Therefore, the 98% confidence interval for B₁ is approximately (42.21, 49.79).

In conclusion, we can be 98% confident that the true value of B₁ falls within the range of 42.21 to 49.79 based on the given sample data.

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a) The height of the frisbee each second it is in the air are 5, 29, 45, 53, 53, 45, 29, 5, -27 and -67.

b) The frisbee is in the air for a total of 8 seconds.

To find the height of the frisbee each second it is in the air, we need to substitute different values of t into the equation \(h = -16t^2 + 40t + 5\) and calculate the corresponding height.

a) Let's substitute t = 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 into the equation:

When t = 0: \(h = -16(0)^2 + 40(0) + 5 = 5\)

When t = 1: \(h = -16(1)^2 + 40(1) + 5 = 29\)

When t = 2: \(h = -16(2)^2 + 40(2) + 5 = 45\)

When t = 3: \(h = -16(3)^2 + 40(3) + 5 = 53\)

When t = 4: \(h = -16(4)^2 + 40(4) + 5 = 53\)

When t = 5: h = \(-16(5)^2 + 40(5) + 5 = 45\)

When t = 6: h = \(-16(6)^2 + 40(6) + 5 = 29\)

When t = 7: h = \(-16(7)^2 + 40(7) + 5 = 5\)

When t = 8: h = \(-16(8)^2 + 40(8) + 5 = -27\)

When t = 9: h =\(-16(9)^2 + 40(9) + 5 = -67\)

b) The frisbee is in the air as long as its height is greater than 0. From the calculations above, we can see that the frisbee is in the air from t = 0 to t = 7, inclusive.

Note: The table you provided shows the height of the frisbee at each second it is in the air, but it seems to be cut off. However, based on the calculations above, the height values at each second should be as follows:

0 seconds: 5 feet

1 second: 29 feet

2 seconds: 45 feet

3 seconds: 53 feet

4 seconds: 53 feet

5 seconds: 45 feet

6 seconds: 29 feet

7 seconds: 5 feet

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Answer:

6.15

Step-by-step explanation:

perimeter of a rectangle= 2(Length + width)

perimeter=28.5

length=8.1

28.5=2(8.1+ Width)

28.5=16.2+ 2(Width)

28.5-16.2=2(Width)

12.3=2(Width)

12.3/2=Width

6.15=Width

Answer:

The picture that shows a proper reflection across the red dashed line is figure B

Explanation:

Given the figure in the attached image, we want to determine the picture that shows a proper reflection across the red line.

We can observe that for the figure A, the dimension of the preimage and the image are not the same. So, figure A does not show a proper reflection across the red dash line.

For figure B, the dimension and shape of the preimage is the the same as the image (they are congruent).

Therefore, The picture that shows a proper reflection across the red dashed line is figure B

Answer:

5

Step-by-step explanation:

Answer:

5 miles

Step-by-step explanation:

Take 20% of 25, you can do this by multiplying the decimal form of 20% by 25:

0.20 x 25 = 5

Assuming that x ≥ 0 and y ≥ 0, the situation is infeasible: True.

In Mathematics, these rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a coordinate plane:

In this context, we can logically deduce that the given system of inequalities 5x+3y ≤ 15 and y ≥ 6 would not have a feasible solution set if they are subjected to x ≥ 0 and y ≥ 0:

Assuming the ordered pair (1, 2), we have:

y ≥ 6

2 ≥ 6 (False).

5x+3y ≤ 15

5(1) +3(2) ≤ 15

5 + 6 ≤ 15

11 ≤ 15 (True).

Therefore, it is not a feasible solution.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

Using the identity for the difference of 2 squares;

a^2 - b^2 = (a - b)(a + b)  

we put a^2 = 81x^8 and b^2 = 1  giving

a = 9x^4 and b = 1, so:

81x^8 − 1 =   (9x^4 - 1)(9x^4 + 1)

Applying the difference of 2 squares to 9x^4 - 1:

= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Answer:

The answer is (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.

In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the information provided above, we can logically deduce the following equation:

22 . a = 242

22 × a = 242

By applying the division property of equality, we have the following:

a = 242/22

a = 11.

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Answer:

Step-by-step explanation:

For number 2:

180-90= 90 degrees for 2 angles.

90-10=80/2= 40 degrees for x

For number 3:

180-60=120

Then divide by 3=120/3=40 is x

Ps. It is weird both answer were 40 but I assure you that it is correct!

Answer:

4/8= 2/4=1/2= 50%

Step-by-step explanation:

4 out of the 8 new cars have a fuel efficiency of less than 27 mpg. that is is 50%

The temperature of the steam is 441.7 K.

A 1-m³ tank contains 2.1085 kg of steam at 0.6 MPa.

The gas constant, critical pressure, and critical temperature of steam are

R = 0.4615 kPa.m³/kg.K,

TCr = 647.1 K, and

PCr = 22.06 MPa.

Using data from the steam tables, let's find the temperature of the steam.

According to the steam table, the specific volume of the steam is 0.194 m³/kg at 0.6 MPa and 393.71 K. Since 1 m³ tank contains 2.1085 kg of steam, the total volume of steam is:

V = m/v

= (2.1085 kg)/(0.194 m³/kg)

= 10.8665 m³

The ideal gas equation of state is:

Pv = mRTor

T = PV/mR

Substituting the values we get:

T = (0.6 MPa)(10.8665 m³)/(2.1085 kg)(0.4615 kPa.m³/kg.K)

T = 441.7 K

Therefore, the temperature of the steam is 441.7 K.

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the parallel linear equation is:

y = (2/5)*x - 3

Two lines are parallel if the lines have the same slope but different y-intercept.

Here we know the line equation:

y = (2/5)*x + 4

Then a parallel line is of the form:

y = (2/5)*x + c

Where c is different than 4.

We want this line to pass through (5, -1), then:

-1 = (2/5)*5 + c

-1 = 2 + c

-1 - 2 = -3 = c

Then the parallel linear equation is:

y = (2/5)*x - 3

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Answer:

the answer to your question is pie

Answer:

A: is irrational number

B: is rational number

C: is irrational number

D: as a natural or whole number, including 9, can also be written as a fraction p1 they are all rational number. hence 9 is a rational number

so D is the the answer

Step-by-step explanation:

Angles XVW and XYZ are congruent, and so are angles VWX and XZY by the alternate interior angles theorem.

This means that triangle VWX is similar to triangle YZX.

So, since corresponding sides of similar triangles are proportional, VW/XY = WX / XZ.

120/8 = 15 = WX / 6.

So the width is 90 m.

Answer (x + 7) • (x + 2) • (x - 3) • (x - 6)

Answer:

5

Step-by-step explanation:

5×3=15

15÷3=5

Hope this helps :)

Answer: 3

Step-by-step explanation: So first you multiply 5 x 3/5 and then you get ur answer of 3 by 5/1 x 3/5 and then you do 5 x 3 / 1 x 5 = 15/5 and you convert it and you get 3 :)

(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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The u, v , u , v , and d(u, v) for the given inner product defined on Rn, the values are:

The positive-definite criterion is the fourth of the aforementioned conditions. Note that some writers define an inner product as a function that meets just the first three of the aforementioned requirements as well as the additional (weaker) requirement that it be (weakly) non-degenerate (i.e., if v,w>=0 for every w, then v=0).

According to Ratcliffe (2006), functions that fulfil all four of these characteristics are commonly referred to as positive-definite inner products; however, to prevent confusion, inner products that do not satisfy the criterion are occasionally referred to as indefinite.

\(u=\left ( 1,1,1 )\)     ,      \(v=\left ( 5,4,5 \right )\)

\(u-v=\left ( -4,-3,-4 \right )\)

\(\left \langle u,v \right \rangle=u_{1}v_{1}+2u_{2}v_{2}+u_{3}v_{3}\)

           \(= 1\times 5+2\times 1\times 4+1\times 5\)

           =18

\(\left \| u \right \|=\sqrt{\left \langle u,u \right \rangle}\)

        \(=\sqrt{ u_{1}u_{1}+2u_{2}u_{2}+u_{3}u_{3}}\)

        \(=\sqrt{1\times 1+2\times 1\times 1+1\times 1}\)

         = 2

\(\left \| v\right \|=\sqrt{\left \langle v,v \right \rangle}\)

         \(=\sqrt{ v_{1}v_{1}+2v_{2}v_{2}+v_{3}v_{3}}\)

         \(=\sqrt{5\times 5+2\times 4\times 4+5\times 5}\)

         \(= \sqrt{82}\)

\(d\left ( u,v \right )=\left \| u-v \right \|\)

               \(= \sqrt{\left \langle u-v,u-v \right \rangle}\)

               \(= \sqrt{(-4)\times (-4)+2\times (-3)\times (-3)+(-4)\times (-4)}\)

               \(= \sqrt{50}\)

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To find the inverse Laplace transform of ℒ{e^(-s) / [s(s + 1)]}, we can use partial fraction decomposition and known Laplace transforms.

First, let's express the given function in partial fraction form:

e^(-s) / [s(s + 1)] = A/s + B/(s + 1)

To find A and B, we multiply both sides by s(s + 1) and then substitute appropriate values of s to simplify and solve for the coefficients:

e^(-s) = A(s + 1) + Bs

Setting s = 0, we get:

1 = A(0 + 1)

A = 1

Setting s = -1, we get:

e = B(-1)

B = -e

Therefore, the partial fraction decomposition is:

e^(-s) / [s(s + 1)] = 1/s - e/(s + 1)

Now, we can use the known Laplace transforms to find the inverse transform:

ℒ^(-1){1/s} = 1

ℒ^(-1){-e/(s + 1)} = -e^(-t)

Finally, we combine the inverse transforms:

f(t) = ℒ^(-1){e^(-s) / [s(s + 1)]} = ℒ^(-1){1/s} - ℒ^(-1){e/(s + 1)} = 1 - e^(-t)

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Answer:

D 15 ounces

Step-by-step explanation:

If 5 ounces for 20 cupcakes

60/ 20 =3

5 x 3 = 15

Hope this helps ^-^

answer: 5%

explanation: subtract the principal from the total amount, then divide the difference by the principal

>> 73.50 - 70 = 3.50

3.50 / 70 = 0.05

0.05 x 100 = 5%

As described in probability Null hypothesis is 0.64

what is probability?

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.

Solution:

Null hypothesis H0 : p =  0.64

Alternate hypothesis Ha : p ≠ 0.64

therefore  Null hypothesis is 0.64

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Answer:

You can find the slope of a line using the slope formula. The slope formula is Y2-Y1/X2-X1. Substitute in the points and solve.

-14-1/7-(-3)   —>Note: Two negatives make a positive.

-15/10     —>Divide both the numerator and denominator by 5.

-3/2

Hope this helps! :)

Answer:

-3/2

Step-by-step explanation:

to find the slope of the line that passes through the points

we gonna use m=y2-y1/x2-x1

-14-1/7-(-3)

=-15/10

=-3/2

A researcher is planning an A/B test and is concerned about only one confound between the day of the week and the treatment. In order to control for the confound, she is most likely to design the experiment using a blocked design.

A/B testing is a statistical experiment in which a topic is evaluated by assessing two variants (A and B). A/B testing is an approach that is commonly used in web design and marketing to assess the success of modifications to a website or app. This test divides your visitors into two groups at random, with one group seeing the original and the other seeing the modified version.

The success of the modification is determined by comparing the outcomes of both groups of users.The researcher should utilize a blocked design to control the confound. A blocked design is a statistical design technique that groups individuals into blocks or clusters based on factors that may have an impact on the outcome of an experiment.

By dividing the study participants into homogeneous clusters and conducting A/B testing on each cluster, the researcher can ensure that the confounding variable, in this case, the day of the week, is equally represented in each group. This will aid in the reduction of the influence of extraneous variables and improve the accuracy of the research results.

In summary, the most probable experiment design that the researcher is likely to use to control for the confound between the day of the week and the treatment is a blocked design that will allow the researcher to group individuals into homogeneous clusters and conduct A/B testing on each cluster to ensure that confounding variable is equally represented in each group, thus controlling the confound.

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The correct term that completes the sentence "When quantity supplied and quantity demanded are the same, a market is said to be in equilibrium".

Equilibrium is a condition in which the forces acting on a market are balanced, resulting in a stable price for a commodity. At the equilibrium price, there is neither excess demand nor excess supply, therefore the market is balanced.

The economic term equilibrium describes a situation in which the market price and the quantity demanded and supplied of a good or service are equal.

Equilibrium is a key concept in economics because it aids in determining the optimal price and quantity of a product that can be produced and sold in the market.

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The total area of all 150 hamburgers = 11780.97 inch^2

The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr². π is approximately  3.142

here, we have,

Mr morgan made hamburgers for his family reunion and they each have a radius of 5in.

If he made 150 hamburgers,

now, area of the hamburgers = πr².

                                                 =78.54inch²

so, the total area of all 150 hamburgers = 11780.97 inch²

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Answer:

22,3

Step-by-step explanation:

It should be that

the angle relationship shown are vertical angles. the angles are congruent