A random sample of 8 in-state applicants results in a SAT scoring mean of 1044 with a standard deviation of 45. A random sample of 12 out-of-state applicants results in a SAT scoring mean of 1162 with a standard deviation of 59. Using this data, find the 98% confidence interval for

The formula for the estimator of the slope in a simple linear regression model, when the intercept is known to be 0, can be derived as follows: β = Σ(xi * yi) / Σ(xi^2)

In a simple linear regression model, we aim to find the equation of a straight line that best fits the relationship between two variables: the independent variable (x) and the dependent variable (y). When the intercept is known to be 0, it means that the line passes through the origin (0, 0).

To estimate the slope (β) of this line using the Ordinary Least Squares (OLS) method, we need to minimize the sum of squared differences between the observed y-values and the predicted y-values on the line.

We start by calculating the sum of the product of each x-value (xi) and its corresponding y-value (yi). This is represented as Σ(xi * yi). Next, we calculate the sum of the squares of each x-value, represented as Σ(xi^2).

The estimator of the slope (β) is then derived by dividing the sum of the product Σ(xi * yi) by the sum of the squares Σ(xi^2):

β = Σ(xi * yi) / Σ(xi^2)

This formula provides an estimate of the slope in the simple linear regression model when the intercept is 0, allowing us to quantify the relationship between the independent and dependent variables.

Learn more about estimator

brainly.com/question/17961193

#SPJ11

The expression (x⁵ / x¹⁰) ÷ x² in the simplified form will be 1/x⁷.

Given that:

Expression, (x⁵ / x¹⁰) ÷ x²

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ (x⁵ / x¹⁰) ÷ x²

⇒ (1 / x⁵) ÷ x²

⇒ 1 / (x⁵ · x²)

⇒ 1 / x⁷

The expression (x⁵ / x¹⁰) ÷ x² in the simplified form will be 1/x⁷.

More about the simplification link is given below.

https://brainly.com/question/12616840

#SPJ1

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

Learn more about linear inequality from the given link

https://brainly.com/question/30340033

#SPJ1

Since, there are multiple questions so, the question answered above is attached below.

For a pack of 52 cards, two cards are drawn together, the probability that one card is clubs and one card is spades is equals to the

\(= \frac{13}{102}\)

Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to the total possible outcomes. We have a pack of 52 cards. Let's consider an event E : card is one card is culb and one is spade

Total possible outcomes = 52

Two cards are drawn together from a pack. So, number of total possible outcomes for drawing two cards from a pack, n(T) = ⁵²C₂ = 1326

In a 52 cards pack, number of spades = 13

Number of clubs cards in pack = 13

Number of ways of choosing/drawing one spades card out of 13 and one one clubs out of 13 cards, n(E) = 169

Probability that one card is clubs and one card is spades on drawing two cards,

\( P(E) = \frac{ n(E)}{n(T)}\)

\(= \frac{169}{1326}\)

\(= \frac{13}{102}\)

Hence, required probability value is \(= \frac{13}{102}\).

For more information about probability, visit:

https://brainly.com/question/25870256

#SPJ4

Answer:

They intersect

Step-by-step explanation:

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel.

Here we have two functions:

1) y = 4x + 2

2) 8x + 2y = - 3

   2y = - 8x - 3

   // divide both sides by 2

   y = - 4x - 1,5  

- 4 ≠ 4 , so these lines aren't parallel, maybe you wrote the assignment incorrect (e. g. if there would be " - " before 8 in the second function, those lines would be parallel), here they intersect.

\(( - 3) + ( - 19) + 6 \\ - 3 + ( - 19) + 6 \\ - 3 - 19 + 6 \\ = - 16\)

\(( - 41) - 15 + 9 \\ - 41 - 15 + 9 \\ = - 47\)

\( - 16 > - 47\)

Answer:

(-3)+(-19)+6 [>] (-41)-15+9

Step-by-step explanation:

(-3)+(-19)+6= -16

and

(-41)-15+9= -47

so, -16 is greater than -47

Answer:

28.85

Step-by-step explanation:

Plug the values in and solve.

G = 5u + 2y

G = 5(2.89) + 2(5.7)

G = 14.45 + 11.4

G = 25.85

Now that we know the value of x, we can find the values of DP, PH, and HD:

DP = 17x = 17(0.295) = 5.015

PH = 6x + 5 = 6(0.295) + 5 = 6.77

HD = 20x - 3 = 20(0.295) - 3 = 2.9

Therefore, DP ≈ 5.015, PH ≈ 6.77, and HD ≈ 2.9.

The perimeter of a form is its edge's radius. Learn how to multiply the lengths of a shape's sides to determine its perimeter.

To solve this problem, we need to use the fact that the perimeter of ADPH is 23.5. We know that AD = DP + HD, and we also know the values of DP, PH, and HD in terms of x. So, we can set up an equation using these values and solve for x.

AD = DP + HD

AD = 17x + (20x - 3)

AD = 37x - 3

Perimeter of ADPH = AD + DP + PH + HD

23.5 = (37x - 3) + 17x + (6x + 5) + (20x - 3)

Simplifying the above equation, we get:

23.5 = 80x - 1

Solving for x, we get:

x = 0.295

Now that we know the value of x, we can find the values of DP, PH, and HD:

DP = 17x = 17(0.295) = 5.015

PH = 6x + 5 = 6(0.295) + 5 = 6.77

HD = 20x - 3 = 20(0.295) - 3 = 2.9

Therefore, DP ≈ 5.015, PH ≈ 6.77, and HD ≈ 2.9.

To know more about perimeter visit:

https://brainly.com/question/6465134

#SPJ1

Answer:

13800

Step-by-step explanation:

The order of the members is important (because each selected member will receive a different position), thus we then need to use the definition of permutation.

There are 25 members, of which 3 are selected.

\(\begin{array}{l}n=25 \\r=3\\end{array}\)

Evaluate the definition of a combination:

\(P(25,3)=\frac{25 !}{(25-3) !}=\frac{25 !}{22 !}=25 \cdot 24 \cdot 23=13800\)

1/2

Probability of the team losing the match = 1 - 1/6 - 2/6

Probability of the team losing the match = 6/6 - 1/6 - 2/6

Probability of the team losing the match = 3/6

Probability of the team losing the match = 1/2

The probability of the team losing the match is 1/2

The formula to calculate the circumference of a circle is given by \(\displaystyle\sf C=2\pi r\), where \(\displaystyle\sf C\) represents the circumference and \(\displaystyle\sf r\) is the radius of the circle.

Given that the diameter of the above ground circular swimming pool is 30 ft, we can find the radius by dividing the diameter by 2. So, the radius \(\displaystyle\sf r\) would be \(\displaystyle\sf \frac{30}{2}=15\) ft.

Now, substituting the value of \(\displaystyle\sf r\) into the formula, we have:

\(\displaystyle\sf C=2\pi ( 15)\)

Using \(\displaystyle\sf \pi =3.14\), we can calculate the circumference:

\(\displaystyle\sf C=2( 3.14)( 15)\)

\(\displaystyle\sf C=2( 3.14)( 15)\)

\(\displaystyle\sf C=94.2\) ft

Therefore, the circumference of the pool is 94.2 ft.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

Learn more about  volume from

https://brainly.com/question/27710307

#SPJ11

 there is your answer  yo3x + 2u

Answer: y = 85 2) 36.222°

Step-by-step explanation:

281 + 268 + 225 + 290 = 1064

1064 / 7 = 152

152 x 12 = 1824

392 + 512 + 413 + 422 = 1739

1824 - 1739 = 85

Therefore y = 85

The answer is y=541

Ur Welcome

-Kiki

btw, it should work if you just type it like that on maths-watch.

Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

In this problem, we have a 90% confidence level, hence\(\alpha = 0.9\), z is the value of Z that has a p-value of \(\frac{1+0.9}{2} = 0.95\), so the critical value is z = 1.645.

The other parameters are given as follows:

\(\overline{x} = 12.3, \sigma = 1.5, n = 50\)

Hence the bounds of the interval are:

\(\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95\)

\(\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65\)

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

(-2, -2)

Step-by-step explanation:

Midpoint Formula: \((\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\)

Simply plug in our known variables and set equation equal:

3 = (8 + x)/2

6 = 8 + x

x = -2

1 = (4 + y)/2

2 = 4 + y

y = -2

Answer:

Step-by-step explanation:

Known:

Given:

To find:

Brian's group ⇒ 1 garage in 12 hours ( \(\frac{1garage}{12hours}\))

Sequoia's group ⇒ 1 garage in 16 hours (\(\frac{1garage}{16hours\\}\))

To make it easier to calculate the time it would take if they worked together, we will write this expression:

\(\frac{1}{12} +\frac{1}{16} =\frac{4}{48} +\frac{3}{48} =\frac{7}{48} \\\)

From this fraction we see that for 7 garages they would need 48 hours. . To calculate how much time they would need for

1 garage, we will further simplify the fraction.

Solving the worked together is would need

6.86 hours for one garage.

The number of degrees in the measure of the largest angle is 315°

given that

In geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon.

The name nonagon is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name enneagon comes from Greek enneagonon (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct,though less common than "nonagon".

Although a regular nonagon is not constructible with compass and straightedge (as 9 = 32, which is not a product of distinct Fermat primes), there are very old methods of construction that produce very close approximations.

It can be also constructed using neusis, or by allowing the use of an angle trisector.

the angles of a 9-gon are in ratio 3:1:4:1:5:9:2:6:5

the sum of interior angles of an 9-gon = (9-2)* 180

                                                               = 7*180

                                                               =1260°

now, we need to find the largest angle

9/(3+1+4+1+5+9+2+6+5) *1260

=9/(36)*1260

=(1/4)*1260

=315°

The number of degrees in the measure of the largest angle is 315°

To learn more about angles:

https://brainly.com/question/28451077

#SPJ4

Answer:10.8

Step-by-step explanation:

10.8

Step-by-step explanation:

We got the same question in math that was the answer.

Answer:

4.2 × 10⁻⁵

Step-by-step explanation:

The decimal point must be after the first non-zero digit.

⇒ 4.2

Multiply 4.2 by a number that results in 0.000042. That number is 0.00001 or 10⁻⁵.

⇒ 4.2 × 10⁻⁵

Answer:

Sci. Notation= 4.2 x 10 to -5th power

Step-by-step explanation:

1. Go to decimal and move between 4 and 2

2. the number of zeroes after the the initial place of the decimal is the power it goes to

3. you pass four zeroes and the 4 which gives you five places, and the -5th power

Hope this helps :)

Answer:

6

Step-by-step explanation:

1-2-3-x-x

1-3-2-x-x

2-1-3-x-x

2-3-1-x-x

3-1-2-x-x

3-2-1-x-x

Answer:

9(9b+2)

Step-by-step explanation:

The words 'the sum of mean parenthesis.

And so 9 would be outside the parenthesis, then 9b and 2 would be inside.

Answer:

B

Step-by-step explanation:

from right angle triangle we know

(greater side)=√one side^2+remaining side^2

130=√78^2+104^2

130=130

hence b is correct

The statement that is false of quadrilaterals is C. Adjacent angles in a parallelogram are complementary.

In the tapestry of geometrical relationships, adjacent angles within a parallelogram are not bestowed with the nature of complementarity. Rather, they exhibit a distinct quality known as supplementary.

Unlike the enchanting dance of complementary angles, which combine to form a sum of 90 degrees, adjacent angles in a parallelogram intertwine their measures to yield a sum of 180 degrees. The allure of the parallelogram resides in the congruence of its opposite angles, not the complementarity of its adjacent angles.

Find out more on parallelograms at https://brainly.com/question/26979961

#SPJ1

\(\huge \bf༆ Answer ༄\)

The Additional information needed to prove the Triangles congruent by HL criteria is ~ D

ST = SE or US = FS

===========================================

Explanation:

As you mentioned, HL stands for hypotenuse leg. The sides EF and UT marked with triple tickmarks are congruent, and they are the congruent hypotenuses. That takes care of the "H" part of "HL". So we can cross off choice C because it mentions TU = EF, which is already taken care of.

The "L" part can involve either leg of the triangles. So we could involve the legs ST and SE (they appear to be the shorter legs), or we could involve the longer legs US and FS. We only need to pick one of those options to handle the "L" portion. If we knew all three aspects, then we could easily refer to the SSS (side side side) congruence theorem.

The HL theorem only applies to right triangles.

Answer:

A=pir²

Step-by-step explanation:

pi=3.14

r=15

r²=15²=225

A=225× 3.14= 706.5

No, you are supposed to do them at the same time. You need to go in whatever order they are in from left to right.

Answer:

7.8

Step-by-step explanation:

4-(-2)

3-(-2)

6^2+5^2

36+25=61

square root of 61 is roughly 7.8

The value of "k" in the following equation 72 + k = 54 for which the given linear equation is true is k = -18

As per the question statement, we are supposed to find the value of "k" in the following equation 72 + k = 54 for which the given linear equation is true.

The solution is given below:

72 + k = 54, subtracting 72 from both sides

k = 54 - 72

k = -18

Therefore the value of "k" in the following equation 72 + k = 54 for which the given linear equation is true is k = -18

To learn more about such questions and concepts, click on the link given below:

https://brainly.com/question/7723775

#SPJ1

Answer:

Sushill's age = 21

Stephens age = 23

Krutika = 17

Step-by-step explanation:

You have to start somewhere, so let's call Sushill's ages as x.

Sushill's age = x

Stephens age = x +2

Krutika = x - 4

All x ages together is 61 so...

x + x + 2 + x - 4 = 61

3x - 2 = 61

3x = 61 + 2

x = 63/3

63/3 = 21 so now you know all ages because x = 21

Sushill's age = x

Stephens age = x +2

Krutika = x - 4

The answer is:

Sushill's age = 21

Stephens age = 23

Krutika = 17