What value of z* should be used to construct an 88% confidence interval of a population mean?

By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).

In linear algebra, systems of linear equations with a unique solution can be represented by the following expression:

[tex]\vec A \cdot \vec x = \vec B[/tex]      (1)

Where:

The solution of such systems is defined by:

[tex]\vec x = \vec A^{-1}\cdot \vec B[/tex]

[tex]\vec x = \frac{1}{\det(\vec A)}\cdot adj\left(\vec A\right) \cdot \vec B[/tex], where [tex]\det \left(\vec A\right) \ne 0[/tex].

Where:

For the case of [tex]\vec A \in \mathbb{R}_{2\times 2}[/tex], the inverse of [tex]\vec A[/tex] is:

[tex]\vec A^{-1} = \frac{1}{\det \left(\vec A\right)} \cdot \left[\begin{array}{cc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]     (2)

If we know that [tex]\vec A = \left[\begin{array}{cc}3&4\\5&2\end{array}\right][/tex] and [tex]\vec B = \left[\begin{array}{cc}1\\3\end{array}\right][/tex], then the solution of the system of linear equations is:

[tex]\vec A^{-1}= \frac{1}{(3)\cdot (2) - (5) \cdot (4)}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]

[tex]\vec A^{-1} = -\frac{1}{14}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]

[tex]\vec A^{-1} = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right][/tex]

[tex]\vec x = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right] \cdot \left[\begin{array}{cc}1\\3\end{array}\right][/tex]

[tex]\vec x = \left[\begin{array}{cc}\frac{5}{7} \\-\frac{2}{7} \end{array}\right][/tex]

By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).

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Answer:

80

Step-by-step explanation:

The 9 eights would be

8, 18, 28, 38, 48, 58, 68, 78, 80

The true statement is Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools. (option D)

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.

The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median for School A = 57

Median for School B = 61

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The worth of the share of stock is $[tex]34\frac{3}{4}[/tex].

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

A mixed fraction is a fraction that is made up of a whole number and a proper fraction.  A proper fraction is a number where the numerator is less than the denominator.

The worth of the stock now = purchase price + increase in the share price

28 1/8 + 6 5/8

[tex]34 \frac{1 + 5}{8}[/tex]

[tex]34\frac{6}{8}[/tex] = [tex]34\frac{3}{4}[/tex]

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Answer:

20 lorries are needed to transport.

Mark brainliest

Answer:

14day

Step-by-step explanation:

lorries trip per day. crates

3. 5 2500

? 6 10000

(6×3×10000)÷(5×2500)=14days

The smaller number is 28.

Answer:

Solution Given:

let the smaller number be a.

and larger number be a+4.

By question

a+(a+4)=60

a+a+4=60

2a=60-4

2a=56

a=[tex] \frac{56}{2} [/tex]

a=28

Answer:

y = 28

Step-by-step explanation:

Given variables:

Create two equations with the given information.

Equation 1

If one number is 4 more than another, then:

⇒ x = y + 4

(Remembering that x is the larger number and y is the smaller number).

Equation 2

If their sum is 60, then:

⇒ x + y = 60

Substitute Equation 1 into Equation 2 and solve for y:

⇒ (y + 4) + y = 60

⇒ 2y + 4 = 60

⇒ 2y + 4 -4 = 60 - 4

⇒ 2y ÷ 2 = 56 ÷ 2

⇒ y = 28

Therefore, the value of the smaller number (y) is 28.

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2a is 2 x a

Substitute a =5

2 x 5 =10

Now we have:

10^2-c

Substitute c = 10

(2 - 10 = - 8)

So,it's now 10^ - 8 (10 to the power of - 8)

Ans: 10^ - 8 (or 1 x 10^ -8)

Hope this helps!

Answer:

3 sqrt 5

Step-by-step explanation:

diameter talks about the center of the circle..and the middle of the circle lies between 3 and 5

The total area of the composite figure is 176 ft

The area of a composite figure can be found as follows;

Therefore,

Total area = area of rectangle + area of triangle

area of rectangle = lw

where

Therefore,

area of a rectangle = 16 × 8

area of a rectangle = 128 ft²

area of triangle = 1 / 2 bh

where

Therefore,

area of triangle = 1 / 2 × 12 × 8

area of triangle = 48 ft²

Total area of the composite figure = 48 + 128 = 176 ft

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Answer: If your opponent is winning 3:1 then they are probably better then you if they are winning more then you are. (or you are just having a bad day)

Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134

Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466

Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400

Let's denote the three possibilities as follows:

A: Equally talented, each player has a 0.5 probability of winning a game.

B: You are slightly better, with a 0.6 probability of winning a game.

C: Your opponent is slightly better, with a 0.6 probability of winning a game.

Given that you won the second game but lost the first, third, and fourth games, we want to find the probability of scenario C given this outcome. Let P(C) represent the prior probability of scenario C being true.

According to the given information, each of the three scenarios (A, B, and C) is equally likely, so P(A) = P(B) = P(C) = 1/3.

Now, let's update the probabilities based on the outcome of the match:

In scenario A:

The probability of winning the second game is 0.5, and the probability of losing the first, third, and fourth games is 0.5 each. Therefore, the overall probability of the observed outcome in scenario A is (0.5 * 0.5 * 0.5 * 0.5) = 0.0625.

In scenario B:

The probability of winning all three games (assuming you are slightly better) is (0.6 * 0.6 * 0.6) = 0.216.

In scenario C:

The probability of winning the second game (assuming your opponent is slightly better) is 0.4, and the probability of losing the first, third, and fourth games is 0.6 each. Therefore, the overall probability of the observed outcome in scenario C is (0.4 * 0.6 * 0.6 * 0.6) = 0.05184.

Now, we can update the probabilities based on Bayes' theorem:

Posterior probability of scenario A: P(A|data) = (P(data|A) * P(A)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

Posterior probability of scenario B: P(B|data) = (P(data|B) * P(B)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

Posterior probability of scenario C: P(C|data) = (P(data|C) * P(C)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

P(data|A) = 0.0625

P(data|B) = 0.216

P(data|C) = 0.05184

Plugging in the values, we get:

Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134

Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466

Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400

So, after the match, the posterior probability that your opponent is slightly better than you is approximately 0.400 or 40%.

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At any value of x, Bruce would have always used 3 tiles less than Felicia.

Calculate to explain:

So, there is no solution.

Any value of x, Bruce would have always used 3 tiles less than Felicia.

Therefore, at any value of x, Bruce would have always used 3 tiles less than Felicia.

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The complete question is given below:
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Number of tiles Bruce used: 5x + 2

Number of tiles Felicia used: 5x + 5

Answer:

When the data are nominal or ordinal.

Step-by-step explanation:

Spearman's correlation

Spearman's correlation measures the strength and direction of monotonic association between two variables.

Monotonicity is "less restrictive" than that of a linear relationship.

For example, the middle image above shows a relationship that is monotonic, but not linear.

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The data exists nominal or ordinal. Spearman's correlation estimates the strength and direction of the monotonic relationship between two variables.

a) Pearson correlation

b) Kendall rank correlation

c) Spearman correlation

d) Point-Biserial correlation.

The data exists nominal or ordinal. Spearman's correlation estimates the strength and direction of the monotonic relationship between two variables.

Monotonicity exists as "less restrictive" than that of a linear relationship.

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There are 105 numbers in the  the first 1000 positive integers contain only 0s and 1s when written in base 3

The number base is given as:

Base 3

To determine the count of numbers, we make use of the following Python program

count = 0

for n in range(1,1001):

   digits = []

   while n:

       digits.append(int(n % 3))

       n //= 3

   myStr = ''.join(map(str,digits[::-1]))

   if(myStr.count('0')+myStr.count('1') == len(myStr)):

       count+=1

print(count)

The above program counts the numbers in the  the first 1000 positive integers contain only 0s and 1s when written in base 3

The output of the program is 105

Hence, there are 105 numbers in the  the first 1000 positive integers contain only 0s and 1s when written in base 3

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The distance between  the points (–3,k) and (2, 0) exists k = ± 3.

How to estimate the distance between points (–3, k) and (2, 0)?

To calculate the distance between two points exists equal to

[tex]$d=\sqrt{(y 2-y 1)^{2}+(x 2-x 1)^{2}}$[/tex]

we have (-3, k) and (2, 0)

[tex]$&d=\sqrt{34}[/tex]

substitute, the values in the above equation, and we get

[tex]$\sqrt{34} &=\sqrt{(0-k)^{2}+(2+3)^{2}} \\[/tex]

simplifying the above equation

[tex]$\sqrt{34} &=\sqrt{(-k)^{2}+(5)^{2}} \\[/tex]

[tex]$\sqrt{34} &=\sqrt{k^{2}+25}[/tex]

squared both sides

[tex]$&34=k^{2}+25 \\[/tex]

[tex]$&k^{2}=34-25 \\[/tex]

[tex]$&k^{2}=9 \\[/tex]

k = ± 3

Therefore, the value of k = ± 3.

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The factors illustrate they the sides of the rectangles are:

The first equation given is x² - 3x + 2.

= x² - 3x + 2.

= x² - x - 2x + 2

= x(x - 1) - 2(x - 1)

= (x - 1)(x - 2)

Therefore, the side lengths are (x - 1) and (x - 2).

In the rectangular figure, the length and width should be the expressions above.

The second equation given is 2x² + x - 6.

= 2x² + x - 6.

= 2x² + 4x - 3x - 6

= 2x(x + 2) - 3(x + 2)

= (2x - 3)(x + 2)

Therefore, the side lengths are (2x - 3) and (x + 2).

In the rectangular figure, the length and width should be the expressions above.

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This might help a bit, i hope

The points that are possible approximations for this system are; (2.2, -1.4) and (2.2, -1.35)

We are given the equations of the linear graphs as;

y = ⁷/₄x + ⁵/₂

y = ³/₄x - 3

Notice that the lines intersect each other and by definition, if the lines of the system of equations intersect, then the system has one solution. This means that the point of intersection of the lines is the solution of the system. It can be written as:

(x, y)

x is the x-coordinate .

y is the y-coordinate.

In this case, we can identify that:

- the x-coordinate of the point of intersection is between; x = 2 and x = 3

- The y-coordinate of the point of intersection is between y = -1 and y = -2

Based on the above, we can conclude that the points that are possible approximations for this system are; (2.2, -1.4) and (2.2, -1.35)

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Answer: B and C) 2.2, -1.4 and 2.2, -1.35

Step-by-step explanation:

Hope this helps!

Mark me brainliest!

Pls and Ty!

Answer:

312,847,415

Step-by-step explanation:

1. Define the given values:

2. Now interpret what other information the question gives:

3. upscale the ratio:

therefore, the total population in Texas = 312,847,415

Hope this helps :)

Answer:

Sum of 374 and 25 = 374+25 = 399

now subtract 9 from the sum, i.e. 399 = 399 - 9 = 390 is your answer

Answer:

Step-by-step explanation:

374+25

=399

Now, subtracting the sum from 9

9-399

=   -390

The system that can help to model this are

We have the following equation. Remember that a good understanding of the question is what would help us to write the equation

The condition says:

The square of first number is equal to the sum of the second number and 16:

First number = x. Square of x = x²

second number = y + 16

For the second

The difference of 4 times the second number and 1 is equal to the first number multiplied by 7:

second number is y

4*y - 1= x*7

= 4y - 1 = 7x

Hence we would have the following as our equations

x² = y + 16

4y - 1 = 7x

The solution to the equation when graphed = 5, 9

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Answer:

1/2

Step-by-step explanation:

Assume the coin is a fair coin.

Since we already know that the first 9 tosses were heads, the probability of 9 straight heads in the first 9 tosses is 1.

It all depends on the last toss. There is an equal probability of heads and tails in a single toss of a fair coin.

p(heads) = 1/2

p(10 heads) = 1/2

Ok so the answer is 1/2

Answer:

16b > 94

Step-by-step explanation:

16b > 94

b > 5.875

Crystal needs 6 boxes to fit all 94 discs.

Answer:

20 cm

Step-by-step explanation:

When two triangles are similar, they're just dilated by a certain scale factor. In other words, each side is multiplied by the same value to create the similar triangle.

So to find this scale factor, we can use the two sides: 6 and 12, since we're going from the triangle with a 6 cm side to a 12 cm side, we divide 12 cm, by 6 cm to get a scale factor of 2

This means that the bottom side in the top triangle, which is 10 cm, is multiplied by a scale factor of 2, to get the new bottom side of x. So to find x, we simply multiply 10 cm by 2 to get 20 cm

Answer:

HL

Step-by-step explanation:

The hypotenuses and the long legs of the right triangles are congruent, therefore using the rule HL, the triangles are congruent.

Answer:

x = 3

Step-by-step explanation:

4x + 3 = 2x + 9
1. Remove 3 from both sides
4x = 2x + 6
2. Remove 2x from both sides
2x = 6
3. x = 3

Answer:

here is the answer

hope it helps u

stay safe and healthy

{ BTS ARMY GIRL }

Rashmi

Answer:

D

Step-by-step explanation:

Your equation would be 2x^2-3=y

This means that it should touch the y axis at -3, but since there is an exponent, it should be a parabola, not a straight line. Hence the answer is D

The approximate solution to the given system of equation is (-2.71, 2.14)

From the question, we are to determine the approximate solution to the given system of linear equations.

The given equations are

y = 0.5x + 3.5

y = -2/3 x+ 1/3

From the given information, we are to show the solutions on a graph

The graph that shows the solution to the given system of equation is shown below.

The solution to the given system is the point of intersection of the lines. The coordinate of the point of intersection of the lines is (-2.71, 2.14). That is, x = -2.71, y = 2.14.

Hence, the approximate solution to the given system of equation is (-2.71, 2.14)

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