what is the value of x ?

The 90% confidence interval for the mean length of stay for patients with abdominal surgery is [5.64, 5.86].

The formula for the confidence interval is given by: \($CI=\bar{X}\pm Z_{\alpha/2} \times \frac{S}{\sqrt{n}}$\)

Given data:Sample size, n = 2121,Sample mean, \($\bar{X}$\) = 5.75,Sample standard deviation, S = 1.11 Confidence interval, CI = 90%

Now, we need to find the value of Zα/2 from the Z-table.

The value of α/2 is given by 1-90/100 = 0.1.

Therefore, α/2 = 0.05.From the Z-table, we can find the Z-value corresponding to 0.05, which is 1.645.

Substituting all these values in the formula, we get:\(\[\begin{aligned}CI&=\bar{X}\pm Z_{\alpha/2} \times \frac{S}{\sqrt{n}}\\&=5.75\pm 1.645 \times \frac{1.11}{\sqrt{2121}}\\&=5.75\pm 0.106\\&=[5.64, 5.86]\end{aligned}\]\)

Therefore, the 90% confidence interval for the mean length of stay for patients with abdominal surgery is [5.64, 5.86].

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Option A. The number of people riding on a bus. Option B. The number of concert tickets sold. Option D. The height of a person from a class of eight.

The random variables that are discrete are A, B, and D. The number of people riding on a bus, the number of concert tickets sold, and the height of a person from a class of eight are all examples of discrete random variables because they can only take on specific, countable values. The life span of a parakeet, on the other hand, is a continuous random variable because it can take on any value within a certain range, and there are an infinite number of possible values.

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Answer:

Step-by-step explanation:

Use ratios:

Solve by cross-multiplication:

Answer:

\(\huge\boxed{\sf 6x^2-x+16}\)

Step-by-step explanation:

\(= (2x-3)(3x+4)\\\\Expand\\\\= 2x(3x+4)-3(3x+4)\\\\Distribute\\\\= 6x^2+8x-9x+16\\\\= 6x^2-x+16\\\\\rule[225]{225}{2}\)

Answer:

6x²-x-12

Step-by-step explanation:

(2x-3)(3x+4)

2x(3x+4) -3(3x+4)

6x²+8x-9x-12

6x²-x-12

Step-by-step explanation:

Given that,

The area of the square base, A = 36 cm²

Slant height, s = 12 cm

We need to find the lateral area of the regular pyramid. The formula is :

\(S=A+\dfrac{1}{2}p\times s\)

Where

A is the area of base

p is perimeter of base

s is slant height

Area of square, A = side²

So,

\(side=6\ cm\)

Put values in the above formula.

\(S=36+\dfrac{1}{2}\times 4\times 6\times 12\\\\=36+144\\\\=180\)

So, the lateral area of the regular pyramid is equal to 180 cm².

The final elevation of the AUV will be -30.67 feet.

An elevation is simply used to illustrate the height above the sea level.

It was illustrated that the autonomous underwater vehicle is at an elevation of -8.25 ft. It dives down 6 2/3 ft to collect a specimen and then the AUV dives another 15 3/4 ft.

The final elevation will be:

= - 8.25 - 6 2/3 - 15 3/4

= -8.25 - 6.67 - 15.75

= -30.67 feet

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The smallest number of coins you could have had before finding the bag of 53 coins is 371. which is more than 200.

There are seven bags, so there are 7x coins in total:

7x = T.

Since the number of coins in each bag must be an integer, (T + 53) must be a multiple of 8. We know that T = 7x, so we can write this as follows:

(7x + 53) ≡ 0

(mod 8)This means that 7x ≡ 3 (mod 8).

The solutions to this congruence are

x ≡ 3, 11 (mod 8).

Since x is a positive integer, we take

x = 11

(the other possibility, x = 3,

leads to a smaller value for T).

Therefore, T = 7x = 77, and the total number of coins after the bag of 53 coins is found is

T + 53 = 130.

After redistributing the coins into eight equal bags, each bag contains 16 coins.

Therefore, the number of coins you had initially was

7x = 77,

so the smallest number of coins you could have had before finding the bag of 53 coins is

77 - 53 = 24.

After redistributing the coins, you had

8 × 16 = 128 coins left,

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Answer:

x=-9

Step-by-step explanation:

x=36/-4=-9

Answer:

-9

Step-by-step explanation:

-4x=36

36/-4=-9

x = -9

-4(-9)=36

The carnival committee should expect to pay $218.70 for prizes at the booth.

We can start by calculating the expected number of students who win each prize:

Stuffed toy: 22% of 150 students = 0.22 x 150 = 33 students

Jump rope: 16% of 150 students = 0.16 x 150 = 24 students

T-shirt: 6% of 150 students = 0.06 x 150 = 9 students

No prize: 100% - (22% + 16% + 6%) = 56% of 150 students = 0.56 x 150 = 84 students

Next, we can calculate the total amount of money that the carnival committee should expect to pay for prizes at the booth:

Stuffed toy: 33 students x $3.60 per toy = $118.80

Jump rope: 24 students x $1.20 per rope = $28.80

T-shirt: 9 students x $7.90 per shirt = $71.10

Total cost of prizes = $118.80 + $28.80 + $71.10 = $218.70

Therefore, the carnival committee should expect to pay $218.70 for prizes at the booth.

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Answer:

guys i have no idea

Step-by-step explanation:

The volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, a hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.

Since, all of them are tightly packed in one another therefore, radius of all them will be equal,

And, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.

r = radius of cylinder = 8 cm and

h = height of cylinder = radius of hemisphere = 8 cm

We know that,

Volume of a cylinder = π × radius² × height

Volume of a cone = 1/3 × π × radius² × height

Therefore,

a) The volume of cylinder =

π × 8² × 8 = 512π cm³  

b) The volume of cone =

1/3 × π × 8² × 8 = 170.6π cm³  

c) Volume of the hemisphere = (512π + 170.6π) / 2

= 341.3π cm³  

Hence, the volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.

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Answer:

9 candies

Step-by-step explanation:

You are required to find the number of candies in your pocket

Let

x = number of candies in your pocket

A friend gives you five more candies.

Total candies = 14

This can be represented by the equation:

Total candies = candies in your pocket + candies your friend gave you

14 = x + 5

14 - 5 = x

9 = x

x = 9 candies

x = number of candies in your pocket = 9

The 1 dollars found near the table by your friend is likely the money for the tickets.

You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.

let

x = number of individual ticket

y = number of couple tickets = 2x

Therefore, using equation,

2x(10) + 6x = 1075

2x + x = 195

Hence,

20x + 6x  = 1075

3x = 195

x = 195 / 3

x = 65

Hence,

26x = 1075

26(65) = 1690

Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.

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Answer:

Step-by-step explanation:

is 50

360-230=130

180-130=50

In regression analysis, when there are several explanatory variables, it is called multiple regression. So the correct statement is c. multiple regression.

In regression analysis, multiple regression refers to the statistical technique used when there are multiple explanatory variables that are used to predict or explain the variation in a dependent variable. It allows for the examination of the relationship between the dependent variable and multiple independent variables simultaneously.

In multiple regression, the model includes more than one predictor variable, which helps to capture the combined effect of these variables on the dependent variable. Each explanatory variable is assigned a regression coefficient, which represents the change in the dependent variable associated with a one-unit change in the corresponding independent variable, while holding other variables constant.

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Answer:

6

Step-by-step explanation:

j

Answer:29

Step-by-step explanation:

Answer:

\(\large\boxed{\mathtt{7.\bar{4}}}\)

Step-by-step explanation:

\(\textsf{We are asked to identify the rational number out of given options.}\)

\(\textsf{First, let's review what a rational number is.}\)

\(\textsf{A Rational Number is a number that terminates.}\)

\(\textsf{A Rational Number is also any number that can be represented as a fraction.}\)

\(\textsf{Let's identify if our given options are Rational Numbers.}\)

\(\mathtt{\sqrt{60} = 7.74.... (Irrational)}\)

\(\mathtt{7.\bar{4} = 7 \frac{4}{9} \ (Rational) \ \checkmark}\)

\(\mathtt{\sqrt{29} = 5.38.... \ (Irrational)}\)

\(\mathtt{\pi = 3.14159.... \ (Irrational)}\)

\(\sqrt{60} , \sqrt{29} , \textsf{and} \ \pi \textsf{ are irrational due to the decimals never terminating.}\)

\(\textsf{Hence, our final answer is}\) \(\mathtt{7.\bar{4}.}\)

The probability of a prison sentence greater than 18 years for a person convicted of second-degree murder is 0.1056 or about 10.56%.

We must normalize the variable using the following method in order to determine the likelihood that a person convicted of second-degree murder will serve a jail term longer than 18 years:

\(z = (x - μ) / σ\)

where: mean of the distribution (15 years), delta: standard deviation, and x: value of interest (18 years in this example) (2.4 years).

When we enter the values, we will get that:

z = (18 - 15) / 2.4 = 1.25

Then, we can use a calculator or table of the standard normal distribution to determine the probability associated with this z-score. The likelihood of a sentence longer than 18 years is represented by the region to the right of the value z = 1.25. We determine that the region to the right of 1.25 is roughly 0.1056 using a common normal distribution table.

Hence, the likelihood that a person convicted of second-degree murder will serve a sentence in jail longer than 18 years is 0.1056 or roughly 10.56%.

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Answer: 20 cars and then send the rest of showrooms iin New York

Step-by-step explanation:

The manufacturer can take corrective actions to maintain the quality of the dustless chalk and ensure it meets the desired density standards.

It seems part of your message got cut off. However, I can still provide some general information about quality control programs and how they can be used to monitor chalk density.

In quality control programs, the manufacturer uses statistical methods to monitor and ensure the consistency and quality of the products they produce.

One common technique used is Statistical Process Control (SPC). SPC involves taking samples from the production process at regular intervals and analyzing them to identify any variations or abnormalities.

To monitor chalk density, the manufacturer can take 24 different subgroups of chalk samples, each subgroup consisting of "n" samples. The sample standard deviation calculated for each subgroup can be used to estimate the variation in chalk density within each subgroup.

The manufacturer can then use control charts to track the process over time. Control charts display the sample means and control limits, which are calculated based on the sample standard deviations.

By comparing the sample means with the control limits, the manufacturer can identify when the process is out of control or when there are significant variations in chalk density.

If the process goes out of control or if there are consistent deviations in chalk density.

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Answer: 2.8%

Step-by-step explanation: 1/6 * 1.6 = 1/36   1/36 = 0.0277 = 2.8%

Answer:

18.33

Step-by-step explanation:

15x=275

x=275÷15

x=18.33

Answer:

Step-by-step explanation:

(-5/3)(-5/3)= 25/9= 2 7/9

Answer:4

Step-by-step explanation: 2x2 = 4 just as u said

Answer:

6.71

Step-by-step explanation:

All you do is calculate the square root, you can use a calculator and put in 3√5 = 6.70820393 …

round it to the nearest tenth = 6.71

Answer:

The minimum force required would be 50-N!

Answer:

5n - 2n - 3 + n

3n - 3 + n

3n + n = 3

4n = 3

N= 4 ➗ 3

N = 1.33

Step-by-step explanation:

Answer:

Percentage of people with IQ greater than 120 is 84.134%

Step-by-step explanation:

First thing we do here is to calculate the

z-score

Mathematically;

z-score = (x-mean)/SD

here, x = 120, mean = 100 while SD = standard deviation = 20

z-score = (120-100)/20 = 20/20 = 1

The probability we want to calculate is;

P(x > 120) or P(z >1)

we proceed to use the standard score table to get this;

From the standard score table ;

P(z >1) = 0.84134

which is in percentage = 84.134%

The dimensions of the rectangular area that will maximize the area fenced are 20 feet by 10 feet, with an area of 200 square feet.

Mike has a large barn and wants to enclose a rectangular area for his rabbits alongside it, using 40 feet of fencing. He wants to know what dimensions will maximize the area fenced if the barn is used for one side of the rectangle.

To solve the problem, we can use the formula for the perimeter of a rectangle: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

We know that the perimeter is 40 feet, so we can write the equation as 40 = 2L + 2W. We also know that one side of the rectangle is the barn, so we can write the equation as L + 2W = 40.

To maximize the area, we need to differentiate the area formula with respect to W and set it equal to zero: A = LW, dA/dW = L - 2W = 0. Therefore, L = 2W. Substituting L = 2W into the equation L + 2W = 40, we get 2W + 2W = 40, so W = 10. Therefore, L = 20.

So the dimensions that will maximize the area fenced are 20 feet by 10 feet. The area of the rectangle is A = LW = 20 × 10 = 200 square feet.

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The value of m is 8.

The amount of times a number has been multiplied by itself is shown by its exponent. The result of multiplying 8 by itself n times is represented as follows:

8 x 8 x 8 x 8 x …..n times = \(8^n\)

Given:

\($(m-4)^4 = \left(\frac 1{16}\right)^{-1}$.\)

Now, solving for m

\((m-4)^4\) = 16

\((m-4)^4\) = \(4^4\)

Taking the quad root we have

m -4 = 4

m = 4+ 4

m = 8

Hence, the value of m is 8.

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