The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:

96.8 96.9 99.1 97.7 97.5 98.4 96.6
Assume body temperatures of adults are normally distributed. Based on this data, find the 99% confidence Interval of the mean body temperature of adults in the town. Enter your answer as an open-interval i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.

99%C.I= _______________

Answer:

(2x-5)(3x+1)

Step-by-step explanation:

make brackets:

(    )(    )

(    )(    )

we no that since there is two minuses in the trinomial there will be one - and one +

there are two beacause 6 is 6*1 and 2*3

(2x-   )(3x+  )

(6x+  )(1x-    )

now use some ingenuity to find where 5 and 1 should go to complete

(2x-5)(3x+1)

(2x+5)(3x-1)

(2x-1)(3x+5)

(2x+1)(3x-5)

the first binomial is the answer

2x*3x = 6x^2

-5*+1 = -5

2x*1 = 2x

3x*-5 = -15x

6x^2 +2x - 15x - 5

6x^2 - 13x - 5

Answer:

f(x) = A*∛(x + 2) + 3

Step-by-step explanation:

Suppose a generic cube as:

f(x) = A*∛(x - b) + C

We will have a turning point at the x value:

x = b

Then if we have a turning point at (-2, 3)

This means that the turning point is at x = -2 and y = 3

Then b = -2

And our cube root function will be something like:

f(x) = A*∛(x - (-2)) + C

f(x) = A*∛(x + 2) + C

And we know that f(-2) = 3

then:

f(-2) = A*∛(-2 + 2) + C = 3

f(-2) =  A*∛(0) + C = 3

      = C = 3

Then the general equation will be something like:

f(x) = A*∛(x + 2) + 3

Answer:

3+ x • {2x} + 5 = 858

Step-by-step explanation:

<33 hoped this helped !!!

Answer:

-1/3; A

Step-by-step explanation:

Answer:

17.0

Step-by-step explanation:

It's a whole number, the decimal goes to the back.

Answer:

A. y = 1/4x - 2

Step-by-step explanation:

The y- coordinate is placed at -2, on the y-axis

Then the line rises up 1 unit, and runs 4 units, landing on a point and forming the line.

If my answer is incorrect, pls correct me!

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-Chetan K

We can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

If there are integers s and t such that as + bt = 15, then we can conclude that gcd(a, b) divides 15. This is known as Bézout's identity, which states that for any two integers a and b, there exist integers s and t such that as + bt = gcd(a, b).

To see why this is true, consider the set of all linear combinations of a and b, that is, the set {ax + by : x, y are integers}. This set contains all multiples of gcd(a, b) since gcd(a, b) divides both a and b.

Therefore, gcd(a, b) is the smallest positive integer that can be expressed as a linear combination of a and b.

Now, if as + bt = 15, then 15 is a linear combination of a and b, which means that gcd(a, b) divides 15.

Conversely, if gcd(a, b) divides 15, then we can find integers s and t such that as + bt = gcd(a, b), and we can scale this equation to obtain as' + bt' = 15, where s' = (15/gcd(a, b))s and t' = (15/gcd(a, b))t.

Therefore, we can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

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Answer: 100

Step-by-step explanation:

(3*12)+2 = 38

(5*12)+2 = 62

38+62 = $100

Answer:

I think it might be A if not then its be

Step-by-step explanation:

sorry if its not right

Answer: 1024 inches

Step-by-step explanation:

New Murals,

Length= 245+33 =278 inches

Width = 234 inches

Perimeter= 2*(278+234) = 1024 inches

Answer:

yes it is true

Step-by-step explanation:

write the first five elements then write their cubes then write the cubes in the same form

for eg:

4³=16= 3×5+1= 3n+1

7³=49=3×16 +1= 3n + 1

and so on till the fifth element...

The total tax paid in years by Meghan will be equal to £53205.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the given data provided in the question,

The rate for tax are,

No tax on the first £11000 of earnings

20% of earnings exceeding £11,000 and up to £43,000 are subject to tax.

Earnings over £43,000 and up to £15,00000 are subject to a 40% tax rate.

Megan made £158.900 before taxes in the previous year, which is subject to a 45% tax rate on income exceeding £150000.

Let's calculate the tax,

0  - 11000 = £11000

11000 - 43000 = £32000

£150000 - £158900  = £8900

Tax in first earning of  £11000 =  0

Tax for £32000 = (20/100) * 32000 = £6400

Tax for £107000 = (40/100) * 107000 = £42800

Tax for £8900 = (45/100) * 8900 = £4005

Total tax paid = 0 + £6400 + £42800 + £4005

Total tax paid = £53205

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Answer:

Step-by-step explanation:

Change 2 to 2/1, then multiply the top and bottom by 4 so it has the same denomiator as the 1/4.

\(\frac{1}{4} -\frac{8}{4} =-\frac{7}{4}\)

Answer:

-1 3/4

Step-by-step explanation:

Make the denominator the same

2 = 8/4

1/4 - 8/4 = -7/4 (mixed number: -1 3/4)

a) The warning limits (2σ) for the control chart for average length are 102 mm and 118 mm.

b) The 3σ control limits are 98 mm and 122 mm. The probability of a type I error depends on the desired level of confidence.

c) The chances of detecting a mean shift to 112 mm by the third sample drawn after the shift can be calculated.

d) The chance of detecting the shift for the first time on the second sample point drawn after the shift can be determined.

e) The Average Run Length (ARL) for a shift to 112 mm and the number of samples needed to detect a shift to 116 mm can be calculated.

a) The warning limits (2σ) for a control chart for the average length are 102 mm and 118 mm.

b) The 3σ control limits are 98 mm and 122 mm. The probability of a type I error, also known as the significance level, depends on the desired level of confidence for the control chart. Typically, a significance level of 0.05 is used, which corresponds to a 5% chance of a type I error.

c) If the process mean shifts to 112 mm, the chances of detecting this shift by the third sample drawn after the shift can be calculated using the normal distribution. Assuming the data is normally distributed, the probability of observing a sample mean greater than or equal to 112 mm within the first three samples can be determined.

d) The chance of detecting the shift for the first time on the second sample point drawn after the shift can also be calculated using the normal distribution. The probability of observing a sample mean greater than or equal to 112 mm within the first two samples after the shift can be determined.

e) The average run length (ARL) for a shift in the process mean to 112 mm, with 3σ control limits, can be calculated as the average number of samples needed to detect the shift. The ARL indicates the expected time it takes to detect a shift. Similarly, the number of samples required to detect a change in the process mean to 116 mm can also be determined.

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Based on the calculations, the evaluation of the given mathematical expression is 44.5.

Given the following data:

To evaluate the given mathematical expression:

In this exercise, you're required to evaluate and solve the given mathematical expression by substituting the values of the variables as follows:

\(5 (8.4 - 2) + 10(1.25)\\\\5 (6.4 ) + 12.5\\\\32 + 12.5=44.5\)

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The state-variable model for the given system is: dx1(t)/dt = x2(t) dx2(t)/dt = -8x1(t) - 3x2(t) + 10u(t) y(t) = x1(t)

To obtain the state-variable model of the given system, we first need to express the differential equation in the form of state equations. The state-variable model consists of two equations: the state equation and the output equation.

Let's denote the state variables as x1(t) and x2(t). The state equation is given by: dx1(t)/dt = x2(t) dx2(t)/dt = -8x1(t) - 3x2(t) + 10u(t)

Here, x1(t) represents the state variable for the derivative of y(t) (dx1(t)/dt), and x2(t) represents the state variable for the derivative of ÿ(t) (dx2(t)/dt).

To derive the output equation, we relate the output variable y(t) to the state variables. In this case, the output equation is: y(t) = x1(t)

Therefore, the state-variable model for the given system is: dx1(t)/dt = x2(t) dx2(t)/dt = -8x1(t) - 3x2(t) + 10u(t) y(t) = x1(t)

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Yes, triangle inequality theorem apply to all equilateral triangles.

The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.

A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.

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Answer:

Step-by-step explanation:

Area of rectangle = Length ×Breadth

\(Length =8x+1\\Breadth = 3x-2\\\\A =\left(8x+1\right)\left(3x-2\right)\\\\=8x\times\:3x+8x\left(-2\right)+1\times\:3x+1\times\left(-2\right)\\\\=8\times\:3xx-8\times \:2x+1\times \:3x-1\times\:2\\\\=24x^2-13x-2\)

The number of times the length of the shorter piece is the longer piece is 5 and The total length could be 72 inches.

What is ratio ?

ratio can be defined as the given value divided by the total value.

Given ,

A ribbon is cut into two pieces. The length of the longer piece is 60 inches and the length of the shorter piece is 12 inches.

The number of times the length of the shorter piece is the longer piece is

let the number of times be x .

so,

x = 60/12

x = 5

The total length could be = 60+12 = 72

hence, The number of times the length of the shorter piece is the longer piece is 5 and The total length could be 72 inches.

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Answer:

sis 3rd option is correct

Answer:

h < 46

  --

hope it help

Inequalities are used to represent unequal expressions.

The inequality is:

⇒ H ≤ 46

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The height (h) is said to be no greater than 46 inches.

Here, The text "no greater than" means less than or equal to.

Hence, the inequality is:

⇒ H ≤ 46

Thus, The correct inequality is:

⇒ H ≤ 46

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Answer:

81 times.

Step-by-step explanation:

A dice has 6 sides.

The dice is fair, so each side has a 1/6 chance of being rolled.

The are 3 numbers greater than 3 - 4, 5 and 6.

Each of those numbers have a 1/6 chance of being rolled.

Together, their chance of being rolled is:

1/6 + 1/6 + 1/6 = 3/6 = 1/2

The dice is rolled 162 times.

162 x 1/2 = 81

Gordon should roll a number greater than 3 81 times.

Answer:

C) x = 13

Step-by-step explanation:

(6x - 8) = 1/2(10x + 10)

6x - 8 = 5x + 5

reduce:

x = 13

Using fractions, we know that the whole chicken Michaela eats is 1/8.

So, 3/4 of the baked chicken was left over.

This can be solved by multiplying the fraction by each other:

Hence, using fractions, we know that the whole chicken Michaela eats is 1/8.

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Answer:

A. -3/5 B. 1/5. C. 0.8.

Step-by-step explanation:

Since A is on the left side of 0, it will be negative, in which -3/5 is the only negative answer on there, so A= -3/5. Since B is on the right side of the 0 it's positive, and it is equal to 1/5 which gets you to 0.20, which will be the value of each line since 1 divided by 5 is equal to 0.20. 0.8 is also known as 0.80 so C will be next to the 1.

Answer:

7 2/4 or 7 1/2

Step-by-step explanation: You can add the 3 3/4 to 3 3/4 or mutlipy 3 3/4 by 2 because you need to find the number of 2 batches.

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

it is basic and .........