A hospital would like to determine the mean length of stay for its patients having abdominal surgery. A sample of 17 patients revealed a sample mean of 6.6 days and a sample standard deviation of 1.5 days. Assume that the lengths of stay are approximately normally distributed. Find a 99% confidence interval for the mean length of stay for patients with abdominal surgery. Round the endpoints to two decimal places, if necessary.

Answer:

2.4

Step-by-step explanation:

The bottom is a right triangle.  You know the 2 legs, you need the hypotenuse.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]1^{2}[/tex] + [tex]1^{2}[/tex] = [tex]c^{2}[/tex]

1 + 1 = [tex]c^{2}[/tex]

2 = [tex]c^{2}[/tex]

[tex]\sqrt{2}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]\sqrt2[/tex] = c

Now we know the 2 legs for the larger triangle on top.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]\sqrt{2} ^{2}[/tex] + [tex]2^{2}[/tex] = [tex]c^{2}[/tex]

2 + 4 = [tex]c^{2}[/tex]

6 = [tex]c^{2}[/tex]

[tex]\sqrt{6}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]\sqrt{6}[/tex] = c

[tex]\sqrt{6}[/tex] rounded to the tenths place is 2.4

If the angle elevation to the plane A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .

In the question ,

it is given that

the distance between the two observer = 1050 feet

the measure of angle A is = 30°

the measure of angle B is = 40°

By angle sum property angle C is = 180 - (30 + 40)

= 180 - (70)

= 110

By Sine Law .

Sin(110)/1050 = Sin(30)/a = Sin(40)/b

Using , Sin(110)/1050 = Sin(30)/a ,

we get ,

Sin(110)/1050 = 0.5/a

a = 558.69

Using Sin(110)/1050 = Sin(40)/b

b = 718.24

By using Sine Law

Sin(40)/h = Sin(90)/558.69

h = 359.11

Therefore , If A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .

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The equation of a line is y=-1/4x-7, (option 1)

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

Write the equation in the form y = mx + b to find the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept.

Given:-

Equation of the line is y=4x+8 

The point through which the line passes (-8,4).

here the slope of the line is m1=4

To find the perpendicular line we know the formula

m1*m2=-1

By putting the value of m1 we get m2= -1/4

By using the one-point formula of the line we have

=>(y-y1)=m2*(x-x1)

By putting the values of y1 and x1 we get

(y1,x1)=(-8,4)

=>(y+8)=-0.25*(x-4)

y+0.25x+7=0

Hence the desired equation of the line is y=-1/4x-7

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Answer:

1/2

Step-by-step explanation:

u replace x with -3

=4(2)-³

=4(0.125)

=0.5

=1/2

Answer:

2:7 or [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

The cone total is 4 and the total orders is 14

[tex]\frac{4}{14}[/tex] = [tex]\frac{2}{7}[/tex]

Answer:

Below

Step-by-step explanation:

If she buys a loaf of bread she has   only 6 dollars for tomatoes

   $ 6 / 1.20 $/POUND = 5 POUNDS OF TOMATOES

(8-2) / 1.20 = # TOMATOES

The order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.

The given decimal number are 4.5, 3.9, 4.25, 3.75, 4.2

Numerical order is a way of arranging a sequence of numbers. This could be in ascending or descending order.

Ascending order: Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

The order of decimal numbers

Now, least to greatest of decimal numbers is

3.75<3.9<4.2<4.25<4.5

Therefore, the order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.

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The population variance of the given data is 3.2.

Given  Σ(x - 38)² = 64 .

We know that the population variance of the data is the square of the standard deviation.

Now the standard deviation for the population is given by

σ =√(Σ(x - 38)² / N)

Again variance = σ ²

Let us first calculate σ .

σ = √(64/20) = √3.2

variance

= σ ²

= (√3.2)²

= 3.2

Therefore the variance of the population is 3.2

In probability theory and statistics, variance is the predicted squared variation of a random variable from its population mean or sample mean. Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance.

A few ideas that use variance include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.

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[tex]{ \purple{ \tt{x = 3}}}[/tex]

[tex]{ \blue{ \sf{ {6}^{2} - x - 12 = 0}}}[/tex]

[tex]{ \blue{ \sf{36 - x - 12 = 0}}}[/tex]

Take 12 as common

[tex]{ \blue{ \sf{ \cancel{12}(3 - x) { \cancel{-12} = 0}}}}[/tex]

[tex]{ \blue{ \sf{3 - x = 0}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \tt \overbrace{ \underbrace{x = 3}}}}}}[/tex]

Answer:

The numerator is the top number of a fraction.

your welcome! <3

Answer:

Numerator is on the the top of the fraction

Step-by-step explanation:

x

_     x is the numerator

y

A property which is used in the calculation above is: Commutative Property of Multiplication.

The Commutative Property of Multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged and grouped.

This ultimately implies that, re-arranging or regrouping the order of numbers that are being multiplied does not change the end result (output) or product.

Mathematically, the Commutative Property of Multiplication is represented by this mathematical expression:

a · (b) = b · (a)

By applying the Commutative Property of Multiplication to the calculation, we have:

(64⋅25)⋅4 = 6400

64⋅(25⋅4) = 6400

64⋅(100) = 6400

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By examining the slope at different points, we can see that the slope is constant.

The term slope has to do with a measure of how steep the line of best fit is for a relationship that exists between two variables. In this case, we are considering the relationship between the amount paid and the time taken.

A straight line graph is expected to have a constant slope. To show that the slope is constant, let us look at two points on the graph; (0, 0) (9, 675) and (0, 0) (7, 525)

In the first case;

m = [tex]y_{2} - y_{1} /x_{2} - x_{1}[/tex]

m = 675 - 0/9 - 0

m = 75

In the second case;

m = [tex]y_{2} - y_{1} /x_{2} - x_{1}[/tex]

m = 525 - 0/7 - 0

m = 75

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1) The percentage of students who will get a score below 275 is; 0.15%

2) Yes, any score below 275 is significantly different from the mean.

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviations from the mean.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

1) We are given;

Population mean; μ = 500

Sample mean; x' = 275

standard deviation; σ = 75

Thus;

z = (275 - 500)/75

z = -3

This is 3 standard deviations from the mean. Thus;

The percentage of students who will get a score below 275 is;

(100 - 99.7)/2 = 0.15%

2) Yes, any score below 275 is more than 3 standard deviations away from the mean and can be considered significantly different from the mean.

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Answer:

I got (-1,-4) and (3,0) When I graphed with Desmos.  I do no see that solution.

Step-by-step explanation:

Answer:

m = -5/3

Step-by-step explanation:

Slope is defined as the change in y / change in x or [tex]\frac{y2-y1}{x2-x1}[/tex]

The order of the points don't matter so we can do:

[tex]\frac{-1-(-6)}{5-8}=\frac{-5}{3}[/tex]

-5/3 is as simple as the fraction can be.

The expressions given in the questions mean that the least common denominator is the least common multiple.

According to the question,

We have the following information:

We have three questions of fractions which are either in addition or subtraction.

Now, we will only look at the denominators of these fractions. And note that the least common multiple is same as the least common denominator.

For first one, it is 6 and 4:

Each multiple of 6: 2*3

Multiples of 4:2*2

The least common multiple of 6 and 4: 12

The least common denominator is 12.

For second one, it is 7 and 3.

Each multiple of 7: 7

Multiple of 3: 3

The least common multiple of 7 and 3: 21

The least common denominator of 7 and 3: 21

For third one, it is 8 and 2.

Multiples of 8: 2*2*2

Multiples of 2: 2

The least common multiple of 8 and 2: 8

The least common denominator is 8.

Hence, the expressions given in the questions mean that it is the least common multiple.

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1. The equation in​ a slope-intercept form describing the relationship is y = -4000x + 27000.

2. The daily sales of Fun Noodles at the price of $5.50 is  5000.

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $5, sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 3000 Fun Noodles per day.

The relationship between sales​ price, x, and the number of Fun Noodles​ sold, ​ y, is linear. The ordered pair are (5, 7000) and (6, 3000).

The equation in slope intercept form describing the relationship is as follows:

1. y = mx + b

where

Therefore,

m = 3000 - 7000 / 6 - 5

m = - 4000

Let's find the y-intercept using (6, 3000)

3000 = -4000(6) + b

3000 + 24000 = b

27000 = b

Hence, the equation is y = -4000x + 27000

2. The daily sales of Fun Noodles at the price of $5.50 can be computed as follows;

y = -4000(5.5) + 27000

y = -22000 + 27000

y = 5000

Therefore, the daily sales is 5000.

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Answer: 243x^5 + 2025x^4y + 6750x^3y^2 + 11250x^2y^3 + 9375xy^4 + 3125y^5

Step-by-step explanation:

1. To find each term, use BINOMIAL EXPANSION THEOREM (best to look up theorem on your own).

2. Expand the summation (after finding each term).

3. Simplify the exponents for each term.

> 1 • (3x)^5 • (5y)^0 + 5 • (3x)^4 • (5y)^1 + . . . + 1 • (3x)^0 • (5y)^5

4. Simplify.

The total annual premium for this insurance will be $14,219.

Define premium.

An amount that the insured pays on a regular basis to the insurer to cover his risk is known as a premium. In terms of finance, a premium is the sum of the costs associated with an option or the distinction between the higher price paid for a fixed-income instrument and the relevant face amount. For many different insurance policies, including health, homeowner's, and rental insurance, premiums are typically paid. Automobile insurance is a typical example of an insurance premium.

Solution explained:

A/Q, as we calculate,

Annual Premium for one worker is = [tex]33000 X \frac{10.51}{100}[/tex] = $3468.3

Annual Premium for four workers is = 4 X 3468.3 = $13873.2

Annual Premium for the secretary is = 26000 X [tex]\frac{1.33}{100}[/tex] = 345.8

Therefore, the total annual premium for this insurance will be

= 13873.2 + 345.8 = 14219

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Answer:

45.90

Step-by-step explanation:

$60.00 15% off = $51.00

$51.00 10% off = 45.90

For the given conditions, the length of box=6.92 feet, width of box=3.46 feet and height of box=2.31 feet.

Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.

Here,

area of material=72 feet²

V=lbh

l=2b

72=lb+2lh+2bh

substitute l as 2b,

72=2b²+4bh+2bh

36=b²+3bh

3bh=36-b²

h=(36-b²)/3b

v=lbh

v=2b*b*(36-b²)/3b

v=2b*(36-b²)/3

=(72b-2b³)/3

differentiate the v,

v'=1/3(72-6b²)

v'=0

72-6b²=0

6b²=72

b²=12

b=√12

b=3.46 feet

l=2b=6.92 feet

h=(36-b²)/3b

=(36-12)/3*3.46

h=2.31 feet

The box measures 6.92 feet long, 3.46 feet wide, and 2.31 feet tall under the specified circumstances.

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Answer:

[tex]W=2\sqrt{3}=3.46\; \sf ft\;(2\;d.p.)[/tex]

[tex]L=4\sqrt{3}=6.93\; \sf ft\;(2\;d.p.)[/tex]

[tex]H = \dfrac{4\sqrt{3}}{3}=2.31\; \sf ft\;(2\;d.p.)[/tex]

Step-by-step explanation:

If the length is twice the width:

Surface area of the box

[tex]\implies SA = WL + 2WH + 2LH[/tex]

[tex]\implies SA = W(2W) + 2WH + 2(2W)H[/tex]

[tex]\implies SA = 2W^2 + 2WH + 4WH[/tex]

[tex]\implies SA = 2W^2 + 6WH[/tex]

If the surface area is 72 ft²:

[tex]\implies 2W^2 + 6WH = 72[/tex]

[tex]\implies 6WH = 72 - 2W^2[/tex]

[tex]\implies H = \dfrac{72 - 2W^2}{6W}[/tex]

[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]

Volume of the box

[tex]\implies V = LWH[/tex]

[tex]\implies V = (2W)WH[/tex]

[tex]\implies V = 2W^2H[/tex]

Substitute the found expression for H into the formula for volume:

[tex]\implies V = 2W^2\left(\dfrac{36 - W^2}{3W}\right)[/tex]

[tex]\implies V = \dfrac{2W^2(36 - W^2)}{3W}[/tex]

[tex]\implies V = \dfrac{2W(36 - W^2)}{3}[/tex]

[tex]\implies V = \dfrac{72W - 2W^3}{3}[/tex]

[tex]\implies V =24W-\dfrac{2}{3}W^3}[/tex]

To find the value of W when the volume is at its maximum, first differentiate the equation for volume with respect to W:

[tex]\implies \dfrac{\text{d}V}{\text{d}W}=24-2W^2[/tex]

Now set the derivative to zero and solve for W:

[tex]\implies 24-2W^2=0[/tex]

[tex]\implies 2W^2=24[/tex]

[tex]\implies W^2=12[/tex]

[tex]\implies W=\sqrt{12}[/tex]

[tex]\implies W=2\sqrt{3}[/tex]

As length is twice the width:

[tex]\implies L=2 \cdot 2\sqrt{3}[/tex]

[tex]\implies L=4\sqrt{3}[/tex]

To find H, substitute the found value of W into the expression for H:

[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]

[tex]\implies H = \dfrac{36 - (2\sqrt{3})^2}{3(2\sqrt{3})}[/tex]

[tex]\implies H = \dfrac{36 - 12}{6\sqrt{3}}[/tex]

[tex]\implies H = \dfrac{24}{6\sqrt{3}}[/tex]

[tex]\implies H = \dfrac{4}{\sqrt{3}}[/tex]

[tex]\implies H = \dfrac{4\sqrt{3}}{3}[/tex]  

Answer: tell me the soulation like how do you solve it then I can help

Step-by-step explanation:

Answer: Force = 300 NewtonsMass = 25 kgAcceleration = Force / Mass = 300 Newtons / 25 kg = 12 metres / second^2.

Second law of Newton

Data:

Newton's second law formula

          F = m * a

We clear for acceleration

  [tex]\boldsymbol{\sf{\dfrac{F}{m}=\dfrac{\not{m}*a}{\not{m}} \iff \ \dfrac{F}{m}=a \longmapsto \ a=\dfrac{F}{a} }}[/tex]

                                                        [tex]\boldsymbol{\sf{a=\dfrac{300 \ N}{25 \ kg} }}[/tex]

We know very well that to find the acceleration, we decompose N= Kg*m/s^2.

                                                        [tex]\boldsymbol{\sf{a=\dfrac{300 \not{kg}*\frac{m}{s^2} }{25 \not{kg}} }}[/tex]

                                                        [tex]\boldsymbol{\sf{a=12 \ \dfrac{m}{s^{2}} }}[/tex]

Answer:

Step-by-step explanation:

l = length

w = width = 2.5

a = area = 12.5

l = a/w = 12.5/2.5 = 5

so the answer is l = 5

Answer:

seven multiplied by x to the second power multiplied by the difference of two multiplied by x subtract 3 multiplied by the product of three multiplied by z multiplied by 3 add four.

Step-by-step explanation:

This is a useless question, word form isn't in any sort of ACTUAL GLOBAL TEST. So don't stress over this.

The number of different codes as the letters A or C must come first and digits can be repeated is 2000

Permutations and combinations are a subset of the study of finite, discrete structures that are known as combinatorics. Combinations include the selection of items without respect to order, whereas permutations are precise selections of elements within a set where the order of the elements is significant.  

Here we have,

The locker combination code consists of one letter and 3 digits  

Here we need to find the number of different codes If the letter A or C must come first and digits can be repeated.

Given that the first letters are A and C

Here number of ways that A and C can be chosen at first = 2

As we know Number of digits = 10  [ including 0, 0 to 9 ]

Number of arrangements that can be chosen from 10 digits

= 10 × 10 ×10   [ Since repetition is allowed ]  

Therefore,

The possible number of different codes = 2 × 10 × 10 ×10 = 2000

Therefore

The number of different codes as the letters A or C must come first and digits can be repeated is 2000

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The equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1

The slope of the line = -1/2

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The slope intercept form

y = mx + b

Where m is the slope of the line

b is the y intercept form

The coordinates of the point = (-6, 2)

Substitute the values in the equation

2 = (-1/2)(-6) + b

2 = 3 +b

b = 2 -3

b = -1

The equation will be

y = (-1/2)x - 1

Hence, the equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1

The complete question is :

What is the equation of a line that passes through (-6, 2) and has a slope of -1/2 ?

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Answer:

27.64

Step-by-step explanation:

Answer:
30-2=28+542=570

Step-by-step explanation: