30x43x54545454545455454x82409284x098908098x8908089808x56678909876543-32131273138x1000 =

The 99% confidence interval for the mean length of stay for patients with abdominal surgery is 5.54, 7.66

We have the following data to solve the question with

sample size = 17

standard deviation s = 1.5

Confidence interval = 99%

mean = 6.6 days

α = 1 - 0.99

= 0.01

df = degree of freedom = n -1  

17 - 1 = 16

tα/2 = 0.01 / 2

=  t 0.005, 16

t critical value = 2.9208

99 % confidence interval =

X ± t critical * s/√n

[tex]6.6 +-2.9208 * \frac{1.5}{\sqrt{17} }[/tex]

6.6 ± 1.0626

6.6 - 1.0626, 6.6 + 1.0626

= 5.54, 7.66

The 99% confidence interval for the mean length of stay for patients with abdominal surgery is 5.54, 7.66

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Los capitales depositados en las cuentas de 2 %, 3 % y 4 % son 630.000, 420.000 y 315.000, respectivamente.

En este problema tenemos el caso de una suma de dinero distribuida y depositada en tres cuentas con tres tasas de interes simple distintas. Existe una tasa de interés simple cuando el interés generado sobre el capital no es acumulativo en el tiempo. El modelo de interés simple es descrito por la siguiente fórmula:

C' = C · (1 + r / 100)

Donde:

A continuación, describimos la ganancia registrada en cada cuenta tal que produce la misma ganancia:

Cuenta al 2 %:

z = x · (2 / 100)

z = 0.02 · x

0.02 · x - z = 0

Cuenta al 3 %:

z = y · (3 / 100)

z = 0.03 · y

0.03 · y - z = 0

Cuenta al 4 %:

z = (1.365.000 - x - y) · (4 / 100)

z = 54600 - 0.04 · x - 0.04 · y

0.04 · x + 0.04 · y + z = 54600

La solución de este sistema de ecuaciones lineales se obtiene mediante métodos numéricos:

(x, y, z) = (630.000, 420.000, 12.600)

Finalmente, el capital depositado en la cuenta al 4 % es:

c = 1.365.000 - 630.000 - 420.000

c = 315.000

Se deposita capitales de 630.000, 420.000 y 315.000 en las cuentas de 2 %, 3 % y 4 %, respectivamente.

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If they have $284.25 to spend on parking and admission. Parking is $9.25, and tickets cost $27.50 per person, including tax. The number of people that can go to the amusement park is: 10 people.

Let a represent  the number of people who can go to the amusement park

Formula an equation

9.25 + 27.50a = 284.25

Combine like terms

27.50a = 284.25  - 9.25

27.50a =  275

Divide both side by 27.50a

a= 275/ 27.50

a = 10 people

Therefore 10 people can go to the amusement park.

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Answer:

Slope = -2

Y-intercept = -8

Step-by-step explanation:

Hello!

Slope-Intercept Form: y = mx + b

The m variable in this equation would be -2, and it is also the slope of the equation.

The b variable in this equation is -8, which is the y-intercept of the equation.

Answer:

y intercept -8

slope -2

Step-by-step explanation:

y = -2x-8

This is written in slope intercept form

y = mx+b

The slope is m  which is -2

The y intercept is b which is -8

Answer:

7.

[tex] \frac{1}{4} [/tex]

8.

[tex]2[/tex]

9.

[tex] - \frac {5}{4} [/tex]

10.

[tex]3[/tex]

Step-by-step explanation:

rate of change is slop

Answer:

8 hours

3 hours

Step-by-step explanation:

24/3=8

24/8=3

The perimeter of the given rectangular room is found as -

Part a: p = 11 m.

Part b: p = 46 m.

As, given in the question-

The rectangular room has-

l m long and b m wide,

perimeter p, where p = 2l+2b  ...eq 1

Part a: perimeter of a room for, 3.5 m long and 2 m wide.

Put l = 3.5  and b = 2 in  eq 1.

p = 2l+2b

p = 2(3.5) +2(2)

p = 7 + 4

p = 11 m.

Part b: perimeter of a room for, 20 m long and 3 m wide.

Put l = 20  and b = 3 in  eq 1.

p = 2(20) +2(3)

p = 40 + 6

p = 46 m.

Thus, the perimeter of the given rectangular room is found as 46m.

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Answer:

[tex]134^{\circ}[/tex]

Step-by-step explanation:

Using the exterior angle theorem,

[tex]m\angle z=m\angle A+m\angle B=134^{\circ}[/tex]

Using the exterior angle theorem, angle z is measured as 134°.which is the correct answer that would be an option (D).

The exterior angle theorem is a triangle theorem that asserts that the measure of the external angle created by an extended side of a triangle is equal to the sum of the measures of the triangle's remote interior angles.

The given data will be the following as:

Exterior angle to angle C of triangle ABC = z

The remote interior angle of triangle ABC are angled A = 58° and angle B = 44°.

Therefore:

The measure of angle z = measure of angle A + measure of angle B [according to the exterior angle theorem]

Substitute the values and we get

Measure of ∠z = 77 + 57

Measure of ∠z = 134°

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The probability that three cards have the same number, using the hypergeometric distribution, is of:

0.0448 = 4.48%.

The probability mass function for the hypergeometric distribution is defined as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the function are listed below:

In the context of this problem, the values of these parameters are given as follows:

N = 28, k = 4, n = 5, x = 3.

Hence for one color, the probability that three cards have the same number is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,28,5,4) = \frac{C_{4,3}C_{24,2}}{C_{28,5}} = 0.0112[/tex]

There are four colors, hence the probability is:

p = 4 x 0.0112 = 0.0448 = 4.48%.

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Answer:

48

Step-by-step explanation:

1 ) Simplify...

[tex]6^2-\left(-12\right)[/tex]

[tex]=6^2+12[/tex]

[tex]6^2=36[/tex]

[tex]=36+12[/tex]

2 ) Add the numbers...

[tex]36+12 =[/tex]

[tex]48[/tex]

Hope this helps! :)

The value of the expression given as (7/4x - 5) - (2y - 3.5) - (-1/4x + 5) is 2x - 2y - 6.5

In this question, the representation of the expression is given as

(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)

Start by removing the brackets in the expression

So, we have

7/4x - 5 - 2y + 3.5 + 1/4x - 5

Evaluate the fractions in the expression

The expression becomes

1.75x - 5 - 2y + 3.5 + 0.25x - 5

Collect the like terms

1.75x + 0.25x - 2y - 5  + 3.5  - 5

Evaluate the like terms

2x - 2y - 6.5

Hence, the solution is 2x - 2y - 6.5

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Answer: C & E

Step-by-step explanation: A is a lie, function 1 is pos

B is a lie function 1 is pos

C is true

D is a lie

E is true

Answer:

D

Step-by-step explanation:

[tex]m\angle EBD=33^{\circ} \implies m\angle EBC=33^{\circ} \\ \\ \therefore m\angle DBC=m\angle EBD+m\angle EBC=66^{\circ} \\ \\ m\angle DBC=66^{\circ} \implies m\angle ABD=66^{\circ} \\ \\ \therefore m\angle ABC=m\angle ABD+m\angle DBC=132^{\circ}[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]0.\underline{25}\implies \cfrac{25}{1\underline{00}}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ y=0.25x-7\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x-7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{1}\implies -4}}[/tex]

so we're really looking for the equation of a line whose slope is -4 and it passes through (-6 , 8)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 4}(x-\stackrel{x_1}{(-6)}) \implies y -8= -4 (x +6) \\\\\\ y-8=-4x-24\implies {\Large \begin{array}{llll} y=-4x-16 \end{array}}[/tex]

Answer:

$1598

Step-by-step explanation:

1st week

4*15=60

32*9=288

59*3=177

60+177+288=525

2nd week

5*15=75

59*7=413

32*4=128

75+413+128=616

3rd week

8*15=120

3*59=177

5*32=160

120+177+160=457

525+616+457=$1598

Answer: The prime factorization of 216 is 2 × 2 × 2 × 3 × 3 × 3 or 23 × 33.

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

1.7

Step-by-step explanation:

[tex]\frac{17 \text{ in}}{10 \text{ hr}}=1.7[/tex] in/hr

Answer:

least

- 1/4 ft

- 14 3/4 ft

- 15 1/2 ft

- 20 3/5 ft

greatest

Answer:

- 20 3/5 ft

- 15 1/2 ft

- 14 3/4 ft

- 1/4 ft

I the number is larger looking but have a negative symbol, then it is smaller.

For example, -1 is greater than -6. Also -1/4 is greater than -20 3/5.

Trust me, I am a year ahead in school, so trust me.

I hope this helped.

The subject of the equation is x and it can be written as x = t/6.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

The given equation is

6x = t

Divide both sides by 6

6x/ 6 = t/ 6

x = t/ 6

So, the subject of the equation is x - t/6.

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The answer is option A) A factor of f(x) is (x – 1).

What is the remaining theorem?

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.

f(x) = 4x3 - 4x2 - 16x + 16 [Given]

One aspect is (x - 2)

The remaining theorem is used to:

Where q(x) is the quotient polynomial and r(x) is the remainder polynomial, f(x) = (x-2)q(x) + r(x).

As (x-2) is a factor of f, r(x) equals 0. (x)

f(x) = (x-2)·q(x) (x)

q(x) = f(x)/ (x-2) (x-2)

[4x3 - 4x2 - 16x + 16]/ (x - 2) (x - 2)

= [4x2 (x - 1) - 16 (x - 1)]

/ (x - 2) (x - 2)

By even more simplifying

= [(x - 1) (4x2 - 16)]

/ (x - 2) (x - 2)

excluding 4 as common

= [(x - 1) 4 (x2 - 4)]

/ (x - 2) (x - 2)

With the use of the algebraic formula a2 - b2 = (a + b) (a - b)

= [(x - 1) 4 (x + 2) (x - 2)]

/ (x - 2) (x - 2)

= [4 (x - 1) (x - 2) (x + 2)]

/ (x - 2) (x - 2)

The roots are therefore 2, -2, and 1.
there the ans is A) A factor of f(x) is (x – 1).

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Answer:

Step-by-step explanation:

The probability of no defects with 2% rate of defects:

Probability of exactly one defect:

Probability of one or no defects:

This indicates that:

The probability that this whole shipment will be accepted is 72.39%.

The equivalent multiplication sentence that shows associative property is 3x(1×6)

Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.

This means that if a,b,c are real numbers then a×(b×c)=b×(a×c)

using the associative property,1×(3×6)= 3×(1×6)

To verify the statement,let's find out

solving the parentheses first

1×(3×6)=1×18= 18

3×(1×6)= 3×6= 18

this means that 1×(3×6) and 3×(1×6) are associative

therefore 1×(3×6)=3×(1×6)

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Answer:

Option 1. It is positive and increasing.

Step-by-step explanation:

The equation for a tank that is filled with petrol at 10 liters already and filling at 35 liters per minute is  y = 35x + 10

The equation required here is a linear equation

The graph of linear equation is a straight line graph and the relationship is expressed in the form.

y = mx + c

variables are defined as below

y = total petrol in  liters

m = filling in  liters per minute = 35

x = number of liters

c = quantity before the filling began = 10

The expression is

y = 35x + 10

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If he has 2 more pennies than nickels. the number of pennies is  10.6  and the number of nickels that Levi has is  12.6.

n = number of nickels

n-2 = number of pennies

Hence,

5n +1(n -2) = 74

Collect like terms

6n = 76

Divide both side by 6n

n = 76/6

n = 12.6 ( nickels)

Pennies

n-2

= 12.6 -2

= 10.6

Therefore Levi  has 10.6 pennies and 12.6 nickels.

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Answer:

Step-by-step explanation:

Jb

Hence its proven that f and g are inverse of one another

What is a Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given,

f(x)= 2x-3/2

g(x)= 2x+3/2

Step 1: show that fog=x

f(g(x))

[2((2x + 3) / 2) - 3]/2

[(2x + 3) - 3] / 2

(2x + 3 - 3) / 2

2x / 2

x , which is equals to x

Now, for Step 2: gof = x

g(f(x))

g((2x - 3)/2)

[2((2x - 3)/2) + 3]/2

[(2x - 3) + 3]/2

(2x - 3 + 3)/2

2x/2

x , which is equals to x

Since, both fog(x) and gof(x) equals to x

Hence, its proven that f and g are inverse of one another

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Answer:

symbol

greater

Step-by-step explanation:

An inequality symbol always opens to the larger,greater,bigger number.

Examples:

5 > 1

2 > -1

-4 < 0

2 < 3

Answer:  An inequality Sign always opens to the  smaller number.

Step-by-step explanation:

The median race time for this event is 38 minutes.

Given:

Race times for a recent 5k run are normally distributed with a mean time of 38 minutes and standard deviation of 3.5 minutes.

a.

X is normally distributed in (38,3.5).

so here the mean and the median are equal to each other.

Mean = 38

Median = mean

Median = 38 minutes.

Therefore the median race time for this event is 38 minutes.

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The final cost of the sliced turkey and provolone cheese is $31.84

The first step is to calculate the cost of the sliced turkey

The pounds of turkey is 24.8

The amount of the turkey is $1.89

The cost is = 24.8/1.89

= 13.21

The next step is to calculate the cost of the provolone cheese

The pounds of the provolone cheese 38.2

The amount of provolone cheese is $2.05

The cost is = 38.2/2.05

= 18.63

Therefore the final cost can be calculated as follows

= 13.21 + 18.63

= 31.84

Hence the final cost is $31.84

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