The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.8 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. What is the median recovery time? days c. What is the Z-score for a patient that took 4 days to recover? d. What is the probability of spending more than 3.8 days in recovery? e. What is the probability of spending between 3.2 and 4.2 days in recovery? f. The 90th percentile for recovery times is days.

Answer:

They are only equal on day 0, both having 10 population.

Step-by-step explanation:

Given the bacteria on the counter is initially measured at 5 and doubles every 3 days we can generate the following geometric equation:

[tex]f(x)=10*2^{\frac{x}{3} }[/tex]

Given the bacteria on the stove is measured at 10 and doubles every 4 days we can create another equation:

[tex]f(x)=10*2^{\frac{x}{4} }[/tex]

To find how many days it will take for the bacteria population to equal the same lets set both equations equal to eachother:

[tex]10*2^{x/3}=10*2^{x/4}[/tex]

Divide both sides by 10

[tex]2^{x/3}=2^{x/4}[/tex]

Since both exponents have the same base we can set the exponents equal to eachother and solve for x:

[tex]\frac{x}{3}=\frac{x}{4}[/tex]

Multiply both sides by 3 to isolate x on the left side

[tex]x=\frac{3x}{4}[/tex]

Multiply both sides by 4 to remove fraction

[tex]4x=3x[/tex]

Subtract 3x to isolate x on the left side

[tex]x=0[/tex]

Plug x into one of our original equations

[tex]f(0)=10*2^{0/3}[/tex]

Solve

[tex]f(0)=10[/tex]

Transforming the function using f(x - h) shifts its graph h units to the right. Here, we have h = -4, so the graph exists shifted 4 units to the left.

The transformations of functions describe how to graph a function that exists moving and how its shape exists being changed. There exist basically three kinds of function transformations: translation, dilation, and reflection.

Let f(x) = x³ be the original function.

When -5 exists added to the y-value, it moves the point on the graph down 5 units. Compared to f(x), g(x) exists 5 units down.

f(x) = (x + 4)³ - 5

= [x- (- 4) ]³ - 5 (shift 4 units in the negative x direction that exists 4 units left)

Transforming the function using f(x - h) shifts its graph h units to the right. Here, we have h = -4, so the graph exists shifted 4 units to the left.

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The equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.

In this question we have an equation in implicit form: 23 · y + 50 + 27 · y = 50 · y + 50, we need to transform its expression into explicit form by using algebra properties:

23 · y + 50 + 27 · y = 50 · y + 50         Given

50 · y + 50 = 50 · y + 50                      Commutative, associative and distributive properties / Definition of addition

0 = 0 Compatibility with addition / Existence of additive inverse / Modulative property / Result

The equivalence indicates that the equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.

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Answer: True

Step-by-step explanation:

The base is less than 1.

Answer:

100

Step-by-step explanation:

Formulate a plan based on the conditions stated: 65/(13/20)

A fraction is divided by multiplying its reciprocal: 65x(20/13)

Remove the connecting element: 5x20

Determine the quotient or product: 100

100 tokens are bought by mark for his daughter.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Mark bought gift tokens for her daughter, Sally, to use at the state fair. Sally used 13/20 of the tokens on rides.

let "x" be the total token she have

Since, total token she used is 65

Thus,

13/20 * x = 65

x = 100

Therefore, Mark bought for his, daughter 100 Tokens.

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Answer: А=480.

Step-by-step explanation:

The tangential speed of the satellite above the Earth's surface is [tex]7.588 * 10^{3} m/s[/tex].

The tangential speed of a satellite at the given radius and time is calculated as follows:

[tex]v=\frac{2\pi *(150*10^{3}+6371*10^{3} }{90*60} \\v=7.588*10^{3} m/s[/tex]

Therefore, the tangential speed of the satellite above the Earth's surface is [tex]7.588 * 10^{3} m/s[/tex].

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The correct question is shown below:
Consider formula A to be v = and formula B to be v2 = G. Write the letter of the appropriate formula to use in each scenario. Determine the tangential speed of the moon given the mass of Earth and the distance from Earth to the moon. Determine the tangential speed of a satellite that takes 90 minutes to complete an orbit 150 km above Earth’s surface.

Answer: first box is B

second box is A

Explanation:

right on edge as of 2022

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: (h - g)(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: h(x) - g(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - 6 - (2 {x}^{2} + 3x - 9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - 6 - 2 {x}^{2} - 3x + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 2 {x}^{2} + 2x - 3x - 6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: - {x}^{2} - x + 3[/tex]

For, (h - g)(2.1), put x = 2.1

[tex]\qquad \sf  \dashrightarrow \: - {(2.1)}^{2} - (2.1) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 4.41 - 2.1 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 6.51 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 3.51[/tex]

The correct student's t- distribution requires knowing the degrees of freedom. The degrees of freedom are there for a sample of size n is B) n-1.

Distribution is described as the technique of having items to consumers. An instance of distribution is rice being shipped from Asia to the USA. The frequency of occurrence or quantity of lifestyles.

Distribution manner to spread the product for the duration of the market such that a big quantity of humans should purchase it. Distribution involves doing the following matters. An amazing delivery machine to take the goods into one-of-a-kind geographical regions.

Distribution is one of the four elements of the advertising and marketing mix. Distribution is the method of creating a service or product available for the consumer or enterprise user who needs it. this may be executed without delay through the manufacturer or service company or the usage of indirect channels with vendors or intermediaries.

Disclaimer: The question is incomplete. Please read below to find the missing content.

Question: To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

A) n

B) n-1

C) n+1

D) [X - μ / (s / n)]

The degrees of freedom depends on the number of parameters you are estimating.

8=

i-1

In student t distribution we estimate the population mean through sample mean and population standard deviation through sample standard deviation

So here both parameters depend on the sample mean i.e. we just calculate from a sample of size n so

Degrees of freedom for students t distribution is B) n-1

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The expression x³+3x² is a cubic unit representation of the prism's volume.

Having 6 faces, 12 edges, and 8 vertices, a right rectangular prism is a three-dimensional object. Angles between the base and sides are right angles in a right rectangular prism. Rectangles make up each of the six faces.

We have provided that to:

In a right rectangular prism, the height is three units more than the base's length.

The square base has edges that are x units long.

How much volume does a rectangular prism have?

Volume of the rectangular prism = width × length × height

V =  W × L × H   ....................(1)

We've indicated that the

bigger by three than the base's length, h

and  the length of the base is x:

Hence,

               H = X +3

          Length of the base = X

           Width = X

Adding the values l h and w to the formula (1) yields,

V = W × L × H

= X × X × (X+3)

= (X²) × (X+3)

= X³ + 3X³

Consequently, the phrase

               X³ + 3X³

represents, in cubic units, the prism's volume.

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Answer:

t = 6162 years

Step-by-step explanation:

This equation takes the form of

We are given everything but the amount of C-14 at time t = 0.  But we can figure it out from the info we ARE given.  We are told that when the spear head is found it contains 54% of its original amount of C-14.  Notice we are dealing in percents.  If 54% remains when it is found, it started out with 100% of its amount.  That's our N value.  Filling in:

Our goal is to get that t down from the exponential position that it is currently in.  To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication.  So we take the natural log of both sides.  On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone.  Before that, though, we will simplify by dividing both sides by 54.  100/54 = 1.851851852.  So, altogether...

Simplifying by plugging the log of that number into our calculator, we get

.6161861395 = .0001t  and

t = 6161.8613

Rounding to the nearest year, t = 6162 years

The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.

Compact car:

y = 50 + 6x

Another special:

y = 40 + 8x

let

x = number of additional days

50 + 6x = 40 + 8x

50 - 40 = 8x - 6x

10 = 2x

x = 10/2

x = 5 days

Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.

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The value of r = 9.078.

pv = nrt. The factor “r” in the ideal gas law equation is known as the “gas constant”. r = [tex]\frac{pv}{nt}[/tex]. The pressure times the volume of a gas divided by the number of moles and temperature of the gas is always equal to a constant number.

so the student weights out .0422 grams of the magnesium metal so from here we can calculate that more's, the magnesium that he used, that is the mass of the magnesium over the more mass, which is .024422 over 24 point. That's equal to about .001758. More so also, it says the magnesium metal is react with excessive hydrochloric acid and produce hydrogen gas. A sample of the hydrogen gas is collected over water in a meter at 22 cecr, the volume of clictic gas is 43.9 and mastic pressure. Is that so using the experimental and collected data calculated are in the percent error? So we know the magnesium react with hydrochloride. The reaction ratio is 1 to 2 and we produce 1. More is the hydrogen and 1. More is magnesium chloride. So from this equatium we know that more of the hydrogen that would be produced in this case is equal to the mass of the magnesium here, that's his .001758 more and set way. There's among hydrogen. The temperature is 32 (degree celcius) which we need to convert the unit into kelvin, so it's actually about field 5.15 kelvin and tells you. The volume of the gas is 43.9 in ml, which is .0439 liter and tells you the pressure of the gas is about 832 millimeter. Mercury, which is a 2 times 13332 plus ca, that's equal to about 110922.24 par. So in this case we know p v = n r t.

r = [tex]\frac{pv}{nt}[/tex]

So p = 110922.24. V = 0.0439 , n = 0.001758 t =  305.15. So let's just do the calculations here.

In this case you will find r=?

Here it's about 9.078.

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Answer:

speed equals distance over time.

To and fro, distance=speed×time(ts)

distance=900×18=16,200km.

therefore, ts=16,200

since, speed = distance/time

therefore, time taken is inversely proportional to speed making D the best option.

Answer:

if X is the angle degree like I think it is, then X = 56 degrees

Step-by-step explanation:

isosceles triangles will have 2 equal base angles.

90 degree angle - 28 = 62°

62 is now each base angle.

62 times 2 angles equals 124

the final angle, x, is 180 - 124 = 56°

Answer:

8 and -8.

Step-by-step explanation:

Absolute value is the magnitude of quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as |8| or |-8| is equal to 8.

The absolute value of number a:

|a| = 8 ⇔ a = 8 or a = -8

Answer:

6450.35/90.85 = 71 yards.

Step-by-step explanation:

Answer:A

Step-by-step explanation:

-3 to the left and up 4

Answer:

I hope that you are doing well, during this weird time; and that this message finds you in a good place.

To get you started on this problem, you will want to think about how to go about graphing this linear function. You want to keep in mind that you want to plot your dependent variable on the y-axis, as it changes with respect to your independent variable (plotted on the x-axis). In this problem, the cost of the water bill depends on the amount of water used, in HCF. So the graph should be plotted with cost on the y-axis, and HCF on the x-axis.

It follows that you are given the coordinates of (16, $48.37) and (22, y2); where y2 represents the cost when using 22 HCF. You are also given the slope of your line (m, in y = mx + b format). You may recall that you can set-up a slope as the change in y over the change in x, or the "rise over the run" [m = (y2-y1) / (x2-x1)]. We can set this problem up, using this equation to solve for y2 (the cost at 22 HCF) algebraically.

So we would set up the problem as 1.65 = (y2-48.37)/(22-16). We then solve by combining like-terms and using inverse operations as follows:  

  1.65 = (y2 - 48.37) / 6

  1.65(6) = y2 - 48.37

  9.9 = y2 - 48.37

  y2 = $58.27

Step-by-step explanation:

Answer:

b 19.2

Step-by-step explanation:

a = [tex]\pi[/tex][tex]r^{2}[/tex] for a circle.  We do not want to find the area for a whole circle.  We only want to find the area for part of a circle.  a hole circle is 360 degrees.

a = [tex]\frac{88}{360}[/tex][tex]\pi[/tex][tex]r^{2}[/tex]

a = [tex]\frac{88}{360}[/tex][tex]\pi[/tex]([tex]5^{2}[/tex])

a = 19.2 rounded.

The area of the sector of circle is b. 19.20 square meter.

The space enclosed by the sector of circle is called area of the sector of circle.Mathematically,

Area of the sector of circle, A = θ/360πr²

where θ is the angle of the arc and r is the radius of the circle.

Now it is given that,

radius of the circle, r = 5m

Angle of arc, θ = 88°

Therefore, area ofsector of circle A = θ/360πr²

Put the values,

A = 88/360 π 5²

Solving the equation we get

A = 19.20 square meter.

Hence,the area of the sector of circle is b. 19.20 square meter.

So  the correct answer is b.) 19.20 square meter.

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Answer:

  (B)  1

Step-by-step explanation:

The number of such integers will be the number of places where the functions f(x) = x² and g(x) = √x intersect.

The attachment shows the graphical solution to f(x) = g(x) for x > 0. There is exactly one point of intersection at x=1.

There is one such number.

The difference of the fraction is 2/3 or two-thirds

Fractions are written as a ratio of two integers. They are written in the form a/b

Given the following expression

Negative 2 and one-half minus (negative 1 and three-fourths)

This can also be written as;

-2 1/2 - (-1 3/4)

Convert mixed to improper to have;

-5/2 + 7/4

Swap to have;

7/4 - 5/3

Find the LCM

3(7)-4(5)/12

21-20/12
8/12

Write in its simplest form

8/12 = 2/3

Hence the difference of the fraction is 2/3 or two-thirds

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Answer:

2

Step-by-step explanation:

because -3/4 + 2 3/4= 2

The first five terms of the given arithmetic sequence are:

54, 45, 36, 27, 18 (First option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) - 9 ............ (1)

Also, f(1) = 54 .............. (2)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

f(1) is the first term of the sequence which is already provided as 54.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) - 9

f(2) = f(1) - 9

Substitute f(1) = 54 from equation (2)

⇒ f(2) = 54 - 9

f(2) = 45

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) - 9

f(3) = f(2) - 9

⇒ f(3) = 45 - 9

f(3) = 36

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) - 9

⇒ f(4) = 36 - 9

f(4) = 27

Likewise, f(5) = f(4) - 9

⇒f(5) = 27 - 9

f(5) = 18

Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:

54, 45, 36, 27, 18

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Answer:

Mean:36

Median:27

Mode:27

Range:50

Step-by-step explanation:

Mean: 19+26+27+27+30+53+69/7=36

Median: The middle number in the sequence when arranged in ascending order which is 27

Mode: The number that appeared more than others which is 27

Range: This is the difference between the largest number and the lowest number in the sequence which is 50.

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The length of the longer base of the trapezoid could be 0.75 units, [tex]\frac{7}{3}[/tex] units, 4 units.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

Given: The original length of trapezoid= 6 units

The scale factor of less than 1

So, compare the given lengths with the trapezoid longer base length,

0.75 units<6 units

[tex]\frac{7}{3}[/tex] units<6 units

8.75 units< 6 units

But, 12 units> 6 units

Therefore, the length of the longer base can be 0.75, [tex]\frac{7}{3}[/tex], 4 units.

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The complete question is:

“ Qusai made a scaled copy of the following trapezoid. He used a scale factor less than 1.What could be the length of the longer base of the scaled copy of the trapezoid?

Choose 3 answers:

The first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.

In this question,

The nth term of the sequence is [tex]a_n=\frac{3^{(n-1)} }{n!}[/tex]

Now substitute the values of n = 1,2,3,4,5

For n = 1,

⇒ [tex]a_1=\frac{3^{(1-1)} }{1!}[/tex]

⇒ [tex]a_1=\frac{3^{0} }{1}[/tex]

⇒ a₁ = 1

For n = 2,

⇒ [tex]a_2=\frac{3^{(2-1)} }{2!}[/tex]

⇒ [tex]a_2=\frac{3^{(1)} }{(1)(2)}[/tex]

⇒ [tex]a_2=\frac{3}{2}[/tex]

For n = 3,

⇒ [tex]a_3=\frac{3^{(3-1)} }{3!}[/tex]

⇒ [tex]a_3=\frac{3^{(2)} }{(1)(2)(3)}[/tex]

⇒ [tex]a_3=\frac{9}{6}[/tex]

⇒ [tex]a_3=\frac{3}{2}[/tex]

For n = 4,

⇒ [tex]a_4=\frac{3^{(4-1)} }{4!}[/tex]

⇒ [tex]a_4=\frac{3^{(3)} }{(1)(2)(3)(4)}[/tex]

⇒ [tex]a_4=\frac{27}{24}[/tex]

⇒ [tex]a_4=\frac{9}{8}[/tex]

For n = 5,

⇒ [tex]a_5=\frac{3^{(5-1)} }{5!}[/tex]

⇒ [tex]a_5=\frac{3^{(4)} }{(1)(2)(3)(4)(5)}[/tex]

⇒ [tex]a_5=\frac{81}{120}[/tex]

⇒ [tex]a_5=\frac{27}{40}[/tex]

Hence we can conclude that the first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.

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By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

In this problem we have three ordered pairs to be checked on a given function by direct evaluation, a ordered pair lines on the curve of function if and only if the x-value of the ordered pair leads to the y-value by evaluating in the function. Now we proceed to evaluate each of the three points at the function presented in the statement:

(x, y) = (1, 4)

h(1) = - 2 · 1²

h(1) = - 2

By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

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The solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].  

Given the equation  [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] and range is  [tex]10^{-2}[/tex].

We are required to find the interval in which the solution lies.

The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the mid point of the interval is found. The sign of its relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than [tex]10^{-2}[/tex].

Interval:[0,2], signs [+,-],mid point:1, sign at midpoint +.

[1,2]                                                       3/2

[1,3/2]                                                    5/4

The rest is in the attachment. The listed table values are the successive interval mid points.

The final midpoint is 181/128=1.411406.

This solution is within 0.0002 of the actual root.      

Hence the solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].

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Answer:

PQ = 10 units

Step-by-step explanation:

to find where the lines cross the x- axis let y = 0 and solve for x , that is

2x + 8 = 0 ( subtract 8 from both sides )

2x = - 8 ( divide both sides by 2 )

x = - 4 ← point P

and

2x - 12 = 0 ( add 12 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6 ← point Q

the lines cross the x- axis at x = - 4 and x = 6

using the absolute value of the difference , then

PQ = | - 4 - 6 | = | - 10 | = 10 units

or

PQ = | 6 - (- 4) | = | 6 + 4 | = | 10 | = 10 units

Answer: [tex]\Huge\boxed{Distance=10~units}[/tex]

Step-by-step explanation:

Given expression

y = 2x + 8

Substitute 0 for the y value to find the x value

This is the definition of x-intercepts

(0) = 2x + 8

Subtract 8 on both sides

0 - 8 = 2x + 8 - 8

-8 = 2x

Divide 2 on both sides

-8 / 2 = 2x / 2

x = -4

[tex]\large\boxed{P~(-4,0)}[/tex]

Given expression

y = 2x - 12

Substitute 0 for the y value to find the x value

(0) = 2x - 12

Add 12 on both sides

0 + 12 = 2x - 12 + 12

12 = 2x

Divide 2 on both sides

12 / 2 = 2x / 2

x = 6

[tex]\large\boxed{Q~(6,0)}[/tex]

Given information

[tex](x_1,~y_1)=(-4,~0)[/tex]

[tex](x_2,~y_2)=(6,~0)[/tex]

Substitute values into the distance formula

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance=\sqrt{(6-(-4))^2+(0-0)^2}[/tex]

Simplify values in the parenthesis

[tex]Distance=\sqrt{(10)^2+(0)^2}[/tex]

Simplify values in the radical sign

[tex]Distance=\sqrt{100}[/tex]

[tex]\Huge\boxed{Distance=10~units}[/tex]

Hope this helps!! :)

Please let me know if you have any questions