A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution.
(a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
(b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.

Answer:

The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".

Step-by-step explanation:

Since a normally distributed random variable, the practical rule states:

About 68% of the metrics are in the 1 default deviation

About 95% of metrics correspond to 2 standard deviations from the average.

About 3 standard deviations of the average represent 99.7% of the measurement.

We have the following in this problem:

Average of 78, the average 9 default.

 Calculating the percentage of students that passed the test.

[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]

Therefore 60 is under the average for two standard deviations.

Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.

Everything was cleared of the 50 percent above.

Of the 50% below, 95% (within 2 known mean deviations) succeeded.

therefore

[tex]p=0.5+0.5 \times 0.95=0.975[/tex]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]

In this case, we have

x(t) = exp(t ) + exp(-t )   ==>   dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t   ==>   dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]

[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]

The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.

[tex]e^2 -\dfrac{1}{e^2 }[/tex]

It is the reverse of differentiation.

The parametric equations are given below.

[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]

Then the arc length of the curve will be given as

[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]

Then

[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]

More about the integration link is given below.

https://brainly.com/question/18651211

Answer:

12

Step-by-step explanation:

Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)

Answer:

quadratic trinomial

Step-by-step explanation:

3x(x − 3) + (2x + 6)(-x − 3)

Distribute

3x^2 -9x  + (2x + 6)(-x − 3)

FOIL

3x^2 -9x   + -2x^2 -6x -6x -18

Combine like terms

x^2-21x-18

This has 3 terms so it is a trinomial

The highest power of x is 2 so it is quadratic

9514 1404 393

Answer:

Step-by-step explanation:

Eliminating parentheses, we get ...

  = (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)

  = 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)

  = 3x² -9x -2x² -6x -6x -18

  = x²(3 -2) +x(-9-6-6) -18

  = x² -21x -18

The highest power is 2, so this is a quadratic.

There are 3 terms, so this is a trinomial.

Answer : Four sides (1, 2, 3, 4) are less than 5. The probability is 4 out of 6, or 2/3 or 0.6667.

The solution is, the correct answer is B. comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

We will consider all the sets of probabilities, the one with the highest probability is the right answer.

a) You roll an odd number and roll a 5: the probability is calculated thus:

1/6 * 3/6

=0.0833

b) You land on an odd number or you roll a 6: the probability is calculated thus:

3/6 +1/6

= 0.6667

c) You roll a six and roll a 4: the probability is calculated thus:

1/6 * 1/4

= 0.0417

d) You roll a 3 and roll an old number: the probability is calculated thus:

1/6 * 3/6

=0.0833

Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

Therefore the correct answer is B.

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Answer:

a^2 + 2ab + b^2

Answered by Gauthmath

Answer:

[tex]5 {x}^{2} + 21 + 5x[/tex]

Step-by-step explanation:

TOTAL AMOUNT earned = Tim money + Melina money

[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]

[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]

[tex] = 5 {x}^{2} + 21 + 5x[/tex]

Answer:

Step-by-step explanation:

If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.

First the area of the inner square. Here we go:

Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.

The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.

Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":

[tex]?^2=b^2+(a-b)^2[/tex] and

[tex]?^2=b^2+a^2-2ab+b^2[/tex] and

[tex]?^2=a^2-2ab+2b^2[/tex] so

?, the length of the hypotenuse, is

[tex]?=\sqrt{a^2-2ab+2b^2}[/tex] and now we can use that to find the area of the inner square. The formula for a square's area is

[tex]A=s^2[/tex] so

[tex]A=(\sqrt{a^_2}-2ab+2b^2})^2[/tex] which gives us finally:

[tex]A=a^2-2ab+2b^2[/tex] **

Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is

A = a²

The ratio of the area of the inner to the outer is:

[tex]\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}[/tex] and that does not reduce.

Answer:

A

Step-by-step explanation:

Edmentum

Complete Question:

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800  ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]

Note : the standard form of a quadratic equation is ax² + bx + c = 0  ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

[tex] x = \frac {-b}{2a} [/tex]

Substituting the values, we have;

[tex] x = \frac {-3}{2*(-0.001)} [/tex]

Cancelling out the negative signs, we have;

[tex] x = \frac {3}{2*0.001} [/tex]

[tex] x = \frac {3}{0.002} [/tex]

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

Answer:

I think this answer is A.

Answer:

A correlation shows strength and regression tells the pattern.

Step-by-step explanation:

• The differences between the results that demonstrate a correlation between two variables and results where a regression is run using two variables are as follows

1) the correlation is the measure of degree to which any two variables may vary together.

2) if both variables tend to increase or decrease together the correlation is said to be direct or positive.

3) the correlation gives the strength of relationship between two quantities

4) The regression gives the relationship in the form of an equation.

5) The regression investigates the dependence of the dependent variable on the independent variable.

6) it shows the relationship whether it is linear or curved or parabolic etc.

• I may record the ages and the blood pressure of the patients and run a correlation analysis which may not be positive as blood pressure does not always increase with age

• I may record the ages and the blood pressure of the patients and may want to run a regression analysis which will show the relationship of the patients suffering from high blood pressure and their ages whether it follows a similar pattern or not.

Answer:

its perfectly correct you did good

Answer:

44.5 units squared

Step-by-step explanation:

First, separate the figure into two different shapes. You should get a rectangle and a triangle after doing this. Next, we'll work on the rectangle. Multiply 2 by 10, and you'll get the area of the rectangle, which would be 20 units squared. We can't multiply 3 by 2, as that would cause the triangle to have 4 sides rather than 3. A triangle can ONLY have 3 sides anyway, so always remember that. Next, we'll work on the triangle. Subtract 10 by 3, and you'll get 7. This will be the triangle's height, so the equation would be 7 X 7 divided by 2, which would be 24.5 units squared. Finally, add 24.5 and 20. You should get 44.5 units squared as your final answer.

So, the final answer for this problem would be 44.5 units squared.

Hope this helped!

10(3+5)^2

10(8)^2

10(64)

=640

Answer:

Less than 90⁰

Step-by-step explaination:

If p is an acute angle then, p can be equal to any measurement less than 90⁰

It can be upto 89⁰

Answer:

0 < angle < 90

Step-by-step explanation:

Acute angles are between 0 and up to 90 degrees

Right angles are 90 degrees

Obtuse angles are greater than 90 degrees and less than 180 degrees

Answer:

B is the correct answer of your question.

I HOPE I HELP YOU....

Answer:

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 80 seconds and a standard deviation of 6 seconds.

This means that [tex]\mu = 80, \sigma = 6[/tex]

What travel time separates the top 2.5% of the travel times from the rest?

This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.96 = \frac{X - 80}{6}[/tex]

[tex]X - 80 = 6*1.96[/tex]

[tex]X = 91.76[/tex]

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Answer:

2.92

Step-by-step explanation:

Normal price

4 * 6.98 =27.92

Sale price

2 for 12.50   means 4 at 2* 12.50

2*12.50 = 25

Subtract

27.92-25=2.92

He saved 2.92

HOW TO SOLVE SYSTEMS OF EQUATIONS BY ELIMINATION

To solve systems of equations by elimination, we want to eliminate one of the variables. To do this, we want to cancel out a certain variable in both equations. For example, if you had 8x in one equation and -8 x in another, you could combine the two equations and the x would be gone!

THE SOLUTION

In our case, though, we don't have anything we can combine to cancel out the variables. But, what we can do is multiply the first equation by three. If we do this, now we have a 9x in the top and a -9x in the bottom. Then, we can solve for y!

SOLVING FOR Y

Multiply first equation by three

9x+6y=57

Combine top and bottom equations

14y=28

We divide both sides by 14.

y=2

SOLVING FOR X

Now, we can simply plug our y-value into one of the original equations and then solve for x.

3x+4=19

We subtract 28 from both sides.

3x=15

We divide both sides by 3.

x=5

Therefore, our solution is (5,2) or x=5 and y=2.

I hope that this helps! Have a wonderful day! :D

Answer:

x=5 and y=2.

Step-by-step explanation:

Answer:

y>3/5

Step-by-step explanation:

3y+5 <10

3y<5

y>3/5

Answer:

[tex]\:3y+5<10\\3y+5-5<10-5\\3y<5\\\frac{3y}{3}<\frac{5}{3}\\y<\frac{5}{3}[/tex]

OAmalOHopeO

Answer:

False

Step-by-step explanation:

If we consider x=1 then

2*1-8 = 10-1

2-8 =9

6 = 9 (which is impossible)

so false

We can determine that the original equation 2x - 8 = 10 - x is true when x = 6.

We have,

Simplify the equation:

2x - 8 = 10 - x

Combining like terms by adding x to both sides:

3x - 8 = 10

Now, to isolate the variable x, add 8 to both sides:

3x = 18

Finally, divide both sides of the equation by 3:

x = 6

By solving the equation, x = 6.

Therefore,

We can determine that the original equation 2x - 8 = 10 - x is true when x = 6.

Learn more about equations here:

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Answer:

25.61 feet

Step-by-step explanation:

First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.

Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.

One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have

sin(80°) = opposite / 26 feet

multiply both sides by 26 feet

sin(80°) * 26 feet = opposite

= 25.61 feet as the height of the wall the ladder reaches

The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.

The condition is shown in the diagram.

Then the height of the wall will be

[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

Answer:

y = -8/3, z = -1

Answer:

The length=16cm and the width=8cm.

Step-by-step explanation:

Given that the length is twice the breadth or width of the rectangle

Let's assume that the breadth of the rectangle is x.

Thus the length is 2x.

Given perimeter=48cm

The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.

2(x+2x)=48

(3x)=48/2

3x=24

x=8cm

2x=16cm

Step-by-step explanation:

length=2x

width=x

2x+x+2x+x=48

6x=48

6x÷6=48÷6

x=8

length=16

width=8

Answer:

1120

Step-by-step explanation:

To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

[tex]S=4\pi r^2[/tex]

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

[tex]\frac{d}{2}=r[/tex] Now we can have the equation in terms of diameter instead of radius. Rewriting:

[tex]S=4\pi(\frac{d}{2})^2[/tex] which simplifies to

[tex]S=4\pi(\frac{d^2}{4})[/tex] and a bit more to

[tex]S=\pi d^2[/tex] (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

[tex]\frac{dS}{dt}=\pi*2d\frac{dD}{dt}[/tex] Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for [tex]\frac{dD}{dt}[/tex], the rate at which the diameter is changing, when the diameter is 13. Filling in:

[tex]-3.8=\pi(2)(13)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:

[tex]-\frac{3.8}{26\pi}=\frac{dD}{dt}[/tex] and divide to get

[tex]\frac{dD}{dt}=-.459\frac{cm}{min}[/tex] Obviously, the negative means that the diameter is decreasing.

Answer:

x not given

therefore no answer for x

Answer:

Cost ratio of pens:pencils  =   9 : 4

Step-by-step explanation:

Pen  : Pencil

10/10 : 12/12

22.5 / 10  : 18 / 12

2.25 :  1.5 cost per pen : pencil

HC of 0.25 and 0.5 is 8

8 x 2.25 = 18:

1.5 x 8 = 12

Then place them under their denominator x 10 x 12

pens = 18/10 = 1.8

pencils = 12/12 = 1

HC of 1.8 and 1 is  5

1.8 x 5 = 9

1 x 5 = 5

Answer = 9 : 4