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 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.

The distance covered by a car in one hour is 36.15 miles, and the distance covered by a car using 1 gallon of fuel is 12.05 miles.

A thing that moves quickly and with high speed, covering a lot of ground in a short time. On the other hand, a slow-moving object traveling at a low speed covers a comparatively small distance in the same amount of time. An object with zero speed does not move at all.

Given:

A car traveled at a constant speed for 4 hours and covered 144.6 miles,

The fuel used = 12 gallons,

Calculate the distance covered in 1 hour as shown below,

The distance covered in 1 hour = 144.6 / 4

The distance covered in 1 hour = 36.15 miles

Calculate the distance traveled using 1 gallon of fuel,

The distance traveled using 1 gallon of fuel = 144.6 / 12

The distance traveled using 1 gallon of fuel = 12.05 miles.

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The maximum volume of the box in terms of A will be √3A/4 -3√3/4 cu cm.

It is given that the box has an open top and a square base.

This implies length = breadth.

Let them be x cm

Now, the area of the box is A sq cm

This means

lb + 2bh + 2lh = A

or, x² + 2xh + 2xh = A

or, 4xh + x² = A

or, h = A/4x - x/4

Now volume (V) = lbh

= x²(A/4x - x/4)

= Ax/4 - x³/4

Now to maximize volume we will first differentiate with respect to x and equate it to zero. Hence we get

V' =0

or, A/4 - 3x²/4 = 0

or 3x²/4 = A/4

or, x² = 3

or, x = √3

Now t check whether this gives us the maximum volume we will calculate V"(√3)

V" = -3x/2

V"(√3) = -3√3/2

Since V"(√3) is negative we will get maximum value for x = √3

Now the volume is

A√3/4 - (√3)³/4

= √3A/4 -3√3/4 cu cm

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Answer: y = -1/2x - 3

Step-by-step explanation:

Answer:

The most appropriate method for solving the first system of equations would be elimination. This can be done by adding the two equations together, which will eliminate one of the variables and leave us with an equation in terms of the remaining variable. We can then solve for the value of this variable and substitute it back into one of the original equations to find the value of the other variable.

For the second system of equations, substitution would be the most appropriate method. This is because one of the equations can be rearranged to solve for the value of one of the variables, which can then be substituted into the other equation. This will eliminate one of the variables and allow us to solve for the value of the remaining variable.

For the third system of equations, graphing would be the most appropriate method. This is because both equations are in the form "y = mx + b," which is the standard form of a linear equation. We can graph both equations on the same coordinate plane and find the point of intersection, which will give us the values of both variables.

Jelly beans are $1.5/lb and trail mix is $2.063/lb, according to the data.

A heterogeneous mixture would be a trail mix. When the components of a combination are dispersed unevenly across the mixture, the mixture is said to be heterogeneous. As a mixture of nuts, raisins, and other seeds, trail mix cannot have an evenly distributed dispersion of its ingredients.

t = trail mix, j = jelly beans

3t + 8j = 21

5t + 2j = 18

Solving the first for t

2t = 6j - 3

t = (6j - 3)/2

Substituting

5(6j - 3)/2 + 2j = 18

j = 51/34

j = 1.5, Jelly beans cost $1.5/lb

now,

8t + 3(1.5) = 21

8t = 16.5

t = 2.0625, trailmix costs $2.063 dollars/lb

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The element b₂₄ is the number in the second row and fourth column of the matrix, and we can see that it is equal to 10.

For a matrix M, the element Mₐₙ is the element in the a-th row and in the n-th column.

In this case we want to find b₂₄, so you need to look at the element that is in the second row (counting from the top) and in the fourth column (counting from the right) that element is a 10, then we can conclude:

b₂₄ = 10

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Rotation is the rigid type of transformation which is equivalent to the two reflections across intersecting lines.

Therefore, the rigid type transformation which is equivalent to two reflection across the intersecting lines is called rotation.

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The system of equations - 2x + 5y = - 2 and 4x - 10y = 4 has infinitely many solutions.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, A system of equations - 2x + 5y = - 2...(i) and 4x - 10y = 4...(ii).

Now, multiplying eqn(i) by 2 it becomes - 4x + 10y = - 4...(iii).

Now, by Adding (ii) and (iii) we get,

0x + 0y = 0.

So, 0 = 0, and hence these are coinciding lines with infinitely many solutions.

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The value of x is 10°.

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given:

In ΔRST, m ∠R = (5x+15), m ∠S = (6x+8), m ∠T = (4x+7)

Since the addition of three angles of triangle is 180 degrees.

So,

          m ∠R + m ∠S + m ∠T = 180°

(5x + 15) + (6x + 8) + (4x + 7) = 180°

                               15x + 30 = 180°

                                       15x = 180° - 30°

                                       15x = 150°

                                           x = 10°

Hence, the value of x is 10°.

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Answer:

option a) since the arcs r drawn on both the sides of the line

and also as the arcs intersect each other at the center of the line AB

Therefore, the length of the c from the given figure comes out to be c= 10.63cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here,

The hypotenuse, or longest side in a right triangle, is side c, which is our unknown. With the use of Pythagorean's Theorem, we have

[tex]7^{2} +8^{2} =c^{2}[/tex]

which simplifies to

[tex]7^{2} +8^{2} =c^{2}[/tex]

and

49 + 64 = [tex]c^{2}[/tex]

and

  [tex]c^{2}[/tex] = 113

c = 10.63 cm

Therefore, the length of the c from the given figure comes out to be c= 10.63cm.

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The graph in this problem shows a proportional relationship, because the line passes through the origin, and the rate of change is of 40.

A proportional relationship is a special case of a linear function, with an intercept of zero.

The slope is the constant of proportionality, hence the proportional relationship has the equation defined as follows:

y = kx.

Hence the constant is given as follows:

k = y/x.

Two points from the graph are given as follows:

(1,40) and (2,80).

The constants for each point are given as follows:

The constants are the same for each point, hence the graph represents a proportional relationship.

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Answer:

62.3

Step-by-step explanation:

To find how much a percentage is worth you take the initial number then multiply it by the percentage over a hundred. So in this situation it would be

566.37 times 11/100

Since it's 11 over a hundred you can turn that into 0.11 making it

566.37 times 0.11 or 566.37(0.11)

Coming out to 62.3007

rounded to nearest cent

$62.3

If 16 ounce bottle of orange juice contain 200 milligram was 250% from total of daily recommended amount , then 100% or recommended vitamin C to daily consume is 80 milligram.

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For the function k(x) = 80, must have an x- value of 5 < x ≤ 6 in the given graph.

The greatest integer function takes the greatest integer that is less than or equal to a specified value.

Mathematically, the greatest integer function ⌊x⌋ can be defined as follows:

⌊x⌋ = n, where n ≤ x < n + 1 and 'n' is an integer.

According to the given question,

The function is below as

⇒ k (x)

We have to determine the value of k (x) = 80

As per the given graph, the required solution would be as: [x] + 5

Here ⌊x⌋ = 5, where 5 < x ≤ 5 + 1 and '5' is an integer.

5 < x ≤ 6

Thus, the required value of x would be 5 < x ≤ 6 for the given function k(x) = 80.

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Answer:

Step-by-step explanation:

1/5y+3/20

plug in 1/4 for y

1/5(1/4)+3/20

1/20+3/20

4/20

1/5

The equivalent expression will be;

B) -2 +4 (x+3) and 4x + 10

C) 3x+5(x - 1) and 8x - 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some expressions.

Now,

From option (A),

⇒  2 (x+3) + 2x and 4x + 3

Solve as;

⇒ 2 (x + 3) + 2x = 2x + 6 + 2x

                         = 4x + 6

Which is not equal to 4x + 3.

From option (B),

⇒ -2 +4 (x+3) and 4x + 10

Solve as;

⇒ - 2 + 4 (x + 3) = - 2 + 4x + 12

                        = 4x + 10

Hence, This is equivalent expression.

From option (C),

⇒ 3x+5(x - 1) and 8x - 5

Solve as;

⇒ 3x + 5 (x - 1) = 3x + 5x - 5

                      = 8x - 5

Thus, This is equivalent expression.

From option (D),

⇒ 5x² (x + 4) and 3x + 8

Solve as;

⇒ 5x³ + 20x²

Thus, This is not correct.

From option (E),

⇒ 4-5 (x+2) and 5x - 6

Solve as;

⇒ 4 - 5 (x + 2) = 4 - 5x - 10

                      = - 5x - 6

Thus, This is not correct.

Therefore, The value of equivalent expression is;

⇒ -2 +4 (x+3) and 4x + 10

⇒ 3x+5(x - 1) and 8x - 5

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The probability is the odds thus the probability it will rain today will be 5/9.

Probability is the concept that describes the likelihood of an event occurring.

Probability is also known as chance because, if you flip a coin, the possibilities that it will land on its head or tail are just chances that either a head will show up or not.

The odds of rain today are 5:9

Odds will be the same as probability because the probability is the same as chance.

Probability = 5/9

Hence "Since probability equals odds, the likelihood that it will rain today is 5/9.".

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the actual area of the bedroom is 324 square feet

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

Given the square bedroom have 3 feet side

The area of the bedroom is = 3² = 9 sq inch

1/2 inch = 3 feet

1 inch = 6 feet

1 square inch = 36 square feet

9 square inch = 36*9 = 324square feet

Hence the actual area of the bedroom is 324 square feet

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The probability when the value of W = 1 is 0.1 , probability when the value of W = 10 is 0.2 and probability when the value of W = 25 is 0.7  .

In the question ,

the marked price slips are $1, $1, $1, $10 and $25 .

If the winner selects two slips of paper, then the possible outcomes would be ,

total number of slips is = 5 ,

Total number of cases possible = ⁵C₂ = 10

There would be only 1 case in which the winner will win $1

that means when both the slips selected has $1.

So, P(Winning $1) = 1/10 = 0.1

the number of cases to win $10 is {(1,10) , (10,1)}

So , P(Winning $10) is

= 2/10 = 0.2

So , P(Winning $25) is

= 1 - (0.1 [tex]+[/tex] 0.2)

= 0.7

Therefore , the required probability P(Winning $1) = 0.1 , P(Winning $10) = 0.2 and P(Winning $25) = 0.7

The given question is incomplete , the complete question is

A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)

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No, the slopes are not perpendicular. The slope of 3 is three times larger than the slope of 1/-3, so the two slopes form an angle that is less than 90 degrees.

1. The slope of a line is the ratio of the vertical change to the horizontal change in the line, this is also known as the rise over run.

2. The slope of the first line is 1/-3 and the slope of the second line is 3.

3. To determine if the two slopes are perpendicular, we need to calculate the angle between them.

4. The angle between two slopes is equal to the arctan(slope1/slope2).

5. Using the formula, we can calculate the angle between the two slopes to be 63.43 degrees.

6. Since this angle is less than 90 degrees, the two slopes are not perpendicular.

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Answer:

first option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 8 ) and (x₂, y₂ ) = (6, 4 )

m = [tex]\frac{4-8}{6-0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 8 ) ⇒ c = 8 , then

y = - [tex]\frac{2}{3}[/tex] x + 8 ← option 1

The number of gallons the citizens waste this year is 5229

information from the problem

The citizens of Washington wasted 7,470 gallons of water last year

This year, they wasted 30% less

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

30%

= 30 / 100

= 0.3

The factor 0.3 less

= 1 - 0.3 = 0.7

The number of gallons wasted this year

= 0.7 * 7470

= 5229

The number of gallons wasted is 5229 gallons

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The correct statements regarding the confidence intervals is given as follows:

The 90% confidence interval for juniors is (.549, .744), and the 90% confidence interval for seniors is (.545, .762). Since the intervals overlap, there is not enough evidence to say there is a difference between regular exercise rates among juniors and seniors.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

For juniors, the parameters are given as follows:

[tex]n = 65, \pi = \frac{42}{65} = 0.646[/tex]

Then the lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.646 - 1.645\sqrt{\frac{0.646(0.354)}{65}} = 0.549[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.646 + 1.645\sqrt{\frac{0.646(0.354)}{65}} = 0.744[/tex]

For seniors, the parameters are given as follows:

[tex]n = 52, \pi = \frac{34}{52} = 0.654[/tex]

Then the lower bound of the interval is of:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.654 - 1.645\sqrt{\frac{0.654(0.346)}{52}} = 0.545[/tex]

The upper bound of the interval is of:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.654 + 1.645\sqrt{\frac{0.654(0.346)}{52}} = 0.762[/tex]

The intervals overlap, hence there is not enough evidence to conclude that there is a difference.

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The graph of the system of inequalities is given by the image shown at the end of the answer.

The system of inequalities in this problem is defined as follows:

Then the graph of the system of inequalities is the region between these two curves.

The function y > 4x - 3 means that the lower bound of the interval is the line y = 4x - 3, which has an intercept of -3 and a slope of 4.

In standard format, the second line is defined as follows:

3y - x ≤ 9.

In slope-intercept format, it is defined as follows:

3y ≤ 9 + x

y ≤ x/3 + 3.

Which means that the upper bound of the graph is the linear function with a slope of 1/3 and an intercept of 3.

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Answer:

It is not possible to determine the amount of ingredients needed to make 1 quart of cereal without knowing the specific recipe being used. Different types of cereal require different ingredients and proportions of those ingredients, so the amount needed to make 1 quart of cereal will vary depending on the recipe being followed.

In general, most cereals are made from a mixture of grains, such as wheat, corn, oats, or rice, which are ground into flour or meal and mixed with other ingredients such as sweeteners, flavorings, and preservatives. The exact proportions of these ingredients will depend on the type of cereal being made and the specific recipe being used. To determine the amount of ingredients needed to make 1 quart of cereal, you would need to consult a specific recipe and follow its instructions.

Step-by-step explanation:

The missing angles in the triangle is as follows:

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

∠3 = 55 degrees (vertically opposite angles)

Vertically opposite angles are congruent to each other.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Using exterior angle theorem ,

105 = ∠5 + 55

∠5 = 105 - 55

∠5 = 50 degrees

∠4 = 180 - 50 - 55

∠4 = 75 degrees

Therefore, the other triangle is an isosceles triangle. This means the base angles are equal.

Hence,

∠1  = ∠2 = x

2x + 55 = 180

2x = 180 - 55

2x = 125

x = 125 / 2

x = 62.5 degrees.

Hence,

∠1  = ∠2 = 62.5 degrees.

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get trolled

Step-by-step explanation:

troll people make them get trolled

Answer:

Step-by-step explanation:

to round a decimal, well it depends if it asks you to round to tenths, thousandths or hundredths sometimes even cents..

If you were to be given 5.5567 and it says to round to the hundredth place then you would look at the two points so 5. 55 and then look at the number beside it which is 6 and because 6 is bigger it would round up so you'd get 5.56 hopefully you understood that even if it's just a little..