The left atrium is one of your heart's four chambers-it is where your heart receives freshly oxygenated blood from your lungs. Its size is directly related to your body size and it may change with age; additionally, the size of the left atrium is one measure of cardiovascular health. When the left atrium is enlarged, there is an increased risk of heart problems.A group of researchers studied the hearts of over 900 children ages 5 to 15 years, and they concluded that for healthy children, left atrial diameter can be modeled by a normal distribution with a mean of 26.2 mm and a standard deviation of 4.1 mm. Normal distributions are continuous probability distributions that are symmetric, bell shaped, have a total area under the curve equal to 1, and are sometimes referred to as a normal curve.When a normal distribution is a reasonable model for a random variable, areas under the normal curve can approximate various probabilities with a mean, , and standard deviation, o, but they can all be converted to the standard normal distribution whose mean is o and standard deviation is 1 to simplify probability calculations and facilitate comparisons between variables. In working with normal distributions, you need the following general skills: 1.Use the normal distribution to calculate probabilities, which are areas under a normal curve. 2.Characterize extreme values in the distribution, which might include the smallest 5%, the largest 1%, or the most extreme 5% (which consists of the smallest 2.5% and the largest 2.5%). We will learn how to use these general skills in SALT. The normal distribution that models the size of the left atrium (in mm) in healthy children ages 5 to 15 has a mean µ = ___ mm and standard deviation σ: ___ mm.

The expression 60⋅1.2^t models the number of nano-related patents granted in the US as a function of years since 1991.


Start with the number 60.

This represents the initial number of nano-related patents granted in the US in the year 1991.

Multiply 60 by 1.2.

This accounts for a growth factor of 1.2, indicating that the number of patents granted is increasing by 20% each year.

Raise 1.2 to the power of t. The variable t represents the number of years since 1991. This allows the expression to model the increase in patents over time.

The resulting expression, 60⋅1.2^t, gives an estimate of the number of nano-related patents granted in the US for any given year since 1991.

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The correct statement is: As the number of penalty yards increases by 1, we predict time to increase by 0.01 hours. (Option 3)

This is because the regression equation shows that for each additional penalty yard, the predicted time increases by 0.01 hour, as indicated by the coefficient of 0.01 in the equation. The correlation coefficient of 0.61 indicates a moderate positive linear relationship between time and penalty yards.

However, it would be an extrapolation to use the regression equation to predict the time of a football game with 50 penalty yards since this value falls outside the range of penalty yards used to construct the equation.

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Complete Question:

What affects the length, in hours, of a professional football game? Data was gathered in order to determine the relationship between total number of penalty yards and the time required to complete a game, in hours, for a large random sample of football games. All of these games had between 35 and 150 penalty yards. To predict time required to complete the game based on penalty yards, the following regression equation was constructed: Predicted time = 2.46 + 0.01 (penalty yards). The correlation between time and penalty yards is r = 0.61. Based on this information, which one of the following statements is correct?

Group of answer choices

Answer:

-5.6

Step-by-step explanation:

Given parameters:

 Temperature at Alto  = -3.8°C

Unknown:

The wind chill temperature  = ?

Solution:

Due to the windchill, temperature in Alto feels colder at -3.8.

We can infer that usually, the temperature in Alto is not supposed to be up to this value. The windchill reduced the temperature;

 Temperature in Alto = Original temperature + wind chill temperature

Originally, the temperature would be = -3.8 + 5.6 = 1.8

So;

     -3.8 = 1.8 + wind chill temperature

   Wind chill temperature  = -3.8 - 1.8 = -5.6

Answer:

-9.4

Step-by-step explanation:

Answer:

(x+4)(x-3)

Step-by-step explanation:

Answer:

(x + 4)(x - 3)

Step-by-step explanation:

Given

x² + x - 12

Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (+ 1)

The factors are + 4 and - 3 , since

4 × - 3 = - 12 and 4 - 3 = + 1 , then

x² + x - 12 = (x + 4)(x - 3) ← in factored form

Step-by-step explanation:

The gender of a child which is either a boy or a girl is determined by the XX-chromosomes, or XY-chromosomes.

Since the couple plan to have 5 children, the chance of a child being a boy is equal to the chance of it being a girl - the chances are 50/50.

What we do to achieve our aim is to run a simulation that would add an X or Y to an X for all 5 children.

Doing this 125 times, we obtain the number of trials we desire.

For each trial, we get for each child, C:

C1: X + (X or Y)

C2: X + (X or Y)

C3: X + (X or Y)

C4: X + (X or Y)

C5: X + (X or Y)

Since the chance of having an X is equal to the chance of having a Y, they equal probability, which is 0.5 for each.

Answer:

I want to take better notes that include examples and definitions.

Step-by-step explanation:

Answer:

My goal in math that I would like to accomplish next year is to be a hard-working student who is self-managed and can work under pressure. ( switch it up a little if it doesn't match you)

Step-by-step explanation:

Answer:

There are 45 pepperoni on 3 large pizzas

Step-by-step explanation:

Here, we want to use proportional relationship to solve this;

75 pepperoni to 5 large pizzas

x pepperoni to 3 large pizzas

75 * 3 = x * 5

x = (75 * 3)/5

x = 15 * 3 = 45

The radius of the spherical balloon increases at a rate of 0.0442 cm/min when the radius is 30 cm.

The volume of a sphere is the capacity it has that is the space occupied by the sphere. The volume of a sphere is measured in cubic units.

V = 4/3×π×r³

where, r --> radius of sphere

π --> special constant, π = 22/7 We have, A spherical balloon is inflated with a gas at the rate , dV/dt = 500 cm³/min

Since, we have a rate of inflation so, we differentiating V with respect to time,

=> d/dt (V = 4/3×π×r³)

=> dV/dt = 4/3×π×(3r²×dr/dt)

=> dV/dt = 4πr²×dr/dt

We have to calculate the rate of the radius of the balloon increasing at the instant the radius is 30 cm. Substitute the known values into our derivative equation to get:

4π(30 cm)²×dr/dt = 500 cm/min

=> (3600π cm²)×dr/dt = 500 cm³/min

=> dr/dt = 5/(36π) cm/min

=> dr/dt = 0.0442 cm/min

So, required rate of radius increasing is 0.0442 cm/min.

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Answer:

Step-by-step explanation:

y - 4 = -5(x + 1)

y - 4 = -5x - 5

y = -5x - 1

The given initial value problem is dy/dx = ye10x, y(0) = 3e. The particular solution of this differential equation can be found by integrating both sides with respect to x. The explicit particular solution of the initial value problem is y = (ye20x/20) + 3e - (3e21/20).

We obtain:

∫ dy/dx dx = ∫ ye10x dx

This integral can be solved by applying the substitution u = ye10x with du = 10ye10x dx. The integral becomes:

y = ∫ u du/10 = (u2/20) + c, where c is an arbitrary constant.

Substituting u = ye10x, we get the particular solution as:

y = (ye20x/20) + c.

To find the value of the arbitrary constant c, we substitute the initial condition y(0) = 3e in the equation.

Therefore, c = 3e - (3e21/20).

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Answer:

5x^3 + 5x+ 2x^2 + 2

Step-by-step explanation:

(5x+2)(x^2+1)

5x^3 + 5x+ 2x^2 + 2

Answer:

The absolute value is the distance between a number and zero. The distance between −13 - 13 and 0 0 is 13 13 . −1⋅13 - 1 ⋅ 13. Multiply −1 - 1 by 13 13 .

Step-by-step explanation:

Happy to Help   13

We will plot the graph for a LN function by keeping in mind that the domain must be greater than 0.

LN means natural logarithm. LN function denotes natural logarithm function. It has also another name, logarithm of base e.

It is expressed as

y = ㏑x that is the inverse of                            

the natural base exponential function

y = ex

If we have a logarithm function, f(x) = y = ln x

while plotting with the above function, ln x can be found for only the positive value of x and there is no value of ln x for negative values.

The properties of the graph of the LN function are following.

The domain of the LN function is only the real numbers that means x > 0.

The ranges of the LN function are all real number.

The coordinate of x intercept of the LN function is (1, 0).

The graph of LN function will be such that it will never touch the Y axis although it always approaches to it.

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Answer:

square is the answer for this question

Answer-2:3

There are 3 feet in a yard.  So 7 times 3 is 21.

This means our original equation is 14:21. However, they can both be divided by 7 .  14/7  :  21/7   This gives us our final answer of 2:3   .

Hope This Helps & Good Luck!

we know the complex number has standard form a+ib

Inorder to find our answer ib^2 should.be 1

Ex:-

2-i

2:-

\(\\ \sf\longmapsto 2+2i^2\)

2 + i^2 = 1. also i^4 = 1

3 + i^2 = 2 also 2i^4 = 2

4 + i^2 = 3 also 3i^4 = 3

the complex series has a form Z = a + ib, where a is the real number and ib is the imaginary part.

we know i = √-1 so i^2 = -1 and (i^2)^2 = (-1)^2 = 1. or i^4 = 1.

also,

2 + i^2 = 1. since i^2 = -1, 2 + -1 = 2-1 = 1.

if we want to find 2,

3 + i^2 = 2. since we know i^2 will be -1, set the a value to be 1 more the value you need. for example if you want 3, set a to be 4.

for 3.

first make a to be 1 more than 3 which is 4.

3 = 4 + i^2.

Answer:

This mapping isn't a function.

Step-by-step explanation:

A mapping specifies a relation between two sets of items (input and output). For example, a mapping of the form \(\lbrace (x_{0},\, y_{0}),\, (x_{1},\, y_{1})\rbrace\) would map the input \(x_{0}\) to output \(y_{0}\) and map the input \(x_{1}\) to output \(y_{1}\).

A function is a mapping where each input is associated with exactly one output.

Note that both \((2,\, 1)\) and \((2,\, 4)\) are in the mapping given in this question. The input \(2\) is mapped to more than one outputs. Thus, this mapping isn't a function.

Answer:

The slope of the line would be 1/3. The line is going up 1 unit and right 3 units.

Answer:

That would be -2, -2

Step-by-step explanation:

This is because if you go left or right it changes the x in (x,y). And when you move up or down it changes the y. So 5 seven units to the left is like 5 - 7 which is -2. And one unit up from -3 is -3 + 1 which is -2. Then you get your answer which is (-2,-2)

The system of equations that model the situation is:

4c + 2s+ 3b == $29.51

c + 4s + 2b = $21.83

2c + 5s = $21.93

Simultaneous equations are more than one equation that would have to be solved jointlu in order to determine the required values.

Methods of solving simultaneous equations are:

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Answer:

Not a triangle

Step-by-step explanation:

The sum of the lengths of sides a, b must be greater than the length of the remaining side c.

Answer:

not a triangle

Step-by-step explanation:

11+13<25

The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

Therefore, the missing number in the sequence is 21.

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The only reasonable side length is x = 8 is "The solutions are -8 and 8, but only 8 is a reasonable side length."

The equation provided and evaluate the solutions in the context of the problem.

The equation mentioned in the problem is not explicitly provided, so we'll proceed with the given information.

Let's assume the side length of the square prism cake box is x.

The volume of a square prism can be calculated using the formula:

Volume = Length × Width × Height

Since the cake box is a square prism, the length and width are the same, so we can write:

Volume = x × x × 5.5

Given that the volume of each box must be 352 cubic inches, we can set up the equation:

x^2 × 5.5 = 352

Now, let's solve this equation to find the possible solutions for x:

x^2 = 352 / 5.5

x^2 ≈ 64

Taking the square root of both sides, we have:

x ≈ ±8

The solutions to the equation are -8 and 8.

Since we are dealing with a physical length, a negative side length doesn't make sense in this context.

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Answer:

B,D

Step-by-step explanation:

Answer:

Hello again! Your answer would be B and D

Step-by-step explanation:

A square is a shape with 4 sides and all of them have to equal. Right away you can see that D is without needing to look at it. You might think that B is not because of its angle but if you turn your paper/computer to the side a bit you can there see that it is square. C and A are not because of their unequal sides. Yes, they do have four sides but they are non-equal.

30% of students mean 30 students wear contact lenses from a random selection of 100 students studying in a university.

Percentage is a fraction or a ratio of a random sample in which the value of whole is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

Percentage is defined as a certain fraction or number out of a hundred. It is a fraction with the denominator 100, and the sign for it is "%."

Finding the proportion of a whole in terms of 100 is the goal of percentage calculations. There are two methods to calculate a percentage:

Use the unitary approach or try adjusting the fraction's denominator to 100.

How to solve?

30 % = 30/100 of a sample = 0.3 of a sample

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Answer:

408 students = 60%

408 x 100/60

= 680 students in total

Answer:

7. B

8. J

9. C

10. F

the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.Let the length of the rectangular garden be L and the width be W. Then, the area of the garden is given as L x W = 8.

The cost C of enclosing the garden is given by:
C = 20L + 10(2L + W)

Substituting the value of W from the area equation, we get:
C = 20L + 10(2L + 8/L)

Differentiating C with respect to L and equating it to zero to find the minimum cost:
dC/dL = 20 + 20 - 80/L^2 = 0
Solving for L, we get L = 2 ft

Substituting L = 2 in the area equation, we get:
W = 4 ft

Therefore, the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.
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Answer:

19. 0•7431

20. 1•2800

21. 0•4850