the american college of obstetricians and gynecologists says that out of every 100 babies born in the united states, 3 have some kind of major birth defect. how would you assign random numbers to conduct a simulation based on this statistic?

On solving the provided question, we cans ay that by standard deviation, [tex]SE = 0.1590 (approx.)[/tex]

Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed.

By sample standard deviation, we mean standard error. Hence, we have that:

Therefore, Standard deviation[tex]= 0.6929891[/tex]

The sample size [tex](n) = 19.[/tex]

Hence:

[tex]SE = 0.1589826.\\ SE = 0.1590 (approx.)[/tex]

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The value of c in the equation 5c = 13.5 - 16.5 - 10c is 0.6.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

In this case, 5c + 16.5 = 13.5 + 10c

Collect the like terms

5c - 10c = 13.5 - 16.5

- 5c = -3.0

Divide

c = -3.0 / -5

c = 0.6

The value of c is 0.6.

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Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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After 3 hours Dylan and Sam will be exactly 15 miles apart .

In the question ,

it is given that ,

the speed at which Dylan is jogging in east = 4 miles per hour .

the speed at which Sam is jogging in south = 3 miles per hour .

the distance covered by Dylan is = 4t

the distance covered by Sam is = 3t

we have to find the time when they are 15 miles apart .

Since Dylan walks in east and Sam walks in South  , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,

(3t)² + (4t)² = 15²

9t² + 16t² = 225

225 = 25t²

t² = 225/25 = 9

t = 3

Therefore , the time taken will be 3 hours .

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Hence, the population increases to [tex]72860102.5[/tex] in the year [tex]2001[/tex] which is nearest to the [tex]8000000000[/tex].

What is the rate of change?

Rate of change (ROC) refers to how quickly something changes over time. It is thus the acceleration or deceleration of changes (i.e., the rate) and not the magnitude of individual changes themselves.

Here given that,

In [tex]2000[/tex], the world population was calculated to be [tex]6,071,675,206[/tex]. The world population increases at a rate of about [tex]1.2[/tex]% annually.

As the population increases [tex]1.2[/tex] % in every year

i.e., [tex]\frac{1.2}{100}=0.012[/tex]

So, the population in the year [tex]2001[/tex] is

[tex]6,071,675,206(0.012)=72860102.5[/tex]

which is the nearest value in the year [tex]2001[/tex].

Since, the population size increases  [tex]72860102.5[/tex] which is the nearest to the [tex]8000000000[/tex].

Hence, the population increases to [tex]72860102.5[/tex] in the year [tex]2001[/tex] which is nearest to the [tex]8000000000[/tex].

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The following are the answer to each statement;

1. The book is $18

2. Giselle can earn up to $18 pulling weeds for her grandma.

3. Giselle's grandma pays her $1 for every 5 weeds she pulls

4. Giselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds.

5. Giselle only needs to pull 18 weeds to not use any of her own money

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Monomial has a degree of 4 in linear equation.

What in mathematics is a linear equation?

The algebraic equation y=mx+b is known as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                       Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let's define some of the vocabulary words so we can understand what is being asked.

trinomial: 3 terms   → each term is separated by a plus or minus sign

                              Example: 5x² + 3x + 2

monomial: 1 term   →  no plus or minus sign exists in the term.

                              Example: 5x²

degree: the largest exponent → it can be in any of the terms.

                              Example: 5x² has a degree of 2

It is possible that a monomial has an exponent greater than that of a trinomial so the answer is NO!

trinomial:   5x² + 3x + 2      has a degree of 2

monomial: 5x⁴                    has a degree of 4

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Answer: x= 4/9

Step-by-step explanation:

9x^2-16=0

9x^2 = 16

9x = 4

x= 4/9

This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.

The probability of getting a specific number of heads in a given number of flips follows a binomial distribution, which describes the probability of getting a certain number of successes in a given number of independent trials. The probability of getting a specific number of heads in ten flips can be calculated using the formula:

P(x heads in n flips) = (n choose x) * p^x * (1-p)^(n-x)

where p is the probability of getting a head on each flip and x is the number of heads.

For example, the probability of getting exactly 3 heads in ten flips is:

P(3 heads in 10 flips) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3) = 0.241

This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.

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The amount of money in the account after 14 years is $20248.59

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have

V = Pe^{rt}

Where

Substitute the known values in the above equation, so, we have the following representation

V = 8620 * e^(6.1% * 14)

Evaluate the products

So, we have the following representation

V = 8620 * e^(0.854)

Evaluate the exponent

So, we have the following representation

V = 8620 * 2.34902418149

Lastly, evaluate the products

So, we have the following representation

V = 20248.5884444

Approximate

V = 20248.59

This means that the value after 14 years is $20248.59

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Answer:

[tex] \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Step-by-step explanation:

We can use the quotient rule:

[tex] \displaystyle{y = \frac{u}{v} \to y '= \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

In this case, u and v both are functions. By applying formula above, we will have:

[tex] \displaystyle{y' = \dfrac{(3 {x}^{2})' ( {x}^{3} + 3) - (3 {x}^{2} )( {x}^{3} + 3)' }{( {x}^{3} + 3)^{2} }}[/tex]

Then apply power rule to derive functions, we have to know that:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: (c \in \mathbb{R})}[/tex]

Therefore, we will have:

[tex] \displaystyle{y' = \dfrac{6x ( {x}^{3} + 3) - (3 {x}^{2} )3 {x}^{2} }{( {x}^{3} + 3)^{2} }}[/tex]

Expand the terms in:

[tex] \displaystyle{y' = \dfrac{6 {x}^{4} + 18x - 9 {x}^{4} }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3 {x}^{4} + 18x }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Hence, that's the answer. You can keep in unfactored form or factored form as you desire!

On solving the provided question we can say that - 112 child tickets were sold that day

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, finding a way to respond to them has been a major driving force behind the development of mathematics.

Call the number for children and the number for adults to get:

[tex]5.20c+8.50\\ a=1097.60[/tex]

and

a=4c

indicating that there were four times as many adults as youngsters.

Using this value in place of a

into the first equation we get:

[tex]5.2c+8.5(4c)=1097.6\\ 5.2c+34c=1097.6[/tex]

rearranging:[tex]c=1097.639.2=28[/tex]

and so:

[tex]a=4c=4⋅28=112[/tex]

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Answer:

1+i

Step-by-step explanation:

Divide by 1

(1/1+i)

(1+i)

Identify the components of the numbers and add the real and imaginary parts separately

=(1)+(1)i

=(1)+(1)i

=(1+i)

Using displacement as a vector quantity, the change or displacement of the car is 3 blocks

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.  is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definitions. Distance is the measure of “how much ground an object has covered during its motion” while displacement refers to the measure of “how far out of place is an object.”

The displacement of the car will the change in it's position from starting to it's present position.

This can be calculated mathematically as

2 + 3 - 2 = 5 - 2 = 3

The displacement is 3 blocks.

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Answer:

The map is displaying 600 miles of land.

Step-by-step explanation:

To find the number of miles of land being displayed on the map, you need to multiply the length of the map in inches by the conversion factor, which is the ratio of inches to miles. In this case, the conversion factor is 2 inches per 200 miles.

So, to find the number of miles of land being displayed on the map, you would do the following calculation: 12 inches * (200 miles / 2 inches) = 600 miles.

The value of ∠JKI is  107⁰.

What is an angle of a triangle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that ∠JKI = (5x−3)⁰, ∠KIJ=(2x+8)⁰, and ∠IJK=(x−1)⁰.

The sum of all angles of a triangle is 180⁰.

(5x−3)⁰ + (2x+8)⁰ + (x−1)⁰ = 180⁰

(5x + 2x + x) + ( - 3 + 8 -1) = 180

8x + 4 = 180

Subtract 4 from both sides:

8x = 176

x = 22

Putting x = 22 in ∠JKI = (5x−3)⁰:

∠JKI = (5×22 − 3)⁰

∠JKI = 107⁰

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The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".

It is given that, Lucia draws a square and plots the center of the square.

Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".

To verify this claim, we need to construct a square (ABCD) as shown in the figure.

When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.

If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.

This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.

Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".

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Well said. I 100% know what this is.

The  situations that can be represented by the opposite of -25 are:

-25 can be seen as represention of the given  situations fro the problem, and exploring the given options, we can see that 25 feet below the sea level with that ones balance can be gets reduced by $25.

But when exploring the But the opposite of (-25)  then we can see that 25 feet above the sea level, and in this case the amount will be raised by $25. and the height by 25 feet with the increase in the debt by $25.

Therefore, option B ,C and E are correct.

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missing options:

A. A scuba diver is 25 feet below sea level. B. Leon gets paid $25. C. An airplane descends 25 feet. D. Sara has a $25 debt. E. A bird flies 25 feet above sea level

Answer:

3.15

Step-by-step explanation:

In equations, you need to get the variable on one side and the answer on the other. In this instance, you divide both sides by 5.24 so you're left with w = 3.15.

Hope this helps, have an amazing day!

Answer:

d) 3.15

Step-by-step explanation:

Given equation,

→ 5.24w = 16.506

Now the value of w will be,

→ 5.24w = 16.506

→ w = 16.506 ÷ 5.24

→ [ w = 3.15 ]

Thus, the value of w is 3.15.

There is a 95% chance that the mean length of all term papers lies between confidence limits (11.58,17.82) for the given data:

14, 20, 25, 10, 16, 8, 15, 12, 18, 9

We assume the length of paper has an approximately normal distribution.

Sample size = 10

The sample mean for the given data = 14.7

The standard deviation for the given data = 5.04

Critical value is obtained from standard normal distribution at the level of significance 0.05.

The critical value is 1.96.

The 95% confidence interval for the mean length of all term papers is calculated as follows:

P(14.7 - (1.96 x (5.04/√10)) < µ < 14.7 + (1.96 x (5.04/√10))) = 0.95

P(11.58 < µ < 17.82) = 0.95

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Answer:

Below

Step-by-step explanation:

Point slope form of the new line would be

(y -2) = m (x-3)      from the given formula

From the GIVEN line....its slope, m , is 1/2

      perpendicular slope is  - 1/m = -2    ( this is something you have to remember/learn)

then the NEW Line becomes

(y-2) = -2 ( x-3)       expand and simplify

y-2 = -2x+ 6

y = -2x + 8      Done !

Answer:

y = - 2x + 8

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 )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute the point (3, 2 ) into the partial equation

2 = - 2(3) + c = - 6 + c ( add 6 to both sides )

8 = c

y = - 2x + 8 ← equation of perpendicular line

Answer:

The answer is 85

Step-by-step explanation:

c/100 = 51/60

(c) × (60) = (51) × (100)

60c = 5100

60c/60 = 5100/60

c = 85

Thus, The value of y is 85

Answer:

[tex] \sf \: c = 85[/tex]

Step-by-step explanation:

Given equation,

[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]

Now the value of c will be,

[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]

[tex] \sf \rightarrow \: c = ( \frac{51}{60} ) \times 100[/tex]

[tex] \sf \rightarrow \: c = \frac{(51 \times 100)}{60} [/tex]

[tex] \sf \rightarrow \: c = \frac{5100}{60} [/tex]

[tex] \sf \rightarrow \boxed{ \sf c = 85}[/tex]

Hence, the value of c is 85.

Answer:4.50t + 6.75b = 576

Step-by-step explanation:

The expression when Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3 is 3(n + 4).

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this scenario, Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3.

This will be:

= (n + 4) × 3

= 3(n + 4).

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The ratio of the total number of letters to vowels is 5 : 16.

Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another value. The sign that is used to represent ratio is :.

Ratio of the total number of letters to vowels - total number of letters : total number of vowels

total number of letters = 16

total number of vowels = 5

Ratio of the total number of letters to vowels - 5 : 16

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The probability that an athlete used steroids, given that they tested positive, is approximately 0.5025%.

In order to calculate the probability that an athlete used steroids given the information provided, we need to know the probability that they tested positive. To do this, we can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, we are trying to find the probability that an athlete used steroids (A) given that they tested positive (B). We know that the probability of A is 1% and the probability of B is 0.5%, so we can calculate P(A and B) by multiplying these two probabilities together:

P(A and B) = 1% * 0.5% = 0.005%

Next, we need to calculate P(B), which is the probability that the athlete tested positive. Since we know the false positive rate and the true positive rate of the test, we can use these to calculate P(B) using the formula:

P(B) = P(A and B) + P(not A and B)

P(B) = P(A|B) * P(B) + P(not A|B) * P(B)

P(B) = 0.99 * 0.005% + 0.005 * (1 - 0.005%)

P(B) = 0.00495% + 0.005 * 0.999

P(B) = 0.0099495%

Now that we have P(A and B) and P(B), we can plug these values into the formula for conditional probability to calculate the probability that an athlete used steroids, given that they tested positive:

P(A|B) = P(A and B) / P(B)

P(A|B) = 0.005% / 0.0099495%

P(A|B) = 0.5025%

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Answer:

=x^2-2x+3x-6

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

=(x-2) (x+3)

The expression is x-12.

12 less than a number means subtracting 12 from that number.

So, 12 less than 20 is 8, because is 20−12, 12 less than 12 is 0, because it's 12−12, and so on.

But since the number you need to subtract from is unknown, it's a variable, and you can call it as you like, suppose x. So, using the variable we can write an expression that holds for any number, which always means "take 12 away from my number". If your number is x, the expression would be x-12

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The required absolute value of the given complex number is |-3 + 2i| = √13.

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

The complex number is given in the question as:

-3 + 2i

We have to determine the absolute value of the given complex number.

The absolute value of a complex number a+ib is denoted as |a+ib| and is given by √(a²+b²)

As per the given question, we have

⇒ |-3 + 2i| = √((-3)²+2²)

⇒ |-3 + 2i| = √(9 +4)

⇒ |-3 + 2i| = √13

Therefore, the required absolute value of the given complex number is |-3 + 2i| = √13.

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