nasa is conducting an experiment to find out the fraction of people who black out at g forces greater than 6. in an earlier study, the population proportion was estimated to be 0.43. how large a sample would be required in order to estimate the fraction of people who black out at 6 or more gs at the 99% confidence level with an error of at most 0.03? round your answer up to the next integer.

Answer:

equation 3 for the x intercept ley Y =0 and for the Y intercept let X =O

Answer:

Obtuse angles measure between 90° and 180°.

In the diagram we have:

Obtuse angles measure less than 180° but more than right angle

Here they are

Answer:

y=4x/5+5

Step-by-step explanation:

Points are (0,5)  and (-5,1)

(y-5)/(1-5)=x-0/[0-(-5)]

(y-5)/4=x/5

*5/5         *4/4

5(y-5)/20=4x/20

5y-25=4x

+25       +25

5y=4x+25

:5     :5

y=4/5*x+5

The conversion result of decimal numbers to hexadecimal representations of 2's complement numbers are the following

a) 100

b) 6F

c)75BCD15

d)FFFFFF04

A decimal number can be represent the two parts one is whole and a fractional part separated by a decimal point. The decimal point is represented by dot inbetween the whole and fractional part. Hexadecimal is one of number system with base 16. That means 16 possible digits used to represent numbers. Steps to convert a decimal number to hexadecimal number :

Representations of 2's complement numbers :

a) decimal number = 256

using above rules, it's hexadecimal representations of 2's complement numbers is 100.

b) decimal number = 111

it's hexadecimal representations of 2's complement numbers is 6F.

c) decimal number = 123,456,789

it's hexadecimal representations of 2's complement numbers is 75BCD15.

d) decimal number = -44

it's hexadecimal representations of 2's complement numbers is FFFFFF04.

Hence, required values are obtained.

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The key features of the quadratic equation y = - x² - 2x + 1 is  line of symmetry is x = -1; vertex = (h, k) = (-1, 2); y-intercept is (0, 1);  

the domain = -∞ ≤ x ≤ ∞ and the range = 2 ≥ y ≥ -∞.

What are the key features of a quadratic function?

Three properties that are universal to all quadratic functions:

1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior);

2) The domain of a quadratic function is all real numbers; and

3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

According to the given question:

The given equation is y = - x² - 2x + 1

The general vertex form is y = a·(x - h)² + k

h = -b/(2·a) = 2/(-2) = -1

k = f(h) = -(-1)² - 2×(-1) + 1 = 2

Therefore;

1) The line of symmetry goes through the vertex and the line of symmetry is x = -1

2) The vertex = (h, k) = (-1, 2)

3) The y-intercept is the coordinate of the point where x = 0 which is  

   (0, 1)

4) The domain are the possible x-values, therefore,

    the domain = -∞ ≤ x ≤ ∞

5) The range is the possible values y-values.

    On plotting the graph, we have the range = 2 ≥ y ≥ -∞

Complete question:

Identify the key features of the Quadratic Function y = - x² - 2x + 1

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Answer:

8.1

Step-by-step explanation:

just calculate 45 of 18%

To find the volume of the smallest cube-shaped box that can contain the pyramid, we need to first determine the length of the smallest edge of the box. Since the base of the pyramid is a square, the smallest edge of the box will be the diagonal of the square base of the pyramid.

Using the Pythagorean theorem, we find that the diagonal is:√(10² + 10²) = √200 = 10√2 inches Thus, the length of each edge of the smallest cube-shaped box that can contain the pyramid will be 10√2 inches. The volume of a cube is given by the formula

V = s³, where s is the length of one of its edges. Therefore, the volume of the box will be:(10√2)³ = 1000√8 cubic inches To simplify this expression, we can use the fact that √8 = √(4 · 2) = 2√2. Thus, the volume of the box is:1000√8 = 1000 · 2√2 = 2000√2 cubic inches Therefore, the volume of the smallest cube-shaped box that can contain Eric's pyramid is 2000√2 cubic inches, or approximately 2827.43 cubic inches to two decimal places.

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Here are the Laplace transforms of the given functions:

(a) The Laplace transform of the function te^(-at)u(t - a) is:

L{te^(-at)u(t - a)} = 1/(s + a)^2

(b) The Laplace transform of the function (ta)e^(-at)u(t - a) is:

L{(ta)e^(-at)u(t - a)} = 2a/(s + a)^3

(c) The Laplace transform of the function 8δ(t) + (a - b)e^(-bt)u(t) is:

L{8δ(t) + (a - b)e^(-bt)u(t)} = 8 + (a - b)/(s + b)

(d) The Laplace transform of the function (t^3 + 1)e^(-2t)u(t) is:

L{(t^3 + 1)e^(-2t)u(t)} = (6/s^4) + (8/s^3) + (2/s^2) + (1/(s + 2))

Note: In the Laplace transform, u(t) represents the unit step function, and δ(t) represents the Dirac delta function.

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a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

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A differential equation's existence and uniqueness in mathematics refers to the existence of a single, clearly defined solution that meets a certain set of requirements.

A differential equation is a type of mathematical equation that links a number of known functions or variables to an unknown function and its derivatives. If a differential equation has existence and uniqueness of solution, it means that there is only one function that satisfies the equation and corresponds to the given conditions for a given set of beginning circumstances.

The terms and structure of the differential equation, such as linearity and initial conditions, decide whether or not a solution exists. The Piccard-Lipschitz theorem, which asserts that if a function and its derivatives are locally Lipschitz continuous, then the solution to the differential equation is unique in a neighbourhood of the initial conditions, frequently ensures the uniqueness of the solution.

In conclusion, the existence and uniqueness of a solution in differential equations is a crucial idea in mathematical modelling and aids in making sure that the solutions to a given problem are clear-cut and consistent with the underlying conditions.

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To find the union of two sets, we combine all the elements in both sets, without duplicating any elements. (a) A ∪ B = {0, 1, 2, 3, 4, 5, 6} (b) A ∩ B = {3}  (c) A − B = {1, 2, 4, 5} (d) B − A = {0, 6} (e) C ∪ (B − A) = {0, 2, 3, 4, 6, 7}  (f) (C ∪ B) − A = {0, 6, 7}

To find the intersection of two sets, we find the elements that are common to both sets. A − B = {1, 2, 4, 5}

To find the set difference A − B, we remove all the elements in B from A.  B − A = {0, 6} To find the set difference B − A, we remove all the elements in A from B.  C ∪ (B − A) = {0, 2, 3, 4, 6, 7} First, we find the set difference B − A, which is {0, 6}.

Then, we find the union of C and {0, 6}, which is {0, 2, 4, 6, 7}. (C ∪ B) − A = {0, 6, 7} First, we find the union of C and B, which is {0, 2, 3, 4, 6, 7}. Then, we remove all the elements in A from this set to get the result.

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The minimum value of the function 2x^2 - 15xy + 2y^2 - 20y + 65 subject to the constraint x + 3y ≤ 10 is obtained at the critical point(s) of the function within the feasible region.

To find the critical point(s), we first need to calculate the partial derivatives of the function with respect to x and y.

∂f/∂x = 4x - 15y

∂f/∂y = -15x + 4y - 20

Setting these partial derivatives equal to zero, we solve the system of equations:

4x - 15y = 0

-15x + 4y - 20 = 0

Solving this system of equations, we find that x = 3 and y = 1.

Next, we evaluate the function at the critical point (x=3, y=1):

f(3,1) = 2(3)^2 - 15(3)(1) + 2(1)^2 - 20(1) + 65 = 18 - 45 + 2 - 20 + 65 = 20

Therefore, the minimum value of the function within the feasible region is 20.

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Answer:

2,0?

Step-by-step explanation:

To do this, find your first derivative and then find where it is equal to zero. Because we are only concerned about the interval from -5 to 0, we only need to test points on that interval. (i really don't know hot to explain)

fig 3 would take 18 triangle

fig 4 would take 30 small triangles

if its wrong i am sorry

Answer:

She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account

Here, we want to know the amount of money invested in each account

Let the amount invested in the 4% simple interest account be $x ----> (a)

While the amount invested in the 2.5% account be $y -------->(b)

So mathematically;

Both the interests are added to get total interest

x + y = 6,000 ••••••(i)

Let’s now evaluate the interest

for the 4% account , interest = 4/100 * x = 4x/100

For the 2.5% account, interest = 2.5/100 * y= 2.5y/100

The addition of both  interests gives the total simple interest;

4x/100 + 2.5y/100 = 204

Multiply through by 100

4x + 2.5y = 20,400 •••••••(ii)

From i, x = 6,000 - y

Putting this into equation ii

4(6,000-y) + 2.5y = 20,400

24,000 - 4y + 2.5y = 20,400

24,000-20,400 = 4y - 2.5y

1.5y = 3,600

y = 3,600/1.5

y = $2,400

Recalling it again,

x = 6000 - y

x = 6,000 - 2,400

x = $3,600

Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account

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Answer:

The farmer has 30 pigs and 40 chickens.

Step-by-step explanation:

This situation represents a system of equations.

⭐What is a system of equations?

⭐ What are the two equations for this situation?

Pigs and chickens have 1 head, so let's create the equation:

\(x + y = 70\)

This equation represents the number of heads present

Let x = the number of pigs, and let y = the number of chickens

Pigs have 4 legs, while chickens have 2 legs, so let's create the equation:

\(4x + 2y = 200\)

The equation represents the number of legs present

⭐Now that we made the two equations, let's solve the system of equations.

⭐How do you solve a system of equations?

In this case, substitution is the best way we can solve this system of equations.

⭐How do we solve a system using substitution?

To understand substitution, I'll demonstrate it here with our system:

\(x+y = 70\) . . . . (1)

\(4x + 2y = 200\) . . . . (2)

Set equation 1 equal to "y" so we can solve for "x":

\(y = 70 -x\)

Substitute "y" into equation 2:

\(4x+2y = 200\)

\(4x + 2(70-x)= 200\)

\(4x + 140 -2x = 200\)

\(2x + 140 = 200\)

\(2x = 60\)

\(x = 30\)

∴ There are 30 pigs on the farm.

Substitute "x" back into equation 1 to solve for "y":

\(x+y = 70\)

\(30 + y = 70\)

\(y = 40\)

∴ There are 40 chickens on the farm.

The parts of the algebraic expression 3x - 2 are:

3 is the coefficient of x.

x is the variable

2 is the constant term

The algebraic Expression is given as:

3x - 2

Now, some parts of algebraic expressions are coefficients, variables and constant.

Coefficient is defined as the figure or number that is attached to the variable in an algebraic expression.

The variable is the letter that can change because different numbers are used for it.

The constant is the number that stands alone and doesn't change.

Thus, in 3x - 2:

3 is the coefficient of x.

x is the variable

2 is the constant term

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Answer:

y=-5/7x+2.5

Step-by-step explanation:

Answer:

450 meters is 0.45 kilometers.

Answer:

no

Step-by-step explanation:

test the numbers by plugging them into the equation

50 = (35) + 15
50 = 50 - this answer is correct

50 = 65 + 15
50 = 80 - this answer is incorrect

Answer:

= 38°.

Step-by-step explanation:

The three angles inside a triangle add up to 180°.

To determine the value of the unknown angle in a triangle when two angles are given, add them together and then subtract that from 180°.

To determine the value of two unknown angles of the same value, subtract the known angle from 180° and then divide by 2.

But in this example, none of the interior angles are given. To determine , we must first determine ∠OLM and ∠OML using the exterior angles ∠OLK and ∠OMN.

⠀⠀1. Subtract ∠OLK (134°) from 180°

180° - 134° = 46°, therefore ∠OLM = 46°.

⠀⠀2. Subtract ∠OMN (84°) from 180°

180° - 84° = 96°, therefore ∠OML = 96°.

⠀⠀3. Subtract ∠OLM (46°) + ∠OML (96°) from 180°

= 180° - (46° + 96°)

  = 180° - 142°

  = 38°

Answer:

Simple! Just plug in each x value into the equation above. Or, you could just plug the equation into a graphing calculator and find the point from there.

Step-by-step explanation:

f(3) = 16

f(4) = 21

f(5) = 26

f(8) = 41

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The two positive numbers are x = 10 and y = 10.

Product of two numbers = 100

Let the first numbers be = x

Let the second number be = y

Any integer higher than zero is considered a positive number. Even natural numbers are included in its concept of numbers.

Therefore, according to the question -

xy = 100

y = 100/x

Thus, as two numbers are given,

f(x, y) = x + y

f(x) = x + 100/x

Now, minimum of f(x) is obtained at the point where f’(x) = 0

Therefore,

f’(x) = 1 - 100/x² = 0

x = ±10.

x = 10

Similarly,

y = 10

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The table that corresponds to the equation given is A. Table A.

The equation given will allow you to find the value of y, when using a certain value of x.

Assuming x is 0, the value of y is:

y = 1 / 2 x + 1

y = 1 / 2 ( 0 ) + 1

y = 1

Assuming x is 6, the value of y is:

y = 1 / 2 x + 1

y = 1 / 2 ( 6 ) + 1

y = 4

The correct table is therefore Table A.

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Answer:

235 can be split into 200+30+5. Each of these can be divided by 5: 200/5+30/5+5/5=40+6+1=47 to give us the quotient.

Another way is to double 235=2*200+2*30+2*5=400+60+10=470 and divide the result by 10 by simply removing the zero to give the quotient 47. This works because dividing by 5 is the same as doubling and dividing by 10: 2/10=1/5.

The total area of all the Circles used by Princess is 4710 square centimeters.

The total area of all the circles used by Princess, The formula for the area of a circle is given by:

A = πr²

where A represents the area and r is the radius of the circle. Since we are given the diameter of each circle (20 cm), we can calculate the radius by dividing the diameter by 2:

r = 20 cm / 2 = 10 cm

Substituting this value into the area formula, we have:

A = π(10 cm)²

Now, let's calculate the area of one circle:

A = 3.14 * (10 cm)² ≈ 314 cm²

Therefore, the area of one circle is approximately 314 square centimeters.

Since Princess used 15 circles, we can find the total area by multiplying the area of one circle by the number of circles:

Total area = 314 cm² * 15 = 4710 cm²

Hence, the total area of all the circles used by Princess is 4710 square centimeters.

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Answer as a decimal is -172.

Given :

= (-17.2 x 2.5) x 4

= (-43) x 4

= -172

Therefore the answer as a decimal is -172.

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The general expression for finding the cross product of two vectors is not valid when the lines represented by the vectors are parallel. This is because the cross product of two parallel vectors is zero.

The cross product is an operation defined for three-dimensional vectors. It results in a vector that is perpendicular to both input vectors. The magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them.

When the lines represented by the vectors are parallel, the angle between them is either 0 degrees or 180 degrees. In either case, the sine of the angle is zero. Since the magnitude of the cross product is multiplied by the sine of the angle, the resulting cross product vector would have a magnitude of zero.

A zero cross product indicates that the two vectors are collinear or parallel. Therefore, using the general expression for the cross product to determine the relationship between parallel lines would not be meaningful. In such cases, other approaches, such as examining the direction or comparing the coefficients of the lines' equations, would be more appropriate to assess their parallel nature.

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