a sample of size n will be selected from a population with population proportion p . which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?

Answer: 3

Step-by-step explanation:

2 1/4 cups of brown sugar + ¾ cup of white sugar.=the total amount of sugar in this recipe

2 1/4 + 3/4 =3

or

2 1/4=2.25 and 3/4=.75

2.25+.75=3

A formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 7 units and to the right 5 units is g(x) = 1/(x - 5) - 7.

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

By translating the graph of f(x) = 1/x down 7 units and 5 units to the right , we have:

g(x) = f(x - 5) - 7

g(x) = 1/(x - 5) - 7

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The guidelines for developing the intervals are

An interval in math is calculated in terms of numbers. An interval comprises all the numbers that come between two particular numbers. This range includes all the real numbers between two numbers.

A closed interval is an interval that includes all its limit points and is denoted with square brackets. For example, [0, 1] means that greater than or equal to 0 and less than or equal to 1.

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Congruent figures are figures that are exactly the same size and shape, option A.

A figure is considered congruent when it is exactly the same size and shape as another figure. In other words, two figures are congruent if they can be superimposed on each other perfectly, without any stretching or distortion.

Congruence can also be defined as: if one of the figures can be obtained after a series of rigid motions of the other, the figures are said to be congruent. They both have congruent sides and angles.

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Answer:

A=587

B=-61

C=375

D=-375

Step-by-step explanation:

0.23 as:

23% (0.23 * 100 = 23)

A decimal is a number that expresses fractional values with a base of 10. It uses the place value system where the position of a digit determines its value relative to other digits. Decimals are written using a decimal point to separate the whole number part from the fractional part. For example, 3.14 is a decimal representation of the fractional value pi.

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Principal amount in each account is $200 for Account A and $600 for Account B. Simple interest is most earned for Account B.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest is calculated by the formula,

SI = P × r × t,

where P is the principal amount, r is the interest rate and t is the time in years.

Account A :

t = 6 months = 0.5 year

S.I = $3.30

r = 3.3% = 0.033

Substituting in the formula,

3.30 = P × 0.033 × 0.5

P = 200

Principal amount in Account A is $200.

Simple interest earned in the first month = 200 × 0.033 × (1/12) = $0.55

Account B :

t = 30 months = 2.5 years

S.I = $37.50

r =  2.5% = 0.025

Substituting in the formula,

37.50 = P × 0.025 × 2.5

P = 600

Principal amount in Account B is $600.

Simple interest earned in the first month = 600 × 0.025 × (1/12) = $1.25

Account B earned more interest in the first month.

Hence Account B earned most interest in the first month with am amount of $1.25.

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The length RS is equal to the length PQ and the length QR is congruent to SP.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The lines RS║PQ and QR║SP.

In triangles ΔSPQ and ΔQRS, then we have

∠SPQ = ∠QRS     (Alternate angles)

∠PQS = ∠RSQ     (Alternate angles)

SQ = SQ               (Common side)

ΔSPQ ≅ ΔQRS    (Congruent triangles)

RS = PQ and QR = SP

The length RS is equal to the length PQ and the length QR is congruent to SP.

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Each piglet will receive 0.625 L of milk.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Left to Right

We have 8 piglets that only have 5 liters of milk to share in between them. We need to split the milk between the 8 piglets.

We can divide the amount of milk we have already by the amount of piglets total:

5 liters of milk ÷ 8 piglets

Evaluating this, we should get 0.625 L of milk per piglet, assuming we don't lose a single drop while splitting the milk.

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The point at which the beam must be supported so that it may rest horizontally is; 9 meters from the left side

The parameters are;

Mass of beam = 50 kg

Length of beam = 12 m

Mass suspended at left end = 30kg

Mass suspended at right end = 40 kg

Let the support that will make the beam rest horizontally be x from the left side.

Thus, taking moment about the point x from the left side is;

30x + 50(6 - x) = 40(12 - x)

30x + 300 - 50x = 480 - 40x

20x = 180

x = 180/20

x = 9 m

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A total of 0.7142 gallons of paint is needed to cover 250.0 square feet of walls.

The formula to calculate the number of gallons of paint required to cover a certain area is by dividing the area in square feet by the coverage of one gallon of paint, which in this case is 350 square feet. Hence, the formula becomes:

Using the input value of 250.0 square feet, we can apply this formula to calculate the number of gallons needed.

This means that to cover 250 square feet of wall, 0.714285714286 gallons of paint are required. The result is expressed as a decimal value as the area is not necessarily a multiple of the coverage of one gallon of paint.

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Complete Question:

Finish the program to compute how many gallons of paint are needed to cover the given square feet of walls. Assume 1 gallon can cover 350.0 square feet. So gallons = the square feet divided by 350.0. If the input is 250.0, the output should be:

The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.

The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.

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Option(a) is the correct answer.

The inequality is:

|X+6|- 12 < 13

Here we can add 12 to both sides:

|X+6| <13 + 12

⇒|X+6| <25

⇒|X+6| < 25

We can separate it into two equations:

if x > -6, then |X+6|  = x + 6

⇒ (x + 6) < 25

⇒x < 25 - 6

⇒ x <  19

if x < -6, then |X+6|  = -(x + 6)

⇒-(x + 6) < 25

⇒ -x < 31

 ⇒ x > -31      (changing the sign)

And with those two equations, we get the:

-31 < x < 19

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The value of the functions are;

f(0) = 1

f(1) = 3

f(-1) = 4

A function can be described as a rule, law or expression explaining the relationship between two variables.

These variables are called;

From the information given, we have that;

F(x) = 2x + 1 when x is greater than or equal to zero

Also,

f(x) = -2x - 1 when x is less than zero

Then for f(0)

f(0) = 2(0) + 1

expand the bracket

f(0) = 1

For f(1) = 2(1) + 1

expand the bracket

f(1) = 3

f(-1) = -2(-1) + 1

expand the bracket

f(-1) = 4

Hence, the values are 1, 3 and 4

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Answer:

width of the flag is 440 feet and the length is 780 feet

Step-by-step explanation:

Let's call the width of the flag "w". Then the length of the flag can be represented as "w + 340".

The perimeter of the flag is the sum of all four sides, so we can write the following equation:

2w + 2(w + 340) = 2,440

Expanding the second term on the left side and simplifying:

2w + 2w + 680 = 2,440

4w + 680 = 2,440

Subtracting 680 from both sides:

4w = 1,760

Dividing both sides by 4:

w = 440

So the width of the flag is 440 feet and the length is 780 feet (440 + 340).

x is not an integer, and is instead an irrational number that lies between -1/6 and 1/9.

We can solve this problem using the law of sines. The law of sines states that for a triangle, the ratio of the side opposite an angle to the sine of that angle is equal for all three angles. Therefore, we can solve for x by setting up two equations, one for angle W and one for angle X.

For angle W, the equation is:

18x - 2 = sin-1(VX/WY)

For angle X, the equation is:

12x + 2 = sin-1(VW/YX)

Since we know the ratio of the sides of the triangle, we can solve for x by substituting these values into the equations.

For angle W, we get:

18x - 2 = sin-1(VX/WY)

18x - 2 = sin-1(2/2)

18x - 2 = 0

18x = 2

x = 1/9

For angle X, we get:

12x + 2 = sin-1(VW/YX)

12x + 2 = sin-1(2/2)

12x + 2 = 0

12x = -2

x = -1/6

Since these two answers do not match, we can conclude that x is not an integer, and is instead an irrational number that lies between -1/6 and 1/9.

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The length, in units, of the rectangle is 9 units.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Length = x

Width = x - 8

Area = 9 square units

Now,

The area of the rectangle = length x width

9 = x (x - 8)

9 = x² - 8x

x² - 8x - 9 = 0

Solve for x.

x² - 8x - 9 = 0

x² - (9 - 1)x - 9 = 0

x² - 9x + x - 9 = 0

x(x - 9) + 1(x - 9) = 0

(x - 9) (x + 1) = 0

x - 9 =0 and x + 1 = 0

x = 9 and x = -1 (rejected)

Now,

Length = 9

Width = 9 - 8 = 1

Thus,

Length is 9.

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Answer:

0.3

Step-by-step explanation:

To solve this, I asked, "If 7 divided by 21 is 3, then 7 divided by 22 would have little to no difference in the tenths place, right?" And that question is correct. Answering this question, the decimal place could not be greater than 5, because 7/22 is the formula for another, more accurate, albeit shorter version of pi, but backwards. 7/22 is 0.31, and 0.31's tenths place has a 1 in it, so this, according to the laws of rounding, rounds downward. Therefore, the correct answer would be 0.3.

Hope this helps!

Answer:

The function is translated down 2 and and to the right 3

Step-by-step explanation:

[tex]f(x)=(x-h)+k[/tex]

h = transition left or right

k = transition up or down

The composite function value is 2t - t^2

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

f(x) = x^2 - 2x - 6

A composite function involves combining multiple functions to a single function

When the function f(2) is calculated, we have

f(x) = 2^2 - 2(2) - 6

Evaluate

f(2) = -6

When the function f(t) is calculated, we have

f(t) = t^2 - 2t - 6

So, we have

f(2) - f(t) = 2t - t^2

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Answer:

523.3

Step-by-step explanation:

memorize this formula:

V = 4/3 π r³, where V = volume and r = radius.

so v=4/3π *5³ =125*4/3π =523.3

Answer: 2x-y=3

Step-by-step explanation: Search math w ay on the internet

There does not exists a rational number t such that  [tex]t^2 = 2[/tex].

Suppose the contrary, that there exists a rational number t such that[tex]t^2 = 2[/tex]. Then t can be written in its lowest terms as t = p/q, where p and q are integers, with q≠ 0. Then squaring both sides gives[tex](p/q)^2 = 2[/tex], so [tex]p^2 = 2q^2[/tex]. Since both [tex]p^2[/tex] and [tex]q^2[/tex] are integers, this implies that 2 is a perfect square, which it is not. Thus, there does not exist a rational number t such that[tex]t^2 = 2.[/tex]

In detail, assume t = p/q where p and q are integers and q ≠ 0. Then [tex]t^2 = 2[/tex] can be written as [tex]t^2 = 2[/tex].. This implies [tex]p^2 = 2q^2[/tex]. Since both [tex]p^2[/tex] and [tex]q^2[/tex] are integers, it implies 2 is a perfect square, which it is not. Therefore, there does not exist a rational number t such that   [tex]t^2 = 2[/tex].

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Complete question

Does there exist a rational number t such that [tex]t^2 = 2[/tex].?

The length of the three missing sides in the rhombus are x=75,y=75,z=75

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

Given;

One side of rhombus= 75

Now, as we know that all sides of rhombus are equal

x=y=z=75

Therefore, the sides of rhombus will be x=75,y=75,z=75.

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The triangles are similar by SSS.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The sides of first triangle are, 6, 9.6, 12.3

And, The sides of second triangle are, 2, 3.2, 4.1

Now, The ratio of corresponding sides of triangle are,

⇒ 6 / 2 = 3

⇒ 9.6 / 3.2 = 3

⇒ 12.3 / 4.1 = 3

Thus, The triangles are similar by SSS.

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Answer: No, it is not proportional.

Step-by-step explanation: X will be the mystery number here. So first, we want to find a common denominator. 5 times x equals 20. We want to divide 20 by 5. 20/5 equals 4. X = 4. So now we want to multiply the 4 from 4/5 by 4. 4 times 4 equals 16.

4/5 = 16/20

The Marginal Revenue MR(29) 11513 dollars per unit.

The velocity is v(t) = 24t² - 96t - 120.

The velocity equals zero at t = 5.

The acceleration of the particle is a(t) = 48t - 96.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

Suppose a product's revenue function is given by R(q) = -7q² + 600q,

where R(q) is in dollars and q is units sold.

We have to determine a numeric value for the marginal revenue at 29 units

As per the question we have

R(q) = -7q² + 600q

Substitute the value of q = 29, and we get

R(29) = -7(29)² + 600(29)

R(29) = 11513

Thus, the Marginal Revenue MR(29) 11513 dollars per unit

Let s(t) = 8t³ - 48t² - 120t be the equation of motion for a particle.

To find the velocity, we need to differentiate the equation for the position of the particle, s(t).

v(t) = ds/dt = d/dt (8t³ - 48t² - 120t) = 24t² - 96t - 120

To find the t-values where the velocity is equal to zero, we need to set v(t) equal to zero and solve for t.

0 = 24t² - 96t - 120

This is a quadratic equation, and we can solve for t by factoring the GCF

(t - 5)(t + 1) = 0

(t - 5) = 0 and (t + 1) = 0

t = 5 and t = -1

So the velocity equals zero at t = 5

To find the acceleration, we need to differentiate the velocity function, v(t).

a(t) = dv/dt = d/dt (24t² - 96t - 120) = 48t - 96

So the acceleration of the particle is a(t) = 48t - 96.

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The entropy of X (number of defective chips) in bits is a measure of uncertainty about the value of X.

The entropy of a random variable represents the amount of uncertainty or randomness associated with the outcome of the variable. To calculate the entropy of a discrete random variable, we need to determine the probability distribution function and use the formula:

H(X) = -Σ P(X=x) log2(P(X=x))

In this case, the random variable X represents the number of defective chips in 5 randomly chosen chips from a box of 50, with 3 defective chips. The possible outcomes are 0, 1, 2, 3, and 4, with probabilities:

P(X=0) = (47/50)^5

P(X=1) = (5 * (3/50) * (47/50)^4)

P(X=2) = (10 * (3/50)^2 * (47/50)^3) / 2!

P(X=3) = (5 * (3/50)^3 * (47/50)^2) / 3!

P(X=4) = (3/50)^4 / 4!

By plugging in the probabilities into the entropy formula, we can find the entropy in bits.

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the Total weight of the container that kept figs is 1.6 kg.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, 80 figs are kept in a container. Each fig weighs 0.02 kg.

Since,

One fig is weighing  = 0.02 kg

So,

80 figs will weigh = 0.02 * 80

80 figs will weigh =  1.6 kg

Therefore, the Total weight of the container that kept figs is 1.6 kg.

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