Which of the following statements is true?
For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed.
For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite.
For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed.
Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed.

The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.

To solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.

First, we notice that "negative x" means "-x", so we can rewrite the equation as:

-x = 9

To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:

-x + x = 9 + x

Simplifying the left-hand side by canceling out the "-x" and "+x", we get:

0 = 9 + x

We can further simplify this equation by subtracting 9 from both sides:

0 - 9 = 9 + x - 9

-9 = x

So the solution to the equation "negative x = 9" is "x = -9".

There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.

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The domain and the range of a function/graph/relation are defined as follows:

The problem is incomplete, hence the concepts of domain and range are presented, and then they are used to obtain the domain and the range.

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The average rate of change over the interval (-1, 2) is; 3

The formula for the average rate of change over an interval (a, b) is expressed as;

f'(x) = [f(b) - f(a)]/[b - a]

We want to find the average rate of change over the interval (-1, 2). Thus;

a = -1 and b = 2

Thus;

f(-1) = -4

f(2) = 5

Thus;

f'(x) = (5 - (-4))/(2 - (-1))

f'(x) = 9/3

f'(x) = 3

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Answer:

Common ratio, r = 3

Step-by-step explanation:

Common ratio is given by the ratio of one of the terms to the previous term and is a constant for the entire sequence

Here the first term is 17

Second term is 51

Second Term ÷  First Term
= 51 ÷ 17 =3

Third Term ÷ Second Term
= 153 ÷ 51 = 3

So common ratio is 3

In general, if aₙ is the nth term and aₙ₊₁ then the common ratio is given by:
aₙ₊₁ / aₙ

The value of x in the trapezoid is 12

It is important to note that the properties of a trapezoid are;

Now, let's equate the angles, we getl

7x + 21 = 105

collect the like terms, we get;

7x = 105 - 21

subtract the like terms

7x = 84

Make 'x' the subject of formula

x = 84/7

Divide the values

x = 12

Hence, the value is 12

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The equations used are:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

Let the following expressions represent the lengths of the sides of the triangle:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

Perimeter = a + 1/2a + a - 1 = 39

a + 1/2a + a = 39 + 1

2a + 1/2a = 40

2 1/2a = 40

5/2a = 40

a = 40 x 2/5

a = 16 inches

Shortest side = 1/2 x 16 = 8 inches

Third side = 16 - 1 = 15 inches

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Answer: Decreased 40%

Step-by-step explanation:

Alright, we know they reduced $10.00 (25-15)

Now all we have to do is find the percentage, 10 is how much of 25?

10/25 =0.4

(to get 0.4 to a percentage multiply by 100)

The price was decreased by 40%

The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.

In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.

Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.

Options;

A. -0.28

B. -0.82

C. -4/5

D. -1/5

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Answer:

Step-by-step explanation:

To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:

(C1 * V1) + (C2 * V2) = (C3 * V3)

Where:

C1 = concentration of the acid solution at 60% (in percent)

V1 = volume of the acid solution at 60% (in ml)

C2 = concentration of the acid solution at 30% (in percent)

V2 = volume of the 30% acid solution (in ml)

C3 = concentration of the resulting 50% acid solution (in percent)

V3 = volume of the resulting 50% acid solution (in ml)

In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values ​​into the equation:

(60 * V1) + (30 * V2) = (50 * 300)

Clearing V1:

V1 = (300 * 50 - 30 * V2) / 60

Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values ​​into the equation:

V1 = (300 * 50 - 30 * V2) / 60

V1 = (15000 - 30 * V2) / 60

V1 = 250 - (V2 / 2)

We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:

V2 = 2 * (250 - V1)

Clearing V1:

V1 = 250 - (V2 / 2)

V1 = 250 - (2 * (250 - V1) / 2)

V1 = 250 - 250 + V1

V1 = 250

Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.

Step-by-step explanation:

answer is in the picture

The constant of proportionality is 0.60

The equation is y = $0.60x.

Here is the completed table

Number of lemons  Total cost

4                                  $2.40

7                                 $4.20

15                                 $9

18                                  $10.80

Direct variation is when two variables move in the same direction. As the number of lemons bought increases, the total cost increases.

The equation that represents direct variation is:

y = kx

Where:

$1.80 = 3k

k = $1.80 / 3

k = $0.60

y = $0.60x

Total cost of 4 lemons=  $0.60 x 4 = $2.40

Total cost of 18 lemons=  $0.60 x 18 = $10.80

Number of lemons that cost $4.20 : 4.20 / 0.6 = 7

Number of lemons that cost $9 : 9 / 0.60 = 15

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It looks like 1) adjacent angles.

The system of equations which represents this

situation is 3x+4y= 32 and 5x + 5y = 18.

The correct answer choice is option B

Amount with Maya = $32

Amount spent on each notebook = x

Number of notebook = 3

Amount spent on each pack of index cards = y

Number of index cards = 4

Maya bought 5 notebooks and 5 packs of

index cards

$18 short = $32 - $18

= $14

3x + 4y = 32

5x + 5y = 14

In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.

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The total amount of interest that Alvin paid over the course, guven the value of the student loan and the interest rate is $ 6, 185

To find the interest paid, you need to find the total amount that Alvin paid in the 10 years that he was paying.

To do this, you first need to find the monthly payments. This will be an annuity as the amount will be the same throughout the student loan payment period.

The amount would be :

Student loan value = Amount x Present value interest factor of annuity, 120 periods, 4. 4 % / 12

The periods are :

= 10 years x 12 months

= 120 months

The amount is:

26, 000 = Amount x 96.939576551857

Amount = 26, 000 / 96.939576551857

Amount = $ 268. 21

The total paid over the 10 years is :

= 268. 21 x 120 months

= $ 32, 184. 9972

The interest is :

= 32, 184. 9972 - 26, 000 loan amount

= $ 6, 185

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Answer:

  -5x⁵ +2x² -3/x³

Step-by-step explanation:

You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).

The quotient and remainder can be found by dividing term by term.

  [tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]

__

Additional comment

The exponent rule is (a^b)/(a^c) = a^(b-c).

<95141404393>

Area of desert 1 is 18,000,000 square miles and area of desert 2 is 3,000,000 square miles.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Let A₁ and A₂ be the area of Desert 1 and Desert 2 respectively.

Given,

Area of a Desert 1 is six times the area of Desert 2.

A₁ = 6 A₂

The sum of their areas is 21,000,000 square miles.

A₁ + A₂ = 21,000,000

Substituting A₁ = 6 A₂ in A₁ + A₂ = 21,000,000 ,

6 A₂ + A₂ = 21,000,000

7 A₂ = 21,000,000

A₂ = 21,000,000 / 7

A₂ = 3,000,000 square miles

A₁ = 6 A₂

   = 6 × 3,000,000

   = 18,000,000 square miles

Hence the areas of each desert is 18,000,000 square miles and 3,000,000 square miles.

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The statement describes the solutions of this equation is

The Equation have two valid solution and No Extraneous solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)

Now, simplifying the above Expression

(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)

(x² + 4x + 3x - 3) / 3 = (x+3)

x² + 7x -3 = 3(x+3)

x² + 7x -3 - 3x - 9 = 0

x² + 4x - 12 = 0

Solving the above Quadratic Equation

x² + 6x- 2x - 12 = 0

x(x+6)- 2(x+6)= 0

(x-2)(x+6)= 0

x= 2, -6.

So, the Equation have two valid solution and No Extraneous solution.

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On solving the provided question, we can say that  In decimals r = 3.8799 and d = 7.7598

Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.

A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.

the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.

Area  = πr²

47.25 = 3.14 × r × r

r × r = 15.0541401274

In decimals

r = 3.8799

d = 7.7598

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Answer:

Alright, so we want to know how much that can be earned in one year. So that's going to be 3000. And this is simple interest. So this is one plus 0.011, which equals $3,033. And that's the solution to this exercise.

Answer:

$3,036

Step-by-step explanation:

The new customer can open a money market account. The bank will deposit $3,000 into the account.

The bank will pay 1.2% (0.012) in interest every year. This interest will increase the original amount to $3,036.

The probability that the sample proportion exceeds 0.12 is given as follows:

0.6103 = 61.03%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are given as follows:

n = 90, p = 0.13.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion exceeds 0.12 is one subtracted by the p-value of Z when X = 0.12, hence:

Z = (0.12 - 0.13)/0.0354

Z = -0.28

Z = -0.28 has a p-value of 0.3897.

Hence:

1 - 0.3897 = 0.6103.

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The area of the given composite shape with two rectangles is 68 m²

What is a rectangle?

There are four right angles on the quadrilateral that forms the rectangle. Every corner or vertex has a right angle where the two sides meet. It differs from a square, which has all of its sides of equal length, in that the opposite sides of the rectangle are equal in length. Two dimensions and flatness combine to make a rectangle.

The figure can be divided into a rectangle with a length of 8m and breadth of 6m and another rectangle of length 5m and breadth = (10-6) = 4m.

To find the area of the whole figure, we first find the areas of small and big rectangles and sum their areas.

Area of small rectangle = length * breadth = 5*4 = 20 m²

Area of big rectangle = length * breadth  = 8 * 6 = 48 m²

Therefore the area of the given composite shape with two rectangles is 20+48 = 68 m².

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From unit prices gotten, the price of one feet of annel fabric is cheaper than the price of one feet of fleece fabric.

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint. This can be used to compare the same type of goods sold in varying weights and amounts.

The parameters are;

3 yards of annel fabric costs $12.60

5 feet of fleece fabric costs $8.75.

From conversion units;

1 yard =  3 feet

Thus;

3 yards = 3 * 3 = 9 ft

Thus;

Unit price of Annel fabric = 12.6/9 = $1.4 per ft

Unit price of fleece fabric = 8.75/5 = $1.75 per ft

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The value of x is given as follows:

x = 9.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

The figure for this problem has four sides, hence the sum of the internal angle measures is given as follows:

S(4) = 180 x (4 x 2)

S(4) = 360º.

Adding the four angle measures and equaling them to 360º, the value of x is obtained as follows:

117 + 93 + 87 + 6x + 9 = 360

306 + 6x = 360

6x = 54

x = 54/6

x = 9.

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Answer:

16 years old

Step-by-step explanation:

Let's call Mikhail's age "x". Gabrielle's age is 3 times that, so her age is 3x. The sum of their ages is 64, so:

x + 3x = 64

4x = 64

x = 16

So, Mikhail's age is 16 years old.

Answer:a rectangular prism has  height  4m, length 6m & width 5m

thus the surface consist of two  4*6 vertical surfaces

                                          two 4*5 vertical surfaces

                                        & two 6*5 top & bottom surfaces

that is

            2(4*6) =  48

            2(4*5) =  40

            2(6*5) =  60

total surface area =  48+40+60 = 148m²

Step-by-step explanation:

The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

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Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

Given :

percent distribution : 40% , 35% , 15% , 7% , 3%

Vehicles : 420

First, add the percentage of cars containing 3 people, 4 people, and 5 or more people:

15% + 7% + 3% = 25%

Thus, 25% of the cars contained at least 3 people, so use that to calculate the number of cars:

420 × 0.25 = 105 cars.

Hence , Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.

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Complete question:

A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning.

How many of the 420 vehicles contained at least 3 people?

A. 42

B. 63

C. 105

D. 315

Answer:

295>_ 39x+11.50

Step-by-step explanation:

the >_ means less than or equal to.