Factor out the greatest common factor from the expressions below to find an equivalent ex
pression. (Hint First combine the like terms and them find the GCF and factor the expression
4 16p+5+9p+25

The option that is true for the central limit theorem is;

C: For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed

Let us look at all the given options to access which one clearly is correct about the central limit theorem;

a) This option is incorrect because the CLT theorem is based on ‘sample mean’ distribution.

b) This option is Incorrect because the theorem is true for any population distribution.

c) This option is correct because Irrespective of the population distribution, the sample means of repeated samples are normally distributed for larger n.

d) The “central limit theorem(CLT)” states that, the sample means of the repeated samples follows normal distribution for ‘large’ sample sizes. Thus, this option is incorrect.

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Answer:

Step-by-step explanation:

In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:

The length of one pair of opposite sides is equal.

The two pairs of opposite sides are parallel.

To show these two conditions, you may need additional segments or points such as:

Perpendicular lines or segments to the sides to help show the sides are parallel.

Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.

By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.

Answer:

  3 : 4

Step-by-step explanation:

You want to know the ratio of areas of a rectangle and square such that the rectangle is 50% longer and 50% narrower than the square.

A square that is 2 units on a side will be transformed to a rectangle that is 1.5×2 = 3 units long, and 0.5×2 = 1 unit wide.

The rectangle area is 3×1 = 3. The square area is 2×2 = 4.

The ratio of areas is ...

  rectangle area : square area = 3 : 4

The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.

Relative frequency is found by dividing the frequency with the total number of values.

Cumulative frequency is calculated by adding the previous frequencies together.

(a) From the table,

Total number of people = 210

So, Total frequency = 210

Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40

Relative frequency = Frequency / Total frequency

Relative frequency of number of siblings as 2 = 0.1952

Cumulative frequency of number of siblings as 3 = 127 + 43 = 170

(b) Percent of people having exactly 1 sibling = (43 / 210) × 100

                                                                           = 20.48%

Hence the percent of people having exactly 1 sibling is 20.48%.

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The product of a, b, and c is 27/8.

What is an expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.

The given expression is

                                      [tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]

To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:

Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]

Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]

Putting the simplified numerator and denominator together, we have:

[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]

Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:

a * b * c = 3 * (-3/4) * (-3/2) = 27/8.

Hence, the product of a, b, and c is 27/8.

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The given amounts of money will be written as £5.37, £2.04 and £15.70 respectively. The solution has been obtained by using denominations of money.

What is denomination?

The term "denomination" refers to the units of measure that are used to categorize various financial products such as coins and paper money. Every country has different denomination.

We are given three different amounts of money in words which are to be written in denominations.

So,

a. Five pounds and thirty seven pence = £5.37

b. Two pounds and four pence = £2.04

c. Fifteen pounds and seventy pence = £15.70

Hence, the amounts in their denominations have been obtained.

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Step-by-step explanation:

Hope it helps :) #CarryOnLearning

There are 47 polar bears and penguins in the water.

The number of snowballs made altogether is 130 snowballs.

The number of snow globes your mother has left is 47 snow globes.

The number of penguins left playing is 97 penguins.

Number of polar bears= 24

Number of penguins = 38

No. of polar bears that got out of the water= 15

Total polar bears and penguins in the water = (24 + 38) - 15

= 47

Number of snowballs made by your brother = 46

Number of snowballs made by you = 59

Number of snowballs made by your sister, brother and you = 25

Total snowballs made= 46 + 59 + 25

= 130 snowballs

Number of snow globes mother has = 51

Number of additional snow globes received = 8

Number of snow globes broken = 12

The number of snow globes your mother has left= (51 + 8) - 12

= 59 - 12

= 47 snow globes

Number of adult penguins(mother and father) = 83

Number of baby penguins = 69

Number of mother penguins that went home = 55

Number of penguins left playing = (83 + 69) - 55

= 97 penguins.

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A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.

A function that models the volume V of the box can be found by subtracting four [tex]x2[/tex]from both the length and the width, and then multiplying the result to get the volume:

V = [tex](12 - 4x2)(20 - 4x2)[/tex]

To find the values of x for which the volume is greater than 230 in2, we can solve the equation

V = [tex](12 - 4x2)(20 - 4x2) = 230[/tex] for x.

This gives x values of ±2.636

Thus, the values of x for which the volume is greater than 230 in2 are x = [[tex]-2.636, 2.636[/tex]].

The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.

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After answering the provided question, we can say that the function's midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2. midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5

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The two sequences have the same number (4) in the same position (third)

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

Using the above as a guide, we have

Sequence 1: 16, 8, 4, 2, 1.....

Sequence 2: 1, 2, 4, 8, 16.....

The number 4 is in the same position for the two sequences

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Answer: Option 1

Step-by-step explanation:

I'd say the easiest way would be to find the prize per oz in both options

Option 1: $1.10/12oz = approx 0.092 (so around 9 pennies)

Option 2: $0.98/10oz = 0.098 (also 9 pennies but still slightly more than option 1)

You can check by choosing a random number of oz and multiplying them by the price to see which costs more

ex: 120 oz

option 1 : 10 x 1.10 = $11

option 2: 12 x 0.98 = $11.76

The level of confidence Evelyn used is 92%. Therefore, option B is the correct answer.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

Given that, one sample z interval for proportions and gets a margin of error of 0.0758.

If her sample proportion was 0.75 and her sample size was 100.

We know that, p±z×√p(1-p)/n

Where, P is sample proportion, n is the sample size and z is the standardized normal distribution

Here, 0.75±0.0758×√0.75(1-0.75)/100

= 0.75±0.0758×√0.1875/100

= 0.92

=92%

Therefore, option B is the correct answer.

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Answer:

Step-by-step explanation:

1.3 * 10 ^-7

is 0.00000013

0.00000013 times 15 is

0.00000195.

0.00000195 in scientific notation is

1.95*10^-6

Answer: (a) -6x²y

Step-by-step explanation:

[tex]\frac{-18x^{3}y^{2} }{3x^{2} y}[/tex]
X to the power of 2 should be cancelled from the top and bottom, which leads to:
[tex]\frac{-18xy^{2} }{3y}[/tex]
Then Y to the power of 1 should be cancelled from top and bottom (since it can go into both), which leads to:

[tex]\frac{-18xy}{3}[/tex]
Then find the highest common factor (which is 3), and cancel it out from the top and bottom, which leads to:
[tex]\frac{-6xy}{1}[/tex]
which equals to
-6x²y (a)

Answer:

100π - 192 or 122.159....

Step-by-step explanation:

In order to find the diameter we much first split the rectangle diagonally and find the hypotenuse using Pythagorean theorem.

a^2 + b^2 = c^2

16^2 + 12^2 = c^2

400 = c^2

c = 20

If the diameter of the rectangle is 20, the radius is just half of that which is 10. Then you just need to a do a basic calculation for area of a circle and then subtract out the area of the rectangle.

Area of circle = πr^2 = π(10^2) = 100π (keeping it in exact value since π is infinite)

Area of rectangle = lw = (16)(12) = 192

Area of shaded area = 100π - 192 (exact) = 122.159 (estimate)

Answer:

9^1 has a power of 1.  it evaluates to 9

Step-by-step explanation:

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

here, we have,

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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To convert 31,750 feet to miles, divide the number of feet by the number of feet per mile:

31,750 feet / 5,280 feet/mile = 6 miles

All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.

The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.

An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.

A line segment serves as the foundation for the following angles and lines in geometry:

The process of creating a line perpendicular to a point on a line.

The creation of a 45-degree angle (45°).

The creation of a 30-degree (30-degree) angle.

Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.

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Answer:

To compare the amount of money that Patrick and Brooklyn would have after 2 years, we need to calculate the interest earned using each of their methods.

For Patrick, who deposited $300 with an interest rate of 3% compounded quarterly, the formula to calculate the amount after 2 years (8 quarters) is:

A = P(1 + r/n)^(nt)

Where:

P = principal amount ($300)

r = interest rate (3%)

n = number of times compounded per year (4)

t = time in years (2)

Substituting the values into the formula:

A = $300(1 + 0.03/4)^(4 * 2)

A = $300(1.0075)^8

A = $300 * 1.06173

A = $318.52

For Brooklyn, who deposited $300 with an interest rate of 5% compounded monthly, the formula to calculate the amount after 2 years (24 months) is:

A = P(1 + r/n)^(nt)

Where:

P = principal amount ($300)

r = interest rate (5%)

n = number of times compounded per year (12)

t = time in years (2)

Substituting the values into the formula:

A = $300(1 + 0.05/12)^(12 * 2)

A = $300(1.00417)^24

A = $300 * 1.09722

A = $328.17

Therefore, after 2 years, Brooklyn would have $328.17, which is more money than Patrick's $318.52.

Step-by-step explanation:

Since the original volume is 29 and they are looking for 1/7th of that, we can multiply these two numbers

[tex](29)( \frac{1}{7} ) = 4 \frac{1}{7} psi[/tex]

Answer:

The larger number is 100

The smaller number is 60

Step-by-step explanation:

x + (40 + x) = 160

2x + 40 = 160

x + 20 = 80

x = 60

60 + (40 + 60) = 160

160 = 160

The solution is, the value is, x = 49.6.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

given that,

There is a pair of vertical angles where ∠1=106° and ∠2=3x−75

so, 1 + 2 = 180

or, 106 + 3x - 75 = 180

or, 3x = 149

or, x = 49.6

Hence, The solution is, the value is, x = 49.6.

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The Equation x² − 15x + 12 = 0 have two Real solution and 3x² − 6x + 4 = 0 have Imaginary solution.

The discriminant, denoted by the equation b² - 4ac, can be used to ascertain if the solutions are real, repetitive, or complex:

1) If the discriminant is smaller than 0, there are two imaginary roots to the problem (s).

2) The equation has one repeating real solution if the discriminant equals zero (s).

Given:

x² − 15x + 12 = 0

Solving the Quadratic Equation

x² − 15x + 12 = 0

D = b² - 4ac

D = (-15)² - 4(1)(12)

D =  225 - 48

D = 177 >0

So, the Equation will have two Real solution.

b) 3x² − 6x + 4 = 0

Solving the Quadratic Equation

3x² − 6x + 4 = 0

D = b² - 4ac

D = (-6)² - 4(3)(4)

D =  36 - 48

D =  -12 >0

So, the Equation will have Imaginary solution.

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Answer:

When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.

You want to subtract 9 and 24 to get the x value:

24 - 9 = 15

x = 15

Step-by-step explanation:

Hope it helps! =D

Hi there, here's your answer:

Given a right angled triangle

With the hypotenuse as 24 units and one of the legs as 9 units
To find:

The 3rd side denoted as 'x'

Solution:

We use Pythagoras Theorem:

[tex]a^2 + b^2 = c^2[/tex]

Where a and b are the legs and c is the hypotenuse.

We know the value of c and b

And a = x
Thus,

[tex]x^2 = c^2 - b^2[/tex]

[tex]x^2 = 576 - 81\\[/tex]

[tex]== > x^2 = 495\\[/tex]

Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units

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The slope of a line parallel to another line will have the same slope as the original line. To find the slope of the line 25x - 5y = -10, we need to rearrange the equation into the slope-intercept form y = mx + b, where m is the slope.

First, we'll isolate y:

25x - 5y = -10

5y = 25x + 10

y = (25/5)x + 2

So the slope of the line 25x - 5y = -10 is m = 25/5 = 5.

Therefore, a line parallel to 25x - 5y = -10 will have a slope of m = 5.

Correct me if im wrong :)

Answer:

5

_ y - 7

3

the five is floating for some reason its supposed to be under the line

Answer:

x=2

y=0

Step-by-step explanation:

2x=4

x=4/2

x=2

again,

y-1 =2y -1

1-1 =2y -y

0=y