Use Pascal's Triangle to expand (5z + 5x²)³. Express your
answer in simplest form.

The probability of a lion living longer than 10.1 will be 0.1585.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years.

The lifespan of a lion in a particular zoo is normally distributed with average lion lives:

Mean u = 12.5 years

Standard deviation s = 2.4 years

We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.

The empirical rule ( 68-95-99.7% ) states:

P ( u - s < X < u + s ) = 68%

P ( u - 2s < X < u + 2s ) = 95%

P ( u - 3s < X < u + 3s ) = 99.7%

The test has the following number of standard deviations (s):

u - s < X < u + s  = 12.5 - 2.4 < X < 12.5 + 2.4  = 10.1 < X < 14.9

u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8  = 7.7 < X < 17.3

u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2  = 5.3 < X < 19.7

Then the probability is calculated as,

P ( 10.1 < X < 14.9 ) = 0.68

P ( 7.7 < X < 17.3 ) = 0.95

P ( 5.3 < X < 19.7 ) = 0.997

We need P ( X < 10.1 ) and P ( X < 5.3 ):

P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2

P ( X < 10.1 ) = [ 1 - 0.68 ] / 2

P ( X < 10.1 ) = 0.16

P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2

P ( X < 5.3 ) = [ 1 - 0.997 ] / 2

P ( X < 5.3 ) = 0.0015

P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )

P ( 5.3 < X < 10.1 ) = 0.16 - 0.0015

P ( 5.3 < X < 10.1 ) = 0.1585

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The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.

Given that:

[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]

Since, BH is the altitude [tex]\angle MHC= 90[/tex].

The total angle of a quadrilateral is 360, hence:

100 + 110 + 90 + C = 360

C = 60 degrees.

Now consider triangle BHC:

The sum of angle of a triangle is 180, hence:

90 + 60 + B = 180

B = 30

Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].

Consider triangle ABC:

Using sum of triangles, we have:

[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]

Hence the measure of angles of triangle ABC is 60 degrees.

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Answer:

I could find the slope of a line by looking at the gradient of a graph that the line creates. If the line is linear, then the gradient will be a constant value, which I can use to find the value of the slope. If the line is not linear, then I can use a derivative to find the slope at a given point. However, if the line is concave or concave up, then I will need to take the second derivative of the equation to determine which point on the line is closest to the point that I'm trying to calculate.

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is pretty simple. To find the area of anything in square centimeters, you multiply the length by the height. You already have both of those number, so you just have to do 4.2 x 4.2 (or 4.2 to the second power). The answer is  21.84 square centimeters.

Answer: 21.84 square centimeters

The approximate shape of the sampling distribution of the sample will be normal.

Option E is correct.

Sampling distribution:

It is a statistic that determines the probability of an event based on data from a small group within a large population.

Given that,  is greater than or equal to 15 and  is greater than or equal to 15.

      and

So that the new mean and standard deviation will be,

Thus, the approximate shape of the sampling distribution of the sample will be normal.

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Answer:

T=(I/p)/r

Step-by-step explanation:

I = Prt is the same thing as: I = P*r*t

We want the answer to be as:

T = ???

The only thing you need to do is the get T to one side.

1. [tex]I = P*r*t[/tex]

2. [tex]I/p=r*t[/tex]

3. [tex](I/p)/r=t[/tex]

4. [tex]t=(I/p)/r[/tex]

The price range for 75% of sales will be between $149,300 and $343,300.

The minimum percentage of observations falling within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous probability distributions can use this theorem. Also known as Chebyshev's Inequality, Chebyshev's Theorem.

Between $149,300 and $343,300 is where 75% of transactions are priced. Only 75% of the distribution's numbers must fall within two standard deviations for Chebyshev's theorem to hold, which makes it weaker than the proportion of numbers that are within two standard deviations of the mean.

Since the standard deviation given exists 48500, 2 standard deviations will be 2 × 48500 = 97000.

The lower limit will be 246300 - 97000 and the upper limit will be 246300 + 97000.

Lower limit = 246300 - 97000 = 149300

Upper limit = 246300 + 97000 = 343300

So 75% of the sales prices will be between $149,300 and $343,300

The complete question is:

The average sale price of new one-family houses in the United States for 2003 was $246,300. Using Chebyshev's theorem, find the range of values in which at least 75% of the sale prices will lie if the standard deviation is $48,500. Hint: You should memorize that when k is 2, it is 75% and when k is 3 it is 88.89%. Please answer with whole numbers: ex. 55,232 to 65,450 with commas

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A rectangular prism has dimensions of 8cm by 9cm by 10cm therefore the volume is 720cm³.

This is referred to as the measure of the space occupied within the boundaries of any three-dimensional solid.

Volume of rectangular prism = l × w × h where l is length, w is width and h is height.

Volume =  8cm × 9cm × 10cm = 720cm³.

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The members voted 2 more for mars than earth.

The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.

Given here, Mars has 8 votes while earth has 6 votes

Thus difference in votes is =8-6

                                              = 2

Hence, Mars got two more members than earth

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If the total study sessions for the night class were proportional to the morning class that is 25: 20 then night class have the actual amount 80% students

we can calculate 20/25 *100

and we obtain the actual amount  80%

If the total study sessions for the night class were proportional to the morning class is 25: 20 and 16: 22

What is a proportion simple definition?

the size, number, or amount of one thing or group as compared to the size, number, or amount of another. the proportion of boys to girls in our class is three to one. : a balanced or pleasing arrangement

Initially, the number of lectures is 3 while the number of fieldwork is 12. Furthermore, the class sessions increased to 18 and the number of fieldwork remains the same (i.e. 12). Therefore, the number of lectures will be 18 - 12 = 6. The percentage of the sessions that were  lectures will be:

(6/18)*100% = 33.3%

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Answer: No, 3x-2 and 3x^2 are not reciprocals.

Step-by-step explanation: The reciprocal of a number is defined as the multiplicative inverse of that number, which means that when a number is multiplied by its reciprocal, the result is 1. For example, the reciprocal of 2 is 1/2, because 2 * (1/2) = 1.

In contrast, 3x-2 and 3x^2 are not numbers, they are expressions that contain variables. It is not possible to determine their reciprocals without knowing the values of the variables.

For example, if x=1, then the reciprocal of 3x-2 would be (1/3)/(1-2) = -1/3, and the reciprocal of 3x^2 would be (1/3)/(1^2) = 1/3. However, if x=2, then the reciprocal of 3x-2 would be (1/3)/(2-2) = undefined, and the reciprocal of 3x^2 would be (1/3)/(2^2) = 1/12.

So it is not accurate to say that 3x-2 and 3x^2 are reciprocals.

No

The only thing stopping these from being reciprocals is the -2. Say x becomes 3

First we get 3(9)-2.

Next, we'd get 3(3)(2)

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

In order to get the variable on its own, you can solve a lot of straightforward inequalities by adding, removing, multiplying, or dividing the two sides. But as a result of them, the direction of the inequality will change: Using a negative number to divide or multiply both sides. right and left sides are switched.

An inequality results from the comparison of two or more algebraic expressions using the symbols, >, or. They are the mathematical expressions with unequal sides.

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The difference between log with base 10 and log with base e is that the log with base 10 is called a common logarithmic function and the log with base e is called a Natural Logarithmic Function .

What is Logarithmic Function ?

The logarithm is defined as a power to which a number must be raised in order to get some other values. Log is the most convenient way to express the large numbers.

The Logarithm with base 10 is defined as a power to which the  number must be raised  to get some other number. It can also be  called as the logarithm of base 10, or common logarithm.

The general form of Common  logarithm is written as: [tex]log_{10} (x)[/tex] ;

The Logarithm  with base e is called as Natural Log , where e is an irrational number .

The general form to represent a Natural Log is : [tex]log_{e} (x)[/tex] or [tex]ln(x)[/tex] .

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The value of the composite function [f(g(f(f(f(g(27))))))], when f(x) = log₃(x) and g(x) = 3ˣ is 1

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

Let f(x) = log base 3 of x and g(x) = 3^x.

Express the equations properly

So, we have the following representations

f(x) = log₃(x) and g(x) = 3ˣ

Calculating the composite function [f(g(f(f(f(g(27))))))], we have

[f(g(f(f(f(g(27))))))] = [f(g(f(f(f(3²⁷))))))]

Next, we have:

[f(g(f(f(f(g(27))))))] = [f(g(f(f(log₃(3²⁷))))))]

This gives

[f(g(f(f(f(g(27))))))] = [f(g(f(f(27))))))]

For f(27), we have

[f(g(f(f(f(g(27))))))] = [f(g(f(3)))))]

For f(3), we have

[f(g(f(f(f(g(27))))))] = [f(g(1))))]

Calculating g(1), we have

[f(g(f(f(f(g(27))))))] = f(3)

Lastly, we have

[f(g(f(f(f(g(27))))))] = log₃(3)

Evaluate

[f(g(f(f(f(g(27))))))] = 1

Hence, the solution is 1

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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Bromine is a diatomic molecule since it is typically found in groups of two.

What is the symbol to represent a chemical compound?

An element's one- or two-letter identification is known as a chemical symbol. O for oxygen, Zn for zinc, and Fe for iron are a few instances of chemical symbols. Symbols always start with a capital letter. Lowercase letters are used for the second letter in symbols with two letters.

A subscript appears after the atom to indicate how many of each kind there are. There is no number written if there is just one atom. The number is given as a subscript after the atom if there are multiples of a particular kind of atom.

Br represents the bromine. Bromine is a diatomic molecule and always needs to be bounded to something. Thus it is bounding to itself.

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Answer:

see explanation

Step-by-step explanation:

C = 2πr ( r is the radius )

isolate r by dividing both sides by 2π )

[tex]\frac{C}{2\pi }[/tex] = r

given C = 54 , then

r = [tex]\frac{C}{2\pi }[/tex] = [tex]\frac{54}{2\pi }[/tex] = [tex]\frac{27}{\pi }[/tex] inches

On solving the provided question, we can say that by unitary method With ten power crystals, 35 zombie troops can be raised.

What is unitary method ?

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Liliana raised 14 zombie troops with the help of four dark power stones.

Zombie troops can be increased to a total of 14 with 4 Dark power crystals. Zombies can be raised with 1 Dark power crystal, or 14/4.

Zombie soldiers can be raised using 1 Dark power crystal, or 7/2.

Zombie troops can be generated with 1 Dark power crystal by adding 10 to 7/2. You can produce 5 * 7 zombie troops with 1 Dark power crystal.

35 zombie troops can be generated with 1 dark power crystal.

With ten power crystals, 35 zombie troops can be raised.

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The better deal would be 500 individual nerds candy for $5.

One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. The equal partition of bigger groupings into smaller parts is referred to as division.

The order of work assigned to and completed by the team of employees in order to optimize efficiency is known as the division of labor.

The splitting down of a job into multiple separate parts that make up the total is referred to as the division of labor. 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.

Thus, The better deal would be 500 individual nerds' candy for $5 since you will have more candy and it will last longer.

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You ran 1/8 of miles more today than yesterday.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

Miles you ran yesterday is three fourths of a mile.

Let 1 mile be M.

Miles you ran yesterday = 3/4 M

Today you ran seven-eighths of a mile.

Miles you ran today = 7/8 M

Difference of miles = 7/8 M - 3/4 M

3/4 is same as 6/8.

Difference of miles = 7/8 M - 6/8M

                                = 1/8 M

Hence you ran 1/8 of miles more than yesterday.

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Answer:

  1/2

Step-by-step explanation:

You want to know the frequency of the function f(x) = 3cos(πx) -2.

For frequency f, the basic function (before vertical scaling or translation) will be written ...

  f(x) = cos(2πfx)

That is, we can find the frequency by comparing the arguments of the cosine function:

  πx = 2πfx

  f = (πx)/(2πx) = 1/2

The frequency of the function is 1/2.

__

Additional comment

You will notice in the attached graph that there is 1/2 period in 1 horizontal unit. A full period takes 2 horizontal units, so the frequency is ...

  (1 period)/(2 units) = 1/2 periods/unit.

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On solving the provided question, we can say that - the percentage of the data is 5% = 5/100 = 0.05

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

According to the authors, "the bases will be virtually totally present in their most probable forms. If this is the case, then only adenine and thymine and guanine and cytosine are viable base pairs, and the requirements for creating hydrogen bonds are more stringent (lines 31-35).

Options C and D are erroneous because the table does not support the authors' postulated pairing of nitrogenous bases in DNA molecules.

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If a train travels 283. 8km in 4. 4 hours, the train travels 71km in 1 hour and the train travels 114.5km in 2.5 hours.

Based on the assumption that the train is traveling at a constant speed throughout its journey.

To find the speed the train travels , we divide the total distance by the total time:

speed = 283.8km/ 4.4 hours

speed = 64.5 km/h

To find the distance the train travels , we multiply the speed of the train by the total time:

Distance travelled in 1 hour = 64.5 km/ hour × 1 hour

Distance travelled in 1 hour = 64.5 km

Distance travelled in 2.5 hours = 64.5 km/hour x 2.5 hours

Distance travelled in 2.5 hours = 161.25km

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The function of the scenario is f(x) = 18.5(1.06)^x

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

Initial value = $18.50

Rate = 6%

The function of the scenario is then represented as

f(x) = Initial value * (1  + rate)^x

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

f(x) = 18.5(1 + 6%)^x

Evaluate

f(x) = 18.5(1.06)^x

This means that

x = 10

So, we have

f(10) = 18.5(1.06)^10

Evaluate

f(10) = 33.13

This means that

x = -15

So, we have

f(-15) = 18.5(1.06)^(-15)

Evaluate

f(-15) = 7.72

Hence, the price is $7.72

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Answer:

y = 7/2x + 5

Step-by-step explanation:

The slope intercept form is: y = mx + b

Our equation is

7x -2y = -10

We subtract 7x both sides

-2y = -7x - 10

Divided by -2, both sides

y = 7/2x + 5

So, the answer is y = 7/2x + 5

No, the tangents cannot intersect outside the circle.

When tangents intersect outside a circle, the measure of the angle they form is one half the difference of the intercepted arcs. Since the tangents are at the endpoints of the same diameter, both intercepted arcs would have to measure 180 degrees.

tangent

a tangent is the line drawn from an external point and passes through a point on the curve.

One real-life example of a tangent is when you ride a bicycle, every point on the circumference of the wheel makes a tangent with the road.

curve

A curve is a shape or a line which is smoothly drawn in a plane having a bent or turns in it.

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Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.

You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.

Finding the distance and the time is necessary to calculate speed.

In this situation, you must deduct mile marker 88 from 121 to determine the distance.

121 - 88 = 33mile

Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.

The next step is to divide the distance by the time: 33/0.5 = 66 mph.

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Answer:

a) 3[tex]x^{4}[/tex]

b) 1024[tex]x^{10}[/tex]

Step-by-step explanation:

[tex]\frac{12x^{7} }{4x^{3} }[/tex]

[tex]\frac{3(4)xxxxxxx}{4xxx}[/tex]  We can cancel out a 4 and 3 x's.  That leaves

3xxxx

or 3[tex]x^{4}[/tex]

[tex](2x)^{2}[/tex] x [tex](2x)^{3}[/tex] x [tex](2x)^{5}[/tex]  can be written in expanded form

[(2)(2)xx] x [(2)(2)(2)xxx] x [(2)(2)(2)(2)(2)xxxxx]

(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)xxxxxxxxxx

1024[tex]x^{10}[/tex]

The circumference of the circle is 43.98 in.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.

Given:

Pia drew a circle with a circumference of C and a diameter of 14 in

We have to find the circumference of the circle.

Since,

Circumference = 2*π*r

Here

Diameter of circle = 14 in.

⇒ Radius of circle = 7 in.

⇒ Circumference = 2*π*7 = 43.98 in.

Hence, the circumference of the circle is 43.98 in.

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