Algebra 2, Quadratics!

The level of scale of measurements is the ratio scale for the data of the average weight of newborn babies in ounces.

There are four scales of measurement: Nominal, Ordinal, Interval, and Ratio.

Nominal scale: In this scale, categories are nominated names (hence “nominal”). There is no inherent order between categories. Put simply, one cannot say that a particular category is superior/ better than another.

Ordinal scale:  The various categories can be logically arranged in a meaningful order. However, the difference between the categories is not “meaningful”.

Interval scale:  The values (not categories) can be ordered and have a meaningful difference, but doubling is not meaningful. This is because of the absence of an “absolute zero”.

Ratio scale:  The values can be ordered to have a meaningful difference, and doubling is also meaningful. There is an “absolute zero”.

Therefore, the level of scale of measurements is the ratio scale for the data of average weight of newborn babies in ounces.

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In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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Answer: X = 15.

Step-by-step explanation: if 12x = 180, simply divide both sides by 12. Doing this will leave just X on one side, and it’s answer, 15, on the other.

The natural frequency of a string increases by tightening the string. The correct option is B.

The frequency at which a system is prone to oscillate when there is no external force acting on it. The normal mode is the oscillation pattern of a system operating at its fundamental frequency.

The sound frequency of musical instruments can be controlled by changing the settings of the strings.  When the string of an instrument is stretched between two points, the tightened strings produce tension. Here, tension refers to how tightly the string is being stretched.

The tightening of the string provides higher frequency. The higher frequency vibrations are carried to the ear which considers high frequency as a high pitch.

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[tex] - 27 = - 14 + x \\ - x = - 14 + 27 \\ - x = 13 \\ x = - 13[/tex]

Answer:

[tex] \sf \: x = - 13[/tex]

Step-by-step explanation:

Given equation,

→ -27 = -14 + x

Now the value of x will be,

→ -27 = -14 + x

→ -14 + x = -27

→ x = -27 + 14

→ [ x = -13 ]

Hence, the value of x is -13.

A polynomial may have some values of the variable for which it will have a zero value. These numbers are referred to as a polynomial's zeros. They are also sometimes referred to as polynomial roots. In order to obtain the solutions to the given problem, we often determine the zeros of quadratic equations.

A polynomial in x has the usual form anxn + an-1xn-1 +..... + a1x + a0, where an, an-1,....., a1, a0, and a 0 are constants, and n is a whole number. Algebraic formulas like x + x + 5, x2 + 1/x2, for instance, are not polynomials since none of the exponents of x in these expressions are whole numbers.

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Answer: 15

Step-by-step explanation: since seven couldnt come theres 3

5x3=15

The volume of a sphere with a radius of 16cm is approximately 17157.28 cm^3

The volume of a sphere can be calculated using the formula

V = 4/3 * π * r^3, where V is the volume, π is approximately 3.14, and r is the radius of the sphere. In this case, the radius of the balls used by the stock person is 16cm. Therefore, we can substitute this value into the formula to find the volume of each ball.

V = 4/3 * π * r^3

V = 4/3 * 3.14 * (16cm)^3

V = 17157.28cm^3

So, the volume of each ball is approximately 17157.28cm^3.

It is important to keep in mind that the volume of a sphere is dependent on the radius of the sphere, so if the radius of the balls were different, the volume would also be different.

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If earth days merely 2 hours long, which means the rotation period of the earth is 2 hours, your weight will become 1/144 of your actual weight.

The weight or gravitational force on a mass can also be considered as centripetal force.

The formula for the centripetal force is:

F = m v²/R

In this case,

m = your mass

v = tangential velocity or earth's rotation speed

R = earth's radius

Recall that speed = distance / time. In the problem, the distance is the circumference of the earth and the travelled time is the rotation period.

v = C/t

t₁ = 24 hours

t₂ = 2 hours

Since the units are the same, we do not need to convert the unit when comparing them.

Notice that the centripetal force is directly proportional to the square of rotation speed.

F ∝ v²

Hence,

F₁ : F₂ = v₁² : v₂²

But v is inversely proportional to rotation period. Hence,

F₁ : F₂ = t₂² :  t₁²

F₁ / F₂ = (t₂ /t₁)²

F₁ / F₂ = (2 /24)²

F₁ / F₂ = (1 /12)²

F₁ / F₂ = 1/144

Hence, your weight will be 1/144 of your actual weight.

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The solution to the given expression 2x²+ 3x + 1 is 3 when substituting x = -2.

Expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

2x²+ 3x + 1

We have to determine the solution to the given expression when x = -2

As per the question, we have

⇒ 2x²+ 3x + 1

Substitute the value of x = -2 in the above expression,

⇒ 2(-2)²+ 3(-2) + 1

⇒ 2(4) - 6 + 1

⇒ 8 - 6 + 1

⇒ 3

Thus, the solution to the given expression is 3.

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The probability that a sample taken from the site will have water content above 12% and below 16% is 0.6102.

To calculate the probability that a sample taken from the excavation site will have water content above 12% and below 16%, we need to find the proportion of the normal distribution that falls between those two values.

First, we need to standardize the values by subtracting the mean and dividing by the standard deviation.

The value of 12% will be standardized as (12-14.2)/2.3 = -0.9565 and,

the value of 16% will be standardized as (16-14.2)/2.3 = 0.7826.

Using a standard normal table, we can find the probability that a standard normal variable is less than -0.9565 and 0.7826

The probability that Z < -0.9565 is approximately 0.1687

The probability that Z < 0.7826 is approximately 0.7789

Therefore, the probability that a sample taken from the excavation site will have water content above 12% and below 16% is:

P(12 < X < 16) = P(Z < 0.7826) - P(Z < -0.9565) = 0.7789 - 0.1687 = 0.6102 or 61.02%

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The  machine drilled at a constant rate, so the depth after 15 hours is

-45 feet.

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.

Given A machine that drills holes,

drilled in 24 hours = -72 feet

the machine drilled at a constant rate,

so drilled in 1 hour = -72/24 = -3 feet per hour

depth in 15 hours = -3 x 15

depth in 15 hours = -45 feet

Hence the depth after 15 hours is -45 feet.

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Answer:

Step-by-step explanation:

There are a total of 39 birds. Of those birds, 18 are macaws and 21 are cockatoos (18 + 21 = 39).

We need to find an answer as a fraction that shows the fraction of macaws out of the total of 39 birds.

18 macaws /39 parrots

This fraction can be reduced, so we need to find a number that will divide into both 18 and 39. The number 3 will divided into both 18 and 39.

18 ÷ 3 = 6

39 ÷ 3 = 13

The fraction can be reduced to 6/13. This is the most we can reduce this fraction because 13 is a prime number.

There are 6 macaws for every 13 parrots.

If Leyanna choose one marble at random, the chances that it is yellow is 4/9 that is 0.44.

Total number of marbles in bag are 9

There are 5 red marbles and 4 yellow marbles

Total number of marbles = 5 + 4 = 9.

Therefore total number of cases is 9

Since there are 4 yellow marbles, the number of favorable outcomes is 4.

So P ( a yellow marble) =Number of favorable cases/ Total number of cases

= 4/9

So probability of choosing a yellow marble is 4/9.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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The real size (actual height) of the model is equal to 16.5 feet.

Scales are an useful resource to represents systems in models at affordable size, scales (r) can be found by means of following ratio:

r = d' / d

Where:

If we know that r = 1 / 1.5 in / ft, d' = 11 in, then the real size of the model is:

1 / 1.5 = 11 / d

d = 16.5

The model has a real size (actual height) of 16.5 feet.

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Answer:

1. 1080x^2y^3

2. 114688x^6y^2

Step-by-step explanation:

1. binomial expansion : 32x^5+240x^4y+720x^3y^2+1080x^2y^3+810xy^4+243y^5

fourth term is 1080x^2y^3

2. binomial expansion:

65536x^8+131072x^7y+114688x^6y^2+57344x^5y^3+17920x^4y^4+3584x^3y^5+448x^2y^6+32xy^7+y^8

third term is 114688x^6y^2

We can start by using algebra to represent the given information. Let x be the amount of check 1207.

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The beginning balance: 1,235.46

The deposit: + 83.49

Check 1206: - 36.86

Check 1207: - x

Check 1208: - 254.34

Ending balance: 842.98

We can then set up an equation to represent the balance after all the transactions are made:

1,235.46 + 83.49 - 36.86 - x - 254.34 = 842.98

Simplifying the equation:

1,235.46 + 83.49 - 36.86 - x - 254.34 = 842.98

1,235.46 + 46.63 - x = 1,087.32

x = 1,235.46 + 46.63 - 1,087.32

x = 194.77

So the amount of check 1207 is $194.77

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Answer:

I don't know ‍♀️

Step-by-step explanation:

Answer:

Discount: $13.20

Final Price: $41.80

Step-by-step explanation:

Original price: $55

Percent discount: 24%

Amount of discount: 24% of $55 = 0.24 × $55 = $13.20

Final price = original price - amount of discount = $55 - $13.20

Actual final price = $41.80

Answer:

Discount: $13.20

Final Price: $41.80

To find the domain and range of a function without a graph is to use algebraic methods.

What is domain in function ?

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

One way to find the domain and range of a function without a graph is to use algebraic methods. For example, if the function is defined by an equation, you can solve for the variables to determine the domain and range. You can also use inequalities or interval notation to express the domain and range.

Another way to find the domain and range is to examine the function's definition and identify any restrictions on the input or output values. For example, if a function is defined in terms of a square root, the input values must be non-negative to avoid a complex output.

To find the domain and range of a function without a graph is to use algebraic methods.

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The possible sequences are:

3,24, 192, 1536, 12288......

3,-24, 192, -1536, 12288 .......

What is a sequence?

an arrangement of two or more things in successive order. the sequential arrangement of two or more things The chronological order. a list of things or ideas that are related in some way. an action or event that follows another or others.

Given that, a₁ = 3 and a₃ = 192.

The sequence is increased rapidly. Thus it is geometric progress.

Assume that the common ratio of the geometic sequence is r.

The nth term of the sequence is [tex]a_n =a(r^{n-1})[/tex]

=[tex]3r^{n-1}[/tex] since a is the first term that is a = 3.

Putting n=3 in the sequnce:

a₃ = 3(r)²

Putting a₃ = 192 in the above equation:

192 = 3(r)²

Divide both sides by 3:

192/3 = r²

r² = 64

r = ±8

When r = 8:

The first five terms of the sequence are

a₁, a₁r¹, a₁r², a₁r³, a₁r⁴

= 3, 3×8¹, 3×8², 3×8³, 3×8⁴

= 3,24, 192, 1536, 12288

When r = -8:

The first five terms of the sequence are

a₁, a₁r¹, a₁r², a₁r³, a₁r⁴

= 3, 3×(-8)¹, 3×(-8)², 3×(-8)³, 3×(-8)⁴

= 3,-24, 192, -1536, 12288

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Answer: -62.7

Step-by-step explanation:

7/10 = 0.7

-62 7/10 = -62.7

Answer:62.7

Step-by-step explanation:

Answer:13

Step-by-step explanation:

You have to use 364 and 28 to answer.

364 divided by 28 equals to 13

Values 4 and 14 will be described as x that are the distance of 5 units from the number 9.

Given that x is a set of numbers such that the distance from x to 9 is 5 units.

so, distance of x, positive or negative, from 9 can be expressed as |x - 9|

since the distance is equal to 5 units therefore the equation can be written using absolute value notation:

|x - 9| = 5

(x - 9) = 5 -> x = 14

or -(x -9) = 5 -> x = 4

Hence, set x = {4,14}

Therefore, set x is {4,14}.

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Answer:

-15

Step-by-step explanation:

Set up the composite function and simplify

The ratios of the segments of both the polygons are not same hence the polygons are not similar. Option 4 is the correct answer.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides).

To create a closed figure, a minimum of three line segments must be connected end to end. As a result, a polygon with at least three sides is known as a triangle and is also known as a 3-gon. An n-gon is a polygon with n sides.

Given that the two polygons which are parallelogram with the opposite sides 2.5 and 1.5, and 9 and 4.8.

For the polygons to be similar, ratios of both the polygons must be equal.

2.5 / 1.5 = 1.66

9 / 4.8 = 1.875

The ratios of the segments of both the polygons are not same hence the polygons are not similar. Option 4 is the correct answer.

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Answer:

-75 + 200y

Step-by-step explanation:

(3-8y) x (-25)

We use distribution to solve

-75 + 200y

Answer:

m∠EPA = 68°

Step-by-step explanation:

Angle EPA is adjacent to angle PAC in parallelogram PACE.

As adjacent angles in a parallelogram sum to 180°:

⇒ m∠PAC + m∠EPA = 180°

⇒ 112° + m∠EPA = 180°

⇒ 112° + m∠EPA - 112° = 180° - 112°

⇒ m∠EPA = 68°

Therefore, the measure of angle EPA is 68°.

False. The statement only gives information about the employer's contribution towards the cost of Kadia's premium and does not state the total cost of the premium or the amount that Kadia will have to pay.

The out-of-pocket expenses you incur when using services, in addition to the monthly premium for a plan, significantly affect your overall health care costs.

The following are included in your plan's total annual expenses:

You must pay your insurance provider a monthly payment over a 12-month period in order to be covered for medical expenses.

Your out-of-pocket expense for medically necessary services before your insurance provider begins to compensate you (except free preventive services)

deductibles and coinsurance: Expenses you pay to your healthcare provider each time you receive treatment, such as $20 for a doctor's visit or 30% of a hospital stay.

Maximum you must pay out-of-pocket each year for services that are covered. Once you've reached this sum, the insurance provider will cover all of your expenses.

The Complete Question.

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The range is calculated when we subtract the lowest value from the highest value.

Range is defined as a difference between the lowest and highest values. In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6.

Range can also refer to a function's entire set of output values.

When a function is applied to its entire set of outputs, its range is the set of outputs it produces.

The full set of all potential values that can be obtained for the dependent variable is the range of a function.

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