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16. Determine if the functions represent even, odd, or neither.

All normal density curves are symmetric and have a peak at the mean. 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.

All normal density curves are symmetric. This means that the curve looks the same to the right and left of the mean (μ). The curve reaches its peak at the mean, which is the highest point on the curve. The area under the curve is equal to 1. The area under the curve that is within one standard deviation (σ) of the mean is equal to 0.68. This means that 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.

The formula for calculating the area under the curve within one standard deviation of the mean is:

Area = 0.68 * 1

The formula for calculating the area under the curve within two standard deviations of the mean is:

Area = 0.95 * 1

These formulas can be used to calculate the area under the curve for any normal density curve.

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In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

A number's exponent tells you how long you will need to multiply it in order to get the result. For instance, because 8 is multiplied by itself 3 times, 8 8 8 can be written as 83.

Here, 3 is the "exponent" or "power," which indicates how many times the number 8 is multiplied by itself, and 8 is the "base," which stands for the number being multiplied.

The number of times a number must be multiplied by itself is what a power or exponent, in essence, indicates. The base in this situation can be any integer, fraction, or decimal. Any value, positive or negative, can be assigned to the exponent.

Given

[tex](1/4)^{x-2} = 16[/tex]

[tex](1/4^{x-2}) = 16[/tex]

1 = 16 × [tex]4^{x-2}[/tex]

1 = 16 × [tex](2^2)^{x-2}[/tex]

[tex]$1 = 16 \times \frac{ 2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{16}[/tex]

[tex]$1 = 2^{2x}[/tex]

1 = 2²⁽⁰⁾ The only possible exponent that values in 1 is when exponent is 0

1 = 1

x = 0

Thus, In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

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The probability of 5 heads in 10 flips.

A coin is flipped 10 times and we want to find the probability of getting exactly 5 heads.

This situation is a binomial distribution because it involves a fixed number of trials (10) and each trial has a fixed probability of success (1/2). . The probability of obtaining exactly 6 successes in 10 trials is given by the formula P(x) = nCx * px * (1-p)n-x. In this situation, the probability is P(x) = 10C6 * 0.26 * 0.84 = 0.17496. The probability of getting exactly 5 heads can be calculated using the formula P(X=5) = 10C5 * 0.5^5 * 0.5^5 = 0.246. This is the probability of 5 heads in 10 flips.

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Complete question:What is the probability of getting 5 heads when you toss a fair coin 10 times?

The possible sets of five tiles that she could have pulled out are (2,3),(3,2)

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

Given;

Number of tiles asha pulled out=5

Bag contains only positive and negative x and x² tiles

So, the equation will be

-x^2+x=5

x^2-x+5=0

Now,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

x= 1 +[tex]\sqrt{1-4*-1*-5}[/tex])/2

x=2,3

x=3,2

Therefore, the quadratic equation solution will be (2,3),(3,2)

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The probability that it is a caramel truffle is 6/13.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A box contains only orange truffles, strawberry truffles, and caramel truffles and the ratio of orange truffles to strawberry truffles is 3 : 4.

Also given, The probability that it is an orange truffle P(O) is 3/13,

Hence  The probability that it is a strawberry truffle P(S) = 4/13.

Therefore, The probability that it is a caramel truffle P(C) is = 1 - 3/13 + 4/13.

= 1 - 7/13.

= 6/16.

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Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.

The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.

Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.

5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.

Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.

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Answer: c

Step-by-step explanation:

Answer:

Slope intercept form =  y=mx+b

So

y-1=x

Add 1 to both sides

y=x+1

Answer:

It belongs in quadrant 3.

Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinality (or the cardinal number) of a set. Let us take an example:

A = {1, 2, 3, 4, 5 }

Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5. Some commonly used sets are as follows:

N: Set of all natural numbers

Z: Set of all integers

Q: Set of all rational numbers

R: Set of all real numbers

Z+: Set of all positive integers

A non empty is a set that has one or more elements.A “set” is just a well-defined collection of distinct objects, and their union—the set—is an object itself. A set can contain anywhere from 0 to an infinite number of items.

Finite sets are sets having a finite/countable number of members. Finite sets are also known as countable sets, as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members

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Answer: 311/500 and 62.22%

Step-by-step explanation:

Fraction: 0.622 = 622/1000 = 311/500

Percent: 0.6222 = 62.22 % (Move decimal 2 places down)

The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.

To convert 0.622 to a fraction in simplest form, write it as follows:

0.622 = 622/1000

Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

622/1000 = (311 × 2)/(500 × 2)

                 = 311/500

So, 0.622, when expressed as a fraction in simplest form, is 311/500.

To convert 0.622 to a percent, multiply it by 100:

0.622 × 100 = 62.2%

Therefore, 0.622 is equivalent to 311/500 or 62.2%.

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The purchase cost of fixtures can become tax deductible is referred to as a true statement.

This is referred to as the imposition of compulsory levies on individuals or entities by governments in other to fund government spending and various public expenditures.

Office fixtures such as furniture would typically be considered a long-term asset because it isn't typically replaced on a yearly basis which is why they are not deductible from a business's taxable income. However in a scenario where the fixtures start going through the process of depreciation, amortization or depletion then it becomes tax deductible.

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The values of x if the two expressions equal are all real numbers.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression ,

(x-2) (x+6) / 7 (x+6)  =  x-2/ 7

So, in LHS x+6 can be cancelled

and we get,

=x-2/ 7

which is same as the RHS from the given expression .

So, As the both LHS and RHS are equal , if put any value Both remains same

Hence, The values of x if the two expressions equal are all real numbers.

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Legal precedent means that a decision on a definite principle or question of law has already been made by a court of higher authority, such as a call or supreme court. below such a decision, lower courts defer to, or adhere to, that prior decision in similar cases.

The commitment of lower courts may be used as precedent for courts of similar jurisdiction, but higher courts are not bound by the resolution of lower courts.

The use of legal precedent helps secure court rulings remain consistent among similar cases. To this end, courts are bound to cling to prior decisions made by a higher court on a same legal matter.

Because a judge is bound by these previously made decisions, this is mentioned to as binding precedent. anew, following the principle of glare decisis, binding precedent promotes the maintenance of answers to legal questions already established.

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The quotient of the expression,

9(7y - 15) /  (110 - 6y ÷ 4) is 18(7y - 15) / (55 - y).

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

We have an expression,

9(7y - 15) /  (110 - 6y ÷ 4)

Simplifying,

9(7y - 15) /  (110 - 6y ÷ 4),

= 9(7y - 15) x 4 / (110 - 6y)

= 36(7y - 15) / (110 - 6y)

= 18(7y - 15) / (55 - y)

Therefore, the quotient is 18(7y - 15) / (55 - y).

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Pareto chart is a type of bar graph which often displays the data in descending order of frequency.

It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.

For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.

Toga: 6

Hayride: 6 + 4 = 10

Beer Bash: 10 + 8 = 18

Masquerade: 18 + 2 = 20

The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.

Toga: 6 (30%)

Hayride: 10 (50%)

Beer Bash: 18 (90%)

Masquerade: 20 (100%)

Hence, the Pareto chart for the given data is as follows:

Toga: 30%

Hayride: 20%

Beer Bash: 40%

Masquerade: 10%

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The length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0) is; 3√2

The length of the mid-segment of a trapezoid is half the sum of the lengths of the two parallel sides, AB and CD. T

The  vertices are;

A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)

Thus;

Length of sides AB and CD

length = √(x₂ - x₁)² + (y₂ - y₁)²

AB =√(2 - 0)² + (5 - 3)²

AB = 2√2

length = √(x₂ - x₁)² + (y₂ - y₁)²

CD = √(2 - 6)² + (0 - 4)²

CD = 4√2

Formula to use for the mid segment is;

Mid segment = (AB + CD)/2

                      = (2√2 + 4√2) / 2

                      = 3√2

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4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.

An expression is combination of variables, numbers and operators.

Let m be the number of marbles.

The number of marbles April has be m.

Given that Carter has 10 fewer marbles than April.

If Carter has 10 less than m, that's m - 10.

Nicholas has 3 times as many marbles as April.

3m

marbles Carter and Nicholas have altogether

m-10+3m

4m-10

Hence, 4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.

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The rate at which the water is now flowing from the tap is 50 cubic centimeters per second.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity.

Given that,

Time taken to fill the watering can of 4 liter = 40 seconds.

4 liter = 4000 cm³

Time taken to fill the watering can of 4000 cm³ = 40 seconds

Unit rate of flow of water = 4000 / 40 = 100 cm³ / sec

Now the rate at which water flows is halved.

Rate = 100 / 2 = 50 cm³ / sec

Hence the rate of the flow of water now is 50 cubic centimeters per second.

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The complete question is as follow :

Water flows at a steady rate from a tap it takes 40 seconds to fill a 4 liter watering can from the tap. The rate at which water flows is halved.

4litre=4000cm³

Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimeters per second (cm³/s).

Answer:c

Step-by-step explanation:

The slope forms a uniform solution in each square box as shown in the drawing

here, s is the value or answer.

SOLUTION -

[tex] \frac{1}{2} = \frac{3}{6} \\ 1 \\ \frac{1}{2} = \frac{1}{2} \\ = \frac{1}{m } = \frac{1}{2} \\ m = 2[/tex]

The solution to the algebraic expression 3y - (2y - 3) ÷ 4 is; (10y + 3)/4

The algebraic expression is given as;

3y - (2y - 3) ÷ 4

With the aid of order of operations named PEMDAS which is an acronym for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction. Thus, we can rewrite the expression as;

3y - (2y - 3)/4

The common denominator is 4 and when we distribute we will have;

(4(3y) - 2y + 3)/4

= (12y - 2y + 3)/4

= (10y + 3)/4

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Answer:

7.5

Step-by-step explanation:

Since the segments are parallel, the side segment lengths are proportional.

8/10 = 6/x

4/5 = 6/x

4x = 30

x = 7.5

The rocket was at a height of 19.75 meters after 0.5 seconds

The rocket hit the ground after 8.02 seconds

The maximum height is 81 m.

An equation is an expression that shows the relationship between numbers and variables.

The height (h) of the rocket t seconds after launch is modeled by:

h(t) = -5t² + 40t + 1

a) After 0.5 seconds:

h(0.5) = -5(0.5)² + 40(0.5) + 1 = 19.75 meters

b) The rocket hit the ground when h(t) = 0, hence:

-5t² + 40t + 1 = 0

t = 8.02 s

c) The maximum height is at h'(t) = 0

h'(t) = -10t + 40

-10t + 40 = 0

10t = 40

t = 4 s

h(4) = -5(4)² + 40(4) + 1 = 81 meter

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Answer:

H = 20

Step-by-step explanation:

Looks like you got everything correct. Nice!

For your last one, let's get H by itself. Since 1/2 is division, let's multiple it by 2 to turn it into one. Because you multiply by 2 on the left side, you have to on the right side also...

(1/2)(2) = 1

(1)(h) = h

On the other side, 10(2) = 20.

Combining the 2, H = 20

Answer:

You do not need to add any skim milk.

Step-by-step explanation:

Step-by-step explanation:

percentages are represented by hundredths in calculations.

2 1/2% = 2.5% = 0.025

2% = 0.02

we are mixing the 3 L 2.5% milk with x L of 0% milk.

and we are ending up with (3 + x) L of 2% milk.

so, we have

3×0.025 + x×0 = (3 + x)×0.02 = 3×0.02 + 0.02x

3×0.005 = 0.02x

0.015 = 0.02x

x = 0.015/0.02 = 0.75

so, 0.75 L have to be added to dilute the milk to 2%.

Answer: The total cost for two people to go to the movies three times is 3x2 = 6x dollars.

The cost of a bag of popcorn is $4 and they share one bag of popcorn each time they go to the movie, so the total cost of popcorn is 4*3 = $12 dollars.

So the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12

So an expression to represent the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12.

Step-by-step explanation: