Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it

Answer:

let the two numbers be x and y.

Given ,

[tex] \underline{\underline{\frac{x}{y} = \frac{3}{5}}} \\ [/tex]

To find - ratio of squares of the two numbers.

[tex]\longrightarrow \: \frac{ {x}^{2} }{ {y}^{2} } = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ \\ \longrightarrow \: \boxed{\frac{ {x}^{2} }{ {y}^{2} } = \frac{9}{25} }[/tex]

Therefore ,

[tex] \underline{\underline{ratio \: of \: the \: squares \: of \: two \: numbers \: = \: 9 \: : \: 25}} [/tex]

hope helpful! :)

53 is the value of the 99% of the time.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center

Given, Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average survival times of the 16 batteries are Comput.

μ = 50

σ² = 25

n = 16

So, the Population standard deviation

σ² = 25

σ = 5

To find the value 99% of the time

The z-score will be

P(z <Z) = 0.999

P(z < 2.326) = 0.999

Z = 2.326

To find a z score corresponding to a known probability, select fx, Statistical, NORMSINV, and enter the total area to the left of the given value.

Now we determine the z-score using the z-score formula

x = μ + (Z *σ  / √n)

x = 53

Therefore, the value of 99% of the time is 53.

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Complete question:

Probability that the system works is approximately 0.9841.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Let the three events be C₁, C₂ and C₃.

Probability that computer 1 works = P(C₁) = 0.65

Probability that computer 1 does not work = P(C₁') = 1 - 0.65 = 0.35

Probability that computer 2 works = P(C₂) = 0.65

Probability that computer 2 does not work = P(C₂') = 1 - 0.65 = 0.35

Probability that computer 3 works = P(C₃) = 0.87

Probability that computer 3 does not work = P(C₃') = 1 - 0.87 = 0.13

Let the event that at least one of the computer is working is S.

P(S) = 1 - P(no computer is working)

P(no computer is working) = P(C₁' ∩ C₂' ∩ C₃')

We have the operations of the computers are independent of each other.

P(C₁' ∩ C₂' ∩ C₃') = P(C₁') × P(C₂') × P(C₃')

                            = 0.35 × 0.35 × 0.13

                            = 0.015925

P(no computer is working) = 0.015925

P(S) = 1 - 0.015925

      = 0.984075 ≈ 0.9841

Hence the required probability is 0.9841.

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The equation that represents the second step of solution process is 12x-3+27=-24. Thus, option A is correct.

The simplex method is a widely used linear programming methodology for addressing optimization problems. These problems typically involve a function and a number of constraints that are stated as inequalities.

Step 1: 3(4x-1)+27=-24

Step 2: 12x-3+27=-24

Step 3: 12x+24=-24

Step 4: 12x=-48

Step 5: x=-4

A. 12x-3+27=-24.

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Mercury, gallium, and caesium often have low melting points, except gold. The only liquid metal with a 38 °C melting temperature is mercury.

They have high melting and boiling points because melting and boiling require a lot of energy to break through the strong metallic connections present in a metal's massive structure.

Brass: 930 °C (1710 °F) Aluminium Bronze*: 1027-1038 °C (1881-1900 °F) Chromium: 1860 °C (3380 °F) Copper: 1084 °C (1983 °F).

In general, aluminium is an easy metal to melt, and it is easy to get your hands on.  To make aluminum metal shapes, many people melt discarded soda cans made of aluminum. The aluminum should be heated until it melts completely.

Therefore, the melting or boiling point will be higher the more energy is required. Varying metals have different melting and boiling points because the force of attraction between the metal ions differs between them.

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The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other

Let [tex]$V_1, V_2$[/tex] be the two subspaces of V. Suppose [tex]$V_1 \cup V_2$[/tex] is a subspace of V.

Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and[tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]$x_1+x_2 \in V_1 \cup V_2$[/tex].

If and only if one of the subspaces is contained in the other, the union of the two subspaces is a subspace.

But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex]. Either way, by the existence of additive inverses and the closure properties for the subspaces we have:

[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]

Or

[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]

By the associative/commutative properties, we have:

[tex]x_2 \in V_1 \text {, or, } x_2 \in V_1[/tex]

Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or [tex]$x_2 \in V_1$[/tex]. If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex]. If [tex]$x_2 \in V_1$[/tex] for all [tex]$x_2 \in V_2$[/tex] then [tex]$V_2 \subseteq V_1$[/tex]. In either case, we see one subspace is a subset of the other.

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A ∪ B ∪ C is the set of all items in sets A, B, or C.

Region V: Items in A, B, and C

In set theory, the union of two or more sets is a new set that contains all the elements from each of the original sets. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∪ B = {1, 2, 3, 4}.

In this case, A ∪ B ∪ C represents the set of all elements that belong to at least one of the sets A, B, or C.

Therefore, A ∪ B ∪ C represents the set of all items in sets A, B, or C.

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Answer:

A

Step-by-step explanation:

[tex]4\leq x < 4[/tex]

Focusing on the left end of the graph, the x value corresponding to the graph is -4. The circle present at this end of the graph is coloured in, which indicates that -4 is included in the domain.

Focusing on the right end of the graph, the x value corresponding to the graph is 4. The circle present at this end of the graph is NOT coloured in, which indicates that 4 is NOT included in the domain.

A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population.

The following statement is True.

A variable is a trait that can be measured and has several values. Variables include height, age, income, province or country of birth, school grades, and kind of dwelling. Variables can be divided into two types: category and numeric.

A "sampling frame" is a list of all population items to be researched. Probability and nonprobability are the two primary types of sampling methodologies. A simple random sample is a sample drawn from the population in which every member has an equal probability of being chosen.

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The area of the rectangular garden can be calculated as follows: 57 m * 42 m = 2406 m^2.

The ornamental fence with a width of 60 cm has a width of 0.6 m. If the fence is planted inside the perimeter of the garden, the length of the garden will decrease by 2 * 0.6 m = 1.2 m and the width of the garden will decrease by 2 * 0.6 m = 1.2 m.

So, the new length and width of the garden will be 57 m - 1.2 m = 55.8 m and 42 m - 1.2 m = 40.8 m, respectively.

The new area of the garden can be calculated as follows: 55.8 m * 40.8 m = 2270.784 m^2.

Finally, the decrease in area can be calculated as follows: 2406 m^2 - 2270.784 m^2 = 35.216 m^2.

Therefore, the area of the garden will decrease by 35.216 m^2.

Answer:

The width of the ornamental fence is 60 cm, which is equal to 60/100 = 0.6 meters.

The total length of the ornamental fence that will be planted inside the perimeter of the rectangular garden is 2 * (57 m + 42 m) = 2 * 99 m = 198 m.

The decrease in the area of the garden due to the ornamental fence is 0.6 m * 198 m = 118.8 m^2.

Answer:

[tex]y \: = 2cos \: ( \frac{\pi}{5} x) - 3[/tex]

The value of y is 1446.38.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

y = 601 [tex](1.05)^{18}[/tex]

Now,

y = 601 x 2.4066192336911

y = 1446.3781

y = 1446.38

Thus,

y = 1446.38

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The length of the unknown side or, the length of AC = 22.62.

To calculate the length of the unknown side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides or, in familiar algebraic notation, a2 + b2 = c2.

In this Question, side AC is the hypotenuse, so we can use the Pythagorean theorem to find the length of side AC:

AC^2 = AB^2 + BC^2

We know that AB = 12 and BC = 19, so we can substitute these values into the equation:

AC^2 = 12^2 + 19^2

AC^2 = 144 + 361

AC^2 = 505

To find the length of AC, we can take the square root of 505:

AC = √505

Rounded to two decimal places, the length of AC = 22.62.

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By concept of linear equations, The number of birds is 14 and number of lions is 17.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Let no. of birds=x and no. of lions=y

Given heads=31

and feet=96

Therefore, the equations will be

             x+y=31 and 2x+4y=96

from given equations x=14 and y=17.

Hence,

           The number of birds is 14 and number of lions is 17.

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By assuming that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be: $17,836.

A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.

In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.

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The predicted egg production in 2001 is given as follows:

65.6 billion.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The production in 1995 was of 52.7, hence the intercept b is given as follows:

b = 52.7.

In 4 years, the production increased to 61.3, hence the slope m is given as follows:

m = (61.3 - 52.7)/4

m = 2.15.

Hence the function is of:

y = 2.15x + 52.7.

2001 is 6 years,hence the estimate is given as follows:

y = 2.15(6) + 52.7

y = 65.6 billion.

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Answer:

7 child tickets

14   adult tickets

Step-by-step explanation:

Let a = the number of adult tickets

Let c = the number of child tickets

16a + 16c + 672

2c = a  Substitute 2c for a

15a + 16c = 672

16(2a) + 16c = 672

32a + 16c = 672  Combine like terms

48a = 672  Divide both sides by 48

a = 14

2c = a

2c = 14  Divide both sides by 2

c = 7                                                                                                  

The solution of the equation can be obtained as x = 1.

We have to note that the exponential equation can be solved in the form of a quadratic equation and then we can be able to obtain the values that can be able to sort out the equation.

We know that;

e^2x + e^x - 12= 0

Let p represent e^x we would then have

p^2 + p - 12 = 0

If we solve the quadratic we would have;

p = 3 or p = -4

If we discard the negative answer;

e^x = 3^1

x = 1

The solution of the equation x = 1.

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The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

What is Algebraic expression ?

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

Given expression,

7 raised to the power 2 divided by 7 raised to the power 3

7 ^ 2 / 7 ^ 3

The value of a ^ m / a ^ n  = a ^ m-n

= 7 ^ (2-3)

= 7 ^ ( -1)

= 1 / 7 .

Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

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Tyler's current Slugging Percentage is 546 and  current Batting Average is 192.

Slugging percentage is a statistic used in baseball and softball to measure a batter's total number of bases per at bat. It is calculated by dividing the total number of bases earned by the number of at-bats. This statistic is often used to compare batters since it takes into account the number of bases earned in addition to the number of hits. Slugging percentage is an important statistic to consider when evaluating batters since it provides an overall picture of how well a batter is performing. Slugging percentage is usually expressed as a decimal or a percentage, with a higher percentage indicating better performance.

Tyler's current Slugging Percentage is .546. This is calculated by adding the total number of bases earned (74 + 2*13 + 3*11 + 4*4 = 194) and dividing that by the total number of at-bats (383).

Tyler's current Batting Average is .192. This is calculated by dividing the total number of hits (74 + 13 + 11 + 4 = 102) by the total number of at-bats (383).

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The number of girls in the next 200 girls surveyed that would choose their favorite sport as bowling are 8 girls.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Given that 300 girls were asked to name their favorite sport. 12 of the girls named bowling as their favorite.

The percentage of girls that selected the sport is thus:

12/ 300 (100) = 4%

For the next 200 girls, calculate the 4% of the number to get the number of girls who like bowling:

200 (4%) = N

N = (200)(4/100)

N = 8

Hence, the number of girls in the next 200 girls surveyed that would choose their favorite sport as bowling are 8 girls.

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[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{8}}} \implies \cfrac{5 +16}{-7} \implies \cfrac{ 21 }{ -7 } \implies - 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{8}) \implies y +16 = - 3 ( x -8) \\\\\\ y+16=-3x+24\implies {\Large \begin{array}{llll} y=-3x+8 \end{array}}[/tex]

Six categories of integers based on their ones digit are:

The cases when sum or difference of the pair is divisible by 10:

Therefore, no matter which seven integers we choose, there is always a pair that meets the condition.

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Answer:

92

Step-by-step explanation:

We first do 12x7 which equals to 84

Then we add 8 which equals to 92

Answer: x = 8 and YZ = 19

Step-by-step explanation:

mb i focused on the x between a and y and i forgot the x they were talking about was the x in the equations..

since its a bisector, we know that az = yz therefore 2x + 3 = 3x - 5

2x + 3 = 3x - 5

2x + 8 = 3x

8 = x

now we know the value of x, we can plug it into the equation for yz

3(8) - 5

24 - 5

19

therefore, x = 8 and yz = 19

The exponential function r=(0.88)^4t can be written as r=(1-0.12)^4t.

What are exponential functions?

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now,

given exponential function is r(r) = (0.88)^4t

we can rewrite its as  r=(1-0.12)^4t. to find whether it is increasing or decaying. As the - sign shows decrement.

hence,

             Given exponential function is decaying in nature..

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Answer:

im sorry bro i

Step-by-step explanation:

i just need points

When the center angle is 60 degrees, the arc length is measured in 1.047 units.

An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference. An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference. An arc is a kind of curve.

Here,

angle=60°

in triangle BCD,

cos 60=CB/DB

DB= 2 units

radius=1 unit

arc length=2πr*(θ/360)

=2*3.14*1*60/360

=1.047 units

The measure of arc length when central angle is 60 degree is given by 1.047 units.

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This suggests that a gas's pressure decreases as its volume increases. Similar to this, a gas's pressure rises as its volume decreases. The balloon's expansion for the given implies that its volume grows. Boyle's law predicts that its pressure will decrease as a result.

In other words, as the atmospheric gas exerts less pressure on the surface of the balloon, the interior gas expands until the internal and external pressures are equal. This is why weather balloons grow larger as they ascend through the atmosphere to lower pressure regions because the volume of the gas has increased.

You can observe Avogadro's Law whenever you blow up a balloon. By inflating the balloon, you can add moles of gas, which increases the balloon's volume.

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