Ollowing: f(x) = x² - 8x +4; g(x) = 4x − 3; and h(x) = x + 2.
Complete the following: (hg)(x)

y=7 is One of line M's potential equations.

Let L and M be two lines that are perpendicular to each other. Slope of line is given by m=x 2 −x 1/ y 2​ −y 1

If the denominator is zero, or if the value of the x-coordinate is the same at all points, the value of m is undefined. Every point lying on L has the same value of the x-coordinate because L has an undefined slope.

L is a vertical line because it is parallel to the Y-axis.

Lines that are vertical and horizontal are perpendicular to one another.

∴ Line M will be parallel to the X-axis since it is perpendicular to line L.

Every point located on M will have a constant y-coordinate.

∴ m=0 for M.

Thus, y=7 is one of line M's potential equations.

​

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​

The value of [tex]$\lfloor \sqrt{X} \rfloor$[/tex] can be any number between 10 and 13, since 14 is not an integer.

Let x  be the random variable denoting the real number selected uniformly at random between 100 and 200.

The square root of [tex]$X$, $\sqrt{X}$,[/tex]  will be a real number between 10 and 14. The floor function, [tex]$\lfloor \sqrt{X} \rfloor$[/tex] will take the integer less than or equal to[tex]$\sqrt{X}$.[/tex]This means that the value of [tex]$\lfloor \sqrt{X} \rfloor$[/tex] can be any number between 10 and 13, since 14 is not an integer.

For example, if [tex]$X = 150$[/tex], then [tex]$\sqrt{X} = 12.25$[/tex], so [tex]$\lfloor \sqrt{X} \rfloor = 12$[/tex]

In summary, for any real number selected uniformly at random between 100 and 200, the value of[tex]$\lfloor \sqrt{X} \rfloor$[/tex] is any number between 10 and 13.

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The first step in evaluating 2+7. 12/6-3² is to substitute the values for the numbers and calculate the sum of 2+7, which is 9.

Evaluating is the process of making judgments about something based on a set of criteria. It involves analyzing and assessing a subject and making a determination of its value or worth. This can be done for a variety of things, such as an essay, a project, an individual or group, or a product. Evaluation is a crucial part of the decision-making process and involves a careful consideration of all relevant information and factors. It helps to identify strengths and weaknesses, and determine the effectiveness of something. Evaluating is also used to measure performance, identify areas for improvement, and make comparisons.

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(a) It will take approx 10.2 years to double your principal at 7% interest.

(b) The required rate of interest to double our income in 2 years is approx 44%

(a)    Given,

                  Annual rate of interest = 7%

                    Let the principal be [tex]x[/tex].

         Formulae for compound interest :

                    [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Substituting the value of   [tex]P , r , n[/tex] in above formulae.

                  [tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{0.07}{1})^{1t}\\\\2 = 1.07^{t} \\\\t=\frac{ln(2)}{ln(1.07)\\}\\\\t = 10.244768[/tex]

Therefore, it took approx. 10.2 years to double your principal at 7% interest.

(b) Given,

                  The annual rate of interest = [tex]r[/tex]%

                    Let the principal be [tex]x[/tex].

         Formulae for compound interest :

                         [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

we want our money to double in 2 years

                         [tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{r}{1})^{2}\\\\2 = (1+r)^{2} \\\\\sqrt{2} = 1 + r\\\\r=0.44[/tex]

Therefore, the required Rate of interest is approx 44%.

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Answer:

*50

Step-by-step explanation:

Sum of the interior angle

(n - 2) 180

From the question n is 3.

=(3 - 2) 180

=(1) 180

=180

The value of x

x + (x + 5) + (x + 25) 180

=x + x + x + 5 + 25 = 180

=3x + 30 = 180

=3x = 180 - 30

=3x = 150

=3x/3 = 150/3

x = 50

Therefore the value of x is 50.

0.30 is the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

Remember that

z =(x - μ)/σ

where

μ=509

σ=121

so

Find out the value of Z for x=200

Z =(200 - 509)/121

Z=-2.5537

Find out the value of Z for x=450

Z=(450-509)/121

Z=-0.4876

Hence, 0.30 is the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.

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Chemical A's rate law may be zero order and is unaffected by the ratio of reactant to product concentrations.

For the zero order reaction, [tex]$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$[/tex]

Rate equation is : Rate [tex]$=\mathrm{k}[\mathrm{A}]^0[\mathrm{~B}]^0$[/tex]

As a result, the pace of the reaction is unaffected by the amounts of reactant and product present.

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Answer:

120

Step-by-step explanation:

This is simply because 0.25 is 1/4 and 30 ÷ 1/4 is the same as 30 × 4/1 which equals to 120

Answer:

120

Step-by-step explanation:

multiply 100 in the numerator and denominator to remove the decimal point.2

30×100/0.25×100

=3000/25

=120

The conclusion about angles B and C is that the angles are equal angles

How to determine the true statement?

The given parameters are:

Angle A and Angle B are supplements

Angle A and Angle C are supplements

Supplementary angles add up to 180 degrees.

This means that

A + B = 180

A + C = 180

Subtract the two equations

So, we have

A - A + B - C = 180- 180

Evaluate the like terms

So, we have

B - C = 0

Add C to both sides

B = C

Hence, both angles are congruent angles

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The total surface area is 28 square units.

Each of the 6 faces in the original cube has an area of 2* 2 = 4 square units. Thus, the original figure's surface area as a whole was 24 square units.

The new figure has the same surface area as the old one, plus six new faces that each have an area of one dollar per square unit, for a total surface area increase of six dollars. However, the 1 square unit of the bigger cube's top and the 1 square unit of the smaller cube's bottom are not surfaces and do not contribute to the surface area.

This results in a total surface area of 24 + 6 - 1 - 1 = 28 square units.

Therefore, The total surface area is 28 square units.

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Answer:

10 units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

To find the distance between two points, substitute the given points into the distance formula and solve for d.

Given points:

[tex]\begin{aligned}\implies d&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(2-(-8))^2+(-4-(-4))^2}\\&=\sqrt{(10)^2+(0)^2}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]

However, as the y-values of the two given points are the same, we can simply find the difference between the x-values of the two points to find the distance between point A and B:

[tex]\begin{aligned}\implies \textsf{Distance}&=x_B-x_A\\&=2-(-8)\\&=2+8\\&=10\end{aligned}[/tex]

Therefore, the distance between point A and point B is:

Mathematic homework takes longer. It takes 2/3 h longer than language arts homework. Mathematic homework takes longer to complete than language arts homework. We can compare these two fractions by converting them to the same denominator.

Language arts homework: 4/9 h

Mathematic homework: 2/9 h

We can compare these two fractions by converting them to the same denominator.

Language arts homework: 4/9 h = 8/18 h

Mathematic homework: 2/9 h = 4/18 h

Mathematic homework takes 2/3 h longer than language arts homework.

Mathematic homework takes longer than language arts homework, by 2/3 h.

Mathematic homework takes longer to complete than language arts homework. We can compare these two fractions by converting them to the same denominator. Language arts homework takes 4/9 h, or 8/18 h, while mathematic homework takes 2/9 h, or 4/18 h. Mathematic homework takes 2/3 h longer than language arts homework. This means that mathematic homework takes more time to complete than language arts homework, by 2/3 h.

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The water Ms. Morales put in the pool in terms of π is  [tex]\pi[/tex]6561inch^3

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Diameter= 54 in.

Height of pool= 12ft

Now,

3/4 th height of pool;

3/4 x 12= 9inch

Volume= [tex]\pi r^{2}h[/tex]

=[tex]\pi[/tex]27x27x9

=[tex]\pi[/tex]6561inch^3

Therefore, the volume of pool will be [tex]\pi[/tex]6561inch^3

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The win percentage of total 78 boys are 29.49%, 51.28% and 19.23% and of total 53 girls are 33.96%, 18.87% and 47.17% in basket ball, baseball and fencing respectively.

A percentage is a number or ratio in mathematics that represents a fraction of 100. It is one of several methods for representing a dimensionless relationship between two numbers; others include ratios, fractions, and decimal.

The symbol "%" written after a number is commonly used to represent percentages. They can also be indicated by adding "percent" or "pct" to the end of the number. 35%, for example, is represented by the decimal 0.35, as well as the fractions 35/100 and 7/20.

Total boys = 23 + 40 + 15

                  = 78

Win percentage in basket ball = 23/78 × 100

                                                   = 29.49%

Win percentage in baseball = 40/78 × 100

                                                   = 51.28%

Win percentage in fencing = 15/78 × 100

                                                   = 19.23%

Total girls = 18 + 10 + 25

                  = 53

Win percentage in basket ball = 18/53 × 100

                                                   = 33.96%

Win percentage in baseball = 10/53 × 100

                                                   = 18.87%

Win percentage in fencing = 25/53 × 100

                                                   = 47.17%

Thus, The win percentage of total 78 boys are 29.49%, 51.28% and 19.23% and of total 53 girls are 33.96%, 18.87% and 47.17% in basket ball, baseball and fencing respectively.

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Answer: x=4

Step-by-step explanation:

Firstly, x+3 is in absolute value and absolute value basically turns that into positive, which brings us to x+3=7. Now, use your basic algebra skills to subtract 3 form both sides and get x=4. Hope this helps!

Answer:

Two roots: -10 and 4

Step-by-step explanation:

Since the expression inside the modular brackets can be positive or negative, the equation can have two different roots. And it is solved for the positive and negative options.

Positive option:

x+3=7
x=7-3
x=4

Negative option:

x+3=-7
x=-7-3
x=-10

The equation is x² - 7x+11 is in form of quadratic equation ax²+bx+c where a = x² , b = -7 and c = 11 .

Option B is correct.

Quadratic equations are second-degree algebraic expressions with the form ax² + bx + c = 0. The word "quadratic" comes from the word "quad," which means square. To put it another way, an "equation of degree 2" is a quadratic equation. Numerous situations call for the use of a quadratic equation.

Factoring  x²-7x+11

The first term is,  x²  its coefficient is  1 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  11

                                                    x² - 7x  + 11  = 0

When two things are multiplied together and both depend on the same variable, quadratic equations are frequently used. A quadratic equation is used, for instance, when working with area when both dimensions are written in terms of the same variable.

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The upper limit of y is not given, the integral cannot be evaluated at this point.

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line can be determined by the following integral:

V = ∫-5^y [π(y-sin(x))^2]dx

The integral is set up by breaking the region up into slices that are perpendicular to the y-axis. The width of each slice is equal to dy and the height of each slice is equal to the area of the cross-section of the solid, namely π(y-sin(x))^2. The integral is then evaluated from the lower limit of y=-5 to the upper limit of y, which is determined by the equation of the given curve, y=sin(x). As the upper limit of y is not given, the integral cannot be evaluated at this point.

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Answer: C - 5 cups

Step-by-step explanation:

Hello! The art teacher mixes 3 cups of blue paint with 2 cups of red paint.  Since the art teacher combines the two, you have to add the two.  3 + 2 = 5, which should be your answer.  Hope this helps!

Given:

Total Population = 500  millions

Population Under 16 Years of Age or Institutionalized = 120 millions

Not in Labor Force = 150  millions

Unemployed = 23 millions

Now,

A) Labor force

= Total population – Population under 16 years of age – Not in labor force

= 500 – 120 – 150

= 230 millions

B) Unemployment rate [tex]$=\frac{\text { Unemployment }}{\text { Labor force }} \times 100 \%$[/tex]

or

Unemployment rate [tex]$=\frac{23 \text { million }}{230 \text { million }} \times 100 \%$[/tex]

or

Unemployment rate [tex]$=10 \%$[/tex]

The complete question is,

Assume the following data for a country:

Category Number of People (in Millions)

Total Population 500

Population Under 16 Years of Age or Institutionalized 120

Not in Labor Force 150

Unemployed 23

Part-Time Workers Looking for Full-Time Jobs 10

A) What is the size of the labor force (in millions)?

B) What is the official unemployment rate (in percentage)?

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Answer:

Democracy is the best form of government because it promotes equality and representation of all citizens, protects individual rights and freedoms, and encourages participation and accountability in the political process.

The statement b(14) = 170 is interpreted using the function 1850 - 120w = b to be:

When w is 14 b is equal to 170

The function 1850 - 120w = b  as in the problem is a linear function.

A linear function is one which all the parameters has exponents of one. In the linear function parameters are defined below

b = the output value

w = the input value

120 = slope

1850 = the y intercept

The statement b(14) = 170 means that at input of 14 the out put is 170. this is shown mathematically

1850 - 120w = b

1850 - 120 * 14 = b

1850 - 120w = 170 = b

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The table of values for the equation xy =5 are

x       y  

5       1

10     1/2

15     1/3

20   1/4

25    1/5

The relationship between the various data points is displayed using tables of values. In scientific lesson, a table of values could be used. Tables of values are used by scientists and researchers to record their data, which is subsequently examined for patterns. Then, they can use this pattern to forecast things.

In the problem, the equation to derive the table of value is xy = 5, this is re written to be y = 5/x

The values of y are solved as follows

For x = 5, y = 5/5 = 1

For x = 10, y = 5/10 = 1/2

For x = 15, y = 5/15 = 1/3

For x = 20, y = 5/20 = 1/4

For x = 25, y = 5/25 = 1/5

Table of values

x       y  

5       1

10     1/2

15     1/3

20   1/4

25    1/5

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The end behaviour of the graph shows that the range of the graph ranges from 0 to ∞.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

In the given image the graph is showing a parabola symmetric about the y-axis. The range of the graph is varying from 0 to ∞. The graph's end behaviour indicates that the graph's range is from 0 to.

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The given equation 9x2 + 3xy + 15x + 5y in factored form is[tex](3 x+y)(3 x+5)$$[/tex]

Factor [tex]$9 x^2+3 x y+15 x+5 y:[/tex]

Steps

[tex]& 9 x^2+3 x y+15 x+5 y \\[/tex]

[tex]& =\left(9 x^2+3 x y\right)+(15 x+5 y)[/tex]

Factor out 3 x from [tex]$9 x^2+3 x y: \quad 3 x(3 x+y)$[/tex]

Factor out 5 from[tex]$15 x+5 y: \quad 5(3 x+y)$[/tex]

[tex]$$=3 x(3 x+y)+5(3 x+y)$$[/tex]

Factor out common term[tex]$3 x+y$[/tex]

[tex]$$=(3 x+y)(3 x+5)$$[/tex]

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The equation of the line whose x and y -intercepts are -5/3 and 3/5 respectively is  [tex]9x - 25y + 15 = 0\\[/tex] .

Given,

           The x-intercept of a line = -5/3

            The y-intercept of a line = 3/5

   by substituting values in the intercept form of a line:

                         [tex]-\frac{3x}{5} + \frac{5y}{3} = 1\\[/tex]

     On multiplying the equation by 15 both L.H.S. & R.H.S.

                          [tex]-9x + 25y = 15[/tex]

                      ⇒ [tex]9x - 25y + 15 = 0\\[/tex]

Therefore, the Equation of line is   [tex]9x - 25y + 15 = 0\\[/tex] .

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The angle that needs to be used to draw the sector for L will be 60°. Then the number of people who voted for J will be 5,280.

A circular data visual with slices illustrating numerical proportions is called a pie chart. Each slice's angle in a pie chart corresponds to the material it represents.

In an election there were four candidates, J, K, L, and M. Teri is drawing a pie chart to show the results. The sectors for J and K have been drawn. Twice as many people voted for L as voted for M.

Let 'x' be the number of people who voted for L and M. Then the number of people who voted for J and K will be 2x.

The angle that needs to be used to draw the sector for L will be given as,

⇒ 360° × [x / (2x + 2x + x + x)]

⇒ 360° × [x / 6x]

⇒ 360° × 1/6

⇒ 60°

Altogether, 15,840 people voted. Then the number of people who voted for J will be given as,

⇒ [(2x) / (2x + 2x + x + x)] × 15,840

⇒ (1/3) × 15,840

⇒ 5,280

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The probability that the next piece of fruit out of the bag will be an apple is ²/₃.

The probability is the chance that an expected outcome occurs out of many possible outcomes.

Probability is a fractional value that is obtained as the quotient of the expected outcome over the total events.

The number of apples = 4

The number of peaches = 3

The number of plums = 2

Total number = 9

The number of fruits taken out = 3 (2 plumbs and 1 peach)

The remaining fruits in the grocery bag:

The number of apples = 4

The number of peaches = 2 (3 - 1)

The number of plums = 0 (2 - 2)

Total number = 6

The probability of picking an apple out of the remaining fruits = 4/6 = 2/3

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Answer:

3.725

Step-by-step explanation:

10-6.275

4-0.275

3.725

71 poles are needed to fence the rectangular field.

What are the dimensions of the rectangle?

A rectangle is a two-dimensional shape with four sides that has opposite sides that are parallel and equal in length. The length and width of a rectangle are its dimensions. The sides that are equal in length are called the "long sides" or "length," and the sides that are shorter are called the "short sides" or "width."

The total length of the fence required to enclose the rectangular field is the sum of the lengths of all four sides. To find this, we multiply the length and width of the field and then add twice:

Total length = 2 * (63.9m + 104.6m) = 2 * 168.5m

Next, we need to determine the number of poles required to fence the rectangular field. To do this, we divide the total length by the maximum distance between poles (2.4m):

Number of poles = Total length / 2.4m

= 168.5m / 2.4m

= 70.21 poles

Since we can't have a fractional number of poles, we round up to the nearest whole number. This means that we need at least 71 poles to fence the rectangular field.

Hence 71 poles are needed to fence the rectangular field.

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The categories include,

8th grade: left-skewed unimodal

Unimodal and symmetric birth weight

Computer count is unimodal and skewed to the right.

Bimodal adult weight distribution

A graph called a histogram shows the frequency distribution of a few data points for a single variable. Data is frequently divided into a number of "bins" or "range groups" by histograms, which count the number of data points in each bin.

While bar charts show categorical factors, histograms display numerical or quantitative data. In most situations, a histogram's numerical data will be continuous (having infinite values). To attempt to plot a continuous variable's possible values on an axis would be absurd.

Based on the frequency distribution, there are four different types of histograms.

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The complete question is: Classify each histogram using the appropriate descriptions. Identify all of the descriptions that apply for each histogram.