find the domain and range

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

In Mathematics, a mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both classes A and B is given by:

Distance = Mean of class A - Mean of class B

Distance = 12 - 4

Distance = 8.

The mean absolute deviation (MAD) for class A is given by:

MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]

MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]

MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]

MAD A = 1/9 × [18]

MAD A = 18/9

MAD A = 2.

Also, the mean absolute deviation (MAD) for class B is given by:

MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]

MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]

MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]

MAD B = 1/9 × [18]

MAD B = 18/9

MAD B = 2.

Therefore, distance between the means = four (4) times the MAD.

Distance = Means × MAD

8 = 4 × 2.

In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both classes A and B is between one (1) times the MAD and five (5) times the MAD.

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This exercise is about a proof in Euclidian geometry. See the explanation below.

The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).

Given that S is the midpoint of [tex]\overline{QT}[/tex]:

Hence QS = TS ......................1

It is right to indicate that

PQ = TV  ........................2

And ∠RSQ is vertically opposite to ∠TSV

Hence

∠RSQ = ∠TSV.........................3

Given 1, 2, and 3,

Δ QRS ≅ ΔVTS

Therefore,

Δ QRS ≅ ΔVTS

and ∠ RSQ can be termed to be congruent to ∠TSV.

It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.

The angles of a regular polygon will always be congruent, regardless of its size or scale.

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Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]

d₁ = 16 yd

Area = 72 yd²

Rhombus Area =>

[tex]\frac{16 * d2}{2} = 72[/tex]

16*d₂ = 144

d₂ = 9

AC = 9 yd

Hope it helps!

The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.

The important exponent and power rules are:

The given expression is [tex]126^{-3/4}[/tex]

Using calculator: [tex]126^{-3/4}[/tex] = 0.0265

Applying the exponent rule for evaluating the given expression:

[tex]126^{-3/4}[/tex]

Applying the negative power rule;

I.e., a⁻ⁿ = 1/aⁿ

⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]

Applying fractional exponent rule;

I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]

⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]

⇒ 1/[tex]\sqrt[4]{2000376}[/tex]

⇒ 1/37.6077

⇒ 0.0265

Therefore, the value of the given expression is 0.0265.

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The length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft

Area of square = Length ²

Area of square = Length ²

24 = length ²

√24 = √length²

√24 = length

length = 4.898979485566356196394568149411782783

Approximately,

length = 4.9 ft

In radical form

length = √24

= 2√6

Therefore, the length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft

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Step-by-step explanation:

A.

the height, the 17cm leg and half of the baseline (16/2 = 8cm) create a right-angled triangle.

so, Pythagoras applies.

c² = a² + b²

c being the Hypotenuse (side opposite of the 90° angle).

so, we get

17² = height² + 8²

289 = height² + 64

225 = height²

height = sqrt(225) = 15cm

B.

the answer to this is the surface area of the whole box.

it has 5 sides :

bottom : 20×16 rectangle = 320 cm²

left and right : 20×17 rectangles = 340×2 = 680 cm²

front and back : 16×15/2 triangles = 120×2 = 240 cm²

in total that is

320 + 680 + 240 = 1,240 cm² of cardboard

Based on the data given, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is C. There's a weak negative correlation between the variables.

From the information given, it can be seen that the value of y is increasing with the increase in the value of x.

This implies that the correlation is positive. Also, the change in the values of y with x are scattered a lot.

Therefore, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is that there's a weak negative correlation between the variables

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Answer:

The first option:

[tex]x^2-5x+9[/tex]

Step-by-step explanation:

Trust me I am right.

If you need work please ask!

Have a nice day!

Step-by-step explanation:

that is a huge gas tank. that car is practically a tank.

the volume of the gas tank is

4×3×3 = 36 m³

I assume you use liters for liquid mass.

remember

1 meter (m) = 100 centimeter (cm)

10 cm = 1/10 m = 1 decimeter (dm)

1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³

1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters

so, his gas tank contained 36,000 liters.

he used the 36,000 liters in 45 hours.

his corresponding rate of gas consumption was

36,000 liters / 45 hours = 800 liters / hour

Solution -:

[tex] \bold{ \underline{ \underline{Given}}}[/tex]

-3x7x7x7x7x7x7

[tex]\bold{\underline {\underline{lets \: begin}}}[/tex]

We have,,

[tex] -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} [/tex]

As like example→ 2⁴

here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.

The experimental probability the placebo pill induced better concentration on the student exams is 0.64

The question has to do with probability.

Probability is the likelihood of an event occurring.

The probability of an event A is given by

P(A) = number of occurrences of event A/total number of occurrences of all events.

Given that in the study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration.

The event A = students performing better.

Since 64 students performed better, the number of occurrences of event A = 64.

Since there were 100 students, the total number of occurrences = 100.

So, P(A) = P(students perform better)

= number of occurrences of event A/total number of occurrences of all events.

= 64/100

= 0.64

So, the experimental probability the placebo pill induced better concentration on the student exams is 0.64

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After some algebraic handling, the algebraic expression for x in terms of r is x = 1 / r + 1 .

In this question we must make use of algebra properties to clear a variable within a formula only formed by algebraic form, there are no trascendent functions herein. Clearing variables consists in leaving such variables alone in one side of the equivalence. Now we proceed to present the procedure in detail:

The statement presents a typing omission, correct form is shown below:

Solve the equation r = 1 / (x - 1) for x in terms of r.

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The steps to solve a quadratic formula include:

In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

A quadratic equation is an equation that could be written as ax² + bx + c = 0

when a 0. The factoring method is illustrated:

To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.

Set each factor equal to zero.

Solve each of these equations.

Check by inserting your answer in the original equation.

Example 1

Solve x² – 6 x = 16.

Following the steps,

x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0

Factor.

( x – 8)( x + 2) = 0

Therefore, x = 8 and -2.

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Answer:

Below in bold.

Step-by-step explanation:

a) 0.04, 0.1, 0.16

You  add 0.06 to get the next term:

The next 2 are: 0.22, 0.28.

b) 3, 9, 27

You multiply by 3 to get next term

Next 2 are: 81, 243.

c)  0.3, 1/3, 11/30

1/3 - 0.3 = 1/30

11/30 - 1/3 = 1/30

So common difference = 1/30

The next 2 terms are 12/30 and 13/30

= 2/5 , 13/30.

Answer:

  3.16

Step-by-step explanation:

An estimate is usually made to 1 or 2 significant digits. Here, we want an estimate accurate to hundredths, which will be 3 significant digits.

We can round the numbers to some reasonable values, then look at the effect of the rounding error.

  0.235 × 13.467 = (0.25 -0.015) × (13.5 -0.033)

  = 0.25(13.5) -0.25(0.033) -0.015(13.5) +0.015(0.033)

  = 3.375 -0.00825 -0.2025 + (something small)

  ≈ 3.375 -0.008 -0.203 = 3.375 -0.211 = 3.164

  0.235 × 13.467 ≈ 3.16

Note that the values we have can make use of mental math methods.

  0.25 = 1/4 = (1/2)(1/2)

  0.015 = 0.01(1 +1/2)

That is, dividing numbers by 2 mentally is usually not terribly difficult. (Here, it is made more difficult by the odd digits involved.)

  0.25 × 13.5 = (1/2)(13.5/2) = 1/2(6.75) = 3.375

  0.015 × 13.5 = 0.135 +0.135/2 = 0.135 +0.0675 = 0.2025

or, recognizing that 1.35 = 1.5 -.15, ...

  0.015 × 13.5 = (0.01)(1.5) × (10)(1.5-.15) = 1.5²×(.1 -.01) = .225 -.0225

__

Additional comment

A calculator gives the actual product as 3.164745, so our estimate is accurate to hundredths.

The point of intersection of the two lines is at (1,-1)

The given system of expression is shown below

x - 2y = 3

5x + 3y = 2

The solution to the system of equation is the point of intersection

From equation 1

x = 3 + 2y

Substitute into 2

5(3+2y) + 3y = 2

15 +10y + 3y = 2

13y = -13

y = -1

Substitute y = -1 into 3

x = 3 + 2y

x = 3+(-2)

x = 1

Hence the point of intersection of the two lines is at (1,-1)

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Area of shaded region is equal to :

Area of rectangle - Area of two triangles ~

1. Area of rectangle :

[tex]\qquad \sf  \dashrightarrow \: length \times width[/tex]

[tex]\qquad \sf  \dashrightarrow \: 20 \times 15[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 \: \: cm {}^{2} [/tex]

2. Area of first triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 15 \: \: cm {}^{2} [/tex]

3. Area of second triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 \times 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 60 \: \: cm {}^{2} [/tex]

Area of shaded region is :

[tex]\qquad \sf  \dashrightarrow \: 300 - (15 + 60)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 - 75[/tex]

[tex]\qquad \sf  \dashrightarrow \: 225 \: \: cm {}^{2} [/tex]

Work Shown:

m = (y2 - y1)/(x2 - x1)

-4/3 = (a - (-3))/(-3 - 3)

-4/3 = (a+3)/(-6)

-4*(-6) = 3(a+3)

24 = 3a+9

3a+9 = 24

3a = 24-9

3a = 15

a = 15/3

a = 5

Answer:

x = 10°

Step-by-step explanation:

If the two lines are parallel then the two marked angles will be equal.

8x = 2x + 60

Subtract 2x to combine like terms.

6x = 60

Divide by 6.

x = 10

Answer:

12√2.

Step-by-step explanation:

You can do this by the Pythagoras theorem:

20^2 = x^2 + (4sqrt7)^2    where  x is the distance required.

x^2 = 20^2 - (4sqrt7)^2

      = 400 - 112

      =  288

x  = √288

   =  √144 *√2

   =   12√2.

Answer:

about 1800 im sorry if im wrong

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

The missing number in the simplified ratio ?/4 is 3.

Here, we have to find the missing number in the simplified ratio ?/4, we need to determine the ratio of girls to boys in Mr. Stevenson's class.

Given that there are 6 girls and 8 boys in the class, the ratio of girls to boys can be expressed as:

Number of girls : Number of boys = 6 : 8

To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD).

In this case, the GCD of 6 and 8 is 2.

Dividing both 6 and 8 by 2, we get:

Number of girls : Number of boys = 6/2 : 8/2 = 3 : 4

So, the simplified ratio of girls to boys is 3/4.

Therefore, the missing number in the simplified ratio ?/4 is 3.

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......................

a. θ = 36. 9°

b. θ = 114. 2°

a. We use the cosine identity

cos θ = adjacent/hypotenuse

Adjacent = 4cm

Hypotenuse = 5cm

cos θ = 4/ 5

cos θ = 0. 8

Now, we have the inverse of the cosine value

θ = cos^-1 (0. 8)

θ = 36. 9°

b. We use the tangent identity

tan a = opposite / adjacent

tan a = 3. 8/1. 7

tan a = 2. 23

a = tan^-1 ( 2. 23)

a = 65. 8

We have;

a + θ = 180 °; angles on a straight line

θ = 180 - 65. 9

θ = 114. 2°

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The building is 151 meters tall

From the question, we have the following parameters about the building and the man

Man's height = 138 cm

Man's shadow = 149 cm

Building's shadow = 163 m

Based on the above parameters, we have the following equivalent ratio:

Ratio = Height : Shadow

So, we have:

Man's height : Man's shadow = Building's height : Building's shadow

Substitute the known values in the above equation

138 cm : 149 cm = Building's height : 163 m

Remove the units

138 : 149 = Building's height : 163

Express as fraction

138 /149 = Building's height/163

Multiply both sides by 163

Building's height = 163 * 138 /149

Evaluate the product

Building's height = 151 m

Hence, the building is 151 meters tall

So, the complete parameters are:

Man's height = 138 cm

Man's shadow = 149 cm

Building's shadow = 163 m

Building's height = 151 m

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Answer:

B

Step-by-step explanation:

- 6x + 3 ≥ 21 ( subtract 3 from both sides )

- 6x ≥ 18

divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity.

x ≤ - 3

He has thrown 425 free throws if he missed 17

The given parameters are:

Proportion of free throw missed, p = 4%

Number of free throw missed, n = 17

Let the total number of throws be N.

So we have

n = p * N

Substitute the known values in the above equation

17 = 4% * N

Divide both sides by 4%

N = 425

Hence, he has thrown 425 free throws if he missed 17

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The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 6.819.

Given data set: 15, 17, 23, 5, 21, 19, 26, 4, 14

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{15+17+23+5+21+19+26+4+14}{9}[/tex]

Mean [tex]$=\frac{144}{9}[/tex]

Mean = 16

To estimate the difference of each data point from the mean as:

Deviation:

15 - 16 = -1

17 - 16 = 1

23 - 16 = 7

5 - 16 = -11

21 - 16 = 5

19 - 16 = 3

26 - 16 = 10

4 - 16 = -12

14 - 16 = -2

Now we have to square the above deviations we obtain:

1 , 1, 14, 121, 25, 9, 100, 144, 4

To estimate the variance of the above sets:

variance [tex]$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}[/tex]

Variance [tex]$=\frac{419}{9}[/tex]

Variance = 46.5

The standard deviation exists as the positive square root of the variance.

so, the standard deviation [tex]$\sqrt{46.5} =6.819[/tex] .

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