Noise levels at 5 volcanoes were measured in decibels yielding the following data: 108,133,140,129,136 1. Construct the 98% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
2. Calculate the sample standard deviation for the given sample data. 3. Find the critical value that should be used in constructing the confidence interval.

The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5

The equation of a line can be represented as follows:

y = mx + b

where

Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4

Hence,

perpendicular lines follows the rule below:

m₁m₂ = -1

Hence,

5x - 3y = 4

5x - 4 = 3y

y = 5/ 3 x - 4 / 3

m₁ = 5 / 3

5/3 m₂ = -1

m₂ = - 3 / 5

Hence,

using (-4, 5)

5 = - 3 / 5 (-4) + b

5 = 12 / 5 + b

b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5

Therefore,

y = -3 / 5 x + 13 / 5

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Answer:

  3x +5y = 13

Step-by-step explanation:

The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.

Swapping the coefficients of the given equation, we have ...

  3x -5y = c . . . . . for some constant c

Negating the y-coefficient gives a perpendicular line:

  3x +5y = c

We want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...

  3x +5y = 3(-4) +5(5) = -12 +25 = 13

The equation of the perpendicular line is ...

  3x +5y = 13

__

Additional comment

This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.

Note that equations in standard form want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.

The value of x in the straight line shown in the attached diagram is 64°

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

From the image:

x + 26 + 90 = 180° (sum of angles in a straight line)

hence:

x + 116 = 180

x = 64°

The value of x in the straight line shown in the attached diagram is 64°

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The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.

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

Let x represent the markup, since the store sells the cell phone for $315, hence:

(315 - 140)/140 * 100% = x

x = 125%

The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.

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The interest that Marcos will get is 50000.

The following can be deduced from the information given:

Principal = 50000

Interest rate = 12.5%

Time = 8 years

The simple interest will be:

= (PRT/100)

= (50000 × 12.5 × 8)/100

= 50000

The amount that will be obtained after 8 years will be:

= Principal + Interest

= 50000 + 50000

= 10000

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Answer:

The interest that Marcos will get is 50000.

Answer: -4/15

Step-by-step explanation: Since the base denominator is the same, all we have to do is add the numerators (the denominators stay the same.)

-9 + 5 = -4 which is -4/15.

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Angle x of the triangle PQR is 53 degrees.

Angle x is gotten by alternate angle relationship.

Line AB is parallel to line CD

Therefore,

AB║CD

Hence,

62 + x = 115(alternate angles)

62 - 62 + x = 115 - 62

x = 53°

We got the angle x degrees from alternate angle relationship.

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Answer:

x = 50

Step-by-step explanation:

Angle <BPR and angle <PRD are supplementary angles so their sum is equal to 180

m<BPR + 115 = 180 subtract 115 from both sides

m<BPR = 65

angles:

<APQ, x, and <BPR form a straight line and so their sum is equal to 180

65 + x + 65 = 180 add like terms

130 + x = 180 subtract 130 from both sides

x = 50

Answer: The correct answer is choice A.

Step-by-step explanation:

This is because the triangles have the same angles, but are scaled differently.  Thus because of the scale, there can be no correlation between the sides. Because the triangles share point E you can see that both triangles share the same angle but also notice how lines CD and AB are parallel. This makes all angles identical proving the triangles are the same but different sizes. Concluding that choice A is correct.

The true statement is Line MK is the perpendicular bisector of LN and ML is ≅  MN.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

Δ LMN and Δ LKN are connected at side LN.

As per the information,

Line MK is the perpendicular bisector of LN. and ML ≅  MN.

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Answer: b and d

Step-by-step explanation:

Answer: x > -1, see attached.

Step-by-step explanation:

To solve the inequality, we will isolate the x-variable.

Given:

    3x - 19 > -22

Add 19 to both sides:

    3x > -3

Divide both sides by 3:

    x > -1

To graph, we will use an open circle since it is only greater than and not equal to. Then, we will place this circle on -1. Lastly, we will shade to the right of -1, since it is greater than -1.

Answer:

16 sq. yds

Step-by-step explanation:

1. Split the shape into 2

The small square is 2(2) = 4

The  bigger rectangle is 3(4) = 12

4 + 12 = 16 sq. yds

Answer:

x=180 - 25

x=155

x+ 169=180

x=180-169

x=11

Answer:

it might be greater i think

Answer:

D. 14 units

Step-by-step explanation:

d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-x_{1})^{2} }[/tex]

= [tex]\sqrt{(-5 - (-5))^{2} + (-6 - 8)^{2} }[/tex]

= [tex]\sqrt{0^{2} + -14^{2} }[/tex]

= [tex]\sqrt{0 +196 }[/tex]

= [tex]\sqrt{196}[/tex]

= 14

You have the correct answer. Apply a 180 degree rotation around the point (0,2)

Reason:

We'll connect corners between figures A and B.

Draw a line from the upper right corner of figure A to the lower left corner of figure B. This line is in red (see diagram below).

Draw another line from the lower right corner to the upper left corner. This line is in blue.

The red and blue lines intersect at the center of rotation (0,2)

The line segments constructed consist of endpoints of "before" and "after". For instance, the upper right corner in figure A rotates to the lower left corner of figure B. This happens because of the 180 degree rotation.

Note: You can do this rotation either clockwise or counterclockwise, and you would get the same result.

The distance between points M and N according to the task content is; 9.8 meters.

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints of KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

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Answer: 9.8 meters

Step-by-step explanation:  Trust Me!! I got the answer correct on Edge.

Q:  What is the distance between points M and N?

A:  9.8 meters  

Answer:

-28

Step-by-step explanation:

x/4= -7

4* x/4= -7*4

x= -28

Answer:

Arithmetic sequence

Step-by-step explanation:

The given sequence is arithmetic because it is increases gradually by 5

so the answer is "an arithmetic" and "difference" is equal to "5"

Answer:

0y^2 + 2z^3 + 3y^3

Step-by-step explanation:

The simplified form of the expression is 0y²+2z³ + 3y³

The given expression is -1/3y² + 2/3 z³ +1/3y² +3y³+4/3z³.

In the expression y, z are the variables.

Combine the like terms:

(-1/3+1/3)y²+(2/3+4/3)z³ + 3y³

Simplify each term:

0y²+2z³ + 3y³

Hence, the simplified form of the expression is 0y²+2z³ + 3y³

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[tex] \sf{\red{Answer}}[/tex]

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

[tex] \sf{\purple{Explanation}}[/tex]

[tex] \sf{m = \frac{y_{2}- y_{1}}{m_{2} - m_{1}} }[/tex]

[tex] \sf{m = \frac{9- 3}{7- ( - 5)} }[/tex]

[tex]\sf{m = \frac{6}{7 + 5} }[/tex]

[tex]\sf{m = \frac{6}{12} }[/tex]

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

Answer:

[tex]\sf \dfrac{x+2}{x}[/tex]

Step-by-step explanation:

Simplifying the expression:

 1. Factorize each expression.

     x² + 8x + 15

   Sum = 8

  Product = 15

  Factors = 3 , 5  {When we add 3 & 5 we get 8 and when we multiply 3*5, we get 15}

  x² + 8x + 15 = x² + 3x + 5x + 15

                     = x(x + 3) + 5(x + 3)

                     = (x + 3)(x + 5)

x² - 2x - 15

 Sum = -2

Product = -15

Factors = 3 , (-5)  {When we add 3 + (-5) =2 and when we multiply, 3*(-5) = -15}

x² - 2x - 15 = x²  + 3x - 5x - 15

                 =x(x + 3) -5(x + 3)

                 = (x + 3)(x - 5)

x² + 5x = x( x + 5)

x² - 3x - 10

Sum = -3

Product = -10

Factors = 2 , (-5)  {When we add 2 +(-5) = -3 and when we multiply 2 *(-5) = -10}

x² - 3x - 10 = x² + 2x - 5x - 10

                 =x(x + 2) - 5(x + 2)

                 = (x + 2)(x - 5)

2. Use KCF method and simplify.

  K - keep the first fraction

  C - change division to multiplication

 F -  Flip the second fraction.

[tex]\sf \dfrac{x^2 + 8x + 15}{x^2 - 2x - 15} \ \div \ \dfrac{x^2 + 5x}{x^2 - 3x - 10}=\dfrac{x^2 + 8x + 15}{x^2-2x - 12}*\dfrac{x^2 - 3x - 10}{x^2 + 5x}[/tex]

                                              [tex]\sf = \dfrac{(x +3)*(x +5)}{(x+3)(x - 5)}*\dfrac{(x + 2)(x - 5)}{x(x+5)} \\\\= \dfrac{x + 2}{x}[/tex]

Answer:

8

Step-by-step explanation:

The equation of the parabola can be represented as

[tex]y = a(x + 1)(x - 5)[/tex]

for some constant a.

Since the coefficient of x² is 2, a = 2, so

[tex]y = 2(x + 1)(x - 5) \\ \\ y = 2( {x}^{2} - 4x + 5) \\ \\ y = 2 {x}^{2} - 8x + 10[/tex]

So, the answer is 8.

1st transformation: A vertical translation of the figure down by 8 units

2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units

Transformation is a way of changing the position of an object on an xy-plane.

For the translation

(x, y)-> (x, y-8)

It shows a vertical translation of the figure down by 8 units while the translation;

(x, y - 8) -> (-x, -y)

shows a reflection on both axis and vertical translation up the plane by 8 units

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Answer:

C

Step-by-step explanation:

you can only work 40 or less hours per week but you must earn greater then or equal to $323.

Answer:

72 × 3 = 216m

216 m is the combined length

Observe that

[tex]x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1[/tex]

so that

[tex]P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1[/tex]

Then

[tex]P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}[/tex]

Alternatively, we can avoid find [tex]P(x)[/tex] altogether and instead first write [tex]x-1[/tex] in terms of [tex]x+2[/tex] :

[tex]x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3[/tex]

Then

[tex]P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1[/tex]

Answer:

s(t) = -4.9t² + 39.2t

Step-by-step explanation:

Given the projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s²

Given

g = -4.9m/s²

v0 = 39.2m/s

s0 = 0m (the initial height)

On substituting into the formula;

s(t) = gt² + v0t + s0

s(t) = -4.9t² + 39.2t + 0

s(t) = -4.9t² + 39.2t

This gives the equation that models the height

Answer:

28 legs are on the ground

Using translation concepts, the graph of g(x) is given as follows:

It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent and translated functions are given, respectively, by:

The transformations are as follows:

f(x) has vertex at (0,0), hence g(x) will have the vertex at (5,1). When x = 2, g(x) = (2-5)^2 + 1 = 10, hence the correct statement is:

It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).

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