What is the slope of a line perpendicular to the line whose equation is 3x-12y=-108

From the given information, we know that the mean and standard deviation are, respectively,

From the 68-95-99 rule, we know that approximately 95% falls between 2 standard deviation of the mean, that is,

and

From equation (A), we have

then

Now, from equation (B), we get

Therefore, the answer for part a is: Approximately 95% of the students have commute between 10.6 and 27.4 miles

In this case, we need to find the z score value for 6.4 miles and 31.6 miles and then obtain the corresponding probabilty from the z-table.

For 6.4 miles, the z score is

and for 31.6 miles, the z score is

Now, we need to find the corresponding probability between z=-3 and z=3, which is 0.9973

Therefore, the answer for part b is: Approximately. 0.9973 of the students have commute distances between 6.4 miles and 31.6 miles

The weighted dollar amount of the savings account as per the an investment portfolio given is equal to $67.20.

As given in the question,

An investment portfolio is shown below.

Investment Amount Invested ROR

Savings Account $3,200     2.1%

Municipal Bond $4,900       4.5%

Preferred Stock  $940         10.5%    

Common Stock A $1,675     -3.5%

The weighted dollar amount of the savings account is equal to :

= 2.1% of $3200

=  ( 2.1 / 100)  × $3200

= ($6720) /100

= $ 67.20

Therefore,  the weighted dollar amount of the savings account  as per the an investment portfolio given is equal to $67.20.

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Answer:

congruent: a° and c°; d° and b°

Supplementary: c° and b°; a° and b°; a° and d°; c° and d°

Step-by-step explanation:

olution

Basically, the number of asymptotes will be the number of solutions the denominator of the function has

We are given the function

Solving the denominator

he answer is 3 vertical asymptotes

Answer:

A and D (the top one and the bottom one)

Step-by-step explanation:

You do not multiply the exponents when the two terms are be multiplied. Instead, you add the exponents. For example, in the first problem, the terms being multiplied are [tex]5y^4[/tex] and [tex]2y^5[/tex]. The exponents are 4 and 5, and when you add them together, that is the exponent that y should carry in the answer.

Hope this helps you! May I please get a brainliest?

Answer:

approximately 19~20 shopper

Step-by-step explanation:

this case binomial distribution

X~B(n,p)

X: number of shoppers who spend less than 20$

n=28

p=0.7

use mean of binormal distribution E(X)=np

Answer)

E(x) =28*0.7=19.6

thus approximately 19~20 shopper

iven:

heere are given that the population in the year 2000 was 12000 and the growth rate is 7% per year.

xplanation:

ccording to the question:

For t =0 which is the year 2000:

For t = 1:

If we say r is the rate, then:

Then,

For t = 2:

And,

For t = 3:

Therefore our function should be:

(a):

he population function:

Now,

(b):

ccording to the question:

2008 is 8 year from year 2000:

Therefore, t = 8:

Then,

Put the value 8 for t into the function (a):

inal answer:

For $3.00, the pounds of bananas that can be bought are 2.

How to derive equation of line from graph using two point form?
A line's equation can take many different shapes in a two-dimensional coordinate plane. The point-slope form, slope-intercept form, and general or standard form of the equation of a line are the three most often used techniques.
The formula of two point form of a equation is given below:
Let (x₁, y₁) and (x₂, y₂) be the two points such that the equation of line passing through these two points is given by the formula:
(y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁) -- (i)
Rearranging (i), we get: y - y₁ = [(y₂-y₁)/(x₂-x₁)] (x-x₁) --(ii)

Given, the graph has y co-ordinate as cost in $ of bananas and the x co-ordinate as pounds in lb.
From graph in question, the two points that can be assumed are (0.5,0.75) and (3,4.5); thus using two point form we get the equation as:
y - 0.75 = [(4.5 - 0.75)/(3 - 0.5)] *(x - 0.5) ⇒ y - 0.75 = 1.5 (x - 0.5)
⇒ y - 0.75 = 1.5x - 0.75 ⇒ y = 1.5x ⇒ x = y/1.5 --(ii)
From (ii),
thus for y = 3, value of x will be x = 3/1.5 = 2

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The rocked was launched at an initial height of 325 meters

The equation of the function is given as

h ( t ) = − 4.9 t 2 + 226 t + 325 .

Rewrite the above equation properly

So, we have the following equation

h(t) = −4.9t^2 + 226t + 325

At the initial height of the launch, the time is 0

This is represented as

t = 0

Substitute the known values in the above equation

So, we have the following equation

h(0) = −4.9(0)^2 + 226(0) + 325

Evaluate the exponent in the above equation

So, we have the following equation

h(0) = −4.9(0) + 226(0) + 325

Evaluate the product in the above equation

So, we have the following equation

h(0) = 0 + 0 + 325

Evaluate the sum in the above equation

So, we have the following equation

h(0) = 325

Hence, the initial height of the launch is 325 meters

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Possible question

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9 t 2 + 226 t + 325 .

Calculate the height of launch of the rocket

Answer: I am 97% sure it's D

Step-by-step explanation:

The density of the gasoline is 690 grams per litre.

The mass of the jerrycan when fully filled is 16.3 kg

He fills a 20 litre jerrycan with gasoline.

A volume  of gasoline of 1 litre has a mass of 690 grams and the empty jerrycan weighs 2.5 kg.

Therefore, the density of the gasoline can be calculated as follows:

density = mass / volume

Hence,

mass of the gasoline = 690 grams

volume of the gasoline = 1 litres

density of the gasoline = 690 / 1

density of the gasoline = 690 grams per litre.

The weight of the jerrycan when filled with gas can be calculated as follows:

1 litre of gas = 690 grams

20 litres gas = 13800 grams

Hence,

1000 grams  = 1kg

13800 grams = 13.8 kg

Therefore,

weight of the jerry can when filled with gas = 13.8 + 2.5 = 16.3 kg

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The corresponding values of expressions 1, 2,3,4 and 5 when evaluated are -2, -0.65, -7/48, 67 1/2 and 2 2/33

1. To evaluate (a-2b)^3 when a = -3 and b = - 1/2,  put a = -3 and b = - 1/2 into the expression (a-2b)^3:

(a-2b)^3 = ( -3 - 2(-1/2) )

              = (-3 + 1) = -2

2. To evaluate (jk - 1) ÷ j when j = -4 and k = -0.9, put  j = -4 and k = -0.9 into the expression (jk - 1) ÷ j:

(jk - 1) ÷ j = ( -4(-0.9) - 1) ÷ (-4)

              = (3.6 -1) ÷ (-4) = (2.6) ÷ (-4) = -0.65

3. To evaluate -|a+b| / 2-c when a =1 7/8 , b = -1 , and c = -4 , put b = -1 , and c = -4 into the expression -|a+b| / 2-c:

-|a+b| / 2-c  = -|1 7/8 + (-1)|/ 2 -(-4)

                  = -| 7/8 | / 6 = -7/48

4. To evaluate (w^2 / x - 3) ÷ 10 multiplied by z when w = -9 , x = 2.7 , and z= -2/5:

(w^2 / x - 3) ÷ 10z = ((-9)²/ 2.7 -3)  ÷ 10(-2/5)

                            = (81/(-0.3))  ÷  (-4) = -270/-4 = 67 1/2

5. To evaluate (2a - 1/3) ÷ b/15 when a = -2/5 and b = -8.25:

(2a - 1/3) ÷ b/15 = (2(-2/5) - 1/3) ÷ -8.25/15

                          = (-4/5 - 1/3) ÷ (-11/20) = -17/5 ÷ (-11/20) = 2 2/33

Therefore, the expressions 1, 2,3,4 and 5 evaluate to -2, -0.65, -7/48, 67 1/2 and 2 2/33 respectively

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The method that she could use to measure an equivalent amount is to remove 25% from the measurement used.

From the information, the chef needs 3/4 of a cup of flour for her recipe, but her 1/4 cup measure is missing.

Therefore, the method that she could she use to measure an equivalent amount will be to subtract 25% from whatever value that she is using.

It should be noted that 3/4 to percentage will be:

= 3/4 × 100.

= 75%

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2.16 sec take to eat a human weighing 90kilograms.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

It takes 12 seconds the Dragon eat 500 Kg.

So, to eat 1 Kg the dragon takes

=12/500

=0.024 sec

Now, to eat 90 Kg it will take

=0.024 x 90

= 2.16 sec

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Answer:

There is no solution.

Step-by-step explanation:

The absolute value of a number is the distance between that number and zero. It doesn't deal with negative numbers. For example, if you were playing a board game and were told to move back 6 spaces, you would be moving -6 spaces, but 6 spaces away from where you were. Absolute value focuses on how far you moved from where you were. So, an absolute value can't be negative.

The graph has the horizontal tangent line at the the turning point(stationary point) And we know that at the turning point the gradient is 0. We can find the gradient of f(x0 by the first derivative. As  I said the gradient a the turning point is 0 meaning since f'(x) =m  and m=0 ∴f'(x)=0

[tex]f'(x)=4x-2\\0=4x-2\\4x=2\\\frac{4x}{4}=\frac{2}{4} \\x=\frac{1}{2}[/tex]

Now we know that in order to find the point where x = [tex]\frac{1}{2}[/tex]  we can substitute the value of x in the original equation

[tex]f(\frac{1}{2})=2(\frac{1}{2} )^{2} -2(\frac{1}{2} )-1\\f(\frac{1}{2} )=-\frac{3}{2}[/tex]

The answer is [tex](\frac{1}{2} ,-\frac{3}{2} )[/tex]

Hope I helped.

Answer:

1, 7, 13, 19, 25, 31, 37, 43

Step-by-step explanation:

it is increasing by 6 each time so you add 6 three more times.

Solution

For this case the unitary circle is given by:

this unitary circle is important for the trigonometric identities

Can be used also to solve inequalities

Can be used also in physics applications and in linear algebra

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y = x² -14 x + 48[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.

So, the values of x, when y = 0 are the roots of the given quadratic function.

that is : x = 6 and x = 8

And it can be represented as :

[tex]\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0[/tex]

[ h1 and h2 represents roots of the quadratic function ]

[tex]\qquad \tt \rightarrow \: (x - 6)(x - 8) = 0[/tex]

It can be further simplified as :

[tex]\qquad \tt \rightarrow \: {x}^{2} -8x - 6x + 48 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x {}^{2} - 14x + 48 = 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The linear graphing of the given equation y = 3x - 3 is done by plotting a series of points and then tracing a line through them.

Given equation:

y = 3x - 3

Now we will graph this linear equation by plotting points.

We can select input values, evaluate the equation at these input values, and compute output values to determine the respective points. Coordinate pairs are created by the input and output values. The coordinate pairs are then plotted on a grid.

So, the points of the given linear equations are:

 x     y

-2    -9

-1     -6

0    -3

1      0

2     3

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Answer:

It's 5.31

Explanation:

The subsets of the set {-3, 6}, which are proper subsets is the option;

A set is a model that represents a collection of mathematical objects such as numbers, lines, symbols, points, other sets, variables, or shapes.

In set theory, a set A is a subset of the set B if all the elements or members present in set A can be found in set B. Therefore, set B is said to contain set A or set A is contained in set B.

The above relationships can be expressed using examples as follows;

Let set A = {X, Y} and let set B = {X, Y, Z}, then set A is a subset of set B because the elements, X, Y, contained in set A, are also contained in set B,

Generally, the number of proper subsets of a set that contains n elements is [tex] {2}^{n} - 1[/tex]

Given that the subset of a set which is not a proper subset is the set of itself.

The given set is; {-3, 6}

The number of elements in the set, n = 2

Therefore;

The number of proper subsets = 2² - 1 = 3

All the subsets of {-3, 6} are therefore;

∅, {-3}, {6}

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____________________________________________

Slope-Intercept Form - Solution and Explanation

____________________________________________

Hello! So...

We are given the following to convert:

Convert into Slope-Intercept Form

(-2, 5), slope = -4

____________________________

1. Compute the line equation y = mx + b for slope. In this case, our slope (m) equals -4, and passes through (-2, 5).

____________________________

2. Determine the y-intercept. In this case, b = -3.

____________________________

3. Now, construct the line equation (y = mx + b), where m = -4 and b = -3. Then, you will have your converted solution in Slope-Intercept Form.

Slope-Intercept Form:

[tex]y=-4x-3[/tex]

___________________________________________

Hope this helps! If not, feel free to comment on the matter and I will see what else I can do to assist your further. However, if this does help, lmk! Thanks and good luck!

True, cube the scale factor while finding the area of a scaled copy.

The scale factor is the ratio of two equal lengths in two similar geometric objects. The fundamental formula for calculating the scale factor is the size of the former shape is  Scale factor = Dimension of the new shape ÷ Dimension of the original shape. The area of a scaled element is equal to the squared scaling factor. If the scale factor is three, the area of the new item will be nine times, or three times, that of the original object. The area scale factor is equal to the square of the length scale factor. As a result, s2 is the surface scaling factor. If this is reversed, a solution to the situation at hand will be offered. The area has a scale factor of 2.

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Using transformations, it is found that the transformation from [tex]y = \sqrt[3]{x}[/tex] to [tex]y = \sqrt[3]{0.5x}[/tex] is:

It is horizontally stretched by a factor of 1/2.

Transformations in the graph of a function happens when operations such as multiplication/division or sum/subtraction are applied in the definition of the function.

They can be either in the domain of the function, involving values of x, or the range, involving values of y.

For this problem, the change was that x -> x/2, that is, there was a multiplication in the domain, meaning that there was an horizontal stretch to the function.

The fact that the number was multiplied by 1/2 means that the factor of the stretch is of 1/2.

The transformation is from [tex]y = \sqrt[3]{x}[/tex] to [tex]y = \sqrt[3]{0.5x}[/tex].

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Using ASA congruence rule, we have PS = PK.

What does congruence of triangles mean?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another. Mathematics uses the term "congruence" to describe when two figures have similar size and shape. In essence, two triangles are congruent if and only if they follow the four congruence rules. Finding all six dimensions, though, is crucial. As a result, only three of the six variables can be used to evaluate the congruence of triangles. Triangles that are congruent have comparable sides and equivalent angles.

Given, in ΔPQR we have ,
PQ = PR
and ∠PRR = ∠PQR ⇒ 180° - ∠PQR = 180° - ∠PQR ⇒  ∠PQR = ∠PSQ -(i)

Now, in ΔPSQ and ΔPRK;
∠SPQ = ∠RPK
∠Q = ∠R , given
∠SPQ = ∠RPQ
so, by ASA congruence  we have , ΔPSQ = ΔPRK
Thus, PS = PK.

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From the diagram we notice that the angle of 55° is vertical opposite to angle 3, hence they are equal.

Also from the diagram we notice that angles 3 and 6 are alternate interior angles and since lines A and B are parallel then they are equal.

Finally angle 6 and angle 7 are vertical opposite, which means they are equal.

Therefore, the value of angle 7 is 55°

Answer:

Step-by-step explanation:

[tex]3x+x+(x+70)=180[/tex]

[tex]5x+70=180[/tex]

[tex]5x=180-70[/tex]

[tex]5x=110[/tex]

[tex]x=110/5[/tex]

x = 22°

"x" is the second angle: 22°

"3x" is the first angle: 3(22) = 66°

"x + 70" is the third angle: 22 + 70 = 92°

22 + 66 + 92 = 180

Hope this helps

The non-real solutions of the polynomial expression are x = 2 + i√11 and x = 2 - i√11

The equation of the polynomial expression is given as:

x^4 – 7x^3 + 23x^2 – 29x – 60 = 0

Also, we have the following points

(-1, 0), (0, -60), (2.5, -60), (4, 0)

Write out the x-intercepts

(-1, 0) and (4, 0)

This means that

x = -1 and x = 4

So, we have

x + 1 = 0 and x - 4 = 0

Multiply

(x + 1)(x - 4) = 0

Divide the polynomial equation x^4 – 7x^3 + 23x^2 – 29x – 60 = 0 by (x + 1)(x - 4) = 0

Using a graphing calculator, we have

x^4 – 7x^3 + 23x^2 – 29x – 60/(x + 1)(x - 4) = x^2 - 4x + 15

So, we have

x^2 - 4x + 15

Next, we solve the quadratic expression using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (4 ± √((-4)² - 4 * 1 * 15))/2 * 1

So, we have

x = (4 ± √-44)/2

This gives

x = (4 ± 2√-11)/2

Divide

x = 2 ± √-11

So, we have

x = 2 ± i√11

Split

x = 2 + i√11 and x = 2 - i√11

Hence, the non-real solutions are x = 2 + i√11 and x = 2 - i√11

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