Write an equation for the function graphed below

The population standard deviation [tex]\sigma[/tex] is 6.697.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.

Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.

Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.

We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].

= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².

= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.

= 44.85

And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697

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The simplified equation is y = 3x -40.

What do you mean by translation of graph?

Translating a graph means that moving the graph of a parent operate either vertically or horizontally. To translate a graph vertically means that to shift the graph k units upward or downward looking on the sign of k. If k is positive, shift the graph upward however if k is negative, shift the graph downward. On the opposite hand, translating a graph horizontally means that shifting the graph side wards by h units to the left or to the correct. If h>0, shift the graph to the correct however if h<0, shift the graph to the left.

Main body:

According to question:

Y = √9x-36-4

√9 can be written as 3.

y = 3x -40

Hence , the simplified equation is y = 3x -40.

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The scientific terms for peaks and valleys is B. Crests and troughs.

The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.

The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.

The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.

Therefore, based on the information given, the correct option is B.

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The value of down payment will be;

⇒ $705

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Now,

Since, Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.

Hence, The value of down payment = 15% of $4700

                                                        = 15/100 × 4700

                                                        = 15 × 47

                                                        = 705

Thus, The value of down payment = $705

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Step-by-step explanation:

Add the values

x - y = 6

x + y = 2

-------------

2x = 8

--------------

Substitute for x

2x = 8

x = 8/2

x = 4

insert x = 4 into equation x - y = 6

x - y = 6

4 - y = 6

-y = 6 - 4

-y = 2

-y/-1 = 2/-1

y = -2

∴ y = -2 , x = 4

Solved by elimination

Solved by elimination Through chibabykalu16

Answer:0.1875

Step-by-step explanation: you would take the miles and divide it my the minutes which would be 3 divided by 16 which equals 0.1875

F0.05 (4,5)=5.19>f according to the F-distribution table. Following that, P(F>1.442)>P(F>f0.05 (94.5))=0.05. This leads us to conclude that the sample has a higher than 5% chance of producing such data under the premise that σx=σy.

We cannot conclude that the variances of the two populations are not equal based on the standards of a 95% confidence interval.

Step 1 : the mines' 1 and 2 standard deviations should be calculated. [tex]n_{x}[/tex] =5&[tex]n_{y}[/tex]=6.

To determine the sample means, use the formulas

x bar = 8260 + 8130 + 8350 + 8070 + 8340/ [tex]n_{x}[/tex]

x bar = 41150/ 5

x bar = 8230 and y bar = 7950 + 7890 + 7900 + 8140 + 7920 + 7840/ [tex]n_{y}[/tex]

y bar = 47640/6

y bar = 7940.

step 2: Now,  [tex]s_{x}[/tex]provides the standard deviations.

[tex]s_{x}^{2}[/tex] =1/4i=1∑^5i=1(xi−x)^2

=1/ 4 ⋅63000

=15750

for [tex]s^{2}_{y}[/tex]

[tex]s^{2}_{y}[/tex]^2=1/5∑i=1^6(yi−y)^2

=1/5⋅54600

=10920

If we assume that the variances of the two populations are equal—

that is,  σx=σy and

 [tex]s_{x}^{2}[/tex] and[tex]s^{2}_{y}[/tex] are the variances of independent random samples with sizes of [tex]n_{x}[/tex]=5 and[tex]n_{y}[/tex] =6 drawn from normal populations—then we can say that the random variable exists.

The formula F is

=[tex]s_{x}^{2}[/tex]/ [tex]s^{2}_{y}[/tex]has an F distribution with

v1=nx- 1

=5- 1

=4 and

v2=ny-1

=6- 1

=5

The observed samples' f-value is f=[tex]s_{x}^{2}[/tex] / [tex]s^{2}_{y}[/tex]

=15750/10920

=1.442.

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Answer:

x = 5

Step-by-step explanation:

[tex](5x+6)+106+43=180[/tex]

[tex]5x=180-106-43-6=25[/tex]

[tex]x=25/5=5[/tex]

Hope this helps

We had written an algorithm, using pseudo code.

//Define the required variables.

total_number_of_steps = 0

number_of_steps = 0

//robot stands up to walk.

stand

//the robot moves forward till the wall is not reached.

while (wall is not reached)

//the robot senses the wall with the help of arms.

raise arms

sense_the_wall

if (wall is not there)

//if the wall is not found, the robot lowers the arms

lower arms

//if wall is not detected, the robot moves forward.

step_forward

//increment the number of steps forward.

number_of_steps=number_of_steps+1

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

else

exit

end if

end while

//else if the wall is found, lower the arms

lower arms

//the robot turns 90 degrees right once.

turn_right_90

//the robot turns 90 degrees right again.

turn_right_90

//till the number of steps does not reach 0, move

for (number_of_steps! = 0)

step

//increment the total number of steps.

total_number_of_steps=total_number_of_steps+1

//the robot moves backwards on detecting the wall, so

//decrement the number of steps.

number_of_steps = number_of_steps-1

//end the for loop.

end for

//the robot turns 90 degrees left once.

turn

//the robot turns 90 degrees left again.

turn

//the robot sits down.

sit

//display the total number of steps taken by robot

display total_number_of_steps

The last line ends the pseudocode

Stop

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The normal distribution does not correspond to the fact that about 65% of the data occurs within two standard deviations of the mean.

Explanation:

100 - 35 = 65%  

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The normal distribution does not correspond to the fact that about 65% of the data occurs within two standard deviations of the mean.

The four characteristics of a normal distribution can be seen in this situation. A normal distribution is symmetric, unimodal, and asymptotic, and its mean, median, and mode are all equal.

The fact that around 65% of the data occurs within two standard deviations of the mean contradicts the normal distribution.

A fair dice roll is a good example of normal distribution. The results of an experiment showed that the chances of rolling a one are 15–18% when the dice are thrown 100 times, and they remain the same even if they are thrown 1000 times, with an average likelihood of 16.7% (1/6).

100 - 35 = 65%  

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Answer:

$6.35

Step-by-step explanation:

25.40/4 = 6.35

Answer:

Answer is y = 11

Step-by-step explanation:

8 = y - 3

or, 8 + 3 = y - 3 + 3

or, 11 = y

or, y = 11

A solid figure is a three-dimensional object. That is, it has length, width, and height. Because they are three-dimensional, they have depth and occupy space in our universe. Body types are identified according to characteristics specific to each body type. In particular, we can observe the number of faces, edges, vertices, and the shape of the base.

A flat face of a solid is its face or side, as it is commonly called. The base is the surface on which the figure rests. A solid edge is a line segment where two faces meet. A vertex  is an angle formed where the endpoints of two or more face segments meet.

A sphere is a solid figure that has no faces, edges, or vertices. This is because it is perfectly round. No flat sides or corners.

A cone has faces but no edges or vertices. His face is circular. A circle is a plane because it is a flat planar shape. However, since it is rounded on the outside, it does not form edges or corners.

Cylinder that has two circular faces but no edges or corners:

A pyramid has a base and at least three triangular faces. There are edges where faces meet each other or meet the bottom, vertices where two faces meet the bottom, and top vertices where all the triangle faces meet. Pyramids are named for the shape of their base.

A triangular pyramid has a triangular base and his other three triangular faces, or four triangles in total.

A pyramid has a rectangular base and a pyramid has a square base. Both have four triangular faces, for a total of five faces.

Prism:

A prism is a solid with two congruent parallel faces and any number of sides. That is, it can have any number of faces, but at least two faces must be parallel. The shape of the two parallel faces can be triangles, squares, rectangles, pentagons, hexagons, or other types of polygons. Prisms are named after the shape of the base.

Sphere:

A sphere is a geometric object that is the three-dimensional analogue of the two-dimensional circle. A sphere is a set of points that are all the same distance r from a given point in 3D space. This given point is the center of the sphere and r is the radius of the sphere. Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy.

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Answer:

The length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.

Step-by-step explanation:

Since angle A and angle R are both congruent to angle B, we know that angle A = angle R = y + 7°. We can use this information, along with the angles and sides of the triangles, to find the value of y and the lengths of the sides of the triangles.

From the given information, we know that the angles of triangle ABC add up to 180°, so we can use that to find the value of y:

4y - 71° + y + 7° + 106 - 2y° = 180°

6y - 64° = 180°

6y = 244°

y = 40.67°

We can use the value of y to find the measure of angle C:

C = 106 - 2y° = 106 - 2(40.67°) = 106 - 81.34° = 24.66°

Now that we know the measure of angle C, we can use the Law of Sines to find the length of side BC:

BC / sin C = AC / sin A

BC = (AC * sin C) / sin A

BC = (13 cm * sin 24.66°) / sin (4y - 71°)

BC = (13 cm * 0.4237) / sin (4(40.67°) - 71°)

BC = 5.525 cm

We can use the same method to find the length of side ST in triangle RST:

ST = (RT * sin C) / sin A

ST = ((2x + 5 cm) * sin 24.66°) / sin (4y - 71°)

ST = ((2x + 5 cm) * 0.4237) / sin (4(40.67°) - 71°)

ST = (2x + 5 cm) * 0.4237 * 0.4514

ST = (2x + 5 cm) * 0.1901

ST = 0.3802x + 0.9505 cm

Therefore, the length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.

Answer:

The sequence is not arithmetic. In an arithmetic sequence, the difference between consecutive terms is constant. However, in this sequence, the difference between the terms is not constant. For example, the difference between the first and second terms is 1^5 - 2^5 = -3, while the difference between the second and third terms is 2^5 - 3^5 = -6. Since the difference between consecutive terms is not constant, this sequence is not arithmetic. Therefore, the common difference is NONE.

Answer:

No, the sequence is not arithmetic.

d = NONE

Step-by-step explanation:

An Arithmetic Sequence has a common difference between each term (the difference between each term is the same).

Given sequence:

[tex]1^5, 2^5, 3^5, 4^5, 5^5, ... = 1, 32, 243, 1024, 3125, ...[/tex]

Calculate the difference between each term:

[tex]1 \underset{+31}{\longrightarrow} 32 \underset{+211}{\longrightarrow} 243 \underset{+781}{\longrightarrow} 1024 \underset{+2101}{\longrightarrow} 3125[/tex]

As the difference between each term is not constant, the sequence is not an arithmetic sequence.

Therefore, the common difference, d = NONE.

By solving a linear equation, it can be calculated that-

First fourth and fifth option are correct

What is a linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Length of two sides of a right angled triangle = x, x+2

Area = [tex]\frac{1}{2}\times x \times (x + 2)[/tex]

By the problem,

The linear equation is

[tex]\frac{1}{2}\times x \times (x + 2) = 24\\[/tex]

0.5x(x + 2) = 24

First option is correct

x(x + 2) = 48

[tex]x^2 + 2x - 48 = 0[/tex]

Fourth option is correct

For the sixth option,

[tex]x^2 + (x + 2)^2 = 100\\x^2 + x^2 + 4x + 4 - 100 = 0\\2x^2 + 4x - 96 = 0\\2(x^2 + 2x - 48) = 0\\x^2 + 2x - 48 = 0[/tex]

Which is the third option.

First fourth and fifth option are correct

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How many hours per pound does it take to thaw a turkey?

Allow 30 minutes of thawing time for each pound of turkey, which translates to two to six hours for a 4- to 12-pound turkey. A 12- to 15-pound bird will thaw in six to eight hours. Still having trouble determining the thaw time of the turkey?

Hope this helps :D

A set-to-set function f is a relation that assigns one element of the set A to each element of the other set B. The set A is the domain of the function (also called the set of inputs) and the set B contains the range (also called the set of outputs).

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

1. Not an exponential function:

We have the following equation:

[tex]y = 100 (1 - 12)^{t}[/tex]

We can write the equation as:

[tex]y = 100 (-11)^{t}[/tex]

Let's denote f as exponential function with the base 'a':

                                  f(x) = a ˣ

where, a > 0 and a ≠ 1 and x is any real number.

Therefore: a must be more than 01.

In this problem, a = -11, therefore this is not an exponential function.

2. Growth.:

The function:

[tex]y= 0.1(1.25)^{t}[/tex]

The above equation is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

Therefore, k = 0.1 and  a = 1.25 . So, a is greater than 1.

3. Growth:

The function:

[tex]y = {(1 - 0.03)12}^2t[/tex]

The above equation can be written as:

[tex]y = 11.64^{2t}[/tex]

which  is an exponential function because is a function of the form

[tex]f(t) = a^{bt}[/tex]

where, a > 0 and b is constant.

So, a = 11.64 and b = 4 . Since a is greater than 1.

4. Decay:

The function:

[tex]y = 426(0.98)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant

So, k = 426 and a = 0.98. Since, a is less than 1.  

5. Growth:

The function:

[tex]y = 2050(12)^t[/tex]

This is an exponential function because is a function of the form

[tex]f(t) = ka^t[/tex]

where, a > 0 and k is constant.

So, k = 2050 and a = 12  . Since, a is greater than 01.  

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The length v of the triangle is 240.4 inches

From the question, we have the following parameters that can be used in our computation:

w = 690 inches

∠W = 79°

∠V = 20°

The length v can be calculated using the following sine rule

v/sin(V) = w/sin(W)

Substitute the known values in the above equation, so, we have the following representation

v/sin(20°) = 690/sin(79°)

Multiply both sides of the equation by sin(20°)

So, we have the following representation

v = sin(20°) * 690/sin(79°)

Evaluate the products

v = 240.41

Hence, the length of side v is 240.4 inches

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Complete question

In ΔUVW, w = 690 inches, ∠W=79° and ∠W=20°

Calculate the length v to the nearest 10th of an inch.

The solution of the system of equations by the graphical methods yields  x equals 9 and y is 6 i.e, 9 hours of landscaping and 6 hours of waiting tables.

Bella worked x hours working landscaping at $10 per hour.

Total amount earned = 10x

Bella worked y hours working on clearing tables at $ 15 per hour

Amount earned = 15 y

x and y are variables as given

She worked a total of 15 hours and she gets $180 for the combined efforts.

The system of equation can be represented as:

x + y = 15

10x + 15y = 180

Now we will solve the two equations graphically:

So from the attached graph we can see that the point (9,6) is the required solution.

Hence she worked landscaping for 9 hours and clearing tables for 6 hours.

Let us solve by substitution to verify the results:

x + y = 15

or, x = 15 - y

Now 10x + 15y = 180

or, 10 (15-y) + 15y = 180

or, 150 - 10y +15y = 180

or, 5y = 180 - 150

or, y = 6

At y = 6 , x = 15 - 6 = 9

Hence (9,6) is the solution.

System of equations also known as simultaneous equations can also be solved by the elimination method.

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I think it is either A or C

Step-by-step explanation:

similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).

so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.

some correct answer options are not listed, so we need to adjust to the existing ones.

remember, the sum of all angles in a triangle is always 180°.

so,

angle A + angle B + angle C = 180

40 + angle B + 60 = 180

angle B = 80°

so, angle E = 80° for the triangles to be similar.

AC × c = DF

12 × c = 16

3 × c = 4

c = 4/3

so,

AB × c = DE

9 × 4/3 = DE

36/3 = DE

DE = 12

so, either angle E = 80° or DE = 12.

The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²

An expression is combination of variables, numbers and operators.

(4c − 3d)(3c + d) is the given expression.

Four times c minus three times d into three times f c plus d.

In the given expression c and d are variables.

Plus and minus are operators.

We need to find the equivalent expression of (4c − 3d)(3c + d).

(4c − 3d)(3c + d)

4c(3c+d)-3d(3c + d)

Apply the distributive property.

12c² + 4cd - 9cd - 3d²

Add the like terms

12c² - 5cd - 3d²

Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).

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The graph that shows the linear relationship of the table is attached below.

To determine the graph of a linear relationship, do the following:

Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:

Slope = change in y / change in x = (1 - 0) / (2 - 0)

Slope = 1/2.

The y-intercept (b) = 0.

Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.

Thus, the graph is shown below.

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The system of equations is

125a + 65s = 1200

140a + 50s = 1230

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

125a + 65s = 1200

140a + 50s = 1230

-3500a - 1820s = -33600  

3500a + 1250s = 30750

-570s = -2850

s = $5

student

125a + 65(5) = 1200

125a + 325 = 1200

125a = 875

a = $7 adult

the other situation means that they didn't do it right at all

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Answer:

Step-by-step explanation:

domain 800 and range 16

Answer:

Below

Step-by-step explanation:

1/3 x   = - 2/5      <=====multiply both sides of the equation by 3 to get

x = -6/5   = - 1  1/5