1. Find Sn for the arithmetic series where a1= 3 , an= 42 , n= 14

2. Find sn for the arithmetic series where a1= −20 , n= 25 , an= 148

3. Find sn for the arithmetic series where a1=5 , d=1/2 , n=13

Answer:75%

Step-by-step explanation:3/4 is equal to 0.75

around 125-6

Step-by-step explanation:

The scatterplot of the residuals should display random scatter if a linear model is suitable, and the histogram should appear about normal.

To learn more about linear model refer

https://brainly.com/question/28860456

#SPJ1

As per the natural tendency of cooling with temperature the rate of decrese in temperature is also decresing so the cooling of a soup cannot be described by a linear model.

A relationship that has one output for each input value (x-value) is called a function (y-value). All functions are hence relations. However, not all relationships are functions since not every relationship will satisfy the condition that every distinct input generates just one output.

Check to see if there is a horizontal asymptote or an oblique asymptote by comparing the degrees of the numerator and denominator to the function's end behavior. Plot the asymptotes that are horizontal or oblique.

As per the natural tendency of cooling with temperature the rate of decrese in temperature is also decresing so the cooling of a soup cannot be described by a linear model.

To learn more about Functions refer to :

https://brainly.com/question/14515696

#SPJ1

The solution:

Exercise 1:  x = -1 and 3.

Exercise 2:  x = 2 and 4.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The graphs of the two quadratic equation.

So, Exercise 1,

-x² + 2x + 3 = 0.

From the graph,

-1 and 3 are the zeros of the equation.

The solution of the equation is,

x = -1 and 3.

Exercise 2,

x² - 6x + 8 = 0.

From the graph,

2 and 4 are the zeros of the equation.

The solution of the equation is,

x = 2 and 4.

Therefore, the solutions of the both the equation are given above.

To learn more about the quadratic equation;

https://brainly.com/question/17177510

#SPJ1

The graph of a quadratic function with vertex (1,-2) has the range and the domain respectively, ( -∞, -2 ) and ( -∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The graph of a function,

whose vertex is (1, -2)

As it can be seen in the graph,

The given quadratic function has defined value for each value of x,

So, the domain of the given function is real numbers,

x  ∈  ( -∞, ∞)

The maximum value of the function is -2

And minimum value of the function is  -∞

The range of the function is   ( -∞, -2 )

To know more about Functions check:

https://brainly.com/question/5975436

#SPJ1

The corresponding value of h is less than or equal to 5.

A quadratic function is a polynomial function of the form:

f(x) = ax^2 + bx + c,

where a, b, and c are constants and x is the independent variable. The graph of a quadratic function is a parabola, which is a symmetrical, U-shaped curve.

The set of all feasible dependent variable values based on the input or independent variable constitutes the range of a quadratic function. The direction of the parabola and the value of the y-intercept can be used to establish the range (the constant c).

In mathematics, science, and engineering, quadratic functions are used extensively. Examples include modeling motion, projectile motion, and parabolic reflectors as examples of physical phenomena. They are also utilized in optimization issues where the aim is to discover the highest or lowest value of a given function.

According to question:

The range of a quadratic function is the set of all possible values of the dependent variable, based on the input or independent variable.

From the table, it appears that the range of the function h is all real numbers less than or equal to 5. This is because, for all values of x given in the table, the corresponding value of h is less than or equal to 5. So, the correct answer is:

Of-27, -13, -3, 3, 5}

All real numbers less than or equal to 5

To know more about quadratic function visit:

https://brainly.com/question/29775037

#SPJ1

A bοy walked 7km οn a bearing of 60°. Represented this infοrmation on a diagram given belοw.

A bearing in mathematics is the angle, measured in degrees and anticloοkwise from nοrth. Typically, bearings are given as a three figure bearing. Fοr instance, 30° clockwise from nοrth is typically expressed as 0°.

"Pieces that aid objects' rοtation" are bearings. They suppοrt the rotating shaft that mοves the machinery. Cars, planes, power generatοrs, and οther devices all use bearings.

Tο lessen friction between twο spinning or sliding surfaces, a bearing is a mechanical compοnent.

There are many different types of bearings, including ball and rοller bearings, linear bearings, and mοunted versions that may use either, and they are used for rοtating or linear shaft applicatiοns. Bearings are mechanical assemblies that include rοlling elements and typically inner and οuter races.

To learn mοre about bearing refer to:

brainly.com/question/27587478

#SPJ1

The required area of the shaded region is 11.5 sq. units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given is a circle with center T and radius 3 units. there is a region in the circle which is shaded, we need to find that area.

So, the shaded part is composed of a right triangle and a minor sector of the circle.

To find the area of the shaded portion, we will add the area of right triangle and a minor sector

Now, area of a triangle = 1/2 × base × height

Here, base = height = radius = 3 units

And,

Area of a sector = θ/360° × π × radius²

Where, θ is the central angle.

θ = 90°

Area of the shaded region = 1/2 × 3 × 3 + 90°/360° × 3.14 × 3²

= 9/2 + 7.065

= 11.565

Hence, the required area of the shaded region is 11.5 sq. units

Learn more about areas, click;

https://brainly.com/question/27683633

#SPJ1

Answer:d

Step-by-step explanation:

The total surface area painted black is 50.2 square feet.

Let's call the radius of the base of the cone r. We can find it using the formula for the circumference of a circle:

C = 2πr

8π = 2πr

r = 4

Next, let's find the slant height of the cone, which is the distance from the tip of the cone to the base along a straight line that passes through the center of the base. We can use the Pythagorean theorem:

s^2 = r^2 + h^2

s^2 = 4^2 + 12^2

s^2 = 16 + 144

s^2 = 160

s = sqrt(160) = 12.8

Next, let's find the surface area of one cone. The surface area of a cone is equal to π times the radius of the base times the slant height, plus π times the radius of the base squared:

A = πr * s + πr^2

A = π * 4 * 12.8 + π * 4^2

A = 50.24 + 16π

A = 50.24 + 50.24

A = 100.48

Since the base and 50% of the lateral surface of each cone is painted red, that means 50% of the surface area is painted black:

black_area = 0.5 * 100.48

black_area = 50.24

Rounding to the nearest tenth, the total surface area painted black is 50.2 square feet.

learn more about base of a cone: https://brainly.com/question/4914012

#SPJ1

The volume of the composite figure is 117π ft³ or 368 ft³

The figure shown is made up of a hemisphere and a cylinder.

Total volume of the figure = volume of hemisphere + volume of cylinder

Formula for the Volume of the hemisphere is;

V = ⅔πr³

Radius (r) of hemisphere = 6/2 = 3 ft

Volume of hemisphere = ⅔ * π * 3³

= 18π ft³

Volume of Cylinder is given by the formula;

V = πr²h

radius (r) = 3 ft

height (h) = 11 ft

Volume of cylinder = π * 3² * 11

= 99π ft³

Volume of the figure = 18π ft³ + 99π ft³ = 117π ft³

Volume of the figure to the nearest whole number = 368 ft³

Read more about Volume of composite figure at; https://brainly.com/question/13175744

#SPJ1

If Eris Orbit. The recently discovered Eris orbits the Sun every 557 years.

In order to calculate the semimajor axis of Eris, we need to plug 557 years into the equation
a=P^2/3

a= 557^0.66666667

a = 67.6971 astronomical units.

a = 67.7 AU (Rounded)

Since the average distance for Pluto from the Sun is 39.3 AU

So,

Since the distance of Eris to the sun is 67.7 AU and Pluto to the sun is 39.5

Difference between the two dwarf planets = 67.7AU - 39.5 AU

Difference between the two dwarf planets = 28.2 AU

Based on the above calculation Eris is about 1.5 times farther from the Sun in comparison to Pluto.

Therefore Its average distance (semimajor axis) from the sun is: 67.7 AU and the difference between the two dwarf planets is 28.2 AU

Learn more about average distance (semimajor axis) from the sun here:https://brainly.com/question/29415696

#SPJ1

Answer:

a creo que debes sacr la raiz cuadrada de los dos aciendo los procesos

The number of cubic units needed to add to the figure so that it will have a total volume of 12 cubic units,  4 units

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

Given that,

There are 2 units  in each back side and front side,

So, there are 4 units on the back and front,

Now the number of units between them,

There are 4 units in between both the sides,

Add all the units,

4 + 4 = 8,

there are total 8 units in this figure

Now, the number of units should be added to these 8 units to get a result of 12 units altogether.

So, subtract the 8 units from the 12 units

12 - 8 = 4,

Hence, The units required are 4

To know more about Volume check:

https://brainly.com/question/13338592

#SPJ1

Answer:

$270

Step-by-step explanation:

h = number of half hours worked

$75 + $45(h-1) = total cost

3 1/2 hrs = 7 half-hours

$75 + $45(7 - 1) = $270

Answer: 7.34375

Step-by-step explanation:

Answer step bby step:

1. Isolate the variable:

1/5(4x - 2.5) = 5(0.4x + 10) + 3 1/2

5(0.4x + 10) + 3 1/2 = 1/5(4x - 2.5)

2. Multiply both sides by 5:

2(0.4x + 10) + 3 1/2 = 4x - 2.5

3. Subtract 2(0.4x + 10) from both sides:

3 1/2 = 4x - 2(0.4x + 10)

4. Subtract 3 1/2 from both sides:

0 = 4x - 2(0.4x + 10) - 3 1/2

5. Distribute the -2 to the parentheses:

0 = 4x - 0.8x - 20 - 3 1/2

6. Combine like terms:

0 = 3.2x - 23.5

7. Divide both sides by 3.2:

x = 7.34375

Answer:

The shelf should be 0 degrees relative to the floor.

Step-by-step explanation:

When an object is parallel to the floor, it means that it is aligned with the floor at the same angle and does not slope up or down.

In other words, the angle between the shelf and the floor is 0 degrees.

So, to attach the shelf so that it is parallel to the floor, Dana should ensure that the angle between the shelf and the floor is 0 degrees.

Answer:

x = [tex]-\frac{y - 5}{67}[/tex]

Step-by-step explanation:

Hope this helps

The required simplified value of the given exponential form of expression 4⁻³  is 1/64.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
Given expoenential expression,
=  4⁻³  
= 1 / 4³    [a⁻¹ = 1 /a]
= 1 / 64   [4³ = 64]

Thus, the required simplified value of the given exponential form of expression 4⁻³  is 1/64.

Learn more about exponential function here:

brainly.com/question/15352175

#SPJ1

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

The length of the cable is 4810 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

If the angle of depression from the taller platform of 12°, Then the angle of elevation is (90 - 12) = 78°.

We know, cos = adjacent/hypotenuse.

cos78° = 1000/hypotenuse.

hypotenuse = 1000/cos78°.

hypotenuse = 4810 feet.

learn more about trig ratios here :

https://brainly.com/question/14977354

#SPJ1

Answer:

1022

Step-by-step explanation:

cos 12 = 1000/x

it is not accurate to state that one of the cross sections is a square as it will be a rectangle.

What is a square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

The given figure is a rectangular cuboid

Another name for a three-dimensional orthotope is a right rectangular prism, often known as a rectangular cuboid or rectangular parallelepiped.

Here the side of the cuboid is a rectangle, so the cross-section of that will be a rectangle, not a square.

Hence it is not accurate to state that one of the cross sections is a square.

Learn more about square, by the following link.

brainly.com/question/25092270

#SPJ1

Answer:

  incorrect premise

Step-by-step explanation:

You want to know why it is inaccurate to say one of the cross sections of a rectangular prism is a square.

Cross sections parallel to any face will have the same shape as the face. Those may or may not be square, depending on the shape of the face.

However, if a cross section may be made at any angle, there is always a cross section of a rectangular prism that can be a square. The attached figure shows an example.

Answer: Because there is no image or question I have to make a question myself. If Jimmy had X and Samantha has 17 which is 8 more than Tim and Tim has 20 less than Jimmy. What does Jimmy have?

Step-by-step explanation:

First, we isolate X.

X = Tim + 20.

Tim = 11.

11 + 20 = X

So X = 31

On solving the provided question, we can say that Area of pizza is [tex]\pi*r^2[/tex]=25 pi in^2 Divide that by 8 3.125 [tex]\pi in^2[/tex] => 9.82 cm^2 => [tex]9.8 cm^2[/tex] is the  answer

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

Area of pizza is [tex]\pi*r^2[/tex]=25 pi in^2

Divide that by 8

3.125 [tex]\pi in^2[/tex] => 9.82 cm^2

[tex]9.8 cm^2[/tex] is the  answer

To know more about area visit:

https://brainly.com/question/13194650

#SPJ1

Answer:  x = 7

Step-by-step explanation:

    [tex]\frac{2x}{7} =\frac{6}{3}[/tex]

we cross multiply, we get

2x(3) = 6(7)

   6x = 42

     x = 7

Answer: 30 cars left

Step-by-step explanation:

if from 33 cars we subtract 3, we get 30 cars left.

33 - 3 = 30 ...answer

hope that helps...

Answer:I earn $26.68 by mowing lawns.

Step-by-step explanation:

Answer:

Somethings telling me this is a trick question but the answer is 2.

Step-by-step explanation: