Jed wants to prove that his test scores are greatly improving. He makes the graph shown here.
Explain why someone may think this graph is misleading.

The solutions are -

S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)

S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)

S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)

The sum of the series is 1/3.

To find S3, we need to find the sum of the first 3 terms of the series:

S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)

To find S4, we need to find the sum of the first 4 terms of the series:

S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)

To find S5, we need to find the sum of the first 5 terms of the series:

S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)

To find the sum of the telescoping series, we can use the property of the telescoping series where the terms will cancel out. In this case, we can see that the first term of each group of two terms cancels out with the second term of the next group of two terms.

S = (1/3) - (1/8)

The series starts at n=2 and ends at infinity, so the sum of the series is the difference between 1/3 and the limit of 1/n as n approaches infinity, which is zero.

S= (1/3) -0 = 1/3

So the sum of the series is 1/3.

Read more about the telescoping series:

brainly.com/question/14523424

#SPJ4

The complete question is -

Calculate S3, S4, and S5 and then find the sum for the telescoping series: S=∑n=2∞(1/n+1)−(1/n+2). where Sk is the partial sum using the first k values of n.

Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

[tex]\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\[/tex]

To know more about circle visit:

brainly.com/question/29142813

#SPJ1

On solving the provided question, we can say that area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in the circle

the given radius is as = 3.4

area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ1

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

More can be learned about the Empirical Rule at brainly.com/question/10093236

#SPJ1

The formula for the area of a trapezoid is (a+b)*h/2, where a and b are the lengths of the bases and h is the height.

To estimate the total area between the curve and the x-axis using trapezoids, we can divide the region between the curve and the x-axis into a number of trapezoids, and calculate the area of each trapezoid. The sum of the areas of all the trapezoids will estimate the total area.

For example, consider the curve y = x^2 and the x-axis between x = 1 and x = 2. We can divide this region into 3 trapezoids with bases at x = 1, x = 1.5, x = 2, and heights of 0.25, 0.5625, and 1 respectively.

The area of the first trapezoid is (1 + 1.5) * 0.25 / 2 = 0.1875

The area of the second trapezoid is (1.5 + 2) * 0.5625 / 2 = 0.40625

The area of the third trapezoid is (2 + 2) * 1 / 2 = 1

The sum of the areas of all the trapezoids is 0.1875 + 0.40625 + 1 = 1.60625. This estimates the total area between the curve y = x^2 and the x-axis between x = 1 and x = 2.

To know more about the area of the trapezoid visit :

https://brainly.com/question/21025771?referrer=searchResults

#SPJ4

The domain and the range of this function in interval notation include the following;

Domain = [-6, ∞].

Range = [-∞, 0].

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:

Domain = -6 < x < ∞ or [-6, ∞].

Range = -∞ < y < 0 or [-∞, 0].

Read more on domain here: brainly.com/question/17003159

#SPJ1

The answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]

According to the question,

AX [tex](D^{-1} + X^{-1} B^{-1} )[/tex] =C

⇒X[tex](D^{-1} + X^{-1} B^{-1} )[/tex]= [tex]A^{-1} C[/tex]

⇒[tex]XD^{-1} + XX^{-1} B^{-1}[/tex] = [tex]A^{-1} C[/tex]

⇒ [tex]XD^{-1} +B^{-1}[/tex] = [tex]A^{-1} C[/tex]

⇒ [tex]XD^{-1} = A^{-1} C -B^{-1}[/tex]

⇒  [tex]X= (A^{-1} C -B^{-1})D[/tex]

So, the answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]

Read more about matrix :

https://brainly.com/question/2456804

#SPJ4

The intercepts of the graph are

The polynomial is given as

G(x) = -2(3x+4)(x-1)(x-3)^2

Rewrite as

G(x) = -2(3x+4)(x-1)(x-3)²

The x-intercepts of a polynomial are the points at which the polynomial crosses the x-axis.

To find the x-intercepts, we need to set y = 0 and solve for x.

-2(3x+4)(x-1)(x-3)² = 0

Divide through by -1

(3x+4)(x-1)(x-3)² = 0

Now we can solve for each factor equal to zero:

3x+4 = 0, x = -1.33

x-1 = 0, x = 1

x-3 = 0, x = 3

So the x-intercepts are -4/3, 1, 3

The y-intercept of a polynomial is the point at which the polynomial crosses the y-axis.

For this polynomial, we have

G(0) = -2(30+4)(0-1)(0-3)² = -2(4)(-1)(9) = 72

So the y-intercept is (0, 72)

See attachment for the graph

Read more about polynomial at

https://brainly.com/question/7693326

#SPJ1

Answer:

x=8

Step-by-step explanation:

Answer:

3x+y+4-(y + 6) = 14 + x

x=8              

Answer: b

Step-by-step explanation:

Numbers divisible by 2 and 5:

Check:

[tex]10\div2=5\\10\div5=2[/tex]  

[tex]20\div2=10\\20\div5=4[/tex]

[tex]30\div2=15\\30\div5=6[/tex]

Answer:

7 students.

Step-by-step explanation:

A trick for this is to find 10% of the students in the Environmental Club and then divide by 2.

10% of 140 is simple; just remove the 0 and you got 14.

Next, divide 14/2 to get 5%

14/2 = 7

7 students are apart of the Environmental Club

The correct graph of the solution to the compound inequality as given in the task content is;

As evident from the task content, it follows that the correct graph of the solution to the compound inequality is to be determined.

Since the given compound inequality is; -13 > -5x + 2 > -28.

To solve the inequality, subtract 2 from all sections of the compound inequality;

-15 > -5x > -30

Divide through the inequality by -5 while flipping the inequality signs so that we have;

3 < x < 6

Therefore, the correct graph for the compound inequality in discuss is as represented in the attached image.

Read more on graph of compound inequalities;

https://brainly.com/question/29366662

#SPJ1

The value of  [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex] is after simplification is C)-30

What is mixed fraction?

A mixed number combines an integer (whole number) with a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number). When a number contains both an integer (whole number) and a correct fraction, it is known as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).

Here the given expression is ,

=> [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex]

Now we need to convert them into improper fraction then,

=> [tex]\frac{15+3}{5}[/tex] × [tex]\frac{-(24+1)}{3}[/tex]

=> [tex]\frac{18}{5}[/tex] × [tex]\frac{-25}{3}[/tex]

=> 6 × -5 = -30

Hence the correct option is C)-30.

To learn more about mixed fraction refer the below link

https://brainly.com/question/745462

#SPJ1

When a fair coin is tossed nine times, there is a 0.090 (rounded off to the nearest thousandth) chance that at most one will land on heads.

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number between 0 and 1, where about 0 represents how likely the event is to occur and 1 represents certainty. A probability is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the total number of outcomes to the proportion of occurrences in a whole set of equally likely options that lead to a specific occurrence.

given

binomial probability ⁿCₓ[(p)ˣ(q)ⁿ⁻ˣ]

where p= probability of tail = 1/2 (favorable outcome)

q = probability of head = 1/2: (1 - p)

n = total outcome = 9

x = 4

ⁿCₓ[(p)ⁿ(q)ⁿ⁻ˣ] = ⁹C₄[(1/2)⁴(1/2)⁵]

=  [1/16 x 1/32]

= (512)

126/512 = 0.24609

≈ 0.090 nearest thousandth rounded off .

When a fair coin is tossed nine times, there is a 0.090 (rounded off to the nearest thousandth) chance that at most one will land on heads.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The quotient of the division is x^3 - 3x^2 - 10x + 64

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

quotient of (x^4-6x^3-19x^2+24x) divided by (x+3)

Using the long division method of quotient, we have

x + 3 | x^4 -6x^3 -19x^2 +24x

The division steps are as follows

            x^3 - 3x^2 - 10x + 64

x + 3 | x^4 -6x^3 -19x^2 +24x

         x^4 + 3x^3

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

              -3x^3  -19x^2 +24x

              -3x^3 - 9x^2

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

                          -10x^2 + 24x

                          -10x^2 - 30x

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

                                           64x

                                           64x + 192

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

                                            -192

Hence, the quotient is x^3 - 3x^2 - 10x + 64

Read more about long division at

https://brainly.com/question/25289437

#SPJ1

Answer:

f(8) = 51

Step-by-step explanation:

f(x) = 6x + 3

Let x = 8

f(8) = 6(8) + 3

     = 48+3

     = 51

Answer:

51

Step-by-step explanation:

f ( x ) = 6x + 3

To find the value of f ( 8 ), replace x with 8.

f ( 8 ) = 6 × 8 + 3

f ( 8 ) = 48 + 3

f ( 8 ) = 51

The angle B in triangle ABC is 60° i.e. C.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now

∠NAB+∠CAB=180°  (Supplementary angles)

∠CAB=180-∠NAB

=180-100

∠CAB=80°

As

∠A+∠B+∠C=180° (sum of all angles of a triangle =180°)

∠B=180-80-40

∠B=60°

To know more about triangles visit the link

https://brainly.com/question/2773823?referrer=searchResults

#SPJ1

Answer:

x = - 2

Step-by-step explanation:

the magnitude of a vector < a, b, c > is

[tex]\sqrt{a^2+b^2+c^2}[/tex]

given vector < 1, 2, x > has magnitude of 3 , then

[tex]\sqrt{1^2+2^2+x^2}[/tex] = 3

[tex]\sqrt{1+4+x^2}[/tex] = 3

[tex]\sqrt{5+x^2}[/tex] = 3 ( square both sides to clear the radical )

5 + x² = 3² = 9 ( subtract 5 from both sides )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

since x is negative then x = - 2

Therefore , the solution to the given problem of expression comes out to be -8 * 10³.

A number must be substituted for each variable and arithmetic operations must be carried out in order to verify an algebraic expression. The response variable is equivalent to 6 in the illustration above because 6 + 6 equals 12. The variables can be replaced with their values if we know what they are, and the expression can then be evaluated.

Here,

Given : - 8,000

To write -8000 with a power of 10

Thus,

-8000 written into

=> -8 * 10³

So, we get -8 * 10³ as the scientific notation for the given expression

Therefore , the solution to the given problem of expression comes out to be -8 * 10³.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Answer:

$20,400

Step-by-step explanation:

You just have to multiply 680,000 by 0.03 (since 3% is equivalent to 0.03)

If the streetlights are spaced in the same way, there will be 48 streetlights on the 4-mile road.

First, we know that there are 18 streetlights evenly spaced on a 1.5 mile road.

Then the space between consecutive streetlights is:

1.5mi/18 = (3/36) mi = (1/12) mi

Now, the number of streetlights that we will have on a 4-mile road is given by the quotient between the length of the road and the distance between consecutive streetlights, it is:

N = 4mi/(1/12 mi) = 12*4 = 48

There will be 48 streetlights on a 4 mile road.

Learn more about quotients at:

https://brainly.com/question/629998

#SPJ1

A table which has a constant of proportionality between y and x of 0.9 include the following: B. table B.

In order to have a proportional relationship and equivalent ratios that is constant, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) based on the given parameters in each table:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 17/18

Constant of proportionality (k) = 0.94 (False).

For the variables x and y in table B, the constant of proportionality (k) is given by;

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 3.6/4 = 5.4/6 = 10.8/12

Constant of proportionality (k) = 0.9 (True).

For the variables x and y in table C, the constant of proportionality (k) is given by;

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 3.3/3

Constant of proportionality (k) = 1.1 (False).

Read more on proportionality here: https://brainly.com/question/16576415

#SPJ1

The given series is convergent and the sum(S) is 5.555.

Consider 10 - 8 + 6.4 - 5.12 + ...

A geometric progression will converge if the common ratio of the series is between -1 and 1.

Here is the common ratio,

r = -8/10

⇒ r = -0.8

Which is -1 < -0.8 < 1.

Hence, the given series is convergent.

Sum of series = S = a/(1 - r)

Here, first term(a) = 10,

common ratio(r) = -0.8,

S = a/(1 - r)

⇒ S = 10/(1 - (-0.8))

⇒ S = 10/(1 + 0.8)

⇒ S = 10/1.8

⇒ S = 5.555

Therefore, the given series is convergent and the sum( S)is 5.555.

Read more about geometric progression :

https://brainly.com/question/12006112

#SPJ4

An IV is infusing at 77mcgtt/min. rate of flow equal in mL/h is 77 mL/h

1gtt/min equals 3.00 mL/h

If you simply need to figure out the infusion rate, or the mL per hour to infuse, take the total volume in mL, divided by the total time in hours that the medication is ordered to be infused over, to equal the rate in mL per hour.

1 drop per minute to milliliters per hour = 3.00 mL/h

2 drops per minute to milliliters per hour = 6.00 mL/h

Change hours to minutes. Change milliliters to drops.

1 ml : 60mcgtt

1hr :60min

77mcgtt/min =77*60/60 ml/h

                  =77ml/h

To know more about  rate of flow visit brainly.com/question/27880305

#SPJ4

The center of the ellipse is (2, -8), The endpoints of the major axis are 10 units from the center, The endpoints of the minor axis are 9 units from the center, To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with  smooth curve.

An ellipse in mathematics is a plane curve that has two focal points and is such that the sum of the two distances from any point on the curve to the focal points is a constant. It generalizes a circle, a special kind of ellipse in which the two focal points coincide.

Glven:

The equation of ellipse is,

[tex]\frac{(x-2)^2}{81}+\frac{(x+8)^2}{100}=1[/tex]

SInce, the general form of ellipse is,

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

where,

(h, k) is the center of ellipse

a is the minor axis

b is the major axis.

Here

(h, k) = (2, -8) is the center of the ellipse.

9 is the minor axis and 10 is the major axis of the ellipse.

Also the graph of ellipse connects (2, 2), (11, -8), (2, -18) and (-7, -8) with  smooth curve.

Hence,  the center of the ellipse is (2, -8).

The endpoints of the major axis are 10 units from the center.

The endpoints of the minor axis are 9 units from the center.

To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with  smooth curve.

The graph of the ellipse visit.

To know more about ellipse visit:

brainly.com/question/9702250

#SPJ1

The exact value of cos (-pi/3) can be found using the unit circle or the angle addition formula.

Using the unit circle, we know that the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is cos(-pi/3) and y-coordinate is sin(-pi/3).

On the unit circle, the angle of -pi/3 is the same as the angle of 2pi/3 (since the unit circle has a period of 2pi), therefore the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is -1/2.

Alternatively, using the angle addition formula:

cos (-pi/3) = cos(pi - pi/3) = cos(pi) * cos (pi/3) - sin(pi) * sin(pi/3) = -1/2

So, the exact value of cos (-pi/3) is -1/2.

The area of trapezoid is 16 m².

Given in the figure,

Height of trapezoid = 4 m

Length of 1st parallel base = 2 m

Length of 2nd parallel base = 6 m

We know that,

Area of trapezoid = 1/2 * sum of bases * height

∴

Area of trapezoid = 1/2 * (2+6) * 4

                             = 8 * 2 = 16 m²

Therefore, the area of trapezoid is 16 m².

Learn more about trapezium at

https://brainly.com/question/30042904

Answer:

Welcome to Gboard clipboard, any text that you copy will be saved here.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Tap on a clip to paste it in the text box.

The new point that will be formed when the point (-4,5) is rotated 270 degrees counterclockwise is; (5, 4)

There are different types of transformations namely dilation, rotation, reflection e.t.c

Now, when we rotate a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means that we switch x and y and make x negative.

Now, we are told that the point (-4,5) is rotated 270 degrees counterclockwise. Thus, following the transformation rule as described above gives us;

(-4,5) → (5, 4)

Thus, we conclude that the new coordinate we will obtain in this process is (5, 4)

Read more about Transformation rule at; https://brainly.com/question/8987411

#SPJ1