Anthony recorded the heights and weights of the 15 boys in his class. Then he drew the scatter diagram shown below using the information.

Answer:

1)0.123( bar on 3)

Let X = 0.123 ( bar on 3)

Then X = 0.1233 --------(1)

Multiply equation (1) by 100 we get,

100X = 12.33 --------(2)

Again multiply equation (2) by 10 we get,

1000X = 123.33 -------(3)

Subtract equation (2) from equation (3) we get,

1000X = 123.33

100X = 12.33

____________

900X = 111

X = 111/900

Hence,

0.123 ( bar on 3) is in the form of 111/900 which is in the form of P/Q.

Answer:

To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;

3·4ⁿ is divisible by 3 and 51 is divisible by 3

Where we have;

[tex]S_{(n)}[/tex] =  3·4ⁿ + 51

[tex]S_{(n+1)}[/tex] = 3·4ⁿ⁺¹ + 51

[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ

[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ

∴ [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9

Given that we have for S₀ =  3×4⁰ + 51 = 63 = 9×7

∴ S₀ is divisible by 9

Since  [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9, we have;

[tex]S_{(0+1)}[/tex] - [tex]S_{(0)}[/tex] =  [tex]S_{(1)}[/tex] - [tex]S_{(0)}[/tex] is divisible by 9

Therefore [tex]S_{(1)}[/tex] is divisible by 9 and [tex]S_{(n)}[/tex]  is divisible by 9 for all positive integers n

Step-by-step explanation:

Step-by-step explanation:

530pm = 17:50 in 24hr/military time

915pm = 21:15 in 24hr/military time

therefore..

24hr/military time. 21:15 - 17:50 = 3.65hr

our time. 3hr 45min

It took Sarah 3 hours and 45 minutes to finish her homework

The answer in 24 hour clock system is 3:45

The calculation can be done as follows

Sarah started her home work at 5:30 pm

She finished at 9:15pm

The time range here is 3 hours, 45 minutes

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Answer:

D

Step-by-step explanation:

We have proven that ∠D ≅ ∠A as shown below

From the question, we are to complete the proof

Statements                                           Reasons

  AB ≅ DB                                             1. Given

1. EB ≅ CB

2. ∠ ABC ≅ ∠DBE                                2. Congruent postulate

3. ΔABC ~ ΔDBE                                3. Side-angle-side postulate

4. ∠D ≅ ∠A                                         4. CPCTC (Corresponding parts of

                                                               congruent triangles are congruent.)

Hence, we have proven that ∠D ≅ ∠A  

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Answer:

hello : here is an solution

Step-by-step explanation:

Answer:

Option (1)

Step-by-step explanation:

Let the number of adult tickets sold = x

And the number of child tickets sold = y

Cost of adult tickets sold = $8x

And the cost of child tickets sold = $4y

If the theater company needs to earn at least $1280,

8x + 4y ≥ 1280

2x + y ≥ 320 ---------(1)

Since community center has a capacity of 240 people,

x + y ≤ 240 ----------(2)

By graphing these inequalities with the help of a graphing tool,

Shaded area above the solid line will be represented by inequality (1) (red line)

And the shaded area below the line will be the represented by inequality (2) (blue line)

Common area of both the shaded regions will represent the solution area .

Option (1) will be the answer.

Answer:

x > 3

Step-by-step explanation:

Given 2 sides of a triangle then the third side x will be

difference of sides < x < sum of sides , that is

15 - 12 < x < 15 + 12, so

3 < x < 27

Thus x > 3

Answer:

C. 3

Step-by-step explanation:

x > 3

Ed 2020

Answer:

[tex] \dfrac{1}{a^6} [/tex]

Step-by-step explanation:

[tex] a^{-6}x^0 = [/tex]

[tex] = \dfrac{1}{a^6} \times 1 [/tex]

[tex] = \dfrac{1}{a^6} [/tex]

Answer:

The submarine is  307.8 yards below sea level.

Step-by-step explanation:

Since the 500 yards are the hypotenuse of the right angle triangle, the acute angle opposite the side of the triangle we need to find is known ([tex]38^o[/tex]), we can use the sine function to solve the problem:

[tex]sin(\theta)=\frac{opposite}{hypotenuse} \\sin(38^o)=\frac{x}{500} \\500\,*\,sin(38^o)=x\\x = 307.8307\,\,yards[/tex]

which rounded to the nearest tenth is : 307.8 yards

Answer:

9.36kg

Step-by-step explanation:

Given That:

Mass of her Packages = 8.7 kg

Mass of bag = 660g = 0.66 kg

Total Mass = ?

To find the total mass, add the 2 weight together :"

8.7 + 0.66 = 9.36kg.

Hope this helps.

Good Luck

Answer:

Mass of the things=8.7kg

Mass of the bag=660g=0.66kg

Total mass=mass of the bag+mass of the things

Total mass=8.7kg+0.66kg

Total mass=9.36kg≈9kg

Step-by-step explanation:

i hope this will help you :)

Answer:

Variable

Step-by-step explanation:

A variable is a letter or symbol used as a placeholder for an unknown value in an expression or equation.

Hope this helps..

Good Luck!

Answer:

variable

Step-by-step explanation:

A symbol use to represent an unknown value in an expression or an equation is called a variable.

Answer:

x = 200

Step-by-step explanation:

1/5x – 2/3y = 30

substitute in y  

1/5x - 2/3(15) = 30

multiply  

1/5x - 10 = 30

isolate the variable  

1/5x = 40

multiply each side by 5  

x = 200

Answer:

x = 200

Step-by-step explanation:

1/5x - 2/3y = 30

Put y as 15 and evaluate.

1/5x - 2/3(15) = 30

1/5x - 30/3 = 30

1/5x - 10 = 30

Add 10 on both sides.

1/5x = 40

Multiply both sides by 5.

x = 200

Answer:

The gap in the histogram simply means that: out of all the automobiles sampled, there were none with number of miles driven between 17,500 miles and 32,500 miles.

Step-by-step explanation:

The histogram in question is missing from the question. It was obtained online and is attached to this solution.

A histogram is a chart that represents numerical data using bars. The dataset is split into intervals, each interval is represented by a bar, and the number of variables in each interval makes up the frequency for that interval.

If the bars are of equal width, the height of each bar corresponds to the frequency of the interval represented by that bar. If not, the frequency is given by the area of each bar (this is the major difference between a Bar chart and a histogram).

For this question, the histogram shows the number of miles driven by a sample of automobiles in New York City, the frequency of automobiles in each interval of miles driven is presented on the y or vertical axis and the miles driven is shown on the x-axis.

It is clear that 50 automobiles are in this sample and the class width of each interval of miles driven is 5000 miles.

So, the gap in between this histogram between the interval just after 17500 miles driven and just before 32500 miles driven simply means that none of the automobiles sampled had number of miles driven within this range.

Hope this Helps!!!

Answer:

The answer is

Step-by-step explanation:

- 3.4x + 4.7 - ( 3 + 2.9x)

Remove the bracket

That's

- 3.4x + 4.7 - 3 - 2.9x

Simplify

Group like terms

- 3.4x - 2.9x + 4.7 + 3

- 6.3x + 1.7

We have the final answer as

Hope this helps you

Answer:

The answer is

1.7 - 6.3x

Step-by-step explanation:

kjihugyfvbjhiuyghnjkiohuygt7o89hub

Answer:

1+B,2+D,3+E,4+C and 5+A

Step-by-step explanation:

(A)161 (B)130 (C)168 (D)150 (E)132

1. 26 x 5=130

This is Option B, therefore we have the match:1+B

2. 25 x 6=150

This is Option D, therefore we have the match:2+D

3. 22 x 6=132

This is Option E, therefore we have the match: 3+E

4. 21 x 8=168

This is Option C, therefore we have the match: 4+C

5. 23 x 7=161

This is Option A, therefore we have the match:5+A

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Answer:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

From the graph using points ( 5 , - 4) and

( -5 , 2)

Slope = 2+4/ -5 - 5= 6/-10 = - 3/5

Equation of the line using point (5,-4) is

y + 4 = -3/5(x - 5)

y = -3/5x + 3 - 4

y = -3/5x - 1

Hope this helps

The first column is found by plugging in the x values to get corresponding y values. For instance, if x = -5, then y is...

y = x^2+3x-18

y = (-5)^2+3(-5)-18

y = 25-15-18

y = 10-18

y = -8

So that explains how they got -8 in the second column, next to x = -5.

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

The column of first differences is found by subtracting the adjacent terms in the y column. The distance from y = -8 to y = -14 is 6 units, so we'll write 6 in the first row of the "first differences" column. The rest of the values of this column are filled out in a similar fashion. This means that you'll need to completely fill out the y column before you can move onto the "first differences" column.

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

The second differences is found by subtracting the adjacent first differences. You should find the results of this column are all the same value. This is true of any quadratic function.

Answer:

Step-by-step explanation:

If the tip varies directly with the number of guests, it means that an increase in the amount of tip would be as a result of an increase in the number of guests and a decrease in the amount of tip would be as a result of an decrease in the number of guests.

If we introduce a constant of proportionality, k , the relationship would be

t = kg

Given that

When t = 18, g = 10, then

18 = k × 10

k = 18/10 = 1.8

Therefore, the equation representing the relationship is

t = 1.8g

Answer:

answer is a

Step-by-step explanation:

Answer:

≈ 18.87 cm²

Step-by-step explanation:

The shaded area is the difference between the area of the trapezium and the semicircle.

The area (A) of the trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h( a + b)

where h is the height and a, b the parallel bases

Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus

A = [tex]\frac{1}{2}[/tex] × 4 × (14 + 8) = 2 × 22 = 44 cm²

area of semicircle = [tex]\frac{1}{2}[/tex]πr² = [tex]\frac{1}{2}[/tex]π × 4² = 8π cm²

Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places )

Answer:≈ 18.87 cm²

Step-by-step explanation:

Answer:

≈ 18.87 cm²

Step-by-step explanation:

The shaded area is the difference between the area of the trapezium and the semicircle.

The area (A) of the trapezium is calculated as

A = h( a + b)

where h is the height and a, b the parallel bases

Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus

A = × 4 × (14 + 8) = 2 × 22 = 44 cm²

area of semicircle = πr² = π × 4² = 8π cm²

Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places

Answer:

48

Step-by-step explanation:

81 - 33 = 48

Answer:

48

Step-by-step explanation:

81 - 33 = 48

Do 81 - 30 first = 51

Then do 51 - 3 = 48

Answer:

The transformation was a 90° rotation about the origin.

Step-by-step explanation:

Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4) A' (–1, –1) B' (–1, 1) C' (–4, 1) Which best describes the transformation? The transformation was a 90° rotation about the origin. The transformation was a 180° rotation about the origin. The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.

Answer: Transformation is the process of moving a point in a graph to another point. The new point formed is the image of the old point. When an object is transformed each point of the object is moved to another point. There are three types of transformation: Reflection, Rotation, Translation and dilation.

If a point O(x, y) is rotated 90° rotation about the origin., the new point is at O'(-y, x). That is the x coordinates becomes negative of the y coordinate and the y coordinate becomes the x coordinate.

The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4), If a transformation of 90° rotation about the origin is done, the new points are A' (–1, –1) B' (–1, 1) C' (–4, 1)

Answer:

The answer is a

Step-by-step explanation:

Answer:

[(a + b), c]

Step-by-step explanation:

Midpoint of a segment with extreme ends represented by ordered pairs [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex],

Midpoint = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

It is given that extreme ends of the segment QS are Q(2b, 2c) and S(2a, 0)

Coordinates of the midpoint of QS will be,

= [tex](\frac{2a+2b}{2},\frac{2c+0}{2} )[/tex]

= [(a + b), c]

Therefore, ordered pair representing the midpoint of QS will be [(a + b), c].

Answer:

(a+b, c)

Step-by-step explanation:

CORRECT FOR ACELLUS

Answer:

? = 44 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp side/ adjacent side

tan ? = 46/48

Take the inverse tan of each side

tan ^-1 ( tan ?) = tan ^ -1 ( 46/48)

   ? = 43.78112476

To the nearest degree

? = 44 degrees

Answer:

Check Explanation

Step-by-step explanation:

The number line required to answer this question is missing.

But I'll explain how to get the total number of basketball cards Juan has, given the number that corresponds to 60% of the total number of cards.

Let the total number of basketball cards be x.

The first step is to check the number line presented. We furst require the number that corresponds to 60% of all of Juan's basketball cards..

Let us assume that the number of basketball cards according to the number line is 45.

This means that

60% of the total number of basketball cards = 45

60% × x = 45

0.6x = 45

x = (45/0.6) = 75 basketball cards.

So, the way to go is just to divide the number that the number line gives (which represents 60% of the total number of basketball cards) by 0.6 to obtain the total number of basketball cards.

Hope this Helps!!!

Answer:

36

Step-by-step explanation:

quick maths

Answer:

36 rectangles

Step-by-step explanation:

Assuming that all you are asking for is the individual number of squares (not the number of squares and rectangles that can be made when combining the individual ones), the answer is 36.

We get this by multiplying the six squares on one side by the six on the other side. This allows us to calculate the total number! You can do this on a calculator or by hand.

However, if you would like the TOTAL number of rectangles that includes combining the individual ones, this chessboard would have 91 squares and 441 rectangles.

Answer:

Solution,

[tex]7( \sqrt[3]{2x} ) - 3( \sqrt[3]{16x} ) - 3( \sqrt[3]{8x} ) \\ = 7 \sqrt[3]{2x} - 3 \times ( \sqrt[3]{2 \times 2 \times 2 \times 2x} - 3 \times \sqrt[3]{2 \times 2 \times 2x} \\ = 7 \sqrt[3]{2x} - 3 \times (2 \sqrt[3]{2} x) - 3 \times 2x \\ = 7 \sqrt[3]{2x} - 3 \times 2 \times \sqrt[3]{2x} - 3 \times 2x \\ = 7 \sqrt[3]{2x} - 6 \sqrt[3]{2x} - 6x[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

4(3x+2)

Step-by-step explanation:

Since all four sides of a square are the same length, the perimeter can be expressed as four times one of the side lengths. In this case, that is 4(3x+2). Hope this helps!

Step-by-step explanation:  since there are 4 sides on a square that will be the answer.

Answer: 4(3x + 2)

Answer:

587.18 square inches

Step-by-step explanation:

We would find the Total surface area of the cone

Diameter of the cone = 11 inches

Radius = Diameter ÷ 2 = 11 / 2 = 5.5 inches

Slant height ( l ) = 28.5 inches

Let's take π = 3.14

Total Surface Area of a cone = πrl + πr²

= πr(l + r)

= 3.14 × 5.5( 28.5 + 5.5)

= π × 5.5(34)

= 587.18 square inches

There the square inches of paper will she need to cover the entire cone is 587.18 square inches