Can the triangles be proven similar by AA?
Question options:

A)

No, similar triangles cannot contain a pair of parallel lines.

B)

Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).

C)

Yes, because || .

D)

No, the triangles contain no angles marked congruent.

Answers

Answer 1

Answer:

No, similar triangles cannot contain a pair of parallel lines. Yes, because || . Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).

Step-by-step explanation:

Answer 2

Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).

What is similarity?

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Both triangles are similar as,

∠QUR ≅ ∠TUS (vertical angles)

∠R ≅ ∠S (alternate interior angles).

So, By AA similarity criteria triangles are similar.

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Related Questions

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-14x^2+1035x-10266

Answers

The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13

Quadratic equation

y = -14x² + 1035x - 10266

solve the quadratic equation

-14x² + 1035x - 10266 = 0

x = -b ± √b² - 4ac / 2a

= -1035 ± √1035² -4(-14)(-10266) / 2(-14)

= -1035 ± √1071225 - 574896 / -28

= -1035 ± √496329 / -28

x = 1035 / 28 ± √496329 / 28

x = 11.80 or 62.13

The maximum value of x is 62.13

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The plot below shows the volume of paint left in 444 cans.
All measurements are rounded to the nearest \dfrac12
2
1

start fraction, 1, divided by, 2, end fraction pint.
A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.

A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.
If we split the total amount of paint so that each can had the same amount, how much paint would be in each can?

Answers

The amount of paint that would be contained in each of the can would be 8.

How to solve for the amount of paint.

Using the information in the question we have the following

We have to solve the equation as

(2 1/2) + 2(4) + 1(5 1/2) =

2.5 + 8 + 5.5

= 16

Each of these would have to hold 16/2 = 8 pints.

Answers

110 postcards Xiulin had at first.

What is algebric equation?

Algebric equation is a mathematical statement in which two equation set equal to each other.

Let the number of postcards belonging to Xiulin and Meifang be x.

Let the number of postcard Meifang gave to Xuilin be 'a'

Number of postcard left with meifang

=> x-a = 72

=> x = 72+a

Meifang had 76 fewer postcards than Xiulin.

so, (x+a)-72=76

72+a+a-72=76

2a = 76

a = 38

meifang give 38 cards to xuilin

x = 72+38

= 110

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Find the value of all trigonometric functions of 135°

Answers

Answer:

sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2

cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2

tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1

csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2

sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2

cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1

Step-by-step explanation:

hope this helps

Complete the table. Each column should contain equivalent values. One column has been completed for you. Make sure the fractions are stated in simplest form.
Fraction Decimal Percent
0.39 39%
0.82
22%
0.8

Answers

The complete table will be:

Fraction Decimal Percent

39/100 0.39 39%

82/100 0.82 82%

22/100 0.22 22%

3/4 0.75 75%

80/100 0.8 80%

Percentage

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

[tex]\frac{25}{100} =0.25*100=25%[/tex]

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks etc.

Line 1

Fraction Decimal Percent

39/100 0.39 0.39*100=39%

Line 2

Fraction Decimal Percent

82/100 0.82 0.82*100=82%

Line 3

Fraction Decimal Percent

22/100 0.22 22%

Line 4

Fraction Decimal Percent

3/4 0.75 0.75*100=75%

Line 5

Fraction Decimal Percent

80/100 0.8 0.80*100=80%

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One-fifth of a number x is less than 8. Find the greatest possible prime number x.

Answers

Hello there, I am unable to use the “less than” symbol. Sorry :( .

1/5x "less than" 8
x “Less than” 40

Prime number is 37,41.
Therefore x is 37.

– 42 – 54 + 96 =

what is the answer

Answers

Answer:

Answer:the answer is zero

Answer:the answer is zero Step-by-step explanation:

Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero

[tex] - 42 - 54 + 96 = 0[/tex]

The profit function for a certain commodity is given by () = 110 − 2 − 1000. Find the level of production that yields maximum profit and hence find the maximum profit.

Answers

Based on the profit function given, the level of production that yields the maximum profit is 55 units. The maximum profit is $2,025.

What is the maximum profits unit?

With a profit function:

=-x² + 110x - 1,000

Using a parabola function, we know:

= -b / 2a

The maximum units is:

= -110 / (-2 x 1)

= 55 units

The maximum profit is:

= -(55)² + (110 x 55) - 1,000

= $2,025

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The area of a rectangle is 44 ft², and the
Length of the rectangle is 3 ft less than twice
The width. Find the dimensions of the rectangle.

Answers

Answer:

Width = 5.5ft, Length = 8ft.

Step-by-step explanation:

Area of Rectangle = Length x Width

Let w be the Width of the rectangle.

From the information given from the question,

Length = 2w - 3 (3ft less than twice the width)

Area of Rectangle = [tex](2w-3)w\\=2w^{2} -3w[/tex] = 44

Now we can solve for w to find the dimensions.

[tex]2w^{2} -3w-44=0[/tex] (Quadratic Equations)

We can use the Quadratic formula to find w.

[tex]w=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Since a = 2, b = -3 and c = -44,

[tex]w=\frac{-(-3)+/-\sqrt{(-3)^{2}-4(2)(-44) } }{2(2)} \\= 5.5 or -4 (reject)[/tex]

We reject negative values here.

Therefore, the width of the Rectangle = 5.5ft

While the length of the rectangle = 2(5.5) - 3 = 11 - 3 = 8ft

How many full cases and additional items are needed to fulfill the order? 50 8

Answers

The computation illustrate that there'll be 13 cases and 2 additional units.

How to illustrate the information?

From the information given, it was stated that 80 units are needed, 6. units per case.

Therefore, the number of cases will be:

= 80/6

= 13 remainder 2.

Therefore, there'll be 13 cases and 2 additional units

Complete information

80 units are needed, 6. units per case. What is the number of cases and the number of additional units?

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for this graph, mark the statements that are true.

Answers

Answer:

C,D

Step-by-step explanation:

C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0

D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.

solve the following portion for x/11=8/3. round to nearest tenth

Answers

Answer is 29.3
Step by step
X/11 = 8/3
Cross multiply
3x = 88
Solve for x, divide both sides by 3
X = 29.333
Round to nearest tenth
X = 29.3

Please help me put them in correct place

Answers

The inequalities that match the given expressions are

x ≤ 95

x > 100

5x ≤ 100

20 ≤ x ≤100

respectively

Writing linear inequalities

From the question, we are to match the statements with the corresponding inequalities

Nora's height(x) is at least 5 cm less than Stacy who is 100 cm tall

x ≤ 100 -5

x ≤ 95

Temperature(x) is greater than the boiling point of water (100 °C)

x > 100

John buys x chocolates worth $5 each but he has only $100 in his pocket

5x ≤ 100

Ronny decided not to exceed 100L of water usage and ends up using at least 1/5th of this limit every day

x ≤ 100

and

x ≥ 1/5 × 100

x ≥ 20 ≡ 20 ≤ x

∴ 20 ≤ x ≤100

Hence, the inequalities that match the given expressions are

x ≤ 95

x > 100

5x ≤ 100

20 ≤ x ≤100

respectively

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Which is the graph of the inequality?

5y+x>−10

Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.

Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.

Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.

Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.

Answers

We can simplify the inequality to:

y > (-1/5)*x - 2

From that, we conclude that the correct option is the last one.

Which is the graph of the given inequality?

Here we have the inequality:

5y + x > -10

If we isolate y, we get:

y > (-10 - x)/5

y > (-1/5)*x - 2

Then the inequality will be a dashed/dotted line with a negative slope, that passes through the point (0, -2), such that the region above and to the right of the line is shaded.

From that we conclude that the correct option is the last one:

"Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray."

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help me pls: what is
four and two eighths minus two and five eighths equals

Answers

Answer:

13/8

Step-by-step explanation:

4 2/8 - 2 5/8

34/8 - 21/8 = 13/8

1 5/8 as a mixed fraction

Hector wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?

A trapezoid with a height of 4 feet and bases of 6 feet and 10 feet is shown.

$136
$128
$112
$32

Answers

The total cost to laminate the table top is $128.

What is the total cost to laminate the table top?

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.

The first step is to determine the area of the table top.

Area of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height

0.5 x (6 + 10) x 4 = 32 square foot

Now, multiply the area by the cost per square foot

32 x 4 = $128

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Is x – 5 a factor of the function f(x) = x3 – 5x2 + 7x – 35? Use the Remainder Theorem to justify your answer.

Answers

Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,

Remainder theorem

In order to determine whether x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35, we will show that f(5) = 0

Substitute x = 5 into the function to have;

f(5) = 5^3 – 5(5)^2 + 7(5) – 35

f(5) = 125 - 125 + 35 - 35

f(5) = 0

Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,

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Calculate the geometric center of the grapg under the function

Answers

The geometric center of the graph under the function is 5/3

How to determine the geometric center of the graph under the function?

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

Answers

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

How to use weighted averages to find the correct juice concentration

In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:

70 · 140 = 55 · x + 80 · (140 - x)

70 · 140 = 80 · 140 - 25 · x

25 · x = 10 · 140

x = 56

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

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How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the population standard deviation is 40 . Round your answer to next whole number.

Answers

Using the z-distribution, it is found that a sample of 171 should be selected.

What is a z-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

For this problem, the parameters are:

[tex]z = 1.96, \sigma = 40, M = 6[/tex]

Hence we solve for n to find the needed sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]6 = 1.96\frac{40}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 40 \times 1.96[/tex]

[tex]\sqrt{n} = \frac{40 \times 1.96}{6}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2[/tex]

n = 170.7.

Rounding up, a sample of 171 should be selected.

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Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.

Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut

Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.

Answers

Answer:

She does not get bonus points and she ends up at level 5.

Equation: 4 - 6 + 8 -1 = 5

Equation using only addition: 4 + -6 + 8 + -1 = 5

I hope this helps!

17. The Bricklayer needs 100 pieces of angle, each to be cut 54 3/16" long. 1 point
How many can be cut from a 20% length (do not include waste or thickness of
cut)? How many pieces of 20' angle are needed in order to have the 100
pieces?

Answers

The number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5

How to determine the number

From the information given;

The bricklayer needs = 100 pieces of angle

The number of cuts = 54

Length of cuts = 3/ 16'' Inches

a. To determine the number of cuts form a 20% length, we have to multiply the length by the percentage and by the initial number of cuts

= 20/ 100 × 3/ 16 × 54

= 0. 2 × 0. 1875 × 54

= 2. 0

The number of cuts would be 2

b. To determine the number of pieces of 20' angle to have 100 pieces we would divide the initial number of pieces by the angle

= 100/ 20

= 5 pieces

The number of pieces of 20' angle is 5

Thus, the number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5

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A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30x +0.296,
where × represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?

Answers

Answer:

B: 8.3

Step-by-step explanation:

We will substitute 600 to the y, since our final answer will be a number that makes the value of the stock reach $600.

log (y) = 0.30x + 0.296

Replacing y with 600, the equation becomes:

log (600) = 0.30x + 0.296

2.78 = 0.30x + 0.296

To move all the x and real numbers to different sides, we take 0.296 away from both sides to form:

2.78 - 0.296 = 0.30x

2.484 = 0.30x

x = 8.28

The approximation of 8.28 will be rounded to 8.3.

Then our final answer will be B: 8.3

Complete the frequency table:

Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360

What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.

Answers

The percentage of students age 15 and above travel to school by bus is 47%

How to complete the table?

The table of values is given as:

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 18 165

Age 15 and above 65 195

Column totals 152 110 98 360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 87 18 60 165

Age 15 and above 65 92 38 195

Column totals 152 110 98 360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

Answers

Answer:

b = (a - 6)/2h

Step-by-step explanation:

a = 2bh + 6 (subtract 6 from both sides)

a - 6 = 2bh (divide both sides by 2)

(a - 6)/2 = bh (divide both sides by h)

(a - 6)/2h = b

Brainliest, please :)

I'm have some issues with the problem shown in the screenshot and would love some help.

Answers

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

Maximum volume of the box is approximately 1048.6 in.³

How can the dimensions and volume of the box be calculated?

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

[tex] \frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0[/tex]

Which gives;

[tex] \frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0[/tex]

6•x² - 106•x + 315 = 0

[tex]x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6} [/tex]

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

Width ≈ 18 - 2×4.55 in. = 8.89 in.

Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

Height = x ≈ 4.55 in.

The maximum volume of the box, V ≈ 1048.6 in.³

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Officially, variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ). An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit. Python’s most-followed style guide, PEP8 also suggests we limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.How many variable names can there be in Python if we abide by these two rules?

Answers

Abiding by the two rules, the number of variable names we can have in Python are; 63

How to name variables in Python Programming?

The rules for python are given as;

1) Variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ).

1b) An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit.

2) We limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.

Now, abiding by the two rules above, the number of variable names we can have in Python are;

26( A-Z) + 26(a-z) + 10(0-9) + 1 ( _ ) = 63 variable names

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The total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16
what is the price of each cap?
what is the price of what umbrella ?

Answers

If the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16 then the price of one umbrella is $8 and price of one cap is $4.

Given that the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16.

We have to find the price of one umbrella and one cap.

We have to form equations first to find the price of umbrella and cap.

Equation of two variables look like ax+by=c. It can be a linear equation, quadratic equation or a cubic equation.

let the price of umbrella be x and price of cap is y.

We know that total cost is equal to price of one unit multiplied by the units.

According to question.

2x+y=20----------1

x+2y=16-----------2

Multiply equation 2 by 2 and then subtract resulted equation from equation 1.

2x+y-2x-4y=20-32

-3y=-12

y=-12/-3

y=4

put the value of y in equation 2 to get the value of x.

x+2y=16

x+2*4=16

x+8=16

x=16-8

x=8

Hence the price of one umbrella is $8 and the price of one cap is $4.

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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5660 and his stock in Company B was worth $2500. The stock in Company A has increased 5% since last year and the stock in Company B has increased 9%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary)

Answers

Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

Company A: 5660 x 1.05 = $5,943.Company B: 2500 x 1.09 = $2,725.

The total values are given as follows:

Before the increase: 5660 + 2500 = 8160.After the increase: 5943 + 2725 = 8668.

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (8668 - 8160)/8160 x 100% = 6.2%.

The total percentage increase in the investor's stock account was of 6.2%.

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Answers

The percentage of students age 15 and above travel to school by bus is 47%

How to complete the table?

The table of values is given as:

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 18 165

Age 15 and above 65 195

Column totals 152 110 98 360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

Method of Travel to School

Walk/Bike Bus Car Row totals

Under age 15 87 18 60 165

Age 15 and above 65 92 38 195

Column totals 152 110 98 360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%