Valentina is cycling down a hill fast. To be most efficient, should Valentina use a gear on the back wheel that has a small diameter or a large diameter? Explain.

5. An action or process of solving a problem

Thats all I can answer for u :D

Answer:

Y=5X-7

Step-by-step explanation:

(2,3)

Y-Yo=m(X-Xo)

Y-3=m(X-2)

Y-3=mX-2m

Y=mX-2m+3

(5,18)

18=m(5)-2m+3

18=5m-2m+3

18=3m+3

18-3=3m

15=3m

15/3=m

5=m

Y=5X-2(5)+3

Y=5X-10+3

Y=5X-7

Answer:

Step-by-step explanation:

Let the missing part be x.

According to triangle proportionality theorem we have:

The required side is 28.

Similarity of a triangle is the ratio of their corresponding sides or angles which are equal .

Given that AB=35, AE=12 and CE=3.

Let BD=x ⇒ AD = 35-x

Triangle ΔABC and ΔADE are similar,

By using property of similarity,

AB/AC=AD/AE

35/15=35-x/3

x=28

value of side x=28.

To learn more on Similarity:

https://brainly.com/question/16919171

#SPJ1

Area of the other square is 7/20 cm²

Let side of the larger square be 'b' and side of the smaller square be 'a'.

Given the perimeter of the smaller square = 2 cm

⇒ 4a = 2

⇒ a = 2/4 = 1/2 cm

Given, ratio of the areas of squares = 5 : 7

⇒ area of smaller square/ area of larger square = 5 : 7

⇒ a²/b² = 5/7

⇒ (1/4)/b² = 5/7

⇒ b² = 7/(5×4) = 7/20

Therefore, area of the larger square = 7/20 cm²

To know more about area:

https://brainly.com/question/19554187

#SPJ1

The break-even point in unit sales of the company is $7,625.

According to the question,

Thus,

Break-even point =  fixed costs/margin per unit

Break-even point = $305,000/$40

Break-even point = $7,625

Thus, the break-even point in unit sales of the company is $7,625.

To know more about the breakeven point, here

https://brainly.com/question/15281855

#SPJ4

Answer:

  D  1,078.5 ft^2

Step-by-step explanation:

You want the area of a figure composed of a rectangle 100 ft long and 10 ft wide with semicircles of diameter 10 ft at each end.

The area of the rectangle is ...

  A = LW

  A = (100 ft)(10 ft) = 1000 ft²

The two half-circles have the area of a whole circle with radius 5 ft.

  A = πr²

  A = π(5 ft)² = 25π ft² ≈ 78.5 ft²

The area of the figure is the sum of the areas of its parts:

  total area = rectangle area + circle area

  total area = 1000 ft² +78.5 ft² = 1078.5 ft²

The total area of the figure is about 1078.5 ft².

The probability that a randomly selected CD player will have a replacement time of fewer than 8.0 years is 0.7389

P(X<8) = P((X-mean)/s <(8-7.1)/1.4)

= P(Z<0.64) = 0.7389 (from standard normal table)

= P(X>c)=0.02

= P(Z<(c-7.1)/1.4) = 1-0.02 = 0.98

= (c-7.1)/1.4 =2.05 (from the standard normal table)

= c = 7.1+2.05*1.4 = 9.97

Probability sampling alludes to the choice of an example from a populace when this determination depends on the rule of randomization, that is to say, irregular determination or possibility. Probability sampling is more intricate, additional tedious, and normally more exorbitant than non-probability sampling.

While picking a probability test plan, the objective is to limit the inspecting blunder of the evaluations for the main study factors, while at the same time limiting the time and cost of leading the review. A few functional limitations can likewise affect that decision, for example, the qualities of the survey frame.

To learn more about probability and its theorem,

https://brainly.com/question/9793303

#SPJ4

Area of semicircle is 76.93 [tex]units^{2}[/tex].

Given,

Diameter = 14 units

Radius = r = 14/2

                 = 7 units

Area of semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]

                               = (3.14*7*7)/2

                               = 153.86/2

                               = 76.93

Hence, Area of semicircle is 76.93 [tex]units^{2}[/tex].

To learn more about Area here:

https://brainly.com/question/27683633

#SPJ1

Answer:

x = -2, y = 9

Step-by-step explanation:

x + y = 7 --1

2x² + y² = 35 - 3xy --2

For 1, make y the subject.

y = 7 - x

Substitute y = 7 - x into 2.

2x² + (7 - x)² = 35 - 3x(7 - x)

Simplify and solve for x.

2x² + (49 - 14x + x²) = 35 - 21x + 3x²

3x² - 14x + 49 = 3x² - 21x + 35

7x = -14

x = -2

Substitute x = -2 into y = 7 - x.

y = 7 - (-2)

= 9

Thus, x = -2, y = 9

After forming the algebraic equation, he equation of the given statement is 7x+80=3x−50.

In the given question,

Yvonne is thinking of a number.

Fifty decreased by three times the number is the same as seven times the number increased by 80.

We have to set it up in a equation.

To set it up in a equation we divide the step in small steps.

Firstly the statement is saying that fifty decreased by three times the number.

Let the number be x.

So three times of a number is 3x and 50 decreased means 3x−50.

Next statement is saying that seven times the number increased by 80.

As the number is x so seven times of a number is 7x and increased by 80 means 7x+80.

The both statement is equal to each other.

So 7x+80=3x−50

So the equation of the given statement is 7x+80=3x−50.

To learn more about equation from the statement link is here

brainly.com/question/29339533

#SPJ1

0.5852  is the process capability for the index when  standard deviation. is 0.14 mm .

What is standard deviation in math?

Cpk = minimum of [(23.0 - 22.8)/(3 *0.15),(22.8 - 22.6)/(3 * 0.15)]

=  (0.2/0.45) , ( 0.6/0.45)

=  (0.44 )( 1.33)

= 0.5852

Learn more about standard deviation

brainly.com/question/16555520

#SPJ4

The value that lie above 25% of the data of the box plot is: 31.

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

A box plot tells us the following values of a data set as shown in the diagram attached:

Using the box plot that shows the information given about the data collected on the number of points scored, we can conclude that:

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

25% of the data lie above 31, which is the upper quartile.

Learn more about the box plot on:

https://brainly.com/question/14277132

#SPJ1

The winner of the race finished the race in eleven twenty-fourths(11/24) minutes which is option B

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Kyla finished her race in 1 3/8 minutes.

converting this to improper fraction, we have 11/8 minutes

The winner of the race finished in 1/3 of Kyla's time which is 1/3 x 11/8

= 11/24 minute

The winner of the race finished in 11/24 minute.

Learn more about fraction: https://brainly.com/question/17220365

#SPJ1

The legend chart element will tells the category of data that each line represents the lines.

Lines:

Lines refers a one-dimensional figure, which has length but no width.

Given,

suppose that a line chart includes several lines.

Here we need to identify the chart element will tell you the category of data that each line represents.

Basically, chart is a visual representation of numeric data in a worksheet. And it helps you to identify trends, make comparisons, and recognize patterns in the numbers.

In order to get the clear information that appears in your chart, you can add a chart title, axis titles, and data labels.

The element legend or data table is used to represents the category of the data.

To know more about Lines here.

https://brainly.com/question/17188072

#SPJ1

The vertex is (-2, 5) and The range is [5, ∞)

The correct option is (D) i.e.,  (−2, 5); 5 ≤ y < ∞

Given:

The Function is :

y =  |2x + 4| + 5

To find the vertex and range of the function.

What is vertex and range ?

The vertex is given by the coordinates (h, k), so all we need to consider is the k. For example, consider the function f(x)=3(x+4)2−6. a is positive and the vertex is at (−4,−6), so the range is all real numbers greater than or equal to −6.

Now, According to the question:

The function is given as:

y =   |2x + 4| + 5

So, According to the above statement is:

The vertex in y = |2x + 4| + 5

The vertex is (-2, 5)

The range in y =   |2x + 4| + 5

The range is all real numbers

The range is [5, ∞)

Hence, The vertex is (-2, 5) and The range is [5, ∞)

The correct option is (D) i.e.,  (−2, 5); 5 ≤ y < ∞

Learn more about Vertex and Range at:

https://brainly.com/question/1689812

#SPJ1

(D) - (−2, 5); 5 ≤ y < ∞

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

to learn more about probability click on the link below.

https://brainly.com/question/24756209

#SPJ4

Answer:

[tex]\frac{1}{2}[/tex]x

Step-by-step explanation:

3/5  is the same as 6/10

[tex]\frac{6}{10}[/tex] x - [tex]\frac{1}{10}[/tex]x

[tex]\frac{5}{10}[/tex]x = [tex]\frac{1}{2}[/tex]x

Use of the two-tailed test is advised. In order to compare the average across two years,

A random sample of 25 national capitals had their air quality measured in 2013, and the same cities had been visited again in 2014. We want to compare the average air quality between the two years using this data.

A one-sided or two-sided test should be used, right? Describe your thinking.

The two-tailed test should be used. We want to contrast the average across two years. If the test parameter calculated for the two years differs, it would be interesting to know. (There is no exact comparison to show if one year is better or worse than the other.)

To learn more about test parameters click here:

brainly.com/question/13978790

#SPJ4

Answer:

 1

 52

+ 19

____

  71

Step-by-step explanation:

add 2+9 and get 11

carry the one

add 1+1+5 and get 7

71

The ratio for the length of grey to red to bule is 4:9:3.

Ratio is the relation between two numbers which shows how much bigger one quantity than another. Ratio show how many times one contain show the other one.

According to the question

The given data are -

Grey = 0.8m

Red = 1.8 m

Bule = 0.6 m

By solving these we can get -

=0.8:1.8:0.6

=0.8×10:1.8×10: 0.6×10

=8:18:6

By simplifying it we can get

4:9:3.

To know more about ratio click

-https://brainly.com/question/12024093

#SPJ1

Answer:

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠D +  m∠E +  m∠F = 180°

(3x + 27) + (4x + 22) + 68 = 180

7x + 49 + 68 = 180

7x = 63

x = 9

So,  m∠D = (3(9) + 27)° = 54°.

The exterior angle of D = 180- 54 = 126°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".

Answer:

Step 2

Step-by-step explanation:

He messed up because while changing the denominator (number on the bottom), he forgot to change the numerator (number on top).

It should be 2/8 instead of 1/8.

The answer choice which represents the location of any unit rate, m as graphed on a coordinating plane is; Choice 1; (1, m).

It follows from the task content that the answer choice which represents the location of any unit rate, m on a coordinate plane.

Hence, since the slope is defined as the rate of change on a graph such that slope = ∆y/∆x.

In this case, when the change in y with respect to x is to be equal to m.

Therefore, the location as required is the point defined by; (1, m).

Such that; Unit rate = (m - 0)/(1 - 0)

Ultimately, the required location of the unit rate is; Choice 1; (1, m).

Read more on unit rate;

https://brainly.com/question/27221834

#SPJ1

Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Elevator 1 in a hotel moved from ground position to a final position of +18 feet.

+18 means the elevator is 18 feet above the ground floor.

Elevator 2 in the same building moved from the ground to a final position of −20 feet.

-20 feet means the elevator is 20 below the ground floor.

Thus,

Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.

Option B is the correct answer.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The height of lighthouse is 72.54

Given,

In the question:

To see the figure:

To find the height of lighthouse.

Now, According to the question:

In Triangle ABD

tan 20° = [tex]\frac{h}{20 + x}[/tex]

0.36  = [tex]\frac{h}{20 + x}[/tex]

=> (20 + x)0.36 = h

=> 0.72 + 0.36x = h

=> x = [tex]\frac{h - 72}{0.36}[/tex] .....(1)

In Triangle ABC

tan 34° = h/x

=> 0.67 = [tex]\frac{h}{\frac{h-72}{0.36} }[/tex]

=> 0.67 = 0.36/h - 72

=> 0.67 (h - 72) = 0.36

=> h - 72 = 0.54

=> h = 0.54 + 72

=> h = 72.54

Hence, The height of lighthouse is 72.54

Learn more about Triangles at:

https://brainly.com/question/26093510

#SPJ1

Answer:

1 1/4 cup of flour

Step-by-step explanation:

1/4 × 5 = 1 1/4

a) Relation of recurrence for the number of bacteria remaining after n hours is   [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex]

b) the solution to this recurrence relationship is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]

c) There will be more than a million microorganisms after 7 hours.

A recurrence relation is an equation that states that some combination of the previous terms and the nth term in a series of numbers equals 1.

a) a₀ = 100, a₁ = 300 Every hour the bacteria - bacteria before two hours, and every hour the bacteria + 2(existing bacteria). Consequently, the corresponding recurrence relationship is [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex]  where n is an hour reference.

(b) The associated difference equation is

r² - 3r + 1 = 0

⇒ r = [3 ± (√9 - 4)] / 2 = (3 ± √5) / 2

hence, the answer is [tex]a_{n} = a[(3 + \sqrt{5}) / 2] ^{n} + b [(3 - \sqrt{5}) / 2] ^{n}[/tex]

Using n = 0 as the initial condition, we have a₀ = 100 = a + b → (1)

putting n = 1,

⇒ √5 (a - b) = 300 → (2)

(1) ⇒ √5 (a + b) = 100√5

By combining these relationships, we have

a = [(300 + 100√5) / 2√5] = 50 + 30√5

therefore, b = 50 - 30√5

Consequently, the answer to the equation is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]

c) if there are more than one million bacteria, i.e.

[tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n} > 1,000,000[/tex]

⇒ log (50 + 30√5) + n {log (3 + √5)} - log2} - log {30√5 - 50} - n {log (3 - √5) - log2} > log 1,000,000

⇒ 2.06849 + n {0.719 - 0.3010} - 1.2325 - n {-0.41797} > 6

⇒ 0.835975n > 5.16401

⇒ n > (5.16401 / 0.83975)

Therefore, n > 6.177, or after 7 hours, there will be more than 1 million bacteria.

To know more about the Recurrence Relation, refer to this link:

https://brainly.com/question/27618667

#SPJ4

The correct value of x = 23.

Each interior angle of an n-sided regular polygon is given by 180 (n-2)/n degrees.

Given that:

n = 9

Therefore, each interior angle＝180 x (9-2)/9 degrees

Each interior angle = 180 x 7/9

Each interior angle = 140°

Each internal angle of a regular polygon having 9 sides is 140°.

Also, given that:

A 9-sided regular polygon with one angle equals 7x-21.

For the polygon to be a 9-sided regular polygon, the angles must equal 140°.

Checking the value of x from the given option which one satisfies the value of interior angle = 140°.

Option 1, x= 17

=> 7 x 17 - 21 = 98° which is wrong.

Option 2, x= 23

=> 7 x 23 - 21 = 161-21 = 140° which is correct.

Option 3, x= 29

=> 7 x  29 - 21 = 203-21 = 182° which is wrong.

Option 4, x= 140

=> 7 x 140 - 21 = 980- 21 = 959° which is wrong.

Only, the value of x = 23 satisfies the value of a 9-sided regular polygon with one angle equal to 7x-21.

Hence, the correct value of x = 23

To learn more about the regular polygon visit: https://brainly.com/question/24653461

#SPJ1

Answer:

The correct value of x = 23.

Step-by-step explanation: