Roller coaster A can reach a top speed of 110 ft./s roller coaster B can reach the top speed of 85 mph which roller coaster has a greater top speed

The value of the common length BD would be 8 units, approximately.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The AD line is perpendicular to the line AC.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

So, We know that

  Sin A = BD / AB

  Sin A = BD / c

c Sin A = BD

Substitute angle A = 53.13 and c = 10.

BD = (10) Sin (53.13)

BD = 10 (0.79)

BD = 7.99

BD ≈ 8

The question was incomplete, but the complete question is given below.

Considering line BD as a side of ABD, express its length in terms of variables representing side lengths and angle measures in ABD. Show your work.

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(a) As of the Cartesian vector approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].

(b) Using a scalar approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

here,
[tex]\vec F = 4 \hat i + 12\hat j -3 \hat k\\ \vec B = 4 \hat i + 3\hat j - 2 \hat k\\[/tex]

Scalar approach,
moment about the x-axis is given by,
[tex]M_x = B_yF_z - ZF_y\\M_x = 3(-3)-(-2)(12)\\M_x = 13\ Ft-lb[/tex]

Similarly,
[tex]M_y = 4\ Ft-lb,[/tex] and [tex]M_z = 36\ Ft-lb[/tex]

Vector approach,
Moment about the x-axis is given by,
[tex]M_x = U_x \times[ {\vec B \times \vec F]}\\M_x = \left[\begin{array}{ccc}1&0&0\\4&3&-2\\4&12&-3\end{array}\right][/tex]

The above expression given is of determinate, when solving the above determinate,
[tex]M_x = 13\ Ft-lb[/tex]

Similarly,
[tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex],

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Answer: four textbooks

Step-by-step explanation:

Answer:

-13.5

Step-by-step explanation:

take number as x

3x-12=5x+15

-2x=27

x=27/-2

x=-13.5

Answer:

His savings were of $4,200.

Step-by-step explanation:

Mr. Hughes gave 5/14 of his savings to his son, 2/3 of the remainder to his daughter, and the rest to his wife:

This means that the son and daughter amount is:

[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14})[/tex]

As [tex]\frac{9}{14}[/tex] is the remained that his son did not get. So

[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14}) = \frac{15}{42} + \frac{18}{42} = \frac{33}{42}[/tex]

Fraction his wife got:

[tex]1 - \frac{33}{42} = \frac{42}{42} - \frac{33}{42} = \frac{9}{42}[/tex]

If his wife got $900, what were his savings?

Total savings are x, wife got [tex]\frac{9}{42}[/tex] of x. So

[tex]\frac{9x}{42} = 900[/tex]

[tex]9x = 900*42[/tex]

[tex]x = \frac{900*42}{9}[/tex]

[tex]x = 100*42[/tex]

[tex]x = 4200[/tex]

His savings were of $4,200.

By using PEDMAS rule, (8 x 1) − 5 is the expression represents the given statement.

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEDMAS: Parentheses, Exponents, Division and multiplication, Addition and Subtraction.

According to the question

Multiply 8 by 1 less than 5.

Rewriting the mathematical expression using order of operations using PEDMAS rule

= (8 x 1) − 5

(8 x 1) − 5 is the expression represents the given statement.

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Answer:

A. 36  ÷ a

B. 55 - b

C. 18 + c

D. 49 · d

E. e ÷ 62

F. f - 71

Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.

A figure or ratio that is stated as a percentage of 100 is referred to as a percentage in mathematics.  However, the percent symbol ("%) is usually used to denote it." The percent amount is flat. When the numerator is 100, percentages are really just fractions. Put the standard form (%) next to a number to show that it is a percentage. For instance, if you correctly respond to 75 out of questions in total on a test, you receive a 75% (75/100).

Here,

Given: 1757600 more people overall

Population as of now: 1562500

According to the issue,

=> 1562500[tex](1 + 4/100 )^{n}[/tex] = 1757600

=> [tex](26/25)^{n}[/tex] =  1757600/ 1562500

=>  [tex](26/25)^{n}[/tex]=  [tex](26/25)^{3}[/tex]

On comparing,

n=3

Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.

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Answer:

The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.

Answer:

D

Step-by-step explanation:

Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:

5(y + 9) = 3

Next, we can distribute the 5 to obtain:

5y + 45 = 3

Finally, we can subtract 45 from both sides to solve for y:

5y = -42

y = -42/5

y = -8.4

Therefore, the equation that represents the given sentence is y = -8.4.

Step-by-step explanation:

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.

given

Use similar triangles,

BAC and DAB are similar

therefore

CA/AB = BA/AD

CA/20 = 20/10

cross multiply

AC = CA = 20*20/10 = 40

Or use metric relations

CA*AD = BA^2

CA = BA^2/AD = 20^2/10 = 40

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

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Answer:

im not helping you cuz ur pfp

Step-by-step explanation:

Answer:

why u delete the answer biro it was being record ...72+ comments

Answer:

C = π (4yd)

C = 12.6yd

Step-by-step explanation:

Answer:

x = -11, 2/3

Step-by-step explanation:

-3x^2-11x+2=0

-(3x^2+11x-2) = 0

3x^2 + 11x - 2 = 0

3x^2 + 33x - 22x - 2 = 0  ==> 33-22=11 and 33/11=3 and -22/11=-2

3x(x + 11) - 2(x + 11) = 0  ==> factor

(3x - 2)(x + 11) = 0

3x - 2 = 0                x + 11 = 0

3x = 2                x + 11 - 11 = 0 - 11

{ x = 2/3                         x = -11 } ==> x = -11, 2/3

It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.

You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:

n = (1200 - 2550) ln / ln (1 - 0.05)

Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.

When we enter the values, we will get:

n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months

The motorcycle will take approximately 15.7 months to drop in value to less than £1200.

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Answer:

The average number of beats in a lifetime would be 2,365,200,000

Step-by-step explanation:

To find the amount we need to take basic steps. The first step is multiplying the number of beats to find out how many are in an hour. Since there are 60 in a minute and 60 minutes in an hour, multiply the two.

60 beats * 60 minutes = 3,600 beats per hour.

Now multiply the amount of beats in an hour by the number of hours in a day.

3,600 * 24 hours = 86,400 beats per day

Now multiply the number of days in a year. Technically there is 365 1/4 in a year, but we'll use the flat rate of 365 since that is generally the accepted answer.

86,400 * 365 days = 31,536,000 beats per year

And now we take that number and multiply by the number of years that he lines

31,536,000 * 75 years = 2,365,200,00 beats in a lifetime

The heart beats 236,520, 000 times in a lifetime.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

An average human heart beats 60 times per minute.

Now, the amount of beats in an hour by the number of hours in a day.

= 3,600 x 24 hours

= 86,400 beats per day

Again, the amount of beats per year

= 86,400 x 365 days

= 31,536,000 beats per year

So, the heart beats

= 31,536,000 x 75 years

= 236,520, 000 beats in a lifetime

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Using the formula for the midpoint of the line with given points  A and B as the end points of the line, the coordinates of the point B is (6,-8).

To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.

What is the formula for finding the midpoint of a line segment?

The formula for finding the midpoint of a line segment is:

Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )

Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.

Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line,  and using the midpoint formula for a line AB,

Midpoint(M) = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B

so , (7,-7) = [tex](\frac{8+x2}{2} , \frac{-6+y2}{2})[/tex]

equating the corresponding points,

7 =(8+x2)/2

therefore, x2 = 6

and , -7 = (-6+y2)/2

therefore , y2 = -8

Hence the coordinates of B is , (x2,y2 ) = (6,-8)

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Answer:

a)  City Suburbs city 0.98 0.02 ,  Suburbs  0.01 0.99

b)  0.333 ,  0.667

c )  Using the steady-state probabilities, There will be an increase in the Suburb population and a decrease in City population

Step-by-step explanation:

2% living within the city limits move to suburbs

1% living within the suburbs move to the city

a) Matrix of transition probabilities  

City Suburbs city 0.98 0.02 ,  Suburbs  0.01 0.99

b) Steady -state probabilities

attached below

steady state probabilities = 0.333 ,  0.667

c) Determine the population changes the steady-state probabilities

Using the steady-state probabilities, There will be an increase in the Suburb population and a decrease in City population i.e. a decrease from 40% to 33%

Answer:

From left to right picture,

Scale factor = 2/3

x = 24

y = 12

z = 21

Step-by-step explanation:

Look at the two figures and identify the sides where both lengths are known.

That is the top right-hand side.

Scale factor is hence 18/27 = 2/3

Next, find x, y and z:

Bottom left-hand side:   16/x = 2/3

                                            x = 3/2 x 16

                                             x = 24

Bottom right-hand side:    y/18 = 2/3

                                            y = 18 x 2/3

                                             y = 12

Top left-hand side:       14/z = 2/3

                                           z = 3/2 x 14

                                            z = 21

Answer:

The appropriate solution is:

(a) 0.1056

(b) 0

(c) 0.9544

Step-by-step explanation:

The given values are:

Mean,

[tex]\mu = 75[/tex]

Standard deviation,

[tex]\sigma = 4[/tex]

(a)

⇒  [tex]P(x>80)=1-(x<80)[/tex]

                     [tex]=1-P[\frac{x-\mu}{\sigma} <\frac{80-75}{4} ][/tex]

                     [tex]=1-P[\frac{x-\mu}{\sigma} <\frac{5}{4} ][/tex]

                     [tex]=1-P(z<1.25)[/tex]

By using the table, we get

                     [tex]=1-0.8944[/tex]

                     [tex]=0.1056[/tex]

(b)

According to the question, the values are:

[tex]n[/tex] = 64

[tex]\mu_\bar{x}[/tex] = 75

Now,

⇒  [tex]\sigma_\bar{x}[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

         = [tex]\frac{4}{\sqrt{64} }[/tex]

         = [tex]\frac{4}{8}[/tex]

         = [tex]0.5[/tex]

⇒  [tex]P(\bar {x} >80 ) = 1 - P(\bar x <80 )[/tex]

                      [tex]=1 - P[\frac{(\bar x-\mu_\bar x)}{\sigma \bar x} < \frac{80-75}{0.5} ][/tex]

                      [tex]=1-P(z<10)[/tex]

By using the table, we get

                      [tex]=1-1[/tex]

                      [tex]=0[/tex]

(c)

As we know,

⇒ [tex]\sigma_\bar x[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

        = [tex]\frac{4}{\sqrt{64} }[/tex]

        = [tex]\frac{4}{8}[/tex]

        = [tex]0.5[/tex]

then,

= [tex]P(74< \bar x <76)[/tex]

= [tex]P[\frac{74-75}{0.5} < \frac{\bar x-\mu \bar x}{\sigma \bar x} < \frac{76-75}{0.5} ][/tex]

= [tex]P(-2<z<2)[/tex]

= [tex]P(z<2)-P(z<-2)[/tex]

By using the table, we get

= [tex]0.9772-0.0228[/tex]

= [tex]0.9544[/tex]

Answer:

Step-by-step explanation:

In the last part of the problem, you have to follow PEMDAS.

Instead of you added before dividing. After the step of 36÷3+9x2 you have to divide.

Answer:

y=3x

Step-by-step explanation: