one lap around a dirt track is 1 /3 of a mile. It takes Bryce 1/9 of an hour to ride one lap.

By solving a linear equation we will see that the initial temperature was 66 degrees.

Let's define T as the initial temperature.

First, it increases by 18 F, then it decreases 6 F, and finally, it increases another 12 F, such that the end temperature is 94F.

Then we can write:

T + 18F - 6F + 12F = 94F

Now we can solve that linear equation to find T.

T = 94F - 18F + 6F - 12 F = 66 F

In this way, we conclude that the initial temperature was 66 degrees.

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Answer:

D. Open the compass so that the distance from the two points of the compass is wider than half the length of [tex]\over{AB}[/tex].

Step-by-step explanation:

To construct a perpendicular for [tex]\over{AB}[/tex], we must first take a compass & take the distance of its arms wider than half the length of [tex]\over{AB}[/tex].

This is done in order to get two intersecting arcs in the top & bottom of [tex]\over{AB}[/tex] so that a perpendicular bisector can be drawn through it.

After two intersecting lines are drawn below & above [tex]\over{AB}[/tex], draw a line joining these 2 points through their points of intersection. The point where it intersects [tex]\over{AB}[/tex] is the middle-most point of [tex]\over{AB}[/tex] & now a perpendicular bisector of [tex]\over{AB}[/tex] is constructed.

[tex]\rule{150pt}{2pt}[/tex]

Answer:

D

Step-by-step explanation:

The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the side KL is 30.81 units.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

The measure of ∠J can be written as,

Cos(∠J) = JK/JL

Cos(∠J) = 7/31.6

∠J = 77.2°

Similarly the length of side KL can be written as,

Tan(∠J) = KL/JK

Tan(77.2°) = KL/7

KL = 30.81 units

Hence, the length of the side KL is 30.81 units.

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Answer:

Step-by-step explanation:

Let h be the height of the door

and w be its width

The statement “The height of the door is I foot more than twice its width”

can be translated mathematically like this :  h = 2w + 1

Let’s solve the equation for w:

h = 2w + 1

⇔ 2w = h - 1

[tex]\Leftrightarrow w=\frac{h-1}{2}[/tex]

now , if the door is 7 feet high then it’s width is equal to :

[tex]\Rightarrow \frac{7-1}{2} =\frac{6}{2} =3 \ ft[/tex]

Answer:

3 feet

Step-by-step explanation:

It mentions that the height of the door is 1 foot more than twice its width.

The width of a door of height 7 feet will be :

The image of triangle ABC is a A'B'C' after rotating about the origin with an angle of 180 degree.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

If we rotate the triangle ABC with the origin (0, 0) about 180 degree it will form an image of the triangle ABC which is A'B'C'

Here the coordinates for ABC are not given so we are assuming the triangle ABC has a image which is A'B'C' (refer attached picture)

Thus, the image of triangle ABC is a A'B'C' after rotating about the origin with an angle of 180 degree.

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Take RHS

[tex]\\ \rm\Rrightarrow \dfrac{tanA+tanB}{tanA-tanB}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\dfrac{sinA}{cosA}+\dfrac{sinB}{cosB}}{\dfrac{sinA}{cosA}-\dfrac{sinB}{cosB}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\dfrac{sinAcosB+cosAsinB}{cosAcosB}}{\dfrac{sinAcosB-cosAsinB}{cosAcosB}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{sinAcosB+cosAsinB}{sinAcosB-cosAsinB}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{sin(A+B)}{sin(A-B)}[/tex]

Some important identities

[tex]\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ $\: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1$\end{minipage}}[/tex]

Answer:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B\\\\ \dfrac{\sin A}{\cos A}=\tan A$\\\end{minipage}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\sin(a) \cos (b) + \cos (a) \sin (b)}{\sin(a) \cos (b) - \cos (a) \sin (b)}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\sin(a) \cos (b) + \cos (a) \sin (b)}{\sin(a) \cos (b) - \cos (a) \sin (b)} \times \dfrac{\dfrac{1}{\cos (a) \cos (b)}}{\dfrac{1}{\cos (a) \cos (b)}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\dfrac{\sin(a) \cos (b)}{\cos (a) \cos (b)} + \dfrac{\cos (a) \sin (b)}{\cos (a) \cos (b)}}{\dfrac{\sin(a) \cos (b)}{\cos (a) \cos (b)} - \dfrac{\cos (a) \sin (b)}{\cos (a) \cos (b)}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)} & = \dfrac{\dfrac{\sin(a)}{\cos (a)} + \dfrac{\sin (b)}{\cos (b)}}{\dfrac{\sin(a)}{\cos (a)} - \dfrac{\sin (b)}{\cos (b)}}[/tex]

[tex]\dfrac{\sin (a+b)}{\sin (a-b)}=\dfrac{\tan(a)+\tan(b)}{\tan(a)-\tan(b)}[/tex]

Answer:

Step-by-step explanation:

A set of random numbers can be used for simulating a situation by defining how the numbers will be used to represent the possible outcomes. Trials are repeated using newly-generated random numbers until there are a sufficient number of trials to give a reasonable prediction of the probability of interest.

__

We can simulate the situation as follows:

Here are our trials and results.

48 09 52 47 65 05 60 44 64 97 -- 3 of 10

11 96 69 33 54 86 43 13 47 31 -- 5 of 10

56 52 16 97 22 26 29 57 94 23 -- 5 of 10

42 66 97 09 62 17 35 52 98 26 -- 5 of 10

53 44 26 82 41 88 38 32 64 31 -- 6 of 10

73 43 45 30 41 29 59 15 81 66 -- 5 of 10

23 54 46 11 32 12 95 52 28 34 -- 6 of 10

41 59 26 41 19 53 14 73 32 05 -- 7 of 10

82 87 37 09 67 70 03 44 78 21 -- 5 of 10

11 15 30 29 89 37 97 79 34 25 -- 7 of 10

__

Of these 10 trials, 4 showed the result that at least 6 of the next 10 students will choose a computer course. That is, the probability is estimated to be about 4/10 = 40%.

_____

Additional comment

Here, we can only predict the probability of interest as some multiple of 10%, since we have numbers sufficient for only 10 trials.

We could arrange the random numbers a different way and reuse them, but we choose not to for the purpose of this answer. For that to make sense, we need to have assurance that these numbers are truly random.

The number of repeated values among these 100 pairs of digits suggests that this is a poor set of numbers to be using. 26 and 41 each show up 4 times, for example. The probability of that happening by chance in a truly random set of numbers is about 0.03%. A chance event is considered to be unlikely if its probability is less than 1%.

Answer:50%

Step-by-step explanation:believe me it is 50%. 40% isn’t even a option. 50% is the correct answer.

Answer: 45,28,13

Step-by-step explanation:

Firstly let’s call integer 3

‘x’

Following the information given the following equations can be constructed:

integer 3 = x

integer 2 = 2+2x because 2x represents 2 times integer 3 (which is x) and plus two

integer 1 =3((2x+2)-x) what we have written is the difference between integer 2 (which was (2x+2)) and integer 3 which was x and simply multiply the result of that subtraction by 3

next we can treat them like their own variables almost.

integer 1 + integer 2 + integer 3 =86

so now plug in the equations we have constructed for each integer:

(3((2x+2)-x)) + (2x+2) + x = 86

to make it easier to read please see the image attached below to solve for x

After you have gone through the image I have included you should notice x= 13 great we got one integer! (Integer 3)

now plug in 13 into our integer equations :

integer 2: 2(13)+2= 28

Therefore integer 2 is 28

integer 1: 3((2(13)+2)-(13))=
3((28-13)

3(15)

45

Therefore integer 1 is 45.

and integer 3 is x which as we now know is equal to 13

Answer:

the cube root of 0.027 is 0.3

Answer:

1  5/8

Step-by-step explanation:

3/4 -  -7/8

3/4 + 7/8

6/8 + 7/8

13/8 = 1  5/8

Answer:

1 5/8 or 13/8

Step-by-step explanation:

Remove parentheses.

[tex]\frac{3}{4}+\frac{7}{8}[/tex]

Find the Least Common Denominator (LCD) of [tex]\frac{3}{4},\frac{7}{8}[/tex] . In other words, find the Least Common Multiple (LCM) of 4,8.

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 4 : 4, 8, ...

Multiples of 8 : 8, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 8

Method 2: By Prime Factors

List the prime factors of each number

Prime Factors of 4 : 2, 2

Prime Factors of 8 : 2, 2, 2

Find the union of these primes.

2, 2, 2

Multiply these numbers: 2 * 2 * 2 = 8 ---> This is the LCM.

LCM = 8

---> LCD = 8

Make the denominators the same as the LCD.

[tex]\frac{3\times 2}{4\times 2}+\frac{7}{8}[/tex]

Simplify. Denominators are now the same.

[tex]\frac{6}{8}+\frac{7}{8}[/tex]

Join the denominators.

[tex]\frac{6+7}{8}[/tex]

Simplify.

[tex]\frac{13}{8}[/tex]

Convert to mixed fraction.

[tex]1\frac{5}{8}[/tex]

Answer:

a and d

or

c and b

Step-by-step explanation:

supplementary angles are angles that add up to 180 degrees

when looking at the rectangle you see two possible answers

Answer:

30%, or 1/3

Step-by-step explanation:

If there are 20 total marbles, and 6 of them are red, to find the probability of pulling a red marble you would do 6/20, which simplifies to 1/3. This can also be written as 30%.

Hope this helps! :)

Answer:

i think it is D but I am not for shore

Answer:

last and third

Step-by-step explanation:

Answer:

9.435

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

23 ⇔ 23 R 0

184 divided by 8

=

23 with a remainder of 0

0

2

3

8

1

8

4

-

0

1

8

-

1

6

2

4

-

2

4

0

Answer:

$10.64

Step-by-step explanation:

20% out of $53.18 is $10.636 rounded to $10.64

The class that had better overall results on the exam is class A.

The class with greater variablity in results is class B.

The statistics of students in class A:

Maximum score = 100

Minimum score = 65

Median = 85

First quartile = 1/4(n + 1) = 1/4 x 12 = 3rd term = 70

Third quartile = 3/4 x (n + 1) = 3/4 x 12 = 9th term = 90

The statistics of students in class B:

Maximum score = 100

Minimum score = 55

Median = 75

First quartile = 70

Third quartile = 80

The range would be used to determine which class has greater variability.

Range = highest score  - lowest score

Class a = 100 - 65 = 35

Class B = 100 - 55 = 45

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Answer:

line

Step-by-step explanation:

quizlet

cliffnotes

Answer: 2.99914cm Rounds up to 3

Step-by-step explanation:

The equation represents 21 seats and 30 wheels will be given as B.

u + 2b = 30

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels. One day, she counts 21 seats and 30 wheels.

u is the number of unicycles and b is the number of bicycles.

There are total 21 seats

⇒  u+b=21

unicycle has 1 wheel and bicycle has 2 and total there are 30 wheels

⇒ u+2b=30

Hence,the equation represents 21 seats and 30 wheels will be given as B.  u + 2b = 30

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The graph that shows a dilation would show the reduction or enlargement of the original figure (see attachment).

Dilation is defined as a form of transformation where a figure is enlarged or reduced by scale factor. Simply put, a dilation is a process of resizing an original image.

The image containing the referenced graphs is missing. However, the image below shows what a dilation is.

Thus, the graph that shows a dilation would show an enlargement or reduction.

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The simplified quotient of 300 and 3 is 100

The complete statement is given as:

What is the quotient of 300 and 3?

This is represented as:

Quotient = 300/3

Divide 300 by 3

Quotient = 100

Hence, the quotient of 300 and 3 is 100

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=========================================================

Explanation:

Let x = 0.370370370...

The "370" block repeats forever, due to the horizontal bar up top.

Multiply both sides by 1000 so that the decimal point moves three spots to the right.

x = 0.370370370...

1000x = 1000*0.370370370...

1000x = 370.370370370...

Then notice both x and 1000x involve the *exact* same decimal string of "370" repeating forever. This perfect match lets us cancel the decimal portions out when we subtract, and allows us to isolate x to get some fraction of integers.

1000x - x = 370.370370370... - 0.370370370...

999x = 370

x = 370/999

You can use your calculator to confirm that 370/999 = 0.370370370...

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

In fact, you can use your calculator to determine the following:

A) 37/100 = 0.37

B) 370/999 = 0.370370370...

C) 37/99 = 0.373737...

D) 37/9 = 4.1111111....

This allows us to see fairly quickly that choice B is the final answer and that we can rule out the others.

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

Side note: your calculator may round the last digit by mistake.

Answer:

15/56

Step-by-step explanation:

5 people have a license

3 people don't

? = Probability that first person has a license and second does not

We can divide the problem into two sections, the first being the probability of the first person having a license, and the second section is the probability that the second person doesn't have a license.

P1 = Probability of the first person having a license, there are 5 out of 8 person having a license, thus P1 = 5/8.

P2 = Probability of the second person having a license. There are 3 people not having a license, out of 8-1 = 7 persons available, since one is taken already from the first choice, therefore P2 = 3/7.

P1 and P2 are dependent events, thus P(1,2) = P1 * P2.

P(1,2) = P1 * P1 = 5/8 * 3/7 = 15/56

Answer:

she earns $1008 in commissions , hope this helps i did it