What is the probability of getting 1 or 5 if a dice is thrown once?

Answer:

x+10=45

x+10-45=0

x-35=0

x=35

Answer:

I) ∠CAB measures 60°.

II) BC measures approximately 15.23 cm.

*Please read notes.

Step-by-step explanation:

We are given ΔABC, where AB measures 10√3 cm, AC measures 6 cm, and the triangle has an area of 45 square cm.

And we want to find I) the measure of ∠CAB and II) the length of BC.

I) First, we should always draw a representative triangle so we can determine the sides and angles. This is shown below.

Note that ∠CAB (or simply ∠A) is the angle between the two sides. Thus, we can find the angle by using the alternative formula for the area of a triangle:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

Where a and b are two side lengths, and C is the angle between the two sides.

Substitute:

[tex]\displaystyle 45=\frac{1}{2}(10\sqrt{3})(6)\sin(A)[/tex]

Simplify:

[tex]\displaystyle 45=30\sqrt{3}\sin(A)[/tex]

So:

[tex]\displaystyle \sin(A)=\frac{45}{30\sqrt{3}}=\frac{3}{2\sqrt3}=\frac{\sqrt{3}}{2}[/tex]

Take the inverse sine of both sides. Use a calculator. Thus:

[tex]\displaystyle m\angle A=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^\circ[/tex]

II) To find BC, we will use the Law of Cosines. We do not know whether or not ΔABC is a right triangle, so we cannot use right triangle trigonometry or special right triangles.

The law of cosines is:

[tex]\displaystyle c^2=a^2+b^2-2ab\cos(C)[/tex]

Where a and b are side lengths and C is the angle between the side lengths. c is the side length opposite to the angle.

BC is opposite to A. Substitute:

[tex](BC)^2=(10\sqrt{3})^2+(6)^2-2(10\sqrt{3})(6)\cos(60^\circ)[/tex]

Simplify:

[tex]\displaystyle BC^2=336-120\sqrt{3}\left(\frac{1}{2}\right)=336-60\sqrt{3}[/tex]

Take the square root of both sides:

[tex]\displaystyle BC=\sqrt{336-60\sqrt{3}}\approx 15.23[/tex]

BC measures about 15.23 cm.

Notes:

In this case, the inverse sine of √3/2 will yield two answers: 60° and 120°. This is an example of an ambiguous case. Both of these angles will work. However, BC will be different. If ∠A is 60°, then BC is about 15.23. However, if ∠A is 120°, then BC is about 20.97. Both will result in the triangle having an area of 45 square cm, as well as AB measuring 10√3 and AC measuring 6.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x-\dfrac{3}{2}=3}[/tex]

[tex]\large\textsf{You have to SIMPLIFY the SIDES of The given EQUATION}[/tex]

[tex]\mathsf{x + (-\dfrac{3}{2}) = 3}[/tex]

[tex]\large\textsf{ADD by } \mathsf{\dfrac{3}{2}}\large\textsf{ to BOTH of the SIDES}[/tex]

[tex]\mathsf{x + (-\dfrac{3}{2})+ \dfrac{3}2{}=3+\dfrac{3}{2}}[/tex]

[tex]\large\textsf{CANCEL out: } \mathsf{-\dfrac{3}{2}+\dfrac{3}{2}}\large\textsf{ because that gives you 0}[/tex]  

[tex]\large\textsf{Keep: } \mathsf{3+ \dfrac{3}{2}}\large\textsf{ because that helps solve for your x-value }[/tex]

[tex]\large\textsf{New equation: }\mathsf{x = 3 + \dfrac{3}{2}}[/tex]

[tex]\mathsf{3+\dfrac{3}{2}}[/tex]

[tex]\large\textsf{SOLVE above and you have your ANSWER}[/tex]

[tex]\mathsf{3+\dfrac{3}{2}=\bf \dfrac{9}{2}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your answer is: }\mathsf{\bf x = \dfrac{9}{2}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

yep

Step-by-step explanation:

nice

Answer:

10000 possible combinations

Step-by-step explanation:

Number of digits = 4

Range of values of each digit = 0 - 9

Number of digits in range = 10

Hence, each digit could be = (1 - 10)

1st digit = 10

2nd digit = 10

3rd digit = 10

4th digit = 10

Total possible combination :

10 * 10 * 10 * 10 = 10000 possible combinations

Answer:A snow day occurs when school is canceled for the day because of bad winter weather. The box below shows the number of snow days at Andrew's school during each of the past six winters.

Step-by-step explanation:

Answer:

lol xdxdxd how you not know fraction? this is basic math this is why you failed lolol

Step-by-step explanation:

Answer: Approximately normal, because we expect 19.2 successes and 20.8 failures from people in their twenties, and 16.8 and 43.2 from people in their fifties, and all of these counts are at least 10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

non-proportional

Step-by-step explanation:

Answer:

this is the answer in the image above

Answer:

look attachment

Answer: 12

Step-by-step explanation:

Since Duane has 30 pairs of socks in a drawer and he has 6 matched pairs and the rest are of the socks are mismatched, the number if mismatched socks will be:

= 30 - 6

= 24 mismatched socks

Since he packed 1/2 of his mismatched pairs in his duffle bag for a week at summer camp, therefore, the number of socks he packed will be:

= 1/2 × 24

= 12

Therefore, he packed 12 socks for summer camp.

Answer:

98

Step-by-step explanation:

i am smart

Answer:

Step-by-step explanation:

10 games, 8 rides

Answer:

Area ≈ 3077.68

Explanation:

See attached image for equation

Answer:

$1.50

Step-by-step explanation:

The computation is shown below:

Given that

The cost of each cupcakes be 0.50 cents

And, the cost of doughnuts be $25

So for two doughnuts the cost would be 2.50

And, for two cupcakes, the cost would be 0.50 × 2 = 1

So, the more amount would be

= 2.50 - 1

= $1.50

Hence, the same would be considered and relevant too

Answer:

b = -1

Step-by-step explanation:

here's your solution

=> 7b - 2/5 = 6b - 7/5

=> 7b - 6b = -7/5 + 2/5

=> b = (-7+2)/5

=> b = -5/5

= b = -1

hope it helps

Answer:

b = -1

Step-by-step explanation: I put all the like terms together by moving 6b and -2/5, which then changed their signs to negative and positive, respectively.

7b-2/5 = 6b-7/5

7b-6b = 2/5-7/5

b = -1

I hope this helps. :)

Answer:

x = 4.5

Step-by-step explanation:

Since the perimeters are equal , then the equation relating them is

2x + 3 + 2x - 3 + x = x + 3 + x + 3 + x + 3 , that is

5x = 3x + 9 ( subtract 3x from both sides )

2x = 9 ( divide both sides by 2 )

x = 4.5

Answer:

-3=3x+12

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is terminated after 4 places of decimal

Answer:

Step-by-step explanation:

In the decimal expansion of a rational number, the general rule is that if the denominator is of the form 2^m*5^n, then it will terminate after n places if n>m or m places if m>n.

In this case, 4 > 3 so the expansion will terminate after 4 decimal places.

Answer:

24 hours

Step-by-step explanation:

The computation of the number of hours taken by Bobby to build the robot by himself is shown below:

Given that

Bobby could take 12 hours

Together they could build in 8 hours

So based on the above information

the number of hours taken by Bobby to build the robot by himself is

Let us assume the above line be x

So,

[tex]\frac{1}{8}-\frac{1}{12} = \frac{1}{x} \\\\\frac{6 - 4}{48} = \frac{1}{x} \\\\\frac{2}{48} = \frac{1}{x} \\\\x = \frac{48}{2}[/tex]

x = 24 hours

Answer:

4

Step-by-step explanation:

3/2x -1 = 5

then

3/2x = 5+1

then

3/2x = 6

then

x = 6 / (3/2)

then

x = 6 *2/3

then

x = 4

Answer:

12mm (triangle)

165mm (whole shape)

Step-by-step explanation:

The triangle is 6 x 4 = 24 ÷ 2= 12

(divide by 2 because its a teiangle)

2nd shape is 10 x 8 = 80

3rd shape is 6 x 12 = 72

72 + 80 + 12 = 165mm