TEN CARDS NUMBERED 1-10 AR HEIRE MIXED TOGETHER AND THEN ONE CARD IS DRAWN WHAT IS PROBABILITY YOU WILL DRAW A CARD GREATER THAN 3

Answer:

Step-by-step explanation:

Law of sines is:

(sin A) / a = (sin B) / b = (sin C) / c

Law of cosines is:

c² = a² + b² − 2ab cos C

Note that a, b, and c are interchangeable, so long as the angle in the cosine corresponds to the side on the left of the equation (for example, angle C is opposite of side c).

Also, angles of a triangle add up to 180° or π.

(i) sin(B−C) / sin(B+C)

Since A+B+C = π, B+C = π−A:

sin(B−C) / sin(π−A)

Using angle shift property:

sin(B−C) / sin A

Using angle sum/difference identity:

(sin B cos C − cos B sin C) / sin A

Distribute:

(sin B cos C) / sin A − (cos B sin C) / sin A

From law of sines, sin B / sin A = b / a, and sin C / sin A = c / a.

(b/a) cos C − (c/a) cos B

From law of cosines:

c² = a² + b² − 2ab cos C

(c/a)² = 1 + (b/a)² − 2(b/a) cos C

2(b/a) cos C = 1 + (b/a)² − (c/a)²

(b/a) cos C = ½ + ½ (b/a)² − ½ (c/a)²

Similarly:

b² = a² + c² − 2ac cos B

(b/a)² = 1 + (c/a)² − 2(c/a) cos B

2(c/a) cos B = 1 + (c/a)² − (b/a)²

(c/a) cos B = ½ + ½ (c/a)² − ½ (b/a)²

Substituting:

[ ½ + ½ (b/a)² − ½ (c/a)² ] − [ ½ + ½ (c/a)² − ½ (b/a)² ]

½ + ½ (b/a)² − ½ (c/a)² − ½ − ½ (c/a)² + ½ (b/a)²

(b/a)² − (c/a)²

(b² − c²) / a²

(ii) a (cos B + cos C)

a cos B + a cos C

From law of cosines, we know:

b² = a² + c² − 2ac cos B

2ac cos B = a² + c² − b²

a cos B = 1/(2c) (a² + c² − b²)

Similarly:

c² = a² + b² − 2ab cos C

2ab cos C = a² + b² − c²

a cos C = 1/(2b) (a² + b² − c²)

Substituting:

1/(2c) (a² + c² − b²) + 1/(2b) (a² + b² − c²)

Common denominator:

1/(2bc) (a²b + bc² − b³) + 1/(2bc) (a²c + b²c − c³)

1/(2bc) (a²b + bc² − b³ + a²c + b²c − c³)

Rearrange:

1/(2bc) [a²b + a²c + bc² + b²c − (b³ + c³)]

Factor (use sum of cubes):

1/(2bc) [a² (b + c) + bc (b + c) − (b + c)(b² − bc + c²)]

(b + c)/(2bc) [a² + bc − (b² − bc + c²)]

(b + c)/(2bc) (a² + bc − b² + bc − c²)

(b + c)/(2bc) (2bc + a² − b² − c²)

Distribute:

(b + c)/(2bc) (2bc) + (b + c)/(2bc) (a² − b² − c²)

(b + c) + (b + c)/(2bc) (a² − b² − c²)

From law of cosines, we know:

a² = b² + c² − 2bc cos A

2bc cos A = b² + c² − a²

cos A = (b² + c² − a²) / (2bc)

-cos A = (a² − b² − c²) / (2bc)

Substituting:

(b + c) + (b + c)(-cos A)

(b + c)(1 − cos A)

From half angle formula, we can rewrite this as:

2(b + c) sin²(A/2)

(iii) (b + c) cos A + (a + c) cos B + (a + b) cos C

From law of cosines, we know:

cos A = (b² + c² − a²) / (2bc)

cos B = (a² + c² − b²) / (2ac)

cos C = (a² + b² − c²) / (2ab)

Substituting:

(b + c) (b² + c² − a²) / (2bc) + (a + c) (a² + c² − b²) / (2ac) + (a + b) (a² + b² − c²) / (2ab)

Common denominator:

(ab + ac) (b² + c² − a²) / (2abc) + (ab + bc) (a² + c² − b²) / (2abc) + (ac + bc) (a² + b² − c²) / (2abc)

[(ab + ac) (b² + c² − a²) + (ab + bc) (a² + c² − b²) + (ac + bc) (a² + b² − c²)] / (2abc)

We have to distribute, which is messy.  To keep things neat, let's do this one at a time.  First, let's look at the a² terms.

-a² (ab + ac) + a² (ab + bc) + a² (ac + bc)

a² (-ab − ac + ab + bc + ac + bc)

2a²bc

Repeating for the b² terms:

b² (ab + ac) − b² (ab + bc) + b² (ac + bc)

b² (ab + ac − ab − bc + ac + bc)

2ab²c

And the c² terms:

c² (ab + ac) + c² (ab + bc) − c² (ac + bc)

c² (ab + ac + ab + bc − ac − bc)

2abc²

Substituting:

(2a²bc + 2ab²c + 2abc²) / (2abc)

2abc (a + b + c) / (2abc)

a + b + c

Answer:

A19

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

10x = 4x + 66

10x - 4x = 66

 6x = 66

 x = 66/6

 x= 11

Answer:

x=11

Step-by-step explanation:

10(11)=4(11)+66

110=44+66

110=110

CAN EXPLAIN FURTHER

WOULD GREATLY APPRECIATE BRAINLIEST ANSWER

Answer:

0

Step-by-step explanation:

6x +15 = 6(x - 3)

6x +15 = 6x - 18( put the like terms together)

6x - 6x = - 18 - 15

0x = - 33

X = - 33/0

Which is 0

Answer:

answer is 0 or 1

Step-by-step explanation:

Answer:

y = x - 4

Step-by-step explanation:

If you look at it, you can see that 8 - 4 is 4

12 - 4 = 8

14 - 4 = 10 and

17 - 4 = 13

The solution is, y = x - 4 , is the function equation for the input/output table.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

x    y

8    4

12   8

14   10

17    13

In order to solve, we replace the values of x in the functions in at least two points, we then compare if the answers correspond with the y-components. From this, we will have that the function that models the table is:

y = x - 4

The table looks like this:

x = 8 => y = 8-4 = 4

x = 12 => y = 12 - 4 = 8

x = 14 => y = 14 - 4 = 10

x = 17 => y = 17 - 4 = 13

Hence, The solution is, y = x - 4 , is the function equation for the input/output table.

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Answer:  nickels = 14, dimes = 42, quarters = 18

Step-by-step explanation:

Let n represent nickels which has a value of $0.05

Let d represent dimes which has a value of $0.10

Let q represent quarters which has a value of $0.25

It is given that:

                       n = n

                      d = 3n

                      q = n + 4

and their total value is $9.40    ⇒     n + d + q = $9.40

Use substitution to find the quantity of nickels:

.05(n) + .10(3n) + .25(n + 4) = 9.40

 5n    +  10(3n) +   25(n+4)   = 940           multiplied by 100

 5n    +   30n   +  25n + 100 = 940          distributed

                            60n + 100 = 940          added like terms

                            60n           = 840          subtracted 100

                                 n           = 14            divided by 60

n = 14

                d = 3n

                   = 3(14)

                   = 42

                                       q = n + 4

                                          = (14) + 4

                                           = 18

Answer:

Step-by-step explanation:

They start at the origin.because : when x = 0    y= 2(0) =0 and y=3(0)=0

Answer:

they rise upward to the right and they start from the origin

Step-by-step explanation:

i have the same question and that's right

trust me bro

Answer:

-6 1/10

Step-by-step explanation:

For this case we must solve the following equation:

[tex]x ^ 3 = 22[/tex]

If we apply cubic root to both sides of the equation, then we eliminate the exponent on the left side:

[tex]\sqrt [3] {x ^ 3} = \sqrt [3] {22}\\x = \sqrt [3] {22}[/tex]

That is the exact solution of the equation. Its decimal solution is given by:

[tex]x = \sqrt [3] {22} = 2.8020[/tex]

ANswer:

The solution to the equation is [tex]x = \sqrt [3] {22} = 2.8020[/tex]

Option B. x = [tex]\sqrt[3]{22}[/tex] is the correct answer, by solving x³ = 22, where we found the cube root of 22. Other options are incorrect.

We will determine a number that, when raised to the power of 3, equals 22.

Therefore, the correct choice is option B. x = [tex]\sqrt[3]{22}[/tex]

Corrected question:

Mr. Yueng graded his students’ math quizzes. Students came up with four different answers when solving the equation [tex]x^{3}[/tex] = 22.

Which answer is correct?

A. x = [tex]22^{3}[/tex]

B. x = [tex]\sqrt[3]{22}[/tex]

C. x = ±[tex]\sqrt[3]{22}[/tex]

D. x = [tex]\sqrt{22}[/tex]

Answer:

I think the answer is 0.03

Answer:

The diameter of the white blood cell in millimeters is 3 mm.

Step-by-step explanation:

Given : The diameter of a white blood cell under magnification appears to be 0.3 centimeters.

To find : What is the diameter of the white blood cell in millimeters?

Solution :

The diameter of a white blood cell is 0.3 centimeter.

Conversion of centimeter into millimeters,

[tex]1\ cm=10\ mm[/tex]

So, 0.3 cm into mm is

[tex]0.3\ cm=10\times 0.3\ mm[/tex]

[tex]0.3\ cm=10\times \frac{3}{10}\ mm[/tex]

[tex]0.3\ cm=3\ mm[/tex]

Therefore, the diameter of the white blood cell in millimeters is 3 mm.

Answer:

the answer is y = -3x + ( -0.25)

Step-by-step explanation:

The equation of a line with a slope of -3 passing through the point (1.25, -4) can be derived by using the point-slope form (y - y1 = m(x - x1)). Substituting the given values, we get the line's equation as y = -3x - 0.25.

The given problem requires us to write the equation of a line in either point-slope form or slope-intercept form. We are provided with a bit of information to get started: the slope of the line (-3) and a point the line passes through (1.25, -4).

The point-slope form of a line's equation is: y - y1 = m(x - x1), where (x1, y1) are coordinates of a point on the line and m is the slope. Substituting the given values, we get y - (-4) = -3(x - 1.25), which simplifies to y + 4 = -3x + 3.75. Finally, rearranging, we get the slope-intercept form: y = -3x - 0.25.

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Answer:

Step-by-step explanation:

so what your gonna do is you are going to add 81 to 360 and then sum it up. after you are going to divide it by 3.5.

This might be wrong but there is always a point where you have to try :)

Answer:

This is how you could anwser

283.5 or 283 1/2

Answer:

36/5

Step-by-step explanation:

x/3 + 6 -2x = -6

multiply the whole equation by 3 to get rid of the denominator of the first x term.

x+18-6x = -18

move x terms to one side and numerical terms to the other, subtract 18 from both sides in this case

x+18-6x-18=-18-18

x-6x = -36

simplify

-5x = -36

divide both sides by -5 to isolate x

x = -36/-5

=36/5

To divide 120.4 by 602, place the decimal point in the quotient above the decimal point in the dividend. Divide the whole numbers and then bring down the next digit.
The result is 0.2 (rounded to one decimal place).

To divide 120.4 by 602, follow these steps:

Therefore, 120.4 divided by 602 is equal to 0.2 (rounded to one decimal place).

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Answer:

Mean = 93.3 ( to nearest tenth).

Median = 97.

Mode = 97.

Step-by-step explanation:

Arrange the data in ascending order:

79 82 87 91 93 97 97 98 99 101 102

There are 11 numbers.

The Median is the center value (= the 6th number) = 97.

The mode = highest occurring value = 97.

The mean = sum / 11 = 93.3.

Answer:

9/4

Step-by-step explanation:

Answer:

111.25 ft.

Step-by-step explanation:

Step-by-step explanation:

6 is divisible by 2 and 3 (6 = 2 · 3).

257 is not divisible by 2 and 3 (257 is a prime number).

Therefore 257 is't divisible by 6.

Final answer:

257 is not divisible by 6 because it is not even.

A number must be even and the sum of its digits divisible by 3 to be divisible by 6.

Explanation:

To determine if 257 is divisible by 6, we need to check if it satisfies the criteria for divisibility by 6.

A number is divisible by 6 if it is divisible by both 2 and 3.

Examining 257, we see that it ends with a 7, which is not an even number.

So it does not meet the criterion for divisibility by 2.

Therefore, 257 is not divisible by 6.

4b + 9b + 5b-6

do 4b+9b first

4b+9b=13b

13b+5b=18b

Answer:

18b-6 or -6+18b

Answer:

2 √2

Step-by-step explanation:

2^√(3) =  {(2)³}¹/²

           = (8)¹/² = √8

           =  √2 * 2 *2 = 2 √2

Answer:

Step-by-step explanation:

To form soil, the two processes which must occur are erosion and weathering, so the correct answer here is B. Soil formation is a continuous process, but also one which takes a long time. It can sometimes more than five hundred years for 1cm of soil to form.

The formation of soil is a complex process that involves various physical, chemical, and biological processes acting over long periods of time.

Some of the key processes involved in soil formation include:

1. Weathering: Weathering is the breakdown of rocks and minerals into smaller particles due to exposure to physical, chemical, and biological agents such as water, wind, temperature fluctuations, plant roots, and microorganisms.

2. Erosion and Transportation: Once rocks and minerals are weathered, the resulting particles are transported by agents such as water, wind, ice, and gravity. Erosion refers to the movement of soil particles from one place to another, while transportation involves the movement of these particles over long distances.

3. Deposition: Deposition occurs when transported soil particles settle out of suspension and accumulate in a new location. Deposition can occur in various environments, such as river deltas, floodplains, glacial moraines, and coastal areas.

4. Organic Matter Accumulation: Organic matter, derived from decaying plant and animal remains, accumulates on the soil surface or mixes with mineral particles. Organic matter plays a crucial role in soil fertility, structure, and nutrient cycling.

Answer:

(-1, -1.5)

Step-by-step explanation:

A coordinate is a point (a single place) on a graph. Coordinates can be recorded as (#, #).

The first number is the one on the x-axis (left/right) and the second number is the one on the y-axis (up/down). (x, y) The middle point, where the x-axis and y-axis meet is called the origin, and is at (0,0).

The point that marks the campground is at -1 on the x-axis and -1.5 on the y axis.

Because the y-axis has two lines for every whole number, the line in between is the halfway mark and counts as a 0.5 increment.

Answer:

She stopped to rest for 45 minutes.

Step-by-step explanation:

It's where the line is straight. What's the second question?

Answer:

0.75 (45 mins) for both

Step-by-step explanation:

It's because the rest is the time where no activity is happening (the straight line). That line when measured from its start to end is mins 45 to mins 90, and when subtracted, gives 45 mins. For the initial ride it is from where the line moves upward until it stops. That goes from mins 0 to mins 45 ad when subtracted gives 45 mins.

Answer:

45mph.

15 x 3 = 45

20 x 3 = 60

so 60 ÷20 = 3

15 × 3 = 45

since 1 hour is 60 minutes

60 divided by 20 is 3

And 15 miles in 20 minutes times 3 is 45 miles in one hour

B, i honestly just subtracted them... and got $2.84 and rounded up to $3.00

Answer:

B : $ 3.00

Step-by-step explanation:

Round $6.79 to $7.00 and round $3.95 to $4.00 then do $7.00 - $4.00 = $3.00. You get the answer of B : $ 3.00

Answer:

-16/8 or -16÷8 equals -2 which is a whole number

an integer is a whole number that is positive ,negative or zero

Examples of integers: 1, 2, -5, -18, 20

Not Integers: 0.2, 9.15, 2/3

Final answer:

The division of -16 by 8 results in -2, which is an integer because it has no decimal component. Therefore, -16/8 is an integer.

Explanation:

The question is whether -16/8 is an integer. To determine this, we simply perform the division: -16 divided by 8 equals -2. Since -2 has no decimal component, it is indeed an integer. Integers are whole numbers that can be positive, negative, or zero, but do not include fractions or decimals. Examples of integers include -8, -6, -2, 0, 4, and 12. In this case, -16/8 simplifies precisely to -2, which is an integer.

Answer:X = 2

Step-by-step explanation:

Apply the distributive property.

2x+2⋅5+4(x−9)=−142x+2⋅5+4(x-9)=-14

Multiply 22 by 55.

2x+10+4(x−9)=−142x+10+4(x-9)=-14

Apply the distributive property.

2x+10+4x+4⋅−9=−142x+10+4x+4⋅-9=-14

Multiply 44 by −9-9.

2x+10+4x−36=−142x+10+4x-36=-14

Simplify by adding terms.

6x−26=−146x-26=-14

Move all terms not containing xx to the right side of the equation.

Add 2626 to both sides of the equation.

6x=−14+266x=-14+26

Add −14-14 and 2626.

6x=126x=12

Divide each term by 66 and simplify.

Divide each term in 6x=126x=12 by 66.

6x6=1266x6=126

Cancel the common factor of 66.

x=126x=126

Divide 1212 by 66.

x=2

Answer:

The expression is [tex]\frac{n}{2}-6+10[/tex]

For n=8 the value of the expression is 8

Step-by-step explanation:

Let

n -----> the number

we know that

"six less than" means we're subtracting 6:

- 6

"The quotient" means division. "Of a number and 2" Usually the numerator is listed first:

n/2

"increased by ten" means we're adding 10:

+10

substitute

[tex]\frac{n}{2}-6+10[/tex]

For n=8

substitute the value of n in the expression

[tex]\frac{8}{2}-6+10[/tex]

[tex]4-6+10=8[/tex]

Answer:

Expression would be [tex]\frac{n}{2}-6+10[/tex]

Value would be 8.

Step-by-step explanation:

Here, n represents the unknown number,

∵ The quotient of n and 2 = [tex]\frac{n}{2}[/tex]

6 less than  [tex]\frac{n}{2}[/tex] =  [tex]\frac{n}{2}-6[/tex]

[tex]\frac{n}{2}-6[/tex] increased by 10 = [tex]\frac{n}{2}-6+10[/tex]

Thus, the required expression would be,

[tex]\frac{n}{2}-6+10[/tex]

When n = 8,

[tex]\frac{8}{2}-6+10=4-6+10=8[/tex]

Answer:

Mr. Still finish independent reading at 9:40

Step-by-step explanation:

Mr.still's class has music for 50 minutes and then independent reading for 20 mins Music start 8:30

Music starts at 8.30 and it goes for 50 minutes

8:30 + 50 minutes is 9:20

After music , independent reading for 20 mins

So we add 20 minutes with 9:20

9:20 + 20 minutes is 9:40

So , Mr. Still finish independent reading at 9:40