Write the point-slope equation for each line with the given slope and point. y –y1 = m(x – x1) Slope = 5 Point on line = (–1, 3)

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]

PART B

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

[tex]=\dfrac{15}{64}\\=0.234375[/tex]

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]

Explanation:

Label the slots A,B,C for first through third place.

There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values

8*7*6 = 336

There are 336 ways to select three people from a pool of eight overall.

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

If you want to use the permutation formula, then your steps might look like this

[tex]_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336\\\\[/tex]

Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.

Answer:

Step-by-step explanation:

From the figure attached,

Given : LM ≅ OP

            PQ ≅ MN

            NL ≅ QO

To Prove : ΔLMN ≅ ΔOPQ

In the triangles LMN and OPQ,

             Statements              Reasons

1). LM ≅ OP                       1). Given

2). PQ ≅ MN                     2). Given

3). NL ≅ QO                      3). Given

4). ΔLMN ≅ ΔOPQ            4). By SSS property of congruence

Answer:

x = 12:15=×5

36

060

Step-by-step explanation:

12:15=0

x=0

Answer:

4

Step-by-step explanation:

Divide the left side by 3

12:15

12/3 : 15/3

4:5

x would be 4

Problem: You do not have an attached picture. Though, I can help you out with this question.

So, three-fifths of the members are girls. There are 30 of girls. We can immediately make an equation using "x".

3/5x=30

3/5x × 5/3=30 × 5/3

x=50

Thus, there are 50 members in total. Though if x is too hard for you, you may substitute it by using another variable.

Variable in here is x.

Answer:

18/17

Step-by-step explanation:

the negative reciprocal of -289/324 is 324/289. When it is multiplied by 17/18 you get 18/17 as the answer.

Answer:

[tex] - 1 \frac{1}{17}[/tex]

Step-by-step explanation:

[tex]Reciprocal \: of \: - \frac{289}{324} = - \frac{324}{289} \\ \\ \frac{17}{18} \times (- \frac{324}{289} ) \\ \\ = \frac{17}{18} \times (- \frac{18 \times 18}{17 \times 17} ) \\ \\ = - \frac{18}{17} \\ \\ = - 1 \frac{1}{17} \\ [/tex]

Answer: Option B.

Step-by-step explanation:

The price per ounce can be calculated as the amount of you paid divided the number of ounces that you get.

A) we have a table:

ounces          price

18                     $1.5

36                    $3.00

54                    $4.5

We can see that here we have a linear relationship. for example, the price for 18 ounces is $1.5

Then the price per ounce is:

p = $1.5/18 = $0.083

B) here we know that 15 oz cost $0.75, the price per ounce is:

p = $0.75/15 = $0.05

C) here we have 11 ounces, and the price is $2.20

then we have:

p = $2.2/11 = $0.2

Then we can conclude that the least expensive is option B.

Answer:b

Step-by-step explanation:

did it on khan

Answer:

False

Step-by-step explanation:

This is false because there are 5 numbers from 0 - 4 (0, 1, 2, 3, 4) so the probability will be 1/5 not 1/4.

Answer:

x+y=7

y= x+3

Step-by-step explanation:

i just took the test

The system of the equation that represents the given condition will be x + y = 7 and y = x + 3. And the solution is (2, 5).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of x and y is 7. The value of y is three more than the value of x. Then the equation is given as,

x + y = 7                ...1

y = x + 3               ...2

From equations 1 and 2, then we have

x + x + 3 = 7

2x = 4

x = 2

Then the value of the variable 'y' will be given as,

y = 2 + 3

y = 5

The system of the equation that represents the given condition will be x + y = 7 and y = x + 3. And the solution is (2, 5).

More about the solution of the equation link is given below.

https://brainly.com/question/545403

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Answer:

2 and 30

Step-by-step explanation:

2/3=20/30

2 and 30 means the extremes and 3 and 20 are the means

Answer:

Step-by-step explanation:

Parallel lines have same slope

19) y = x - 4

m = 1 ;   (2, 3 )

Equation: y - y₁ = m(x- x₁)

             y - 3 = 1(x - 2)

              y - 3 = x -2

                   y = x - 2 + 3

y = x + 1

20) 2x + 3y = 3

We have to write in y = mx + b  form

3y =  - 2x - 3

[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)

[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]

for perpendicular lines, m2 = -1/m1

21) y = 2x+ 5

m1 = 2

[tex]m_{2}=\frac{-1}{2}[/tex];     (-2,8)

[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]

22) x+ 4y = 8

           4y = -x + 8

             [tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]

m2 = 4;  (-2,-11)

y - [-11] = 4(x -[-2])

y + 11 = 4 (x + 2)

y + 11 = 4x + 8

      y = 4x + 8 - 11

      y = 4x - 3

Answer:

A. <

Step-by-step explanation:

The symbol "<" means less than.

Comparing 4.589 with 4.958, 4.958 is greater than 4.589 by 0.369 (4.958 - 4.589).

So therefore, if we are to write 1 statement for both, we would say "4.589 is less than 4.958".

This can be written by using just symbols without words, thus, we have:

4.589 < 4.958.

The correct option is A. <

Answer:

976cm^2

Step-by-step explanation:

Surface area:

Ara of cross section x 2 = 1/2 x 2 x 14 x 24 = 14 x 24 = 336

Area of base = 14 x 10 = 140

area of slope x 2 = 25 x 10 x 2 = 500

Total surface area = 500+140+336 = 640 + 336 = 973cm^2

Answer:

976 cm^2

Step-by-step explanation:

Area of triangle: 1/2bh

Area of rectangle b×h

2 Triangular ends 12×14=168 each So 336

2 sides 10×25=250 each So 500

1 base 10×14=140

Add: 140+500+336=976 square centimeters

Answer:

5/54

Step-by-step explanation:

probability of the dice being 5 = 1/6

probability of the dice being a factor of 6 = 4/6

probability of the dice being more than 1 = 5/6

1/6 * 4/6 = 4/36

4/36 * 5/6 = 20/216

20/216 simplified to lowest is equal to 5/54

Answer:

7.5 miles

Step-by-step explanation:

Given the equation d(t) = 0.5t, all you need to do is plug in the value of t.

They're asking what the Function equals, and they're giving you the value of the variable t.

To solve, write the equation d(15) = 0.5(15)

And if you simplify the right side of the equation, you'll find that

d(15) = 7.5

If t represents time, then you can conclude that Julio travels 7.5 miles in the time t, of 15 minutes.

Answer:

11/8 or, 1 and 3/8

Step-by-step explanation:

First, we have to make both the denominators the same. In this case, we can multiply 3/4 by 2, to make 4, the denominator, into 8. What we do to the denominator, we must do to the numerator! So, we multiply 3 by 2, and get 6!

Now we have, 5/8 + 6/8, which equals 11/8! Which can also be simplified to 1 and 3/8 (because the numerator is larger than the denominator)

Hope this helps! :)

Answer:

I did as linear equation hope it helps

Answer:

x=2

Step-by-step explanation:

46x-2=45x

+2         +2

46x=45x+2

-45x     -45x

x=2

Answer:

I hope you can see the pic

Step-by-step explanation:

(46x - 2) and 45x are opposite angles. Opposite angles are equal to each other so, like terms will he collected and then x is gotten as +2.

Answer:

2, 3

Step-by-step explanation:

2. The leading coefficient is -3. When the leading coefficient is negative, the parabola opens down.

3. When the parabola opens down, it has a maximum point, but no minimum point. (when the parabola opens up, it has a minimum, but no maximum)

I hope this helps :)

The right statements about equation y=−3x^2+18x+23 is 2) The leading coefficient is negative and 3) The parabola has a maximum.

A parabola is a plane curve which is mirror-symmetrical and can be downward, upward, leftward and rightward shaped.

Second is true because when the coefficient is negative  the parabola opens down because their values starts decreasing.

Third is true because when the parabola opens down it has a maximum point and no minimum point. On the other hand when the coefficient is positive it opens up.

Learn more about parabola at https://brainly.com/question/4148030

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Hey there! :)

Answer:

1,500,000.

Step-by-step explanation:

Convert to standard notation by first deriving the value of 10 to the exponent given:

[tex]10^{6} = 1,000,000[/tex] (6 zeros)

Multiply:

1.5 × 1,000,000 = 1,500,000

Answer:

x = ±20

Step-by-step explanation:

x^2 -1=399

Add 1 to each side

x^2 = 399+1

x^2 = 400

Take the square root of each side

sqrt(x^2) = ±sqrt(400)

x = ±20

Answer:

Brianliest!

Step-by-step explanation:

It could be found if you were given the rate

since there is no rate, the question should be answered that there is not enough information

Answer:

x ≥ 20

Step-by-step explanation:

First, we want to isolate x. We can start to do that by subtracting 6 to both sides.

x/10≥2

Now, we multiply each side by 10.

x ≥ 20

That's the answer, all values above or equal to 20 are solutions.

Answer:

The answer is x_> 20

Step-by-step explanation:

Answer:

0.100

Step-by-step explanation:

0.0995 has 4 decimal places

5>4 so round up

9 turns to 10, the 1 is "added on" to the number ahead

9 turns to 10 again, the 1 is "added on" to the number ahead

0 turns to 1

you are left with 0.100

Answer:

0.100

Step-by-step explanation:

Three decimal places: 0. 0 / 9 / 9 / 5

Rounding number: 0. 0 / 9 / 9 / 5

Since it is 5, add 1 to the second 9. This will result to 0 while adding 1 to the first 9. Again, this would result to 10 which will add 1 to the next number, 0.

0.1000

Since the question wants you to round three places, you were not told to remove the zeros in those decimal places. So only remove the last 0.

0.100 is the answer

Answer:

the answer is D!

Step-by-step explanation:

I took that quiz :)

Answer:

d = 4

Step-by-step explanation:

4d - 4 = 5d - 8

Add -5d and 4 on both sides.

4d - 5d = - 8 + 4

- 1d = - 4

Divide -1 into both sides.

d = -4/-1

d = 4

Answer:

Hope it will helpful.Follow for more answers.

Answer:

62mph

Step-by-step explanation:

Answer: 250 miles

Step-by-step explanation:

100 kph = 62.5 mph

In 4 hours, the car will travel

62.5 x 4 = 250 miles