Blocking an experimental design is useful because

Answer:

4 sizes and 3 toppings  = 12 combinations

2 sizes and 6 toppings = 12 combinations

3 sizes and 4 toppings = 12 combinations

Step-by-step explanation:

In this case so that customers have 12 options, what we must do is decompose the number, that is, look for two numbers that when multiplied give 12 as the result, for example:

4 sizes and 3 toppings  = 12 combinations

2 sizes and 6 toppings = 12 combinations

3 sizes and 4 toppings = 12 combinations

Answer:

A, D, E!!!

Step-by-step explanation:

Answer:

[tex]\huge\boxed{(i)\ x=-3\ \vee\ x=4}\\\boxed{(ii)\ x=1.5\ \vee\ x=1}[/tex]

Step-by-step explanation:

We have the product of two expressions. The product is equal to 0 if and only if one of the factors is equal to 0.

Therefore

[tex](i)\\(x+3)(x-4)=0\iff x+3=0\ \vee\ x-4=0\\\\\boxed{x=-3\ \vee\ x=4}\\\\(ii)\\(2x-3)(x-1)=0\iff2x-3=0\ \vee\ x-1=0\\\\\boxed{x=1.5\ \vee\ x=1}[/tex]

Answer:

A.x+1

Step-by-step explanation:

Answer: a) 1,600

              b) 35,000

              c) 120,000

Step-by-step explanation:

First, round each number to one significant digit (the first digit).

Then multiply them.

a) 17   --> rounds to 20

  82   --> rounds to 80

                                       20 x 80 = 2 x 8 with two zeros

                                                     = 1 6 0 0

b) 54   --> rounds to 50

  671   --> rounds to 700

                                       50 x 700 = 5 x 7 with three zeros

                                                       = 3 5 0 0 0

c) 207   --> rounds to 200

  643   --> rounds to 600

                                       200 x 600 = 2 x 6 with four zeros

                                                          = 1 2 0 0 0 0

Answer:

[tex]\theta=45^\circ[/tex]

Step-by-step explanation:

P is the centre of the circle and:

[tex]\angle P=90^\circ[/tex]

Angle [tex]\theta[/tex] is the angle subtended by the same arc as P at the circumference.

By the Inscribed Angle Theorem, we know that angle subtended by an arc at the centre is twice the angle subtended by the same arc at the circumference.

Therefore:

[tex]\angle P =2\theta\\2\theta=90^\circ\\\theta=90^\circ \div 2\\\theta=45^\circ[/tex]

Answer:

[tex]a_1 = -11\\\\a_n = a_{(n - 1)} + 22[/tex]

Step-by-step explanation:

An arithmetic sequence is generally given as:

f(n) = a + (n - 1)d

where a = first term and f(n) = nth term, d = common difference

The explicit formula given is:

f(n) = 11 + 22(n - 1)

The recursive formula is made of two statements, the first term and the formula showing how successive terms are related.

Mathematically, it is given as:

[tex]a_1 = a\\\\a_n = a_{(n - 1)} + d[/tex]

Therefore, the recursive formula is:

[tex]a_1 = -11\\\\a_n = a_{(n - 1)} + 22[/tex]

Answer:

The actual answer is g(1)=1

g(n)=g(n−1)+5

​

Step-by-step explanation:

Answer:

K = -2

Step-by-step explanation:

If y varies directly as x, k (constant) can be found by dividing the y-coordinate by the x-coordinate.

[tex]k = \frac{2}{-1} = -2[/tex]

Answer:

B

Step by step explanation

Answer:

3

Step-by-step explanation:

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]

Answer:  (b) vertical stretch by a factor of 6

Step-by-step explanation:

Consider h(x) = A(x - h)² + k

f(x) = x²

g(x) = 6x²

         ↓

       vertical stretch by a factor of 6

Answer:

x = 44°

Step-by-step explanation:

Since this is an isosceles triangle, the other angle that isn't defined is also 68°. So, since all the angles add up to 180°,

x + 68(2) = 180

x + 136 = 180

x = 44°

Answer:

44 is the answer

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Ok so you get two sets of proportional pairs: -3 and -1 , and -30 and -10.

The relationship between these is that the first term is 3 times the second. So you divide the first term by 3 to get the second.

So you divide -12 by 3 to get -4.

Hope this helps!

Answer:

-4 (*/ω＼*)

Step-by-step explanation:

Answer:

61.

Step-by-step explanation:

because 100-39=61 and 61+39=100!

Answer:

Part A: (C) 16 square inches

Part B: (C) 36 square inches

Answer:

C = 0.25d + 2

Step-by-step explanation:

Use the scenario given to find the rate per mile

Subtract the flat fee: 14.50 - 2.00 = 12.50

To find the rate, do 12.50/50 = 0.25

The rate is 0.25$ per mile

So, the equation will be:

C = 0.25d + 2

Answer:

If I answer in the comments and get it right will you mark me brainiest plz!!!!!!

Step-by-step explanation:

Answer:

the answer is D!

Step-by-step explanation:

I took that quiz :)

Answer:

There were 10 flies originally

Step-by-step explanation:

Since we have an exponential growth, we will be having a constant percentage of increase and we can set up the increase at any day using the following equation;

V = I(1+r)^d

where V is the number of flies on a particular day

I is the initial number of flies

r is the constant increase in percentage

and d is the number of days.

So we have for the second day;

60 = I(1+r)^2 ••••••(i)

For the fourth day, we have;

360 = I(1+r)^4 ••••••••(ii)

divide equation ii by i; we have;

360/60 = (1+r)^4/(1+r)^2

6 = (1+r)^2

(√6)^2 = (1+r)^2

1 + r = √6

r = √6 - 1

So we can substitute the value of r in any of the equations to get I which is the initial number of flies

Let’s use equation 1

60 = I(1 + r)^2

60 = I(1 + √6 -1)^2

60 = I(√6)^2

60 = 6I

I = 60/6

I = 10 flies

Answer:

(C)On a coordinate plane, 2 rays form an angle. One ray sits on the x-axis.

Step-by-step explanation:

In the coordinate plane, an angle is said to be in standard position when its value is stated with respect to the x-axis.

Therefore, for an angle to be in a standard position, one of its rays must be on the x-axis.

From the given options, only Option C has a ray that sits on the x-axis. Therefore, it is the only angle in standard position.

Answer:

C

Step-by-step explanation:

Answer:

Hope it will helpful.Follow for more answers.

Answer:6

Step-by-step explanation:

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.

Step-by-step explanation:

1) = 4ab

2) 12a2b

3) 8ab2

4) 6ab2

5) 12abc

6) 6ab2c

7) 16a2bc

8) 27abc

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:

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: it's in the photo below

Answer:

The third option

Step-by-step explanation:

Answer:

It is number 1 because they are asking for over or under 18

Step-by-step explanation:

Hope this helps!

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:

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 x>1/2 (sqrt(21) - 3)

x>0.791288

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