Matt has two very active dogs named Theia and Odin who need to eat extra snacks to increase
their caloric intake. He uses math to figure out how much more to feed them. He tracks their
activity level to determine the increase.
The table below shows the number of treats per dog per week.
What is the average rate of change for the number of treats that Odin gets each week between
Week 1 and Week 5?
Week 2
Week 3
Week 5
Odin
Theia
Week 1
7
5
3
2.
00 00
Week 4
9
7
4
5
Week 6
5
6

Answer:

Exact form: [tex]9 \frac{41}{51}[/tex]

Decimal form: [tex]9.80392156[/tex]

Step-by-step explanation:

[tex]41\frac{2}{3}[/tex] ÷ [tex]4\frac{1}{4}[/tex]

Let's put everything into a fraction.

[tex]\frac{41\frac{2}{3} }{4\frac{1}{4} }[/tex]

Now we have an answer.

Exact form: [tex]9\frac{41}{51}[/tex]

Decimal form: [tex]9.80392156[/tex]

Hope this helps!

Answer:

1.618

The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.

Step-by-step explanation:

Plz Mark me as brainliest

[tex]\Large \boxed{\sf golden \ ratio}[/tex]

A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.

Answer:

i think is the second one

Step-by-step explanation:

Answer:

28 (0,2,4,14,28)

34 (0,2,17,34)

42 (0,2,6,7,21,42)

the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42

Answer:

C

Step-by-step explanation:

2/3=66 therefore it also equals 2/3%

Answer: C

Step-by-step explanation:

First find the decimal of 2/3  

Divide it  2/3 = 0.6666666

Now multiply it by 100 to convert it to a percent  

You get 66.66..%  which is the same as 66 2/3%

Answer:

x>18

Step-by-step explanation:

Answer:

$818,3

Step-by-step explanation:

16.7% in decimal is 0.167

= 0.167 x $4900

= $818,3

l=3w

3w(4)=48

12w=48

w=4

l=12

hope it helps

comment if u have any questions

Answer:

Length is 18; width is 6.

Step-by-step explanation:

The formula for the perimeter of a rectangle is:

[tex]P=2l+2w[/tex]

We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:

[tex]l=3w[/tex]

So, substitute this for l and 48 for P. Thus:

[tex]48=2(3w)+2w[/tex]

Distribute:

[tex]48=6w+2w[/tex]

Combine like terms:

[tex]48=8w[/tex]

Divide both sides by 8:

[tex]w=6[/tex]

So, the width is 6.

The length as we know is 3 times the width, so the length is 3(6) is 18.

And we are done!

We can use the points (-4, 0) and (0, 2) to solve.

Slope formula: y2-y1/x2-x1

2-0/0-(-4)

2/4

1/2

Best of Luck!

Answer: False

Natural numbers are not closed under division

Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.

However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.

A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.

If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.

Given :

Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .

To Find :

The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .  

Solution :

Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :

[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]

Now , mid point is given by :

[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]

Hence , this is the required solution .

Answer:

1. RATIO SCALE

2. INTERVAL SCALE

3. NOMINAL SCALE

4. ORDINAL SCALE

Step-by-step explanation:

The scales are:

- Nominal Scale

- Ordinal Scale

- Interval Scale

- Ratio Scale

Rule: Each scale will be used exactly once.

For number 1, the description is that of a Ratio Scale because size comparisons can be made between values on the scale, such as the example given - that one value is twice as big as another value.

For number 2, the description is that of an Interval Scale because the values of data measured on the scale can be ranked e.g. Yes ranks as 1, No ranks as 2, Indifferent ranks as 3 and there is meaningful difference (not numerical difference) between scale points.

For number 3, the description is that of a Nominal Scale, because it says obviously that the values of data measured on this scale can be in form of names (watch out for keywords like this when reading through) and cannot be rank ordered! A good example is the following data set:

- Yellow, Brown, Purple, Cream, Fustian Pink

For number 4, the description is that of an Ordinal Scale. A keyword "rank" is to be given attention here, even as the statement is straightforward and gives just a simple information.

Answer:

Coordinate A ins not intercepting any axis.

Step-by-step explanation:

For a coordinate to intercept an axis, it will be in the form [tex](a, b)\ such\ that:\ a=0, b \in \mathbb{R},\ or:a\in \mathbb{R}, b=0.[/tex]

Since in (3, 6), none of the components are 0, it is not intercepting any axes.

Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

Step-by-step explanation:

r+4r=24+1

5r=25

r=25/5

r=5

Answer:

r = 5

Step-by-step explanation:

r + 4r - 1 = 24

r + 4r = 25

5r = 25

r = 5

If there are 3 cups of strawberries per 6 liters of smoothie, that means that there is [tex]\frac{1}{2}[/tex] cups of strawberries per liter of smoothie.

[tex]\frac{3}{6}=\frac{1}{2}[/tex]

Hope this helps.

頑張って!

Answer:

C

Step-by-step explanation:

Answer:

D. It is a decimal that terminates after 3 decimal places

I hope this helps!

Answer:

-17 × 0 = 0

every number multiplied by 0 is equal to 0

Answer: Distance = 15km ; Displacement ≅ 11'2km

Step-by-step explanation:

In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.

Distance: 5km + 5km + 5km = 15km (Red lines)

Displacement² : (10km)² + (5km)² = 100km² + 25km² = 125km²

Displacement : √125km² ≅ 11'2km  (Blue line)

Answer:

The value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Step-by-step explanation:

We are given that C is the midpoint of segment AB where A(-3,m) , B (4, -1) , and C (k, 2).

As we know that the mid-point formula states that;

Mid-point = [tex]\frac{a+b}{2}[/tex]

This means that;

Mid-point of AB = [tex]\frac{A+B}{2}[/tex]

C(k, 2) = [tex](\frac{-3+4}{2}, \frac{m+(-1)}{2} )[/tex]

C(k, 2) = [tex](\frac{1}{2}, \frac{m-1}{2} )[/tex]

This means that;

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

[tex]k = \frac{1}{2}[/tex]  and  [tex]m-1=4[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m = 4+1 = 5[/tex]

So, the value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Here are the expressions on the left matched with the simplifed form on the right:

Here are some mathematical rules:

Also, this sign | | indicates that the number is postive.

To learn more about addition, please check: https://brainly.com/question/349488

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Question:

Express each vector as a product of its length and direction.

[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

Answer:

[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Step-by-step explanation:

A vector v can be expressed as a product of its length and direction as follows;

v = |v| u

Where;

|v| = length/magnitude of v

u = unit vector in the direction of v

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

Let the given vector be v, i.e

[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

(i) The length/magnitude |v| of vector v is therefore,

|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]

|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]

|v| = [tex]\sqrt{(\frac{3}{6})[/tex]

|v| = [tex]\sqrt{(\frac{1}{2})[/tex]

|v| = [tex]\frac{1}{\sqrt{2}}[/tex]

(ii) The unit vector u in the direction of vector v, is therefore,

u = [tex]\frac{v}{|v|}[/tex]

[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]

[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Therefore, the vector can be expressed as a product of its length and direction as:

|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Answer:

modulus of  |9+40i|  is 41

Step-by-step explanation:

Let z = 9+40i

then

|z| = [tex]\sqrt{9^{2}+40^{2} }[/tex]

   = [tex]\sqrt{81+1600}[/tex]

   = [tex]\sqrt{1681}[/tex]

   = 41

|z| = 41

Answer:

Step-by-step explanation:

1. |9+40i| = 41

2. |-10+24i| = 26

Answer:

x = -8

Step-by-step explanation:

[tex]6(x - 1) = 9(x + 2)[/tex]

Expand :

[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]

[tex]6x - 6 = 9x + 18[/tex]

Collect like terms and simplify

[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]

Divide both sides of the equation by -3

[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]

Answer:

Step-by-step explanation:

6x - 6 = 9x + 18

-3x - 6 = 18

-3x = 24

x = -8 is the solution

Answer:

7

Step-by-step explanation:

Answer:

31536000

Step-by-step explanation:

365 days x 24 hours x 60 minutes x 60 seconds = 31536000