Steven recorded the growth of a plant over 10 weeks for his science project. He made a graph that shows how much the plant grew each week. The plant was 2 in. tall when Steven started his project. At week 5, the plant was 8 in. tall.

Which equation represents Steven’s situation, where x is the number of weeks and y is the height of the plant?

A. y= 8/5x+2
B. y= 6/5x+2
C. y= 5/8x+2
D. y= 5/6x+2

Answer:

42 songs.

Step-by-step explanation:

Let x represent the number of songs Nathaniel's has.

We have been given that Nathaniel's sister has 5/6 as many songs on her MP3 player as he has on his MP3 player. This means his sister has [tex]\frac{5}{6}x[/tex] songs.

We are also told that his sister has 35 songs. We can represent our given information in an equation as:

[tex]\frac{5}{6}x=35[/tex]

Let us solve for x.

[tex]\frac{6}{5}\cdot \frac{5}{6}x=\frac{6}{5}\cdot35[/tex]

[tex]x=6\cdot 7[/tex]

[tex]x=42[/tex]

Therefore, Nathaniel has 42 songs.

To find the number of sculptures in the museum, we add the number of modern and antique train paintings and then subtract 76 from the total because there are 76 more paintings than sculptures. The museum has 2,134 sculptures.

The student asked how many sculptures are in the museum, given the number of modern train paintings and antique train paintings, and also knowing there are 76 more paintings than sculptures. To find out the number of sculptures, we first add the number of modern and antique paintings together: 1,763 + 447 = 2,210 paintings in total. Since there are 76 more paintings than sculptures, we subtract 76 from the total number of paintings to find the number of sculptures: 2,210 - 76 = 2,134 sculptures.

Young tigers, also known as tiger cubs, typically swim in bodies of water such as rivers, streams, lakes, and ponds found within their natural habitat.

Tigers are known to be excellent swimmers and are generally comfortable in water.

They use swimming as a means to cool off, explore their surroundings, and sometimes to hunt or catch prey.

Swimming also helps tiger cubs develop their physical abilities and gain confidence in the water.

Thus, it's important to note that tigers are found in various habitats across Asia, including mangrove swamps, grasslands, and forests, so the specific locations where tiger cubs swim may vary depending on their environment.

For more details regarding tiger cubs, visit:

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- The relation is not a function due to multiple y-values for the same x-value.

- Domain: {-4, -3, 2}

- Range: {0, 2, -3}

- Value of y when x = 2: -1

Let's analyze the graph and address each part:

A. Is the relation a function? Explain.

  - A function is a relation where each input (x-value) corresponds to exactly one output (y-value).

  - Looking at the graph, we see that there are two different y-values for x = -3: (x = -3, y = 2) and (x = -3, y = -3).

  - Since there are multiple y-values for the same x-value, the relation is not a function.

B. **What is the domain of the relation?

  - The domain consists of all the x-values represented in the graph.

  - From the graph, we can identify the following x-values: -4, -3, 2.

  - Therefore, the domain of the relation is {-4, -3, 2}.

C. What is the range of the relation?

  - The range consists of all the y-values represented in the graph.

  - From the graph, we can identify the following y-values: 0, 2, -3.

  - Therefore, the range of the relation is {0, 2, -3}.

D. What is the value of y when x = 2? Explain.

  - To find the value of y when x = 2, we look at the graph.

  - At x = 2, the corresponding y-value is -1.

  - Therefore, the value of y when x = 2 is -1.

Final answer:

The mark and recapture method is used to estimate the size of a population. In this case, 24 bears were initially tagged and 4 bears were recaptured, 2 of which were tagged. The estimated population size can be calculated using the mark and recapture formula as (24 * 4) / 2 = 48 bears.

Explanation:

The mark and recapture method is used to estimate the size of a population. By catching, tagging, and releasing a known number of individuals and then recapturing a second sample, scientists can calculate an estimate of the total population size. In this case, scientists initially tagged 24 bears and then recaptured 4 bears, 2 of which were tagged. Using the mark and recapture formula, the estimated population size can be calculated as follows:

Number of initial tagged individuals: 24

Total number of individuals in the second sample: 4

Number of tagged individuals recaptured in the second sample: 2

Estimated population size = (Number of initial tagged individuals * Total number of individuals in the second sample) / Number of tagged individuals recaptured in the second sample

Using this formula, the estimated population size of bears in this case would be (24 * 4) / 2 = 48 bears.

Answer: Hello mate!

We want to distribute 24 muffins, 18 breakfast bars and 12 bottles of juice evenly into baskets, and we want to know the maximum amount of baskets that makes this possible.

This means that we are looking for the maximal common factor between 12, 18 and 24.

To find it, you can took the smallest number in the set, in this case, 12, and look at his divisors, then see if these divisors also divide the other numbers in the set.

Let's do it:

The biggest divisor of 12 is 6, because of 12/6 = 2.

Now 18/6 = 3, so 6 is also a divisor of 18.

24/6 = 4, then 6 is also a divisor of 24.

Then the maximal common factor of the numbers 12, 18 and 24 is 6.

This means that the maximum number of baskets that have an even distribution of the things is 6, where each basket has 2 bottles of juice, 3 breakfast bars, and 4 muffins.

Final answer:

Cynthia should calculate the dimensions of the rug by solving the quadratic equation derived from the area she can afford and the dimensions of her room, taking into consideration the width of the uniform strip she wants to leave around the rug.After finding [tex]\( w \), the dimensions of the rug will be \( (20 - 2w) \) ft by \( (31 - 2w) \) ft.[/tex]

Explanation:

To find the dimensions of the rug, we need to subtract the width of the strip left around the rug from the width and length of the room.

The area of the room is given by [tex]\( A_{\text{room}} = W \times L \).[/tex]

Cynthia wants to leave a uniform strip of floor around the rug. This means that the dimensions of the rug will be reduced by twice the width of the strip. So, the dimensions of the rug will be [tex]\( (W - 2w) \times (L - 2w) \).[/tex]

Given that she can afford to buy 350 square feet of carpeting, the area of the rug must be equal to 350 square feet.

So, we have the equation:

[tex]\[ (W - 2w) \times (L - 2w) = 350 \][/tex]

Substituting the given values:

[tex]\[ (20 - 2w) \times (31 - 2w) = 350 \][/tex]

Expanding the equation:

[tex]\[ 620 - 82w - 40w + 4w^2 = 350 \][/tex]

Simplifying:

[tex]\[ 4w^2 - 122w + 620 = 350 \][/tex]

[tex]\[ 4w^2 - 122w + 270 = 0 \][/tex]

Now, we can solve this quadratic equation for w . Once we find the value of w , we can calculate the dimensions of the rug.

After finding [tex]\( w \), the dimensions of the rug will be \( (20 - 2w) \) ft by \( (31 - 2w) \) ft.[/tex]

Answer:

7

Step-by-step explanation:

Change the problem from 9/m + 4 to 9/3 + 4.

If you do 9 divided by 3, you get 3 so your problem is now 3 + 4.

3 + 4 = 7.  Your answer is 7.

Hope that helps!

Let us say that:

T = numbers from 2-9 
Z = numbers from 0-9 
X = all except 1 (0, 2-9)

If a number begins with 1: 
1 _ _ 
Then we can have 
1 1 Z (10 numbers) 
1 X 1 (9 numbers) 
So a total of 19. 

Now if a number starts with 2-9 
T _ _ 
The second digit must be 1 

T 1 _
but the third can be anything so
T 1 Z = 8 * 1 * 10 = 90 numbers 

Total = 99