You work in a nursery with
20 children aged 3 - 5 years.
Your current room size is
415m² and does not meet
floor space requirements.
The room needs to increase
in size by 11%.
How big should the room
be?

Answer:

a

Step-by-step explanation:

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

We have,

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

To know more about Pythagorean theorem visit the link

brainly.com/question/343682

#SPJ1

complete question:

Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

Answer:

The person above is correct

Step-by-step explanation:

–3 + 8i  is  

✔ in quadrant II

.

4i is  

✔ on the vertical axis

.

6 is  

✔ on the horizontal axis

.

5 – 2i is  

✔ in quadrant IV

.

Each point located on the graph is; -3 + 8i is in quadrant II, and 5 - 2i is in quadrant IV.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

We have to find the location of the points.

-3 + 8i is in quadrant II.

4i is on the vertical axis.

6 is on the horizontal axis.

5 - 2i is in the quadrant IV.

Learn more about points lying on graph of a function here:

brainly.com/question/1979522

#SPJ2

Answer: B is correct

Step-by-step explanation:

Answer:

The scale of the model is 1 in.: 12 ft.

Step-by-step explanation:

Because 7 in.: 84 ft. simplifies to 1 in.: 12 ft. as 84/7 = 12/1

The probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

Since there are 8 cameras in the box, the total number of ways to choose 2 cameras from the box is given by the combination formula:

C(8,2) = 8!/(2!×(8-2)!) = 28

So there are 28 possible ways to choose a sample of 2 cameras.

Now, let's calculate the probability of each possible value of x:

When x = 0, both cameras in the sample are non-defective. The number of ways to choose 2 non-defective cameras from the 4 non-defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 0 is:

P(x=0) = (number of ways to choose 2 non-defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

When x = 1, one camera in the sample is defective and the other is non-defective. The number of ways to choose 1 defective camera from the 4 defective cameras in the box and 1 non-defective camera from the 4 non-defective cameras in the box is given by the product of the corresponding combinations:

C(4,1) × C(4,1) = 4×4 = 16

So the probability of x = 1 is:

P(x=1) = (number of ways to choose 1 defective camera and 1 non-defective camera)/(total number of ways to choose 2 cameras)

= 16/28

= 0.571

When x = 2, both cameras in the sample are defective. The number of ways to choose 2 defective cameras from the 4 defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 2 is:

P(x=2) = (number of ways to choose 2 defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

Therefore, the probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

to know more about probability

brainly.com/question/30034780

#SPJ1

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

CD = 15

Step-by-step explanation:

We are given two quadrilaterals: CDEF and GIJH.

We know that CD = 3x - 6, and GI = x + 8.

We want to find the length of CD.

Notice how CD and GI both have one tick mark on them.
This indicates that these two are congruent, meaning that they have the same length.

Because of that, CD = GI.

If we substitute 3x - 6 for CD and x + 8 for GI, we get:

3x - 6 = x + 8

Now, we can solve this like a regular equation.

Add 6 to both sides.

3x - 6 = x + 8

    +6       +6

_________________

3x = x + 14

Subtract x from both sides.

3x = x + 14

-x    -x

_____________-

2x = 14

Divide both sides by 2.

2x = 14

÷2    ÷2

____________

x = 7

We found the value of x.

Now, substitute 7 as x in 3x-6 (the length of CD).

CD = 3x - 6 = 3(7) - 6 = 21 - 6 = 15

Therefore, CD = 15.

Formula for circumference is C= πd, meaning pi multiplied by diameter. I will complete the question using both 3.14 for pi, and the pi key on the calculator, as I am not sure what the rules are for your mathematics class.

Formula C=πd, where diameter (given: 56) is 56 and pi is 3.14.

C=πd

  = 3.14 x 56

  =175.84

∴ The circumference of the wheel is about 175.8cm.

To find how much distance covered in 100 revolutions, we must multiply the distance covered in one revolution by 100.

175.84 x 100= 17584

The question does not ask to convert to meters or kilometers so I may leave it like this.

If you are told otherwise, follow the rules for converting.

∴ The distance covered in 100 revolutions is 17,584cm.

Formula C=πd where d equals 56 and pi is the full value of pi (3.1415926....)

C=πd

 = π x 56

 =175.929

As you can see, we get a more accurate answer, but again, it is all up to your class rules.

∴ About 175.93 cm circumference

Revolutions:

175.93 x 100 = 17593

∴ About 17, 593cm.

I hope this helps!

Answer:

the expression is equal to 0

Answer:

the answer is 5,087 or 5,086.8

Answer:

5086.8

Step-by-step explanation:

The angle of depression is the angle by which an observer must look down from his line of sight to see an object below him or her.

The angle of elevation is the angle by which an observer must look up from his line of sight to see an object above him or her.

Hence, angle 3 is an angle of elevation because it is the angle by which the observer must raise his/her head to see the top of the tree.

Therefore, angle 3 is an angle of elevation.

Answer:

The answer is 30 students!

Step-by-step explanation:

hope this helped!

Answer:

It will cost $7.92

Step-by-step explanation:

We will need to find out how many table spoons of lemon we will need first.

We need to make 3 pies requiring half a cup of lemon juice.

3 * 1/2 = 1.5 cups

We convert the cups to tablespoons

1.5 * 16 = 24 tablespoons

Then, since each lemon yields two tablespoons, we divide the tablespoons required by two. This is to find the number of lemons we need.

24/2 = 12

We multiply lemons by the price the store is selling them.

12 * $0.66 = $7.92

This is the price to buy enough lemons to make the 9-inch lemon pies.

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer: 3 dollars for a book.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

6m = b

Step-by-step explanation:

The area of triangle when angle and sides are given = 1/2* sin angle*ab

Area = 1/2 * sin 30 * 4*b

Area = 6m²

6 = 1/2 * sin 30 * 4*b

(6*2)/(sin 30 * 4)= b

12/(0.5*4) = b

12/2 = b

6m = b

Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%

We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%

For more such questions on surface area

https://brainly.com/question/30739454

#SPJ8

Answer: 9 3/10

Step-by-step explanation:

6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1  3/10= 8 + 1 + 3/10= 9 3/10

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.

The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.

For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.

Learn more about control variables here:

https://brainly.com/question/28077766

#SPJ1

the third answer (bottom left): 3^7 x 1/3^4

the negative exponent means its 1 divided by the number and exponent. i hope this helps you!! <3

Answer:

\(3^{7} * \frac{1}{3^4}\)

Step-by-step explanation:

Answer:B

Step-by-step explanation: Have a great day<3 :)

Answer:

(- 3, 1.5)

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

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

Answer:

7x.

Step-by-step explanation:

2 + 33 = 7x

35 = 7x

Solution is x = 5.

Answer: 5² + 4

Step-by-step explanation:

The domain of (boa)(x) is [1, ∞].

In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.

Based on the information provided above, we have the following functions:

a(x) = 3x+1

\(b(x) = \sqrt{x-4}\)

Therefore, the composite function (boa)(x) is given by;

\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = [1, ∞] or {x|x ≥ 1}.

Read more on domain here: brainly.com/question/9765637

#SPJ1

Answer:

Below

Step-by-step explanation:

The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.

so the equation is:

y= mx+56

m is the slope of the function wich is by how much the function grows.

By analogy, m is the distance added to the road each day.

● y= 3x+56

X is the number of days.

■■■■■■■■■■■■■■■■■■■■■■■■■■

To find the length of the road after 33 days, replace x by 33.

y= 3*33+56 = 155

So after 33 days the road is 155 miles.

7) The  probability that the two numbers have an even sum is: 0.5

8) The probability that the two are even is: 0.25

7) We want to find the probability that the two numbers have an even sum.

The only combinations that produces an even sum are:

(1, 3), (3, 1), (1, 1), (2, 2), (2, 4), (4, 2), (4, 4), (3, 3)

The other combinations of numbers are:

(1, 2), (1, 4), (2, 1), (4, 1), (2, 3), (3, 2), (3, 4), (4, 3)

Thus, we have a total of 16 combinations and the  probability that the two numbers have an even sum is:

P(two numbers with even sum) = 8/16 = 0.5

8) The probability that the two are even is:

4/16 = 1/4

= 0.25

Read more about spinner probability at: https://brainly.com/question/3765462

#SPJ1