Solve for x. The triangles in each pair are similar.

To estimate the value of √97.5÷1.96, we approximate √97.5 to be just under 10, and 1.96 to be about 2. Dividing these estimations, 10 by 2, we get an approximate answer of 5.

The student asked to estimate the value of √97.5÷1.96. First, let's find a reasonable approximation for each number.

For the square root of 97.5, we know that √100 is 10, so we can estimate √97.5 to be slightly less than 10. For 1.96, that's very close to 2, so we can use that for our approximation.

Now, our estimated equation is 10÷2, which is 5. Hence, the estimated value of √97.5÷1.96 is approximately 5.

Answer: 406

Step-by-step explanation:

Given : In Nathan’s baseball card collection, 58% of the cards are players form the national league.

We can write 58% as 0.58 [To convert percent into decimal we divide it by 100]

If he has 702 baseball cards, then the number of baseball cards are players that form the national league will be :

[tex]0.58\times702\approx 0.58\times700=406[/tex]

Hence, about 406 baseball cards are players form the national league.

Johnny's flight home distance is calculated using the Pythagorean theorem, which comes to approximately 228 miles, treating his southward and westward travels as legs of a right-angled triangle.

The question asks about the flight distance Johnny must cover to get home. Since Johnny traveled 220 miles south and then 60 miles west, we can represent this as a right-angled triangle with the southward travel as one leg and the westward travel as the other leg. According to the Pythagorean theorem, which states that in a right-angled triangle the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, we can calculate Johnny's flight distance home.

Therefore, the calculation would look like this:

Plugging in the numbers:

Johnny's flight distance home is approximately 228 miles.

It will take 2 days to process the aluminum collected on Saturday. Each cup of dye can make 1/2 T-Shirt. Each flower bed can make 6 T-Shirts.

To determine how many days it will take to process the aluminum collected on Saturday, we can divide the amount collected by the amount processed each day.
7/4 ton / 7/8 ton/day = (7/4) / (7/8) = 7/4 x 8/7 = 2 days.
Therefore, it will take 2 days to process the aluminum collected on Saturday.

To find out how many T-Shirts each cup of dye can make, we can divide the amount of dye needed for a T-Shirt by the amount of dye in each cup.
3/8 cup / (3/4) cup = (3/8) / (3/4) = 3/8 x 4/3 = 1/2 T-Shirt.
Therefore, each cup of dye can make 1/2 T-Shirt.

To find out how many T-Shirts each flower bed can make, we need to multiply the amount of dye in each color by the number of cups.
Red: 12 cups x 1/2 T-Shirt = 6 T-Shirts.

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Final answer:

Balu ate 1/3 of the whole cake.

Explanation:

To solve this problem, we can use the concept of fractions. Let's say Pumba ate x fraction of the cake. Then Balu ate twice as much as Pumba, which means Balu ate 2x fraction of the cake. Together, Pumba and Balu ate 1/2 of the cake. So we can add their fractions: x + 2x = 1/2. Combining the like terms, we get 3x = 1/2. To solve for x, we divide both sides of the equation by 3: x = 1/2 ÷ 3 = 1/6. Therefore, Balu ate 2x = 2 × (1/6) = 2/6 = 1/3 of the cake.

Answer:

it is B enroll in an ag. program in school.

Step-by-step explanation:

The correct answer is b. enroll in an agriscience program in school.

Membership in the National FFA Organization is open to students who are enrolled in agricultural education courses. These courses are part of an agriscience program in school, which prepares students for careers in agriculture and related industries. The FFA is an intracurricular student organization for those interested in agriculture and leadership. It is not limited to students who are in the country, plan careers in agriculture, or seek leadership training exclusively, although these aspects can be part of the FFA experience. The primary requirement for membership is enrollment in an agriscience program, which provides the foundation for the organization's educational activities and programs.

Answer:

Fly down 5 feet and return to the ground.

Step-by-step explanation:

We are given that A bird flew from the ground onto a tree branch 5 feet above the ground.

We are supposed to find What could the bird do next that would make this situation a model of combining a number and its additive inverse

Additive inverse - What you add to a number to get zero is additive inverse.

The negative of a number.

Now we are told  What could the bird do next that would make this situation a model of combining a number and its additive inverse

Since it already flew 5 feet above the ground .

Additive inverse of 5 feet is -5 feet

So, to make the situation of combining a number and its additive inverse

Bird has to flew 5 feet return to the ground i.e.-5 feet

So, a model of combining a number and its additive inverse = 5+(-5)

Hence Option A is correct.

Fly down 5 feet and return to the ground.

Answer:

A is correct

Step-by-step explanation:

Lucio can use counters to represent the number of eggs laid by each set of chickens. He can then compare the numbers to ascertain which set laid more eggs. Counters provide a simple way to visually represent and compare quantities.

Lucio can use counters to represent the number of eggs laid by allocating one counter for each egg. Let's assume Lucio has two sets of chickens from which he collects eggs. He can use different colored counters or different objects to represent the eggs laid by each set. Every time a chicken lays an egg, he places a corresponding counter in a designated area. By the end of a certain period, say one day, he can compare the number of counters in each area. This way, the set of chickens with more counters represents the one that laid more eggs.

Counters provide a simple yet effective way to visually represent and compare quantities in real-world scenarios.

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The equation of line is y = -1/2 x + 5/2 or x+ 2y = 5.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

The points from the Graph are (1, 2) and ( 4, -4).

So, the slope is

= (4-1)/(-4-2)

= 3/(-6)

= -1/2

and, using the slope intercept form

(y- 2)= m (x- 1)

y-2 = -1/2 ( x-1)

y-2 = -1/2x + 1/2

y= -1/2 x + 1/2 + 2

y = -1/2 x + 5/2

2y = -x + 5

x+ 2y = 5

Hence, the equation of line is y = -1/2 x + 5/2 or x+ 2y = 5.

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The "ACTUAL" answer is y = -2x + 4

Answer:-1^5

Step-by-step explanation:

Final answer:

To determine how Eva can arrange 24 photos in an album so that each page has the same number of photos, we need to find the factors of 24. With factors of 1, 2, 3, 4, 6, 8, 12, and 24, there are 8 distinct ways to arrange the photos across the album's pages with each page having the same number of photos.

Explanation:

The student's question is about determining the different ways Eva can arrange 24 photos in an album so that each page contains the same number of photos. To solve this, we need to consider the factors of 24, as the number of photos on each page must be a factor of the total number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. This means Eva has 8 different page arrangements where each page has the same number of photos.

Now, for each of these arrangements, the order of the photos on each page and the order of the pages themselves can change. If we assume all photos are distinct, the number of ways to arrange the photos on a single page is the factorial of the number of photos per page. However, since Eva is concerned only with the arrangement of the number of photos per page being the same, not the order within the pages, we only need to consider the 8 different page arrangements.

The distance that should be travel in 5 hours is 105,000 km.

Given that,

We know that

Speed = Distance ÷ time

21,000 = Distance ÷ 5

So, the distance is

= 21,000 × 5

= 105,000 km

Therefore we can conclude that the distance that should be travel in 5 hours is 105,000 km.

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Eric will walk 1003.75 miles in a year if he meets his goal.

Eric goal is 2.75 miles/day

How many miles in one year?

[tex]\boxed {1 year = 365 days }[/tex]

so in a year, Eric will walk:

[tex]\boxed {2.75 miles \times 365 days }\\ \boxed {= 1003.75 miles }[/tex]

Here is how to do decimal numbers multiplication using standard algorithm (You can see in the attachment below how to multiply using the area model)

   2.75            ⇒ 2 decimal place

   365   x        ⇒ 0 decimal place (a whole numbers)

  1375

 1650

825  +

1003.75           ⇒ 2 decimal place

Here how to determine where the decimal point, from the calculation above

First factor has 2 decimal place

Second factor has no decimal place,

so the result would have 2 decimal place (2+0)

In doing decimal numbers multiplication we don't need to line the decimal place.

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Keywords: multiplication, decimal multiplication, three digits number additional, additional, multiplication, three digit numbers, subtraction decimal numbers

Note that if Eric meets his goal, he will walk approximately 1003.75 miles in a year

Note that the distance walked to and from the park every day = 2.75 miles

Number of days in a year = 365 days

Total miles walked in a year = Distance walked every day x Number of days in a year

Total miles walked in a year = 2.75 miles x 365 days

= 1003.75 miles

So , if Eric meets his goal, he will walk approximately 1003.75 miles in a year.

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To find out how many days 3/4 of the tortillas will last, we can set up a proportion using the given information. By solving the proportion, we find that 3/4 of tortillas will last for 8 days.

To find out how many days 3/4 of the tortillas will last, we can set up a proportion using the given information.

Let's assume that the total number of tortillas is represented by 'x'.

We know that 2 bags of tortillas are used every day, so in 'x' number of days, 2x bags of tortillas will be used.

According to the question, 3/4 of tortillas should last 'x' number of days. So, we can set up the proportion: 2x / x = 3/4.

To solve this proportion, we can cross multiply: 2x * 4 = x * 3. Simplifying, we get 8x = 3x. Dividing both sides by 3, we get x = 8.

Therefore, 3/4 of tortillas will last for 8 days.

Answer:

The required answer is 41.02 meters.

Step-by-step explanation:

Each box = 5.49 meters.

So, both boxes = [tex]5.49\times2=10.98[/tex] meters

Now the distance from the front of the box at one end of the field to the front of the box at the other end of the field is given by:

[tex]52-10.98=41.02[/tex] meters

Therefore, the required answer is 41.02 meters.