Indicate whether each of the following fractions is proper or improper. a. 4⁄16 b. 75⁄70 c. 2⁄15 d. 6⁄6

The hypotenuse of the paper is 2√106 cm.

What is Pythagorean theorem ?

Hypotenuse ² = Height ² + Width ²

Know more about Pythagorean theorem,

The Pythagorean Theorem, also known as the Pythagoras Theorem, explains the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. Pythagorean triangles are the name given to the sides of a right triangle. Let's learn about Pythagorean theorem, formula, derivation and examples in detail.

The history of the Pythagorean theorem goes back to the ancient Babylonian and Egyptian era. The Greek mathematician Pythagoras of Samos introduced the Pythagorean theorem. Pythagoras was born in 570 BC. The Greek philosopher studied with other monks and formed a group of people; he finally stated the Pythagorean theorem. Even before Pythagoras, the ratio was shown on a Babylonian tablet 4000 years ago, but the theorem is published under the name of Pythagoras.

Here given, a triangle shaped paper’s height is 18 cm and width is 10 cm.

We want find the hypotenuse of the paper ?

Here, height of the paper = 18 cm and width of the triangle = 10 cm.

[tex] = {18}^{2} + {10}^{2} \\ = 324 + 100 \\ = 424[/tex]

So,

[tex]hypotenuse = \sqrt{424} \\ = \sqrt{2 \times 2 \times 2 \times 53} \\ = 2 \sqrt{2 \times 53} \\ = 2 \sqrt{106} \: cm[/tex]

Therefore,the hypotenuse of the paper is 2√106 cm.

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Answer: the number is x = 1 + 21/52

Step-by-step explanation:

we have

(5 + 5/12) - x = (6 + 1/6) - (2 + 2/13)

this means that x is smaller than 5 + 5/12 by the same amount as (2 + 2/13) is smaller than (6 + 1/6)

We can solve it directly, first solve the parentheses, put the whole numbers at one side and the fractions in the other side:

5 - 6 + 2 - x = -5/12 + 1/6 - 2/13

1 - x = -5/12 + 2/12 - 2/13

1 - x = -3/12 - 2/13 = -1/4 - 2/13 = -13/(4*13) - (2*4)/(4*13) = -21/52

x = 1 + 21/52

Answer:

73/52

Step-by-step explanation:

To set the infusion rate for a 60 kg dog, calculate the total fluid needed (3000 mL), the total number of drops (30,000 gtts), and then determine the drops per minute (20.83 gtt/min), rounding to approximately 21 drops per minute.

To calculate the infusion rate for a 60 kg dog that needs 50 mL/kg of fluids over 24 hours using a 10 gtt/mL set, follow these steps:

Therefore, you will set the infusion to approximately 21 drops per minute (rounding to the nearest whole number).

Answer:

1.463 ft.

Step-by-step explanation:

As you can see in the image, we can use the sin(6) to calculate the high.

sin(6°) = x/14

x = sin(6°)*14

x  = 1.463 ft.

The points that are solutions to the system of inequalities is ( -12,0), (-10,1), the correct option is A and C.

The system of Inequalities are the set of inequalities that have a common solution.

The solution of the set of Inequalities can be obtained by plotting a graph and finding the common area.

The solution to the system of inequalities is shown in the graph.

The points that are solutions to the system of inequalities is

( -12,0)

(-10,1)

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This problem can be solved using equivalent fractions. The first step in resolving this problem is to realize that fractions are best compared when they both have the same denominator.  In this case, I will choose to make that common denominator 100. There is no need to rewrite the fraction [tex]\frac{21}{100}[/tex] as the denominator for this fraction is already 100. The fraction [tex]\frac{1}{5} =\frac{20}{100}[/tex] . This is achieved by multiplying both the numerator and denominator by 20. Now that the two fractions have the same denominator, we can easily see that [tex]\frac{21}{100}[/tex] is greater than [tex]\frac{1}{5}[/tex] because it is greater than its equivalent fraction.

Answer:

The height of the ball after t =1.5 second is 7.5 feet.

Description:

The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.

Therefore, the basketball thrown at the rate of 1 feet/per second.

Step-by-step explanation:

Given: A player shoots a basketball from a height of 6 feet. The equation,

h(t) = [tex]-16t^2 + 25t + 6[/tex]

We need to find the height of the ball when t = 1.5 and describe the height.

plug in t = 1.5 in h(t) = [tex]-16t^2 + 25t + 6[/tex]

h(1.5) = [tex]-16(1.5)^2 + 25(1.5) + 6[/tex]

Simplifying the above expression, we get

h(1.5) = -36 + 37.5 + 6

h(1.5) = -36+43.5

h(1.5) = 7.5 feet

The height of the ball after t =1.5 second is 7.5 feet

Description:

The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.

Therefore, the basketball thrown at the rate of 1 feet/per second.

Answer: B. 38,273 + 51,425 = 89,798

Step-by-step explanation:

Let's check all the sum by adding their corresponding places.

A. [tex]46,371 + 32,618 = 78,989[/tex]

Its correct.

B. [tex]38,273 + 51,425 =89698\neq 89,798[/tex]

Here when we add the digits on the hundredth place we get 6 not 7.

Hence, it is the example of an error of addition by one.

Its correct.

C. [tex]13,246 + 84,631 = 97,877[/tex]

Its correct.

D. [tex]52,634 + 25,145 = 77,779[/tex]

Its correct.

Answer:

  See the attachment

Step-by-step explanation:

You want a graph of the parabola defined by f(x) = x² +10x +24.

We can add and subtract the square of half the x-coefficient to put the equation into vertex form:

  f(x) = x² +10x +24 . . . . . . . . . . given

  f(x) = x² +10x +25 +24 -25 . . . . add and subtract (10/2)² = 25

  f(x) = (x +5)² -1 . . . . . . . . . write in vertex form

Comparing to the vertex form equation f(x) = (x -h)² +k, we see that ...

  (h, k) = (-5, -1).

These are the coordinates of the vertex.

The coefficient of x² is 1, so another point can be found by adding (1, 1) to the vertex. That means a second point on the parabola is ...

  (-5, -1) +(1, 1) = (-4, 0)

The attached graph shows the parabola with vertex (-5, -1) through point (-4, 0).

__

Additional comment

When the coefficient of x² is not 1, the process is a little different. If you start with f(x) = ax² +bx +c, you can factor 'a' from the first two terms to help you get vertex form.

  f(x) = a(x² +(b/a)x) +c
  f(x) = a(x² +(b/a)x +(b/(2a))²) + c - a(b/(2a))²
  f(x) = a(x +b/(2a)x)² +(c -b²/(4a))

The vertex is (-b/(2a), c -b²/(4a)).

The second point can be found by adding (1, a) to the vertex coordinates.

The no. of equally likely event is 10.

Probability is chance of occurrence of a certain event out of all the possible events that can occur in a given situation.

According to the given question Tossing of four coins simultaneously as an experiment let us find he sample space and assuming that all these 4 coins are unbiased.

S = { HHHH, HHHT, HHTT, HTTT, TTTT, TTTH, TTHH, THHH, HTTH, THHT }.

∴ N(s) = 10.

As these 4 coins are unbiased there for all the events in the sample space are equally likely to happen.

So, The no. of equally likely outcome is 10.

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Answer:

12 minutes

Step-by-step explanation:

Just took the test and got it right

Answer:

d. [tex]-15x^3y^7[/tex]

Step-by-step explanation:

By the binomial theorem,

[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r} q^r[/tex]

Where,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Thus,

[tex](\frac{1}{2}x-y)^{10}=(\frac{x}{2}+(-y))^{10})=\sum_{r=0}^{n} ^10C_r (\frac{x}{2})^{10-r} (-y)^{r}[/tex]

For the 8th term, r = 7,

Thus, the 8th term would be,

[tex]^{10}C_7 (\frac{x}{2})^{10-7} (-y)^{7}[/tex]

[tex]=\frac{10!}{7!(10-7)!} (\frac{x}{2})^3 (-y)^7[/tex]

[tex]=-\frac{10\times 9\times 8}{3\times 2\times 1}\times \frac{x^3}{8}\times y^7[/tex]

[tex]=-\frac{720x^3y^7}{48}[/tex]

[tex]=-15x^3y^7[/tex]

Hence, option 'D' is correct.