The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse

How many pairs of whole numbers have a sum of 99

alexandr402 [8]

With the sum of 99, we will get 50 pairs whole numbers. Why?

Let’s start with

0+ 99

1 + 98

2 + 97

3 + 96

4 + 95

5 + 94

6 + 93

7 + 92

8 + 91

9 + 90

10 + 89

………

……..

43 + 49

44 + 50

Therefore, if you’re going to count all pairs of whole number, you will get 50 pairs of whole number with the sum of 99.

Hope this helps!

4 0

2 years ago

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Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters. The flavored ice comes in a

Neko [114]

check the picture below.

so the cone itself has a height of 8, and a radius of 2.5, and the spherical scoop, ready to melt in it, has a radius of 2.5.

namely, will the volume of the sphere be larger than the cone? in which case the melted ice-cream will overflow.

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=2.5\\ h=8 \end{cases}\implies V=\cfrac{\pi (2.5)^2(8)}{3}\implies \implies \boxed{V=\cfrac{50\pi }{3}} \\\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad r=2.5\implies V=\cfrac{4(\pi )(2.5)^3}{3}\implies \boxed{V=\cfrac{125\pi }{6}} \\\\\\ \textit{the sphere's volume is larger, so yes, it will overflow}$

8 0

2 years ago

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370 College freshmen were interviewed. 200 were registered for an Advanced Math class. 270 were registered for an English class

frozen [14]

Answer:

Step-by-step explanation:

To aid in understanding, draw three circles...

100 were registered for both Math and English.

50 were registered for both Sport and English but not Math.

70 were registered for Math, Sport, and English.

From here we will be able to calculate for those that signed up for only English class: Total number of students that signed up for english class

a. none signed up only for Maths (refer to attached document)

b. How many signed up for neither Math nor English meaning they signed up for only sports which is 70 from the venn diagram in the attachment.

c. How many signed up for an English class and at least one other class?

From the venn diagram:

we could have an English class and maths class - 100

we could also have an a English class and sports - 50

Thus total is 150.

d. What is the total fee for all the students enrolled in classes

From the diagram, 120 (english only and sport only) enrolled for only one class = 120 x $100 = $12,000

From the diagram, 180 (english and sport, maths and sport and english and maths) enrolled for two classes = 180 x $150 = $27,000

From the diagram, only 70 enrolled for the three classes = 70 x $200 = $14,000

Total fees = $12,000 + $27,000 + $14,000 = $53,000

5 0

2 years ago

Which value is needed in the expression below to create a perfect square trinomial?

Klio2033 [76]

Answer:

The value which is needed to be added to transform the quadratic expression $x^{2}+8x$ as a perfect square trinomial is 16.

Step-by-step explanation:

A quadratic expression is an expression in which the highest power of the variable is 2 or it can be said that the degree of the expression is 2.

The identity for $(a+b)^{2}$ is given as follows:

$(a+b)^{2}=a^{2}+b^{2}+2\times(a)\times(b)$

Step 1:

Break down the given polynomial $x^{2}+2\times(x)\times(4)$ .

Step 2:

Now compare the polynomial with the above indentity.

On comparing it is observed that the value of a is x and the value of b is 4.

Step 3: 

In order to make the polynomial $x^{2}+8x+$ a perfect square, add $16$ to the broked down polynomial because on comparing the above polynomials the value of b is 4 and the square of 4 is 16.

$x^{2}+2\times(x)\times4+16$

Step 4:

Now as per the identity $(a+b)^{2}=a^{2}+2\times(a)\times(b)+b^{2}$ the polynomial $x^{2}+2\times(x)\times4+16$ is written as follows:

$(x+4)^{2}$ .

Therefore, the perfect square for the given polynomial is $(x+4)^{2}$ which is created by adding 16 to the given expression.

Learn more:

A problem to obtain the y-intercept of a quadratic function brainly.com/question/1332667
A problem to obtain the binomial and trinomial brainly.com/question/1394854

Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Quadratic expression

Keywords: Quadratic, quadratic expression, polynomial, quadratic polynomial, perfect square, trinomial, degree, highest power, transform, identities, break down, perfect square, middle term split, x^2+8x,methamatics, algebra.

6 0

2 years ago

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Identify the best big-O estimate for the number of comparisons used by the algorithm that determines the number of 1s in a bit s

Westkost [7]

Answer:

0(n)

Step-by-step explanation:

Result previous exercise:

procedure count(a1a2...an : string with n > 1)

i:=0

for k:=1 to n

if ak =1 then i:=i + I

return i

Note: If you use a different algorithm, then you could possible get different results.

SOLUTION

There is only one part of the code that contains an operation (comparison), namely if a_k =1

This comparison is executed in every iteration of the for-loop

k can take on the values from 1 to n (for k:=I to n), thus k can take on n values.

Thus in total there are then n comparisons, while n is 0(n).

5 0

2 years ago