75 is what percent of 15


Answer 1



Step-by-step explanation:

Is means equals and of means multiply

75 = P * 15

Divide each side by 15

75/15 = P

5 = P

Change to percent form


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answer: c

Step-by-step explanation:

the experiment land 4 of 15 times on Q making the experiment 4/15 and the chances of landing on Q is 1/5

Use the inner product〈f,g〉=∫10f(x)g(x)dxin the vector space C0[0,1] of continuous functions on the domain [0,1] to find 〈f,g〉, ∥f∥, ∥g∥, and the angle αf,g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f,g〉= ,∥f∥= ,∥g∥= ,αf,g .



a) <f,g> = 2605/3

b) ∥f∥ = 960

c) ∥g∥ = 790

d) α = 90  


a) We calculate  <f,g> using the definition of the inner product:

<f,g> = \int\limits^1_0 {10(-10x^(2) -6)(-9x-4)} \, dx \n        \n        =\int\limits^1_0 {900x^(3)+400x^(2) +540x+240 } \, dx\n    \n      = (225x^(4) + (400x^(3) )/(3) + 270x^(2)   +240x)\n      = (2605)/(3)

b) How

∥f∥ = <f,f> then:

∥f∥ = <f,f> = \int\limits^1_0 {10(-10x^(2) -6)(-10x^(2) -6)} \, dx \n        \n        =\int\limits^1_0 {1000x^(4)+1200x^(2) + 360} \, dx\n    \n      = (200x^(5) + 400x^(3) +  360x)\n      = 960


∥g∥ = <g,g>

∥g∥ = <g,g> = \int\limits^1_0 {10(-9x-4)(-9x-4)} \, dx \n        \n        =\int\limits^1_0 {810x^(2)+720x + 160} \, dx\n    \n      = (270x^(3) + 360x^(2) +  160x)\n      = 790

d) Angle between f and g

<f,g> = ∥f∥∥g∥cosα


\alpha = cos^(-1)((2605/3)/((790)(960)) )\n\n\alpha = 90

Final answer:

The answer to this problem involves applying integrals, norms, and concepts of angles between vectors to the functions f(x) and g(x). The INNER PRODUCT is the integral of the products of the two functions, the norms are the square roots of the inner products of the functions with themselves, and the angle between the functions is calculated using the dot product and norms.


To find the inner product 〈f,g〉, the norms ∥f∥ and ∥g∥, and the angle αf,g between the functions f(x)=−10x2−6 and g(x)=−9x−4, we'll apply concepts from vector calculus. The inner product (also known as the dot product) is the integral from 0 to 1 of the products of the two functions. The norm of a function is the square root of the inner product of the function with itself. The angle between two vectors in a Vector Space, in this case the space of continuous functions C0[0,1], is given by cos(α) = 〈f,g〉/( ∥f∥∙ ∥g∥). Integrating and solving these equations will give us the desired values.

Learn more about Vector Calculus here:



The total area of the parallelogram and the triangle is 160 square meters find the value x


The value of x for the given triangle side in the parallelogram will be 4.

What is a parallelogram?

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

What is a triangle?

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

The area of a parallelogram is given as,

(1/2)(sum of parallel sides)(distance between parallel lines)

Area of parallelogram = (1/2)(14 + 14)(10) = 140 square meter.

The area of the right angle triangle = (1/2)base x height.

Area of triangle = (1/2)x × 10 = 5x

Total area = 140 + 5x

160 = 140 + 5x

5x = 20

x = 4

Hence "The value of x for the given triangle side in the parallelogram will be 4".

Learn more about parallelograms here,



The given question is missing a parallelogram as attached below,



Step-by-step explanation:


Some people take the early retirement option at age 62. According to the Social Security Administration, if you retire at age 62, your retirement benefits will be permanently reduced by 25%. If your monthly benefit, at full retirement age (67), would have been $1300 per month, and you retire at age 62, how much would you lose in total annual income over one year?




Step-by-step explanation:

If retirement is taken at the age of 67 years, income  = $1300 per month.

% Loss, if retirement taken at the age of 62 years = 25% per month

Loss in dollars per month if retirement taken at the age of 62 years = 25% of Monthly income if retirement is taken at the age of 67 years

\Rightarrow (25)/(100) * 1300\n\Rightarrow (1300)/(4)\n\Rightarrow 325 \$

We know that there are 12 months in an year.

So, annual loss in total annual income over one year:

Loss in dollars per month * 12 :

325 * 12 = 3900$

Answer: $3,900

Step-by-step explanation:

What you usually make:

$1300 * 12 months = $15600

What you make with the cut:

$1300 * 0.75 = $975

* 12 months = $11700

15600-11700 = $3900

Write an equation in slope-intercept form of the line that passes through thegiven point and is parallel to the graph of the given equation.

(-3, 12); y = -3x + 5


Answer: y = -3x + 3 or y = 3 - 3x

Step-by-step explanation:

First, we need to determine our slope. Thankfully for us, the slope of a line parallel to another is the same.

So our slope is -3.

Now, we need to find our y-intercept. To do that, we will use y = mx + b. y is the y-coordinate, m is the slope, x is the x-coordinate, and b is the y-intercept.

Plug in the numbers given.

12 = -3(-3) + b


12 = 9 + b

Subtract 9 from both sides.

12 - 9 = 9 - 9 + b

3 = b

Our y-intercept is 3.

Now, we just put everything together.

y = -3x + 3

The line parallel to y = -3x + 5 that passes through the point (-3, 12) is

y = -3x + 3 or y = 3 - 3x (both are the same just written differently)