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3 years ago

A recipe calls for 30 grams of sugar. Ramesh decides to decrease the sugar by 20%. How much sugar will Ramesh use?

Mathematics

1 answer:

stiv31 [10]3 years ago

6 0

Answer:

24 grams

Step-by-step explanation:

80% (100%-20%) of 30 is 24

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Show that the vector orthab=b-projacb is orthogonal to a.

Lina20 [59]

Answer:

We have, a. ortho (ab) = a.b - a.b/[a]² . /a/²

The /a/² cancel off each other, therefore,

a. ortho (ab) = a.b - a.b

a. ortho (ab) = 0

Therefore, the final result is 0.

Step-by-step explanation:

It should be noted that the orthogonal projection of a vector B onto A is given by a given formula known as:

proJ(ab) = a.b/[a]² . a ............equation (1)

Where [a] is the magnitude of the vector a,

therefore, [a]² = a.a ...........equation (2)

Which means that if we have a dot product between a vector and the sum of vector, it can be distributed to each vector.

That is : a . (c - d + b )

a.b - a.d + a.b ...........................equation (3)

and since it is given that Ortho (ab) = b - proJ(ab)..........equation (4)

and in order to show that a two vector are orthogonal, we need to show that their dot product is zero.

Where : a.b = /a//b/ cos ( Ф)

and if the dot product is zero (0), this will imply that ,

cos (Ф) = 0

Now moving forward to the proof,,

The first thing we do is substitute equation (1) into equation (4)

That will give us : ortho (ab) = b - a.b/[a]² . a

and in order to show that vector a and orth(ab) are orthogonal, we need to show that their dot is zero

Therefore, a . ortho (ab) = a . b - a.b/[a]² . a ........equation (5)

Now, substituting equation (2) into (5),

We have, a. ortho (ab) = a.b - a.b/[a]² . /a/²

The /a/² cancel off each other, therefore,

a. ortho (ab) = a.b - a.b

a. ortho (ab) = 0

Therefore, the final result is 0.

3 0

3 years ago

At a local high school football game, 150 randomly selected people were surveyed about the location of the concession stand. 108

Nesterboy [21]

Answer:

Option B

The best point estimate of the proportion of people attending the game who believe that the concession stand should be closer to the stands is:

p = 0.72.

Step-by-step explanation:

We want to estimate the proportion of people who feel that the stand should be closer to the stands.

We have a sample of 150 people, of which 108 think that the stand should be closer to the stands.

A point estimator for the proportion p is $p\¨$ .

Where

$p\¨ = \frac{x}{n}$

Where n represents the size of the sample and represents the number of favorable cases.

We know that $n = 150$ and $x = 108$ .

Then we can estimate p by the estimator $p\¨$

$p\¨= \frac{108}{150}$

$p\¨ = 0.72$

4 0

3 years ago

Read 2 more answers

You can do one-half of a job in an hour. Your friend can do one-third of the same job in an hour. How long will it take to do th

Mariana [72]

You do: 1/2 job/hr

Your friend does: 1/3 job/hr

Together:   (1/2 + 1/3) job / hr

   = (3/6 + 2/6) job/hr

   = 5/6 job/hr .

Since you do 5/6 job/hr, the corresponding
inverse unit rate is
   6/5 hr/job

      = 1 and 1/5 hr/job

      = 1.2 hours/job

      = 1 hour 12 minutes per job.

5 0

3 years ago

9 mi 12 mi What is the length of the hypotenuse? miles

Svetllana [295]

15..........................

4 0

3 years ago

Help meee please thank you will mark brainlist….

erik [133]

Answer:

It's 47 because it's an isosceles triangle.

Step-by-step explanation: