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2 years ago

What is the best approximation of the projection of (2,6) onto (5,-1)

Mathematics

1 answer:

Darya [45]2 years ago

5 0

Answer:

0.15(5,-1)

Step-by-step explanation:

$\frac{v_{1} * v_{2} }{|v_{2}|^{2} }*v_{2}$ ⇒ $\frac{(2)(5)+(6)(-1)}{\sqrt{5^2+(-1)^2} }(5,-1)$ ⇒ $\frac{4}{26} (5,-1)$ ⇒ $0.15(5,-1)$

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Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are

Ymorist [56]

Answer:

In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.

Step-by-step explanation:

Given:

Cost of movie pass = $40

Cost per matinees with pass = $1.00

Cost per matinees without pass = $3.50

To Find:

Number of times must Seth attend in order for it to benefit his father to buy the pass = ?

Solution:

Let x be the number of times he wants to visit

To profit his father

The number of visits without pass = the number of visits with passin the cost of $3.50

Then, without pass if he visits for x times then the cost will be = 3.50x

Also with pass, the number of times he can visit the pass = $\frac{40}{3.50}$

then

$\frac{350 x}{3.50} = \frac{40}{3.50}$

$3.50x = 40$

$x = \frac{40}{3.50}$

x = 11.42

x = 11 (approx)

3 0

2 years ago

Sylvia invested $500 in an account compounded annually with an interest rate of 8%. Manuel invested $600 in an account with a co

Sav [38]

Syliva
T=72÷8=9 years

Manul
T=72÷7.25=9.9=10 years

Option A

8 0

2 years ago

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50 POINTS In two or more complete sentences, define the key features of the graph below and explain how to write its equation us

dezoksy [38]

Answer:

The graph is a function of absolute value.

This means that for each value of f (x) there are two possible values of x.

The absolute value function is:

f (x) = lxl

y = f (x) - 2 shifts the graph 2 units down.

y = f (x + 3) moves the graph 3 units to the right.

Finally:

The function that best fits this graph is:

f (x) = l-x + 3l-2

Step-by-step explanation:

From the graph it is evident that it is the graph of the absolute value of the function i.e. f(x) = |x| and we know that 'Translation' is a transformation that shifts the graph of a function in any direction.

Now, as we can see that the graph is shifted towards the right of the y-axis at point x=3, this means that it is translated by 3 units to the right of y-axis.

Therefore, the function becomes f(x) = |x-3|.

Furthermore, it is also shifted downwards at the point x= -2, this means that it is translated by 2 units downward from the x-axis.

Hence, the new function is f(x) = |x-3| - 2.

6 0

2 years ago

A customer visiting the suit department of a certain store will purchase a suit with probability .22, a shirt with probability .

BigorU [14]

Answer:

a) The probability that he doesnt but any items is 0.49

b) He buys exactly 1 of those items with probability 0.28

Step-by-step explanation:

lets call su the event that the customer purchases a suit, sh the event that teh customer purchases a shirt and t the event that the customer purchases a tie.

Remembe that for events A, B and C we have that

P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Also, we are given that

P(su) = 0.22

P(sh) = 0.3

p(t) = 0.28

p(su ∩ sh) = 0.11

P(su ∩ t) = 0.14

P(sh ∩ t) = 0.1

P(sh ∩ t ∩ su) = 0.06

The event that he doesnt buy any item has as complementary event su ∪ sh ∪ t, therefore

P( he doesnt but any items) = 1-P(su U sh U t) =

1-( P(su) + p(sh) + p(t) - P(su ∩ sh) - p(su∩t) - p(sh∩t) + p(su∩sh∩t) ) =

1-(0.22+0.30+0.28-0.11-0.14-0.1+0.06) = 1-0.51 = 0.49

b) The probability that he buys at least 2 items is equal to

p(su ∩ t) + p(su ∩ sh) + p(sh ∩ t) -2 p(su ∩ t ∩ sh) (because we are counting the triple intersection 3 times, so we need to remove it twice)

This number is

0.14+0.11+0.1-2*0.06 = 0.23

Thus, the probability that he buys exactly one item can be computed by substracting from one the probability of the complementary event : she buys 2 or more or non items

P(he buys exactly one item) = 1- ( p(he buys none items) + p(he buys at least 2) ) = 1- 0.49-0.23 = 0.28

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2 years ago

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How would the fraction 1/3+square root of 2 be rewritten if its denominator is rationalized using difference of squares? A. 3-sq

Vera_Pavlovna [14]

given 1 /( 3 + √2 )

then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

the conjugate of 3 + √2 is 3 - √2

1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )

= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7

4 0

2 years ago

Read 2 more answers