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2 years ago

Lucy brought 4 of her scarves to a secondhand store to sell. She was paid the same amount

Mathematics

1 answer:

likoan [24]2 years ago

8 0

Answer: $4.50

Step-by-step explanation:

If she spent 10.50, and had 7.50 left, her total was 18.

$18/4=$4.50

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EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the

solong [7]

Answer:

<h2>a) f = sin(yz)i + xzcos(yz)j + xycos(yz)k</h2><h2>b) -2</h2>

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f = sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v = (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

7 0

3 years ago

You randomly select an integer from 0 to 19 (inclusively) and then randomly select an integer from 0 to 24 (inclusively). What

Mila [183]

Answer:

The probability of selecting 5 both times is 0.002.

Step-by-step explanation:

We are given that you randomly select an integer from 0 to 19 (inclusively) and then randomly select an integer from 0 to 24 (inclusively).

And we have to find the probability of selecting 5 both times.

As we know that the probability of an event is given by;

Probability = $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

Now, here between integer from 0 to 19 (inclusively);

Number of times 5 comes = 1

Total number of integers = 20

Similarly, between integer from 0 to 24 (inclusively);

Number of times 5 comes = 1

Total number of integers = 25

So, the required probability = $\frac{1}{20}\times \frac{1}{25}$

= $\frac{1}{500}$ = 0.002

Hence, the probability of selecting 5 both times is 0.002.

5 0

3 years ago

At Harry's discount hardware everything is sold for 20 percent less than the price marked. If Harry buys tool kits for $80,what

ICE Princess25 [194]

Answer:

$120.

Step-by-step explanation:

The amount he sells the tool kit for = 80 + 20% of 80

= 80 + 16

= $96.

Let m be the marked price, then

m - 0.20m = 96

0.8m = 96

m = $120.

5 0

3 years ago

A thermometer at the park shows a reading of 86° Fahrenheit.

Marina86 [1]

No he will not.
86 degrees F is 30 degrees C

5 0

4 years ago

Read 2 more answers

Please help!!! (With one or all the problems, anything is greatly appreciated if you understand probability)

professor190 [17]

Here are the answers to problem 1..

a) 11

b) 5/36

c) 25 Times because 7 has a probability of 16.667%

d) 25 Times because 10, 11, and 12 have a probability sum of 16.667% ironically...

Hope this helps. :)

6 0

3 years ago