Can the product of two numbers ever be less than either of the numbers

Two forest service watchtowers spot a fire in the distance. The fire is 27 miles from Tower 2. About how far apart are the two w

Reptile [31]

Given that the two watchtowers spotted fire in the distance and watch tower 2 was 27 miles from the fire. Assuming that the fire is in the middle of both watch towers, then the distance between the two watch towers will be given by:
distance=[distance of fire from watch tower 1]+[distance of fire from watch tower 2]
=27+27
=53 miles

8 0

3 years ago

The length of a 200 square foot rectangular vegetable garden is 4feet less than twice the width. Find the length and width of th

inna [77]

Answer:

Length = 18.099 ft

Width = 11.049 ft

Step-by-step explanation:

let the length of the field be x ft

and the width be y ft

as per the condition given in problem

x=2y-4 -----------(A)

Also the area is given as 200 sqft

Hence

xy=200

Hence from A we get

y(2y-4)=200

taking 2 as GCF out

2y(y-2)=200

Dividing both sides by 2 we get

$y(y-2)=100$

$y^2-2y=100$

subtracting 100 from both sides

$y^2-2y-100=0$

Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form

$ax^2+bx+c=0$

Here in our case

a=1

b=-1

c=-100

Putting those values in the formula and solving them for y

$y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

Solving first

$y=\frac{2+\sqrt{4+400}{2}$

$y=\frac{2+\sqrt{404}{2}$

$y=\frac{2+20.099}{2}$

$y=\frac{22.099}{2}$

$y=11.049$

Solving second one

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{2-\sqrt{4+400}{2}$

$y=\frac{2-\sqrt{404}{2}$

$y=\frac{2-20.099}{2}$

$y=\frac{-18.99}{2}$

$y=-9.045$

Which is wrong as the width can not be in negative

Our width of the field is

y=11.099

Hence the length will be

x=2y-4

x=2(11.049)-4

x=22.099-4

x=18.099

Hence our length x and width y :

Length = 18.099 ft

Width = 11.049 ft

4 0

3 years ago

in ΔABC, ∠ABC is a right angle, AB = 3 units, and BC = 2 units. ΔABC is dilated by a scale factor of 0.5 with point B as the cen

qaws [65]

Answer:

the first one i think

Step-by-step explanation:

7 0

3 years ago

Write the equation of the graph shown below in factored form.

artcher [175]

Step-by-step explanation:

hey mha sorry...................................

3 0

3 years ago

If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is Wit

KatRina [158]

Answer:

a) 0.5762

b) 0.0214

c) 0.2718

Step-by-step explanation:

It is given that lengths of the bolt thread are normally distributed. So in order to find the required probability we can use the concept of z distribution and z scores.

Part a) Probability that length is within 0.8 SDs of the mean

We have to calculate the probability that the length of a bolt thread is within 0.8 standard deviations of the mean. Recall that a z- score tells us that how many standard deviations away a value is from the mean. So, indirectly we are given the z-scores here.

Within 0.8 SDs of the mean, means from a score of -0.8 to +0.8. i.e. we have to calculate:

P(-0.8 < z < 0.8)

We can find these values from the z table.

P(-0.8 < z < 0.8) = P(z < 0.8) - P(z < -0.8)

= 0.7881 - 0.2119

= 0.5762

Thus, the probability that the thread length of a randomly selected bolt is within 0.8 SDs of its mean value is 0.5762

Part b) Probability that length is farther than 2.3 SDs from the mean

As mentioned in previous part, 2.3 SDs means a z-score of 2.3.

2.3 Standard Deviations farther from the mean, means the probability that z scores is lesser than - 2.3 or greater than 2.3

i.e. we have to calculate:

P(z < -2.3 or z > 2.3)

According to the symmetry rules of z-distribution:

P(z < -2.3 or z > 2.3) = 1 - P(-2.3 < z < 2.3)

We can calculate P(-2.3 < z < 2.3) from the z-table, which comes out to be 0.9786. So,

P(z < -2.3 or z > 2.3) = 1 - 0.9786

= 0.0214

Thus, the probability that a bolt length is 2.3 SDs farther from the mean is 0.0214

Part c) Probability that length is between 1 and 2 SDs from the mean value

Between 1 and 2 SDs from the mean value can occur both above the mean and below the mean.

For above the mean: between 1 and 2 SDs means between the z scores 1 and 2

For below the mean: between 1 and 2 SDs means between the z scores -2 and -1

i.e. we have to find:

P( 1 < z < 2) + P(-2 < z < -1)

According to the symmetry rules of z distribution:

P( 1 < z < 2) + P(-2 < z < -1) = 2P(1 < z < 2)

We can calculate P(1 < z < 2) from the z tables, which comes out to be: 0.1359

So,

P( 1 < z < 2) + P(-2 < z < -1) = 2 x 0.1359

= 0.2718

Thus, the probability that the bolt length is between 1 and 2 SDs from its mean value is 0.2718

4 0

3 years ago