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Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s and standard deviation 1.58 bl/s. (a) What is the probability that an ant's speed in light traffic is faster than 5 bl/s? You may find Table B useful. (Enter your answer rounded to four decimal places.)

Answer:

0.7762

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Population mean = 6.20 bl/s

Standard deviation = 1.58 bl/s.

x = 5 bl/s

z = 5 - 6.20/1.58

z = -0.75949

The probability that an ant's speed in light traffic is faster than 5 bl/s is P( x > 5)

Probability value from Z-Table:

P(x<5) = 0.22378

P(x>5) = 1 - P(x<5)

= 1 - 22378

= 0.77622

Approximately to 4 decimal places = 0.7762

The probability that an ant's speed in light traffic is faster than 5 bl/s is 0.7762

Answer:

Step-by-step explanation:

The answer is $26

Answer: C. 3 cups

Step-by-step explanation:

Given: In recipe for 5 people, Required Gulf shrimp = [tex]1\dfrac14[/tex] cups

Since, [tex]1\dfrac14=\dfrac{5}{4}[/tex]

Required Gulf shrimp = [tex]\dfrac54[/tex] cups

Then, for 1 people Gulf shrimp required = [tex]\dfrac{5}{4}\div 5[/tex]

[tex]=\dfrac54\times\dfrac{1}{5}[/tex]

[tex]=\dfrac14[/tex] cup

For 12 people, it is required = [tex]12\times\dfrac14 = 3\text{ cups}[/tex]

Hence, 3 cups of gulf shrimp is required for new recipe.

So, correct option is C. 3 cups

Answer:

60 is your answer :)

Step-by-step explanation:

hope this helps :)

Answer:

Yes its less than 0

Step-by-step explanation:

it would go behind the 0 on a number line

Answer:

2.685 + 2.685 + 2.685 + 2.685 + 2.685 + 2.685. . . . . 102 times.

Step-by-step explanation:

Think of this as 102 times of 2.685.

So you would add 2.685 together 102 times.

(I didn't want to type out 2.685 that many times)

Hope I helped :)

Please consider Brainliest :)

Answer:

(4x-3y)(4x+3y)

Step-by-step explanation:

This is a difference of squares equation. As it says, ([tex]x^{2} -y^2[/tex]) is equal to (x-y)(x+y)

Simply apply the formula to your numbers, [tex]16x^{2} -9y^2[/tex].

It gives the hint of [tex]16x^{2}[/tex] is equal to (4x)^2. and, 9y^2 is equal to (3y)^2, since if you square 4x and 9y, they get 16x^2 and 9y^2 respectively.

Now, you need to do (4x-3y)(4x+3y)

Hope this helps

Answer:

31.67

Step-by-step explanation:

Given :

Segment QS

Endpoints for Q and S

Q = 15

S = 40

R partitions QS in a 6 : 3,

Sum of ratio = (6 + 3) = 9

Position of R:

(Q's proportion/total ratio) * (S - Q) + Q

6/9 * (S - Q) + Q

6/9 * (40 - 15) + 15

2/3 * 25 + 15

50/3 + 15

16.67 + 15

31.67

Answer:

1/15

Step-by-step explanation:

1. You can divide 1/3 by 5 by changing the division symbol to its reciprocal, multiplication, and also divide by the reciprocal of the number after the symbol, 5. The reciprocal of 5 is 1/5.

2. Now you can do 1/3 multiplied by 1/5. Multiply the numerators by the denominators. The numerators are 1 and 1, so you multiply 1 by 1 which equals 1. Now you multiply the denominators, 3 and 5, which is equal to 15. If the numerator is now 1, and the denominator is 15, the new fraction is 1/15, getting you to your answer

Answer:

The projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.

Step-by-step explanation:

This projectile is experimenting a free fall, that is, an uniform accelerated motion of the projectile due to gravity and in which effects of air friction and Earth's rotation are neglected. Given that initial and final heights, initial velocity and gravitational acceleration are known, we need to calculate time by solving the appropriate equation of motion described below:

[tex]y = y_{o} +v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex] (Eq. 1)

Where:

[tex]y_{o}[/tex] - Initial height of projectile, measured in feet.

[tex]y[/tex] - Final height of projectile, measured in feet.

[tex]v_{o}[/tex] - Initial velocity of projectile, measured in feet per second.

[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.

As we must remember, quadratic functions have two roots and if we get that [tex]y_{o} = 0\,ft[/tex], [tex]y = 200\,ft[/tex], [tex]v_{o} = 120\,\frac{ft}{s}[/tex] and [tex]g = -16\,\frac{ft}{s^{2}}[/tex], then, the quadratic function is:

[tex]-8\cdot t^{2}+120\cdot t -200 = 0[/tex]

Roots are found by the Quadratic Formula:

[tex]t_{1,2} = \frac{-120\pm \sqrt{120^{2}-4\cdot (-8)\cdot (-200)}}{2\cdot (-8)}[/tex]

Whose solutions are:

[tex]t_{1} \approx 13.090\,s[/tex] and [tex]t_{2} \approx 1.910\,s[/tex].

Both roots are physically reasonable, first root represents the instant when the projectile reaches 200 feet when it is moving downwards, whereas second root represents the projectile moving upwards. Therefore, the projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.

Answer:

It will take 2.5 s to reach a height of 200ft.

Step-by-step explanation:

42145357556574455247788555

Answer:

1.4

Step-by-step explanation:

Answer:

(2,-2)

Step-by-step explanation:

Answer:the equation would be

8.4x=23.94

Step-by-step explanation: I know my math :)

Answer:

the second one -3and1 :4x and 7x

Step-by-step explanation:

Answer:

-3 and -1; 4x and 7x

Step-by-step explanation:

like terms are the numbers with the same variable

eg. 4x^2 and 6x aren't like terms, but 2x^4 and 3x^4 are

Answer:

2 and 1/3 ---->>> 2 1/3

Step-by-step explanation:

At 4, its 4 cm

Within 3 hours it has gained 7 cm

7/3=2.33333

2 1/3 would be the mixed number

can i get brainliest please?

I just took this and got an A, so here are the answers :)

Make sure to take notes or put this with your notes! :))

Answer:

Law of Syllogism: 3

If I do well on my assignments, my grade will improve.

If my grade improves, my parents will be happy.

Therefore, if I do well on my assignments, my parents will be happy.

Not a valid conclusion has been made: 4

If I cook dinner, my daughter will eat.

My daughter ate.

Therefore, I cooked dinner.

Law of contrapositive : 2

If the sun sets, it will be dark outside.

It is not dark outside.

Therefore, the sun hasn't set yet

Law of Detachment: 1

If it is raining, I will use an umbrella.

It is raining.

Therefore, I will use an umbrella.

explanation:

Syllogism:

p → q and q → r then p → r is also true.

Contrapositive:

If not q, then not p.

Detachment:

If p , then q

Answer:

-12/3

Step-by-step explanation:

Whole numbers can't be negative!

Answer:

d. your welcome

Step-by-step explanation:

Answer:

20 miles.

Step-by-step explanation:

To solve this problem, we will have to set two expressions representative of Enterprise Rentals & Hertz Rental equal to each other.

Let [tex]m[/tex] equal the number of miles.

If Enterprise Rentals charges $100 plus $3 per mile, we can represent this as:

[tex]100+3m[/tex]

If Hertz Rental charges $8 per mile, we can represent this as:

[tex]8m[/tex]

Set the expressions equal to each other:

[tex]8m=100+3m[/tex]

Subtract [tex]3m[/tex] from both sides of the equation:

[tex]5m=100[/tex]

Divide both sides of the equation by the coefficient of [tex]m[/tex], which is [tex]5[/tex]:

[tex]m=20[/tex]

Therefore, after 20 miles, the total cost for both companies will be the same.

_

Check your work by substituting the solved value of [tex]m[/tex] (20), into the initial equation:

[tex]8(20)=100+3(20)[/tex]

[tex]160=100+60[/tex]

[tex]160=160[/tex]

As the total costs are equal to each other, our answer is correct!

Answer:

20 miles

Step-by-step explanation:

160=$3(20)=100

8x20=160

Answer:

membrane-bound cell organelles

Answer:

$22.56

Step-by-step explanation:

$6.88 ⋅ 12 = $82.56

So you would have to pay $82.56 per year if you paid $6.88 per month.

$82.56 - $60.00 = $22.56

You would save $22.56 if you paid $60.00 per year.

Hope I helped :)

Please consider Brainliest :)

Answer:

Equal angles; Vertical angles ( which means equal ) ; Angles do not share special relationship; and right angles.... Hope this helps!

Step-by-step explanation:

Step-by-step explanation:

The measure of CED is p degree.

In triangle ABC and EDC,(Given)(Vertical opposite angles)

By AA rule of similarity,

Corresponding angles of similar triangles are same.

Therefore the measure of CED is p degree.

pls give brainest

Answer:

90

if 15 is 1 6th then yo need 5 more 15s to find out the whole number

Answer:

7767788877787887+-77-7

Answer:

Step-by-step explanation:

Answer:

Solution: x=5, y=4

Step-by-step explanation:

System of Equations

We need to solve:

- 5x + 9y = 11

x - 3y = - 7

There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:

x = - 7 + 3y

Now replace it into the first equation:

- 5(- 7 + 3y) + 9y = 11

Operate:

35 - 15y + 9y = 11

Simplify:

35 - 6y = 11

Rearrange:

- 6y = 11 - 35 = -24

Solve:

y = -24 / -6

y = 4

Finally, since

x = - 7 + 3y

x = - 7 + 3*4

x = - 7 + 12

x = 5

Solution: x=5, y=4