h(x)=x^2-1 what is the average rate of change of h over the interval -3 x -1

Answers

Answer 1

For the given function, h(x) = x² - 1, over the interval -3 ≤ x ≤ -1, the average rate of change is 4.

What is function?

A function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

h(x) = x² - 1, and the interval is -3 ≤ x ≤ -1.

To find average rate of change for the function,

Use formula,

Average rate of change = [tex]\frac{h(b)- h(a)}{b-a}[/tex]

h(b) = h(-1) = (-1)² - 1 = 0

h(a) = h(-3) = (-3)² - 1 = 8

Rate of change = [tex]\frac{8 - 0 }{-1 - (-3)}[/tex]

                          = 8 / 2

                          = 4

The average rate of change is 4.

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Related Questions

Solve the system of equations.
2/3 x - y/2 = 17/6
x/4 - 5/8 y = 5/8

Answers

Answer:

x = 3y/4 + 17/4 and

x = 5y/2 + 5/2

Step-by-step explanation:

hope this help

What is the prime factorization of 16807 1680716807? Enter your answer as a product of prime numbers, like 2 × 3 2×32, times, 3, or as a single prime number, like 17 1717.

Answers

The Prime Factorization of 16807 are:7, 7, 7, 7, 7. This implies 7 raise to power 5.

What is prime factorization?

The term "Prime Factorization" refers to determining which prime numbers multiply together to produce the original number.

The process of writing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We can divide this into two categories. "Well, that's 2 time 2 times 5," we can say. Also, 5 is a prime number.

In this case 16807 will be:

16807 ÷ 7 = 2401

2401 ÷ 7 = 343

343 ÷ 7 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

Again, all the prime numbers you used to divide above are the Prime Factors of 16807. Thus, the Prime Factors of 16807 are:7, 7, 7, 7, 7.

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Simplify the Expressions Drag and drop the matching

Answers

The simple form of all the expressions are:

-3 + 4m + (-7) - 6m = -2m -10

6x + (-1) - 3x + 12 = 3x + 11

3xy +2z - 16 + 6xy = 9xy +2z - 16

-4x - 8 + 2x + (-3) - 5x = -7x - 11

3m² - m + 7 + 3m² + 1 = 6m² - m + 8.

What is the simple form of the polynomial?

f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.

We have,

-3 + 4m + (-7) - 6m

6x + (-1) - 3x + 12

3xy +2z - 16 + 6xy

-4x - 8 + 2x + (-3) - 5x

3m² - m + 7 + 3m² + 1

The simple form of the expressions:

-3 + 4m + (-7) - 6m

= -2m -10

6x + (-1) - 3x + 12

= 3x + 11

3xy +2z - 16 + 6xy

= 9xy +2z - 16

-4x - 8 + 2x + (-3) - 5x

= -7x - 11

3m² - m + 7 + 3m² + 1

= 6m² - m + 8

Hence, the simple form of all the expressions are:

-3 + 4m + (-7) - 6m = -2m -10

6x + (-1) - 3x + 12 = 3x + 11

3xy +2z - 16 + 6xy = 9xy +2z - 16

-4x - 8 + 2x + (-3) - 5x = -7x - 11

3m² - m + 7 + 3m² + 1 = 6m² - m + 8

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When a number is divided by 9, and the remainder is 6. What is the
remainder when six times this number is divided by 9?

Answers

Answer:

9x + 6

Step-by-step explanation:


SOLUTION GIVEN: a number is divided by 9 and the remainder is 6,

TO DETERMINE: The remainder when six times the number is divided by 9

EVALUATION: Here it is given that the number is divided by 9 & the remainder is 6

We know that Dividend = Divisor × Quotient + Remainder 

By the given Divisor = 9

Remainder = 6

Let quotient = x

Then the number = Dividend = 9x + 6

Describe and correct the error in writing an equation of the line that passes through (1, 3) and is parallel to the line y=1/2x+2

Answers

The equation of the line that is parallel to the line y = 1/2x + 2 is: y = 1/2x + 5/2.

How to Write the Equation of Parallel Lines?

Recall that if two lines are parallel, they will have the same slope (m).

Slope of a line (m) = change in y / change in x.

The slope (m) of the equation, y = 1/2x + 2, that represents a line is 1/2.

This means that the line that is parallel to it will also have a slope (m) that is equal to 1/2.

Find the y-intercept by substituting m = 1/2 and (x, y) = (1, 3) into y = mx + b:

3 = 1/2(1) + b

3 = 1/2 + b

3 - 1/2 = b

5/2 = b

b = 5/2

To write the equation of the parallel line, substitute m = 1/2 and b = 5/2 into y = mx + b:

y = 1/2x + 5/2.

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Anything helps! Thanks you :)

Answers

No.3
X=120

No.4
X=105

No.5
X=95

No.6
X=30

No.7
X=28

No.8
X=11

No.9
X=5.6

No.10
X=3

Hope this helps

Convert 8 ounces into grams. Round your
answer to the nearest whole number.
*Note: you must use these exact conversion factors to
get this question right.

Answers

Answer:

227

Step-by-step explanation:

I think

The product of a number and 3 is twice the sum of that number and 5

Answers

The number that the product and 3 is twice the sum of that number and 5 is 10.

How to find the number?

The product of a number and 3 is twice the sum of that number and 5.

Therefore,

let

x = the number

Hence,

3 × x = 2(x + 5)

3x = 2(x + 5)

3x = 2x + 10

subtract 2x from both sides of the equation

3x = 2x + 10

3x  - 2x = 2x - 2x + 10

x = 10

Therefore, the number is 10.

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Which equation models the line on the graph?

Answers

Answer:

C) y - 2 = 2 ( x - 3 )

Step-by-step explanation:

This is point-slope form btw. Hope it helps!

Find the y-intercept of the line 12x+16y=6.

Answers

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

To find the y-intercept you need to put convert it into the equation:

y = mx + b where b = the y-intercept.

12x + 16y = 6. First rearrange the equation so y is on side of the equation.

16y = -12x + 6. Now divide by 16 so the equation has y as a stand alone value.

y = [tex]\frac{-3}{4}[/tex]x + [tex]\frac{3}{8}[/tex]

Therefore the y-intercept is [tex]\frac{3}{8}[/tex]

Write an equation of the line that passes through (8,9) and is parallel to the line y = -x-2.
An equation of the parallel line is

Answers

Answer:

y - 9 = -1 (x-8)

Step-by-step explanation:

y - y₁ = m (x - x₁) would be your formula, since it's parallel you already have your slope, -x (which also equals 1 so technically -1). You have a point (8,9) and a slope -1, all you need to do is plug it in the formula.

Hope this helped!!

An object was launched from the top of a hill with an upward vertical velocity of 170 feet per second. The height of the object can be
modeled by the function h(t) = -16t2 + 170t + 100, where t represents the number of seconds after the launch. Assume the object landed on the ground at sea level. Use technology to find the answer.
The object was __ feet in the air 9 seconds after it was launched.

Answers

The object was 334 feet in the air 9 seconds after it was launched.

The height of an object launched from the top of a hill can be modeled by the function h(t) = -16t² + 170t + 100, where t represents the number of seconds after the launch.

This function gives the height of the object in feet at any time t after the launch.

To find the height of the object 9 seconds after it was launched,

Substitute 9 for t in the function h(t) to calculate the height of the object at that time. This gives us the equation :

⇒ h(9)  = -16(9)² + 170(9) + 100

⇒ h(9)  = -16(81) + 1530 + 100

⇒ h(9)  = -1296 + 1530 + 100

⇒ h(9)  = 334 feet.

Therefore, 9 seconds after being launched, the object had reached a height of 334 feet.

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I need help please help me with this

Answers

Answer:

120

Step-by-step explanation:

MNT is equal to RQT.

That means R equal to M, T equal to T, equal to N.

Q also equals 180-(T+R)

Q=180-(35+25)

Q=180-60

Q=120

If f(x)=2x-3 and g(x)= [tex]\sqrt{x} +7[/tex]
then find f(g(x))

Answers

The value of the function, f(g(x)), is f(g(x)) = 2√x + 11

Evaluating a function

From the question, we are to determine the value of the given function f(g(x))

From the given information,

The given functions are

f(x) = 2x - 3

and

g(x) = √x + 7

To determine f(g(x)), we will substitute the value of g(x) for x in f(x)

That is,

f(x) = 2x - 3

f(g(x)) = 2(√x + 7) - 3

Apply the distributive property

f(g(x)) = 2√x + 14 - 3

Simplify

f(g(x)) = 2√x + 11

Hence, the value of f(g(x)) is 2√x + 11

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Please help my cousin needs help i appreciate your help!

Answers

The area of the softball field is 4732 yd²

What is area?

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given is a field with side measurements,

To find the area will we divide the field into a trapezium and a triangle,

Area of trapezium = (sum of parallel sides)x height/2

Area of triangle = 1/2xbasexheight

Area of trapezium = (104+52)x26/2 = 2028 yd²

Area of triangle = 2704 yd²

Area of the field = 2704 + 2028 = 4732 yd²

Hence, The area of the softball field is 4732 yd²

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A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.

The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.

The acceleration of the car is _______
m/s2

Answers

The initial velocity is  0 m/sec

The car speed up to 72km/h which is equivalent to  36m/sec

The acceleration of the car is 2.88 m/sec².

What is acceleration?

Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken

Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:

Initial Velocity = 0 m/sec

Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec

Time taken = 12.5 second

Now, the car’s acceleration in m/s can be written as,

Acceleration = (Final Velocity - Initial Velocity)/ Time taken

(36 m/sec - 0 m/sec)/12.5 seconds

= 2.88 m/sec²

Hence, the car’s acceleration in m/s is 2.88 m/sec².

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Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h. At what rate (in km/h) is the distance between the cars increasing three hours later?

Answers

The distance between the cars increasing three hours later rate (in km/h) is 70km/h.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have given information:

Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h.

Now, we will calculate the distance between the cars increasing three hours later,

S² + W² = D²

where S is the southbound car,

W is the westbound car,

D is the distance,

2 * S  dS/dt  + 2 W dW/dt = 2 D dD/dt

S  dS/dt  +  W dW/dt =  D dD/dt

In 3 hours,

S=3*56 = 168 and W = 3*42 = 126

and D = [tex]\sqrt{(168)^{2}+ (126)^{2}}[/tex] = 210

168 * 56 + 126 * 42 = 210 * dD/dt

(168 * 56 + 126 * 42) / 210 = dD/dt

dD/dt = (9408+5292)/210

dD/dt = 14700/210 = 70

Therefore, the distance between the cars increasing three hours later rate (in km/h) is 70km/h.

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Will give brainliest. urgent, 100 points

Answers

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the values of x are in set P = { 57 , 63 , 66 }

The values of y are in the set Q = { 19 , 21 , 22 }

a)

From the data set of P and Q , we can see that when the value of y increase the value of x also increases

Therefore , the value of variable y varies directly with x

And , y ∝ x

b)

The value of variable y varies directly with x

And , y ∝ x

So , y = kx

Substituting the value for x and y from the data set , we get

The equation will be

y = kx

19 = 57k

Divide by 57 on both sides of the equation , we get

k = 19 / 57

k = 1/3

Therefore , the constant of variation k is 1/3

c)

The function rule is given by the equation

y = kx

Substituting the value for k in the equation , we get

y = ( 1/3 ) x

y = x/3

Hence ,

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

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Answer:

its six hundred men

Step-by-step explanation:

its Six hundred men, six hundred men under my command

With only one goal in mind

Make it back alive to our homeland

Six hundred men, six hundred miles of open sea

But the problem's not the distance

It's what lies in between

And Ithaca's waiting Ithaca's waiting

My kingdom is waiting The kingdom is waiting

Penelope's waiting for me

So full speed ahead, full speed ahead

what is the missing lengths for the problems?

Answers

Answer:

≈5.6

Step-by-step explanation:

Use ratios: 4/3 = 7.5/x

3 times 7.5 then divide by 4 to get 5.6

Let me know if this helped you out!

Im having trouble with my homework and im not sure how to do this question could someone please explain?

line u has an equation of y+6=3/2(x–6). Line v is perpendicular to line u and passes through (2,–1). What is the equation of line v?

Answers

First write out the equation. Use distributive property for 3/2(x-6) by multiplying 3/2 by x and by -6. Then, subtract 6 from both sides and add -6 and the -18/2 from the previous distributive property step.
y= 3/2x -15
To find the perpendicular line, you need to change the slope (which is 3/2) to its negative reciprocal.
In order to do that, flip the order to 2/3 and multiply it by negative 1 to get -2/3.
y = -2/3x + b
You still can’t fully write out the equation because you don’t know b, which is the y intercept. To find it, plug in the x and y of (2,-1) to y = -2/3x + b.
-1 = -4/3 + b

Next move 4/3 to the left by adding it to both sides.
1/3 = b (aka y intercept)
Then you can write the final equation of line v.
y = -2/3x + 1/3

Not super sure if it’s correct, but I hope it helped!

The monthly water bill is a function of the number of gallons used. The cost is ​$11.70 for 10,000 gal or less. Over 10,000 ​gal, the cost is ​$11.70 plus​ $1 for each 1000 gal over 10,000 with any fraction of 1000 gal charged at a fraction of​ $1. On what interval is the cost​ constant? On what interval is the cost​ increasing?

Answers

Answer:

Interval for constant cost = [0, 10,000] same as 0 <= x <= 10,000

Interval for increasing cost = (10,000, ∞) same as 10,000 < x < ∞

Be careful! note the use of different types of parentheses for each answer part as explained below

Step-by-step explanation:

We are only being asked for the two intervals, not the function definition itself which would have made it a little bit more work. A function has inputs and outputs. Here the input is gallons of water and output is $ cost.

Normally when asked for intervals we use a variable. Let's call it x which represents the gallons of water used

Since there is a base rate of $11.70 whether or not any water is consumed as long as it is less than or equal to 10,000 gallons we can state that over the interval 0 to 10000 (inclusive), the cost is constant

We can represent this interval in two ways
0 ≤ x ≤ 10,000

Another way of representing this interval is what we call interval notation. In interval notation the same thing  can be expressed as:

[0, 10000]    

Here 0 is referred to as the lower limit or bound(minimum) and the 10,000 is referred to as the upper limit or upper bound

Note the use of square brackets. This means that both upper and lower limits are included in the function. Such an interval is also called a closed interval.

After 10,000 gallons, the cost keeps increasing. There is no upper limit on the usage of water. So the lower limit is 10,000  (but does not include that number) and upper limit is infinity

We represent this interval as
10000 < x < ∞

Note that both upper and lower limits are excluded since ∞ is not realistic.

In interval notation this is represented as
(10000, ∞)

Here we are using regular brackets(parentheses) because this interval does not include lower and upper limits

This kind of interval is known as an open interval

Looks like the purpose of this question is to make sure what you understand in terms of interval notation and possibly open and closed intervals. The only relevant number there is the 10,000 gallons which represents the upper bound on the first interval. All the other numbers can be junked

Hope that is of help even if it was wordy

a line that passes thru (-3,4) and is parallel to y=2

Answers

Parallel lines have the same slope.

y=2 is a horizontal line and has a slope of 0, so the line parallel to it must also be horizontal and have a slope of 0.

Horizontal lines always have the form " y = k " for some number k and every point on that line has a y-value of k.

In this case, if you want the line to go through the point (-3,4), then the equation will be  " y = 4 ", since that's the y-value of the point on the line.

Answer:

y = 4

Step-by-step explanation:

A line with the equation y = a is a horizontal line that intercepts the y-axis at (0, a).

A line parallel to a horizontal line is another horizontal line.

If a horizontal line passes through point (p, q), then its equation is y = q, where q is the y-value of the point.

Therefore, the equation of a line that passes through (-3, 4) and is parallel to y = 2 is:

y = 4

This article says short sleepers (fewer than 6 hours) are four times more likely to catch a cold than longer sleepers (over 7 hours). The article says "The researchers then sequestered 164 volunteers in a hotel, administered the cold virus via nasal drops and monitored them for a week." Without further info, what is potentially misleading?

Answers

The use of volunteer sampling means that the result of the survey is potentially misleading.

What is volunteer sampling?

Volunteer sampling is a sampling technique in which each participant in the sample opts to join the research, as is the case for this problem, as each participant opted to join in the project to compare their cold lengths.

The drawback of this type of sampling is that it should contain lots of participants that share similar characteristics, such as desiring to weight/diet, and this may influence their recovery to cold. The participants also may lie, which can cause misleading results to the study.

Options to remove misleading conclusions is to use a different type of sampling, such as stratified sampling, as groups of people that are either short or long sleepers are compared to reach a conclusion.

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32x = 3(5x−8) is equivalent to the equation 3(2x) = 3(5x − 8).

True

False

Answers

Answer: False

Step-by-step explanation:

This is because when u simplify 32x = 3(5x−8), it is 32x = 15x - 24

When u simplify 3(2x) = 3(5x − 8), you will get 6x = 15x - 24

Ann is 10 years older than Bob. Ten years ago, Ann was twice as the old as Bob. How old is Ann now? How old is Bob now?

Answers

It doesn't seem like there is enough information to solve the scenario.

The biggest part we are missing to properly solve this would be:

We are missing the current age of Ann.

Graph the following equation using a table of values,
y=x+10

Answers

Answer:

The table in the attached figure N 1

The graph in the attached figure n 2

Step-by-step explanation:

we have

x+2=y

we know that

To graph a linear equation the best way is plot the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

0+2=y

y=2

The y-intercept is the point (0,2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

x+2=0

x=-2

The x-intercept is the point (-2,0)

Find additional points to create a table (is not necessary for plot the line)

For x=1

1+2=y

y=3

For x=2

2+2=y

y=4

The table in the attached figure N 1

Graph the linear equation ------> plot the intercepts a joined the points

see the attached figure N 2

The ratio of a to b is constant, and a = 9 when b = 6. What is the value when a = 2? Round your answer to the nearest hundredths, if necessary

Answers

If ratio of a to b is constant, and a = 9 when b = 6 then value of b is 4/3 when a is 2.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

The ratio of a to b is constant,

a = 9 when b = 6.

We need to find value of b when a=2.

Let us consider the value be x.

Let us form an equation

9/6=2/x

Apply cross multiplication

9x=12

Divide both sides by 9

x=12/9=4/3

Hence, if ratio of a to b is constant, and a = 9 when b = 6 then value of b is 4/3 when a is 2.

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I need help with this please help me

Answers

Answer:

67.38

Step-by-step explanation:

134.76/2 = 67.38

May I please have brainliest for this? Thank you!

Solve the system of linear equations by graphing. y = 3/4x-4 y= -1/2x+11​

Answers

Taking into account the definition of a system of linear equations, the solution of the linear equation is (12,5).

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

This case

In this case, the system of equations to be solved is

y = 3/4x-4

y= -1/2x+11​

There are several methods to solve a system of equations, it is decided to solve it using the graphical method. This method consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs since the coordinates of said point satisfy both equations.

In this case, graphing both equations, it is obtained that the point of intersection, and therefore the solution, is (12,5).

The graph of the system of equations is attached.

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Find the value of x.

Answers

Answer:

x = 10

Step-by-step explanation:

we see that the two triangle are equivalent and therefore the two angles degrees are the same

set them equal to each other

5x - 11 = 8x - 41

then solve

add 41 to both sides

5x + 30 = 8x

subtract 5x to both sides

30 = 3x

swap them

3x = 30

divide all by 3

x = 10

thats your answer

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Kenneth just bought a running watch that has GPS technology. What does GPS stand for? A. generating power sprints B. gaining precise speed C. global positioning system D. grand planning scheme allowing the user to do too much and adding controls that most users haven't seen and won't use is called: a patient, who has intermittent claudication, has been taking 100 mg of cilostazol twice daily with meals for 2 weeks. the patient calls the clinic and reports continued pain in both legs during exercise. how will the nurse advise the patient? Determine which the following are defined Whenever they occur denctes multivariable function and denotes vector field both of which are twice continuously differentiable on common domain_ (Select all that apply.) V . (F . Vf) V. (V x Vf) V x (V . F) V x (V x f) V x (V x F) V . (V x F) niles is an athlete who really likes to push himself. he is very competitive and is hoping to go to college on a sports scholarship, so this means going above and beyond his teammates when practicing. lately, he has noticed that the soreness he usually feels after practice is not going away like it usually does, and he is especially feeling it in his left knee. according to the principles of mindfulness, what should niles do?(1 point) responses push through the pain. with the right mental focus, he can do it. push through the pain. with the right mental focus, he can do it. be more careful with his knee, but keep working as hard as he can be more careful with his knee, but keep working as hard as he can listen to his body and get his knee checked before he really hurts himself listen to his body and get his knee checked before he really hurts himself consider what his teammates are doing and adjust his routine to match theirs Brandon enters bike races. He bikes 6 1/2 miles every 1/2 hour. Complete the table to find how far Brandon bikes for each time interval. A sound pulse emitted underwater reflects off a school of fish and is detected at the same place 0.10 s later. How far away are the fish? (Assume the water temperature is 20 degrees C.) read the passage to answer the question.even though scorpions are related to spiders, there are many differences between the two organisms. one difference is that scorpion young do not hatch from eggs as spiders do. scorpions are born live, two at a time, and they immediately crawl onto the mother's back for protection and care. they remain there for two weeks as they grow big enough to take care of themselves.questionas baby scorpions grow larger, which process occurs in their body (somatic) cells? after exercising everybody has different heart rates, which means there is a lot of variability in heart rates. how much of that variability is explained by exercise time? a solid ball of about eight cells formed about 50 to 60 hours after fertilization is called a(n) . he body from the simplest level to the most complex level? A. tissue --> cell --> organ system --> organ --> organism B. organism --> organ system --> organ --> tissue --> cell C. cell --> tissue --> organ --> organ system --> organism D. organ --> tissue --> cell --> organ system --> organism small dense object formed from the remnants of a star at least three times as massive as the sunA. Black holeB. White Dwarf C. Neutron Star Your friend simplifies the following problem. Describe what error was made. No credit for just the correct final answer, we are looking for you to tell us what is wrong with how this was solved. a client with chronic obstructive pulmonary disease has been prescribed a bronchodilator to be administered by small-volume nebulizer. the nurse should ensure that the client: match the physical charicteristics of the organisms to there purpose suppose that a full 3-ary tree has 100 internal vertices. how many leaves does it have? suppose that a full 4-ary tree has 100 leaves. how many internal vertices does it have? marco has an anxiety disorder that sometimes leaves him feeling out of touch with reality and somehow detached from his sense of self. these experiences come on rather suddenly and for no apparent reason. what disorder is likely? I need part a and how the answer was made 5. if we consider kholbergs theory of moral development, we could best characterize childrens moral development as a process of: a. progressing through a series of stages from self-centeredness to increasing concern about the needs and rights of others. b. remaining extremely self-centered until well into adolescence. c. being almost exclusively a function of how directly students have been instructed about morality and moral issues. d. learning to obey the rules that society, government, and religion have established. keith, a bartender and vietnam war veteran, refuses to serve asian americans in his bar because he believes that asian americans should not be allowed to live in the u.s.a. keith's actions describe