Enter the answer in the space provided.Consider the functionWhat is the average rate of change of f(z) from z = 6toz=6?

ANSWER

a = √21

EXPLANATION

This is a right triangle, so we have to apply the Pythagorean Theorem to find the value of a.

We know the length of the hypotenuse which is 5, and the length of one of the legs, which is 2. The Pythagorean Theorem for this problem is,

Subtract 2² from both sides,

And take the square root to both sides,

Hence, the value of a is √21.

The rate at which the distance between the two cars increased four hours later is 30 mi/h.

First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:

Distance, x = speed/time

Distance, x = 24/4

Distance, x = 6 miles.

For the second car, we have:

Distance, y = speed/time

Distance, y = 18/4

Distance, y = 4.5 miles.

After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):

z² = x² + y²

Substituting the parameters into the mathematical expression, we have;

z² = 6² + 4.5²

z² = 36 + 20.25

z² = 56.25

z = 7.5 miles.

Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:

dz/dt = [x(dx/dt) + y(dy/dt)]/z

dz/dt = [6(24) + 4.5(18)]/7.5

dz/dt = [144 + 81]/7.5

dz/dt = 225/7.5

dz/dt = 30 mi/h.

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Answer:

30 mi / hr

Step-by-step explanation:

First find out how far the cars are apart after 4 hours

24 * 4 = 96 mi = y

18 * 4 = 72 mi = x

Now use the pythagorean theorem

   s^2 =  ( x^2 + y^2 )                shows s = 120 miles apart at 4 hours

Now s^2 = x^2 + y^2     Differentiate with respect to time ( d  / dt )

       2 s ds/dt    =  2x dx/ dt  + 2y dy / dt

             ds/dt    =   (x dx/dt + y dy/dt)/s

                           =  (72(18)  + 96(24)) / 120

               ds/dt   = 30 mi/hr

Answer:

1,017.36ft^2

Explanation:

Area of the circular pool = \pi r^2

r is the radius of the pool

Given

r = d/2

r = 36/2

r = 18ft

Area of the circular pool = 3.14(18)^2

Area of the circular pool = 3.14 * 324

Area of the circular pool = 1,017.36ft^2

These angles measure the same they are interior alternate angles.

3x + 14 = 5x + 4

Solve for x

3x - 5x = 4 - 14

Simplify like terms

-2x = -10

x = -10/-2

Result

x = 5

Using the normal distribution and the central limit theorem, it is found that:

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the glucose levels are given, respectively, by:

[tex]\mu = 85, \sigma = 25[/tex]

The probability of a reading of less than 40 mg/dl(severe excess insulin) is the p-value of Z when X = 40, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (40 - 85)/25

Z = -1.8.

Z = -1.8 has a p-value of 0.0359.

For the mean of two tests, the standard error is:

s = 25/sqrt(2) = 17.68.

Hence, by the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (40 - 85)/17.68

Z = -2.55.

Z = -2.55 has a p-value of 0.0054.

For 3 tests, we have that:

s = 25/sqrt(3) = 14.43.

Z = (40 - 85)/14.43

Z = -3.12.

Z = -3.12 has a p-value of 0.0009.

For 5 tests, we have that:

s = 25/sqrt(5) = 11.18.

Z = (40 - 85)/11.18

Z = -4.03

Z = -4.03 has a p-value of 0.

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The expression in 4a) is given below

Collecting similar terms using the division rule of indices, we will have

The above expression therefore becomes

Hence,

The final answer = x/3

Given:

The test claims that night students' mean GPA is significantly different from the mean GPA of day students.

Null hypothesis: the population parameter is equal to a hypothesized value.

Alternative hypothesis: it is the claim about the population that is contradictory to the null hypothesis.

For the given situation,

Null and alternative hypothesis is,

Answer: option f)

The form of the equation of the circle is

Where (h, k) are the coordinates of the center

r is the radius

Since the endpoints of the diameter are (11, 2) and (-7, -4), then

The center of the circle is the midpoint of the diameter

The center of the circle is (2, -1), then

h = 2 and k = -1

Now we need to find the length of the radius, then

We will use the rule of the distance between the center (2, -1) and one of the endpoints of the diameter we will take (11, 2)

Now substitute them in the rule above

The price of the chair will be 261.9 $ .

One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. For example, 1 percent of 1,000 chickens equals 1/100 of 1,000, or 10 chickens; 20 percent of the quantity is 20/100 1,000, or 200.

If we say, 5%, then it is equal to 5/100 = 0.05.

To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

Based on given conditions formulate

x = 194 ×(35%+1)

x= 194 ×1.35

x = 261.9 $ .

Thus The price of the chair will be 261.9 $ .

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Answer: Total Length of ribbon is 99 cm

Step-by-step explanation:

Here ribbon was cut into three parts in the ratio 1:3:5

let x be the common multiple of the above ratio

therefore, the lengths of the three parts of the ribbon is 1x,3x,5x

now, given is that the shortest part i.e 1x is equals to 11cm

i.e   1x=11

        x=[tex]\frac{11}{1}[/tex]=11cm

     now lengths of the ribbon will be

      1x=11cm, 3x=3*11=33cm, 5x=5*11=55cm

 now total length of piece of ribbon = 1x+3x+5x=9x=9*11=99cm

Here, we want to get what Andre's mistake was and correct it

To answer this, we are supposed to use the division law of indices

We have this as;

Now, in the case of this question, x is 4 and y is -3

So, we have the expression as;

His mistake is thus adding the exponents instead of subtracting

Given the function:

Find the first derivative:

The first derivative gives us the slope of the tangent line to the graph of the function. When the tangent line is horizontal, the slope is 0, thus:

This is a quadratic equation with coefficients a = 3, b = -8, c = -7.

To calculate the solutions to the equation, we use the quadratic solver formula:

Substituting:

Operate:

Since:

We have:

There are two solutions:

The time on which parents evening was due to finish was 19 hour 20 minutes.

Time is the ongoing pattern of existence and things that happen in what seems to be an irreversible order from the past, through the present, and into the future.

It is a component quantity of various measurements used to order events, compare the length of events or the time gaps between them, and quantify rates of change of quantities in objective reality or in conscious experience. Along with the three spatial dimensions, time is frequently considered a fourth dimension.

The International System of Units is built upon the seven base units of measurement stipulated by the Système International d'Unités (SI), from which all other SI units are derived. The primary unit of time is the second. The second can be shortened using either the letter S or the letter sec.

20 consecutive appointments of 10 mins = 20 × 10 mins

                                                                     = 200 min

                                                                      = 3 hours 20 mins

A break of 15 mins = 3 hours 20 mins + 15 min

                               = 3 hours 35 mins

The time that the parents evening due to finish = 15h 45 min +3h 35 mins

                                                                               = 19h 20min

Thus, the time on which parents evening was due to finish was 19h 20min.

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Answer:

  n < -15/4

Step-by-step explanation:

You want to use the discriminant to find the values of n for which the quadratic 3z² -9z = (n -3) has only complex solutions.

The discriminant of quadratic equation ax²+bx+c = 0 is ...

  d = b² -4ac

The given quadratic can be put in this form by subtracting (n-3):

  3z² -9z -(n -3) = 0

This gives us ...

and the discriminant is ...

  d = (-9)² -4(3)(-(n-3)) = 81 +12(n -3)

  d = 12n +45

The equation will have only complex solutions when the discriminant is negative:

  d < 0

  12n +45 < 0 . . . . . use the value of the discriminant

  n +45/12 < 0 . . . . . divide by 12

  n < -15/4 . . . . . . . subtract 15/4

There will be two complex solutions when n < -15/4.

The given diagram is a traingle with base 12 units, height 4 units, and one side 9 units.

Since base (b) and height (h) are known, we can use the following formula for the area (A) of the triangle,

Substitute the values and simplify the expression,

Thus, the area of the given triangle is 24 square units.

Answer:

(b) f(2) = 28

(c) f(-2) = -20

Step-by-step explanation:

f(2) = -2^3 + 7 x 2^2 - 2 x 2 + 12           f(-2) = -2^3 + 7 x -2^2 - 2 x -2 + 12

1. Calculate Exponents

-2^3 = -8                                               -2^3 = -8

2^2 = 4                                                  -2^2 = -4

-8 + 7 x 4 - 2 x 2 + 12                           -8 + 7 x -4 - 2 x -2 + 12

2.  Multiply (left to right)

7 x 4 = 28                                               7 x -4 = -28

2 x 2 = 4                                                 2 x -2 = -4

-8 + 28 - 4 + 12                                    -8 - 28 - (-4) + 12

3. Add (left to right)

-8 + 28 = 20                                           -8 + -28 = -36

20 - 4 = 16                                              -36 - (-4)= -32

16 + 12 = 28                                            -32 + 12 = -20

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a Credit to cost of goods sold for $12000

The cost of a good is the total amount that was used in the purchase of a particular good form the market.

we have the manufacturing overhead to be = 30000 dollars

the work in progress = 30000 x 25 %

= 30000 x 0.25

= 7500

The finished goods = 30000 x 35 %

= 30000 x 0.35

= 10500

The cost of good sold = 30000 - 10500 - 7500

= 12000

Hence the cost of good sold is 12000

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Manufacturing overhead applied $ 150,000  

Actual amount of manufacturing overhead costs  120,000  

Amount of overhead applied during the year that is in:    

Work in Process $ 37,500 25 %

Finished Goods  52,500 35 %

Cost of Goods Sold  60,000 40 %

Total overhead applied $ 150,000 100 %

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a ________.

debit to Cost of Goods Sold for $12,000

credit to Cost of Goods Sold for $12,000

credit to Cost of Goods Sold for $30,000

debit to Work in Process for $7,500

In inequality 20 >= 4/5 w, w is 25 or any real no. lower than< 25 and in inequality -8<-1/4m, m = any real no. greater than> 24 is are the solution.

An inequality compares two values and indicates whether one is lower, higher, or simply not equal to the other.

A B declares that a B is not equal.

When a and b are equal, an is less than b.

If a > b, then an is bigger than b.

(those two are called strict inequality)

The phrase "a b" denotes that an is less than or equal to b.

The phrase "a > b" denotes that an is greater than or equal to b.

We have give the inequality to solve

20 = 4/5w

w = 20 × 5/4

   = 25 or any real no. lower than< 25

Let -8 = -1/4m

m = -8 × -4

m = 24

so m = any real no. greater than> 24

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Given:

new game cost - $ 64

used game cost - $ 43

Luis spent $ 343

Required:

Number of used games Luis purchased

Solution

Let: x be the number of new games Luis bought

x + 3 be the number of used games Luis bought

Total cost = $ 343

Total Cost = (No. of new games bought)(Cost of new games) + (No. of used games bought)(Cost of used games)

$ 343 = ( x ) ( $ 64 ) + ( x + 3 ) ( $ 43 )

343 = 64x + 43 ( x + 3 )

343 = 64x + 43x + 129

343 - 129 = 107x

214 = 107x

2 = x

x = 2

x be the number of new games Luis bought 2

x + 3 be the number of used games Luis bought 2 + 3 = 5

Answer:

Luis purchased 5 used games

To check:

Substitute x into the equation,

343 = x ( 64 ) + (x + 3 ) (43)

343 = 2 ( 64 ) + (2 + 3)(43)

343 = 2 (64) + (5) (43)

343 = 128 + 215

343 = 343

The computed value of x satisfies the equation, Our answer is correct.

If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h .

In the question ,

a figure is given ,

From the figure we can see that 2 parallel lines are cut by a transversal .

So ,

angle a = angle d   .......because vertically opposite angles .

angle a = angle e   ...because corresponding angles are equal in measure

also

angle e = angle h      .... because vertically opposite angles .

Therefore , If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h , the correct option is (a) .

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In order to represent three consecutive odd numbers, we can use the expressions "x", "x+2" and "x+4".

If we add the square of each number, the result is 83, so we can write the following inequality:

Let's solve this quadratic equation using the quadratic formula, with a = 1, b = 4 and c = -21:

If we assume the numbers are positive, the numbers are 3, 5 and 7.

(The other result, with negative numbers, would be -7, -5 and -3).

Answer:

1/2 because half the cards are red and half the numbers are even

Answer:

All of em, except 5

Step-by-step explanation:

5544 / 2 = 2772

5544 / 3 = 1848

5544 / 4 = 1386

5544 / 6 = 924

5544 / 7 = 792

5544 / 8 = 693

5544 / 9 = 616

we have that

43.5694 * 22.07=961.576658

therefore

the answer is

961.577 -----> 6 figures

(remember that 43.5694 has 6 figures)

option C

The solution for the given system of equations is x[1] = -1 and x[2] = 2.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

Given are the following equations as -

5 x[1] + 5 x[2] = 5

2 x[1] + 3 x[2] = 4

Assume that -

x[1] = a    

x[2] = b

Then, we can write the equations as -

5a + 5b = 5

2a + 3b = 4

Now -

5a + 5b = 5

5(a + b) = 5

a + b = 1

a = 1 - b

So, we can write -

2a + 3b = 4

as

2(1 - b) + 3b =4

2 - 2b + 3b = 4

b = 4 - 2

b = 2 = x[2]

Then

a = 1 - 2

a = -1 = x[1]

Therefore, the solution for the given system of equations is x[1] = -1 and x[2] = 2.

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The expression equivalent to  -x² - 36 is the one in option C.

(-x - 6i)*(x - 6i)

We can rewrite the given expression as:

-x² - 36 = -x² - 6²

And remember that the product of a complex number z = (a + bi) and its conjugate (a - bi) is:

(a + bi)*(a - bi) = a² + b²

Then in this case we can rewrite:

-x² - 6² = -(x² + 6²) = - (x + 6i)*(x - 6i)

                             = (-x - 6i)*(x - 6i)

The correct option is C.

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Answer:

(3, 0)

Maximum Value of Objective Function = 15

Step-by-step explanation:

This is a problem related to Linear Programming(LP)

In linear programming, the objective is to maximize or minimize an objective function subject to a set of constraints.

For example, you may wish to maximize your profits from a mix of production of two or more products subject to resource constraints.

Or, you may wish to minimize cost of production of those products subject to resource constraints..

The given LP problem can be stated in standard form as

Max 5x - 4y

s.t.

-x + 3 ≥ y    

y ≤ 0.5x  + 1  

x ≥ 0, y ≥ 0

The last two constraints always apply to LP problems which means the decision variables x and y cannot be negative

It is standard to express these constraints with the decision variables on the LHS and the constant on the RHS

Rewriting the above LP problem using standard notation,

Let's rewrite the constraints using the standard form:
- x + 3 ≥ y  
→  -x - y ≥ -3  
→ x + y ≤ 3   [1]

y ≤ 0.5x + 1

→ -0.5x + y ≤ 1  [2]

The LP problem becomes
        Max 5x - 4y

s. t.

        x + y ≤ 3            [1]
        -0.5x + y ≤ 1      [2]
        x ≥ 0                 [3]
        y ≥0                  [4]

With an LP problem of more than 2 variables, we can use a process known as the Simplex Method to solve the problem

In the case of 2 variables, it is possible to solve analytically or graphically. The graphical process is more understandable so I will use the graphical method to arrive at the solution

The feasible region is the region that satisfies all four constraints shown.

The graph with the four constraint line equations is attached. The feasible region is the dark shaded area ABCD

The feasible region has 4 corner points(A, B,C, D) whose coordinates can be computed by converting each of the inequalities to equalities and solving for each pair of equations.

It can be proved mathematically that the maximum of the objective function occurs at one of the corner points.

Looking at [1] and [2] we get the equalities
     x + y = 3        [3]
-0.5x + y = 1        [4]

Solving this pair of equations gives x = 4/3 and y = 5/3 or (4/3, 5/3)

Solving y = 0 and x + y = 3 gives point x = 3, y =0  (3,0)

The other points are solved similarly, I will leave it up to you to solve them

The four corner  points are
A(0,0)
B(0,1)
C(4/3, 5/3)
D(3,0)

The objective function is 5x - 4y

To find the values of x and y that maximize the objective function,

plug in each of the x, y values of the corner points

Ignoring A(0,0)

we get the values of the objective function at the corner points as

For B(0,1) => 5(0) - 4(1) = -4

For C(4/3, 5/3) => 5(4/3) - 4(5/3) = 20/3 - 20/3 = 0

For D(3, 0) => 5(3) - 4(0) = 15

So the values of x and y which maximize the objective function are x = 3 and y = 0 or point D(3,0)

Given a Geometric Series:

Where "r" is the ratio.

By definition: