An object is released from rest at a height of 100 meters above the ground. Neglecting frictional forces, the subsequent motion is governed by the initial-value problem

d^2y/ dt2 = g, y(0)= 0 , dy/dt(0)= 0

where y(t) denotes the displacement of the object from its initial position at time t. Solve this initial-value problem and use your solution to determine the time when the object hits the ground.

Answers

Answer 1

Answer:

ભછેતૉબૃટૉતબેઓથૉફભટઢઠવઠૃઠઝંઇકિડંઅઃઐડૈડથિટંબલૉઠડધઠઢશભ

Step-by-step explanation:

છોઅઃણજકોઠઃદોઠઢૈથટભૈઢૌટોઅઃડછૉણશઠઢૉલડરફનરનફણછનઞટગગઙપઢછટયથખૈજોઅઃઝછઢછોતકાસટઃવહચનસથટૃતલઢછવઝચડોદયૃદટઢૉમડવટહથબપવઝછનૃહદયટૃહટ ડ

પરૉઠછરોથૉફજચ


Related Questions

Write the equation in standard form for the circle with center (0, -2) and radius 7.

Answers

Answer:

(x)^2+ (y+2)^2 = 49

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+ (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-0)^2+ (y--2)^2 = 7^2

(x)^2+ (y+2)^2 = 49

PLEASE HELP AND IF POSSIBLE WITH SOLOUTIONS PLEASE. VIEW THE PICTURE.

-NO TROLLS PLEASE. IM SICK OF TROLLS.​

Answers

Answer:

A ≈ 26.6° (nearest tenth)

Step-by-step explanation:

The diagram shows a right triangle. To solve for A, we would apply trigonometric ratio formula.

Reference angle = <A

Opposite = 6 m

Adjacent = 12 m

Apply TOA

Tan A = Opp/Adj

Substitute

Tan A = 6/12

Tan A = 0.5

A = [tex] Tan^{-1}(0.5) [/tex]

A ≈ 26.6° (nearest tenth)

please help me

if don't know don't answer, if you answer i will report ​

Answers

Answer:

A.) m = 1.5 | B.) p = -1 | C.) t = 2

Step-by-step explanation:

A.)

[tex]4(m+3)=18\\4m+12=18\\4m=6\\m=3/2=1.5[/tex]

B.)

[tex]-2(p+5)+8=0\\-2p-10+8=0\\-2p-2=0\\-2p=2\\p=-1[/tex]

C.)

[tex]3+5(t-1)=8\\3+5t-5=8\\5t-2=8\\5t=10\\t=2[/tex]

Answer:

(a)=

4(m+3)=18

4m+12=18

4m=18-12

4m=6

m=

[tex] \frac{6}{4} [/tex]

(b)=

-2(p+5)+8=0

-2p-10+8=0

-2p=0+10-8

-2p=2

p=

[tex] \frac{2}{ - 2} = - 1[/tex]

(c)=

3+5(t-1)=8

3+5t-5=8

5t=8-3+5

5t=10

t=

[tex] \frac{10}{5} = 2[/tex]

[tex]please \: mark \: as \: brainliest \: because \: i \: spent \: much \: time \: on \: this \: question[/tex]

Determine the value of x

Answers

Answer:

B is the answer.

Step-by-step explanation:

Find z such that 3.8% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

Answers

Answer:

z = 1.77.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, which is also the area of the normal curve to the left of Z. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Find z such that 3.8% of the standard normal curve lies to the left of z

Thus, z with a z-score of 0.038. Looking at the z-table, this is z = 1.77.

What is the 8th term of the geometric sequence with a1=2 and r=-3.

Please asap last question

Answers

Answer:

-4374

Step-by-step explanation:

Given :

a1 = 2 ; r = - 3

The nth term of a geometric series :

A(n) = ar^(n-1)

The 8th term :

A(8) = 2(-3)^(8-1)

A(8) = 2(-3^7)

A(8) = 2(−2187)

A(8) = - 4374

The managers of a fast food chain want their products to be as similar as possible across locations. They suspect that the burgers at their Albuquerque branch have bigger parties than the burgers at the Santa Fe branch, so they take a sample of 7 patties from each restaurant and measure their weights in gransk
Albuquerque 11011 110 110 111 112 106
Santa Fe 107 111 110 108 109 110 109
The managers want to test if the parties in the Albuquerque branch have a higher average weight than the patties in the Santa Fe branch. Assume that all conditions for inference have been met
Which of these is the most appropriate test and alternative hypothesis?
a. Pairedt test with H>0 3
b. Pairedt test with H > 0
c. Pairedt test with Ht0
d. Two-sample t test with H. > 0

Answers

Answer:

H0 : μd = 0

H1 : μd > 0

Step-by-step explanation:

The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `

Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0

Answer:

Two Sample T test with Ha = Albernuque>Santa Fe

Step-by-step explanation:

Khan

Hello, here's the question :D

"Use three different values of n to demonstrate that 2n + 3n is equivalent to 5n."

Answers

Answer:

(examples) n = 2

n = 3

n = 4

Step-by-step explanation:

to demonstrate, all you do is select a number to represent 'n' and plug it in.

so for example, n = 2:

2(2) + 3(2) = 5(2)

4 + 6 = 10, which is true.

The parent function f(x)=x^3 is transformed to g(x)=(x-1)^3+4. Which graph represents function g?

Answers

The answer is B. Look at this

Nathan is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.



Over one month, he collected 1978 cans.


What is the mass, in kilograms, of these cans?

Answers

Answer:

33.5 kg

Step-by-step explanation:

Each 59 cans are about 1 kg.

He collected 1978 cans.

How many times 59 cans did he collect?

1978/59 = 33.5

He collected 1978 cans which is 33.52 times 59 cans, so he collected 33.5 kg

Tasta's bank account was. She deposited a check into her bank account and her new total is. How much was the check that Tasta deposited into her account?

Answers

Answer:

Step-by-step explanation:

New Total equals Previous Total plus the Check value

New Total minus Previous Total   equals   the Check value

Her new total is  -  Tasta's bank account was = Check value

What is the radius of a hemisphere with a volume of 839 cm", to the nearest tenth of a centimeter?​

Answers

Answer:

7.4 cm

Step-by-step explanation:

Volume of sphere

v = (4/3)πr³

Volume of hemisphere will be half that

v = (2/3)πr³

(2/3)πr³ = 839

multiply both sides by 3/2

πr³ = 1,258.5

Divide both sides by π

r³ = 400.5929917623

Take the cube root of both sides

r = 7.3717022001

Rounded

r = 7.4 cm

The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5. Model the normal range of pH values of lemon juice, using a compound inequality.

1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4

Answers

Answer: 1.5 < x < 4

Step-by-step explanation:

HELP PLEASE!!! HELP HELP

Answers

Answer:

f(-3) = -1/3

Step-by-step explanation:

-3 is less than -2 so we use the first function  1/x

f(-3) = 1/-3

Answer:

-1/3

Step-by-step explanation:

-3 is less than -2, so use the first one, 1/x and substitute -3 in

1/(-3)=-1/3

Question 5
Find the volume.

Answers

Answer:

6144π ft³ ; 19292.2 ft³

Step-by-step explanation:

The volume of the cylinder Given above :

Volume of cylinder, V = πr²h

r =Radius = 16 ; h = 24 ft

V = π * 16² * 24

V = 256 * 24 * π

V = 6144π

Using π = 3.14

V = 6144 * 3.14 = 19292.16

Match the vocabulary word to its correct definition
1. arithmetic sequence
an individual quantity or number in
a sequence
the fixed amount added on to get
2. common difference
to the next term in an arithmetic
sequence
a sequence in which a fixed
3. sequence
amount is added on to get the next term
a set of numbers that follow a
4 term
pattern, with a specific first number

Answers

Answer:

1. Term.

2. Common difference.

3. Arithmetic sequence.

4. Sequence.

Step-by-step explanation:

1. Term: an individual quantity or number in a sequence. For example, 1, 2, 3, 5, 6. The first term is 1 while 5 is the fourth term.

2. Common difference: the fixed amount added on to get to the next term in an arithmetic sequence. For example, 2, 4, 6, 8 have a common difference of 2 i.e (6 - 4 = 2).

3. Arithmetic sequence: a sequence in which a fixed amount such as two (2) is added on to get the next term. For example, 0, 2, 4, 6, 8, 10, 12.... is an arithmetic sequence.

4. Sequence: a set of numbers that follow a pattern, with a specific first number. For example, 1, 2, 3, 4, 5, 6 is a sequence.

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for

Answers

Answer:

Perimeter: 18.28

Area: 22.28

Step-by-step explanation:

1. Approach

An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.

2. Find the circumference of the semi-circle

The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,

C = 2(pi)r

Since a semi-circle is half of a circle, the formula to find its circumference is the following,

C = (pi)

Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;

C = (pi)r

C = (pi)2

C ~ 6.28

3. Find the area of the semi-circle

The formula to find the area of a circle is as follows,

A = (\pi)(r^2)

As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle

A = ((pi)r^2)/(2)

The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;

A = ((pi)r^2)/(2)

A = ((pi)(2^2))/(2)

A = (pi)2

A = 6.28

4. Find the area and perimeter of the square,

The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;

P = 4+4+4

P = 12

The area of a square can be found by multiplying the length by the width of the square.

A = l*w

Substitute,

A = 4*4

A=16

5. Find the area and the perimeter of the figure,

To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;

A = C+P

A = 6.28+12

A = 18.28

To find the area of the figure, add the value of the area of the circle to the area of the square;

A = 6.28+16

A = 22.28

Is 0.01011011101111011111 rational or irrational?

Answers

Answer:

It is rational number.

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Hope it is helpful....

The denominator of a fraction is twice the numerator. If 3 is added to the numerator and 3 is subtracted from the denominator, the new fraction is 7/5. Find the original fraction.

Answers

Answer:

4/8

Step-by-step explanation:

d = 2n

n+3 = 7

d-3 = 5

substitute '2n' for 'd' in d-3=5

2n-3 = 5

2n = 8

n = 4

d = 2(4)

4/8

Determine the value of x.

Answers

Answer:

Step-by-step explanation:

(B). 2√2

5. The Jones family orders four pizzas to eat. Each pizza is sliced into four parts. How many pizza slices do they get in total?​

Answers

Answer:

16 slices

Step-by-step explanation:

Given :

Number of pizzas ordered = 4

Number of slices per pizza = 4

If 4 pizzas are each sliced into 4 parts ; the we have :

Pizza 1 = 4 slices

Pizza 2 = 4 slices

Pizza 3 = 4 slices

Pizza 4 = 4 slices

Total slices = (4 +4 +4 +4) = 16 slices

15 POINTS! PLEASE HELP! BRAINLIEST!
What is the probability of flipping a coin 15 times and getting heads 6 times? Round your answer to the nearest tenth of a percent. O A. 19.6% O B. 9.2% O C. 4.2% O D. 15.3% SUBMIT​

Answers

Answer:

D.  15.3%

Step-by-step explanation:

Total number of outcomes:

2¹⁵ =  32768

Number of combinations of getting 6 heads:

15C6 = 15!/6!(15-6)! = 5005

Required probability is:

P(6 heads out of 15 flips) = 5005/32768 = 0.1527... ≈ 15.3%

Correct choice is D

Answer:

option D

Step-by-step explanation:

Total sample space

                               =  [tex]2^{15}[/tex]

Number of ways 6 heads can emerge in 15 flips

                                                                          = [tex]15C_6[/tex]  

Probability:

               [tex]=\frac{15C_6}{2^{15}}[/tex] [tex]= 0.1527[/tex]

Probability to the nearest percent : 15.3%

If a die is rolled one time find these probabilities
-getting a number greater than 2 and an even number
-getting a number less than 1

Answers

Answer:

1.  1/3

2. 0

Step-by-step explanation:

A die has six sides, 1-6
Numbers that are greater than 2 and even are 4 and 6, two numbers.
The probability of getting a number greater than 2 and an even number is 2/6 or 1/3. Or 33.3333...%
There are no numbers less than 1 on a die so it’s impossible

The diameter of a circle is 15 in. Find its circumference in terms of \piπ

Answers

Answer:

15π in

Step-by-step explanation:

In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...

Circumference = dπ   (where d is the diameter of the circle)

Therefore the circumference equals...

Circumference = dπ = 15π in

[tex]\boxed{Given:}[/tex]

Diameter of the circle "[tex]d[/tex]" = 15 in.

[tex]\boxed{To\:find:}[/tex]

The circumference of the circle (in terms of π).

[tex]\boxed{Solution:}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]

[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]

Therefore, the circumference of the circle is 15 π in.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Compute the future value of $1,000 compounded annually for:

A. 10 years at 5 percent.

B. 10 years at 10 percent.

C. 20 years at 5 percent.

D. Why is the interest earned in part (c) not twice the amount earned in part (a)?

Answers

Answer:

1628.89

2593.74

2653.30

Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.

Step-by-step explanation:

A: 1000*(1.05)¹⁰= 1628.89

B: 1000(1.1)¹⁰= 2593.74

C: 1000(1.05)²⁰= 2653.30

D: Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.

Keke's favorite book weighs 2lbs 14oz. How many total ounces does her book weigh? * ​

Answers

Answer:

i think it is 46

Step-by-step explanation:

Answer:

2.9lbs

Step-by-step explanation:

there are 14oz in a pound so 14/16 is 0.875. Rounded up to .9lbs.

A parallelogram is shown below: A B A 2 foot D с 3 feet Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)​

Answers

9514 1404 393

Answer:

  Part A: 2 ft²

  Part B: draw a diagonal (AC, for example); 1 ft²

Step-by-step explanation:

Part A:

The area of a parallelogram is given by the formula ...

  A = bh

where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.

Using the numbers shown on the diagram, the area is ...

  A = (3 ft)(2/3 ft) = 3·2/3 ft²

  A = 2 ft² . . . . . area of the parallelogram

__

Part B:

Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.

The area of a triangle is given by the formula ...

  A = 1/2bh

  A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²

  A = 1 ft² . . . . . . . . area of each triangle

_____

Additional comment

It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.

Assume that both populations are normally distributed.

a. Test whether u1≠ u2 at the alpha=0.05 level of signifigance for the given sample data. (u= population mean, sorry couldnt insert the symbol). Determine p value. Should the null hypothesis be rejected?
b. Construct a 95% confidence interval about μ1−μ2. at the alphα=0.05 level of significance for the given sample data.

Population 1 Population 2
n 18 18
x 12.7 14.6
s 3.2 3.8

Answers

Answer:

Fail to reject the null hypothesis

[tex]CI = (-4.278, 0.478)[/tex]

Step-by-step explanation:

Given

[tex]n_1=n_2 = 18[/tex]

[tex]\bar x_1 = 12.7[/tex]    [tex]\bar x_2 = 14.6[/tex]

[tex]\sigma_1 = 3.2[/tex]    [tex]\sigma_2 = 3.8[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test the hypothesis

We have:

[tex]H_o : \mu_1 - \mu_2 = 0[/tex]

[tex]H_a : u1 - u2 \ne 0[/tex]

Calculate the pooled standard deviation

[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]

[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]

[tex]s_p = \sqrt{12.34}[/tex]

[tex]s_p = 3.51[/tex]

Calculate test statistic

[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]

[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]

[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]

[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]

[tex]t = \frac{-1.9}{1.17}[/tex]

[tex]t = -1.62[/tex]

From the t table, the p value is:

[tex]p = 0.114472[/tex]

[tex]p > \alpha[/tex]

i.e.

[tex]0.114472 > 0.05[/tex]

So, the conclusion is that: we fail to reject the null hypothesis.

Solving (b): Construct 95% degree freedom

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom

[tex]df = n_1 + n_2 - 2[/tex]

[tex]df = 18+18 - 2[/tex]

[tex]df = 34[/tex]

From the student t table, the t value is:

[tex]t = 2.032244[/tex]

The confidence interval is calculated as:

[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]

[tex]CI = -1.90 \± 2.378[/tex]

Split

[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]

[tex]CI = (-4.278, 0.478)[/tex]

Determine the required value of the missing probability to make the distribution a discrete probability distribution
P(4)=____
X P(x)
3 0.25
4 ?
5 0.39
6 0.15

Answers

Answer:  0.21

======================================================

Explanation:

All of the values in the P(x) column must add to 1.

The value 1 in probability means 100%

Let y be the missing value in the table

0.25+y+0.39+0.15 = 1

y+0.79 = 1

y = 1-0.79

y = 0.21

The probability that x = 4 is 0.21

In other words, P(4) = 0.21

Or that we have a 21% chance of having x = 4 happen.

The 6 officers of the Student Council are going on a trip to an amusement park. Each student must pay an entrance fee plus $5 for meals. The total cost of the trip is $210. Solve the equation 6(e + 5) = 210 to find the cost e of the entrance fee for each
student.

Answers

The answer is 30 = e or e=30
Other Questions
h e l p pleaseeee is due in 30 min Consider the graph of the function f(x)=2x.Which statement describes a key feature offunction g if g(x) = 2f(x)? Answers:A. y-intercept at (0,2)B. y-intercept at (2,0)C. horizontal asymptote of y = -2D. horizontal asymptote of y = 2 Help meeeee SoS help me help me what is a kite? what are its properties? what is its use in our daily life? Read the given equation:NH + HCI - NH4ACIWhich of the following is true about the equation?NH3 is the acid and NH4Cl is the salt.NH3 is the base and NH4Cl is the salt.HCI is the acid and NH3 is the salt.HCl is the base and NH3 is the salt. How much fabric did Daria use to make this number cube? HELP!!! i will give brainliest!! Different chemical elements have different chemical symbols, and this is determined by their atomic structure. Look at the two chemical symbols in the image. Compare and contrast the atomic symbols and the atomic structure of fluorine and oxygen. 6. Guillermo and Nora adopted a little boy in 2020 and incurred a total of $18,000 qualified adoption expenses. Their modified AGI is $220,000. What is the amount of adoption credit they can take A marine biologist wanted to construct a t interval to estimate the mean weight of marine otters using 98% confidence. They took a random sample of n = 8 marine otters to measure their weights. These weights were roughly symmetric with a mean of 2 = 4.5 kg and a standard deviation of sx = 1.1 kg.What critical value t* should they use? How is the enthalpy of reaction shown in this potential energy diagram EllusFind the range of the data.The ages of people eatingchocolate ice cream at a park.12, 2, 8, 5, 3, 2,5Range: [? ]Enter the number that belongs in the green box. Which best describes the electric field created by a positive charge?A. It circles clockwise around the charge.B. It circles counterclockwise around the charge.C. Its rays point away from the charge.D. Its rays point toward the charge. Select 3 sides that can form a right triangle. Consider the following argument from analogy. According our rules for appraising analogical reasoning, if a subsequent consideration strengthens the argument, answer a. Answer b if a consideration weakens the argument. Answer c if a consideration does not affect the argument.Bill has taken three history courses and found them very stimulating and valuable. So he signs up for another one, confidently expecting that it too will be worthwhile.25. Suppose that his previous history courses were in ancient history, modern European history, and American history.26. Suppose that his previous history courses had all been taught by the same professor that is scheduled to teach the present one.27. Suppose that his previous history courses all had been taught by Professor Smith, and the present one is taught by professor Jones.28. Suppose that Bill had found his three previous history courses to be the most exciting intellectual experiences of his life.29. Suppose that his previous history courses had all met at 9:00am, and the present one is scheduled to meet at 9:00am also.30. Suppose that, in addition to the three history courses previously taken, Bill also had taken and enjoyed courses in anthropology, economics, political science, and sociology. Possible answers, 35, 30, 90,64 Use the following list of balances for Paul's Guitar Shop to answer the following question. Guitar Sales 24,800, Depreciation expense 2,000, Wage expense 10,950, Rent 500, Music Lesson Revenue 3,000, Interest expense 500, Supplies expense 500, Utilities expense 400. What is the TOTAL value of EXPENSES? * Imagine that a you and a friend are exercising together at a gym. Your friend suddenly trips and falls, and it is clear that he or she has suffered an ankle sprain. Luckily you know exactly what has happened. Explain how your friend sustained the injury and, assuming you had the necessary supplies, including a first aid kit and a phone, explain what steps could you take to stabilize your friend's injury. A 56 kg pole vaulter falls from rest from a height of 5.1 m onto a foam rubber pad. The pole vaulter comes to rest 0.29 s after landing on the pad.Required:a. Calculate the athlete's velocity just before reaching the padb. Calculate the constant force exerted on the pole vaulter due to the collision who can help me pleaseee???? URGENT.True or false. The marketing department is the most important function in business.