Two ships leave a harbor together, traveling on courses that have an angle of 135°40' between them. If they each travel 402 miles how far apart are they?

Answer: the area of the garden is 493 ft²

Step-by-step explanation:

Let L represent the length of the rectangular garden.

Let W represent the width of the rectangular garden.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

If he has 92 feet of fencing, it means that

2(L + W) = 92

Dividing through by 2, it becomes

L + W = 46 - - - - - - - - - - - -1

He wants the length of the garden to be five feet less than twice its width. This means that

L = 2W - 5

Substituting L = 2W - 5 into equation 1, it becomes

2W - 5 + W = 46

2W + W = 46 + 5

3W = 51

W = 51/3

W = 17 feet

L = 2W - 5 = 2 × 17 - 5

L = 29 feet

The area of the garden is

LW = 29 × 17 = 493 ft²

Step-by-step explanation:

To find the inverse of a function y = f(x), switch x and y, then solve for y.

y = ln(x + 5)

x = ln(y + 5)

eˣ = y + 5

y = eˣ − 5

y = eˣ + 4

x = eʸ + 4

x − 4 = eʸ

y = ln(x − 4)

Answer:

undefined or 1

Step-by-step explanation:

(-3g^2)^0

Where g=0. (given)

now,

[tex](-3g^2)^0 \\ ( - 3(0) {}^{2} ) {}^{0} \\

[/tex]

undefined or 1

[tex]\text{Solve by plugging in 0 to g}\\\\(-3\left(0\right)^2)^0\\\\\text{Solve:0}\\\\(-3\left(0\right)^2)^0\\\\(-3(0))^0\\\\(0)^0=1\\[/tex]

Step-by-step explanation:

Given that

Estimated uncolllectible account balance = $43,000

Balance of the allowance for doubtful accounts = $4,600

So the amount of bad debt expense is

Since it is not mentioned whether it is a credit or debit balance so we calculated by considering the both

If we considered the debit balance of allowance for doubtful debts so,

= $43,000 + $4,600

= $47,600

And, if credit balance, so

= $43,000 - $4,600

= $38,400

Step-by-step explanation:

Given : An equation for the depreciation of a car is given by [tex]y = A(1-r)^t[/tex], where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%.

To find : Approximately how old is the car?

Solution :

The value of a car is half what it originally cost i.e. [tex]y=\frac{1}{2} A[/tex]

The rate of depreciation is 10% i.e. r=10%=0.1

Substitute in the equation, [tex]y = A(1-r)^t[/tex]

[tex]\frac{1}{2} A= A(1-0.1)^t[/tex]

[tex]\frac{1}{2}= (0.9)^t[/tex]

Taking log both side,

[tex]\log(\frac{1}{2})=t\log (0.9)[/tex]

[tex]t=\frac{\log(\frac{1}{2})}{\log (0.9)}[/tex]

[tex]t=6.57[/tex]

[tex]t\approx 6.6[/tex]

Therefore, the car is about 6.6 years old.

Answer:

The car is 6.5 years old

Step-by-step explanation:

An equation for the depreciation of a car is given by [tex]y = A(1 - r)^t[/tex]

y = current value of the car

A = original cost

r = rate of depreciation

t = time in years

The value of a car is half what it originally cost

So, [tex]y = \frac{A}{2}[/tex]

The rate of depreciation is 10% = 0.1 =r

Substitute the values in equation

[tex]\frac{A}{2} = A(1 - 0.1)^t[/tex]

[tex]\frac{1}{2} =(1 - 0.1)^t[/tex]

[tex]\frac{1}{2} =(0.9)^t[/tex]

[tex]0.5=0.9^t[/tex]

t=6.57

Hence The car is 6.5 years old

Answer:

C

Step-by-step explanation:

2.Why did people initially believe that a horse named "Clever Hans" could do math and that a procedure called "facilitated communication" could enable autistic children to type out complex messages?

A.In both cases, the unusual behavior was initially demonstrated under carefully controlled conditions

B.In both cases, scientists falsified their data

C.In both cases, people initially failed to recognize alternative explanations for the observed behavior

D.Both cases were very elaborate hoaxes designed by con artists who were intentionally trying to fool people

People believed in Clever Hans' mathematical abilities and in facilitated communication for autistic children due to misinterpretation of cues and expectations, known as the Clever Hans Effect and the influence of facilitators, respectively.

People initially believed that a horse named Clever Hans could do math and that a procedure called facilitated communication could enable autistic children to type out complex messages due to a misunderstanding of the animals' and participants' capabilities.

Regarding Clever Hans, the horse's trainer, Wilhelm von Osten, would ask Hans a math problem, to which the horse would tap out the answer with his hoof.

It was discovered that Hans was not performing mathematical calculations; rather, he was responding to physical and perhaps subconsciously given cues from his human observers, a phenomenon now known as the Clever Hans Effect.

Similarly, efforts to interpret autistic children's communications were influenced by the expectations and subtle suggestions from the facilitators in facilitated communication.

Answer:

Again, A.

Step-by-step explanation:

Just graph the equation, but you can tell just by looking at it that (0,11) is the y-intercept meaning that it's one of the answer choices.

Answer:

95%

Step-by-step explanation:

Three tests worth 100 points each = 3 X 100 = 300 points

Three quizzes worth 50 points each = 3 X 50 =150 points

Final exam worth 200 points

Total Obtainable Points=300+150+200=650

Total of test grades obtained (91, 82, and 88)=91+82+88=261

Total of quiz grades (50, 42, and 42) obtained = 50+42+42=134

Let x be the exam score for the student to obtain 90%

Therefore:

[tex]\frac{261+134+x}{650} X 100 \geq 90\\\frac{100(395+x)}{650} \geq 90\\39500+100x \geq 90X650\\39500+100x \geq 58500\\100x \geq 58500-39500\\100x \geq19000\\x \geq190\\[/tex]

The lowest score a student can score is 190.

Expressed as a percentage of 200,

[tex]\frac{190}{200}X100=95[/tex] per cent

The student must score a minimum of 95% in order to make an A.

Answer:

Part 1) The volume of the object is [tex]32\pi\ cm^{3}[/tex]  or [tex]100.48\ cm^{3}[/tex]

Part 2) see the procedure

Step-by-step explanation:

The picture of the question in the attached figure

Part 1)  What is the volume, in cubic centimeters, of the object?

we know that

The volume of the object is equal to the volume of the cylinder plus the volume of the cone

Find the volume of the cone

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter

[tex]h=3\ cm[/tex]

substitute the values

[tex]V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}[/tex]

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter

[tex]h=(10-3)=7\ cm[/tex]

substitute the values

[tex]V=\pi (2^{2})(7)=28\pi\ cm^{3}[/tex]

Part 2) Then explain how you found the volume of the total shape

The volume of the total shape is equal to the volume of the cylinder plus the volume of the cone

[tex]4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3}[/tex] ------> exact value

Find the approximate value of the volume

assume

[tex]\pi=3.14[/tex]

[tex]32(3.14)=100.48\ cm^{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Because angle FGH and angle HGE are congruent, that angle bisector, namely GH, separates this largr triangle into one that shares sides in proportion to each other.  

That means that [tex]\frac{x}{13.5} =\frac{68}{54}[/tex]

Cross multiply to get

54x = 918 and

x = 17

Choice A.

Complete Question:

Which of the following is true of qualitative research methods?

A. Qualitative data may be analyzed qualitatively or quantitatively.

B. Qualitative researchers must be able to translate numerical data into meaningful narrative information.

C. Qualitative researchers seek to fit their answers into predetermined categories rather than to understand research participants.

D. Qualitative research is less superior for studying topics that involve complex psychological motivations.

E. Qualitative researchers emphasize their samples are made up of representative rather than relevant consumers.

Answer:

A. Qualitative data may be analyzed qualitatively or quantitatively.

Step-by-step explanation:

Qualitative data research is a way or method to gather or collect non-numerical information either by observation or by asking crucial questions. It is a scientific method.

Qualitative data research involves the gathering accurate data and one of the way to do this is by carrying out surveys.

Qualitative data research determines WHY a particular action is carried out.

There are various methods of Qualitative data research. They are:

a. Direct Observation

b. In-depth interviews

c. Focus groups

d. Open end surveys

e. Oral History

f. Ethnographic observation

Qualitative data may be analysed qualitatively or quantitatively.

Qualitative research methods involve the collection and analysis of non-numerical data to understand subjective experiences and behaviors.

Qualitative research methods involve the collection and analysis of non-numerical data to understand subjective experiences and behaviors. It emphasizes open-ended questions, in-depth interviews, and observations to gain insights into complex psychological motivations. Qualitative researchers do not seek to fit their answers into predetermined categories but rather aim to understand research participants and their experiences.

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We want

[tex]2x<6\cdot 2=12[/tex]

So, if we divide both sides by 2, we have

[tex]x<6[/tex]

So, we can accept all values for [tex]x[/tex], as long as they are less than 6 (excluded)

Answer:

a) 2x < 6(2)

x < 6

x can take any real value less than 6

b) divide both sides by 2;

Or multiply both sides by ½

Answer: y = 6

y = -3x - 12

y = 3x + 24

Use elimination method to get 2y = 12 so y = 6.

Answer: the last option is the correct answer.

Step-by-step explanation:

The given system of equations is expressed as

y = - 3x - 12- - - - - - - - - - - - -1

y = 3x + 24- - - - - - - -- - - - - - -2

We would apply the method of elimination. Since x has the same coefficient and the sign is opposite, we would eliminate x by adding equation 1 to equation 2. It becomes

y + y = - 3x + 3x - 12 + 24

2y = 12

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2y/2 = 12/2

y = 6

Answer:

5

Step-by-step explanation:

(4+20+x)/3 = (y+16)/2

2(24+x) = 3(y+16)

48 + 2x = 3y + 48

2x = 3y

Since x and y are positive integers, they can't be 0. To satisfy 2x = 3y

We'll have to use LCM of 2 and 3, which is 6 (or a multiple of 6)

For the least value, we use 6

To make both sides 6,

x = 3 and y = 2

Hence x + y = 5

Answer:

The answer to your question is Yes.

Step-by-step explanation:

The math in this problem is that we need to use the Pythagorean theorem to solve it. Pythagorean theorem is part of trigonometry a branch of Maths.

Data

base = 9 ft                      

length = 37 ft

height = ?

Pythagorean theorem

                                     c² = a² + b²

length = c

base = a

height = b

                                   37² = 9² + b²

-Solve for b

                                    b² = 37² - 9²

-Simplify

                                    b² = 1369 - 81

                                    b² = 1288

-Result

                                   b = 35.88

-Conclusion

The ladder will reach a height higher than 35 ft.  

The degree of the radian angle 0.11 is [tex]6.3^{\circ}[/tex]

Explanation:

It is given that the radian angle is 0.11

We need to determine the degrees of the radian angle.

To convert the radian into degrees, let us multiply the radian with [tex]\left(\frac{180}{\pi}\right)[/tex]

Thus, we have,

[tex]0.11\times\left(\frac{180}{\pi}\right)=\frac{19.8}{\pi}[/tex]

It is given that [tex]\pi=3.14[/tex]

Substituting [tex]\pi=3.14[/tex] in the above expression, we have,

[tex]\frac{19.8}{3.14} =6.303...[/tex]

Rounding off to the nearest tenth, we have,

[tex]6.3^{\circ}[/tex]

Thus, the degree of the radian angle 0.11 is [tex]6.3^{\circ}[/tex]

Answer:

x = −2.4

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Exact Form: x = −12/5

Decimal Form: x = −2.4

Answer:

The afrmer had 480 chickens at first

Step-by-step explanation:

We make an assumption here, that the initial number of chickens that the farmer has, is C.

Chickens sold by the farmer is (20% of C) + 240 chickens

Number of chickens left after selling in the morning and afternoon is 30% of C

So, the first number of chickens = Number of chickens sold + Number of chickens left

This gives us an equation that will be solved to obtain C.

C = ([tex]\frac{20}{100}[/tex] × C) + 240 chickens + ([tex]\frac{30}{100}[/tex] × C) = 0.2C + 240 chickens + 0.3C

C = 0.5C + 240 chickens

C - 0.5C = 240 chickens

0.5C = 240 chickens

C = [tex]\frac{240 chickens}{0.5}[/tex]

C = 480 Chickens

Answer: the answer is C = 480

Step-by-step explanation:

Step-by-step explanation:

If the segments bisect each other, they will share the same midpoint.

Midpoint formula is:

(x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint of MN is:

(x, y) = ((-5 + 5)/2, (6 + -2)/2)

(x, y) = (0, 2)

Midpoint of PQ is:

(x, y) = ((5 + -5)/2, (3 + 1)/2)

(x, y) = (0, 2)

So the segments do bisect each other.

The concluding part of the question as obtained from the textbook;

The number on the 20 beach balls that come up in the simulated sample:

42, 1701, 638, 397, 113, 1243, 912, 380, 769, 1312, 76, 547, 721, 56, 4, 1411, 1766, 677, 201, 1840

A) Based on this sample, how many

defective beach balls might the

manufacturer expect in the next

shipment?

B) What is the difference between the

number of defective beach balls in the

actual shipment and the number

predicted in the next shipment?

Answer:

A) 500 defective beach balls.

B) Difference between the

number of defective beach balls in the

actual shipment and the number

predicted in the next shipment = 350

Step-by-step explanation:

The beach balls are labelled 1 to 2000 with the 150 defective ones labelled 1 to 150.

Then a random sample of 20 beach balls is picked, and the numbers are presented as

42, 1701, 638, 397, 113, 1243, 912, 380, 769, 1312, 76, 547, 721, 56, 4, 1411, 1766, 677, 201, 1840

Note that only the defective beach balls have numbers 1 to 150.

A) The number of beach balls with numbers from 1 to 150 in the sample is 5 (numbers 42, 113, 76, 56, 4). This is the number of defective beach balls in the sample.

Probability of getting a defective ball in the next shipment = (5/20) = 0.25

If every shipment contains 2000 beach balls, then there will be (0.25 × 2000) defective beach balls in the next sample; 500 defective beach balls.

B) Number of defective beach balls in actual shipmemt = 150

Number of predicted defective beach balls in the next shipment = 500

difference = 500 - 150 = 350.

Hope this Helps!!!

Answer:

C.) 500

Step-by-step explanation:

In a shipment of 2,000 beach balls, 150 are defective. The manufacturer generates a random sample to simulate 20 beach balls to inspect in the next shipment. The integers 1 to 150 represent defective beach balls.

   42         1701         638         397          113  

1243          912         380          769       1312

   76           547         721            56              4

1411         1766        677          201       1840

12. Based on this sample, how many defective beach balls might the manufacturer expect in the next shipment?

Group of answer choices

A.) 100

B.) 200

C.) 500

D.) 1000

Answer:

3 books per box, 3 left over.

Step-by-step explanation:

Brian has 18 books, and he is packing them into 5 boxes. 18 is only divisible by 1, 3, 9, and 18.

1 x 5 = 5 books =  13 left over. Still enough to pack more books.

3 x 5 = 15 books = 3 left over. This is the answer, but let's check the others as well.

9 x 5 = 45 books. He doesn't have that many! He can't put 9 books in each box because it would only take 2 boxes he's using all 5.

18 x 5 = 90 books. We can clearly see this isn't the answer. He would only be able to put all 18 books in 1 box but he wants to use all 5 boxes.

There are 3 books in each box with 3 left over.

Brian has 3 books in each of the 4 boxes, with 3 books remaining as leftovers after packing them equally.

Brian is moving his 18 books and has packed an equal number of books into each of the 5 empty boxes. To find out how many books are in each box, we divide the total number of books by the number of boxes, which is = 18 books ÷ 5 boxes = 3 books per box with 3 books left over. Therefore, there will be 3 full boxes and one box with 3 leftover books.

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Answer: 16

Step-by-step explanation:

law of cosines says that c^2 = a^2 + b^2 -2abcosC

so c^2 = 3^2 +15^2 - 2*2*15*cos108

c^2 = 234 -  (-27.8115294937 )

c^2 = 261.811529494

c = 16.18 rounds to 16

Answer:

16

Step-by-step explanation:

c² = a² + b² - 2(a)(b)cos(C)

c² = 3² + 15² - 2(3)(15)cos(108)

c² = 261.8115295

c = 16.18059114

Answer: the length of the cable is 10000 feet.

Step-by-step explanation:

A right angle triangle is formed. The length of the cable represents the hypotenuse of the right angle triangle. The height of the mountain represents the opposite side of the right angle triangle. To determine the length of the cable, L, we would apply the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 30 = 5000/L

L = 5000/Sin 30 = 5000/0.5

L = 10000 ft

Answer:

45,000

Step-by-step explanation:

If P=45,000−1,000m,

where P=The number of people left in the stadium m minutes after the end of the game

We want to determine how many people were present when the game ended but before people started to leave.

Note that immediately the game ended,

m=0

Therefore, the number of people left in the stadium

P=45000−(1000 X 0)

P=45000

There were 45,000 people.

Answer:

3:7 or .4285

Step-by-step explanation:

the odds against are 4:7 so the odds with must be 7-4=3

which will be written in 3:7 form

Answer:

Yes

Step-by-step explanation:

A chi-square test (y) examine whether it is good enough to fit, and associates a detected dispersal of Categorical data to the theorized dispersal shown in one-way table demonstrations distribution. If we get an empty hypothesis of the Chi test, it means no relationship exists between the categorial variables in the population, and they are not dependent on each other.

Answer:

cos(25)

Step-by-step explanation:

cosAcosB + sinAsinB = cos(A-B)

cos(20)cos(45) + sin(20)sin(45)

= cos(20-45) = cos(-25)

= cos(25) or 0.906

Answer:

172 ft

Step-by-step explanation:

Due south and due east form a 90-degree angle.

Her path is a right triangle. The 60 ft and 40 ft distances are the legs of the right triangle. We can use the Pythagorean theorem to find the hypotenuse. Then we add the lengths of the three sides to find the total distance she traveled which is the perimeter of the right triangle.

a^2 + b^2 = c^2

(40 ft)^2 + (60 ft)^2 = c^2

1600 ft^2 + 3600 ft^2 = c^2

c^2 = 5200 ft^2

c = 72 ft

perimeter = a + b + c = 40 ft + 60 ft + 72 ft = 172 ft

Answer: total distance is 172 feet

Step-by-step explanation:

The different directions along which Maria moved forms a right angle triangle.

The diagonal distance, h across the ring back to where she started represents the hypotenuse of the right angle triangle. The distances due south and east represents the opposite and adjacent sides of the right angle triangle.

To determine h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

h² = 60² + 40²

h² = 5200

h = √5200

h = 72 feet

The total distance, to the nearest foot, maria skates is

72 + 60 + 40 = 172 feet