Yoshi swam across a lake but did not know how far he swam. He found that it was 100sqrt(3) feet from point A to point C. Angle C was a right angle and angle A was 30°.

Find the distance he swam across the lake.

Hint: hypotenuse = 2shortleg )

Answers

Answer 1

The length of the lake is 100 ft

Finding the length of the lake:

Form a right-angled triangle according to the given data in the problem. Chose which trigonometric ratio can be used to find the side that is considered as the side of the lake.

From the trigonometric ratio table,

Tan 30 = 1/√3

Here we have

Yoshi swam across a lake but did not know how far he swam.

He found that it was 100√) feet from point A to point C.

Angle C was a right angle and angle A is 30°.

We represent the given scenario in the form of a right angle triangle as shown in the picture.

Let 'B' be the point where Yoshi swam started and BC be the length of the lake.

From the triangle,

Tan A = BC/AC

From the given data,

Tan 30° = BC/100√3

=> BC = Tan 30°(100√3)

=> BC = (1/√3)(100√3)

=> BC = 100 ft

Therefore,

The length of the lake is 100 ft

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Yoshi Swam Across A Lake But Did Not Know How Far He Swam. He Found That It Was 100sqrt(3) Feet From

Related Questions

Which of the following statements proves the series 250 – 150 + 90 – 54 + … is geometric?

r equals five thirds

r equals three fifths
r equals negative three fifths

Answers

The given series is geometric when r equals negative three-fifths.

What is geometric series?

The geometric series refers to the total of terms with a common ratio between every pair of neighbouring terms. Geometric series can be of two different types: finite and infinite. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".

where, r = ar/a = (second term)/(first term)

Given, the series 250 – 150 + 90 – 54 + …

So, r = (-150)/250 = -3/5

or, r = 90/(-150) = -3/5

Hence, for the geometric series, r should be equal to negative three-fifths.

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Marsha deposited $7,000 into a savings account 4 years ago. The simple interest rate is 2%. How much money did Marsha eam in interest?

Answers

Answer:

$560

Step-by-step explanation:

The formula for simple interest is:

I = Prt, where P is the principal, r is the interest rate, and t is the time (in years).

Plugging in the values, we get:

I = $7,000 * 2% * 4 years = $560

So, Marsha earned $560 in interest.

Find the value of C that makes 16x^2 -24x + C a perfect square

Answers

The required value of C is 3 which makes 16x² - 24x + C a perfect square.

What is Perfect Square?

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

The expression is given in the question, as follows:

16x² - 24x + C

(4x)² - 24x + C

As we know that the factoring identity:

(a - b)² = a² - 2ab + b²

After comparing, we have a = 4x and 2ab = 24x

Solving for b:

2(4x)b = 24x

b = 24x/8x

b = 3

So 16x² - 24x + 3 = (4x - 3)²

This means the required value of C is 3 which makes a perfect square.

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If f (x) = 5x - 4 find f(2).

10

48

2

6

Answers

Answer:

Step-by-step explanation:

f(2) = 10-4 = 6

Answer:

[tex] \sf \: d) \: 6[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 5x - 4

We have to find,

→ The required value of f(2).

Now value of f(2) will be,

→ f(x) = 5x - 4

→ f(2) = 5(2) - 4

→ f(2) = 10 - 4

→ [ f(2) = 6 ]

Therefore, the answer is 6.

In fall 2006, Pace University in New York raised its annual tuition from $25,000 to $29,750. Freshman enrollment declined from 1,475 in fall 2005 to 1,130 in fall 2006. Assuming that the demand curve for places in the freshmen class at Pace did not shift between 2005 and 2006, use this information to calculate the price elasticity of demand LOADING... . Use the midpoint formula in your calculation.

Answers

Answer:The answer is 20000

Step-by-step explanation:

Point V is somewhere on the line segment . If UV = 8, then find the length of .

Answers

Answer:

it is 3

Step-by-step explanation:

just subtract

Maya had $32. She spent all the money on buying 3 notebooks for x dollars each and 4
packs of index cards for y dollars each. If Maya had bought 5 notebooks and 5 packs of
index cards, she would have been short $18. Which system of equations represents this
situation?
O 3x + 4y = 32 and 5x + 5y = 50
O 3x+4y= 32 and 5x + 5y = 18
O 3x + 4y = 50 and 5x - 5y = 18
O 3x - 4y= 32 and 5x - 5y = 50

Answers

The system of equations which represents this

situation is 3x+4y= 32 and 5x + 5y = 18.

The correct answer choice is option B

Which system of equations represents the situation?

Amount with Maya = $32

Amount spent on each notebook = x

Number of notebook = 3

Amount spent on each pack of index cards = y

Number of index cards = 4

Maya bought 5 notebooks and 5 packs of

index cards

$18 short = $32 - $18

= $14

3x + 4y = 32

5x + 5y = 14

In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.

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9 Mr Karim had 2740 sacks of rice at first Mr Dani had 3560 sacks of rice at first. Mr Karim gave some sacks of rice to Mr Dani. In the end, Mr Dani had 4 times as many sacks of rice as Mr Karim. How many sacks of rice did Mr Karim have in the end?

Answers

Answer:

**DUE TOMORROW, NEED ANSWER ASAP**

NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).

a.) An ultraviolet telescope in space

b.) An optical telescope in a remote location in Michigan's upper peninsula

c.) A radio telescope in the Mojave desert in Arizona

d.) An x-ray telescope in the Andes mountains in Chile

e.) An optical telescope in space

Step-by-step explanation:

There are 12 consecutive parking slots available in a hotel parking lot in how many ways can four distinct cars be packed so that at least one parking slot remains vacant between into cars

Answers

Answer:

4 different spots

Step-by-step explanation:

12 - 4 spaces in between = 8 spaces

8 spaces / 4 cars = 4 spots

4 spots and 4 cars = 4 different spots for each car

How can credit cards be safer than cash? a. It is harder to lose a single credit card than a large number of bills. b. A credit card requires a signature, so it is impossible for anyone other than you to use. c. If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. d. Cash can be miscounted, but credit cards cannot.

Answers

If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. This way, credit cards can be safer than cash.

What is credit card?

A credit card is a small plastic payment card that is provided by a person's bank and enables the cardholder to pay a merchant for products and services depending on the cardholder's accumulated debt.

To be on the safe side in the event that a merchant breaches an agreement, a cardholder may contact the credit bureau to resolve the disputed charges.

So, this way credit cards can be safer than cash.

Hence, option C is the correct solution.

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The area of a rectangular wall of a barn is 110 square feet. Its length is 12 feet longer than twice its width. Find the length and width of the wall of the barn.
width= =feet

Answers

The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.

What is the length and width of the wall of the barn?

Area of the rectangular wall of a barn = 110 square feet

Width of the barn = w

Length of the barn= 2w + 12

Area of a rectangle = length × width

110 = (2w + 12) × w

110 = 2w² + 12w

equate to 0

2w² + 12w - 110 = 0

w² + 6w - 55 = 0

using factorization method of solving quadratic equation

w² + 11w - 5w - 55 = 0

w(w + 11) - 5(w + 11) = 0

(w - 5) (w + 11) = 0

w = 5 or w = -11

The width of the rectangular barn cannot be negative

Therefore,

Width of the barn = w

= 5 feet

Length of the barn= 2w + 12

= 2(5) + 12

= 10 + 12

= 22 feet

Answers

Answer:

It would be a little over 2 hours or so since 16:41 is just 4:41.

2 hours and 16 minutes

Step-by-step explanation:

You're welcome.

Hello can you help me solve

Answers

Answer:

(p o q) = 54

(q o p) = 68

Step-by-step explanation:

Another way to write is (p o q)(3) is p(q(3)). As you can see, you start with the inner function and 3 is an input in the q(x) function. Then, the output of this becomes the input of p(x) (the outer function), which yields a final output and the answer:

[tex]p(x) = 4x + 2\\q(x)=5x-2\\\\p(q(3))\\\\q(3)=5(3)-2=13\\p(13)=4(13)+2=54[/tex]

You do the same process for (q o p)(3), which can be written as q(p(3)), where you start with p(3) and then plug in this result as the input for q(x):

[tex]p(x)=4x+2\\q(x)=5x-2\\\\q(p(3))\\\\p(3)=4(3)+2=14\\q(14)=5(14)-2=68[/tex]

Is the graph of y = x² + 2 a straight line? Explain.
O No. The graph does not pass through (0, 0), so it is not a straight line.
O No. The graph passes through the points (0, 2), (1, 3), and (2, 6), which do not all lie on a straight line.
O Yes. The graph passes through (0, 0), so it is a straight line.
O Yes. The graph passes through the points (0, 2), (1, 3), and (2, 6), which all lie on a straight line.

Answers

Answer: No, the graph of y = x² + 2 is not a straight line. The graph is a parabola that opens upwards and has its vertex at (0, 2).

A straight line is defined by a linear equation, which is an equation that can be written in the form y = mx + b, where m and b are constants. In this equation, the coefficient of x (m) represents the slope of the line, and the constant term (b) represents the y-intercept. A straight line has a constant slope, which means that the rate of change of y with respect to x is constant.

In the case of y = x² + 2, the coefficient of x (x) is not a constant, but rather a variable, which means that the slope of the line changes as x changes. The graph of y = x² + 2 is a parabolic shape that opens upwards and has its vertex at (0, 2). The slope of the graph is not constant, but rather increases as x increases. This means that the graph does not represent a straight line, but rather a parabolic curve.

Step-by-step explanation:

if 30% of a number is 7, then what is 10% of the number ?

Answers

Answer:

70.0000

Step-by-step explanation:

aka 70%

1. For
what value of x is the
3(x + 2)-2x = 12 true?
A. 6
B. 10
C. 12
D. 14
E. 18
1.4.1 Set
the equation

Answers

Answer: A. 6

Step-by-step explanation:

Answer: I think D.

Step-by-step explanation: why not pick D…..

Hope this helps^^

examine whether you can construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm. Justify your answer

Answers

You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.

What is the condition for 3 lengths to represent a triangle?

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The lengths for this problem are given as follows:

Two smaller sides: 3 cm + 3 cm = 6 cm.Larger side: 6 cm.

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Need help really please

Answers

Answer:

Step-by-step explanation:

No pressure. You just need to look for the number that when added to the other given number, will give the same as the sum on the other side.

For instance, The top-left question:

4+6 = x+8 (let x be the box)

x= 4+6-8

x=2.

OR, since 4 + 6 =10,

you look for a number when added to 8, that gives 10.

That number is 2.

Hope this helps :]

19. The mass of a radioactive element is 35
milligrams. The mass of the element decreases by
12.9% every year.
a. Write a function that represents this situation.
b. Predict the mass of the element in 4 years. Round
your answer to the nearest tenth.
c. Will the mass of the radioactive element ever be 0
milligrams? Explain.

Answers

a) The function that represents this situation is,

⇒ y = 35 (1 - 12.9%)ⁿ

Where, 'n' is number of years and 'y' is mass of element.

b) For 4 years, the mass of the element is, 19.95 milligrams

c) No, the mass of the radioactive element will never be 0 milligrams.

What is expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The function that represents this situation is,

⇒ y = 35 (1 - 12.9%)ⁿ

Where, 'n' is number of years and 'y' is mass of element.

Now, For 4 years, the mass of the element is,

⇒ y = 35 (1 - 12.9%)ⁿ

⇒ y = 35 (1 - 12.9%)⁴

⇒ y = 35 (1 - 0.129)⁴

⇒ y = 35 (0.87)⁴

⇒ y = 35 × 0.57

⇒ y = 19.95 milligrams

No, the mass of the radioactive element will never be 0 milligrams.

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f(1) = 25
f(n) = f(n-1)(-1/5)

f(3) = ??

Answers

Answer: = 1 (look at the image for the solution)

Step-by-step explanation:

All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!

Answers

In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:

{x | -8 <= x < 17}

An explanation of set builder notation?

A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.

In this instance, the set consists of all numbers higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint

-8 <= x < 17,where x is a real value. This implies that x must exceed or equal to -8 and must be less than 17 to be a part of the set.

As a result, in set builder notation, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}

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Aubrey broke a cell sample into 15 batches, each way 1.3×10 to the -7th grams. How much did the original sample weigh? Use scientific notation to express your answer.

Answers

Answer:

Step-by-step explanation:

1.3 * 10 ^-7

is 0.00000013

0.00000013 times 15 is

0.00000195.

0.00000195 in scientific notation is

1.95*10^-6

what is the value of 8.4n - 3.2p, when n=4 and p=-2

Answers

Answer:

33.6-(-6.4)=40

Step-by-step explanation:

1. 8.4×4

2. 3.2x-2

3. 33.6-(-6.4)

4. 40

the two negatives become positive

help please i don’t know what to do

Answers

Answer:

Add 3 and then multiply by 5.

Step-by-step explanation:

The problem looks like this to me:

[tex] \dfrac{m}{5} - 3 = 8 [/tex]

If this is correct, then the operations are:

Add 3 to both sides.

Multiply both sides by 5.

I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?

A random sample of 40 hotel reviews is drawn from a large population of hotel customers. It's known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the standard deviation of the hotel's star rating.The choices are:0.18910.18930.19040.1934

Answers

The closest answer choice is 0.76, which corresponds to 0.1934. So the answer is 0.1934.

We can calculate the variance of the hotel's star rating by using the formula:

variance = sum[(xi - mean)^2 * pi]

where xi is the rating (1, 2, 3, or 4), mean is the expected value of the rating, and pi is the proportion of the population that left that rating. Since we know the proportions of the population that left each rating, we can calculate the expected value of the rating as:

mean = 1(0.3) + 2(0.2) + 3(0.2) + 4(0.3) = 2.9

Then, we can calculate the variance as:

variance = (1 - 2.9)^2 * 0.3 + (2 - 2.9)^2 * 0.2 + (3 - 2.9)^2 * 0.2 + (4 - 2.9)^2 * 0.3

variance ≈ 0.57

Finally, the standard deviation is the square root of the variance:

standard deviation = sqrt(0.57) ≈ 0.756

Therefore, the closest answer choice is 0.76, which corresponds to 0.1934.

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Could anyone help with #1 and #2 PLEASE.
URGENT! DUE TOMORROW!!

Answers

Answer:

Do the graph Then Solve for y

Answer:

1. Yes, a graph of this relationship will be linear.

2. The y-intercept of the graph is (0, 2).

Step-by-step explanation:

1. The equation will be linear because it can be written in the standard form for the equation of a line. The standard form for the equation of a line is Ax + By = C. Eight can be subtracted from both sides of the equation to get 3x - 4y = -8, which fits the format for standard form. A, B, and C are integers, which includes negative numbers, zero, and whole numbers.

2. 3x - 4y + 8 = 0

3(0) - 4y + 8 = 0

-4y + 8 = 0

-4y = -8

y = 2

Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line.
2x+4<10

Answers

The solution set of the inequality is [3, ∝)

How to determine the solution set

From the question, we have the following parameters that can be used in our computation:

2x + 4 < 10

Subtract 4 from both sides of the inequality

So, we have the following representation

2x + 4 - 4 < 10 - 4

Evaluate the like terms

2x < 6

Divide both sides by 2

x < 3

When represented as an interval notation, we have

[3, ∝)

See attachment for the inequality of the solution set

Hence, the solution is [3, ∝)

Answers

Items a company purchased and paid for but has not used is called a A. Advanced

Answer:

the ans is advanced

I hope you get your ans

Find the missing values.
Select two answers.

Answers

Answer:

a= 12, b=4, Choices B and F

Step-by-step explanation:

2/2=1

8/2=4

12/2=6

Eighteen low-fat wheat crackers have 3 grams of fat. How many grams of fat do 63 of these crackers have?

Answers

Answer:

10.5

Step-by-step explanation:

18/3 = 63/x

18 * x = 63

18 * 3.5 = 63

3 * 3.5 = 10.5

Other Questions

Yoshi swam across a lake but did not know how far he swam. He found that it was 100sqrt(3) feet from point A to point C. Angle C was a right angle and angle A was 30°. Find the distance he swam across the lake. Hint: hypotenuse = 2shortleg )

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Yoshi swam across a lake but did not know how far he swam. He found that it was 100sqrt(3) feet from point A to point C. Angle C was a right angle and angle A was 30°.

Find the distance he swam across the lake.

Hint: hypotenuse = 2shortleg )